번역된 기고 제목: 해류의 영향에 따른 어뢰 앵커 설치의 유체 역학 특성에 대한 수치 분석

Translated title of the contribution: NUMERICAL ANALYSIS OF THE HYDRODYNAMICS CHARACTERISTICS OF TORPEDO ANCHOR INSTALLATION UNDER THE INFLUENCE OF OCEAN CURRENTS

The gravity-installed anchor (GIA) is a type of the anchor foundation that is installed by penetrating the seabed using the weight of the anchor body. It has the advantages of high installation efficiency, low cost, and no requirement of additional installation facilities. The GIA type used in this study is the torpedo anchor, which has been ap-plied in practical cases widely. The purpose of this study is to investigate the numerical analysis of the anchor trans-porting during the installation of the torpedo anchor under the action of ocean currents. Therefore, this article con-siders external environmental conditions and the different forms of torpedo anchors by using computational fluid dynamics (CFD) software, FLOW-3D, to simulate the fluid-solid interaction effect on the torpedo anchor. The falling time, impact velocity, displaced angle, and horizontal displacement of the torpedo anchor were observed at an installation height (i.e., the distance between the seabed and the anchor release height) of 85 meters. The obtained results show that when the current velocity is greater, the torpedo anchor will have a larger displaced angle, which will affect the impact velocity of the anchor on the seabed and may cause insufficient penetration depth, leading to installation failure.

중력설치형 앵커(GIA)는 앵커 본체의 무게를 이용하여 해저를 관통하여 설치하는 앵커 기초의 일종이다. 설치 효율성이 높고, 비용이 저렴하며, 추가 설치 시설이 필요하지 않다는 장점이 있습니다. 본 연구에서 사용된 GIA 유형은 어뢰앵커로 실제 사례에 널리 적용되어 왔다.

본 연구의 목적은 해류의 작용에 따라 어뢰앵커 설치 시 앵커 이송에 대한 수치해석을 연구하는 것이다. 따라서 이 기사에서는 어뢰 앵커에 대한 유체-고체 상호 작용 효과를 시뮬레이션하기 위해 전산유체역학(CFD) 소프트웨어인 FLOW-3D를 사용하여 외부 환경 조건과 다양한 형태의 어뢰 앵커를 고려합니다.

어뢰앵커의 낙하시간, 충격속도, 변위각, 수평변위 등은 설치높이(즉, 해저와 앵커 해제 높이 사이의 거리) 85m에서 관찰되었다. 얻은 결과는 현재 속도가 더 높을 때 어뢰 앵커의 변위 각도가 더 커져 해저에 대한 앵커의 충격 속도에 영향을 미치고 침투 깊이가 부족하여 설치 실패로 이어질 수 있음을 보여줍니다.

다양한 수력학적 및 기하학적 조건에서 아래에 반원형 게이트가 결합된 두 개의 직사각형 복합 웨어의 배수 계수

ABSTRACT

Two-component composite hydraulic structures are commonly employed in irrigation systems. The first component, responsible for managing the overflow, is represented by a weir consisting of two rectangles. The second component, responsible for regulating the underflow, is represented by a semicircular gate. Both components are essential for measuring, directing, and controlling the flow. In this study, we experimentally investigated the flow through a combined two-rectangle sharp-crested weir with a semicircular gate placed across the channel as a control structure. The upper rectangle of the weir has a width of 20 cm, while the lower rectangle has varying widths (W2 ) of 5, 7, and 9 cm and depths (z) of 6, 9, and 11 cm. Additionally, three different values were considered for the gate diameter (d), namely 8, 12, and 15 cm. These dimensions were tested interchangeably, including a weir without a gate (d = 0), under different water head conditions. The results indicate that the discharge passing through the combined structure of the two rectangles and the gate is significantly affected by the weir and gate dimensions. After analyzing the data, empirical formulas were developed to predict the discharge coefficient (Cd ) of the combined structure. It is important to note that the analysis and results presented in this study are limited to the range of data that were tested.

2성분 복합 수력 구조물은 일반적으로 관개 시스템에 사용됩니다. 오버플로 관리를 담당하는 첫 번째 구성 요소는 두 개의 직사각형으로 구성된 웨어로 표시됩니다.

언더플로우 조절을 담당하는 두 번째 구성 요소는 반원형 게이트로 표시됩니다. 두 구성 요소 모두 흐름을 측정, 지시 및 제어하는 데 필수적입니다. 본 연구에서 우리는 제어 구조로 수로를 가로질러 배치된 반원형 게이트를 갖춘 결합된 두 개의 직사각형 뾰족한 둑을 통한 흐름을 실험적으로 조사했습니다.

웨어의 위쪽 직사각형은 폭이 20cm인 반면, 아래쪽 직사각형은 5, 7, 9cm의 다양한 폭(W2)과 6, 9, 11cm의 깊이(z)를 갖습니다. 또한 게이트 직경(d)에 대해 8, 12, 15cm의 세 가지 다른 값이 고려되었습니다.

이러한 치수는 게이트가 없는 둑(d = 0)을 포함하여 다양한 수두 조건에서 상호 교환적으로 테스트되었습니다. 결과는 두 개의 직사각형과 게이트가 결합된 구조를 통과하는 방전이 위어와 게이트 크기에 크게 영향을 받는다는 것을 나타냅니다.

데이터를 분석한 후, 결합구조물의 유출계수(Cd)를 예측하기 위한 실험식을 개발하였다. 본 연구에서 제시된 분석 및 결과는 테스트된 데이터 범위에 국한된다는 점에 유의하는 것이 중요합니다.

[1] S. S. Ibrahim, R. A. Jafer, and B. M. A. S. Ali, “An Experimental Study of a Combined Oblique Cylindrical Weir and Gate Structure,” Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10483–10488, Apr. 2023, https://doi.org/10.48084/etasr.5646. [2] F. Rooniyan, “The Effect of Confluence Angle on the Flow Pattern at a Rectangular Open Channel,” Engineering, Technology & Applied Science Research, vol. 4, no. 1, pp. 576–580, Feb. 2014, https://doi.org/10.48084/etasr.395. [3] A. S. Kote and P. B. Nangare, “Hydraulic Model Investigation on Stepped Spillway’s Plain and Slotted Roller Bucket,” Engineering, Technology & Applied Science Research, vol. 9, no. 4, pp. 4419–4422, Aug. 2019, https://doi.org/10.48084/etasr.2837. [4] S. M. Kori, A. A. Mahessar, M. Channa, A. A. Memon, and A. R. Kori, “Study of Flow Characteristics Over a Rounded Edge Drop Structure in Open Channel,” Engineering, Technology & Applied Science Research, vol. 9, no. 3, pp. 4136–4139, Jun. 2019, https://doi.org/ 10.48084/etasr.2584. [5] F. Granata, F. Di Nunno, R. Gargano, G. de Marinis, “Equivalent Discharge Coefficient of Side Weirs in Circular Channel—A Lazy Machine Learning Approach,” Water, vol. 11, no.11, 2019, Art. no. 2406, https://doi.org/10.3390/w11112406. [6] S. Salehi and A. H. Azimi, “Discharge Characteristics of Weir-Orifice and Weir-Gate Structures,” Journal of Irrigation and Drainage Engineering, vol. 145, no. 11, Nov. 2019, Art. no. 04019025, https://doi.org/10.1061/(ASCE)IR.1943-4774.0001421. [7] M. G. Bos, Ed., Discharge Measurement Structures. Wageningen, The Netherlands: International Institute for Land Reclamation and Improvement, 1989. [8] S. Emami, J. Parsa, H. Emami, A. Abbaspour, “An ISaDE algorithm combined with support vector regression for estimating discharge coefficient of W-planform weirs,” Water Supply, vol. 21, no.7, pp. 3459–3476, 2021, https://doi.org/10.2166/ws.2021.112. [9] A. B. Altan-Sakarya, M. A. Kokpinar, and A. Duru, “Numerical modelling of contracted sharp-crested weirs and combined weir and gate systems,” Irrigation and Drainage, vol. 69, no. 4, pp. 854–864, 2020, https://doi.org/10.1002/ird.2468. [10] P. Ackers, W. R. White, J. A. Perkins, A. J. M. Harrison, Weirs and Flumes for Flow Measurement, New York, NY, USA: Wiley, 1978. [11] A. Alhamid, D. Husain, and A. Negm, “Discharge equation for simultaneous flow over rectangular weirs and below inverted triangular weirs,” Arab Gulf Journal of Scientific Research, vol. 14, no. 3, pp. 595– 607, Dec. 1996. [12] N. Rajaratnam and K. Subramanya, “Flow Equation for the Sluice Gate,” Journal of the Irrigation and Drainage Division, vol. 93, no. 3, pp. 167– 186, Sep. 1967, https://doi.org/10.1061/JRCEA4.0000503. [13] A. Zahiri, H. Md. Azamathulla, and S. Bagheri, “Discharge coefficient for compound sharp crested side weirs in subcritical flow conditions,” Journal of Hydrology, vol. 480, pp. 162–166, Feb. 2013, https://doi.org/10.1016/j.jhydrol.2012.12.022. [14] S. A. Sarhan and S. A. Jalil, “Analysis of Simulation Outputs for the Mutual Effect of Flow in Weir and Gate System,” Journal of University of Babylon for Engineering Sciences, vol. 26, no. 6, pp. 48–59, Apr. 2018, https://doi.org/10.29196/jubes.v26i6.1050. [15] M. Muhammad and S. Abdullahi, “Experimental Study of Flow over Sharp Crested Rectangular-Triangular Weir Models,” in Nigeria Engineering Conference Proceedings, Zaria – Nigeria, Jan. 2014, pp. 34–45. [16] M. Piratheepan, N. E. F. Winston, and K. P. P. Pathirana, “Discharge Measurements in Open Channels using Compound Sharp-Crested Weirs,” vol. 40, no. 3, pp. 31-38, Jul. 2007, https://doi.org/10.4038/engineer.v40i3.7144. [17] H. A. Hayawi, A. A. Yahia, G. A. Hayawi, “Free combined flow over a triangular weir and under rectangular gate,” Damascus University Journal, vol. 24, no. 1, pp. 9–22, 2008. [18] A.-A. M. Negm, A. M. Al-Brahim, and A. A. Alhamid, “Combined-free flow over weirs and below gates,” Journal of Hydraulic Research, vol. 40, no. 3, pp. 359–365, May 2002, https://doi.org/10.1080/ 00221680209499950. [19] A. A. Alhamid, A.-A. M. Negm, and A. M. Al-Brahim, “Discharge Equation for Proposed Self-cleaning Device,” Journal of King Saud University – Engineering Sciences, vol. 9, no. 1, pp. 13–23, Jan. 1997, https://doi.org/10.1016/S1018-3639(18)30664-0. [20] S. I. Khassaf and M. Habeeb, “Experimental Investigation for Flow Through Combined Trapezoidal Weir and Rectangular Gate,” International Journal of Scientific & Engineering Research, vol. 5, no. 4, pp. 809–814, 2014. [21] A. A. G. Alniami, D. G. A. M. Hayawi, and H. A. M. Hayawi, “Coefficient Of Discharge For A Combined Hydraulic Measuring Device,” Al-Rafidain Engineering Journal, vol. 17, no. 6, pp. 92–100, Dec. 2009, https://doi.org/10.33899/rengj.2009.43616. [22] J. M. Samani and M. Mazaheri, “Combined Flow over Weir and under Gate,” Journal of Hydraulic Engineering, vol. 135, no. 3, pp. 224–227, Mar. 2009, https://doi.org/10.1061/(ASCE)0733-9429(2009)135:3(224). [23] B. Balouchi and G. Rakhshandehroo, “Using Physical and Soft Computing Models to Evaluate Discharge Coefficient for Combined Weir–Gate Structures Under Free Flow Conditions,” Iranian Journal of Science and Technology, Transactions of Civil Engineering, vol. 42, no. 4, pp. 427–438, Dec. 2018, https://doi.org/10.1007/s40996-018-0117-0. [24] M. A. R. Eltoukhy, F. S. Abdelhaleem, T. H. Nasralla, S. Shaban, “Effect of Compound Weir and below Circular Gate Geometric Characteristics on its Discharge Coefficient,” International Journal of Scientific & Engineering Research, Vol. vol. 11, no. 10, pp. 1115–1130, Oct. 2020. [25] C. E. Kindsvater and R. W. Carter, “Discharge Characteristics of Rectangular Thin-Plate Weirs,” Transactions of the American Society of Civil Engineers, vol. 124, no. 1, pp. 772–801, Jan. 1959, https://doi.org/10.1061/TACEAT.0007696. [26] H. R. Henry, “Discussion of Diffusion of Submerged Jets,” Transactions of ASCE, vol. 115, no. 1, pp. 687–694, Jan. 1950.

프로필 오목부가 탁도 퇴적물에 미치는 영향: 전 세계 대륙 경계에 대한 해저 협곡의 통찰력

Kaiqi Yu ^{a}, Elda Miramontes ^{bc}, Matthieu J.B. Cartigny ^{d}, Yuping Yang ^{a}, Jingping Xu ^{a} ^{a}Department of Ocean Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Rd., Shenzhen 518055, Guangdong, China ^{b}MARUM-Center for Marine Environmental Sciences, University of Bremen, Bremen, Germany^{c} Faculty of Geosciences, University of Bremen, Bremen, Germany ^{d}Department of Geography, Durham University, South Road, Durham DH1 3LE, UK

Received 10 August 2023, Revised 13 March 2024, Accepted 13 March 2024, Available online 17 March 2024, Version of Record 20 March 2024.

What do these dates mean?Show lessAdd to MendeleyShareCite

•The impact of submarine canyon concavity on turbidite deposition was assessed.

•Distribution of turbidite deposits varies with changes in canyon concavity.

•Three distinct deposition patterns were identified.

•The recognized deposition patterns align well with the observed turbidite deposits.

Abstract

Submarine canyons are primary conduits for turbidity currents transporting terrestrial sediments, nutrients, pollutants and organic carbon to the deep sea. The concavity in the longitudinal profile of these canyons (i.e. the downstream flattening rate along the profiles) influences the transport processes and results in variations in turbidite thickness, impacting the transfer and burial of particles. To better understand the controlling mechanisms of canyon concavity on the distribution of turbidite deposits, here we investigate the variation in sediment accumulation as a function of canyon concavity of 20 different modern submarine canyons, distributed on global continental margins. In order to effectively assess the isolated impact of the concavity of 20 different canyons, a series of two-dimensional, depth-resolved numerical simulations are conducted. Simulation results show that the highly concave profile (e.g. Surveyor and Horizon) tends to concentrate the turbidite deposits mainly at the slope break, while nearly straight profiles (e.g. Amazon and Congo) result in deposition focused at the canyon head. Moderately concave profiles with a smoother canyon floor (e.g. Norfolk-Washington and Mukluk) effectively facilitate the downstream transport of suspended sediments in turbidity currents. Furthermore, smooth and steep upper reaches of canyons commonly contribute to sediment bypass (i.e. Mukluk and Chirikof), while low slope angles lead to deposition at upper reaches (i.e. Bounty and Valencia). At lower reaches, the distribution of turbidite deposits is consistent with the occurrence of hydraulic jumps. Under the influence of different canyon concavities, three types of deposition patterns are inferred in this study, and verified by comparison with observed turbidite deposits on the modern or paleo-canyon floor. This study demonstrates a potential difference in sediment transport efficiency of submarine canyons with different concavities, which has potential consequences for sediment and organic carbon transport through submarine canyons.

Introduction

Submarine canyons are pivotal links in source-to-sink systems on continental margins (Sømme et al., 2009; Nyberg et al., 2018; Pope et al., 2022a, Pope et al., 2022b) that provide efficient pathways for moving prodigious volumes of terrestrial materials to the abyssal basin (Spychala et al., 2020; Heijnen et al., 2022). When turbidity currents, the main force that transports the above mentioned sediments (Xu et al., 2004; Xu, 2010; Talling et al., 2013; Stevenson et al., 2015), slow down after entering a flatter and/or wider stretch of the canyon downstream, the laden sediments settle, often rapidly, to form a deposit called turbidite that is known for organic carbon burial, hydrocarbon reserves and the accumulation of microplastics (Galy et al., 2007; Pohl et al., 2020a; Pope et al., 2022b; Pierdomenico et al., 2023). A set of flume experiments by Pohl et al. (2020b) revealed that the variation of bed slope plays a dominant role in controlling the sizes and locations of the deposit: a) a more gently dipping upper slope leads to upstream migration of upslope pinch-out; b) the increase of lower slope results in a decrease of the deposit thickness (Fig. 1a).

From upper continental slopes to deepwater basins, turbidity currents are commonly confined by submarine canyons that facilitate the longer distance transport of sediments (Eggenhuisen et al., 2022; Pope et al., 2022a; Wahab et al., 2022, Li et al., 2023a). The concavity, defined here as the downstream flattening rate of profiles (Covault et al., 2011; Chen et al., 2019; Seybold et al., 2021; Soutter et al., 2021a), of the longitudinal bed profile of the submarine canyons is therefore a key factor that determines hydrodynamic processes of turbidity currents, including the accumulation of sediments along the canyon thalweg (Covault et al., 2014; de Leeuw et al., 2016; Heerema et al., 2022; Heijnen et al., 2022). Due to the comprehensive impacts of sediment supply, grain size, climate change, regional tectonics, associated river and self-incision, the concavity of submarine canyons on global continental margins varies greatly (Parker et al., 1986; Harris and Whiteway, 2011; Casalbore et al., 2018; Nyberg et al., 2018; Soutter et al., 2021a, Li et al., 2023b), which is much more complex than the two constant slope setup of Pohl et al. (2020b)’s flume experiment (Fig. 1a). This raises the question of how the more complex concavity influences the dynamics of turbidity currents and the resultant distribution of turbidite deposits. For instance, the longitudinal profile concavity can also be increased by steepening the upper slope and/or gentling the lower slope of canyons (Fig. 1b). Parameters, known as significant factors influencing flow dynamics, include dip angle (Pohl et al., 2019), bed roughness (Baghalian and Ghodsian, 2020), obstacle presence (Howlett et al., 2019), and confinement conditions (Soutter et al., 2021b). However, the role of channel concavity in determining the downstream evolution of flow dynamics remains poorly understood (Covault et al., 2011; Georgiopoulou and Cartwright, 2013), and it is still unclear whether changes in concavity can result in different locations of pinch-out points and variations in turbidite deposit thicknesses (Pohl et al., 2020b).

In this study, we hypothesize that a more concave profile resulting from a steeper upper slope and a gentler lower slope may lead to a downstream migration of the upslope pinch-out and an increase of deposit thickness (Fig. 1b). This hypothesis is tested in 20 modern submarine canyons (shown in Fig. 2) whose longitudinal profiles are extracted from the GEBCO_2022 grid. Due to the lack of data describing the turbidite thickness trends in these canyons, we used a numerical model (FLOW-3D® software) to simulate the depositional process. The simulation results allow us to address at least two questions: (1) How does the concavity affect the distribution and thickness of turbidite deposits along the canyon thalwegs? (2) What is the impact of canyon concavity on the dynamics of the turbidity currents? Such answers on a global scale are undoubtedly helpful in understanding not only the sediment transport processes but also the efficient transfer and burial of organic carbon along global continental margins.

Section snippets

Submarine canyons used in this study

The longitudinal profiles of 20 modern submarine canyons are obtained using Global Mapper® from a public domain database GEBCO_2022 (doi:https://doi.org/10.5285/e0f0bb80-ab44-2739-e053-6c86abc0289c). The GEBCO_2022 grid provides elevation data, in meters, on a 15 arc-second interval grid. The 20 selected submarine canyons, which span the typical distance covered by turbidity currents, have been chosen from a diverse range of submarine canyon and channel systems that extend at least 250 km

Concavity of longitudinal canyon profiles

The NCI and α values of all 20 canyon profiles utilized in this study are plotted in Fig. 4, indicating the majority of these submarine canyons typically exhibit a concave profile, characterized by a negative NCI, except for the Amazon. In most of the profiles, the NCI is lower than −0.08, with the most concave point (indicated by the minimum ratio α) located closer to the canyon head than to the profile end, and their upper reaches are steeper than lower reaches, typically observed as the

Validation of the hypothesis

As previously mentioned in this paper, one of the primary objectives of this study is to evaluate the hypothesis inferred from the flume tank experiment of Pohl et al. (2020b): whether a more concave canyon profile can exert a comparable influence on turbidite deposits as the steepness of the lower and upper slopes in a slope-break system (Fig. 1). Shown as the modeling results, the deposition pattern of this study is more ‘irregular’ compared with the flume tank experiment (Pohl et al., 2020b

Conclusion

Based on global bathymetry, this study simulates the depositional behavior of turbidity currents flowing through the 20 different submarine canyons on the margins of open ocean and marginal sea. Influenced by the different concavities, the resulted deposition patterns are characterized by a variable distribution of turbidite deposits.

1)The simulation results demonstrate that the accumulation of turbidite deposits is primarily observed in downstream regions near the slope break for highly concave

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study is supported by the Shenzhen Natural Science Foundation (JCYJ20210324105211031). Matthieu J. B. Cartigny was supported by Royal Society Research Fellowship (DHF/R1/180166). We thank the Chief Editor Zhongyuan Chen, the associate editor and two reviewers for their constructive comments that helped us improve our manuscript.

M. Azpiroz-Zabala et al.Newly recognized turbidity current structure can explain prolonged flushing of submarine canyonsSci. Adv.(2017)

N. Babonneau et al.Sedimentary Architecture in Meanders of a Submarine Channel: Detailed Study of the Present Congo Turbidite Channel (Zaiango Project)J. Sediment. Res.(2010)

R. Basani et al.MassFLOW-3DTM as a simulation tool for turbidity currents: some preliminary results

H.L. Brooks et al.Disconnected submarine lobes as a record of stepped slope evolution over multiple sea-level cyclesGeosphere(2018)

S.A. Chen et al.Aridity is expressed in river topography globallyNature(2019)

J.A. Covault et al.The natural range of submarine canyon-and-channel longitudinal profilesGeosphere(2011)

J.A. Covault et al.Deep-water channel run-out length: insights from seafloor geomorphologyJ. Sediment. Res.(2012)

J.A. Covault et al.Submarine channel initiation, filling and maintenance from sea-floor geomorphology and morphodynamic modelling of cyclic stepsSedimentology(2014)

J. de Leeuw et al.Morphodynamics of submarine channel inception revealed by new experimental approachNat. Commun.(2016)

J. de Leeuw et al.Entrainment and suspension of sand and gravelEarth Surf. Dyn.(2020)

J.T. Eggenhuisen et al.The Sediment Budget Estimator (SBE): a process model for the stochastic estimation of fluxes and budgets of sediment through submarine channel systemsJ. Sediment. Res.(2022)

T.H. Ellison et al.Turbulent entrainment in stratified flowsJ. Fluid Mech.(1959)

R.I. Ferguson et al.A simple universal equation for grain settling velocityJ. Sediment. Res.(2004)

A.M. Fernandes et al.Flow substrate interactions in aggrading and degrading submarine channelsJ. Sediment. Res.(2020)

Flow ScienceFLOW-3D User Manual v11. 2(2018)

V. Galy et al.Efficient organic carbon burial in the Bengal fan sustained by the Himalayan erosional systemNature(2007)

Z. Ge et al.How is a turbidite actually deposited?Sci. Adv.(2022)

B. Gomez et al.An assessment of bed load sediment transport formulae for gravel bed riversWater Resour. Res.(1989)

W.H. Graf et al.Suspension flows in open channels; experimental studyJ. Hydraul. Res.(2010)

C.J. Heerema et al.How distinctive are flood-triggered turbidity currents?J. Sediment. Res.(2022)

D.M. Howlett et al.Response of unconfined turbidity current to deep-water fold and thrust belt topography: orthogonal incidence on solitary and segmented foldsSedimentology(2019)

S. Kim et al.Seismostratigraphic and geomorphic evidence for the glacial history of the Northwestern Chukchi Margin, Arctic OceanJ. Geophys. Res. Earth Surf.(2021)

M. Liu et al.Two distinct types of turbidity currents observed in the Manila Trench, South China SeaCommun. Earth Environ.(2023)

There are more references available in the full text version of this article.

Alireza Khoshkonesh^{1}, Blaise Nsom^{2}, Saeid Okhravi^{3}*, Fariba Ahmadi Dehrashid^{4}, Payam Heidarian^{5}, Silvia DiFrancesco^{6} ^{1 }Department of Geography, School of Social Sciences, History, and Philosophy, Birkbeck University of London, London, UK. ^{2} Université de Bretagne Occidentale. IRDL/UBO UMR CNRS 6027. Rue de Kergoat, 29285 Brest, France. ^{3} Institute of Hydrology, Slovak Academy of Sciences, Dúbravská cesta 9, 84104, Bratislava, Slovak Republic. ^{4}Department of Water Science and Engineering, Faculty of Agriculture, Bu-Ali Sina University, 65178-38695, Hamedan, Iran. ^{5 }Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, 25123 Brescia, Italy.^{ } ^{6}Niccol`o Cusano University, via Don C. Gnocchi 3, 00166 Rome, Italy. * Corresponding author. Tel.: +421-944624921. E-mail: saeid.okhravi@savba.sk

Abstract

This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.

이 연구는 두 개의 서로 다른 침식층에 대한 댐 파괴파 진화에 대한 기질 수준 차이와 재료 구성의 영향을 종합적으로 조사하는 것을 목표로 했습니다. VOF(유체량) 방법을 활용하여 자유 표면 이류를 추적하고 문헌의 실험 데이터를 사용하여 파동 진화를 재현했습니다.

모델 검증을 위해 메쉬 해상도, 난류 시뮬레이션 방법 및 침대 하중 전달 방정식을 포함하는 포괄적인 민감도 분석을 수행했습니다. LES(Large Eddy Simulation), 비평형 퇴적물 플럭스 및 van Rijn(1984)의 하상 부하 공식의 구현은 대체 접근 방식에 비해 더 높은 정확도를 산출했습니다.

연구 결과는 댐 붕괴 형태역학적 특성에 대한 기질 수준 차이와 재료 구성의 중요한 영향을 강조합니다. 기판 수준 차이가 감소하면 유속, 파면 진행, 자유 표면 높이, 기판 침식 및 기타 관련 매개변수가 감소했습니다.

초기 공기 포집은 파면에서 상당한 것으로 입증되었으며, 이는 바닥 경계면을 따라 뚜렷한 공기-물 상호 작용을 보여줍니다. 기판 레벨 차이가 4배로 증가함에 따라 Shields 매개변수는 1/3로 감소했으며, 파면에서 가장 높은 베드 근처 농도가 관찰되었습니다.

이 연구는 댐 파괴파 전파와 형태학적 변화를 지배하는 요인들의 복잡한 상호 작용에 대한 새로운 통찰력을 제공하여 이 복잡한 현상에 대한 이해를 향상시킵니다.

Aleixo, R., Soares-Frazão, S., Zech, Y., 2010. Velocity profiles in dam-break flows: water and sediment layers. In: Proc. Int. Conf. on Fluvial Hydraulics “River Flow 2010”, pp. 533–540. An, S., Ku, H., Julien, P.Y., 2015. Numerical modelling of local scour caused by submerged jets. Maejo Int. J. Sci. Technol., 9, 3, 328–343. Bahmanpouri, F., Daliri, M., Khoshkonesh, A., Namin, M.M., Buccino, M., 2021. Bed compaction effect on dam break flow over erodible bed; experimental and numerical modeling. J. Hydrol., 594, 125645. https://doi.org/10.1016/j.jhydrol.2020.125645 Baklanov, A., 2007. Environmental risk and assessment modelling – scientific needs and expected advancements. In: Ebel, A., Davitashvili, T. (Eds.): Air, Water and Soil Quality Modelling for Risk and Impact Assessment Springer, Dordrecht, pp. 29–44. Biscarini, C., Di Francesco, S., Nardi, F., Manciola, P., 2013. Detailed simulation of complex hydraulic problems with macroscopic and mesoscopic mathematical methods. Math. Probl. Eng., 928309. https://doi.org/10.1155/2013/928309 Cao, Z., Pender, G., Wallis, S., Carling, P., 2004. Computational dam-break hydraulics over erodible sediment bed. J. Hydraul. Eng., 130, 7, 689–703. Catucci, D., Briganti, R., Heller, V., 2021. Numerical validation of novel scaling laws for air entrainment in water. Proc. R. Soc. A, 477, 2255,20210339. https://doi.org/10.1098/rspa.2021.0339 Dehrashid, F.A., Heidari, M., Rahimi, H., Khoshkonesh, A., Yuan, S., Tang, X., Lu, C., Wang, X., 2023. CFD modeling the flow dynamics in an open channel with double-layered vegetation. Model. Earth Syst. Environ., 9, 1, 543–555. Desombre, J., Morichon, D., Mory, M., 2013. RANS v2-f simulation of a swash event: Detailed flow structure. Coastal Eng., 71, 1–12. Dodangeh, E., Afzalimehr, H., 2022. Incipient motion of sediment particles in the presence of bed forms under decelerating and accelerating flows. J. Hydrol. Hydromech., 70, 1, 89–102. Dong, Z., Wang, J., Vetsch, D.F., Boes, R.M., Tan, G., 2019. Numerical simulation of air entrainment on stepped spillways. In: E-proceedings of the 38th IAHR World Congress (pp. 1494). September 1–6, 2019, Panama City, Panama. DOI: 10.3850/38WC092019-0755 Flow3D [computer software]. 2023. Santa Fe, NM: Flow Science, Inc. Fraccarollo, L., Capart, H., 2002. Riemann wave description of erosional dam-break flows. J. Fluid Mech., 461, 183–228. Gu, Z., Wang, T., Meng, W., Yu, C.H., An, R., 2023. Numerical investigation of silted-up dam-break flow with different silted-up sediment heights. Water Supply, 23, 2, 599–614. Gualtieri, P., De Felice, S., Pasquino, V., Doria, G.P., 2018. Use of conventional flow resistance equations and a model for the Nikuradse roughness in vegetated flows at high submergence. J. Hydrol. Hydromech., 66, 1, 107–120. Heller, V., 2011. Scale effects in physical hydraulic engineering models. J. Hydraul. Res., 49, 3, 293–306. Hirt, C.W., 2003. Modeling turbulent entrainment of air at a free surface. Flow Science, Inc. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 39, 1, 201– 225. Issakhov, A., Zhandaulet, Y., Nogaeva, A., 2018. Numerical simulation of dam break flow for various forms of the obstacle by VOF method. Int. J. Multiphase Flow, 109, 191–206. Khayyer, A., Gotoh, H., 2010. On particle-based simulation of a dam break over a wet bed. J. Hydraul. Res., 48, 2, 238–249. Khoshkonesh, A., Daliri, M., Riaz, K., Dehrashid, F.A., Bahmanpouri, F., Di Francesco, S., 2022. Dam-break flow dynamics over a stepped channel with vegetation. J. Hydrol., 613,128395. https://doi.org/10.1016/j.jhydrol.2022.128395 Khoshkonesh, A., Nsom, B., Gohari, S., Banejad, H., 2019. A comprehensive study on dam-break flow over dry and wet beds. Ocean Eng., 188, 106279. https://doi.org/10.1016/j.oceaneng.2019.106279 Khoshkonesh, A., Sadeghi, S.H., Gohari, S., Karimpour, S., Oodi, S., Di Francesco, S., 2023. Study of dam-break flow over a vegetated channel with and without a drop. Water Resour. Manage., 37, 5, 2107–2123. Khosravi, K., Chegini, A.H.N., Cooper, J., Mao, L., Habibnejad, M., Shahedi, K., Binns, A., 2021. A laboratory investigation of bedload transport of gravel sediments under dam break flow. Int. J. Sediment Res., 36, 2, 229–234. Kim, Y., Zhou, Z., Hsu, T.J., Puleo, J.A., 2017. Large eddy simulation of dam‐break‐driven swash on a rough‐planar beach. J. Geophys. Res.: Oceans, 122, 2, 1274–1296. Kocaman, S., Ozmen-Cagatay, H., 2012. The effect of lateral channel contraction on dam break flows: Laboratory experiment. J. Hydrol., 432, 145–153. Leal, J.G., Ferreira, R.M., Cardoso, A.H., 2006. Dam-break wavefront celerity. J. Hydraul. Eng., 132, 1, 69–76. Leal, J.G.A.B., Ferreira, R.M., Cardoso, A.H., 2003. Dam-break wave propagation over a cohesionless erodible bed. In: Proc. 30rd IAHR Congress, 100, 261–268. Li, Y. L., Ma, Y., Deng, R., Jiang, D.P., Hu, Z., 2019. Research on dam-break induced tsunami bore acting on the triangular breakwater based on high order 3D CLSVOF-THINC/WLICIBM approaching. Ocean Eng., 182, 645–659. Li, Y.L., Yu, C.H., 2019. Research on dam-break flow induced front wave impacting a vertical wall based on the CLSVOF and level set methods. Ocean Eng., 178, 442–462. Mei, S., Chen, S., Zhong, Q., Shan, Y., 2022. Detailed numerical modeling for breach hydrograph and morphology evolution during landslide dam breaching. Landslides, 19, 12, 2925–2949. Meng, W., Yu, C.H., Li, J., An, R., 2022. Three-dimensional simulation of silted-up dam-break flow striking a rigid structure. Ocean Eng., 261, 112042. https://doi.org/10.1016/j.oceaneng.2022.112042 Meyer-Peter, E., Müller, R., 1948. Formulas for bed-load transport. In: IAHSR 2nd meeting, Stockholm, appendix 2. IAHR. Nielsen, P., 1984. Field measurements of time-averaged suspended sediment concentrations under waves. Coastal Eng., 8, 1, 51–72. Nielsen, P., 2018. Bed shear stress, surface shape and velocity field near the tips of dam-breaks, tsunami and wave runup. Coastal Eng., 138, 126–131. Nsom, B., Latrache, N., Ramifidisoa, L., Khoshkonesh, A., 2019. Analytical solution to the stability of gravity-driven stratified flow of two liquids over an inclined plane. In: 24th French Mechanics Congress in Brest. Brest, p. 244178. Nsom, B., Ravelo, B., Ndong, W., 2008. Flow regimes in horizontal viscous dam-break flow of Cayous mud. Appl. Rheol., 18, 4, 43577-1. https://doi.org/10.1515/arh-2008-0012 Oguzhan, S., Aksoy, A.O., 2020. Experimental investigation of the effect of vegetation on dam break flood waves. J. Hydrol. Hydromech., 68, 3, 231–241. Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2022. Effects of bedmaterial gradation on clear water scour at single and group of piles. J. Hydrol. Hydromech., 70, 1, 114–127. Okhravi, S., Gohari, S., Alemi, M., Maia, R., 2023. Numerical modeling of local scour of non-uniform graded sediment for two arrangements of pile groups. Int. J. Sediment Res., 38, 4, 597–614. Parambath, A., 2010. Impact of tsunamis on near shore wind power units. Master’s Thesis. Texas A&M University. Available electronically from https://hdl.handle.net/1969.1/ETD-TAMU2010-12-8919 Pintado-Patiño, J.C., Puleo, J.A., Krafft, D., Torres-Freyermuth, A.,

Hydrodynamics and sediment transport under a dambreak-driven swash: An experimental study. Coastal Eng., 170,

https://doi.org/10.1016/j.coastaleng.2021.103986 Riaz, K., Aslam, H.M.S., Yaseen, M.W., Ahmad, H.H., Khoshkonesh, A., Noshin, S., 2022. Flood frequency analysis and hydraulic design of bridge at Mashan on river Kunhar. Arch. Hydroengineering Environ. Mech., 69, 1, 1–12. Ritter, A., 1892. Die Fortpflanzung der Wasserwellen. Zeitschrift des Vereines Deutscher Ingenieure, 36, 33, 947–954. (In German.) Smagorinsky, J., 1963. General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weather Rev., 91, 3, 99–164. Soulsby, R.L., 1997. Dynamics of marine sands: a manual for practical applications. Oceanogr. Lit. Rev., 9, 44, 947. Spinewine, B., Capart, H., 2013. Intense bed-load due to a sudden dam-break. J. Fluid Mech., 731, 579–614. Van Rijn, L.C., 1984. Sediment transport, part I: bed load transport. J. Hydraul. Eng., 110, 10, 1431–1456. Vosoughi, F., Rakhshandehroo, G., Nikoo, M.R., Sadegh, M.,

Experimental study and numerical verification of silted-up dam break. J. Hydrol., 590, 125267. https://doi.org/10.1016/j.jhydrol.2020.125267 Wu, W., Wang, S.S., 2008. One-dimensional explicit finite-volume model for sediment transport. J. Hydraul. Res., 46, 1, 87–98. Xu, T., Huai, W., Liu, H., 2023. MPS-based simulation of dam-break wave propagation over wet beds with a sediment layer. Ocean Eng., 281, 115035. https://doi.org/10.1016/j.oceaneng.2023.115035 Yang, S., Yang, W., Qin, S., Li, Q., Yang, B., 2018. Numerical study on characteristics of dam-break wave. Ocean Eng., 159, 358–371. Yao, G.F., 2004. Development of new pressure-velocity solvers in FLOW-3D. Flow Science, Inc., USA.

대규모 홍수 구호 작업에 대한 일반적인 흐름 회로 현상의 영향은 많은 보고서에서 연구되었으며 비교적 자세하게 연구되었습니다. 그러나 유량 변동이 제방 암거 작동에 미치는 악영향에 대해서는 많이 언급되지 않았습니다.

실제 운영에 따르면 에너지 소산 탱크 또는 뒷마당의 국부적 불안정성, 운하 지붕의 부력 또는 붕괴, 하류 또는 제방 본체 일부 등 암거 구조 및 제방 시스템에 영향을 미치는 흐름 회로의 부정적인 영향이 많이 있음을 알 수 있습니다.

홍수기 운영 시 암거 및 제방의 안전성을 확보하기 위해서는 유동현상으로 인한 사업에 미치는 유해영향을 최소화할 필요가 있으며 본 연구에서는 이를 검증하고자 합니다.

제방을 통과하는 암거의 동적 회로 현상은 FLOW-3D 소프트웨어를 사용하여 수학적 모델로 시뮬레이션됩니다. 제방을 통한 암거 작동에 잠재적으로 영향을 미칠 수 있는 동맥 유형이 연구에서 구체적으로 논의됩니다.

동시에 암거와 제방 위치는 이 기사에서 지적한 흐름 회로 현상에 의해 부정적인 영향을 받을 가능성이 더 높습니다. 또한 Phuc Tho 마을의 제방을 가로지르는 암거 게이트 뒤의 회로 현상을 줄이기 위한 구조적, 비구조적 조치도 연구되고 평가됩니다.

이를 토대로 운영하수관로의 구조를 저해하지 않고 회로를 축소할 수 있는 방안을 제안한다.

The flow fluctuation has been studied in quite extensively for large-scale flood control works, however, this issue has been less addressed for culverts through levee. The operational experience has shown that there are many negative impacts of flow dynamics on the culvert structure and levee system such as the uplift instability, the local surface erosion of the stilling basin or the downstream channel, collapsing of part of the levee system, etc. According to the requirement of sluice and levee safety during flood season, the task of reducing fluctuation needs to be performed. The article not only pointed out the types of fluctuation that need to pay attention behind the operation gate, but also specified the locations where the sluice and levee could be destructively affected by the fluctuation. In addition, structural and non-structural countermeasures reducing negative impacts of fluctuation are also mentioned. Research has proposed measures to reduce flow dynamics for operating culverts without interfering with their structure.

Hệ thống giám sát thiên tai Việt Nam (2023). http://vndms.dmc.gov.vn/ (Accessed: 28 February 2023). Viện Thủy Công (2015) Nghiên cứu đánh giá các sự cố đê, cống dưới đê và đề xuất giải pháp xử lý. HyCI. Nguyễn Phương Dung (2017) Thí nghiệm xác định ảnh hưởng của áp lực thủy động tới độ dày bản đáy bể tiêu năng và sân sau ở công trình tháo. TLU. Nguyễn Chiến (2015) Tính toán thủy lực công trình tháo nước. NXB Xây dựng. Nguyễn Ngọc Thắng (2019) Đề cương Đề tài cấp Bộ ‘Nghiên cứu đánh giá nguyên nhân, các biện pháp đã áp dụng và đề xuất giải pháp xử lý sự cố cống dưới đê đảm bảo an toàn chống lũ’. ‘Flow 3D’ (2023). (User’s Manual). Yong Peng (2018) ‘Experimental Optimization of Gate-Opening Modes to Minimize Near-Field Vibrations in Hydropower Stations’, Water, 10(1435). Available at: https://doi.org/doi:10.3390/w10101435. Guibing HUANG (2021) ‘Pressure Fluctuations Characteristics of the Stilling Basin with a Negative Step’, Hydraulic and Civil Engineering Technology VI [Preprint]. Available at: https://doi.org/doi:10.3233/ATDE210196. O. Fecarotta (2016) Experimental results on the physical model of an USBR type II stilling basin. Taylor & Francis Group.

Ali Poorkarimi^{1} Khaled Mafakheri^{2} Shahrzad Maleki^{2}

Journal of Hydraulic Structures J. Hydraul. Struct., 2023; 9(4): 76-87 DOI: 10.22055/jhs.2024.44817.1265

Abstract

중력에 의한 침전은 부유 물질을 제거하기 위해 물과 폐수 처리 공정에 널리 적용됩니다. 이 연구에서는 침전조의 제거 효율에 대한 입구 및 배플 위치의 영향을 간략하게 설명합니다. 실험은 CCD(중심복합설계) 방법론을 기반으로 수행되었습니다. 전산유체역학(CFD)은 유압 설계, 미래 발전소에 대한 계획 연구, 토목 유지 관리 및 공급 효율성과 관련된 복잡한 문제를 모델링하고 분석하는 데 광범위하게 사용됩니다. 본 연구에서는 입구 높이, 입구로부터 배플까지의 거리, 배플 높이의 다양한 조건에 따른 영향을 조사하였다. CCD 접근 방식을 사용하여 얻은 데이터를 분석하면 축소된 2차 모델이 R^{2} = 0.77의 결정 계수로 부유 물질 제거를 예측할 수 있음이 나타났습니다. 연구 결과, 유입구와 배플의 부적절한 위치는 침전조의 효율에 부정적인 영향을 미칠 수 있음을 보여주었습니다. 입구 높이, 배플 거리, 배플 높이의 최적 값은 각각 0.87m, 0.77m, 0.56m였으며 제거 효율은 80.6%였습니다.

Sedimentation due to gravitation is applied widely in water and wastewater treatment processes to remove suspended solids. This study outlines the effect of the inlet and baffle position on the removal efficiency of sedimentation tanks. Experiments were carried out based on the central composite design (CCD) methodology. Computational fluid dynamics (CFD) is used extensively to model and analyze complex issues related to hydraulic design, planning studies for future generating stations, civil maintenance, and supply efficiency. In this study, the effect of different conditions of inlet elevation, baffle’s distance from the inlet, and baffle height were investigated. Analysis of the obtained data with a CCD approach illustrated that the reduced quadratic model can predict the suspended solids removal with a coefficient of determination of R^{2} = 0.77. The results showed that the inappropriate position of the inlet and the baffle can have a negative effect on the efficiency of the sedimentation tank. The optimal values of inlet elevation, baffle distance, and baffle height were 0.87 m, 0.77 m, and 0.56 m respectively with 80.6% removal efficiency.

Shahrokhi, M., F. Rostami, M.A. Md. Said, S.R.S. Yazdi, and Syafalni, (2013). Experimental investigation of the influence of baffle position on the flow field, sediment concentration, and efficiency of rectangular primary sedimentation tanks. Journal of Hydraulic Engineering,. 139(1): p. 88-94.

Shahrokhi, M., F. Rostami, M.A.M. Said, and S.R.S. Yazdi, (2012). The effect of number of baffles on the improvement efficiency of primary sedimentation tanks. Applied Mathematical Modelling,. 36(8): p. 3725-3735.

Borna, M., A. Janfeshan, E. Merufinia, and A. Asnaashari, (2014). Numerical simulations of distribution and sediment transmission in pre-settled pools using Finite Volume Method and comparison with experimental results. Journal of Civil Engineering and Urbanism,. 4(3): p. 287-292.

Rad, M.J., P.E. Firoozabadi, and F. Rostami, (2022). Numerical Investigation of the Effect Dimensions of Rectangular Sedimentation Tanks on Its Hydraulic Efficiency Using Flow-3D Software. Acta Technica Jaurinensis,. 15(4): p. 207-220.

Hirom, K. and T.T. Devi, (2022). Application of computational fluid dynamics in sedimentation tank design and its recent developments: A review. Water, Air, & Soil Pollution,. 233: p. 1- 26.

Shahrokhi, M., F. Rostami, M.A.M. Said, S.-R. Sabbagh-Yazdi, S. Syafalni, and R. Abdullah, (2012). The effect of baffle angle on primary sedimentation tank efficiency. Canadian Journal of Civil Engineering,. 39(3): p. 293-303.

Tarpagkou, R. and A. Pantokratoras, (2014). The influence of lamellar settler in sedimentation tanks for potable water treatment—A computational fluid dynamic study. Powder Technology,. 268: p. 139-149.

Ekama, G. and P. Marais, (2004). Assessing the applicability of the 1D flux theory to full-scale secondary settling tank design with a 2D hydrodynamic model. Water research,. 38(3): p. 495- 506.

Gharagozian, A., (1998). Circular secondary clarifier investigations using a numerical model., University of California, Los Angeles.

Shahrokhi, M., F. Rostami, and M.A.M. Said, (2013). Numerical modeling of baffle location effects on the flow pattern of primary sedimentation tanks. Applied Mathematical Modelling,. 37(6): p. 4486-4496.

Razmi, A.M., R. Bakhtyar, B. Firoozabadi, and D.A. Barry, (2013). Experiments and numerical modeling of baffle configuration effects on the performance of sedimentation tanks. Canadian Journal of Civil Engineering,. 40(2): p. 140-150.

Liu, Y., P. Zhang, and W. Wei, (2016). Simulation of effect of a baffle on the flow patterns and hydraulic efficiency in a sedimentation tank. Desalination and Water Treatment,. 57(54): p. 25950-25959.

Saeedi, E., E. Behnamtalab, and S. Salehi Neyshabouri, (2020). Numerical simulation of baffle effect on the performance of sedimentation basin. Water and environment journal,. 34(2): p. 212-222.

Miri, J.K., B. Aminnejad, and A. Zahiri, (2023). Numerical Study of Flow Pattern, Sediment Field and Effect of the Arrangement of Guiding Blades (Baffles) on Sedimentation in PreSedimentation Basins by Numerical Models. Water Resources,. 50(1): p. 68-81.

Heydari, M.M., M. Rahbani, and S.M.M. Jamal, (2014). Experimental and numerical investigations of baffle effect on the removal efficiency of sedimentation basin. Advances in Environmental Biology,: p. 1015-1022.

Guo, H., S.J. Ki, S. Oh, Y.M. Kim, S. Wang, and J.H. Kim, (2017). Numerical simulation of separation process for enhancing fine particle removal in tertiary sedimentation tank mounting adjustable baffle. Chemical engineering science,. 158: p. 21-29.

Farhoud Kalateh ^{a},*, Ehsan Aminvash ^{a} and Rasoul Daneshfaraz ^{b} ^{a} Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran ^{b} Faculty of Engineering, University of Maragheh, Maragheh, Iran *Corresponding author. E-mail: f.kalateh@gmail.com

ABSTRACT

The main goal of the present study is to investigate the effects of macro-roughnesses downstream of the inclined drop through numerical models. Due to the vital importance of geometrical properties of the macro-roughnesses in the hydraulic performance and efficient energy dissipation downstream of inclined drops, two different geometries of macro-roughnesses, i.e., semi-circular and triangular geometries, have been investigated using the Flow-3D model. Numerical simulation showed that with the flow rate increase and relative critical depth, the flow energy consumption has decreased. Also, relative energy dissipation increases with the increase in height and slope angle, so that this amount of increase in energy loss compared to the smooth bed in semi-circular and triangular elements is 86.39 and 76.80%, respectively, in the inclined drop with a height of 15 cm and 86.99 and 65.78% in the drop with a height of 20 cm. The Froude number downstream on the uneven bed has been dramatically reduced, so this amount of reduction has been approximately 47 and 54% compared to the control condition. The relative depth of the downstream has also increased due to the turbulence of the flow on the uneven bed with the increase in the flow rate.

본 연구의 주요 목표는 수치 모델을 통해 경사 낙하 하류의 거시 거칠기 효과를 조사하는 것입니다. 수력학적 성능과 경사 낙하 하류의 효율적인 에너지 소산에서 거시 거칠기의 기하학적 특성이 매우 중요하기 때문에 두 가지 서로 다른 거시 거칠기 형상, 즉 반원형 및 삼각형 형상이 Flow를 사용하여 조사되었습니다.

3D 모델 수치 시뮬레이션을 통해 유량이 증가하고 상대 임계 깊이가 증가함에 따라 유동 에너지 소비가 감소하는 것으로 나타났습니다. 또한, 높이와 경사각이 증가함에 따라 상대적인 에너지 소산도 증가하는데, 반원형 요소와 삼각형 요소에서 평활층에 비해 에너지 손실의 증가량은 경사낙하에서 각각 86.39%와 76.80%입니다.

높이 15cm, 높이 20cm의 드롭에서 86.99%, 65.78%입니다. 고르지 못한 베드 하류의 프루드 수가 극적으로 감소하여 이 감소량은 대조 조건에 비해 약 47%와 54%였습니다. 유속이 증가함에 따라 고르지 못한 층에서의 흐름의 난류로 인해 하류의 상대적 깊이도 증가했습니다.

Key words

flow energy dissipation, Froude number, inclined drop, numerical simulation

REFERENCES

Abbaspour, A., Taghavianpour, T. & Arvanaghi, H. 2019 Experimental study of the hydraulic jump on the reverse bed with porous screens. Applied Water Science 9, 155. Abbaspour, A., Shiravani, P. & Hosseinzadeh Dalir, A. 2021 Experimental study of the energy dissipation on rough ramps. ISH Journal of Hydraulic Engineering 27, 334–342. Akib, S., Ahmed, A. A., Imran, H. M., Mahidin, M. F., Ahmed, H. S. & Rahman, S. 2015 Properties of a hydraulic jump over apparent corrugated beds. Dam Engineering 25, 65–77. AlTalib, A. N., Mohammed, A. Y. & Hayawi, H. A. 2015 Hydraulic jump and energy dissipation downstream stepped weir. Flow Measurement and Instrumentation 69, 101616. Bayon-Barrachina, A. & Lopez-Jimenez, P. A. 2015 Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics 17, 662–678. Canovaro, F. & Solari, L. 2007 Dissipative analogies between a schematic macro-roughness arrangement and step–pool morphology. Earth Surface Processes and Landforms: The Journal of the British Geomorphological Research Group 32, 1628–1640. Daneshfaraz, R., Ghaderi, A., Akhtari, A. & Di Francesco, S. 2020 On the effect of block roughness in ogee spill-ways with flip buckets. Fluids 5, 182. Daneshfaraz, R., Aminvash, E., Di Francesco, S., Najibi, A. & Abraham, J. 2021a Three-dimensional study of the effect of block roughness geometry on inclined drop. Numerical Methods in Civil Engineering 6, 1–9. Daneshfaraz, R., Aminvash, E., Ghaderi, A., Abraham, J. & Bagherzadeh, M. 2021b SVM performance for predicting the effect of horizontal screen diameters on the hydraulic parameters of a vertical drop. Applied Science 11, 4238. Daneshfaraz, R., Aminvash, E., Ghaderi, A., Kuriqi, A. & Abraham, J. 2021c Three-dimensional investigation of hydraulic properties of vertical drop in the presence of step and grid dissipators. Symmetry 13, 895. Dey, S. & Sarkar, A. 2008 Characteristics of turbulent flow in submerged jumps on rough beds. Journal of Engineering Mechanics 134, 49–59. Ead, S. A. & Rajaratnam, N. 2002 Hydraulic jumps on corrugated beds. Journal of Hydraulic Engineering 128, 656–663. Fang, H., Han, X., He, G. & Dey, S. 2018 Influence of permeable beds on hydraulically macro-rough flow. Journal of Fluid Mechanics 847, 552–590. Federico, I., Marrone, S., Colagrossi, A., Aristodemo, F. & Antuono, M. 2019 Simulating 2D open-channel flows through an SPH model. European Journal of Mechanics-B/Fluids 34, 35–46. Ghaderi, A., Dasineh, M., Aristodemo, F. & Aricò, C. 2021 Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13, 674. Ghare, A. D., Ingl, R. N., Porey, P. D. & Gokhale, S. S. 2010 Block ramp design for efficient energy dissipation. Journal of Energy Dissipation 136, 1–5. Habibzadeh, A., Rajaratnam, N. & Loewen, M. 2019 Characteristics of the flow field downstream of free and submerged hydraulic jumps. Proceedings of the Institution of Civil Engineers-Water Management 172, 180–194. Hajiahmadi, A., Ghaeini-Hessaroeyeh, M. & Khanjani, M. J. 2021 Experimental evaluation of vertical shaft efficiency in vortex flow energy dissipation. International Journal of Civil Engineering 19, 1445–1455.

Katourani, S. & Kashefipour, S. M. 2012 Effect of the geometric characteristics of baffle on hydraulic flow condition in baffled apron drop. Irrigation Sciences and Engineering 37, 51–59. Kurdistani, S. M., Varaki, M. E. & Moayedi Moshkaposhti, M. 2024 Apron and macro roughness as scour countermeasures downstream of block ramps. ISH Journal of Hydraulic Engineering 1–9. Lopardo, R. A. 2013 Extreme velocity fluctuations below free hydraulic jumps. Journal of Engineering 1–5. Mahmoudi-Rad, M. & Najafzadeh, M. 2023 Experimental evaluation of the energy dissipation efficiency of the vortex flow section of drop shafts. Scientific Reports 13, 1679. Matin, M. A., Hasan, M. & Islam, M. R. 2018 Experiment on hydraulic jump in sudden expansion in a sloping rectangular channel. Journal of Civil Engineering 36, 65–77. Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2019 A numerical approach to solve fluid-solid two-phase flows using time splitting projection method with a pressure correction technique. Progress in Computational Fluid Dynamics, an International Journal 19, 357–367. Moghadam, K. F., Banihashemi, M. A., Badiei, P. & Shirkavand, A. 2020 A time-splitting pressure-correction projection method for complete two-fluid modeling of a local scour hole. International Journal of Sediment Research 35, 395–407. Moradi-SabzKoohi, A., Kashefipour, S. M. & Bina, M. 2011 Experimental comparison of energy dissipation on drop structures. JWSS – Isfahan University of Technology 15, 209–223. (in Persian). Mouaze, D., Murzyn, F. & Chaplin, J. R. 2005 Free surface length scale estimation in hydraulic jumps. Journal of Fluids Engineering 127, 1191–1193. Nicosia, A., Carollo, F. G. & Ferro, V. 2023 Effects of boulder arrangement on flow resistance due to macro-scale bed roughness. Water 15, 349. Ohtsu, I. & Yasuda, Y. 1991 Hydraulic jump in sloping channel. Journal of Hydraulic Engineering 117, 905–921. Pagliara, S. & Palermo, M. 2012 Effect of stilling basin geometry on the dissipative process in the presence of block ramps. Journal of Irrigation and Drainage Engineering 138, 1027–1031. Pagliara, S., Das, R. & Palermo, M. 2008 Energy dissipation on submerged block ramps. Journal of Irrigation and Drainage Engineering 134, 527–532. Pagliara, S., Roshni, T. & Palermo, M. 2015 Energy dissipation over large-scale roughness for both transition and uniform flow conditions. International Journal of Civil Engineering 13, 341–346. Parsaie, A., Dehdar-Behbahani, S. & Haghiabi, A. H. 2016 Numerical modeling of cavitation on spillway’s flip bucket. Frontiers of Structural and Civil Engineering 10, 438–444. Pourabdollah, N., Heidarpour, M. & Abedi Koupai, J. 2018 Characteristics of free and submerged hydraulic jumps in different stilling basins. In: Proceedings of the Institution of Civil Engineers-Water Management. Thomas Telford Ltd, pp. 1–11. Roushangar, K. & Ghasempour, R. 2019 Evaluation of the impact of channel geometry and rough elements arrangement in hydraulic jump energy dissipation via SVM. Journal of Hydroinformatics 21, 92–103. Samadi-Boroujeni, H., Ghazali, M., Gorbani, B. & Nafchi, R. F. 2013 Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering 40, 841–847. Shekari, Y., Javan, M. & Eghbalzadeh, A. 2014 Three-dimensional numerical study of submerged hydraulic jumps. Arabian Journal for Science and Engineering 39, 6969–6981. Tokyay, N. D., Evcimen, T. U. & Şimsek, Ç. 2011 Forced hydraulic jump on non-protruding rough beds. Canadian Journal of Civil Engineering 38, 1136–1144. Wagner, W. E. 1956 Hydraulic model studies of the check intake structure-potholes East canal. Bureau of Reclamation Hydraulic Laboratory Report Hyd, 411. Witt, A., Gulliver, J. S. & Shen, L. 2018 Numerical investigation of vorticity and bubble clustering in an air-entraining hydraulic jump. Computers & Fluids 172, 162–180.

험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.

침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.

수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.

모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.

침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.

Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.

Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].

The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:

where Q_{f} is the free flow discharge, B is the channel width, g is the acceleration due to gravity, h_{o} is the water head in free-flow condition, and C_{d} is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, h_{o}, and the weir height, P as C_{d} = 0.605 + 0.08 (h_{o}/P).

Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).

The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.

[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher h_{o}/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, H_{o}/(H_{o} + L), where H_{o} is the total head and L is the crest length.

In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Q_{s}, to the corresponding free-flow discharge, Q_{f}, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���

[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Y_{t} is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (h_{o}/L)^{−2.425} for triangular weirs.

The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.

Section snippets

Governing equations

Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump

Verification of numerical model

The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and

Conclusions

A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (33)

H.M. Fritz et al.Hydraulics of embankment weirsJ. Hydraul. Eng.(1998)

P.K. Swamee et al.Viscosity and surface tension effects on rectangular weirsThe ISH Journal of Hydraulic Engineering(2001)

R. BaddourHead-discharge equation for the sharp-crested polynomial weirJ. Irrigat. Drain. Eng.(2008)

A.R. VatankhahHead-discharge equation for sharp-crested weir with piecewise-linear sidesJ. Irrigat. Drain. Eng.(2012)

A.H. Azimi et al.A note on sharp-crested weirs and weirs of finite crest lengthCan. J. Civ. Eng.(2012)

A.H. Azimi et al.Discharge characteristics of weirs of finite crest length with upstream and downstream rampsJ. Irrigat. Drain. Eng.(2013)

A.H. Azimi et al.Submerged flows over rectangular weirs of finite crest lengthJ. Irrigat. Drain. Eng.(2014)

A.H. Azimi et al.Water surface characteristics of submerged rectangular sharp-crested weirsJ. Hydraul. Eng.(2016)

M. Bijankhan et al.Experimental study and numerical simulation of inclined rectangular weirsJ. Irrigat. Drain. Eng.(2018)

A.H. AzimiAn Introduction to Hydraulic Structure” in Water Engineering Modeling and Mathematic Tools(2021)

웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.

유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.

수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.

수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.

수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.

그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.

더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.

둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

1 Introduction

Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].

Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [1, 2]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S_{0} is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].

Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.

Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [7, 9]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.

Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?

2 Materials and Methods

2.1 Physical Model Configuration

This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m^{3}/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.

Table 1 Experimental conditions considered for calibration

Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S_{0} = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.

2.3 Governing Equations

FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (x, y, z, t). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [4, 13]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (x, y, z) applicable to the model are as follows:

�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR

(1)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x

(2)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y

(3)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z

(4)

where (u, v, w) are the velocity components, (A_{x}, A_{y}, A_{z}) are the flow area components, (G_{x}, G_{y}, G_{z}) are the mass accelerations, and (f_{x}, f_{y}, f_{z}) are the viscous accelerations in the directions (x, y, z), ρ is the fluid density, R_{SOR} is the spring term, V_{f} is the volume fraction associated with the flow, and P is the pressure. The k–ε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard k–ε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:

In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, G_{k} is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants α_{ε} = α_{k} = 1.39, C_{1ε} = 1.42, and C_{2ε} = 1.68, eff is the effective viscosity, μ_{eff} = μ + μ_{t} [15]. Here, μ is the hydrodynamic density coefficient, and μ_{t} is the turbulent density of the fluid.

2.4 Meshing and the Boundary Conditions in the Model Setup

The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = G_{coarse}/G_{fine}). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis

The results of u_{1} = u_{max} (u_{1} = velocity component along the x_{1} axis and u_{max} = maximum velocity of u_{1} in a section perpendicular to the invert of the fishway) at Q = 0.035 m^{3}/s, × 1/l = 0.66, and Y_{1}/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4, x_{1} = the distance from a given weir in the x-direction, Y_{1} = the water depth measured in the y-direction, Y_{0} = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity u_{max} and zero velocity, and l = the pool length.

The apparent index of convergence (p) in the GCI method is calculated as follows:

�=ln(�3−�2)(�2−�1)/ln(�)

(7)

f_{1}, f_{2}, and f_{3} are the hydraulic parameters obtained from the numerical simulation (f_{1} corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:

GCIfine=1.25|ε|��−1

(8)

Here, ε = (f_{2} − f_{1})/f_{1} is the relative error, and f_{2} and f_{3} are the values of hydraulic parameters considered for medium and small grids, respectively. GCI_{12} and GCI_{23} dimensionless indices can be calculated as:

GCI12=1.25|�2−�1�1|��−1

(9)

Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI_{12}) are lower compared to coarse grid (GCI_{23}), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI_{23}/r^{p}GCI_{12}) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation

The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Z_{max} boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).

The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).

3 Results

3.1 Verification of Numerical Results

Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.

MAPE(%)100×1�∑1�|�exp−�num�exp|

(10)

RMSE(−)1�∑1�(�exp−�num)2

(11)

Here, X_{exp} is the value of the laboratory data, X_{num} is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x_{1} = distance from a given weir in the x-direction and Y_{1} = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].

3.2 Flow Regime and Discharge-Depth Relationship

Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [2, 20]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Q_{t}* and L/w, where Q_{t}* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:

��∗=���0���

(12)

Q is the total discharge, B is the width of the channel, S_{0} is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Q_{t}* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Q_{t}* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Q_{t}* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].

For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:

�+=��ℎ�ℎ=23�d�

(13)

where h is the water depth above the weir, and C_{d} is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].

�d=0.57+0.075ℎ�

(14)

The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Q_{o} and the total outflow is Q, the change in the ratio of Q_{o}/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Q_{o}/Q.

3.3 Depth-Averaged Velocity Distributions

To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.

On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S_{0} = 5% were 0.83 and 1.01 m/s; at S_{0} = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S_{0} = 5 and 10% were 0.17 and 0.26 m/s, respectively.

Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.

On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m^{3}/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.

Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.

3.4 Turbulence Characteristics

The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:

�=12(�x′2+�y′2+�z′2)

(15)

where u_{x}, u_{y}, and u_{z} are fluctuating velocities in the x, y, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S_{0} = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.

Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S_{0} = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S_{0} = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.

For TKE size, the average value (TKE_{ave}) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m^{2}/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKE_{ave} in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m^{2}/s, an orifice reduces TKE_{ave} values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKE_{ave} values in the pool. For example, for Model B with q = 0.18 m^{2}/s, increasing the bed slope from 5 to 10% increases the TKE_{ave} value by 14.34%. Increasing the distance between weirs increases the TKE_{ave} values in the pool. For example, in Model B with S_{0} = 10% and q = 0.3 m^{2}/s, the TKE_{ave} in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.

Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.

The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S_{0} = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S_{0} = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.

The average value of turbulence intensity (TI_{ave}) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m^{2}/s. For a given discharge, a given gradient, and a given spacing of weirs, the TI_{ave} is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m^{2}/s, the presence of an orifice increases TI_{ave} from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TI_{ave} in the pool increases with increasing bed slope. For Model B with q = 0.18 m^{2}/s, TI_{ave} increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TI_{ave} in the pool. In Model B with S_{0} = 10% and q = 0.3 m^{2}/s, the TI_{ave} in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.

3.5 Energy Dissipation

To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:

�=����0��

(16)

where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S_{0} = 5%, and S_{0} = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S_{0} = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.

To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:

ε=�1−�2�1

(17)

where ε is the energy dissipation rate, and E_{1} and E_{2} are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S_{0} = 5%, L/B = 0.61, and q = 0.08 m^{3}/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m^{3}/s.m, the energy dissipation rate at S_{0} = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.

4 Discussion

This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.

When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.

In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.

The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.

The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.

5 Conclusions

A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:

The calculated dimensionless discharge (Q_{t}*) confirmed three different flow regimes: when the corresponding range of Q_{t}* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Q_{t}* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Q_{t}* is greater than 1, the streaming flow is at values of L/B = 0.61.

For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.

In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.

As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.

The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.

For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S_{0} = 10%).

For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.

For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).

Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.

Availability of data and materials

Data is contained within the article.

References

Katopodis C (1992) Introduction to fishway design, working document. Freshwater Institute, Central Arctic Region

Marriner, B.A.; Baki, A.B.M.; Zhu, D.Z.; Thiem, J.D.; Cooke, S.J.; Katopodis, C.: Field and numerical assessment of turning pool hydraulics in a vertical slot fishway. Ecol. Eng. 63, 88–101 (2014). https://doi.org/10.1016/j.ecoleng.2013.12.010ArticleGoogle Scholar

Dasineh, M.; Ghaderi, A.; Bagherzadeh, M.; Ahmadi, M.; Kuriqi, A.: Prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods. Mathematics 9, 3135 (2021)ArticleGoogle Scholar

Silva, A.T.; Bermúdez, M.; Santos, J.M.; Rabuñal, J.R.; Puertas, J.: Pool-type fishway design for a potamodromous cyprinid in the Iberian Peninsula: the Iberian barbel—synthesis and future directions. Sustainability 12, 3387 (2020). https://doi.org/10.3390/su12083387ArticleGoogle Scholar

Santos, J.M.; Branco, P.; Katopodis, C.; Ferreira, T.; Pinheiro, A.: Retrofitting pool-and-weir fishways to improve passage performance of benthic fishes: effect of boulder density and fishway discharge. Ecol. Eng. 73, 335–344 (2014). https://doi.org/10.1016/j.ecoleng.2014.09.065ArticleGoogle Scholar

Ead, S.; Katopodis, C.; Sikora, G.; Rajaratnam, N.J.J.: Flow regimes and structure in pool and weir fishways. J. Environ. Eng. Sci. 3, 379–390 (2004)ArticleGoogle Scholar

Guiny, E.; Ervine, D.A.; Armstrong, J.D.: Hydraulic and biological aspects of fish passes for Atlantic salmon. J. Hydraul. Eng. 131, 542–553 (2005)ArticleGoogle Scholar

Zhong, Z.; Ruan, T.; Hu, Y.; Liu, J.; Liu, B.; Xu, W.: Experimental and numerical assessment of hydraulic characteristic of a new semi-frustum weir in the pool-weir fishway. Ecol. Eng. 170, 106362 (2021). https://doi.org/10.1016/j.ecoleng.2021.106362ArticleGoogle Scholar

Roache, P.J.: Perspective: a method for uniform reporting of grid refinement studies. J. Fluids Eng. 1994(116), 405–413 (1994)ArticleGoogle Scholar

Guo, S.; Chen, S.; Huang, X.; Zhang, Y.; Jin, S.: CFD and experimental investigations of drag force on spherical leak detector in pipe flows at high Reynolds number. Comput. Model. Eng. Sci. 101(1), 59–80 (2014)Google Scholar

Ahmadi, M.; Kuriqi, A.; Nezhad, H.M.; Ghaderi, A.; Mohammadi, M.: Innovative configuration of vertical slot fishway to enhance fish swimming conditions. J. Hydrodyn. 34, 917–933 (2022). https://doi.org/10.1007/s42241-022-0071-yArticleGoogle Scholar

Ahmadi, M.; Ghaderi, A.; MohammadNezhad, H.; Kuriqi, A.; Di Francesco, S.J.W.: Numerical investigation of hydraulics in a vertical slot fishway with upgraded configurations. Water 13, 2711 (2021)ArticleGoogle Scholar

Celik, I.B.; Ghia, U.; Roache, P.J.; Freitas, C.J.J.: Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. Trans. ASME (2008). https://doi.org/10.1115/1.2960953ArticleGoogle Scholar

Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C.: Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13(5), 674 (2021)ArticleGoogle Scholar

Branco, P.; Santos, J.M.; Katopodis, C.; Pinheiro, A.; Ferreira, M.T.: Pool-type fishways: two different morpho-ecological cyprinid species facing plunging and streaming flows. PLoS ONE 8, e65089 (2013). https://doi.org/10.1371/journal.pone.0065089ArticleGoogle Scholar

Natália Melo da Silva1^{ 1}; Jorge Luis Zegarra Tarqui^{2},Edna Maria de Faria Viana ^{3}

Abstract

저수지 침전은 수력 발전의 지속 가능한 발전을 위한 주요 문제 중 하나이며 브라질에 매우 중요합니다. 브라질의 주요 에너지원은 수력발전소에서 나옵니다. 소규모 수력 발전소(SHP)는 재생 에너지의 보완적 발전을 위한 중요한 대안입니다.

이들의 설계, 건설, 운영 및 재동력을 최적화하기 위해 저수지 내 퇴적물의 유체 역학 및 이동을 연구하는 것이 매우 중요합니다.

3차원 전산유체역학 – CFD 3D 모델링은 복잡한 흐름 문제에 가장 적합한 방법입니다. 제안된 방법은 MG Jeceaba 자치구에 위치한 PCH Salto Paraopeba의 유체 역학 및 퇴적물 이동 현상을 재현하고 평가하는 것을 목표로 하며, 취수구의 완전한 침전으로 인해 작동이 중단되었습니다.

모델의 검증은 미나스제라이스 연방대학교의 수력학 연구 센터(CPH)에 구축된 축소된 물리적 모델의 실험 데이터를 사용하여 수행됩니다.

Abstract: The reservoir silting is one of the main problems for sustainable development in the generation of hydroelectric energy and it is of great significance for Brazil. The main source of energy in Brazil comes from hydroelectric power plant. The Small Hydroelectric Power Plant (SHP) are an important alternative for complementary generation of renewable energy. Seeking to optimize the design, construction, operation, and repowering of these, it is extremely important to study the hydrodynamics and transport of sediments in their reservoirs. Threedimensional Computational Fluid Dynamics – CFD 3D modeling is the most appropriate method for complex flow problems. The proposed method aims to reproduce and evaluate the hydrodynamic and sediment transport phenomena of the PCH Salto Paraopeba, located in the municipality of Jeceaba, MG, which stopped working due to the complete silting up of its water intake. The validation of the model will be done using experimental data from the reduced physical model, built at the Hydraulic Research Center (CPH) at the Federal University of Minas Gerais.

Keywords

퇴적물 수송, 물리적 모델, 소규모 수력 발전소, Sediment transport, physical model, Small Hydroelectric Power Plant.

REFERÊNCIAS

ALBARELLO, L. “Guia para implantação de pequenas centrais hidrelétricas- PCHs”. Dissertação de Mestrado. Trabalho de Conclusão de Curso de Especialista. Programa de Pós-Graduação em Eficiência Energética Aplicada aos Processos Produtivos. UFSM, Panambi /RS, 2014.

ANEEL, SIGA – Sistema de Informações de Geração da ANEEL. Disponível em: . Acesso em 10 de maio de 2023.

CAMPELLO, B.S.C. “Estudo Da Velocidade de Queda e do Início do Movimento das Partículas de Borracha e Areia”. Dissertação de Mestrado. Programa de Pós-Graduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG, 2017.

CAMPOS, A.S. “A Importância do Coeficiente de Rugosidade de Manning na Avaliação Numérica do Assoreamento de Reservatórios A Fio D’água”. Dissertação de Mestrado. Programa de PósGraduação em Saneamento, Meio Ambiente e Recursos Hídricos. UFMG, Belo Horizonte /MG, 2018.

CARVALHO, N. O. et al. Guia de avaliação de assoreamento de reservatórios, ANEEL, Brasília, 2000.

CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 1994.

CARVALHO, N. O. Hidrossedimentologia prática, CPRM, Rio de Janeiro, 2008.

EMIG, PCH Salto do Paraopeba. Disponível em: < https://www.cemig.com.br/usina/pch-salto-doparaopeba/>. Acesso em 12 de maio de 2023.

ELETROBRÁS; Instituto de Pesquisas Hidráulicas – IPH. Diagnóstico das Condições sedimentológicas dos Principais Rios Brasileiros. UFRGS, Rio de Janeiro, 1992.

FLOW-3D®. FLOW-3D® 2022R2 – User Manual. Disponível em: < https://users.flow3d.com/flow3d/> FORTUNA, A.O. (2000). Técnicas Computacionais para Dinâmica dos Fluidos – Conceitos Básicos e Aplicações. São Paulo – SP.

GONÇALVES, M.O. “Análise Comparativa Entre Modelo Reduzido e Modelos Computacionais Uni e Bidimensionais”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de Recursos Hídricos e Ambiental. UFRP, Curitiba/PR, 2017.

HILLEBRAND, G.; KLASSEN, I.; OLSEN, N. R. B. (2017). “3D CFD modelling of velocities and sediment transport in the Iffezheim hydropower reservoir”. Hydrology Research 48 (1), pp. 147–159. JULIEN, P. Y. (2010). Erosion and sedimentation, Cambridge University Press, Cambridge, UK, 2nd edn.

MAHMOOD, K. (1987). Reservoir sedimentation – impact, extent and mitigation. World Bank Tech. Paper No. 71. Washington, DC.

MIRANDA, R.B. “A influência do assoreamento na geração de energia hidrelétrica: estudo de caso na Usina de Três Irmãos – SP”. Dissertação de Mestrado. Programa de Pós-Graduação em Ciências da Engenharia Ambiental. USP, São Carlos/SP, 2011.

MOHAMMAD, M.E.; AL-ANSARI, N.; KNUTSSON, S.; LAUE, J. (2020). “A Computational Fluid Dynamics Simulation Model of Sediment Deposition in a Storage Reservoir Subject to Water Withdrawal”. Water, 12, 959.

OLIVEIRA, M. A.“Repotenciação de pequenas centrais hidrelétricas: Avaliação técnica e econômica”. Dissertação de Mestrado. Programa de Pós-Graduação em Engenharia de Energia. UNIFEI, Itajubá/MG, 2012.

SALIBA, A.P.M. Notas de aula, Modelos fundo móvel, Disciplina Introdução a Modelagem Física em Engenharia, Universidade Federal de Minas Gerais. Belo Horizonte, 2020.

SOARES, W.S. “Taxa de Assoreamento no Reservatório da Usina Hidrelétrica do Funil, MG”. Dissertação de Mestrado. Programa de Pós-Graduação em Tecnologias e Inovações Ambientais. UFLA, Lavras/MG, 2015.

Assessing the interaction of waves and porous offshore structures such as rubble mound breakwaters plays a critical role in designing such structures optimally. This study focused on the effect of the geometric parameters of a sloped rubble mound breakwater, including the shape of the armour, method of its arrangement, and the breakwater slope. Thus, three main design criteria, including the wave reflection coefficient (K_{r}), transmission coefficient (K_{t}), and depreciation wave energy coefficient (K_{d}), are discussed. Based on the results, a decrease in wavelength reduced the K_{r} and increased the K_{t} and K_{d}. The rubble mound breakwater with the Coreloc armour layer could exhibit the lowest K_{r} compared to other armour geometries. In addition, a decrease in the breakwater slope reduced the K_{r} and K_{d} by 3.4 and 1.25%, respectively. In addition, a decrease in the breakwater slope from 33 to 25° increased the wave breaking height by 6.1% on average. Further, a decrease in the breakwater slope reduced the intensity of turbulence depreciation. Finally, the armour geometry and arrangement of armour layers on the breakwater with its different slopes affect the wave behaviour and interaction between the wave and breakwater. Thus, layering on the breakwater and the correct use of the geometric shapes of the armour should be considered when designing such structures.

파도와 잔해 더미 방파제와 같은 다공성 해양 구조물의 상호 작용을 평가하는 것은 이러한 구조물을 최적으로 설계하는 데 중요한 역할을 합니다. 본 연구는 경사진 잔해 둔덕 방파제의 기하학적 매개변수의 효과에 초점을 맞추었는데, 여기에는 갑옷의 형태, 배치 방법, 방파제 경사 등이 포함된다. 따라서 파동 반사 계수(K_{r}), 투과 계수(K_{t}) 및 감가상각파 에너지 계수(K_{d})에 대해 논의합니다. 결과에 따르면 파장이 감소하면 K가 감소합니다._{r}그리고 K를 증가시켰습니다_{t} 및 K_{d}. Coreloc 장갑 층이 있는 잔해 언덕 방파제는 가장 낮은 K를 나타낼 수 있습니다._{r} 다른 갑옷 형상과 비교했습니다. 또한 방파제 경사가 감소하여 K가 감소했습니다._{r} 및 K_{d} 각각 3.4%, 1.25% 증가했다. 또한 방파제 경사가 33°에서 25°로 감소하여 파도 파쇄 높이가 평균 6.1% 증가했습니다. 또한, 방파제 경사의 감소는 난류 감가상각의 강도를 감소시켰다. 마지막으로, 경사가 다른 방파제의 장갑 형상과 장갑 층의 배열은 파도 거동과 파도와 방파제 사이의 상호 작용에 영향을 미칩니다. 따라서 이러한 구조를 설계 할 때 방파제에 층을 쌓고 갑옷의 기하학적 모양을 올바르게 사용하는 것을 고려해야합니다.

Keywords

Rubble mound breakwater

Computational fluid dynamics

Armour layer

Wave reflection coefficient

Wave transmission coefficient

Wave energy dissipation coefficient

References

Sollitt, C.K.; Cross, R.H.: Wave transmission through permeable breakwaters. In Coastal Engineering. pp. 1827–1846. (1973)

Sulisz, W.: Wave reflection and transmission at permeable breakwaters of arbitrary cross-section. Coast. Eng. 9(4), 371–386 (1985)ArticleGoogle Scholar

Kobayashi, N.; Wurjanto, A.: Numerical model for waves on rough permeable slopes. J. Coast. Res.149–166. (1990)

Wurjanto, A.; Kobayashi, N.: Irregular wave reflection and runup on permeable slopes. J. Waterw. Port Coast. Ocean Eng. 119(5), 537–557 (1993)ArticleGoogle Scholar

van Gent, M.R.: Numerical modelling of wave interaction with dynamically stable structures. In Coastal Engineering 1996. pp. 1930–1943. (1997)

Liu, P.L.F.; Wen, J.: Nonlinear diffusive surface waves in porous media. J. Fluid Mech. 347, 119–139 (1997)ArticleMathSciNetMATHGoogle Scholar

Troch, P.; De Rouck, J.: Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters. In Coastal Engineering. pp. 1638–1649. (1999)

Liu, P.L.F.; Lin, P.; Chang, K.A.; Sakakiyama, T.: Numerical modeling of wave interaction with porous structures. J. Waterw. Port Coast. Ocean Eng. 125(6), 322–330 (1999)ArticleGoogle Scholar

Abdolmaleki, K.; Thiagarajan, K.P.; Morris-Thomas, M.T.: Simulation of the dam break problem and impact flows using a Navier-Stokes solver. Simulation 13, 17 (2004)Google Scholar

Higuera, P.; Lara, J.L.; Losada, I.J.: Realistic wave generation and active wave absorption for Navier-Stokes models: application to OpenFOAM®. Coast. Eng. 71, 102–118 (2013)ArticleGoogle Scholar

Higuera, P.; Lara, J.L.; Losada, I.J.: Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: application. Coast. Eng. 83, 259–270 (2014)ArticleGoogle Scholar

Dentale, F.; Donnarumma, G.; Carratelli, E.P.; Reale, F.: A numerical method to analyze the interaction between sea waves and rubble mound emerged breakwaters. WSEAS Trans. Fluid Mech 10, 106–116 (2015)Google Scholar

Dentale, F.; Reale, F.; Di Leo, A.; Carratelli, E.P.: A CFD approach to rubble mound breakwater design. Int. J. Naval Archit. Ocean Eng. 10(5), 644–650 (2018)ArticleGoogle Scholar

Koley, S.: Wave transmission through multilayered porous breakwater under regular and irregular incident waves. Eng. Anal. Bound. Elem. 108, 393–401 (2019)ArticleMathSciNetMATHGoogle Scholar

Koley, S.; Panduranga, K.; Almashan, N.; Neelamani, S.; Al-Ragum, A.: Numerical and experimental modeling of water wave interaction with rubble mound offshore porous breakwaters. Ocean Eng. 218, 108218 (2020)ArticleGoogle Scholar

Pourteimouri, P.; Hejazi, K.: Development of an integrated numerical model for simulating wave interaction with permeable submerged breakwaters using extended Navier-Stokes equations. J. Mar. Sci. Eng. 8(2), 87 (2020)ArticleGoogle Scholar

Cao, D.; Yuan, J.; Chen, H.: Towards modelling wave-induced forces on an armour layer unit of rubble mound coastal revetments. Ocean Eng. 239, 109811 (2021)ArticleGoogle Scholar

Díaz-Carrasco, P.; Eldrup, M.R.; Andersen, T.L.: Advance in wave reflection estimation for rubble mound breakwaters: the importance of the relative water depth. Coast. Eng. 168, 103921 (2021)ArticleGoogle Scholar

Vieira, F.; Taveira-Pinto, F.; Rosa-Santos, P.: Damage evolution in single-layer cube armoured breakwaters with a regular placement pattern. Coast. Eng. 169, 103943 (2021)ArticleGoogle Scholar

Booshi, S.; Ketabdari, M.J.: Modeling of solitary wave interaction with emerged porous breakwater using PLIC-VOF method. Ocean Eng. 241, 110041 (2021)ArticleGoogle Scholar

Aristodemo, F.; Filianoti, P.; Tripepi, G.; Gurnari, L.; Ghaderi, A.: On the energy transmission by a submerged barrier interacting with a solitary wave. Appl. Ocean Res. 122, 103123 (2022)ArticleGoogle Scholar

Teixeira, P.R.; Didier, E.: Numerical analysis of performance of an oscillating water column wave energy converter inserted into a composite breakwater with rubble mound foundation. Ocean Eng. 278, 114421 (2023)ArticleGoogle Scholar

Burgan, H.I.: Numerical modeling of structural irregularities on unsymmetrical buildings. Tehnički vjesnik 28(3), 856–861 (2021)Google Scholar

Jones, I.P.: CFDS-Flow3D user guide. (1994)

Al Shaikhli, H.I.; Khassaf, S.I.: Stepped mound breakwater simulation by using flow 3D. Eurasian J. Eng. Technol. 6, 60–68 (2022)Google Scholar

Hirt, C.W.; Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)ArticleMATHGoogle Scholar

Ghaderi, A.; Dasineh, M.; Aristodemo, F.; Aricò, C.: Numerical simulations of the flow field of a submerged hydraulic jump over triangular macroroughnesses. Water 13(5), 674 (2021)ArticleGoogle Scholar

Yakhot, V.; Orszag, S.A.; Thangam, S.; Gatski, T.B.; Speziale, C.G.: Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4(7), 1510–1520 (1992)ArticleMathSciNetMATHGoogle Scholar

Van der Meer, J.W.; Stam, C.J.M.: Wave runup on smooth and rock slopes of coastal structures. J. Waterw. Port Coast. Ocean Eng. 118(5), 534–550 (1992)ArticleGoogle Scholar

Goda, Y.; Suzuki, Y. Estimation of incident and reflected waves in random wave experiments. In: ASCE, Proceedings of 15th International Conference on Coastal Engineering, (Honolulu, Hawaii). vol. 1, pp. 828–845. (1976)

Zanuttigh, B.; Van der Meer, J.W.: Wave reflection from coastal structures. In: AA.VV., Proceedings of the XXX International Conference on Coastal Engineering, World Scientific, (San Diego, CA, USA, September 2006). pp. 4337–4349. (2006)

Seelig W.N.; Ahrens J.P.: Estimation of wave reflection and energy dissipation coefficients for beaches, revetments, and breakwaters. CERC, Technical Paper, Fort Belvoir. vol. 81, p. 41 (1981)

Mase, H.: Random wave runup height on gentle slope. J. Waterw. Port Coast. Ocean Eng. 115(5), 649–661 (1989)ArticleGoogle Scholar

^{2} Researcher of Imam Hossein University, Faculty of Engineering and Passive Defense

^{3} Ivanki University, Iran.

10.22124/JCR.2023.24324.1618

Abstract

개방 수로의 심한 수력 구배는 침전으로 인한 심각한 침식과 문제를 일으킵니다. 패브릭 콘크리트는 기존의 콘크리트 표면을 대체할 수 있는 높은 실행 속도를 가진 독특한 제품입니다. 이 제품의 기계적 저항 매개변수에 따르면 부식 요인에 대한 우수한 내구성 외에도 직물 콘크리트의 응용 분야 중 하나는 운하 및 수로 암거 표면에 사용하는 것입니다. 이 연구에서는 먼저 사다리꼴 단면의 개방 채널 흐름을 직선 경로 상태의 3가지 공통 채널 형상, 굴곡 및 편차가 있는 경로, 마지막으로 채널 하단의 높이가 변경된 채널 경로를 포함하는 9가지 시나리오에서 시뮬레이션합니다. 각 주에서 flow-3d 소프트웨어를 사용한 흐름 난류 모델링과 함께 3개의 서로 다른 흐름 체제가 조사되었습니다.

FLOW-3D 소프트웨어를 사용한 유동 난류 모델링과 함께 다양한 유동 체제가 조사되었습니다. ABAQUS 소프트웨어를 사용하여 패브릭 콘크리트 구성요소와 연결 영역을 모델링하고, 콘크리트 표면과 취약한 연결 영역에 동일한 힘을 가하여 생성된 응력의 양을 확인했습니다. 결과는 생성된 응력이 직물 콘크리트의 인장 및 압축 응력 용량에 비해 매우 낮다는 것을 보여줍니다. 흐름과 콘크리트의 수력 연구를 검증하기 위해 관련 실험실 결과가 사용되었습니다.

Severe hydraulic gradients in open channels cause severe bed erosion and problems caused by sedimentation. Fabric concrete is a unique product with high execution speed that can replace traditional concrete surfaces. According to the mechanical resistance parameters of this product, in addition to its good durability against corrosive factors, one of the applications of fabric concrete is its use on the surface of canals and water course culverts. In this research, first, the flow of open channels in trapezoidal section is simulated under 9 scenarios, which include 3 common channel geometries in the state of a straight path, a path with bends and deviations, and finally, a channel path with a change in height at the bottom of the channel. In each of the states, 3 different flow regimes have been investigated along with flow turbulence modeling using flow-3d software.

Different flow regimes have been investigated along with flow turbulence modeling using flow-3d software. Using ABAQUS software, fabric concrete components and their connection areas have been modeled, and by applying forces equated to the concrete surface and vulnerable connection areas, the amount of created stresses has been checked. The results show that the created stresses are very low compared to the tensile and compressive stress capacity of fabric concrete. In order to validate the hydraulic studies of flow and concrete, the relevant laboratory results have been used.

In river engineering, the stepped spillway of a dam is an important component that may be used in various ways. It is necessary to conduct research dealing with flood control in order to investigate the method, in which energy is lost along the tiered spillways. In the past, several research projects on stepped spillways without baffles have been carried out utilizing a range of research approaches. In the present study, machine learning techniques such as Support Vector Machine (SVM) and Regression Tree (RT) are used to analyze the energy dissipation on rectangular stepped spillways that make use of baffles in a variety of configurations and at a range of channel slopes. The results of many experiments indicate that the amount of energy that is lost increases with the number of baffles that are present in flat channels with slopes and rises. In order to evaluate the efficiency and usefulness of the suggested model, the statistical indices that were developed for the experimental research are used to validate the models that were created for the study. The findings indicate that the suggested SVM model properly predicted the amount of energy that was dissipated when contrasted with RT and the method that had been developed in the past. This study verifies the use of machine learning techniques in this industry, and it is unique in that it anticipates energy dissipation along stepped spillways utilizing baffle designs. In addition, this work validates the use of machine learning methods in this field.

Keywords

Rectangular Stepped Spillways, Baffle Arrangements, Channel Slope, Support Vector Machine (SVM), Regression Tree (RT)

Introduction

To regulate water flows downstream of a dam, a spillway structure is employed, with stepped spillways preventing water from overflowing and causing damage to the dam. These spillways consist of a channel with built-in steps or drops. Flow patterns observed include nappe flow, transition flow, and skimming flow [1]. Numerous scholars have looked at the energy dissipation in stepped spillways [2-4]. Boes and Hager [5] looked at the benefits of stepped spillways, such as their simplicity of construction, less danger of cavitation, and smaller stilling basins at downstream dam toes owing to considerable energy loss along the chute. Hazzab and Chafic [7] conducted an experimental study on energy dissipation in stepped spillways and reported on flow configurations. Additionally, the Manksvill dam spillway was examined using a 1:25 scale physical wooden model [6]. For moderately inclined stepped channels, Stefan and Chanson [8] explored air-water flow measurements. Daniel [9] discussed how the existence of steps and step heights affect stepped spillways’ ability to dissipate energy. A comparison of the smooth invert chute flow with the self aerated stepped spillway. The energy dissipation in stepped spillways was investigated using various methods. Katourany [10] compared experimental findings to conventional USBR outcomes to examine the effects of different baffle widths, spacing between baffle rows, and step heights of baffled aprons. Salmasi et al. [11] assessed the energy dissipation of through-flow and over-flow in gabion stepped spillways, discovering that gabion spillways with pervious surfaces dissipated energy more efficiently than those with concrete walls. Other forms of stepped spillways, such as inclined steps and steps with end sills, were also quantitatively studied for energy dissipation [12]. Saedi and Asareh [13] examined how the number of drop stairs affected energy dissipation in stepped drops and suggested using stepped drops to increase energy dissipation by providing flow path roughness. Al-Husseini [14] found that decreasing the number of steps and downstream slopes led to an increase in flow energy dissipation, and that the use of cascade spillways reduced energy dissipation compared to the original step spillway. MARS and ANN methods were used to estimate energy dissipation in flow across stepped spillways under skimming flow conditions, with both models proving reliable [15]. Frederic et al. [16] evaluated the energy dissipation effectiveness and stability of the Mekin Dam spillway by confirming that flow did not result in transitional flow and by calculating safety factors at various intervals. A numerical model was developed to validate a physical model examining the impact of geometrical parameters on the dissipation rate in flows through stepped spillways [17]. The regulation of the rates of dissipation is studied using a particular kind of fuzzy inference system (FIS). The findings are compared with a predefined numerical database to determine the predicted energy dissipation under various circumstances. The findings show that the suggested FIS may be a useful tool for the operational management of dissipator structures while taking various geometric characteristics into account. Nasralla [18] studied the four phases of the spillway and conducted eighteen runs to enhance energy dissipation through the contraction-stepped spillway. The study considered alternative baffle placements, heights, and widths. The results showed that downstream baffles on the stepped spillway of the stilling basin improve energy dissipation. Using the Flow 3D software, Ikinciogullari [19] quantitatively analyzed the energy dissipation capabilities of trapezoidal stepped spillways using four distinct models and three different discharges. The findings showed that trapezoidal stepped spillways are up to 30% more efficient in dissipating energy than traditional stepped spillways. In previous works, only a few machine learning algorithms were used to forecast energy dissipation across a rectangular stepped spillway without baffles. Therefore, this study used machine learning approaches such as Support Vector Machine (SVM) and Regression Tree (RT) to predict energy dissipation across a rectangular stepped spillway with varied rectangular-shaped baffle configurations at different channel slopes. The study compared these models using statistical analysis to assess their efficiency in predicting energy dissipation over rectangular stepped spillways with baffles. 2. Materials and Methods 2.1. Experimental Setup The experiments were carried out at the Hydraulics laboratory of Delhi Technological University. The tests were performed in a rectangular tilting flume of 8m long, 0.30m wide and 0.40m deep which has a facility to make it horizontal and sloping as well (shown in Figure 1). The flume consists of an inlet section, an outlet section, and a collecting tank at the downstream end which is used to measure the discharge. Figure 2 depicts the model of a rectangular stepped spillway prepared using an acrylic sheet having a width of 0.30m, a height of 0.20m and a base length of 0.40m. A total of four steps were designed with a step height of 0.05m, the step length is 0.10m and rectangular-shaped baffles of length 0.10m and height of 0.05m were arranged in different manner. Figure 3 represents the different baffle arrangements used in the experimental work. At first, the experiment was conducted for no baffle condition. Thereafter the experiment was conducted for the first arrangement of three baffles, in which two baffles were placed at a distance of 0.10m from the toe of the spillway and a distance of 0.10m was maintained between the first two baffles and the third baffle was placed between the first two baffles at a distance of 0.20m from the toe of the spillway (figure 4a). After that, the experiment was conducted for the third arrangement of baffles which consists of five baffles, two more baffles were introduced at a distance of 0.30m from the toe of the spillway and a distance of 0.10m was maintained between them (figure 4b). The baffles used in the experiment were rectangular shaped which had a height of 0.05m and length of 0.10m. The experiments were conducted for five different discharges 2 l/s, 4 l/s, 6 l/s, 8 l/s and 10 l/s. For the purpose of determining the head values both upstream and downstream of the spillway model, a point gauge with a precision of 0.1mm was used. In order to determine the average velocities of the upstream and downstream portions, respectively, a pitot static tube was used in conjunction with a digital manometer.

Fine sediments enter into the river through various sources such as channel bed, bank, and catchment. It has been regarded as a type of pollution in river. Fine sediments present in a river have a significant effect on river health. Benthic micro-organism, plants, and large fishes, all are part of food chain of river biota. Any detrimental effect on any of these components of food chain misbalances the entire riverine ecosystem. Numerous studies have been carried out on the various environmental aspects of rivers considering the presence of fine sediment in river flow. The present paper critically reviews many of these aspects to understand the various environmental impacts of suspended sediment on river health, flora and fauna.

Introduction The existence of fine sediment in a river system is a natural phenomenon. But in many cases it is exacerbated by the manmade activities. The natural cause of fines being in flow generally keeps the whole system in equilibrium except during some calamites whereas anthropogenic activities leading to fines entering into the flow puts several adverse impacts on the entire river system and its ecology. Presence of fines in flow is considered as a type of pollution in water. In United States, the fine sediment in water along with other non point source pollution is considered as a major obstacle in providing quality water for fishes and recreation activities (Diplas and Parker 1985). Sediments in a river are broadly of two types, organic and inorganic, and they both move in two ways either along the bed of the channel called bed load or in suspension called suspended load and their movements depend upon fluid flow and sediment characteristics. Further many investigators have divided the materials in suspension into two different types. One which originates from channel bed and bank is called bed material suspended load and another that migrates from feeding catchment area is called wash load. A general perception is that wash loads are very fine materials like clay, silt but it may not always be true (Woo et al. 1986). In general, suspended materials are of size less than 2 mm. The impact of sand on the various aspects of river is comparatively less than that of silt and clay. The latter are chemically active and good carrier of many contaminants and nutrients such as dioxins, phosphorous, heavy and trace metals, polychlorinated biphenyl (PCBs), radionuclide, etc. (Foster and Charlesworth 1996; Horowitz et al. 1995; Owens et al. 2001; Salomons and Förstner 1984; Stone and Droppo 1994; Thoms 1987). Foy and Bailey-Watt (1998) reported that out of 129 lakes in England and Wales, 69% have phosphorous contamination. Ten percent lakes, rivers, and bays of United States have sediment contaminants with chemicals as reported by USEPA. Several field and experimental studies have been conducted considering, sand, silt, and clay as suspended material. Hence, the subject reported herein is based on considering the fine sediment size smaller than 2 mm. Fine sediments have the ability to alter the hydraulics of the flow. Presence of fines in flow can change the magnitude of turbulence, it can change the friction resistance to flow. Fines can change the mobility and permeability of the bed material. In some extreme cases, fines in flow may even change the morphology of the river (Doeg and Koehn 1994; Nuttall 1972; Wright and Berrie 1987). Fines in the flow adversely affect the producer by increasing the turbidity, hindering the photosynthesis process by limiting the light penetration. This is ultimately reflected in the entire food ecosystem of river (Davis-Colley et al. 1992; Van Niewenhuyre and Laparrieve 1986). In addition, abrasion due to flowing sediment kills the aquatic flora (Edwards 1969; Brookes 1986). Intrusion of fines into the pores of river bed reduces space for several invertebrates, affects the spawning process (Petts 1984; Richards and Bacon 1994; Schalchli 1992). There are several other direct or indirect, short-term or long-term impacts of fines in river. The present paper reports the physical/environmental significance of fines in river. The hydraulic significance of presence of fines in the river has been reviewed in another paper (Effect of fine sediments on river hydraulics – a research review – http://dx.doi.org/10.1080/09715010.2014.982001).

References

Adams, J.N., and Beschta, R.L. (1980). “Gravel bed composition in oregon coastal streams.” Can. J. Fish. Aquat.Sci., 37, 1514–1521.10.1139/f80-196 [Crossref], [Web of Science ®], [Google Scholar]

Alabaster, J.S., and Llyod, R.L. (1980). Water quality criteria for fresh water, Butterworth, London, 297. [Google Scholar]

Aldridge, D.W., Payne, B.S., and Miller, A.C. (1987). “The effects of intermittent exposure to suspended solids and turbulence on three species of freshwater mussels.” Environ. Pollution, 45, 17–28.10.1016/0269-7491(87)90013-3 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Barton, B.A. (1977). “Short-term effects of highway construction on the limnology of a small stream in southern Ontario.” Freshwater Biol., 7, 99–108.10.1111/fwb.1977.7.issue-2 [Crossref], [Web of Science ®], [Google Scholar]

Bash, J., Berman, C., and Bolton, S. (2001). Effects of turbidity and suspended solids on salmonids, Center for Streamside Studies, University of Washington, Seattle, WA. [Google Scholar]

Baxter, C.V., and Hauer, F.R. (2000). “Geomorphology, hyporheic exchange, and selection of spawning habitat by bull trout (Salvelinus confuentus).” Can. J. Fish. Aquat.Sci., 57, 1470–1481.10.1139/f00-056 [Crossref], [Web of Science ®], [Google Scholar]

Berkman, H.E., and Rabeni, C.F. (1987). “Effect of siltation on stream fish communities.” Environ. Biol. Fish., 18, 285–294.10.1007/BF00004881 [Crossref], [Web of Science ®], [Google Scholar]

Beschta, R.L., and Jackson, W.L. (1979). “The intrusion of fine sediments into a stable gravel bed.” J. Fish. Res. Board Can., 36, 204–210.10.1139/f79-030 [Crossref], [Google Scholar]

Boon, P.J. (1988). “The impact of river regulation on invertebrate communities in the UK.” Reg. River Res. Manage., 2, 389–409.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]

Brookes, A. (1986). “Response of aquatic vegetation to sedimentation downstream from river channelization works in England and Wales.” Biol. Conserv., 38, 352–367. [Crossref], [Web of Science ®], [Google Scholar]

Carling, P.A. (1984). “Deposition of fine and coarse sand in an open-work gravel bed.” Can. J. Fish. Aquat. Sci., 41, 263–270.10.1139/f84-030 [Crossref], [Web of Science ®], [Google Scholar]

Carling, P.A., and McCahon, C.P. (1987). “Natural siltation of brown trout (Salmo trutta L.) spawning gravels during low-flow conditions.” Regulated streams, J.F. Craig and J.B. Kemper, eds., Plenum Press, New York, NY, 229–244.10.1007/978-1-4684-5392-8 [Crossref], [Google Scholar]

Carter, J., Owens, P.N., Walling, D.E., and Leeks, G.J.L. (2003). “Fingerprinting suspended sediment sources in a large urban river system.” Sci. Total Environ., 314–316, 513–534.10.1016/S0048-9697(03)00071-8 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Chang, H.H. (1988). Fluvial processes in river engineering, Krieger, Malabar Florida, 432. [Google Scholar]

Chapman, D.W. (1988). “Critical review of variables used to define effects of fines in redds of large salmonids.” Trans. Am. Fish. Soc., 117, 1–21.10.1577/1548-8659(1988)117<0001:CROVUT>2.3.CO;2 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Church, M.A., Mclean, D.G., and Wolcott, J.F. (1987). “River bed gravel sampling and analysis.” Sediment transport in gravel-bed rivers, C.R. Thorne, J.C. Bathrust, and R.D. Hey, eds., John Willey, Chichester, 43–79. [Google Scholar]

Cline, L.D., Short, R.A., and Ward, J.V. (1982). “The influence of highway construction on the macroinvertebrates and epilithic algae of a high mountain stream.” Hydrobiologia, 96, 149–159.10.1007/BF02185430 [Crossref], [Web of Science ®], [Google Scholar]

Collins, A.L., Walling, D.E., and Leeks, G.J.L. (1997). “Fingerprinting the origin of fluvial suspended sediment in larger river basins: combining assessment of spatial provenance and source type.” Geografiska Annaler, 79A, 239–254.10.1111/1468-0459.00020 [Crossref], [Google Scholar]

Cordone, A.J., and Kelly, D.W. (1961). “The influence of inorganic sediment on the aquatic life of stream.” Calif. Fish Game, 47, 189–228. [Google Scholar]

Culp, J.M., Wrona, F.J., and Davies, R.W. (1985). “Response of stream benthos and drift to fine sediment depositionversus transport.” Can. J. Zool., 64, 1345–1351. [Crossref], [Web of Science ®], [Google Scholar]

Davies-Colley, R.J., Hickey, C.W., Quinn, J.M., and Ryan, P.A. (1992). “Effects of clay discharges on streams.” Hydrobiologia, 248, 215–234.10.1007/BF00006149 [Crossref], [Web of Science ®], [Google Scholar]

Dhamotharan, S., Wood, A., Parker, G., and Stefan, H. (1980). Bed load transport in a model gravel stream. Project Report No. 190. St. Anthony Falls Hydraulic Laboratory, University of Minnesota. [Google Scholar]

Diplas, P., and Parker, G. (1985). Pollution of gravel spawning grounds due to fine sediment. Project Report, No. 240. St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN. [Google Scholar]

Doeg, T.J., and Koehn, J.D. (1994). “Effects of draining and desilting a small weir on downstream fish and macroinvertebrates.” Reg. River Res. Manage., 9, 263–277.10.1002/(ISSN)1099-1646 [Crossref], [Web of Science ®], [Google Scholar]

Droppo, I.G., and Ongley, E.D. (1994). “Flocculation of suspended sediment in rivers of southeastern Canada.” Water Res., 28, 1799–1809.10.1016/0043-1354(94)90253-4 [Crossref], [Web of Science ®], [Google Scholar]

Einstein, H.A. (1968). “Deposition of suspended particles in a gravel bed.” J. Hydraul. Eng., 94, 1197–1205. [Google Scholar]

Erman, D.C., and Ligon, F.K. (1988). “Effects of discharge fluctuation and the addition of fine sediment on stream fish and macroinvertebrates below a water-filtration facility.” Environ. Manage., 12, 85–97.10.1007/BF01867380 [Crossref], [Web of Science ®], [Google Scholar]

Farnsworth, K.L., and Milliman, J.D. (2003). “Effects of climatic and anthropogenic change on small mountainous rivers: the Salinas River example.” Global Planet. Change, 39, 53–64.10.1016/S0921-8181(03)00017-1 [Crossref], [Web of Science ®], [Google Scholar]

Foster, I.D.L., and Charlesworth, S.M. (1996). “Heavy metals in the hydrological cycle: trends and explanation.” Hydrol. Process., 10, 227–261.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]

Foy, R.H., and Bailey-Watts, A.E. (1998). “Observations on the spatial and temporal variation in the phosphorus status of lakes in the British Isles.” Soil Use Manage., 14, 131–138.10.1111/sum.1998.14.issue-s4 [Crossref], [Web of Science ®], [Google Scholar]

Frostick, L.E., Lucas, P.M., and Reid, I. (1984). “The infiltration of fine matrices into coarse-grained alluvial sediments and its implications for stratigraphical interpretation.” J. Geol. Soc. London, 141, 955–965.10.1144/gsjgs.141.6.0955 [Crossref], [Web of Science ®], [Google Scholar]

Gagnier, D.L., and Bailey, R.C. (1994). “Balancing loss of information and gains in efficiency in characterizing stream sediment samples.” J. North Am. Benthol. Soc., 13, 170–180.10.2307/1467236 [Crossref], [Web of Science ®], [Google Scholar]

Gammon, J.R. (1970). The effect of inorganic sediment on stream biota. Environmental Protection Agency, Water Pollution Control Research, Series, 18050 DWC 12/70. USGPO, Washington, DC. [Google Scholar]

Graham, A.A. (1990). “Siltation of stone-surface periphyton in rivers by clay-sized particles from low concentrations in suspention.” Hydrobiologia, 199, 107–115.10.1007/BF00005603 [Crossref], [Web of Science ®], [Google Scholar]

Greig, S.M., Sear, D.A., and Carling, P.A. (2005). “The impact of fine sediment accumulation on the survival of incubating salmon progeny: Implications for sediment management.” Sci. Total Environ., 344, 241–258.10.1016/j.scitotenv.2005.02.010 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Harrod, T.R., and Theurer, F.D. (2002). “Sediment.” Agriculture, hydrology and water quality, P.M. Haygarth and S.C. Jarvis, eds., CABI, Wallingford, 502. [Crossref], [Google Scholar]

Horowitz, A.J., Elrick, K.A., Robbins, J.A., and Cook, R.B. (1995). “Effect of mining and related activities on the sediment trace element geochemistry of Lake Coeur D’Alene, Idaho, USA part II: Subsurface sediments.” Hydrol. Process., 9, 35–54.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]

Hynes, H.B.N. (1970). The ecology of running waters, Liverpool University Press, Liverpool. [Google Scholar]

Khullar, N.K. (2002). “Effect of wash load on transport of uniform and nonuniform sediments.” Ph.D. thesis, Indian Institute of Technology Roorkee. [Google Scholar]

Kondolf, G.M. (1995). “Managing bedload sediment in regulated rivers: Examples from California, USA.” Geophys. Monograph, 89, 165–176. [Google Scholar]

Langer, O.E. (1980). “Effects of sedimentation on salmonid stream life.” Report on the Technical Workshop on Suspended Solids and the Aquatic Environment, K. Weagle, ed., Whitehorse. [Google Scholar]

Lemly, A.D. (1982). “Modification of benthic insect communities in polluted streams: combined effects of sedimentation and nutrient enrichment.” Hydrobiologia, 87, 229–245.10.1007/BF00007232 [Crossref], [Web of Science ®], [Google Scholar]

Levasseur, M., Bergeron, N.E., Lapointe, M.F., and Bérubé, F. (2006). “Effects of silt and very fine sand dynamics in Atlantic salmon (Salmo salar) redds on embryo hatching success.” Can. J. Fish. Aquat. Sci., 63, 1450–1459.10.1139/f06-050 [Crossref], [Web of Science ®], [Google Scholar]

Lewis, K. (1973a). “The effect of suspended coal particles on the life forms of the aquatic moss Eurhynchium riparioides (Hedw.).” Fresh Water Biol., 3, 251–257.10.1111/fwb.1973.3.issue-3 [Crossref], [Google Scholar]

Lewis, K. (1973b). “The effect of suspended coal particles on the life forms of the aquatic moss Eurhynchium riparioides (Hedw.).” Fresh Water Biol., 3, 391–395.10.1111/fwb.1973.3.issue-4 [Crossref], [Google Scholar]

Lisle, T. (1980). “Sedimentation of Spawning Areas during Storm Flows, Jacoby Creek, North Coastal California.” Presented at the fall meeting of the American Geophysical Union, San Francisco, CA. [Google Scholar]

Marchant, R. (1989). “Changes in the benthic invertebrate communities of the thomson river, southeastern Australia, after dam construction.” Reg. River Res. Manage., 4, 71–89.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]

McNeil, W.J., and Ahnell, W.H. (1964). Success of pink salmon spawning relative to size of spawning bed material. US Fish and Wildlife Service. Special Scientific Report, Fisheries 469. Washington, DC. [Google Scholar]

Milhous, R.T. (1973). “Sediment transport in a gravel bottomed stream.” Ph.D. thesis, Oregon State University, Corvallis, OR. [Google Scholar]

Milliman, J.D., and Syvitski, J.P.M. (1992). “Geomorphic/tectonic control of sediment discharge to the oceans: the importance of small mountainous rivers.” J. Geol., 100, 525–544.10.1086/jg.1992.100.issue-5 [Crossref], [Web of Science ®], [Google Scholar]

Mohnakrishnan, A. (2001). Reservoir sedimentation, Seminar on Reservoir Sedimentation, Ooty. [Google Scholar]

Mohta, J.A., Wallbrink, P.J., Hairsine, P.B., and Grayson, R.B. (2003). “Determining the sources of suspended sediment in a forested catchment in southeastern Australia.” Water Resour. Res., 39, 1056. [Web of Science ®], [Google Scholar]

Morris, G.L. (1993). “A global perspective of sediment control measures in reservoirs.” Notes on sediment management in reservoirs, S. Fan and G. Morris, eds., Water Resources Publications, Colorado, 13–44. [Google Scholar]

Morris, L.G., and Fan, J. (2010). Reservoir Sedimentation hand book – design and management of dams, reservoirs and watershed for sustainable use. McGraw-Hill, 440 and 499. [Google Scholar]

Newcombe, C.P., and Macdonald, D.D. (1991). “Effects of suspended sediments on aquatic ecosystems.” North Am. J. Fish. Manage., 11, 72–82.10.1577/1548-8675(1991)011<0072:EOSSOA>2.3.CO;2 [Taylor & Francis Online], [Google Scholar]

Nuttal, P.M. (1972). “The effects of sand deposition upon the macroinvertebrate fauna of the River Camel, Cornwall.” Freshwater Biol., 2, 181–186.10.1111/fwb.1972.2.issue-3 [Crossref], [Google Scholar]

Olsson, T.I., and Petersen, B. (1986). “Effects of gravel size and peat material on embryo survival and alevin emergence of brown trout, Salmo trutta L.” Hydrobiologia, 135, 9–14.10.1007/BF00006453 [Crossref], [Web of Science ®], [Google Scholar]

Owens, P.N., Walling, D.E., and Leeks, G.J.L. (2000). “Tracing fluvial suspended sediment sources in the catchment of the River Tweed, Scotland, using composite fingerprints and a numerical mixing model.” Tracers in eomorphology, I.D.L. Foster, ed., Wiley, Chichester, 291–308. [Google Scholar]

Owens, P.N., Walling, D.E., Carton, J., Meharg, A.A., Wright, J., and Leeks, G.J.L. (2001). “Downstream changes in the transport and storage of sediment-associated contaminants (P, Cr and PCBs) in agricultural and industrialized drainage basins.” Sci. Total Environ., 266, 177–186.10.1016/S0048-9697(00)00729-4 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Phillips, J.M., and Walling, D.E. (1995). “An assessment of the effects of sample collection, storage and resuspension on the representativeness of measurements of the effective particle size distribution of fluvial suspended sediment.” Water Res., 29, 2498–2508.10.1016/0043-1354(95)00087-2 [Crossref], [Web of Science ®], [Google Scholar]

Quinn, J.M., Davies-Coley, R.J., Hickey, C.W., Vickers, M.L., and Ryan, P.A. (1992). “Effects of clay discharges on streams.” Hydrobiologia, 248, 235–247.10.1007/BF00006150 [Crossref], [Web of Science ®], [Google Scholar]

Reiser, D.W., and White, R.G. (1990). “Effects of stream flow reduction on Chinook salmon egg incubation and fry quality.” Rivers, 1, 110–118. [Google Scholar]

Richards, C., and Bacon, K.L. (1994). “Influence of fine sediment on macroibvertebrates colonization of surface and hyporheic stream substrate.” Great Basin Nat., 54, 106–113. [Google Scholar]

Richards, C., Host, G.H., and Arthur, J.W. (1993). “Identification of predominant environmental factors structuring stream macroinvertebrate communities within a large agricultural catchment.” Freshwater Biol., 29, 285–294.10.1111/fwb.1993.29.issue-2 [Crossref], [Web of Science ®], [Google Scholar]

Rosenberg, D.M., and Wiens, A.P. (1978). “Effects of sediment addition on macrobenthic invertebrates in a Northern Canadian River.” Water Res., 12, 753–763.10.1016/0043-1354(78)90024-6 [Crossref], [Web of Science ®], [Google Scholar]

Salomons, W., and Förstner, U. (1984). Metals in the hydrocycle, Sringer Verglag, New York, NY.10.1007/978-3-642-69325-0 [Crossref], [Google Scholar]

Schalchli, U. (1992). “The clogging of coarse gravel river beds by fine sediment.” Hydrobiologia, 235–236, 189–197.10.1007/BF00026211 [Crossref], [Web of Science ®], [Google Scholar]

Scrivener, J.C., and Brownlee, M.J. (1989). “Effects of forest harvesting on spawning gravel and incubation survival of chum (Oncorhynchus keta) andcoho salmon (O. kisutch) in Carnation Creek, British Columbia.” Can. J. Fish. Aquat. Sci., 46, 681–696.10.1139/f89-087 [Crossref], [Web of Science ®], [Google Scholar]

Sear, D.A. (1993). “Fine sediment infiltration into gravel spawning beds within a regulated river experiencing floods: Ecological implications for salmonids.” Reg Rivers Res. Manage., 8, 373–390.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]

Soutar, R.G. (1989). “Afforestation and sediment yields in British fresh waters.” Soil Use Manage., 5, 82–86.10.1111/sum.1989.5.issue-2 [Crossref], [Web of Science ®], [Google Scholar]

Stone, M., and Droppo, I.G. (1994). “In-channel surficial fine-grained sediment laminae: Part II: Chemical characteristics and implications for contaminant transport in fluvial systems.” Hydrol. Process., 8, 113–124.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]

Thoms, M.C. (1987). “Channel sedimentation within the urbanized River Tame, UK.” Reg. Rivers Res. Manage., 1, 229–246.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]

Trimble, S.W. (1983). “A sediment budget for Coon Creek, Driftless area, Wisconsin, 1853–1977.” Am. J. Sci., 283, 454–474.10.2475/ajs.283.5.454 [Crossref], [Web of Science ®], [Google Scholar]

U.S. Department of Health, Education and Welfare. (1965). Environmental Health Practices in recreational Areas, Public Health Service, Publication No. 1195. [Google Scholar]

Van Nieuwenhuyse, E.E., and LaPerriere, J.D. (1986). “Effects of placer gold mining on primary production in subarctic streams of Alaska.” J. Am. Water Res. Assoc., 22, 91–99. [Crossref], [Google Scholar]

Vörösmarty, C.J., Meybeck, M., Fekete, B., Sharma, K., Green, P., and Syvitski, J.P.M. (2003). “Anthropogenic sediment retention: major global impact from registered river impoundments.” Global Planet. Change, 39, 169–190.10.1016/S0921-8181(03)00023-7 [Crossref], [Web of Science ®], [Google Scholar]

Walling, D.E. (1995). “Suspended sediment yields in a changing environment.” Changing river channels, A. Gurnell and G. Petts, eds., Wiley, Chichester, 149–176. [Google Scholar]

Walling, D.E., and Moorehead, D.W. (1989). “The particle size characteristics of fluvial suspended sediment: an overview.” Hydrobiologia, 176–177, 125–149.10.1007/BF00026549 [Crossref], [Web of Science ®], [Google Scholar]

Walling, D.E., Owens, P.N., and Leeks, G.J.L. (1999). “Fingerprinting suspended sediment sources in the catchment of the River Ouse, Yorkshire, UK.” Hydrol. Process., 13, 955–975.10.1002/(ISSN)1099-1085 [Crossref], [Web of Science ®], [Google Scholar]

Walling, D.E., Owens, P.N., Waterfall, B.D., Leeks, G.J.L., and Wass, P.D. (2000). “The particle size characteristics of fluvial suspended sediment in the Humber and Tweed catchments, UK.” Sci. Total Environ., 251–252, 205–222.10.1016/S0048-9697(00)00384-3 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Wilbur, C.G. (1983). Turbidity in the aquatic environment: an environmental factor in fresh and oceanic waters, Charles C. Thomas, Springfield, IL, 133. [Google Scholar]

Woo, H.S., Julien, P.Y., and Richardson, E.V. (1986). “Washload and fine sediment load.” J. Hydraul. Eng., 112, 541–545.10.1061/(ASCE)0733-9429(1986)112:6(541) [Crossref], [Google Scholar]

Wood, P.J., and Armitage, P.D. (1997). “Biological effects of fine sediment in the lotic environment.” Environ. Manage., 21, 203–217.10.1007/s002679900019 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]

Wooster, J.K., Dusterhoff, S.R., Cui, Y., Sklar, L.S., Dietrich, W.E., and Malko, M. (2008). “Sediment supply and relative size distribution effects on fine sediment infiltration into immobile gravels.” Water Res. Res., 44, 1–18. [Crossref], [Web of Science ®], [Google Scholar]

Wren, G.Daniel, Bennett, J.Sean, Barkdoll, D.Brian, and Khunle, A.Roger. (2000). Studies in suspended sediment and turbulence in open channel flows, USDA, Agriculture Research Service, Research Report No. 18. [Google Scholar]

Wright, J.F., and Berrie, A.D. (1987). “Ecological effects of groundwater pumping and a natural drought on the upper reaches of a chalk stream.” Reg. River Res. Manage., 1, 145–160.10.1002/(ISSN)1099-1646 [Crossref], [Google Scholar]

Zhang, H., Xia, M., Chen, S.J., Li, Z., and Xia, H.B. (1976). “Regulation of sediments in some medium and small-sized reservoirs on heavily silt-laden streams in China.” 12th International Commission on Large Dams (ICOLD) Congress, Q. 47, R. 32, Mexico City, 1123–1243. [Google Scholar]

Field observations provide valuable data regarding nearshore tsunami impact, yet only in inundation areas where tsunami waves have already flooded. Therefore, tsunami modeling is essential to understand tsunami behavior and prepare for tsunami inundation. It is necessary that all numerical models used in tsunami emergency planning be subject to benchmark tests for validation and verification. This study focuses on two numerical codes, NAMI DANCE and FLOW-3D^{®}, for validation and performance comparison. NAMI DANCE is an in-house tsunami numerical model developed by the Ocean Engineering Research Center of Middle East Technical University, Turkey and Laboratory of Special Research Bureau for Automation of Marine Research, Russia. FLOW-3D^{®} is a general purpose computational fluid dynamics software, which was developed by scientists who pioneered in the design of the Volume-of-Fluid technique. The codes are validated and their performances are compared via analytical, experimental and field benchmark problems, which are documented in the ‘‘Proceedings and Results of the 2011 National Tsunami Hazard Mitigation Program (NTHMP) Model Benchmarking Workshop’’ and the ‘‘Proceedings and Results of the NTHMP 2015 Tsunami Current Modeling Workshop”. The variations between the numerical solutions of these two models are evaluated through statistical error analysis.

현장 관찰은 연안 쓰나미 영향에 관한 귀중한 데이터를 제공하지만 쓰나미 파도가 이미 범람한 침수 지역에서만 가능합니다. 따라서 쓰나미 모델링은 쓰나미 행동을 이해하고 쓰나미 범람에 대비하는 데 필수적입니다.

쓰나미 비상 계획에 사용되는 모든 수치 모델은 검증 및 검증을 위한 벤치마크 테스트를 받아야 합니다. 이 연구는 검증 및 성능 비교를 위해 NAMI DANCE 및 FLOW-3D®의 두 가지 숫자 코드에 중점을 둡니다.

NAMI DANCE는 터키 중동 기술 대학의 해양 공학 연구 센터와 러시아 해양 연구 자동화를 위한 특별 조사국 연구소에서 개발한 사내 쓰나미 수치 모델입니다. FLOW-3D®는 Volume-of-Fluid 기술의 설계를 개척한 과학자들이 개발한 범용 전산 유체 역학 소프트웨어입니다.

코드의 유효성이 검증되고 분석, 실험 및 현장 벤치마크 문제를 통해 코드의 성능이 비교되며, 이는 ‘2011년 NTHMP(National Tsunami Hazard Mitigation Program) 모델 벤치마킹 워크숍의 절차 및 결과’와 ”절차 및 NTHMP 2015 쓰나미 현재 모델링 워크숍 결과”. 이 두 모델의 수치 해 사이의 변동은 통계적 오류 분석을 통해 평가됩니다.

Apotsos, A., Buckley, M., Gelfenbaum, G., Jafe, B., & Vatvani, D. (2011). Nearshore tsunami inundation and sediment transport modeling: towards model validation and application. Pure and Applied Geophysics,168(11), 2097–2119. https://doi.org/10.1007/s00024-011-0291-5.ArticleGoogle Scholar

Barberopoulou, A., Legg, M. R., & Gica, E. (2015). Time evolution of man-made harbor modifications in San Diego: effects on Tsunamis. Journal of Marine Science and Engineering,3, 1382–1403.ArticleGoogle Scholar

Basu, D., Green, S., Das, K., Janetzke, R. and Stamatakos, J. (2009). Numerical Simulation of Surface Waves Generated by a Subaerial Landslide at Lituya Bay, Alaska. Proceedings of 28th International Conference on Ocean, Offshore and Arctic Engineering. Honolulu, Hawaii, USA.

Briggs, M. J., Synolakis, C. E., Harkins, G. S., & Green, D. R. (1995). Laboratory experiments of tsunami run-up on a circular island. Pure and Applied Geophysics,144(3/4), 569–593.ArticleGoogle Scholar

Cheung, K. F., Bai, Y., & Yamazaki, Y. (2013). Surges around the Hawaiian Islands from the 2011 Tohoku Tsunami. Journal of Geophysical Research: Oceans,118, 5703–5719. https://doi.org/10.1002/jgrc.20413.Google Scholar

Choi, B. H., Dong, C. K., Pelinovsky, E., & Woo, S. B. (2007). Three-dimensional Simulation of Tsunami Run-up Around Conical Island. Coastal Engineering,54, 618–629.ArticleGoogle Scholar

Cox, D., T. Tomita, P. Lynett, R.A., Holman. (2008). Tsunami Inundation with Macroroughness in the Constructed Environment. Proceedings of 31st International Conference on Coastal Engineering, ASCE, pp. 1421–1432.

Flow Science. (2002). FLOW-3D User’s Manual.

Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics,39, 201–225.ArticleGoogle Scholar

Horrillo, J., Grilli, S. T., Nicolsky, D., Roeber, V., & Zang, J. (2015). Performance benchmarking Tsunami models for NTHMP’s inundation mapping activities. Pure and Applied Geophysics,172, 869–884.ArticleGoogle Scholar

Kim, K. O., Kim, D. C., Choi, B.-H., Jung, T. K., Yuk, J. H., & Pelinovsky, E. (2015). The role of diffraction effects in extreme run-up inundation at Okushiri Island due to 1993 Tsunami. Natural Hazards and Earth Systems Sciences,15, 747–755.ArticleGoogle Scholar

Liu, P. L.-F. (1994). Model equations for wave propagations from deep to shallow water. (P.-F. Liu, Ed.) Advances in Coastal and Ocean Engineering, 1, 125–158.

Liu, P. L.-F., Yeh, H., & Synolakis, C. E. (2008). Advanced numerical models for simulating Tsunami waves and run-up. Advances in Coastal and Ocean Engineering,10, 344.Google Scholar

Lynett, P. J., Gately, K., Wilson, R., Montoya, L., Arcas, D., Aytore, B., et al. (2017). Inter-model analysis of Tsunami-induced coastal currents. Ocean Modelling,114, 14–32.ArticleGoogle Scholar

Lynett, P. J., Wu, T.-R., & Liu, P. L.-F. (2002). Modeling wave run-up with depth-integrated equations. Coastal Engineering,46(2), 89–107.ArticleGoogle Scholar

Macias, J., Castro, M. J., Ortega, S., Escalante, C., & Gonzalez-Vida, J. M. (2017). Performance benchmarking of Tsunami-HySEA model for nthmp’s inundation mapping activities. Pure and Applied Geophysics,174, 3147–3183.ArticleGoogle Scholar

Matsuyama, M., & Tanaka, H. (2001). An experimental study of the highest run-up height in the 1993 Hokkaidō Nansei-Oki Earthquake Tsunami. Proceedings of ITS,2001, 879–889.Google Scholar

National Tsunami Hazard Mitigation Program. 2012. Proceedings and Results of the 2011 NTHMP Model Benchmarking Workshop. Boulder: U.S. Department of Commerce/NOAA/NTHMP; (NOAA Special Report). p. 436.

National Tsunami Hazard Mitigation Program. (2017). Proceedings and Results of the National Tsunami Hazard Mitigation Program 2015 Tsunami Current Modeling Workshop, February 9-10, 2015, Portland, Oregon: compiled by Patrick Lynett and Rick Wilson, p 194.

Necmioglu, O., & Ozel, N. M. (2014). An earthquake source sensitivity analysis for Tsunami propagation in the Eastern Mediterranean. Oceanography,27(2), 76–85.ArticleGoogle Scholar

Nichols, B.D. and Hirt, C.W. (1975). Methods for Calculating Multi-Dimensional, Transient Free Surface Flows Past Bodies. Proceedings of 1st International Conference Num. Ship Hydrodynamics. Gaithersburg.

Nicolsky, D. J., Suleimani, E. N., & Hansen, R. A. (2011). Validation and verification of a numerical model for Tsunami propagation and run-up. Pure and Applied Geophysics,168(6), 1199–1222.ArticleGoogle Scholar

Park, H., Cox, D. T., Lynett, P. J., Wiebe, D. M., & Shin, S. (2013). Tsunami inundation modeling in constructed environments: a physical and numerical comparison of free-surface elevation, velocity, and momentum flux. Coastal Engineering,79, 9–21.ArticleGoogle Scholar

Patel, V. M., Dholakia, M. B., & Singh, A. P. (2016). Emergency preparedness in the case of Makran Tsunami: a case study on Tsunami risk visualization for the Western Parts of Gujarat, India. Geomatics Natural Hazard and Risk,7(2), 826–842.ArticleGoogle Scholar

Pelinovsky, E., Kim, D.-C., Kim, K.-O., & Choi, B.-H. (2013). Three-dimensional simulation of extreme run-up heights during the 2004 Indonesian and 2011 Japanese Tsunamis. Vienna: EGU General Assembly.Google Scholar

Rueben, M., Holman, R., Cox, D., Shin, S., Killian, J., & Stanley, J. (2011). Optical measurements of Tsunami inundation through an urban waterfront modeled in a large-scale laboratory basin. Coastal Engineering,58, 229–238.ArticleGoogle Scholar

Shuto, N. (1991). Numerical simulation of Tsunamis—its present and near future. Natural Hazards,4, 171–191.ArticleGoogle Scholar

Synolakis, C. E. (1986). The run-up of long waves. Ph.D. Thesis. California Institute of Technology, Pasadena, California.

Synolakis, C. E., Bernard, E. N., Titov, V. V., Kanoglu, U. & Gonzalez, F. (2007). Standards, criteria, and procedures for NOAA evaluation of Tsunami Numerical Models. 55 p. Seattle, Washington: NOAA OAR Special Report, Contribution No 3053, NOAA/OAR/PMEL.

Synolakis, C. E., Bernard, E. N., Titov, V. V., Kanoglu, U., & Gonzalez, F. I. (2008). Validation and verification of Tsunami numerical models. Pure and Applied Geophysics,165, 2197–2228.ArticleGoogle Scholar

Tolkova, E. (2014). Land-water boundary treatment for a tsunami model with dimensional splitting. Pure and Applied Geophysics,171(9), 2289–2314.ArticleGoogle Scholar

Velioglu, D. (2017). Advanced two- and three-dimensional Tsunami models: benchmarking and validation. Ph.D. Thesis. Middle East Technical University, Ankara.

Velioglu, D., Kian, R., Yalciner, A.C. and Zaytsev, A. (2016). Performance assessment of NAMI DANCE in Tsunami evolution and currents using a benchmark problem. (R. Signell, Ed.) J. Mar. Sci. Eng., 4(3), 49.

Wu, T. (2001). A unified theory for modeling water waves. Advances in Applied Mechanics,37, 1–88.ArticleGoogle Scholar

Wu, N.-J., Hsiao, S.-C., Chen, H.-H., & Yang, R.-Y. (2016). The study on solitary waves generated by a piston-type wave maker. Ocean Engineering,117, 114–129.ArticleGoogle Scholar

Yalciner, A. C., Dogan, P. and Sukru. E. (2005). December 26 2004, Indian Ocean Tsunami Field Survey, North of Sumatra Island. UNESCO.

Yalciner, A. C., Gülkan, P., Dilmen, I., Aytore, B., Ayca, A., Insel, I., et al. (2014). Evaluation of Tsunami scenarios For Western Peloponnese, Greece. Bollettino di Geofisica Teorica ed Applicata,55, 485–500.Google Scholar

Yen, B. C. (1991). Hydraulic resistance in open channels. In B. C. Yen (Ed.), Channel flow resistance: centennial of manning’s formula (pp. 1–135). Highlands Ranch: Water Resource Publications.Google Scholar

Zaitsev, A. I., Kovalev, D. P., Kurkin, A. A., Levin, B. V., Pelinovskii, E. N., Chernov, A. G., et al. (2009). The Tsunami on Sakhalin on August 2, 2007: mareograph evidence and numerical simulation. Tikhookeanskaya Geologiya,28, 30–35.Google Scholar

The authors wish to thank Dr. Andrey Zaytsev due to his undeniable contributions to the development of in-house numerical model, NAMI DANCE. The Turkish branch of Flow Science, Inc. is also acknowledged. Finally, the National Tsunami Hazard Mitigation Program (NTHMP), who provided most of the benchmark data, is appreciated. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Author notes

Deniz Velioglu SogutPresent address: 1212 Computer Science, Department of Civil Engineering, Stony Brook University, Stony Brook, NY, 11794, USA

Authors and Affiliations

Middle East Technical University, 06800, Ankara, TurkeyDeniz Velioglu Sogut & Ahmet Cevdet Yalciner

Velioglu Sogut, D., Yalciner, A.C. Performance Comparison of NAMI DANCE and FLOW-3D^{®} Models in Tsunami Propagation, Inundation and Currents using NTHMP Benchmark Problems. Pure Appl. Geophys.176, 3115–3153 (2019). https://doi.org/10.1007/s00024-018-1907-9

Numerical study of the flow at a vertical pile with net-like scour protection matt Minxi Zhanga,b , Hanyan Zhaoc , Dongliang Zhao d, Shaolin Yuee , Huan Zhoue , Xudong Zhaoa , Carlo Gualtierif , Guoliang Yua,b,∗ a SKLOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China b KLMIES, MOE, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China c Guangdong Research Institute of Water Resources and Hydropower, Guangzhou 510610, China d CCCC Second Harbor Engineering Co., Ltd., Wuhan 430040, China e CCCC Road & Bridge Special Engineering Co., Ltd, Wuhan 430071, China f Department of Structures for Engineering and Architecture, University of Naples Federico II, Italy

Abstract

현재 또는 파도 환경에서 말뚝 또는 부두의 국부 세굴은 전 세계적으로 상부 구조물의 안전을 위협합니다. 말뚝이나 부두에서 세굴 방지 덮개로 그물 모양의 매트를 적용하는 것이 제안되었습니다. 매트는 국부 세굴 구덩이의 흐름을 약화 및 확산시켜 국부 세굴을 줄이고 퇴적물 퇴적을 강화합니다. 매트로 덮힌 말뚝의 흐름을 조사하기 위해 수치 시뮬레이션을 수행했습니다. 시뮬레이션 결과는 매트의 두께 dt(2.6d95 ~ 17.9d95)와 개구부 크기 dn(7.7d95 ~ 28.2d95)을 최적화하는 데 사용되었습니다. 매트가 국부 속도를 상당히 감소시키고 말뚝에서 와류를 소멸시켜 국부 세굴 범위를 실질적으로 감소시키는 것으로 밝혀졌습니다. 매트의 개구부 크기가 작을수록 베드에서의 유동확산이 더 효과적이었으며 말뚝에서 더 작은 베드전단응력이 관찰되었다. 본 연구에서 고려한 유동 조건의 경우 상대 두께 T = 7.7 및 상대 개구 크기 S = 7.7인 매트가 세굴 방지에 효과적일 수 있습니다.

Fig. 26. Distribution of the turbulent kinetic energy on the y-z plane (X = 0.5) for various S

References

[1] C. He, Mod. Transp. Technol. 17 (3) (2020) 46–59 in Chinese. [2] X. Wen, D. Zhang, J. Tianjin Univ. 54 (10) (2021) 998–1007 (Science and Technology)in Chinese. [3] M. Zhang, H. Sun, W. Yao, G. Yu, Ocean Eng. 265 (2020) 112652, doi:10.1016/j. oceaneng.2022.112652. [4] K. Wardhana, F.C. Hadipriono, J. Perform. Constr. Fac. 17 (3) (2003) 144–150, doi:10.1061/(ASCE)0887-3828(2003)17:3(144). [5] R. Ettema, G. Constantinescu, B.W. Melville, J. Hydraul. Eng. 143 (9) (2017) 03117006, doi:10.1061/(ASCE)HY.1943-7900.0001330. [6] C. Valela, C.D. Rennie, I. Nistor, Int. J. Sediment Res. 37 (1) (2021) 37–46, doi:10.1016/j.ijsrc.2021.04.004. [7] B.W. Melville, A.J. Sutherland, J. Hydraul. Eng. 114 (10) (1988) 1210–1226, doi:10.1061/(ASCE)0733-9429(1988)114:10(1210). [8] E.V. Richardson, S.R. Davis, Evaluating Scour At Bridges, 4th ed., United States Department of Transportation, Federal Highway Administration, Washington, DC., 2001. [9] D.M. Sheppard, B. Melville, H. Demir, J. Hydraul. Eng. 140 (1) (2014) 14–23, doi:10.1061/(ASCE)HY.1943-7900.0000800. [10] A.O. Aksoy, G. Bombar, T. Arkis, M.S. Guney, J. Hydrol. Hydromech. 65 (1) (2017) 26–34. [11] D.T. Bui, A. Shirzadi, A. Amini, et al., Sustainability 12 (3) (2020) 1063, doi:10. 3390/su12031063. [12] B.M. Sumer, J. Fredsoe, The Mechanics of Scour in Marine Environments. World Advanced Series on Ocean Engineering, 17, World Scientific, Singapore, 2002. [13] J. Unger, W.H. Hager, Exp. Fluids 42 (1) (2007) 1–19. [14] G. Kirkil, S.G. Constantinescu, R. Ettema, J. Hydraul. Eng. 134 (5) (2008) 82–84, doi:10.1061/(ASCE)0733-9429(2008)134:5(572). [15] B. Dargahi, J. Hydraul. Eng. 116 (10) (1990) 1197–1214. [16] A. Bestawy, T. Eltahawy, A. Alsaluli, M. Alqurashi, Water Supply 20 (3) (2020) 1006–1015, doi:10.2166/ws.2020.022. [17] Y.M. Chiew, J. Hydraul. Eng. 118 (9) (1992) 1260–1269. [18] D. Bertoldi, R. Kilgore, in: Hydraulic Engineering ’93, ASCE, San Francisco, California, United States, 1993, pp. 1385–1390. [19] Y.M. Chiew, J. Hydraul. Eng. 121 (9) (1997) 635–642. [20] C.S. Lauchlan, B.W. Melville, J. Hydraul. Eng. 127 (5) (2001) 412–418, doi:10. 1061/(ASCE)0733-9429(2001)127:5(412). [21] P.F. Lagasse, P.E. Clopper, L.W. Zevenbergen, L.G. Girard, National Cooperative Highway Research Program (NCHRPReport 593), Countermeasures to protect bridge piers from scour, Washington, DC, NCHRP, 2007. [22] S. Jiang, Z. Zhou, J. Ou, J. Sediment Res. (4) (2013) 63–67 in Chinese. [23] A. Galan, G. Simarro, G. Sanchez-Serrano, J. Hydraul. Eng. 141 (6) (2015) 06015004, doi:10.1061/(ASCE)HY.1943-7900.0001003. [24] Z. Zhang, H. Ding, J. Liu, Ocean Eng. 33 (2) (2015) 77–83 in Chinese. [25] C. Valela, C.N. Whittaker, C.D. Rennie, I. Nistor, B.W. Melville, J. Hydraul. Eng. 148 (3) (2022) 04022002 10.1061/%28ASCE%29HY.1943-7900.0001967. [26] B.W. Melville, A.C. Hadfield, J. Hydraul. Eng. 6 (2) (1999) 1221–1224, doi:10. 1061/(ASCE)0733-9429(1999)125:11(1221). [27] V. Kumar, K.G. Rangaraju, N. Vittal, J. Hydraul. Eng. 125 (12) (1999) 1302–1305. [28] A.M. Yasser, K.S. Yasser, M.A. Abdel-Azim, Alex. Eng. J. 54 (2) (2015) 197–203, doi:10.1016/j.aej.2015.03.004. [29] S. Khaple, P.R. Hanmaiahgari, R. Gaudio, S. Dey, Acta Geophys. 65 (2017) 957– 975, doi:10.1007/s11600-017-0084-z. [30] C. Valela, I. Nistor, C.D. Rennie, in: Proceedings of the 6th International Disaster Mitigation Specialty Conference, Fredericton, Canada, Canadian Society for Civil Engineering, 2018, pp. 235–244. [31] A. Tafarojnoruz, R. Gaudio, F. Calomino, J. Hydraul. Eng. 138 (3) (2012) 297– 305, doi:10.1061/(ASCE)HY.1943-7900.0000512. [32] H. Tang, S. Fang, Y. Zhou, K. Cai, Y.M. Chiew, S.Y. Lim, N.S. Cheng, in: Proceedings of the 2nd International Conference Scour and Erosion (ICSE-2), Singapore. Singapore, Nanyang Technological University, 2004. [33] W. Zhang, Y. Li, X. Wang, Z. Sun, J. Sichuan Univ. 06 (2005) 34–40 (Engineering Science Edition)in Chinese. [34] S. Yang, B. Shi, Trans. Oceanol. Limnol. 5 (2017) 43–47 in Chinese. [35] H. Wang, F. Si, G. Lou, W. Yang, G. Yu, J. Waterw. Port Coast. Ocean Eng. 141 (1) (2015) 04014030, doi:10.1061/(ASCE)WW.1943-5460.0000270. [36] L.D. Meyer, S.M. Dabney, W.C. Harmon, Trans. ASAE 38 (3) (1995) 809–815. [37] G. Spyreas, B.W. Wilm, A.E. Plocher, D.M. Ketzner, J.W. Matthews, J.L. Ellis, E.J. Heske, Biol. Invasions 12 (5) (2010) 1253–1267, doi:10.1007/ s10530-009-9544-y. [38] T. Lambrechts, S. François, S. Lutts, R. Muñoz-Carpena, C.L. Bielders, J. Hydrol. 511 (2014) 800–810, doi:10.1016/j.jhydrol.2014.02.030. [39] G. Yu, Dynamic Embedded Anchor with High Frequency Micro Amplitude Vibrations. CN patent No: ZL200810038546.0, 2008. [40] X. Chen, M. Zhang, G. Yu, Ocean Eng. 236 (2021) 109315, doi:10.1016/j. oceaneng.2021.109315. [41] F. Gumgum, M.S. Guney, in: Proceedings of the 6th International Conference Engineering and Natural Sciences (ICENS), Serbia, Belgrade, 2020. [42] H. Zhao, S. Yue, H. Zhou, M. Zhang, G. Yu, Ocean Eng. 40 (5) (2022) 111–120 in Chinese. [43] B. Blocken, C. Gualtieri, Environ. Modell. Softw. 33 (2012) 1–22, doi:10.1016/j. envsoft.2012.02.001. [44] N.D. Bennett, B.F. Croke, G. Guariso, et al., Modell. Softw. 40 (2013) 1–20, doi:10.1016/j.envsoft.2012.09.011. [45] X. Zhao, Effectiveness and Mechanism of Lattice On Sedimentation and Anti-Erosion of Local Scour Hole At Piers, Shanghai Jiao Tong University, Shanghai, China, 2023. [46] M. Zhang, G. Yu, Water Resour. Res. 53 (9) (2017) 7798–7815, doi:10.1002/ 2017WR021066.

이 연구에서는 세 가지 다른 말뚝 뚜껑 높이에서 직사각형 말뚝 캡이 있는 복잡한 부두 주변의 지역 세굴 및 관련 흐름 유체 역학을 조사합니다. 말뚝 캡 높이가 초기 모래층에 대해 선택되었으며, 말뚝 캡이 흐름에 노출되지 않고(사례 I), 부분적으로 노출되고(사례 II) 완전히 노출(사례 III)되도록 했습니다. 실험은 맑은 물 세굴 조건 하에서 재순환 수로에서 수행되었으며, 입자 이미지 유속계 (PIV) 기술을 사용하여 다른 수직면에서 순간 유속을 얻었습니다. 부분적으로 노출된 파일 캡 케이스는 최대 수세미 깊이(MSD)를 보여주었습니다. 사례 II에서 MSD가 발생한 이유는 난류 유동장 분석을 통해 밝혀졌는데, 이는 말뚝 캡이 흐름에 노출됨에 따라 더 높은 세굴 깊이를 담당하는 말뚝 가장자리에서 와류 생성에 지배적으로 영향을 미친다는 것을 보여주었습니다. 유동장에 대한 파일 캡의 영향은 평균 속도, 소용돌이, 레이놀즈 전단 응력 및 난류 운동 에너지 윤곽을 통해 사례 III에서 두드러지게 나타났지만 파일 캡이 베드에서 떨어져 있었기 때문에 파일 캡 모서리는 수세미에 직접적인 영향을 미치지 않았습니다.

In this study, the local scour and the associated flow hydrodynamics around a complex pier with rectangular pile-cap at three different pile-cap elevations are investigated. The pile-cap elevations were selected with respect to the initial sand bed, such that the pile-cap was unexposed (case I), partially exposed (case II), and fully exposed (case III) to the flow. The experiments were performed in a recirculating flume under clear-water scour conditions, and the instantaneous flow velocity was obtained at different vertical planes using the particle image velocimetry (PIV) technique. The partially exposed pile-cap case showed the maximum obtained scour-depth (MSD). The reason behind the MSD occurrence in case II was enunciated through the analysis of turbulent flow field which showed that as the pile-cap got exposed to the flow, it dominantly affected the generation of vortices from the pile-cap corners responsible for the higher scour depth. The effect of the pile-cap on the flow field was prominently seen in case III through the mean velocities, vorticity, Reynolds shear stresses and turbulent kinetic energy contours, but since the pile-cap was away from the bed, the pile-cap corners did not show any direct effect on the scour.

Adrian, R. J. (2013). Structure of turbulent boundary layers. In Jeremy G. Venditti, James L. Best, Michael Church, & Richard J. Hardy (Eds.), Coherent flow structures at earth’s surface (pp. 17–24). John Wiley and Sons. [Crossref], [Google Scholar]

Adrian, R. J., & Westerweel, J. (2011). Particle image velocimetry, No. 30. Cambridge University Press. [Google Scholar]

Alemi, M., & Maia, R. (2018). Numerical simulation of the flow and local scour process around single and complex bridge piers. International Journal of Civil Engineering, 16(5), 475–487. https://doi.org/10.1007/s40999-016-0137-8 [Crossref], [Google Scholar]

Alemi, M., Pêgo, J. P., & Maia, R. (2019). Numerical simulation of the turbulent flow around a complex bridge pier on the scoured bed. European Journal of Mechanics – B/Fluids, 76, 316–331. https://doi.org/10.1016/j.euromechflu.2019.03.011 [Crossref], [Web of Science ®], [Google Scholar]

Amini, A., Hamidi, S., Shirzadi, A., Behmanesh, J., & Akib, S. (2021). Efficiency of artificial neural networks in determining scour depth at composite bridge piers. International Journal of River Basin Management, 19(3), 327–333. https://doi.org/10.1080/15715124.2020.1742138 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Arneson, L. A., Zevenbergen, L. W., Lagasse, P. F., & Clopper, P. E. (2015). Evaluating scour at bridges, 5th ed. hydraulic engineering circular No. 18 (HEC-18). Federal Highway Administration. [Google Scholar]

Ataie-Ashtiani, B., & Aslani-Kordkandi, A. (2012). Flow field around side-by-side piers with and without a scour hole. European Journal of Mechanics – B/Fluids, 36, 152–166. https://doi.org/10.1016/j.euromechflu.2012.03.007 [Crossref], [Web of Science ®], [Google Scholar]

Ataie-Ashtiani, B., Baratian-Ghorghi, Z., & Beheshti, A. A. (2010). Experimental investigation of clear-water local scour of compound piers. Journal of Hydraulic Engineering, 136(6), 343–351. https://doi.org/10.1061/(ASCE)0733-9429(2010)136:6(343) [Crossref], [Web of Science ®], [Google Scholar]

Avallone, F., Discetti, S., Astarita, T., & Cardone, G. (2015). Convergence enhancement of single-pixel PIV with symmetric double correlation. Experiments in Fluids, 56(4), 71. https://doi.org/10.1007/s00348-015-1938-2 [Crossref], [Web of Science ®], [Google Scholar]

Beheshti, A. A., & Ataie-Ashtiani, B. (2010). Experimental study of three-dimensional flow field around a complex bridge pier. Journal of Engineering Mechanics, 136(2), 143–154. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000073 [Crossref], [Web of Science ®], [Google Scholar]

Beheshti, A. A., & Ataie-Ashtiani, B. (2016). Scour hole influence on turbulent flow field around complex bridge piers. Flow, Turbulence and Combustion, 97(2), 451–474. https://doi.org/10.1007/s10494-016-9707-8 [Crossref], [Web of Science ®], [Google Scholar]

Cameron, S. M., Nikora, V. I., & Marusic, I. (2019). Drag forces on a bed particle in open-channel flow: Effects of pressure spatial fluctuations and very-large-scale motions. Journal of Fluid Mechanics, 863, 494–512. https://doi.org/10.1017/jfm.2018.1003 [Crossref], [Web of Science ®], [Google Scholar]

Cheng, N., & Emadzadeh, A. (2017). Laboratory measurements of vortex-induced sediment pickup rates. International Journal of Sediment Research, 32(1), 98–104. https://doi.org/10.1016/j.ijsrc.2016.04.005 [Crossref], [Web of Science ®], [Google Scholar]

Coleman, S. E. (2005). Clearwater local scour at complex piers. Journal of Hydraulic Engineering, 131(4), 330–334. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(330) [Crossref], [Web of Science ®], [Google Scholar]

Das, S., & Mazumdar, A. (2015). Turbulence flow field around two eccentric circular piers in scour hole. International Journal of River Basin Management, 13(3), 343–361. https://doi.org/10.1080/15715124.2015.1012515 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Esmaeili Varaki, M., Radice, A., Samira Hossini, S., & Fazl Ola, R. (2019). Local scour at a complex pier with inclined columns footed on capped piles: Effect of the pile arrangement and of the cap thickness and elevation. ISH Journal of Hydraulic Engineering, 1–10. https://doi.org/10.1080/09715010.2019.1702109 [Taylor & Francis Online], [Google Scholar]

Ferraro, D., Tafarojnoruz, A., Gaudio, R., & Cardoso, A. H. (2013). Effects of pile cap thickness on the maximum scour depth at a complex pier. Journal of Hydraulic Engineering, 139(5), 482–491. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000704 [Crossref], [Web of Science ®], [Google Scholar]

Gaudio, R., Tafarojnoruz, A., & Calomino, F. (2012). Combined flow-altering countermeasures against bridge pier scour. Journal of Hydraulic Research, 50(1), 35–43. https://doi.org/10.1080/00221686.2011.649548 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Gautam, P., Eldho, T., & Behera, M. (2016). Experimental study of scour around a complex pier with elliptical pile-cap. In J. Harris, R. Whitehouse, & S. Moxon (Eds.), Scour and Erosion: Proceedings of the 8th International Conference on Scour and Erosion (Oxford, UK, 12-15 September 2016) (pp. 759–765). CRC Press. [Crossref], [Google Scholar]

Gautam, P., Eldho, T. I., Mazumder, B. S., & Behera, M. R. (2019). Experimental study of flow and turbulence characteristics around simple and complex piers using PIV. Experimental Thermal and Fluid Science, 100, 193–206. https://doi.org/10.1016/j.expthermflusci.2018.09.010 [Crossref], [Web of Science ®], [Google Scholar]

Graf, W. H., & Istiarto, I. (2002). Flow pattern in the scour hole around a cylinder. Journal of Hydraulic Research, 40(1), 13–20. https://doi.org/10.1080/00221680209499869 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Hjulstrom, F. (1935). Study of the morphological activity of Rivers as illustrated by the River fyris bulletin, vol. 25. Geological Institute of Upsala. [Google Scholar]

Kumar, A., & Kothyari, U. C. (2012). Three-dimensional flow characteristics within the scour hole around circular uniform and compound piers. Journal of Hydraulic Engineering, 138(5), 420–429. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000527 [Crossref], [Web of Science ®], [Google Scholar]

Mashahir, M. B., Zarrati, A. R., & Rezayi, M. J. (2004). Time development of scouring around a bridge pier protected by collar. In Proceedings 2nd International Conference on Scour and Erosion (ICSE-2). November 14–17, 2004, Singapore. [Google Scholar]

Melville, B. W. (2008). The physics of local scour at bridge piers. In Proceedings of the 4th International Conference on Scour and Erosion (ICSE-4). November 5-7, 2008, Tokyo, Japan (pp. 28–40). [Google Scholar]

Melville, B. W., & Chiew, Y. M. (1999). Time scale for local scour at bridge piers. Journal of Hydraulic Engineering, 125(1), 59–65. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:1(59) [Crossref], [Web of Science ®], [Google Scholar]

Melville, B. W., & Raudkivi, A. J. (1977). Flow characteristics in local scour at bridge piers. Journal of Hydraulic Research, 15(4), 373–380. https://doi.org/10.1080/00221687709499641 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Moreno, M., Maia, R., & Couto, L. (2016a). Effects of relative column width and pile-cap elevation on local scour depth around complex piers. Journal of Hydraulic Engineering, 142(2), 04015051. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001080 [Crossref], [Web of Science ®], [Google Scholar]

Moreno, M., Maia, R., & Couto, L. (2016b). Prediction of equilibrium local scour depth at complex bridge piers. Journal of Hydraulic Engineering, 142(11), 04016045. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001153 [Crossref], [Web of Science ®], [Google Scholar]

Nezu, I., & Rodi, W. (1986). Open-channel flow measurements with a laser Doppler anemometer. Journal of Hydraulic Engineering, 112(5), 335–355. https://doi.org/10.1061/(ASCE)0733-9429(1986)112:5(335) [Crossref], [Web of Science ®], [Google Scholar]

Radice, A., & Tran, C. K. (2012). Study of sediment motion in scour hole of a circular pier. Journal of Hydraulic Research, 50(1), 44–51. https://doi.org/10.1080/00221686.2011.641764 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Richardson, J. R., & York, K. (1999). Hydrodynamic countermeasures for local pier scour. Transportation Research Record: Journal of the Transportation Research Board, 1690(1), 186–192. https://doi.org/10.3141/1690-21 [Crossref], [Google Scholar]

Saw, E., Debue, P., Kuzzay, D., Daviaud, F., & Dubrulle, B. (2018). On the universality of anomalous scaling exponents of structure functions in turbulent flows. Journal of Fluid Mechanics, 837, 657–669. https://doi.org/10.1017/jfm.2017.848 [Crossref], [Web of Science ®], [Google Scholar]

Schlichting, H. (1968). Boundary layer theory (Vol. 960). McGraw-Hill. [Google Scholar]

Sheppard, D. M., Demir, H., & Melville, B. W. (2011). Scour at wide piers and long skewed piers (Vol. 682). Transportation Research Board. [Google Scholar]

Tafarojnoruz, A., Gaudio, R., & Calomino, F. (2012). Bridge pier scour mitigation under steady and unsteady flow conditions. Acta Geophysica, 60(4), 1076–1097. https://doi.org/10.2478/s11600-012-0040-x [Crossref], [Web of Science ®], [Google Scholar]

Tafarojnoruz, A., Gaudio, R., & Dey, S. (2010). Flow-altering countermeasures against scour at bridge piers: A review. Journal of Hydraulic Research, 48(4), 441–452. https://doi.org/10.1080/00221686.2010.491645 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Tennekes, H., & Lumley, J. L. (1972). A first course in turbulence. MIT press. [Crossref], [Google Scholar]

Veerappadevaru, G., Gangadharaiah, T., & Jagadeesh, T. R. (2011). Vortex scouring process around bridge pier with a caisson. Journal of Hydraulic Research, 49(3), 378–383. https://doi.org/10.1080/00221686.2011.568195 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Veerappadevaru, G., Gangadharaiah, T., & Jagadeesh, T. R. (2012). Temporal variation of vortex scour process around caisson piers. Journal of Hydraulic Research, 50(2), 200–207. https://doi.org/10.1080/00221686.2012.666832 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Vijayasree, B. A., Eldho, T. I., Mazumder, B. S., & Ahmad, N. (2019). Influence of bridge pier shape on flow field and scour geometry. International Journal of River Basin Management, 17(1), 109–129. https://doi.org/10.1080/15715124.2017.1394315 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]

Yang, Y., Melville, B. W., Sheppard, D. M., & Shamseldin, A. Y. (2018). Clear-water local scour at skewed complex bridge piers. Journal of Hydraulic Engineering, 144(6), 04018019. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001458 [Crossref], [Web of Science ®], [Google Scholar]

Yang, Y., Melville, B. W., Macky, G. H., & Shamseldin, A. Y. (2020). Temporal evolution of clear-water local scour at aligned and skewed complex bridge piers. Journal of Hydraulic Engineering, 146(4), 04020026. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001732 [Crossref], [Web of Science ®], [Google Scholar]

A numerical study was performed on the embankment weir overflows with various surface roughness and tailwater submergence, to better understand the effects of weir roughness on discharge performances under the free and submerged conditions. The variation of flow regime is captured, from the free overflow, submerged hydraulic jump, to surface flow with increasing tailwater depth. A roughness factor is introduced to reflect the reduction in discharge caused by weir roughness. The roughness factor decreases with the roughness height, and it also depends on the tailwater depth, highlighting various relations of the roughness factor with the roughness height between different flow regimes, which is linear for the free overflow and submerged hydraulic jump while exponential for the surface flow. Accordingly, the effects of weir roughness on overflow discharge appear nonnegligible for the significant roughness height and the surface flow regime occurring under considerable tailwater submergence. The established empirical expressions of discharge coefficient and submergence and roughness factors make it possible to predict the discharge over embankment weirs considering both tailwater submergence and surface roughness.

자유 및 침수 조건에서 방류 성능에 대한 둑 거칠기의 영향을 더 잘 이해하기 위해 다양한 표면 거칠기와 테일워터 침수를 갖는 제방 둑 범람에 대한 수치 연구가 수행되었습니다.

자유 범람, 수중 수압 점프, 테일워터 깊이가 증가하는 표면 유동에 이르기까지 유동 체제의 변화가 캡처됩니다. 위어 거칠기로 인한 배출 감소를 반영하기 위해 거칠기 계수가 도입되었습니다.

조도 계수는 조도 높이와 함께 감소하고, 또한 테일워터 깊이에 따라 달라지며, 서로 다른 흐름 영역 사이의 조도 높이와 조도 계수의 다양한 관계를 강조합니다.

이는 자유 범람 및 수중 수압 점프에 대해 선형인 반면 표면에 대해 지수적입니다. 흐름. 따라서 월류 방류에 대한 웨어 조도의 영향은 상당한 조도 높이와 상당한 방수 침수 하에서 발생하는 표면 흐름 체제에 대해 무시할 수 없는 것으로 보입니다.

방류계수와 침수 및 조도계수의 확립된 실증식은 방류수 침수와 지표조도를 모두 고려한 제방보 위의 방류량을 예측할 수 있게 합니다.

References

Kindsvater C. E. Discharge characteristics of embankment -shaped weirs (No. 1617) [R]. Washington DC, USA: US Government Printing Office, 1964.Google Scholar

Fritz H. M., Hager W. H. Hydraulics of embankment weirs [J]. Journal of Hydraulic Engineering, ASCE, 1998, 124(9): 963–971.ArticleGoogle Scholar

Azimi A. H., Rajaratnam N., Zhu D. Z. Water surface characteristics of submerged rectangular sharp-crested weirs [J]. Journal of Hydraulic Engineering, ASCE, 2016, 142(5): 06016001.ArticleGoogle Scholar

Felder S., Islam N. Hydraulic performance of an embankment weir with rough crest [J]. Journal of Hydraulic Engineering, ASCE, 2017, 143(3): 04016086.ArticleGoogle Scholar

Hakim S. S., Azimi A. H. Hydraulics of submerged traingular weirs and weirs of finite-crest length with upstream and downstream ramps [J]. Journal of Irrigation and Drainage Engineering, 2017, 143(8): 06017008.ArticleGoogle Scholar

Safarzadeh A., Mohajeri S. H. Hydrodynamics of rectangular broad-crested porous weirs [J]. Journal of Hydraulic Engineering, ASCE, 2018, 144(10): 04018028.Google Scholar

Sargison J. E., Percy A. Hydraulics of broad-crested weirs with varying side slopes [J]. Journal of Irrigation and Drainage Engineering, 2009, 35(1): 115–118.ArticleGoogle Scholar

Yang Z., Bai F., Huai W. et al. Lattice Boltzmann method for simulating flows in the open-channel with partial emergent rigid vegetation cover [J]. Journal of Hydrodynamics, 2019, 31(4): 717–724.ArticleGoogle Scholar

Fathi-moghaddam M., Sadrabadi M. T., Rahmanshahi M. Numerical simulation of the hydraulic performance of triangular and trapezoidal gabion weirs in free flow condtion [J]. Flow Measurement on Instrumentation, 2018, 62: 93–104.ArticleGoogle Scholar

Zerihun Y. T. A one-dimensional Boussinesq-type momentum model for steady rapidly varied open channel flows [D]. Doctoral Thesis, Melbourne, Australia: The University of Melbourne, 2004.Google Scholar

Pařílková J., Říha J., Zachoval Z. The influence of roughness on the discharge coefficient of a broad-crested weir [J]. Journal of Hydrology and Hydromechanics, 2012, 60(2): 101–114.ArticleGoogle Scholar

Říha J., Duchan D., Zachoval Z. et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs [J]. Journal of Hydrology and Hydromechanics, 2019, 67(4): 322–328.ArticleGoogle Scholar

Yan X., Ghodoosipour B., Mohammadian A. Three-dimensional numerical study of multiple vertical buoyant jets in stationary ambient water [J]. Journal of Hydraulic Engineering, ASCE, 2020, 146(7): 04020049.ArticleGoogle Scholar

Qian S., Xu H., Feng J. Flume experiments on baffle-posts for retarding open channel flow: By C. UBING, R. ETTEMA and CI THORNTON, J. Hydraulic Res. 55 (3), 2017, 430–437 [J]. Journal of Hydraulic Research, 2019, 57(2): 280–282.ArticleGoogle Scholar

Sun J., Qian S., Xu H. et al. Three-dimensional numerical simulation of stepped dropshaft with different step shape [J]. Water Science and Technology Water Supply, 2020, 21(1): 581–592.Google Scholar

Qian S., Wu J., Zhou Y. et al. Discussion of “Hydraulic performance of an embankment weir with rough crest” by Stefan Felder and Nushan Islam [J]. Journal of Hydraulic Engineering, ASCE, 2018, 144(4): 07018003.ArticleGoogle Scholar

Mohammadpour R., Ghani A. A., Azamathulla H. M. Numerical modeling of 3-D flow on porous broad crested weirs [J]. Applied Mathematical Modelling, 2013, 37(22): 9324–9337.ArticleGoogle Scholar

Savage B. M., Brian M. C., Greg S. P. Physical and numerical modeling of large headwater ratios for a 15° labyrinth spillway [J]. Journal of Hydraulic Engineering, ASCE, 2016, 142(11): 04016046.ArticleGoogle Scholar

Al-Husseini T. R., Al-Madhhachi A. S. T., Naser Z. A. Laboratory experiments and numerical model of local scour around submerged sharp crested weirs [J]. Journal of King Saud University Science, 2020, 32(3): 167–176.ArticleGoogle Scholar

Zerihun Y. T., Fenton J. D. A Boussinesq-type model for flow over trapezoidal profile weirs [J]. Journal of Hydraulic Research, 2007, 45(4): 519–528.ArticleGoogle Scholar

Flow Science, Inc. FLOW-3D ® Version 12.0 Users Manual (2018) [EB/OL]. Santa Fe, NM, USA: Flow Science, Inc., 2019.Google Scholar

Bazin H. Expériences nouvelles sur l’ecoulement par déversoir [R]. Paris, France: Annales des Ponts et Chaussées, 1898.MATHGoogle Scholar

Hager W. H., Schwalt M. Broad-crested weir [J]. Journal of Irrigation and Drainage Engineering, 1994, 120(1): 13–26.ArticleGoogle Scholar

Citizens’ daily needs such as; transportation, communication, clean water and sewage are supplied with infrastructure systems. Horizontal and vertical expansion in the cities due to the increase in population leads to serious demand for infrastructural improvements. The infrastructure systems in developing cities are required to be designed in a satisfactory capacity to supply the increasing demand for residential and industrial constructions. The districts having insufficient infrastructure systems inevitably confront heavy traffic, flood, air pollution problems, and also having difficulties with the inadequacy of parking area, clear and potable water, communication. The problems may cause social and health problems over time. At this point, it is wished to emphasize that the primary factor of citycivilization development depends on infrastructural systems and it is meaningful to name the engineering field like civil engineering, literally leads civilization. Dropshafts, commonly used in the urban storm and sewage water systems produced generally circular are used for energy dissipation and flow direction control. Aeration is significant for the working principle of the flow in dropshaft and this study is made mainly for this two-phase (air-water) physics of dropshafts. Chanson showed that aeration and energy dissipation is directly linked to each other (2002), but the influencing factors and the action mechanisms of the factors on the phenomena are not discovered entirely. By the comprehension of the factors, more effective dropshafts will be able to design. This study aims to guide the more comprehensive investigation of design factors using Computational Fluid Dynamics-CFD programs. The reasons for the preference of the programs are the cost-effectiveness of material, workmanship and duration relative to hydraulic modelling. The competence of the inputs, outputs and solution system of the CFD code is validated by the comparison of previous hydraulic modelling results.

Keywords

CFD, Dropshaft, Sewer system, Storm Water System, Two-Phase Flow

A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves. In this study, the validation was carried out firstly to verify the accuracy of the present model. Furthermore, the scour evolution and scour mechanism were analyzed respectively. In addition, two revised models were proposed to predict the equilibrium scour depth S_{eq} around USAF. At last, a parametric study was carried out to study the effects of the Froude number F_{r} and Euler number E_{u} for the S_{eq.} The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KC_{s,p} < 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KC_{rms,a} < 4. The higher F_{r} and E_{u} both lead to the more intensive horseshoe vortex and larger S_{eq}.

The rapid expansion of cities tends to cause social and economic problems, such as environmental pollution and traffic jam. As a kind of clean energy, offshore wind power has developed rapidly in recent years. The foundation of offshore wind turbine (OWT) supports the upper tower, and suffers the cyclic loading induced by waves, tides and winds, which exerts a vital influence on the OWT system. The types of OWT foundation include the fixed and floating foundation, and the fixed foundation was used usually for nearshore wind turbine. After the construction of fixed foundation, the hydrodynamic field changes in the vicinity of the foundation, leading to the horseshoe vortex formation and streamline compression at the upside and sides of foundation respectively [1,2,3,4]. As a result, the neighboring soil would be carried away by the shear stress induced by vortex, and the scour hole would emerge in the vicinity of foundation. The scour holes increase the cantilever length, and weaken the lateral bearing capacity of foundation [5,6,7,8,9]. Moreover, the natural frequency of OWT system increases with the increase of cantilever length, causing the resonance occurs when the system natural frequency equals the wave or wind frequency [10,11,12]. Given that, an innovative foundation called umbrella suction anchor foundation (USAF) has been designed for nearshore wind power. The previous studies indicated the USAF was characterized by the favorable lateral bearing capacity with the low cost [6,13,14]. The close-up of USAF is shown in Figure 1, and it includes six parts: 1-interal buckets, 2-external skirt, 3-anchor ring, 4-anchor branch, 5-supporting rod, 6-telescopic hook. The detailed description and application method of USAF can be found in reference [13].

Figure 1. The close-up of umbrella suction anchor foundation (USAF).

Numerical and experimental investigations of scour around OWT foundation under steady currents and waves have been extensively studied by many researchers [1,2,15,16,17,18,19,20,21,22,23,24]. The seabed scour can be classified as two types according to Shields parameter θ, i.e., clear bed scour (θ < θ_{cr}) or live bed scour (θ > θ_{cr}). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(R_{d}) (R_{d} is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with R_{d} increases, but the effects of R_{d} can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θ, KC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.

KC=UwmTD��=�wm��(1)

where, U_{wm} is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.

There are two prerequisites to satisfy the formation of horseshoe vortex at upstream pile edges: (1) the incoming flow boundary layer with sufficient thickness and (2) the magnitude of upstream adverse pressure gradient making the boundary layer separating [1,15,16,18,20]. The smaller KC results the lower adverse pressure gradient, and the boundary layer cannot separate, herein, there is almost no horseshoe vortex emerging at upside of pile. Sumer et al. [1,15] carried out several sets of wave flume experiments under regular and irregular waves respectively, and the experiment results show that there is no horseshoe vortex when KC is less than 6. While the scale and lifespan of horseshoe vortex increase evidently with the increase of KC when KC is larger than 6. Moreover, the wake vortex contributes to the scour at lee-side of pile. Similar with the case of horseshoe vortex, there is no wake vortex when KC is less than 6. The wake vortex is mainly responsible for scour around pile when KC is greater than 6 and less than O(100), while horseshoe vortex controls scour nearly when KC is greater than O(100).

Sumer et al. [1] found that the equilibrium scour depth was nil around pile when KC was less than 6 under regular waves for live bed scour, while the equilibrium scour depth increased with the increase of KC. Based on that, Sumer proposed an equilibrium scour depth predicting equation (Equation (2)). Carreiras et al. [33] revised Sumer’s equation with m = 0.06 for nonlinear waves. Different with the findings of Sumer et al. [1] and Carreiras et al. [33], Corvaro et al. [21] found the scour still occurred for KC ≈ 4, and proposed the revised equilibrium scour depth predicting equation (Equation (3)) for KC > 4.

Rudolph and Bos [2] conducted a series of wave flume experiments to investigate the scour depth around monopile under waves only, waves and currents combined respectively, indicting KC was one of key parameters in influencing equilibrium scour depth, and proposed the equilibrium scour depth predicting equation (Equation (4)) for low KC (1 < KC < 10). Through analyzing the extensive data from published literatures, Raaijmakers and Rudolph [34] developed the equilibrium scour depth predicting equation (Equation (5)) for low KC, which was suitable for waves only, waves and currents combined. Khalfin [35] carried out several sets of wave flume experiments to study scour development around monopile, and proposed the equilibrium scour depth predicting equation (Equation (6)) for low KC (0.1 < KC < 3.5). Different with above equations, the Khalfin’s equation considers the Shields parameter θ and KC number simultaneously in predicting equilibrium scour depth. The flow reversal occurred under through in one wave period, so sand particles would be carried away from lee-side of pile to upside, resulting in sand particles backfilled into the upstream scour hole [20,29]. Considering the backfilling effects, Zanke et al. [36] proposed the equilibrium scour depth predicting equation (Equation (7)) around pile by theoretical analysis, and the equation is suitable for the whole range of KC number under regular waves and currents combined.

where, γ is safety factor, depending on design process, typically γ = 1.5, K_{wave} is correction factor considering wave action, K_{hw} is correction factor considering water depth.

where, n is the 1/n’th highest wave for random waves

For predicting equilibrium scour depth under irregular waves, i.e., random waves, Sumer and Fredsøe [16] found it’s suitable to take Equation (2) to predict equilibrium scour depth around pile under random waves with the root-mean-square (RMS) value of near-bed orbital velocity amplitude U_{m} and peak wave period T_{P} to calculate KC. Khalfin [35] recommended the RMS wave height H_{rms} and peak wave period T_{P} were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with U_{m} and mean zero-crossing wave period T_{z}. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (F_{r}) and Euler number (E_{u}) to equilibrium scour depth respectively.

2. Numerical Method

2.1. Governing Equations of Flow

The following equations adopted in present model are already available in Flow 3D software. The authors used these theoretical equations to simulate scour in random waves without modification. The incompressible viscous fluid motion satisfies the Reynolds-averaged Navier-Stokes (RANS) equation, so the present numerical model solves RANS equations:

where, V_{F} is the volume fraction; u, v, and w are the velocity components in x, y, z direction respectively with Cartesian coordinates; A_{i} is the area fraction; ρ_{f} is the fluid density, f_{i} is the viscous fluid acceleration, G_{i} is the fluid body acceleration (i = x, y, z).

2.2. Turbulent Model

The turbulence closure is available by the turbulent model, such as one-equation, the one-equation k-ε model, the standard k-ε model, RNG k-ε turbulent model and large eddy simulation (LES) model. The LES model requires very fine mesh grid, so the computational time is large, which hinders the LES model application in engineering. The RNG k-ε model can reduce computational time greatly with high accuracy in the near-wall region. Furthermore, the RNG k-ε model computes the maximum turbulent mixing length dynamically in simulating sediment scour model. Therefore, the RNG k-ε model was adopted to study the scour around anchor under random waves [41,42].

where, k_{T} is specific kinetic energy involved with turbulent velocity, G_{T} is the turbulent energy generated by buoyancy; ε_{T} is the turbulent energy dissipating rate, P_{T} is the turbulent energy, Diff_{ε} and Diff_{kT} are diffusion terms associated with V_{F}, A_{i}; CDIS1, CDIS2 and CDIS3 are dimensionless parameters, and CDIS1, CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from P_{T} and k_{T}.

2.3. Sediment Scour Model

The sand particles may suffer four processes under waves, i.e., entrainment, bed load transport, suspended load transport, and deposition, so the sediment scour model should depict the above processes efficiently. In present numerical simulation, the sediment scour model includes the following aspects:

2.3.1. Entrainment and Deposition

The combination of entrainment and deposition determines the net scour rate of seabed in present sediment scour model. The entrainment lift velocity of sand particles was calculated as [43]:

where, α_{i} is the entrainment parameter, n_{s} is the outward point perpendicular to the seabed, d_{*} is the dimensionless diameter of sand particles, which was calculated by Equation (15), θ_{cr} is the critical Shields parameter, g is the gravity acceleration, d_{i} is the diameter of sand particles, ρ_{i} is the density of seabed species.

In Equation (14), the entrainment parameter α_{i} confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43]. n_{s} is the outward pointing normal to the seabed interface, and n_{s} = (0,0,1) according to the Cartesian coordinates used in present numerical model.

The shields parameter was obtained from the following equation:

θ=U2f,m(ρi/ρf−1)gd50�=�f,m2(��/�f−1)��50(16)

where, U_{f,m} is the maximum value of the near-bed friction velocity; d_{50} is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].

The critical shields parameter θ_{cr} was obtained from the Equation (17) [44]

The sand particles begin to deposit on seabed when the turbulence energy weaken and cann’t support the particles suspending. The setting velocity of the particles was calculated from the following equation [44]:

This is called bed load transport when the sand particles roll or bounce over the seabed and always have contact with seabed. The bed load transport velocity was computed by [45]:

where, q_{b,i} is the bed load transport rate, which was obtained from Equation (20), δ_{i} is the bed load thickness, which was calculated by Equation (21), c_{b,i} is the volume fraction of sand i in the multiple species, f_{b} is the critical packing fraction of the seabed.

where, C_{s,i} is the suspended sand particles mass concentration of sand i in the multiple species, u_{s,i} is the sand particles velocity of sand i, D_{f} is the diffusivity.

The velocity of sand i in the multiple species could be obtained from the following equation:

where, u¯�¯ is the velocity of mixed fluid-particles, which can be calculated by the RANS equation with turbulence model, c_{s,i} is the suspended sand particles volume concentration, which was computed from Equation (24).

cs,i=Cs,iρi�s,�=�s,���(24)

3. Model Setup

The seabed-USAF-wave three-dimensional scour numerical model was built using Flow-3D software. As shown in Figure 2, the model includes sandy seabed, USAF model, sea water, two baffles and porous media. The dimensions of USAF are shown in Table 1. The sandy bed (210 m in length, 30 m in width and 11 m in height) is made up of uniform fine sand with median diameter d_{50} = 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.

Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.

Table 1. Numerical simulating cases.

3.1. Mesh Geometric Dimensions

In the simulation of the scour under the random waves, the model includes the umbrella suction anchor foundation, seabed and fluid. As shown in Figure 3, the model mesh includes global mesh grid and nested mesh grid, and the total number of grids is 1,812,000. The basic procedure for building mesh grid consists of two steps. Step 1: Divide the global mesh using regular hexahedron with size of 0.6 × 0.6. The global mesh area is cubic box, embracing the seabed and whole fluid volume, and the dimensions are 210 m in length, 30 m in width and 32 m in height. The details of determining the grid size can see the following mesh sensitivity section. Step 2: Set nested fine mesh grid in vicinity of the USAF with size of 0.3 × 0.3 so as to shorten the computation cost and improve the calculation accuracy. The encryption range is −15 m to 15 m in x direction, −15 m to 15 m in y direction and 0 m to 32 m in z direction, respectively. In order to accurately capture the free-surface dynamics, such as the fluid-air interface, the volume of fluid (VOF) method was adopted for tracking the free water surface. One specific algorithm called FAVORTM (Fractional Area/Volume Obstacle Representation) was used to define the fractional face areas and fractional volumes of the cells which are open to fluid flow.

Figure 3. The sketch of mesh grid.

3.2. Boundary Conditions

As shown in Figure 2, the initial fluid length is 210 m as long as seabed. A wave boundary was specified at the upstream offshore end. The details of determining the random wave spectrum can see the following wave parameters section. The outflow boundary was set at the downstream onshore end. The symmetry boundary was used at the top and two sides of the model. The symmetric boundaries were the better strategy to improve the computation efficiency and save the calculation cost [46]. At the seabed bottom, the wall boundary was adopted, which means the u = v = w= 0. Besides, the upper steel tube of USAF was set as no-slip condition.

3.3. Wave Parameters

The random waves with JONSWAP wave spectrum were used for all simulations as realistic representation of offshore conditions. The unidirectional JONSWAP frequency spectrum was described as [47]:

where, α is wave energy scale parameter, which is calculated by Equation (26), ω is frequency, ω_{p} is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ω_{p} and 0.09 for ω > ω_{p} respectively.

α=0.0076(gXU2)−0.22�=0.0076(���2)−0.22(26)

ωp=22(gU)(gXU2)−0.33�p=22(��)(���2)−0.33(27)

where, X is fetch length, U is average wind velocity at 10 m height from mean sea level.

In present numerical model, the input key parameters include X and U for wave boundary with JONSWAP wave spectrum. The objective wave height and period are available by different combinations of X and U. In this study, we designed 9 cases with different wave heights, periods and water depths for simulating scour around USAF under random waves (see Table 2). For random waves, the wave steepness ε and Ursell number U_{r} were acquired form Equations (28) and (29) respectively

ε=2πgHsT2a�=2���s�a2(28)

Ur=Hsk2h3w�r=�s�2ℎw3(29)

where, H_{s} is significant wave height, T_{a} is average wave period, k is wave number, h_{w} is water depth. The Shield parameter θ satisfies θ_{>}θ_{cr} for all simulations in current study, indicating the live bed scour prevails.

Table 2. Numerical simulating cases.

3.4. Mesh Sensitivity

In this section, a mesh sensitivity analysis was conducted to investigate the influence of mesh grid size to results and make sure the calculation is mesh size independent and converged. Three mesh grid size were chosen: Mesh 1—global mesh grid size of 0.75 × 0.75, nested fine mesh grid size of 0.4 × 0.4, and total number of grids 1,724,000, Mesh 2—global mesh grid size of 0.6 × 0.6, nested fine mesh grid size of 0.3 × 0.3, and total number of grids 1,812,000, Mesh 3—global mesh grid size of 0.4 × 0.4, nested fine mesh grid size of 0.2 × 0.2, and total number of grids 1,932,000. The near-bed shear velocity U_{*} is an important factor for influencing scour process [1,15], so U_{*} at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U_{*1,2} is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.

Figure 4. Comparison of near-bed shear velocity U_{*} with different mesh grid size.

The nested mesh block was adopted for seabed in vicinity of the USAF, which was overlapped with the global mesh block. When two mesh blocks overlap each other, the governing equations are by default solved on the mesh block with smaller average cell size (i.e., higher grid resolution). It is should be noted that the Flow 3D software used the moving mesh captures the scour evolution and automatically adjusts the time step size to be as large as possible without exceeding any of the stability limits, affecting accuracy, or unduly increasing the effort required to enforce the continuity condition [51].

3.5. Model Validation

In order to verify the reliability of the present model, the results of present study were compared with the experimental data of Khosronejad et al. [52]. The experiment was conducted in an open channel with a slender vertical pile under unidirectional currents. The comparison of scour development between the present results and the experimental results is shown in Figure 5. The Figure 5 reveals that the present results agree well with the experimental data of Khosronejad et al. [52]. In the first stage, the scour depth increases rapidly. After that, the scour depth achieves a maximum value gradually. The equilibrium scour depth calculated by the present model is basically corresponding with the experimental results of Khosronejad et al. [52], although scour depth in the present model is slightly larger than the experimental results at initial stage.

Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].

Secondly, another comparison was further conducted between the results of present study and the experimental data of Petersen et al. [17]. The experiment was carried out in a flume with a circular vertical pile in combined waves and current. Figure 4 shows a comparison of time evolution of scour depth between the simulating and the experimental results. As Figure 5 indicates, the scour depth in this study has good overall agreement with the experimental results proposed in Petersen et al. [17]. The equilibrium scour depth calculated by the present model is 0.399 m, which equals to the experimental value basically. Overall, the above verifications prove the present model is accurate and capable in dealing with sediment scour under waves.

In addition, in order to calibrate and validate the present model for hydrodynamic parameters, the comparison of water surface elevation was carried out with laboratory experiments conducted by Stahlmann [53] for wave gauge No. 3. The Figure 6 depicts the surface wave profiles between experiments and numerical model results. The comparison indicates that there is a good agreement between the model results and experimental values, especially the locations of wave crest and trough. Comparison of the surface elevation instructs the present model has an acceptable relative error, and the model is a calibrated in terms of the hydrodynamic parameters.

Figure 6. Comparison of surface elevation between the present study and Stahlmann [53].

Finally, another comparison was conducted for equilibrium scour depth or maximum scour depth under random waves with the experimental data of Sumer and Fredsøe [16] and Schendel et al. [22]. The Figure 7 shows the comparison between the numerical results and experimental data of Run01, Run05, Run21 and Run22 in Sumer and Fredsøe [16] and test A05 and A09 in Schendel et al. [22]. As shown in Figure 7, the equilibrium scour depth or maximum scour depth distributed within the ±30 error lines basically, meaning the reliability and accuracy of present model for predicting equilibrium scour depth around foundation in random waves. However, compared with the experimental values, the present model overestimated the equilibrium scour depth generally. Given that, a calibration for scour depth was carried out by multiplying the mean reduced coefficient 0.85 in following section.

Figure 7. Comparison of equilibrium (or maximum) scour depth between the present study and Sumer and Fredsøe [16], Schendel et al. [22].

Through the various examination for hydrodynamic and morphology parameters, it can be concluded that the present model is a validated and calibrated model for scour under random waves. Thus, the present numerical model would be utilized for scour simulation around foundation under random waves.

4. Numerical Results and Discussions

4.1. Scour Evolution

Figure 8 displays the scour evolution for case 1–9. As shown in Figure 8a, the scour depth increased rapidly at the initial stage, and then slowed down at the transition stage, which attributes to the backfilling occurred in scour holes under live bed scour condition, resulting in the net scour decreasing. Finally, the scour reached the equilibrium state when the amount of sediment backfilling equaled to that of scouring in the scour holes, i.e., the net scour transport rate was nil. Sumer and Fredsøe [16] proposed the following formula for the scour development under waves

St=Seq(1−exp(−t/Tc))�t=�eq(1−exp(−�/�c))(30)

where T_{c} is time scale of scour process.

Figure 8. Time evolution of scour for case 1–9: (a) Case 1–5; (b) Case 6–9.

The computing time is 3600 s and the scour development curves in Figure 8 kept fluctuating, meaning it’s still not in equilibrium scour stage in these cases. According to Sumer and Fredsøe [16], the equilibrium scour depth can be acquired by fitting the data with Equation (30). From Figure 8, it can be seen that the scour evolution obtained from Equation (30) is consistent with the present study basically at initial stage, but the scour depth predicted by Equation (30) developed slightly faster than the simulating results and the Equation (30) overestimated the scour depth to some extent. Overall, the whole tendency of the results calculated by Equation (30) agrees well with the simulating results of the present study, which means the Equation (30) is applicable to depict the scour evolution around USAF under random waves.

4.2. Scour Mechanism under Random Waves

The scour morphology and scour evolution around USAF are similar under random waves in case 1~9. Taking case 7 as an example, the scour morphology is shown in Figure 9.

Figure 9. Scour morphology under different times for case 7.

From Figure 9, at the initial stage (t < 1200 s), the scour occurred at upstream foundation edges between neighboring anchor branches. The maximum scour depth appeared at the lee-side of the USAF. Correspondingly, the sediments deposited at the periphery of the USAF, and the location of the maximum accretion depth was positioned at an angle of about 45° symmetrically with respect to the wave propagating direction in the lee-side of the USAF. After that, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.

According to previous studies [1,15,16,19,30,31], the horseshoe vortex, streamline compression and wake vortex shedding were responsible for scour around foundation. The Figure 10 displays the distribution of flow velocity in vicinity of foundation, which reflects the evolving processes of horseshoe vertex.

Figure 10. Velocity profile around USAF: (a) Flow runup and down stream at upstream anchor edges; (b) Horseshoe vortex at upstream anchor edges; (c) Flow reversal during wave through stage at lee side.

As shown in Figure 10, the inflow tripped to the upstream edges of the USAF and it was blocked by the upper tube of USAF. Then, the downflow formed the horizontal axis clockwise vortex and rolled on the seabed bypassing the tube, that is, the horseshoe vortex (Figure 11). The Figure 12 displays the turbulence intensity around the tube on the seabed. From Figure 12, it can be seen that the turbulence intensity was high-intensity with respect to the region of horseshoe vortex. This phenomenon occurred because of drastic water flow momentum exchanging in the horseshoe vortex. As a result, it created the prominent shear stress on the seabed, causing the local scour at the upstream edges of USAF. Besides, the horseshoe vortex moved downstream gradually along the periphery of the tube and the wake vortex shed off continually at the lee-side of the USAF, i.e., wake vortex.

Figure 11. Sketch of scour mechanism around USAF under random waves.

Figure 12. Turbulence intensity: (a) Turbulence intensity of horseshoe vortex; (b) Turbulence intensity of wake vortex; (c) Turbulence intensity of accretion area.

The core of wake vortex is a negative pressure center, liking a vacuum cleaner [11,42]. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortex. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow at the downside of USAF. As is shown in Figure 12, the turbulence intensity was low where the downflow occurred at lee-side, which means the turbulence energy may not be able to support the survival of wake vortex, leading to accretion happening. As mentioned in previous section, the formation of horseshoe vortex was dependent with adverse pressure gradient at upside of foundation. As shown in Figure 13, the evaluated range of pressure distribution is −15 m to 15 m in x direction. The t = 450 s and t = 1800 s indicate that the wave crest and trough arrived at the upside and lee-side of the foundation respectively, and the t = 350 s was neither the wave crest nor trough. The adverse gradient pressure reached the maximum value at t = 450 s corresponding to the wave crest phase. In this case, it’s helpful for the wave boundary separating fully from seabed, which leads to the formation of horseshoe vortex with high turbulence intensity. Therefore, the horseshoe vortex is responsible for the local scour between neighboring anchor branches at upside of USAF. What’s more, due to the combination of the horseshoe vortex and streamline compression, the maximum scour depth occurred at the upside of the USAF with an angle of about 45° corresponding to the wave propagating direction. This is consistent with the findings of Pang et al. [48] and Sumer et al. [1,15] in case of regular waves. At the wave trough phase (t = 1800 s), the pressure gradient became positive at upstream USAF edges, which hindered the separating of wave boundary from seabed. In the meantime, the flow reversal occurred (Figure 10) and the adverse gradient pressure appeared at downstream USAF edges, but the magnitude of adverse gradient pressure at lee-side was lower than the upstream gradient pressure under wave crest. In this way, the intensity of horseshoe vortex behind the USAF under wave trough was low, which explains the difference of scour depth at upstream and downstream, i.e., the scour asymmetry. In other words, the scour asymmetry at upside and downside of USAF was attributed to wave asymmetry for random waves, and the phenomenon became more evident for nonlinear waves [21]. Briefly speaking, the vortex system at wave crest phase was mainly related to the scour process around USAF under random waves.

Figure 13. Pressure distribution around USAF.

4.3. Equilibrium Scour Depth

The KC number is a key parameter for horseshoe vortex emerging and evolving under waves. According to Equation (1), when pile diameter D is fixed, the KC depends on the maximum near-bed velocity U_{wm} and wave period T. For random waves, the U_{wm} can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude U_{wm,rms} or the significant value of near-bed velocity amplitude U_{wm,s}. The U_{wm,rms} and U_{wm,s} for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period T_{a}, peak wave period T_{p}, significant wave period T_{s}, the maximum wave period T_{m}, 1/10′th highest wave period T_{n = 1/10} and 1/5′th highest wave period T_{n = 1/5} for random waves, so the different combinations of U_{wm} and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KC_{rms,s} was calculated by U_{wm,rms} and T_{s}. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KC_{rms,p}. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KC_{rms,p} > 6 under random waves.

Table 3.U_{wm,rms} and KC for case 1~9.

Table 4.U_{wm,s} and KC for case 1~9.

Raaijmakers and Rudolph [34] proposed the equilibrium scour depth predicting model (Equation (5)) around pile under waves, which is suitable for low KC. The format of Equation (5) is similar with the formula proposed by Breusers [54], which can predict the equilibrium scour depth around pile at different scour stages. In order to verify the applicability of Raaijmakers’s model for predicting the equilibrium scour depth around USAF under random waves, a validation of the equilibrium scour depth S_{eq} between the present study and Raaijmakers’s equation was conducted. The position where the scour depth S_{eq} was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of S_{eq} with different KC between the present study and Raaijmakers’s model.

Figure 14. Sketch of the position where the S_{eq} was evaluated.

Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (a) KC_{rms,s}, KC_{rms,a}; (b) KC_{rms,p}, KC_{rms,m}; (c) KC_{rms,n = 1/10}, KC_{rms,n = 1/5}; (d) KC_{s,s}, KC_{s,a}; (e) KC_{s,p}, KC_{s,m}; (f) KC_{s,n = 1/10}, KC_{s,n = 1/5}.

As shown in Figure 15, there is an error in predicting S_{eq} between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of S_{eq} with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KC_{s,p}. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as

As the Figure 16 shown, through trial-calculation, when ∆S/D = 0.05, the results calculated by Equation (31) show good agreement with the simulating results of the present study. The maximum error is about 18.2% and the engineering requirements have been met basically. In order to further verify the accuracy of the revised model for large KC (KC_{s,p} > 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d_{50} = 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KC_{s,p} is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KC_{s,p} < 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KC_{s,p} > 8.

Figure 16. Comparison of S_{eq} between the simulating results and the predicting values by Equation (31).

Figure 17. Comparison of S_{eq}/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).

In ocean environment, the waves are composed of a train of sinusoidal waves with different frequencies and amplitudes. The energy of constituent waves with very large and very small frequencies is relatively low, and the energy of waves is mainly concentrated in a certain range of moderate frequencies. Myrhaug and Rue [37] thought the 1/n’th highest wave was responsible for scour and proposed the stochastic model to predict the equilibrium scour depth around pile under random waves for full range of KC. Noteworthy is that the KC was denoted by KC_{rms,a} in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.

As shown in Figure 18, compared with the simulating results, the stochastic model underestimates the equilibrium scour depth around USAF generally. Although the error exists, the varying trend of S_{eq} with KC_{rms,a} obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.

Figure 18. Comparison of S_{eq} between the simulating results and the predicting values by Equation (8).

The Figure 19 lists the deviation value ∆S_{eq}/D′ between the predicting values and simulating results with different KC_{rms,a} and n. Then, fitted the relationship between the ∆S′and n under different KC_{rms,a}, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆S_{eq}/D′ to Equation (8).

The comparison between the predicting results by Equation (33) and the simulating results of present study is shown in Figure 20. According to the Figure 20, the varying trend of S_{eq} with KC_{rms,a} obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.

Figure 20. Comparison of S_{eq} between the simulating results and the predicting values by Equation (33).

In order to further verify the accuracy of the Equation (33) for large KC (KC_{rms,a} > 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d_{50} = 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KC_{rms,a} was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KC_{rms,a} (KC_{rms,a} < 4), the error between the predicting values and experimental results increases with decreasing of n for KC_{rms,a} > 4. Therefore, the predicting results are the most favorable for n = 2 when KC_{rms,a} > 4.

Figure 21. Comparison of S_{eq} between the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] and the predicting values by Equation (33).

Noteworthy is that the present model was built according to prototype size, so the errors between the numerical results and experimental data of References [16,21] may be attribute to the scale effects. In laboratory experiments on scouring process, it is typically impossible to ensure a rigorous similarity of all physical parameters between the model and prototype structure, leading to the scale effects in the laboratory experiments. To avoid a cohesive behaviour, the bed material was not scaled geometrically according to model scale. As a consequence, the relatively large-scaled sediments sizes may result in the overestimation of bed load transport and underestimation of suspended load transport compared with field conditions. What’s more, the disproportional scaled sediment presumably lead to the difference of bed roughness between the model and prototype, and thus large influences for wave boundary layer on the seabed and scour process. Besides, according to Corvaro et al. [21] and Schendel et al. [55], the pile Reynolds numbers and Froude numbers both affect the scour depth for the condition of non fully developed turbulent flow in laboratory experiments.

4.4. Parametric Study

4.4.1. Influence of Froude Number

As described above, the set of foundation leads to the adverse pressure gradient appearing at upstream, leading to the wave boundary layer separating from seabed, then horseshoe vortex formatting and the horseshoe vortex are mainly responsible for scour around foundation (see Figure 22). The Froude number F_{r} is the key parameter to influence the scale and intensity of horseshoe vortex. The F_{r} under waves can be calculated by the following formula [42]

Fr=UwgD−−−√�r=�w��(34)

where U_{w} is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude U_{wm,rms} is used for calculating U_{wm}.

Figure 22. Sketch of flow field at upstream USAF edges.

Tavouktsoglou et al. [25] proposed the following formula between F_{r} and the vertical location of the stagnation y

yh∝Fer�ℎ∝�r�(36)

where e is constant.

The Figure 23 displays the relationship between S_{eq}/D and F_{r} of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as F_{r} increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of F_{r}, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high F_{r} leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher F_{r} leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between S_{eq}/D and F_{r} as following

lg(Seq/D)=Aexp(B/Fr)+Clg(�eq/�)=�exp(�/�r)+�(37)

where A, B and C are constant.

Figure 23. The fitting curve between S_{eq}/D and F_{r}.

Figure 24. Sketch of adverse pressure gradient at upstream USAF edges.

Took the Equation (37) to fit the simulating results with A = −0.002, B = 0.686 and C = −0.808, and the results are shown in Figure 23. From Figure 23, the simulating results evenly distribute around the Equation (37) and the varying trend of S_{eq}/D and F_{r} in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of S_{eq}/D with F_{r} around USAF under random waves.

4.4.2. Influence of Euler Number

The Euler number E_{u} is the influencing factor for the hydrodynamic field around foundation. The E_{u} under waves can be calculated by the following formula. The E_{u} can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude U_{m,rms} is used for calculating U_{m}.

Eu=U2mgD�u=�m2��(38)

where U_{m} is depth-averaged flow velocity.

The Figure 25 displays the relationship between S_{eq}/D and E_{u} of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of S_{eq}/D and F_{r}, the equilibrium scour depth appears a logarithmic increase as E_{u} increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of E_{u}, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.

Figure 25. The fitting curve between S_{eq}/D and E_{u}.

Therefore, the variation of F_{r} and E_{u} reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of S_{eq}/D and E_{u} in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of S_{eq}/D with E_{u} around USAF under random waves. Additionally, according to the above description of F_{r}, it can be inferred that the higher F_{r} and E_{u} both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.

5. Conclusions

A series of numerical models were established to investigate the local scour around umbrella suction anchor foundation (USAF) under random waves. The numerical model was validated for hydrodynamic and morphology parameters by comparing with the experimental data of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22]. Based on the simulating results, the scour evolution and scour mechanisms around USAF under random waves were analyzed respectively. Two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves. Finally, a parametric study was carried out with the present model to study the effects of the Froude number F_{r} and Euler number E_{u} to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.(1)

The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.(2)

The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.(3)

The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KC_{s,p}. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KC_{s,p} < 8.(4)

Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KC_{rms,a} < 4. However, contrary to the case of low KC_{rms,a}, the predicting results are the most favorable for n = 2 when KC_{rms,a} > 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21].(5)

The same formula (Equation (37)) is applicable to express the relationship of S_{eq}/D with E_{u} or F_{r}, and it can be inferred that the higher F_{r} and E_{u} both lead to the more intensive horseshoe vortex and larger S_{eq.}

Author Contributions

Conceptualization, H.L. (Hongjun Liu); Data curation, R.H. and P.Y.; Formal analysis, X.W. and H.L. (Hao Leng); Funding acquisition, X.W.; Writing—original draft, R.H. and P.Y.; Writing—review & editing, X.W. and H.L. (Hao Leng); The final manuscript has been approved by all the authors. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities (grant number 202061027) and the National Natural Science Foundation of China (grant number 41572247).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

References

Sumer, B.M.; Fredsøe, J.; Christiansen, N. Scour Around Vertical Pile in Waves. J. Waterw. Port. Coast. Ocean Eng.1992, 118, 15–31. [Google Scholar] [CrossRef]

Rudolph, D.; Bos, K. Scour around a monopile under combined wave-current conditions and low KC-numbers. In Proceedings of the 6th International Conference on Scour and Erosion, Amsterdam, The Netherlands, 1–3 November 2006; pp. 582–588. [Google Scholar]

Nielsen, A.W.; Liu, X.; Sumer, B.M.; Fredsøe, J. Flow and bed shear stresses in scour protections around a pile in a current. Coast. Eng.2013, 72, 20–38. [Google Scholar] [CrossRef]

Ahmad, N.; Bihs, H.; Myrhaug, D.; Kamath, A.; Arntsen, Ø.A. Three-dimensional numerical modelling of wave-induced scour around piles in a side-by-side arrangement. Coast. Eng.2018, 138, 132–151. [Google Scholar] [CrossRef]

Li, H.; Ong, M.C.; Leira, B.J.; Myrhaug, D. Effects of Soil Profile Variation and Scour on Structural Response of an Offshore Monopile Wind Turbine. J. Offshore Mech. Arct. Eng.2018, 140, 042001. [Google Scholar] [CrossRef]

Li, H.; Liu, H.; Liu, S. Dynamic analysis of umbrella suction anchor foundation embedded in seabed for offshore wind turbines. Géoméch. Energy Environ.2017, 10, 12–20. [Google Scholar] [CrossRef]

Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Vanem, E.; Carvalho, H.; Correia, J.A.F.D.O. Editorial: Advanced research on offshore structures and foundation design: Part 1. Proc. Inst. Civ. Eng. Marit. Eng.2019, 172, 118–123. [Google Scholar] [CrossRef]

Chavez, C.E.A.; Stratigaki, V.; Wu, M.; Troch, P.; Schendel, A.; Welzel, M.; Villanueva, R.; Schlurmann, T.; De Vos, L.; Kisacik, D.; et al. Large-Scale Experiments to Improve Monopile Scour Protection Design Adapted to Climate Change—The PROTEUS Project. Energies2019, 12, 1709. [Google Scholar] [CrossRef][Green Version]

Wu, M.; De Vos, L.; Chavez, C.E.A.; Stratigaki, V.; Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Troch, P. Large Scale Experimental Study of the Scour Protection Damage Around a Monopile Foundation Under Combined Wave and Current Conditions. J. Mar. Sci. Eng.2020, 8, 417. [Google Scholar] [CrossRef]

Sørensen, S.P.H.; Ibsen, L.B. Assessment of foundation design for offshore monopiles unprotected against scour. Ocean Eng.2013, 63, 17–25. [Google Scholar] [CrossRef]

Prendergast, L.; Gavin, K.; Doherty, P. An investigation into the effect of scour on the natural frequency of an offshore wind turbine. Ocean Eng.2015, 101, 1–11. [Google Scholar] [CrossRef][Green Version]

Fazeres-Ferradosa, T.; Chambel, J.; Taveira-Pinto, F.; Rosa-Santos, P.; Taveira-Pinto, F.; Giannini, G.; Haerens, P. Scour Protections for Offshore Foundations of Marine Energy Harvesting Technologies: A Review. J. Mar. Sci. Eng.2021, 9, 297. [Google Scholar] [CrossRef]

Yang, Q.; Yu, P.; Liu, Y.; Liu, H.; Zhang, P.; Wang, Q. Scour characteristics of an offshore umbrella suction anchor foundation under the combined actions of waves and currents. Ocean Eng.2020, 202, 106701. [Google Scholar] [CrossRef]

Yu, P.; Hu, R.; Yang, J.; Liu, H. Numerical investigation of local scour around USAF with different hydraulic conditions under currents and waves. Ocean Eng.2020, 213, 107696. [Google Scholar] [CrossRef]

Sumer, B.M.; Christiansen, N.; Fredsøe, J. The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves. J. Fluid Mech.1997, 332, 41–70. [Google Scholar] [CrossRef]

Sumer, B.M.; Fredsøe, J. Scour around Pile in Combined Waves and Current. J. Hydraul. Eng.2001, 127, 403–411. [Google Scholar] [CrossRef]

Petersen, T.U.; Sumer, B.M.; Fredsøe, J. Time scale of scour around a pile in combined waves and current. In Proceedings of the 6th International Conference on Scour and Erosion, Paris, France, 27–31 August 2012. [Google Scholar]

Petersen, T.U.; Sumer, B.M.; Fredsøe, J.; Raaijmakers, T.C.; Schouten, J.-J. Edge scour at scour protections around piles in the marine environment—Laboratory and field investigation. Coast. Eng.2015, 106, 42–72. [Google Scholar] [CrossRef]

Qi, W.; Gao, F. Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci. China Ser. E Technol. Sci.2014, 57, 1030–1039. [Google Scholar] [CrossRef][Green Version]

Corvaro, S.; Marini, F.; Mancinelli, A.; Lorenzoni, C.; Brocchini, M. Hydro- and Morpho-dynamics Induced by a Vertical Slender Pile under Regular and Random Waves. J. Waterw. Port. Coast. Ocean Eng.2018, 144, 04018018. [Google Scholar] [CrossRef]

Schendel, A.; Welzel, M.; Schlurmann, T.; Hsu, T.-W. Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coast. Eng.2020, 161, 103751. [Google Scholar] [CrossRef]

Fazeres-Ferradosa, T.; Taveira-Pinto, F.; Romão, X.; Reis, M.; das Neves, L. Reliability assessment of offshore dynamic scour protections using copulas. Wind. Eng.2018, 43, 506–538. [Google Scholar] [CrossRef]

Fazeres-Ferradosa, T.; Welzel, M.; Schendel, A.; Baelus, L.; Santos, P.R.; Pinto, F.T. Extended characterization of damage in rubble mound scour protections. Coast. Eng.2020, 158, 103671. [Google Scholar] [CrossRef]

Ettema, R.; Melville, B.; Barkdoll, B. Scale Effect in Pier-Scour Experiments. J. Hydraul. Eng.1998, 124, 639–642. [Google Scholar] [CrossRef]

Umeda, S. Scour Regime and Scour Depth around a Pile in Waves. J. Coast. Res. Spec. Issue2011, 64, 845–849. [Google Scholar]

Umeda, S. Scour process around monopiles during various phases of sea storms. J. Coast. Res.2013, 165, 1599–1604. [Google Scholar] [CrossRef]

Baykal, C.; Sumer, B.; Fuhrman, D.R.; Jacobsen, N.; Fredsøe, J. Numerical simulation of scour and backfilling processes around a circular pile in waves. Coast. Eng.2017, 122, 87–107. [Google Scholar] [CrossRef][Green Version]

Miles, J.; Martin, T.; Goddard, L. Current and wave effects around windfarm monopile foundations. Coast. Eng.2017, 121, 167–178. [Google Scholar] [CrossRef][Green Version]

Miozzi, M.; Corvaro, S.; Pereira, F.A.; Brocchini, M. Wave-induced morphodynamics and sediment transport around a slender vertical cylinder. Adv. Water Resour.2019, 129, 263–280. [Google Scholar] [CrossRef]

Yu, T.; Zhang, Y.; Zhang, S.; Shi, Z.; Chen, X.; Xu, Y.; Tang, Y. Experimental study on scour around a composite bucket foundation due to waves and current. Ocean Eng.2019, 189, 106302. [Google Scholar] [CrossRef]

Carreiras, J.; Larroudé, P.; Seabra-Santos, F.; Mory, M. Wave Scour Around Piles. In Proceedings of the Coastal Engineering 2000, American Society of Civil Engineers (ASCE), Sydney, Australia, 16–21 July 2000; pp. 1860–1870. [Google Scholar]

Raaijmakers, T.; Rudolph, D. Time-dependent scour development under combined current and waves conditions—Laboratory experiments with online monitoring technique. In Proceedings of the 4th International Conference on Scour and Erosion, Tokyo, Japan, 5–7 November 2008; pp. 152–161. [Google Scholar]

Khalfin, I.S. Modeling and calculation of bed score around large-diameter vertical cylinder under wave action. Water Resour.2007, 34, 357. [Google Scholar] [CrossRef][Green Version]

Zanke, U.C.; Hsu, T.-W.; Roland, A.; Link, O.; Diab, R. Equilibrium scour depths around piles in noncohesive sediments under currents and waves. Coast. Eng.2011, 58, 986–991. [Google Scholar] [CrossRef]

Myrhaug, D.; Rue, H. Scour below pipelines and around vertical piles in random waves. Coast. Eng.2003, 48, 227–242. [Google Scholar] [CrossRef]

Myrhaug, D.; Ong, M.C.; Føien, H.; Gjengedal, C.; Leira, B.J. Scour below pipelines and around vertical piles due to second-order random waves plus a current. Ocean Eng.2009, 36, 605–616. [Google Scholar] [CrossRef]

Myrhaug, D.; Ong, M.C. Random wave-induced onshore scour characteristics around submerged breakwaters using a stochastic method. Ocean Eng.2010, 37, 1233–1238. [Google Scholar] [CrossRef]

Ong, M.C.; Myrhaug, D.; Hesten, P. Scour around vertical piles due to long-crested and short-crested nonlinear random waves plus a current. Coast. Eng.2013, 73, 106–114. [Google Scholar] [CrossRef]

Yakhot, V.; Orszag, S.A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput.1986, 1, 3–51. [Google Scholar] [CrossRef]

Yakhot, V.; Smith, L.M. The renormalization group, the e-expansion and derivation of turbulence models. J. Sci. Comput.1992, 7, 35–61. [Google Scholar] [CrossRef]

Mastbergen, D.R.; Berg, J.V.D. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology2003, 50, 625–637. [Google Scholar] [CrossRef]

Soulsby, R. Dynamics of Marine Sands; Thomas Telford Ltd.: London, UK, 1998. [Google Scholar] [CrossRef]

Van Rijn, L.C. Sediment Transport, Part I: Bed Load Transport. J. Hydraul. Eng.1984, 110, 1431–1456. [Google Scholar] [CrossRef][Green Version]

Zhang, Q.; Zhou, X.-L.; Wang, J.-H. Numerical investigation of local scour around three adjacent piles with different arrangements under current. Ocean Eng.2017, 142, 625–638. [Google Scholar] [CrossRef]

Yu, Y.X.; Liu, S.X. Random Wave and Its Applications to Engineering, 4th ed.; Dalian University of Technology Press: Dalian, China, 2011. [Google Scholar]

Pang, A.; Skote, M.; Lim, S.; Gullman-Strand, J.; Morgan, N. A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Appl. Ocean Res.2016, 57, 114–124. [Google Scholar] [CrossRef]

Higuera, P.; Lara, J.L.; Losada, I.J. Three-dimensional interaction of waves and porous coastal structures using Open-FOAM®. Part I: Formulation and validation. Coast. Eng.2014, 83, 243–258. [Google Scholar] [CrossRef]

Corvaro, S.; Crivellini, A.; Marini, F.; Cimarelli, A.; Capitanelli, L.; Mancinelli, A. Experimental and Numerical Analysis of the Hydrodynamics around a Vertical Cylinder in Waves. J. Mar. Sci. Eng.2019, 7, 453. [Google Scholar] [CrossRef][Green Version]

Flow3D User Manual, version 11.0.3; Flow Science, Inc.: Santa Fe, NM, USA, 2013.

Khosronejad, A.; Kang, S.; Sotiropoulos, F. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour.2012, 37, 73–85. [Google Scholar] [CrossRef]

Stahlmann, A. Experimental and Numerical Modeling of Scour at Foundation Structures for Offshore Wind Turbines. Ph.D. Thesis, Franzius-Institute for Hydraulic, Estuarine and Coastal Engineering, Leibniz Universität Hannover, Hannover, Germany, 2013. [Google Scholar]

Breusers, H.N.C.; Nicollet, G.; Shen, H. Local Scour Around Cylindrical Piers. J. Hydraul. Res.1977, 15, 211–252. [Google Scholar] [CrossRef]

Schendel, A.; Hildebrandt, A.; Goseberg, N.; Schlurmann, T. Processes and evolution of scour around a monopile induced by tidal currents. Coast. Eng.2018, 139, 65–84. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng.2021, 9, 886. https://doi.org/10.3390/jmse9080886

AMA Style

Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886

Find Other Styles

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

For more information on the journal statistics, click here.

Multiple requests from the same IP address are counted as one view.

Erick Mattos-Villarroel ^{a}, Jorge Flores-Velázquez ^{b}, Waldo Ojeda-Bustamante ^{c}, Carlos Díaz-Delgado ^{d}, Humberto Salinas-Tapia ^{d}Show moreAdd to MendeleyShareCite

^{a}Mexican Institute of Water Technology, Mexico ^{b}Postgraduate College, Hydrosciences, Carr. Mex-Tex Km 36.5, Texcoco, Mexico State, 56230, Mexico ^{c}Agricultural Engineering Graduate Program, University of Chapingo, Mexico^{d} Inter-American Institute of Water Science and Technology, Mexico

•Optimizing the geometric design of weirs can improve hydraulic performance.

•Labyrinth type weirs allow the discharge capacity to be increased compared to linear weirs.

•Hydraulic heads with ratio H_{T}/P > 0.5 generated sub-atmospheric pressures on the side walls of the weir.

•Numerical simulation it is a strong tool to analyze and get optimized the weir function.

Abstract

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R^{2} = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with H_{T}/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when H_{T}/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.

Alkistis Stergiopoulou^{1}, Vassilios Stergiopoulos_{2} ^{1}Institut für Wasserwirtschaft, Hydrologie und Konstruktiven Wasserbau, B.O.K.U. University, Muthgasse 18, 1190 Vienna, (actually Senior Process Engineer at the VTU Engineering in Vienna, Zieglergasse 53/1/24, 1070 Vienna, Austria). ^{2} School of Pedagogical and Technological Education, Department of Civil Engineering Educators, ASPETE Campus, Eirini Station, 15122 Amarousio, Athens, Greece. Received 4 Jan. 2021; Received in revised form 8 Aug. 2021; Accepted 8 Aug. 2021; Available online 14 Aug. 2021

Abstract

This paper presents a short view of the first Archimedean Screw Turbines CFD modelling results, which were carried out within the recent research entitled “Rebirth of Archimedes in Greece: contribution to the study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for recovering the hydraulic potential of Greek natural and technical watercourses”. This CFD analysis, based to the Flow-3D code, concerns typical Tubular Archimedean Screw Turbines (TASTs) and shows some promising performances for such small hydropower systems harnessing the important unexploited hydraulic potential of natural and technical watercourses of Greece, of the order of several TWh / year and of a total installed capacity in the range of thousands MWs.

CFD; Flow-3D; TAST; Small Hydro; Renewable Energy; Greek Watercourses.

Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).

References.

[1] A. Stergiopoulou, Computational and experimental investigation of the hydrodynamic behaviour of screw hydro turbine, Ph.D. Thesis, NTUA, 2017. [2] B. Pelikan, A. Lashofer, Verbesserung der Strömungseigenschaften sowie Planungs-und Betriebsoptimierung von Wasserkraftschnecken, Research Project, BOKU University, Vienna, 2012. [3] G. Müller, J. Senior, Simplified theory of Archimedean screws, Journal of Hydraulic Research 47 (5) (2009) 666-669. [4] C. Rorres, The turn of the screw: Optimal design of an Archimedes screw, Journal of Hydraulic Engineering, 80 (2000) 72-80. [5] A. Stergiopoulou, V. Stergiopoulos, Return of Archimedes: Harnessing with new Archimedean spirals the hydraulic potential of the Greek watercourses, in: Proceedings of the Conference for Climate Change, Thessaloniki, 2009. [6] A. Stergiopoulou, V. Stergiopoulos, from the old Archimedean screw pumps to the new Archimedean screw turbines for hydropower production in Greece, in: Proceedings of CEMEPE Conference, Mykonos, June 21-26, 2009. International Journal of Energy and Environment (IJEE), Volume 12, Issue 1, 2021, pp.19-30 [7] V. Stergiopoulos, A. Stergiopoulou, E. Kalkani, Quo Vadis Archimedes Nowadays in Greece? Towards Modern Archimedean Turbines for Recovering Greek Small Hydropower Potential, in: Proceedings of 3rd International Scientific “Energy and Climate Change” Conference, Athens, 2010. [8] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Greece beyond the horizon of the era of transition: Archimedean screw hydropower development terra incognita, International Journal of Energy and Development, v.6, Issue 6, pp. 627-536, 2015. [9] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Experimental and theoretical research of zero head innovative horizontal axis Archimedean screw turbines, Journal of Energy and Development, v.6, Issue 5, pp. 471-478, 2015. [10] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Back to the Future: Rediscovering the Archimedean screws as modern turbines for harnessing Greek small hydropower potential, in: Proceedings of the Third International Conference CEMEPE 2011 & SECOTOX, Skiathos, 2011. [11] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439- 445, May 2018. [12] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439- 445, May 2018. [13] A. Stergiopoulou, V. Stergiopoulos, Towards an inventory of the archimedean small hydropower potential of Greece, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT Volume 11, Issue 2, 2020 pp.137-144. [14] Flow Science, FLOW-3D Manual, 2013. [15] K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, Pearson, 2007. [16] C. Hirsch, Numerical Computation of internal and external flows: The fundamentals of Computational Fluid dynamics, John Wiley & Sons, 2007. [17] A. Stergiopoulou, V. Stergiopoulos and E. Kalkani, An eagle’s CFD view of Studying Innovative Archimedean Screw Renewable Hydraulic Energy Systems, Proceedings of the 4th International Conference on Environmental Management, Engineering, Planning and Economics (CEMEPE) and SECOTOX Conference, Mykonos island, Greece, pp.454-460 June 24-28, 2013. [18] A. Stergiopoulou, V. Stergiopoulos, A., E. Kalkani, Computational Fluid Dynamics Study on a 3D Graphic Solid Model of Archimedean Screw Turbines, Fresenius Environmental Bulletin, vol.23- No1, 2014. [19] Α. Stergiopoulou, Kalkani E., “Towards a First C.F.D. Study of Innovative Archimedean Inclined Axis Hydropower Turbines”, International Journal of Engineering Research & Technology (IJERT), Vol. 2 Issue 9, September – 2013, pp. 193-199. [20] A. Stergiopoulou, V. Stergiopoulos, A first CFD study of small hydro energy recovery from the Attica water supply network, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT, Volume 11, Issue 3, 2020 pp.157-166.

이 백서는 Flow-3D를 적용하여 다양한 흐름 배출 및 식생 시나리오가 흐름 속도(세로, 가로 및 수직 속도 포함)에 미치는 영향을 조사합니다.

실험적 측정을 통한 검증 후 식생직경, 식생높이, 유량방류량에 대한 민감도 분석을 수행하였다. 종방향 속도의 경우 흐름 구조에 가장 큰 영향을 미치는 것은 배출보다는 식생 직경에서 비롯됩니다.

그러나 식생 높이는 수직 분포의 변곡점을 결정합니다. 식생지 내 두 지점, 즉 상류와 하류의 횡속도를 비교하면 수심에 따른 대칭적인 패턴을 확인할 수 있다. 식생 지역의 가로 및 세로 유체 순환 패턴을 포함하여 흐름 또는 식생 시나리오와 관계없이 수직 속도에 대해서도 동일한 패턴이 관찰됩니다.

또한 식생의 직경이 클수록 이러한 패턴이 더 분명해집니다. 상부 순환은 초목 캐노피 근처에서 발생합니다. 식생지역의 가로방향과 세로방향의 순환에 관한 이러한 발견은 침수식생을 통한 3차원 유동구조를 밝혀준다.

This paper applies the Flow-3D to investigate the impacts of different flow discharge and vegetation scenarios on the flow velocity (including the longitudinal, transverse and vertical velocities). After the verification by using experimental measurements, a sensitivity analysis is conducted for the vegetation diameter, the vegetation height and the flow discharge. For the longitudinal velocity, the greatest impact on the flow structure originates from the vegetation diameter, rather than the discharge. The vegetation height, however, determines the inflection point of the vertical distribution. Comparing the transverse velocities at two positions in the vegetated area, i.e., the upstream and the downstream, a symmetric pattern is identified along the water depth. The same pattern is also observed for the vertical velocity regardless of the flow or vegetation scenario, including both transverse and vertical fluid circulation patterns in the vegetated area. Moreover, the larger the vegetation diameter is, the more evident these patterns become. The upper circulation occurs near the vegetation canopy. These findings regarding the circulations along the transverse and vertical directions in the vegetated region shed light on the 3-D flow structure through the submerged vegetation.

Key words

Submerged rigid vegetation

longitudinal velocity

transverse velocity

vertical velocity

open channel

References

Angelina A., Jordanova C. S. J. Experimental study of bed load transport through emergent vegetation [J]. Journal of Hydraulic Engineering, ASCE, 2003, 129(6): 474–478.ArticleGoogle Scholar

Li Y., Wang Y., Anim D. O. et al. Flow characteristics in different densities of submerged flexible vegetation from an open-channel flume study of artificial plants [J]. Geomorphology, 2014, 204: 314–324.ArticleGoogle Scholar

Bai F., Yang Z., Huai W. et al. A depth-averaged two dimensional shallow water model to simulate flow-rigid vegetation interactions [J]. Procedia Engineering, 2016, 154: 482–489.ArticleGoogle Scholar

Huai W. X., Song S., Han J. et al. Prediction of velocity distribution in straight open-channel flow with partial vegetation by singular perturbation method [J]. Applied Mathematics and Mechanics (Engilsh Editon), 2016, 37(10): 1315–1324.ArticleMathSciNetGoogle Scholar

Wang P. F., Wang C. Numerical model for flow through submerged vegetation regions in a shallow lake [J]. Journal of Hydrodynamics, 2011, 23(2): 170–178.ArticleGoogle Scholar

Wang W. J., Cui X. Y., Dong F. et al. Predictions of bulk velocity for open channel flow through submerged vegetation [J]. Journal of Hydrodynamics, 2020, 32(4): 795–799.ArticleGoogle Scholar

Zhang M., Li C. W., Shen Y. Depth-averaged modeling of free surface flows in open channels with emerged and submerged vegetation [J]. Applied Mathematical Modelling, 2013, 37(1–2): 540–553.ArticleMathSciNetGoogle Scholar

Huai W., Wang W., Hu Y. et al. Analytical model of the mean velocity distribution in an open channel with double-layered rigid vegetation [J]. Advances in Water Resources, 2014, 69: 106–113.ArticleGoogle Scholar

Panigrahi K., Khatua K. K. Prediction of velocity distribution in straight channel with rigid vegetation [J]. Aquatic Procedia, 2015, 4: 819–825.ArticleGoogle Scholar

Huai W. X., Zeng Y. H., Xu Z. G. et al. Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation [J]. Advances in Water Resources, 2009, 32(4): 487–492.ArticleGoogle Scholar

Chen S. C., Kuo Y. M., Li Y. H. Flow characteristics within different configurations of submerged flexible vegetation [J]. Journal of Hydrology, 2011, 398(1–2): 124–134.ArticleGoogle Scholar

Yagci O., Tschiesche U., Kabdasli M. S. The role of different forms of natural riparian vegetation on turbulence and kinetic energy characteristics [J]. Advances in Water Resources, 2010, 33(5): 601–614.ArticleGoogle Scholar

Wu F. S. Characteristics of flow resistance in open channels with non-submerged rigid vegetation [J]. Journal of Hydrodynamics, 2008, 20(2): 239–245.ArticleGoogle Scholar

Huai W., Hu Y., Zeng Y. et al. Velocity distribution for open channel flows with suspended vegetation [J]. Advances in Water Resources, 2012, 49: 56–61.ArticleGoogle Scholar

Pu J. H., Hussain A., Guo Y. K. et al. Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction [J]. Water Science and Engineering, 2019, 12(2): 121–128.ArticleGoogle Scholar

Zhang M. L., Li C. W., Shen Y. M. A 3D non-linear k-ε turbulent model for prediction of flow and mass transport in channel with vegetation [J]. Applied Mathematical Modelling, 2010, 34(4): 1021–1031.ArticleMathSciNetGoogle Scholar

Anjum N., Tanaka N. Numerical investigation of velocity distribution of turbulent flow through vertically double-layered vegetation [J]. Water Science and Engineering, 2019, 12(4): 319–329.ArticleGoogle Scholar

Wang W., Huai W. X., Gao M. Numerical investigation of flow through vegetated multi-stage compound channel [J]. Journal of Hydrodynamics, 2014, 26(3): 467–473.ArticleGoogle Scholar

Ghani U., Anjum N., Pasha G. A. et al. Numerical investigation of the flow characteristics through discontinuous and layered vegetation patches of finite width in an open channel [J]. Environmental Fluid Mechanics, 2019, 19(6): 1469–1495.ArticleGoogle Scholar

Aydin M. C., Emiroglu M. E. Determination of capacity of labyrinth side weir by CFD [J]. Flow Measurement and Instrumentation, 2013, 29: 1–8.ArticleGoogle Scholar

Hao W. L., Wu W. Q., Zhu C. J. et al. Experimental study on vertical distribution of flow velocity in vegetated river channel [J]. Water Resources and Power, 2015, 33(2): 85–88(in Chinese).Google Scholar

Pietri L., Petroff A., Amielh M. et al. Turbulent flows interacting with varying density canopies [J]. Mécanique and Industries, 2009, 10(3–4): 181–185.ArticleGoogle Scholar

Li Y., Du W., Yu Z. et al. Impact of flexible emergent vegetation on the flow turbulence and kinetic energy characteristics in a flume experiment [J]. Journal of Hydro-environment Research, 2015, 9(3): 354–367.ArticleGoogle Scholar

Li W. Q., Wang D., Jiao J. L. et al. Effects of vegetation patch density on flow velocity characteristics in an open channel [J]. Journal of Hydrodynamics, 2018, 31(5): 1052–1059.ArticleGoogle Scholar

Langre E. D., Gutierrez A., Cossé J. On the scaling of drag reduction by reconfiguration in plants [J]. Comptes Rendus Mécanique, 2012, 340(1–2): 35–40.ArticleGoogle Scholar

Fathi-Maghadam M., Kouwen N. Nonrigid, nonsubmerged, vegetative roughness on floodplains [J]. Journal of Hydraulic Engineering, ASCE, 1997, 123(1): 51–57.ArticleGoogle Scholar

Liang D., Wu X. A random walk simulation of scalar mixing in flows through submerged vegetations [J]. Journal of Hydrodynamics, 2014, 26(3): 343–350.ArticleMathSciNetGoogle Scholar

Ghisalberti M., Nepf H. Mass transport in vegetated shear flows [J]. Environmental Fluid Mechanics, 2005, 5(6): 527–551.ArticleGoogle Scholar

Mahdi Feizbahr,^{1}Navid Tonekaboni,^{2}Guang-Jun Jiang,^{3,4}and Hong-Xia Chen^{3,4} Academic Editor: Mohammad Yazdi

Abstract

강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.

Abstract

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [1–14]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [15–27]. Consequently, it is necessary to study the effects of the passive factors on the active domain [28–36]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [38–41].

One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [43–45]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [47, 48].

Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity is another form of current resistance. The reason for using the ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where n, f, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, S_{f} = slope of energy line, which in uniform flow is equal to the slope of the canal bed, = gravitational acceleration, and K_{n} is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, K_{s} = bed roughness size, and A = constant coefficient.

On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

By using equation (6), equation (5) is converted as follows:

Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [45, 55].

One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [47, 57, 58] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [45, 59–61]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [49, 63–66] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where is the depth of water change, S_{0} is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where are mass accelerations in the directions x, y, z and are viscosity accelerations in the directions x, y, z and are obtained from the following equations:

Shear stresses in equation (11) are obtained from the following equations:

The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).

Table 1

The studied models.

The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After seconds, this model reached a convergence accuracy of .

Figure 1

The simulated model and its boundary conditions.

Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

Any control and simulation system has some inputs that we should determine to test any technology [70–77]. Determination and true implementation of such parameters is one of the key steps of any simulation [23, 78–81] and computing procedure [82–86]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [87, 88]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

Figure 2

Modeling the plant with cylindrical tubes at the bottom of the canal.

Figure 3

Velocity profiles in positions 2 and 5.

The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

2. Modeling Results

After analyzing the models, the results were shown in graphs (Figures 4–14 ). The total number of experiments in this study was 48 due to the limitations of modeling.

Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5

Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6

Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7

Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8

Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.

Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10

Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11

Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12

Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13

Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5–10, which can be justified by increasing the speed and, of course, increasing the Froude number.

With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 5–8 and 10, 11), which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

Figure 15

Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 16

Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 17

Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 18

Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.

Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.

Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [2, 7, 8, 15, 18, 89–94]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [95–99].

Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

Nomenclature

n:

Manning’s roughness coefficient

C:

Chézy roughness coefficient

f:

Darcy–Weisbach coefficient

V:

Flow velocity

R:

Hydraulic radius

g:

Gravitational acceleration

y:

Flow depth

Ks:

Bed roughness

A:

Constant coefficient

:

Reynolds number

∂y/∂x:

Depth of water change

S_{0}:

Slope of the canal floor

Sf:

Slope of energy line

Fr:

Froude number

D:

Characteristic length of the canal

G:

Mass acceleration

:

Shear stresses.

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

References

H. Yu, L. Jie, W. Gui et al., “Dynamic Gaussian bare-bones fruit fly optimizers with abandonment mechanism: method and analysis,” Engineering with Computers, vol. 20, pp. 1–29, 2020.View at: Publisher Site | Google Scholar

X. Zhao, D. Li, B. Yang, C. Ma, Y. Zhu, and H. Chen, “Feature selection based on improved ant colony optimization for online detection of foreign fiber in cotton,” Applied Soft Computing, vol. 24, pp. 585–596, 2014.View at: Publisher Site | Google Scholar

J. Hu, H. Chen, A. A. Heidari et al., “Orthogonal learning covariance matrix for defects of grey wolf optimizer: insights, balance, diversity, and feature selection,” Knowledge-Based Systems, vol. 213, Article ID 106684, 2021.View at: Publisher Site | Google Scholar

C. Yu, M. Chen, K. Chen et al., “SGOA: annealing-behaved grasshopper optimizer for global tasks,” Engineering with Computers, vol. 4, pp. 1–28, 2021.View at: Publisher Site | Google Scholar

W. Shan, Z. Qiao, A. A. Heidari, H. Chen, H. Turabieh, and Y. Teng, “Double adaptive weights for stabilization of moth flame optimizer: balance analysis, engineering cases, and medical diagnosis,” Knowledge-Based Systems, vol. 8, Article ID 106728, 2020.View at: Google Scholar

J. Tu, H. Chen, J. Liu et al., “Evolutionary biogeography-based whale optimization methods with communication structure: towards measuring the balance,” Knowledge-Based Systems, vol. 212, Article ID 106642, 2021.View at: Publisher Site | Google Scholar

Y. Zhang, R. Liu, X. Wang et al., “Towards augmented kernel extreme learning models for bankruptcy prediction: algorithmic behavior and comprehensive analysis,” Neurocomputing, vol. 430, 2020.View at: Google Scholar

H.-L. Chen, G. Wang, C. Ma, Z.-N. Cai, W.-B. Liu, and S.-J. Wang, “An efficient hybrid kernel extreme learning machine approach for early diagnosis of Parkinson׳s disease,” Neurocomputing, vol. 184, pp. 131–144, 2016.View at: Publisher Site | Google Scholar

J. Xia, H. Chen, Q. Li et al., “Ultrasound-based differentiation of malignant and benign thyroid Nodules: an extreme learning machine approach,” Computer Methods and Programs in Biomedicine, vol. 147, pp. 37–49, 2017.View at: Publisher Site | Google Scholar

C. Li, L. Hou, B. Y. Sharma et al., “Developing a new intelligent system for the diagnosis of tuberculous pleural effusion,” Computer Methods and Programs in Biomedicine, vol. 153, pp. 211–225, 2018.View at: Publisher Site | Google Scholar

X. Xu and H.-L. Chen, “Adaptive computational chemotaxis based on field in bacterial foraging optimization,” Soft Computing, vol. 18, no. 4, pp. 797–807, 2014.View at: Publisher Site | Google Scholar

M. Wang, H. Chen, B. Yang et al., “Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses,” Neurocomputing, vol. 267, pp. 69–84, 2017.View at: Publisher Site | Google Scholar

L. Chao, K. Zhang, Z. Li, Y. Zhu, J. Wang, and Z. Yu, “Geographically weighted regression based methods for merging satellite and gauge precipitation,” Journal of Hydrology, vol. 558, pp. 275–289, 2018.View at: Publisher Site | Google Scholar

F. J. Golrokh, G. Azeem, and A. Hasan, “Eco-efficiency evaluation in cement industries: DEA malmquist productivity index using optimization models,” ENG Transactions, vol. 1, 2020.View at: Google Scholar

D. Zhao, L. Lei, F. Yu et al., “Chaotic random spare ant colony optimization for multi-threshold image segmentation of 2D Kapur entropy,” Knowledge-Based Systems, vol. 8, Article ID 106510, 2020.View at: Google Scholar

Y. Zhang, R. Liu, X. Wang, H. Chen, and C. Li, “Boosted binary Harris hawks optimizer and feature selection,” Engineering with Computers, vol. 517, pp. 1–30, 2020.View at: Publisher Site | Google Scholar

L. Hu, G. Hong, J. Ma, X. Wang, and H. Chen, “An efficient machine learning approach for diagnosis of paraquat-poisoned patients,” Computers in Biology and Medicine, vol. 59, pp. 116–124, 2015.View at: Publisher Site | Google Scholar

L. Shen, H. Chen, Z. Yu et al., “Evolving support vector machines using fruit fly optimization for medical data classification,” Knowledge-Based Systems, vol. 96, pp. 61–75, 2016.View at: Publisher Site | Google Scholar

X. Zhao, X. Zhang, Z. Cai et al., “Chaos enhanced grey wolf optimization wrapped ELM for diagnosis of paraquat-poisoned patients,” Computational Biology and Chemistry, vol. 78, pp. 481–490, 2019.View at: Publisher Site | Google Scholar

Y. Xu, H. Chen, J. Luo, Q. Zhang, S. Jiao, and X. Zhang, “Enhanced Moth-flame optimizer with mutation strategy for global optimization,” Information Sciences, vol. 492, pp. 181–203, 2019.View at: Publisher Site | Google Scholar

M. Wang and H. Chen, “Chaotic multi-swarm whale optimizer boosted support vector machine for medical diagnosis,” Applied Soft Computing Journal, vol. 88, Article ID 105946, 2020.View at: Publisher Site | Google Scholar

Y. Chen, J. Li, H. Lu, and P. Yan, “Coupling system dynamics analysis and risk aversion programming for optimizing the mixed noise-driven shale gas-water supply chains,” Journal of Cleaner Production, vol. 278, Article ID 123209, 2020.View at: Google Scholar

H. Tang, Y. Xu, A. Lin et al., “Predicting green consumption behaviors of students using efficient firefly grey wolf-assisted K-nearest neighbor classifiers,” IEEE Access, vol. 8, pp. 35546–35562, 2020.View at: Publisher Site | Google Scholar

H.-J. Ma and G.-H. Yang, “Adaptive fault tolerant control of cooperative heterogeneous systems with actuator faults and unreliable interconnections,” IEEE Transactions on Automatic Control, vol. 61, no. 11, pp. 3240–3255, 2015.View at: Google Scholar

H.-J. Ma and L.-X. Xu, “Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory,” IEEE Transactions on Automatic Control, vol. 66, 2020.View at: Google Scholar

H. J. Ma, L. X. Xu, and G. H. Yang, “Multiple environment integral reinforcement learning-based fault-tolerant control for affine nonlinear systems,” IEEE Transactions on Cybernetics, vol. 51, pp. 1–16, 2019.View at: Publisher Site | Google Scholar

J. Hu, M. Wang, C. Zhao, Q. Pan, and C. Du, “Formation control and collision avoidance for multi-UAV systems based on Voronoi partition,” Science China Technological Sciences, vol. 63, no. 1, pp. 65–72, 2020.View at: Publisher Site | Google Scholar

C. Zhang, H. Li, Y. Qian, C. Chen, and X. Zhou, “Locality-constrained discriminative matrix regression for robust face identification,” IEEE Transactions on Neural Networks and Learning Systems, vol. 99, pp. 1–15, 2020.View at: Publisher Site | Google Scholar

X. Zhang, D. Wang, Z. Zhou, and Y. Ma, “Robust low-rank tensor recovery with rectification and alignment,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 1, pp. 238–255, 2019.View at: Google Scholar

X. Zhang, J. Wang, T. Wang, R. Jiang, J. Xu, and L. Zhao, “Robust feature learning for adversarial defense via hierarchical feature alignment,” Information Sciences, vol. 560, 2020.View at: Google Scholar

X. Zhang, R. Jiang, T. Wang, and J. Wang, “Recursive neural network for video deblurring,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 03, p. 1, 2020.View at: Publisher Site | Google Scholar

X. Zhang, T. Wang, J. Wang, G. Tang, and L. Zhao, “Pyramid channel-based feature attention network for image dehazing,” Computer Vision and Image Understanding, vol. 197-198, Article ID 103003, 2020.View at: Publisher Site | Google Scholar

X. Zhang, T. Wang, W. Luo, and P. Huang, “Multi-level fusion and attention-guided CNN for image dehazing,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 3, p. 1, 2020.View at: Publisher Site | Google Scholar

L. He, J. Shen, and Y. Zhang, “Ecological vulnerability assessment for ecological conservation and environmental management,” Journal of Environmental Management, vol. 206, pp. 1115–1125, 2018.View at: Publisher Site | Google Scholar

Y. Chen, W. Zheng, W. Li, and Y. Huang, “Large group Activity security risk assessment and risk early warning based on random forest algorithm,” Pattern Recognition Letters, vol. 144, pp. 1–5, 2021.View at: Publisher Site | Google Scholar

J. Hu, H. Zhang, Z. Li, C. Zhao, Z. Xu, and Q. Pan, “Object traversing by monocular UAV in outdoor environment,” Asian Journal of Control, vol. 25, 2020.View at: Google Scholar

P. Tian, H. Lu, W. Feng, Y. Guan, and Y. Xue, “Large decrease in streamflow and sediment load of Qinghai-Tibetan Plateau driven by future climate change: a case study in Lhasa River Basin,” Catena, vol. 187, Article ID 104340, 2020.View at: Publisher Site | Google Scholar

A. Stokes, C. Atger, A. G. Bengough, T. Fourcaud, and R. C. Sidle, “Desirable plant root traits for protecting natural and engineered slopes against landslides,” Plant and Soil, vol. 324, no. 1, pp. 1–30, 2009.View at: Publisher Site | Google Scholar

T. B. Devi, A. Sharma, and B. Kumar, “Studies on emergent flow over vegetative channel bed with downward seepage,” Hydrological Sciences Journal, vol. 62, no. 3, pp. 408–420, 2017.View at: Google Scholar

G. Ireland, M. Volpi, and G. Petropoulos, “Examining the capability of supervised machine learning classifiers in extracting flooded areas from Landsat TM imagery: a case study from a Mediterranean flood,” Remote Sensing, vol. 7, no. 3, pp. 3372–3399, 2015.View at: Publisher Site | Google Scholar

L. Goodarzi and S. Javadi, “Assessment of aquifer vulnerability using the DRASTIC model; a case study of the Dezful-Andimeshk Aquifer,” Computational Research Progress in Applied Science & Engineering, vol. 2, no. 1, pp. 17–22, 2016.View at: Google Scholar

K. Zhang, Q. Wang, L. Chao et al., “Ground observation-based analysis of soil moisture spatiotemporal variability across a humid to semi-humid transitional zone in China,” Journal of Hydrology, vol. 574, pp. 903–914, 2019.View at: Publisher Site | Google Scholar

L. De Doncker, P. Troch, R. Verhoeven, K. Bal, P. Meire, and J. Quintelier, “Determination of the Manning roughness coefficient influenced by vegetation in the river Aa and Biebrza river,” Environmental Fluid Mechanics, vol. 9, no. 5, pp. 549–567, 2009.View at: Publisher Site | Google Scholar

M. Fathi-Moghadam and K. Drikvandi, “Manning roughness coefficient for rivers and flood plains with non-submerged vegetation,” International Journal of Hydraulic Engineering, vol. 1, no. 1, pp. 1–4, 2012.View at: Google Scholar

F.-C. Wu, H. W. Shen, and Y.-J. Chou, “Variation of roughness coefficients for unsubmerged and submerged vegetation,” Journal of Hydraulic Engineering, vol. 125, no. 9, pp. 934–942, 1999.View at: Publisher Site | Google Scholar

M. K. Wood, “Rangeland vegetation-hydrologic interactions,” in Vegetation Science Applications for Rangeland Analysis and Management, vol. 3, pp. 469–491, Springer, 1988.View at: Publisher Site | Google Scholar

C. Wilson, O. Yagci, H.-P. Rauch, and N. Olsen, “3D numerical modelling of a willow vegetated river/floodplain system,” Journal of Hydrology, vol. 327, no. 1-2, pp. 13–21, 2006.View at: Publisher Site | Google Scholar

R. Yazarloo, M. Khamehchian, and M. R. Nikoodel, “Observational-computational 3d engineering geological model and geotechnical characteristics of young sediments of golestan province,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar

G. E. Freeman, W. H. Rahmeyer, and R. R. Copeland, “Determination of resistance due to shrubs and woody vegetation,” International Journal of River Basin Management, vol. 19, 2000.View at: Google Scholar

N. Kouwen and T. E. Unny, “Flexible roughness in open channels,” Journal of the Hydraulics Division, vol. 99, no. 5, pp. 713–728, 1973.View at: Publisher Site | Google Scholar

S. Hosseini and J. Abrishami, Open Channel Hydraulics, Elsevier, Amsterdam, Netherlands, 2007.

C. S. James, A. L. Birkhead, A. A. Jordanova, and J. J. O’Sullivan, “Flow resistance of emergent vegetation,” Journal of Hydraulic Research, vol. 42, no. 4, pp. 390–398, 2004.View at: Publisher Site | Google Scholar

F. Huthoff and D. Augustijn, “Channel roughness in 1D steady uniform flow: Manning or Chézy?,,” NCR-days, vol. 102, 2004.View at: Google Scholar

M. S. Sabegh, M. Saneie, M. Habibi, A. A. Abbasi, and M. Ghadimkhani, “Experimental investigation on the effect of river bank tree planting array, on shear velocity,” Journal of Watershed Engineering and Management, vol. 2, no. 4, 2011.View at: Google Scholar

A. Errico, V. Pasquino, M. Maxwald, G. B. Chirico, L. Solari, and F. Preti, “The effect of flexible vegetation on flow in drainage channels: estimation of roughness coefficients at the real scale,” Ecological Engineering, vol. 120, pp. 411–421, 2018.View at: Publisher Site | Google Scholar

S. E. Darby, “Effect of riparian vegetation on flow resistance and flood potential,” Journal of Hydraulic Engineering, vol. 125, no. 5, pp. 443–454, 1999.View at: Publisher Site | Google Scholar

V. Kutija and H. Thi Minh Hong, “A numerical model for assessing the additional resistance to flow introduced by flexible vegetation,” Journal of Hydraulic Research, vol. 34, no. 1, pp. 99–114, 1996.View at: Publisher Site | Google Scholar

T. Fischer-Antze, T. Stoesser, P. Bates, and N. R. B. Olsen, “3D numerical modelling of open-channel flow with submerged vegetation,” Journal of Hydraulic Research, vol. 39, no. 3, pp. 303–310, 2001.View at: Publisher Site | Google Scholar

U. Stephan and D. Gutknecht, “Hydraulic resistance of submerged flexible vegetation,” Journal of Hydrology, vol. 269, no. 1-2, pp. 27–43, 2002.View at: Publisher Site | Google Scholar

F. G. Carollo, V. Ferro, and D. Termini, “Flow resistance law in channels with flexible submerged vegetation,” Journal of Hydraulic Engineering, vol. 131, no. 7, pp. 554–564, 2005.View at: Publisher Site | Google Scholar

W. Fu-sheng, “Flow resistance of flexible vegetation in open channel,” Journal of Hydraulic Engineering, vol. S1, 2007.View at: Google Scholar

P.-f. Wang, C. Wang, and D. Z. Zhu, “Hydraulic resistance of submerged vegetation related to effective height,” Journal of Hydrodynamics, vol. 22, no. 2, pp. 265–273, 2010.View at: Publisher Site | Google Scholar

J. K. Lee, L. C. Roig, H. L. Jenter, and H. M. Visser, “Drag coefficients for modeling flow through emergent vegetation in the Florida Everglades,” Ecological Engineering, vol. 22, no. 4-5, pp. 237–248, 2004.View at: Publisher Site | Google Scholar

G. J. Arcement and V. R. Schneider, Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains, US Government Printing Office, Washington, DC, USA, 1989.

Y. Ding and S. S. Y. Wang, “Identification of Manning’s roughness coefficients in channel network using adjoint analysis,” International Journal of Computational Fluid Dynamics, vol. 19, no. 1, pp. 3–13, 2005.View at: Publisher Site | Google Scholar

E. T. Engman, “Roughness coefficients for routing surface runoff,” Journal of Irrigation and Drainage Engineering, vol. 112, no. 1, pp. 39–53, 1986.View at: Publisher Site | Google Scholar

M. Feizbahr, C. Kok Keong, F. Rostami, and M. Shahrokhi, “Wave energy dissipation using perforated and non perforated piles,” International Journal of Engineering, vol. 31, no. 2, pp. 212–219, 2018.View at: Publisher Site | Google Scholar

M. Farzadkhoo, A. Keshavarzi, H. Hamidifar, and M. Javan, “Sudden pollutant discharge in vegetated compound meandering rivers,” Catena, vol. 182, Article ID 104155, 2019.View at: Publisher Site | Google Scholar

V. T. Chow, Open-channel Hydraulics, Mcgraw-Hill Civil Engineering Series, Chennai, TN, India, 1959.

X. Zhang, R. Jing, Z. Li, Z. Li, X. Chen, and C.-Y. Su, “Adaptive pseudo inverse control for a class of nonlinear asymmetric and saturated nonlinear hysteretic systems,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 916–928, 2020.View at: Google Scholar

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: the phase space perspective,” Optics and Lasers in Engineering, vol. 71, pp. 20–32, 2015.View at: Publisher Site | Google Scholar

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Scientific Reports, vol. 7, no. 1, pp. 7654–7722, 2017.View at: Publisher Site | Google Scholar

B.-H. Li, Y. Liu, A.-M. Zhang, W.-H. Wang, and S. Wan, “A survey on blocking technology of entity resolution,” Journal of Computer Science and Technology, vol. 35, no. 4, pp. 769–793, 2020.View at: Publisher Site | Google Scholar

Y. Liu, B. Zhang, Y. Feng et al., “Development of 340-GHz transceiver front end based on GaAs monolithic integration technology for THz active imaging array,” Applied Sciences, vol. 10, no. 21, p. 7924, 2020.View at: Publisher Site | Google Scholar

J. Hu, H. Zhang, L. Liu, X. Zhu, C. Zhao, and Q. Pan, “Convergent multiagent formation control with collision avoidance,” IEEE Transactions on Robotics, vol. 36, no. 6, pp. 1805–1818, 2020.View at: Publisher Site | Google Scholar

M. B. Movahhed, J. Ayoubinejad, F. N. Asl, and M. Feizbahr, “The effect of rain on pedestrians crossing speed,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 6, no. 3, 2020.View at: Google Scholar

A. Li, D. Spano, J. Krivochiza et al., “A tutorial on interference exploitation via symbol-level precoding: overview, state-of-the-art and future directions,” IEEE Communications Surveys & Tutorials, vol. 22, no. 2, pp. 796–839, 2020.View at: Publisher Site | Google Scholar

W. Zhu, C. Ma, X. Zhao et al., “Evaluation of sino foreign cooperative education project using orthogonal sine cosine optimized kernel extreme learning machine,” IEEE Access, vol. 8, pp. 61107–61123, 2020.View at: Publisher Site | Google Scholar

G. Liu, W. Jia, M. Wang et al., “Predicting cervical hyperextension injury: a covariance guided sine cosine support vector machine,” IEEE Access, vol. 8, pp. 46895–46908, 2020.View at: Publisher Site | Google Scholar

Y. Wei, H. Lv, M. Chen et al., “Predicting entrepreneurial intention of students: an extreme learning machine with Gaussian barebone harris hawks optimizer,” IEEE Access, vol. 8, pp. 76841–76855, 2020.View at: Publisher Site | Google Scholar

A. Lin, Q. Wu, A. A. Heidari et al., “Predicting intentions of students for master programs using a chaos-induced sine cosine-based fuzzy K-Nearest neighbor classifier,” Ieee Access, vol. 7, pp. 67235–67248, 2019.View at: Publisher Site | Google Scholar

Y. Fan, P. Wang, A. A. Heidari et al., “Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis,” Expert Systems with Applications, vol. 157, Article ID 113486, 2020.View at: Publisher Site | Google Scholar

E. Rodríguez-Esparza, L. A. Zanella-Calzada, D. Oliva et al., “An efficient Harris hawks-inspired image segmentation method,” Expert Systems with Applications, vol. 155, Article ID 113428, 2020.View at: Publisher Site | Google Scholar

S. Jiao, G. Chong, C. Huang et al., “Orthogonally adapted Harris hawks optimization for parameter estimation of photovoltaic models,” Energy, vol. 203, Article ID 117804, 2020.View at: Publisher Site | Google Scholar

Z. Xu, Z. Hu, A. A. Heidari et al., “Orthogonally-designed adapted grasshopper optimization: a comprehensive analysis,” Expert Systems with Applications, vol. 150, Article ID 113282, 2020.View at: Publisher Site | Google Scholar

A. Abbassi, R. Abbassi, A. A. Heidari et al., “Parameters identification of photovoltaic cell models using enhanced exploratory salp chains-based approach,” Energy, vol. 198, Article ID 117333, 2020.View at: Publisher Site | Google Scholar

M. Mahmoodi and K. K. Aminjan, “Numerical simulation of flow through sukhoi 24 air inlet,” Computational Research Progress in Applied Science & Engineering (CRPASE), vol. 03, 2017.View at: Google Scholar

F. J. Golrokh and A. Hasan, “A comparison of machine learning clustering algorithms based on the DEA optimization approach for pharmaceutical companies in developing countries,” ENG Transactions, vol. 1, 2020.View at: Google Scholar

H. Chen, A. A. Heidari, H. Chen, M. Wang, Z. Pan, and A. H. Gandomi, “Multi-population differential evolution-assisted Harris hawks optimization: framework and case studies,” Future Generation Computer Systems, vol. 111, pp. 175–198, 2020.View at: Publisher Site | Google Scholar

J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “Bayesian hierarchical model-based information fusion for degradation analysis considering non-competing relationship,” IEEE Access, vol. 7, pp. 175222–175227, 2019.View at: Publisher Site | Google Scholar

J. Guo, H. Zheng, B. Li, and G.-Z. Fu, “A Bayesian approach for degradation analysis with individual differences,” IEEE Access, vol. 7, pp. 175033–175040, 2019.View at: Publisher Site | Google Scholar

M. M. A. Malakoutian, Y. Malakoutian, P. Mostafapour, and S. Z. D. Abed, “Prediction for monthly rainfall of six meteorological regions and TRNC (case study: north Cyprus),” ENG Transactions, vol. 2, no. 2, 2021.View at: Google Scholar

H. Arslan, M. Ranjbar, and Z. Mutlum, “Maximum sound transmission loss in multi-chamber reactive silencers: are two chambers enough?,,” ENG Transactions, vol. 2, no. 1, 2021.View at: Google Scholar

N. Tonekaboni, M. Feizbahr, N. Tonekaboni, G.-J. Jiang, and H.-X. Chen, “Optimization of solar CCHP systems with collector enhanced by porous media and nanofluid,” Mathematical Problems in Engineering, vol. 2021, Article ID 9984840, 12 pages, 2021.View at: Publisher Site | Google Scholar

Z. Niu, B. Zhang, J. Wang et al., “The research on 220GHz multicarrier high-speed communication system,” China Communications, vol. 17, no. 3, pp. 131–139, 2020.View at: Publisher Site | Google Scholar

B. Zhang, Z. Niu, J. Wang et al., “Four‐hundred gigahertz broadband multi‐branch waveguide coupler,” IET Microwaves, Antennas & Propagation, vol. 14, no. 11, pp. 1175–1179, 2020.View at: Publisher Site | Google Scholar

Z.-Q. Niu, L. Yang, B. Zhang et al., “A mechanical reliability study of 3dB waveguide hybrid couplers in the submillimeter and terahertz band,” Journal of Zhejiang University Science, vol. 1, no. 1, 1998.View at: Google Scholar

B. Zhang, D. Ji, D. Fang, S. Liang, Y. Fan, and X. Chen, “A novel 220-GHz GaN diode on-chip tripler with high driven power,” IEEE Electron Device Letters, vol. 40, no. 5, pp. 780–783, 2019.View at: Publisher Site | Google Scholar

M. Taleghani and A. Taleghani, “Identification and ranking of factors affecting the implementation of knowledge management engineering based on TOPSIS technique,” ENG Transactions, vol. 1, no. 1, 2020.View at: Google Scholar

The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.

Highlights

A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.

Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.

Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.

지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.

Booij N, Ris RC, Holthuijsen LH (1999) A third-generation wave model for coastal regions: 1. Model description and validation. J Geophys Res Ocean 104(C4):7649–7666. https://doi.org/10.1029/98JC02622ArticleGoogle Scholar

Celliers L, Schleyer MH (2002) Coral bleaching on high-latitude marginal reefs at Sodwana Bay, South Africa. Mar Pollut Bull 44:1380–1387ArticleGoogle Scholar

Chen SC (2018) Performance assessment of FLOW-3D and XFlow in the numerical modelling of fish-bone type fishway hydraulics https://doi.org/10.15142/T3HH1J

Flow Science Inc (2018) FLOW-3D, Version 12.0 Users Manual. Santa Fe, NM, https://www.flow3d.com/

Flow Science Inc (2019) FLOW-3D, Version 12.0 [Computer Software]. Santa Fe, NM, https://www.flow3d.com/

Franco A, Moernaut J, Schneider-Muntau B, Strasser M, Gems B (2020) The 1958 Lituya Bay tsunami – pre-event bathymetry reconstruction and 3D numerical modelling utilising the computational fluid dynamics software Flow-3D. Nat Hazards Earth Syst Sci 20(8):2255–2279ArticleGoogle Scholar

Fringer OB, Gerritsen M, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Model 14(3):139–173ArticleGoogle Scholar

Hirt CW, Sicilian JM (1985) A porosity technique for the definition of obstacles in rectangular cell meshes. In: Proceedings of 4th International Conference on Ship Hydrodynamics https://ci.nii.ac.jp/naid/10009570543/en/

Hocker LO, Hruska MA (2004) Interleaving synchronous data and asynchronous data in a single data storage file

Lim A, Wheeler AJ, Price DM, O’Reilly L, Harris K, Conti L (2020) Influence of benthic currents on cold-water coral habitats: a combined benthic monitoring and 3D photogrammetric investigation. Sci Rep 10(1):19433. https://doi.org/10.1038/s41598-020-76446-yArticleGoogle Scholar

Morris T (2009) Physical oceanography of Sodwana Bay and its effect on larval transport and coral bleaching. PhD thesis, Cape Peninsula University of Technology

Pope SB (2001) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar

Porter SN (2009) Biogeography and potential factors regulating shallow subtidal reef communities in the Western Indian Ocean. PhD thesis, University of Cape Town

Porter SN, Schleyer MH (2019) Environmental variation and how its spatial structure influences the cross-shelf distribution of high-latitude coral communities in South Africa. Diversity. https://doi.org/10.3390/d11040057ArticleGoogle Scholar

Ramsay PJ, Mason TR (1990) Development of a type zoning model for Zululand coral reefs, Sodwana Bay, South Africa. J Coastal Res 6(4):829–852Google Scholar

Roberts H, Richardson J, Lagumbay R, Meselhe E, Ma Y (2013) Hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white ditch hydrodynamic and sediment transport modeling using FLOW-3D for siting and optimization of the LCA medium diversion at white D (December)

Roberts MJ, Ribbink AJ, Morris T, Berg MAVD, Engelbrecht DC, Harding RT (2006) Oceanographic environment of the Sodwana Bay coelacanths (Latimeria chalumnae), South Africa: coelacanth research. South Afr J Sci 102(9):435–443Google Scholar

Rogers JS, Monismith SG, Koweek DA, Torres WI, Dunbar RB (2016) Thermodynamics and hydrodynamics in an atoll reef system and their influence on coral cover. Limnol Oceanogr 61(6):2191–2206. https://doi.org/10.1002/lno.10365ArticleGoogle Scholar

Schleyer MH, Celliers L (2003) Coral dominance at the reef-sediment interface in marginal coral communities at Sodwana Bay, South Africa. Mar Freshw Res 54(8):967–972. https://doi.org/10.1071/MF02049ArticleGoogle Scholar

Schleyer MH, Porter SN (2018) Chapter One – drivers of soft and stony coral community distribution on the high-latitude coral reefs of South Africa. advances in marine biology, vol 80, Academic Press, pp 1–55, https://doi.org/10.1016/bs.amb.2018.09.001

Sebens KP, Grace SP, Helmuth B, Maney EJ Jr, Miles JS (1998) Water flow and prey capture by three scleractinian corals, Madracis mirabilis, Montastrea cavernosa and Porites porites, in a field enclosure. Mar Biol 131(2):347–360ArticleGoogle Scholar

Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164ArticleGoogle Scholar

Stocking J, Laforsch C, Sigl R, Reidenbach M (2018) The role of turbulent hydrodynamics and surface morphology on heat and mass transfer in corals. J R Soc Interface 15:20180448. https://doi.org/10.1098/rsif.2018.0448ArticleGoogle Scholar

Wyatt ASJ, Lowe RJ, Humphries S, Waite AM (2010) Particulate nutrient fluxes over a fringing coral reef: relevant scales of phytoplankton production and mechanisms of supply. Mar Ecol Prog Ser 405:113–130ArticleGoogle Scholar

Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González, Wilson Enrique Amaya Tequia Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202. Tunja – Boyacá – Colombia

Abstract

홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.

Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.

Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade
and Abaunza Tabares, 2021)Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source:
made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface
configuration and flow regime, of some grating types (source: produced with FlowSight®)

References

Alia Md., S., and Sabtu, N. (2020). Comparison of Different Methodologies for Determining the Efficiency of Gully Inlets. In F. M. Nazri (Ed.), Proceedings of AICCE‘19: Transforming the Nation for a Sustainable Tomorrow (Vol. 53, pp. 1275-1284). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030- 32816-0_99 Antunes do Carmo, J. S. (2020). Physical Modelling vs. Numerical Modelling: Complementarity and Learning. July. https://doi. org/10.20944/preprints202007.0753.v1 Aragón-Hernández, J. L. (2013). Modelación numérica integrada de los procesos hidráulicos en el drenaje urbano [Universidad Politécnica de Cataluña]. In Doctoral Tesis. https:// upcommons.upc.edu/handle/2117/95059?locale-attribute=es Argue, J. R., and Pezzaniti, D. (1996). How reliable are inlet (hydraulic) models at representing stormwater flow? Science of the Total Environment, 189-190, 355-359. https://doi.org/10.1016/0048-9697(96)05231-X Banco Mundial, O. (2019). Agua: Panorama general. https:// www.bancomundial.org/es/topic/water/overview Cárdenas-Quintero, M., Carvajal-Serna, L. F., and Marbello-Pérez, R. (2018). Evaluación numérica tridimensional de un sumidero de reja de fondo (Three-Dimensional Numerical Assessment of Grate Inlet). SSRN Electronic Journal, November. https://doi.org/10.2139/ssrn.3112980 Carvalho, R. F., Lopes, P., Leandro, J., and David, L. M. (2019). Numerical Research of Flows into Gullies with Different Outlet Locations. Water, 11(2), 794. https://doi.org/10.3390/ w11040794 Chaparro Andrade, F. G., and Abaunza Tabares, K. V. (2021). Importancia de los sumideros, su funcionamiento y diseño en redes de alcantarillado caso de estudio sector nororiental Tunja. Universidad Santo Tomás. Cortés Zambrano, M., Amaya Tequia, W. E., and Gamba Fernández, D. S. (2020). Implementation of the hydraulic modelling of urban drainage in the northeast sector, Tunja, Boyacá. Revista Facultad de Ingeniería Universidad de Antioquia. https://doi. org/10.17533/udea.redin.20200578 Cosco, C., Gómez, M., Russo, B., Tellez-Alvarez, J., Macchione, F., Costabile, P., and Costanzo, C. (2020). Discharge coefficients for specific grated inlets. Influence of the Froude number. Urban Water Journal, 17(7), 656-668. https://doi.org/10.1080/1573062X.2020.1811881 Despotovic, J., Plavsic, J., Stefanovic, N., and Pavlovic, D. (2005). Inefficiency of storm water inlets as a source of urban floods. Water Science and Technology, 51(2), 139-145. https://doi. org/10.2166/wst.2005.0041 Ellis, J. B., and Marsalek, J. (1996). Overview of urban drainage: Environmental impacts and concerns, means of mitigation and implementation policies. Journal of Hydraulic Research, 34(6), 723-732. https://doi.org/10.1080/00221689609498446 Fang, X., Jiang, S., and Alam, S. R. (2010). Numerical simulations of efficiency of curb-opening inlets. Journal of Hydraulic Engineering, 136(1), 62-66. https://doi.org/10.1061/(ASCE) HY.1943-7900.0000131 Faram, M. G., and Harwood, R. (2000). CFD for the Water Industry; The Role of CFD as a Tool for the Development of Wastewater Treatment Systems. Hydro International, 21-22. Faram, M. G., and Harwood, R. (2002). Assessment of the effectiveness of stormwater treatment chambers using computational fluid dynamics. Global Solutions for Urban Drainage, 40644(September 2002), 1-14. https://doi. org/10.1061/40644(2002)7 Flow Science, I. (2018). FLOW-3D® Version 12.0 Users Manual. In FLOW-3D [Computer software]. https://www.flow3d.com Flow Science, I. (2019). FLOW-3D® Version 12.0 [Computer software] (No. 12). https://www.flow3d.com Ghanbari, R., and Heidarnejad, M. (2020). Experimental and numerical analysis of flow hydraulics in triangular and rectangular piano key weirs. Water Science, 00(00), 1-7. https://doi.org/10. 1080/11104929.2020.1724649

Gómez, M., and Russo, B. (2005a). Comparative study of methodologies to determine inlet efficiency from test data. HEC-12 methodology vs UPC method. Water Resources Management, Algarve, Portugal., 80(October 2014), 623-632. https://doi. org/10.2495/WRM050621 Gómez, M., and Russo, B. (2005b). Comparative study among different methodologies to determine storm sewer inlet efficiency from test data. 10th International Conference on Urban Drainage, August, 21-26. https://www.researchgate.net/publication/255602448_Comparative_study_among_different_methodologies_to_determine_storm_sewer_inlet_efficiency_ from_test_data Gómez, M., Recasens, J., Russo, B., and Martínez-Gomariz, E. (2016). Assessment of inlet efficiency through a 3D simulation: Numerical and experimental comparison. Water Science and Technology, 74(8), 1926-1935. https://doi.org/10.2166/ wst.2016.326 Gómez, M., and Russo, B. (2011). Methodology to estimate hydraulic efficiency of drain inlets. Proceedings of the Institution of Civil Engineers: Water Management, 164(2), 81-90. https://doi. org/10.1680/wama.900070 Gómez Valentin, M. (2007). Hidrología urbana. In Hidrología Urbana (pp. 135-147). Instituto Flumen. Jakeman, A. J., Letcher, R. A., and Norton, J. P. (2006). Ten iterative steps in development and evaluation of environmental models. Environmental Modelling and Software, 21, 602-614. https://doi.org/10.1016/j.envsoft.2006.01.004 Jang, J. H., Hsieh, C. T., and Chang, T. H. (2019). The importance of gully flow modelling to urban flood simulation. Urban Water Journal, 16(5), 377-388. https://doi.org/10.1080/1573062X.2019.1669198 Kaushal, D. R., Thinglas, T., Tomita, Y., Kuchii, S., and Tsukamoto, H. (2012). Experimental investigation on optimization of invert trap configuration for sewer solid management. Powder Technology, 215-216, 1-14. https://doi.org/10.1016/j.powtec.2011.08.029 Khazaee, I., and Mohammadiun, M. (2010). Effects of flow field on open channel flow properties using numerical investigation and experimental comparison. International Journal of Energy and Environment, 1(6), 1083-1096. https://doi.org/10.1016/ S0031-9384(10)00122-8 Kleidorfer, M., Tscheikner-Gratl, F., Vonach, T., and Rauch, W. (2018). What can we learn from a 500-year event? Experiences from urban drainage in Austria. Water Science and Technology, 77(8), 2146-2154. https://doi.org/10.2166/wst.2018.138 Leitão, J. P., Simões, N. E., Pina, R. D., Ochoa-Rodriguez, S., Onof, C., and Sá Marques, A. (2017). Stochastic evaluation of the impact of sewer inlets‘ hydraulic capacity on urban pluvial flooding. Stochastic Environmental Research and Risk Assessment, 31(8), 1907-1922. https://doi.org/10.1007/s00477-016- 1283-x Lopes, P., Leandro, J., Carvalho, R. F., Russo, B., and Gómez, M. (2016). Assessment of the ability of a volume of fluid model to reproduce the efficiency of a continuous transverse gully with grate. Journal of Irrigation and Drainage Engineering, 142(10), 1-9. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001058 Mohsin, M., and Kaushal, D. R. (2016). 3D CFD validation of invert trap efficiency for sewer solid management using VOF model. Water Science and Engineering, 9(2), 106-114. https://doi. org/10.1016/j.wse.2016.06.006 Palla, A., Colli, M., Candela, A., Aronica, G. T., and Lanza, L. G. (2018). Pluvial flooding in urban areas: the role of surface drainage efficiency. Journal of Flood Risk Management, 11, S663-S676. https://doi.org/10.1111/jfr3.12246 Russo, B. (2010). Design of surface drainage systems according to hazard criteria related to flooding of urban areas [Universitat Politècnica de Catalunya]. https://dialnet.unirioja.es/servlet/ tesis?codigo=258828 Sedano-Cruz, K., Carvajal-Escoar, Y., and Ávila Díaz, A. J. (2013). ANÁLISIS DE ASPECTOS QUE INCREMENTAN EL RIESGO DE INUNDACIONES EN COLOMBIA. Luna Azul, 37, 219-218. https://www.redalyc.org/articulo.oa?id=321729206014 Spaliviero, F., May, R. W. P., Escarameia, M. (2000). Spacing of road gullies. Hydraulic performance of BS EN 124 gully gratings. HR Walingford, 44(0). https://doi.org/10.13140/ RG.2.1.1344.0889 Téllez-Álvarez, J., Gómez, M., and Russo, B. (2020). Quantification of energy loss in two grated inlets under pressure. Water (Switzerland), 12(6). https://doi.org/10.3390/w12061601 Téllez Álvarez, J., Gómez, V., Russo, B., and Redondo, J. M. (2003). Performance assessment of numerical modelling for hydraulic efficiency of a grated inlet. 1, 6-8. https://doi.org/10.16309/j.cnki.issn.1007-1776.2003.03.004 Téllez Álvarez, J., Gómez Valentin, M., Paindelli, A., and Russo, B. (2017). ACTIVIDAD EXPERIMENTAL DE I+D+i EN INGENIERÍA HIDRÁULICA EN ESPAÑA. In L. J. Balairón Pérez and D. López Gómez (Eds.), Seminario 2017, Comunicaciones de las líneas prioritarias (pp. 41-43). Universitat Politècnica de València. https://doi.org/10.1017/CBO9781107415324.004 Téllez Álvarez, J., Gómez Valentin, M., and Russo, B. (2019). Modelling of Surcharge Flow Through Grated Inlet. In P. Gourbesville and G. Caignaert (Eds.), Advances in Hydroinformati-

cs. Springer, Singapore. https://doi.org/10.1007/978-981- 4451-42-0 UNDRR, I., and CRED, I. (2018). Pérdidas económicas, pobreza y Desastres 1998 – 2017 (Vol. 6, Issue 1). https://doi.org/10.12962/ j23373520.v6i1.22451 Vyzikas, T., and Greaves, D. (2018). Numerial Modelling. In D. Greaves and G. Iglesias (Eds.), Wave and Tidal Energy (pp. 289-363). John Wiley and Sons Ltd. https://doi. org/10.1002/9781119014492 Yakhot, V., and Orszag, S. A. (1986). Renormalization Group Analysis of Turbulence. I . Basic Theory. Journal of Scientific Computing, 1(1), 3-51. https://doi.org/10.1007/BF01061452 Yakhot, V., and Smith, L. M. (1992). The renormalization group, the ɛ-expansion and derivation of turbulence models. Journal of Scientific Computing, 7(l), 35-61. https://doi.org/10.1007/ BF01060210 Yazdanfar, Z., and Sharma, A. (2015). Urban drainage system planning and design – Challenges with climate change and urbanization: A review. Water Science and Technology, 72(2), 165-https://doi.org/10.2166/wst.2015.207

Assistant Professor, Faculty of Civil Engineering, K. N. Toosi Univ. of Technology, Tehran 1996715433, Iran; formerly, Postdoctoral Research Fellow, Dept. of Civil and Environmental Engineering, Amirkabir Univ. of Technology (Tehran Polytechnic), Tehran 1591634311, Iran. ORCID: https://orcid.org/0000-0002-5162-6332. Email: mohammad.tehrani@kntu.ac.ir

https://doi.org/10.1061/JHEND8.HYENG-12914

Received: May 15, 2021

Accepted: September 30, 2022

Published online: December 21, 2022Journal of Hydraulic Engineering

chute 여수로에서는 난류 경계층 가장자리가 충분히 길면 자유 표면에 접근하는 시작점의 하류에서 자체 통기가 발생합니다. 시작 지점의 하류에서 공기-물 혼합물을 포함하는 층이 팽창 효과와 함께 흐름을 통해 점진적으로 확장됩니다.

유동 벌킹은 측벽 건현 설계 측면에서 필수적입니다. 또한 고체 경계 근처에 충분한 양의 공기를 도입하면 캐비테이션 손상을 방지할 수 있습니다. 현재 연구에서, 매끄러운 chute 을 따라 유동 벌킹과 함께 깊이와 자유 표면 위치에 걸쳐 자체 폭기 및 공기 농도 프로파일을 예측하기 위해 2D 수치 모델이 개발되었습니다.

개발된 모델은 혼합물 연속성, 기단 및 공기-물 혼합물 운동량 보존의 일방향 포물선 방정식의 해를 다룹니다. 이러한 방정식은 행진 기법과 Prandtl의 혼합 길이 난류 모델을 활용하여 자유 표면에 대한 동적 방정식과 함께 해결됩니다.

프로토타입 측정 및 실험실 테스트를 통해 얻은 실험 데이터를 사용하여 수치 모델의 정확도를 평가했습니다. 관련 결과는 경계층 발달의 유도된 시작점, 자체 유입 흐름 내의 공기 농도 프로파일 및 그에 따른 흐름의 벌킹 측면에서 비교되었습니다.

실용적인 목적을 위한 수치 모델의 기능은 상당히 정확한 결과에 따라 의미가 있으며 추가 연구를 위한 새로운 지평을 밝힙니다.

In chute spillways, self-aeration occurs downstream of the inception point, where the turbulent boundary layer edge approaches the free surface, if they are long enough. Downstream of the inception point, a layer containing an air–water mixture extends gradually through the flow with the bulking effect. Flow bulking is essential in terms of sidewall freeboard design. In addition, the introduction of enough air quantity near the solid boundaries prevents cavitation damage. In the present work, a 2D numerical model was developed for the prediction of self-aeration and air concentration profiles across the depth and the free-surface location, together with flow bulking along the smooth chutes. The developed model deals with the solution of the one-way direction parabolic equations of mixture continuity, air mass, and air–water mixture momentum conservation. These equations are solved accompanied by the dynamic equation for the free surface, utilizing the marching technique and Prandtl’s mixing length turbulent model. The experimental data obtained by prototype measurements and laboratory tests were used to assess the accuracy of the numerical model. The relevant results were compared in terms of the induced inception point of the boundary layer development, air concentration profiles within self-entrained flows, and the consequent bulking of the flow. The capability of the numerical model for practical purposes is signified in accordance with the fairly accurate obtained results, shedding light on new horizons for further research.

Fatemehsadat Mirshafiee^{1}, Emad Shahbazi ^{2}, Mohadeseh Safi ^{3}, Rituraj Rituraj^{ 4},* ^{1}Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran 1999143344 , Iran ^{2}Department of Mechatronic, Amirkabir University of Technology, Tehran 158754413, Iran ^{3}Department of Mechatronic, Electrical and Computer Engineering, University of Tehran, Tehran 1416634793, Iran ^{4} Faculty of Informatics, Obuda University, 1023, Budapest, Hungary

Correspondence: rituraj88@stud.uni-obuda.hu

ABSTRACT

본 연구는 지속가능한 에너지 변환기의 전력 및 수소 발생 모델링을 위한 데이터 기반 방법론을 제안합니다. 파고와 풍속을 달리하여 파고와 수소생산을 예측합니다.

또한 이 연구는 파도에서 수소를 추출할 수 있는 가능성을 강조하고 장려합니다. FLOW-3D 소프트웨어 시뮬레이션에서 추출한 데이터와 해양 특수 테스트의 실험 데이터를 사용하여 두 가지 데이터 기반 학습 방법의 비교 분석을 수행합니다.

결과는 수소 생산의 양은 생성된 전력의 양에 비례한다는 것을 보여줍니다. 제안된 재생 에너지 변환기의 신뢰성은 지속 가능한 스마트 그리드 애플리케이션으로 추가로 논의됩니다.

This study proposes a data-driven methodology for modeling power and hydrogen generation of a sustainable energy converter. The wave and hydrogen production at different wave heights and wind speeds are predicted. Furthermore, this research emphasizes and encourages the possibility of extracting hydrogen from ocean waves. By using the extracted data from FLOW-3D software simulation and the experimental data from the special test in the ocean, the comparison analysis of two data-driven learning methods is conducted. The results show that the amount of hydrogen production is proportional to the amount of generated electrical power. The reliability of the proposed renewable energy converter is further discussed as a sustainable smart grid application.

Key words

Cavity, Combustion efficiency, hydrogen fuel, Computational Fluent and Gambit.

Figure 1. The process of power and hydrogen production with Searaser.Figure 2. The cross-section A-A of the two essential parts of a SearaserFigure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor systemFigure 4. The boundary conditions of the control volumeFigure 5. The wind velocity during the period of the experimental test

REFERENCES

Kalbasi, R., Jahangiri, M., Dehshiri, S.J.H., Dehshiri, S.S.H., Ebrahimi, S., Etezadi, Z.A.S. and Karimipour, A., 2021. Finding the best station in Belgium to use residential-scale solar heating, one-year dynamic simulation with considering all system losses: economic analysis of using ETSW. Sustainable Energy Technologies and Assessments, 45, p.101097.

Megura M, Gunderson R. Better poison is the cure? Critically examining fossil fuel companies, climate change framing, and corporate sustainability reports. Energy Research & Social Science. 2022 Mar 1;85:102388.

Holechek JL, Geli HM, Sawalhah MN, Valdez R. A global assessment: can renewable energy replace fossil fuels by 2050?. Sustainability. 2022 Jan;14(8):4792.

Ahmad M, Kumar A, Ranjan R. Recent Developments of Tidal Energy as Renewable Energy: An Overview. River and Coastal Engineering. 2022:329-43.

Amini E, Mehdipour H, Faraggiana E, Golbaz D, Mozaffari S, Bracco G, Neshat M. Optimization of hydraulic power take-off system settings for point absorber wave energy converter. Renewable Energy. 2022 Jun 4.

Claywell, R., Nadai, L., Felde, I., Ardabili, S. 2020. Adaptive neuro-fuzzy inference system and a multilayer perceptron model trained with grey wolf optimizer for predicting solar diffuse fraction. Entropy, 22(11), p.1192.

McLeod I, Ringwood JV. Powering data buoys using wave energy: a review of possibilities. Journal of Ocean Engineering and Marine Energy. 2022 Jun 20:1-6.

Olsson G. Water interactions: A systemic view: Why we need to comprehend the water-climate-energy-food-economics-lifestyle connections.

Malkowska A, Malkowski A. Green Energy in the Political Debate. InGreen Energy 2023 (pp. 17-39). Springer, Cham.

Mayon R, Ning D, Ding B, Sergiienko NY. Wave energy converter systems–status and perspectives. InModelling and Optimisation of Wave Energy Converters (pp. 3-58). CRC Press.

Available online at: https://www.offshore-energy.biz/uk-ecotricity-introduces-wave-power-device-searaser/ (9/27/2022)

Mousavi SM, et al.,. Deep learning for wave energy converter modeling using long short-term memory. Mathematics. 2021 Apr 15;9(8):871.

Mega V. The Energy Race to Decarbonisation. InHuman Sustainable Cities 2022 (pp. 105-141). Springer, Cham.

Li R, Tang BJ, Yu B, Liao H, Zhang C, Wei YM. Cost-optimal operation strategy for integrating large scale of renewable energy in China’s power system: From a multi-regional perspective. Applied Energy. 2022 Nov 1;325:119780.

Ardabili S., Abdolalizadeh L., Mako C., Torok B., Systematic Review of Deep Learning and Machine Learning for Building Energy, Frontiers in Energy Research, 10, 2022.

Penalba M, Aizpurua JI, Martinez-Perurena A, Iglesias G. A data-driven long-term metocean data forecasting approach for the design of marine renewable energy systems. Renewable and Sustainable Energy Reviews. 2022 Oct 1;167:112751.

Torabi, M., Hashemi, S., Saybani, M.R., 2019. A Hybrid clustering and classification technique for forecasting short‐term energy consumption. Environmental progress & sustainable energy, 38(1), pp.66-76.

Rivera FP, Zalamea J, Espinoza JL, Gonzalez LG. Sustainable use of spilled turbinable energy in Ecuador: Three different energy storage systems. Renewable and Sustainable Energy Reviews. 2022 Mar 1;156:112005.

Raza SA, Jiang J. Mathematical foundations for balancing single-phase residential microgrids connected to a three-phase distribution system. IEEE Access. 2022 Jan 6;10:5292-303.

Takach M, Sarajlić M, Peters D, Kroener M, Schuldt F, von Maydell K. Review of Hydrogen Production Techniques from Water Using Renewable Energy Sources and Its Storage in Salt Caverns. Energies. 2022 Feb 15;15(4):1415.

Lv Z, Li W, Wei J, Ho F, Cao J, Chen X. Autonomous Chemistry Enabling Environment-Adaptive Electrochemical Energy Storage Devices. CCS Chemistry. 2022 Jul 7:1-9.

Dehghan Manshadi, Mahsa, Milad Mousavi, M. Soltani, Amir Mosavi, and Levente Kovacs. 2022. “Deep Learning for Modeling an Offshore Hybrid Wind–Wave Energy System” Energies 15, no. 24: 9484. https://doi.org/10.3390/en15249484

Ishaq H, Dincer I, Crawford C. A review on hydrogen production and utilization: Challenges and opportunities. International Journal of Hydrogen Energy. 2022 Jul 22;47(62):26238-64.

Maguire JF, Woodcock LV. On the Thermodynamics of Aluminum Cladding Oxidation: Water as the Catalyst for Spontaneous Combustion. Journal of Failure Analysis and Prevention. 2022 Sep 10:1-5.

Mohammadi, M. R., Hadavimoghaddam, F., Pourmahdi, M., Atashrouz, S., Munir, M. T., Hemmati-Sarapardeh, A., … & Mohaddespour, A. (2021). Modeling hydrogen solubility in hydrocarbons using extreme gradient boosting and equations of state. Scientific reports, 11(1).

Ma S, Qin J, Xiu X, Wang S. Design and performance evaluation of an underwater hybrid system of fuel cell and battery. Energy Conversion and Management. 2022 Jun 15;262:115672.

Ahamed R, McKee K, Howard I. A Review of the Linear Generator Type of Wave Energy Converters’ Power Take-Off Systems. Sustainability. 2022 Jan;14(16):9936.

Nejad, H.D., Nazari, M., Nazari, M., Mardan, M.M.S., 2022. Fuzzy State-Dependent Riccati Equation (FSDRE) Control of the Reverse Osmosis Desalination System With Photovoltaic Power Supply. IEEE Access, 10, pp.95585-95603.

Zou S, Zhou X, Khan I, Weaver WW, Rahman S. Optimization of the electricity generation of a wave energy converter using deep reinforcement learning. Ocean Engineering. 2022 Jan 15;244:110363.

Wu J, Qin L, Chen N, Qian C, Zheng S. Investigation on a spring-integrated mechanical power take-off system for wave energy conversion purpose. Energy. 2022 Apr 15;245:123318.

Papini G, Dores Piuma FJ, Faedo N, Ringwood JV, Mattiazzo G. Nonlinear Model Reduction by Moment-Matching for a Point Absorber Wave Energy Conversion System. Journal of Marine Science and Engineering. 2022 May;10(5):656.

Forbush DD, Bacelli G, Spencer SJ, Coe RG, Bosma B, Lomonaco P. Design and testing of a free floating dual flap wave energy converter. Energy. 2022 Feb 1;240:122485.

Rezaei, M.A., 2022. A New Hybrid Cascaded Switched-Capacitor Reduced Switch Multilevel Inverter for Renewable Sources and Domestic Loads. IEEE Access, 10, pp.14157-14183.

Lin Z, Cheng L, Huang G. Electricity consumption prediction based on LSTM with attention mechanism. IEEJ Transactions on Electrical and Electronic Engineering. 2020;15(4):556-562.

Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.

Ghalandari, M., 2019. Flutter speed estimation using presented differential quadrature method formulation. Engineering Applications of Computational Fluid Mechanics, 13(1), pp.804-810.

Li Z, Bouscasse B, Ducrozet G, Gentaz L, Le Touzé D, Ferrant P. Spectral wave explicit navier-stokes equations for wavestructure interactions using two-phase computational fluid dynamics solvers. Ocean Engineering. 2021 Feb 1;221:108513.

Zhou Y. Ocean energy applications for coastal communities with artificial intelligencea state-of-the-art review. Energy and AI. 2022 Jul 29:100189.

Miskati S, Farin FM. Performance evaluation of wave-carpet in wave energy extraction at different coastal regions: an analytical approach (Doctoral dissertation, Department of Mechanical and Production Engineering).

Gu C, Li H. Review on Deep Learning Research and Applications in Wind and Wave Energy. Energies. 2022 Feb 17;15(4):1510.

Aazami, R., 2022. Optimal Control of an Energy-Storage System in a Microgrid for Reducing Wind-Power Fluctuations. Sustainability, 14(10), p.6183.

Kabir M, Chowdhury MS, Sultana N, Jamal MS, Techato K. Ocean renewable energy and its prospect for developing economies. InRenewable Energy and Sustainability 2022 Jan 1 (pp. 263-298). Elsevier.

Babajani A, Jafari M, Hafezisefat P, Mirhosseini M, Rezania A, Rosendahl L. Parametric study of a wave energy converter (Searaser) for Caspian Sea. Energy Procedia. 2018 Aug 1;147:334-42.

He J. Coherence and cross-spectral density matrix analysis of random wind and wave in deep water. Ocean Engineering. 2020;197:106930

Ijadi Maghsoodi, A., 2018. Renewable energy technology selection problem using integrated h-swara-multimoora approach. Sustainability, 10(12), p.4481.

Band, S.S., Ardabili, S., Sookhak, M., Theodore, A., Elnaffar, S., Moslehpour, M., Csaba, M., Torok, B., Pai, H.T., 2022. When Smart Cities Get Smarter via Machine Learning: An In-depth Literature Review. IEEE Access.

Shamshirband, S., Rabczuk, T., Nabipour, N. and Chau, K.W., 2020. Prediction of significant wave height; comparison between nested grid numerical model, and machine learning models of artificial neural networks, extreme learning and support vector machines. Engineering Applications of Computational Fluid Mechanics, 14(1), pp.805-817.

Liu, Z., Mohammadzadeh, A., Turabieh, H., Mafarja, M., 2021. A new online learned interval type-3 fuzzy control system for solar energy management systems. IEEE Access, 9, pp.10498-10508.

Bavili, R.E., Mohammadzadeh, A., Tavoosi, J., Mobayen, S., Assawinchaichote, W., Asad, J.H. 2021. A New Active Fault Tolerant Control System: Predictive Online Fault Estimation. IEEE Access, 9, pp.118461-118471.

Akbari, E., Teimouri, A.R., Saki, M., Rezaei, M.A., Hu, J., Band, S.S., Pai, H.T., 2022. A Fault-Tolerant Cascaded SwitchedCapacitor Multilevel Inverter for Domestic Applications in Smart Grids. IEEE Access.

Band, S.S., Ardabili, S., 2022. Feasibility of soft computing techniques for estimating the long-term mean monthly wind speed. Energy Reports, 8, pp.638-648.

Tavoosi, J., Mohammadzadeh, A., Pahlevanzadeh, B., Kasmani, M.B., 2022. A machine learning approach for active/reactive power control of grid-connected doubly-fed induction generators. Ain Shams Engineering Journal, 13(2), p.101564.

Ponnusamy, V. K., Kasinathan, P., Madurai Elavarasan, R., Ramanathan, V., Anandan, R. K., Subramaniam, U., … & Hossain, E. A Comprehensive Review on Sustainable Aspects of Big Data Analytics for the Smart Grid. Sustainability, 2021; 13(23), 13322.

Ahmad, T., Zhang, D., Huang, C., Zhang, H., Dai, N., Song, Y., & Chen, H. Artificial intelligence in sustainable energy industry: Status Quo, challenges and opportunities. Journal of Cleaner Production, 2021; 289, 125834.

Wang, G., Chao, Y., Cao, Y., Jiang, T., Han, W., & Chen, Z. A comprehensive review of research works based on evolutionary game theory for sustainable energy development. Energy Reports, 2022; 8, 114-136.

Iranmehr H., Modeling the Price of Emergency Power Transmission Lines in the Reserve Market Due to the Influence of Renewable Energies, Frontiers in Energy Research, 9, 2022

Farmanbar, M., Parham, K., Arild, Ø., & Rong, C. A widespread review of smart grids towards smart cities. Energies, 2019; 12(23), 4484.

Quartier, N., Crespo, A. J., Domínguez, J. M., Stratigaki, V., & Troch, P. Efficient response of an onshore Oscillating Water Column Wave Energy Converter using a one-phase SPH model coupled with a multiphysics library. Applied Ocean Research, 2021; 115, 102856.

Mahmoodi, K., Nepomuceno, E., & Razminia, A. Wave excitation force forecasting using neural networks. Energy, 2022; 247, 123322.

Wang, H., Alattas, K.A., 2022. Comprehensive review of load forecasting with emphasis on intelligent computing approaches. Energy Reports, 8, pp.13189-13198.

Clemente, D., Rosa-Santos, P., & Taveira-Pinto, F. On the potential synergies and applications of wave energy converters: A review. Renewable and Sustainable Energy Reviews, 2021; 135, 110162.

Felix, A., V. Hernández-Fontes, J., Lithgow, D., Mendoza, E., Posada, G., Ring, M., & Silva, R. Wave energy in tropical regions: deployment challenges, environmental and social perspectives. Journal of Marine Science and Engineering, 2019; 7(7), 219.

Farrok, O., Ahmed, K., Tahlil, A. D., Farah, M. M., Kiran, M. R., & Islam, M. R. Electrical power generation from the oceanic wave for sustainable advancement in renewable energy technologies. Sustainability, 2020; 12(6), 2178.

Guo, B., & Ringwood, J. V. A review of wave energy technology from a research and commercial perspective. IET Renewable Power Generation, 2021; 15(14), 3065-3090.

López-Ruiz, A., Bergillos, R. J., Lira-Loarca, A., & Ortega-Sánchez, M. A methodology for the long-term simulation and uncertainty analysis of the operational lifetime performance of wave energy converter arrays. Energy, 2018; 153, 126-135.

Safarian, S., Saryazdi, S. M. E., Unnthorsson, R., & Richter, C. Artificial neural network integrated with thermodynamic equilibrium modeling of downdraft biomass gasification-power production plant. Energy, 2020; 213, 118800.

Kushwah, S. An oscillating water column (OWC): the wave energy converter. Journal of The Institution of Engineers (India): Series C, 2021; 102(5), 1311-1317.

Pap, J., Mako, C., Illessy, M., Kis, N., 2022. Modeling Organizational Performance with Machine Learning. Journal of Open Innovation: Technology, Market, and Complexity, 8(4), p.177.

Pap, J., Mako, C., Illessy, M., Dedaj, Z., Ardabili, S., Torok, B., 2022. Correlation Analysis of Factors Affecting Firm Performance and Employees Wellbeing: Application of Advanced Machine Learning Analysis. Algorithms, 15(9), p.300.

Alanazi, A., 2022. Determining Optimal Power Flow Solutions Using New Adaptive Gaussian TLBO Method. Applied Sciences, 12(16), p.7959.

Shakibjoo, A.D., Moradzadeh, M., Din, S.U., 2021. Optimized Type-2 Fuzzy Frequency Control for Multi-Area Power Systems. IEEE access, 10, pp.6989-7002.

Zhang, G., 2021. Solar radiation estimation in different climates with meteorological variables using Bayesian model averaging and new soft computing models. Energy Reports, 7, pp.8973-8996.

Cao, Y., Raise, A., Mohammadzadeh, A., Rathinasamy, S., 2021. Deep learned recurrent type-3 fuzzy system: Application for renewable energy modeling/prediction. Energy Reports, 7, pp.8115-8127.

Tavoosi, J., Suratgar, A.A., Menhaj, M.B., 2021. Modeling renewable energy systems by a self-evolving nonlinear consequent part recurrent type-2 fuzzy system for power prediction. Sustainability, 13(6), p.3301.

Bourouis, S., Band, S.S., 2022. Meta-Heuristic Algorithm-Tuned Neural Network for Breast Cancer Diagnosis Using Ultrasound Images. Frontiers in Oncology, 12, p.834028.

Mosavi, A.H., Mohammadzadeh, A., Rathinasamy, S., Zhang, C., Reuter, U., Levente, K. and Adeli, H., 2022. Deep learning fuzzy immersion and invariance control for type-I diabetes. Computers in Biology and Medicine, 149, p.105975.

Almutairi, K., Algarni, S., Alqahtani, T., Moayedi, H., 2022. A TLBO-Tuned Neural Processor for Predicting Heating Load in Residential Buildings. Sustainability, 14(10), p.5924.

Ahmad, Z., Zhong, H., 2020. Machine learning modeling of aerobic biodegradation for azo dyes and hexavalent chromium. Mathematics, 8(6), p.913.

Mosavi, A., Shokri, M., Mansor, Z., Qasem, S.N., Band, S.S. and Mohammadzadeh, A., 2020. Machine learning for modeling the singular multi-pantograph equations. Entropy, 22(9), p.1041.

Ardabili, S., 2019, September. Deep learning and machine learning in hydrological processes climate change and earth systems a systematic review. In International conference on global research and education (pp. 52-62). Springer, Cham.

Moayedi, H., (2021). Suggesting a stochastic fractal search paradigm in combination with artificial neural network for early prediction of cooling load in residential buildings. Energies, 14(6), 1649.

Rezakazemi, M., et al., 2019. ANFIS pattern for molecular membranes separation optimization. Journal of Molecular Liquids, 274, pp.470-476.

Mosavi, A., Faghan, Y., Ghamisi, P., Duan, P., Ardabili, S.F., Salwana, E. and Band, S.S., 2020. Comprehensive review of deep reinforcement learning methods and applications in economics. Mathematics, 8(10), p.1640.

Samadianfard, S., Jarhan, S., Salwana, E., 2019. Support vector regression integrated with fruit fly optimization algorithm for river flow forecasting in Lake Urmia Basin. Water, 11(9), p.1934.

Moayedi, H., (2021). Double-target based neural networks in predicting energy consumption in residential buildings. Energies, 14(5), 1331.

Mohammadzadeh S, D., Kazemi, S.F., 2019. Prediction of compression index of fine-grained soils using a gene expression programming model. Infrastructures, 4(2), p.26.

Karballaeezadeh, N., Mohammadzadeh S, D., Shamshirband, S., Hajikhodaverdikhan, P., 2019. Prediction of remaining service life of pavement using an optimized support vector machine (case study of Semnan–Firuzkuh road). Engineering Applications of Computational Fluid Mechanics, 13(1), pp.188-198.

Rezaei, M. Et al., (2022). Adaptation of A Real-Time Deep Learning Approach with An Analog Fault Detection Technique for Reliability Forecasting of Capacitor Banks Used in Mobile Vehicles. IEEE Access v. 21 pp. 89-99.

Khakian, R., et al., (2020). Modeling nearly zero energy buildings for sustainable development in rural areas. Energies, 13(10), 2593.

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

Maryam Bagheri^{a}, Seyed M. Ali Zomorodian^{b}, Masih Zolghadrc, H. M^{d}. Azamathulla ^{d},* and C. Venkata Siva Rama Prasad^{e} ^{a }Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran ^{b }Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran ^{c }Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran ^{d} Civil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad ^{e} Department of Civil Engineering, St. Peters Engineering College, Hyderabad, India *Corresponding author. E-mail: azmatheditor@gmail.com

ABSTRACT

측면 분기기(흡입구)의 상류측에서 유동 분리는 분기기 입구에서 맴돌이 전류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 분기 용량 및 효율성을 감소시킵니다. 따라서 분리구역의 크기를 파악하고 그 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.

본 연구에서는 분리 구역의 크기를 줄이기 위한 방법으로 분출구 입구에 7가지 유형의 조면화 요소와 4가지 다른 방류가 있는 3가지 다른 베드 인버트 레벨의 설치(총 84회 실험)를 조사했습니다. 또한 3D 전산 유체 역학(CFD) 모델을 사용하여 분리 구역의 흐름 패턴과 치수를 평가했습니다.

결과는 조도 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 조도 계수에 따라 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 방법을 결합하면 분리 구역 치수를 최대 63%까지 줄일 수 있습니다.

Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions.

Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone.

Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

Key words

discharge ratio, flow separation zone, intake, three dimensional simulation

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced
roughness coefficient and invert level changesFigure 1 | Laboratory channel dimensions.Figure 2 | Roughness plates.Figure 4 | Effect of roughness on separation zone dimensions.Figure 10 | Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).Figure 11 | Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12 | Velocity vector for flow condition Q¼22 l/s, near surface.

REFERENCES

Abbasi, A., Ghodsian, M., Habibi, M. & Salehi Neishabouri, S. A. 2004 Experimental investigation on dimensions of flow separation zone at lateral intakeentrance. Research & Construction; Pajouhesh va Sazandegi 62, 38–44. (In Persian). Al-Zubaidy, R. & Hilo, A. 2021 Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD). Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2021.11.172. Chow, V. T. 1959 Open Channel Hydraulics. McGraw-Hill, New York. Jalili, H., Hosseinzadeh Dalir, A. & Farsadizadeh, D. 2011 Effect of intake geometry on the sediment transport and lateral flow pattern. Iranian Water Research Journal 5 (9), 1–10. (In Persian). Jamshidi, A., Farsadizadeh, D. & Hosseinzadeh Dalir, A. 2016 Variations of flow separation zone at lateral intake entrance using submerged vanes. Journal of Civil Engineering Urban 6 (3), 54–63. Journal homepage. Available from: www.ojceu.ir/main. Karami Moghaddam, K. & Keshavarzi, A. 2007 Investigation of flow structure in lateral intakes of 55° and 90° with rounded entrance edge. In: 03 National Congress on Civil Engineering University of Tabriz. Available from: https://civilica.com/doc/16317. (In Persian). Karami, H., Farzin, S., Sadrabadi, M. T. & Moazeni, H. 2017 Simulation of flow pattern at rectangular lateral intake with different dike and submerged vane scenarios. Journal of Water Science and Engineering 10 (3), 246–255. https://doi.org/10.1016/j.wse.2017.10.001. Kasthuri, B. & Pundarikanthan, N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering 113 (4), 543–548. Keshavarzi, A. & Habibi, L. 2005 Optimizing water intake angle by flow separation analysis. Journal of Irrigation and Drain 54, 543–552. https://doi.org/10.1002/ird.207. Kirkgöz, M. S. & Ardiçlioğ lu, M. 1997 Velocity profiles of developing and developed open channel flow. Journal of Hydraulic Engineering 1099–1105. 10.1061/(ASCE)0733-9429(1997)123:12(1099). Nakato, T., Kennedy, J. F. & Bauerly, D. 1990 Pumpstation intake-shoaling control with submerge vanes. Journal of Hydraulic Engineering. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:1(119). Neary, V. S. & Odgaard, J. A. 1993 Three-dimensional flow structure at open channel diversions. Journal of Hydraulic Engineering. ASCE 119 (11), 1224–1230. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:11(1223). Nikbin, S. & Borghei, S. M. 2011 Experimental investigation of submerged vanes effect on dimensions of flow separation zone at a 90° openchannel junction. In: 06rd National Congress on Civil Engineering University of Semnan. (In Persian). Available from: https:// civilica.com/doc/120494. Odgaard, J. A. & Wang, Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.

Ramamurthy, A. S., Junying, Q. & Diep, V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic Engineering. See: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135). Seyedian, S., Karami Moghaddam, K. & Shafai Begestan, M. 2008 Determining the optimal radius in lateral intakes of 55° and 90° using variation of flow velocity. In: 07th Iranian Hydraulic Conference. Power & Water University of Technology (PWUT). (In Persian). Available from: https://civilica.com/doc/56251. Zolghadr, M. & Shafai Bejestan, M. 2020 Six legged concrete (SLC) elements as scour countermeasures at wing wall bridge abutments. International Journal of River Basin Management. doi: 10.1080/15715124.2020.1726357. Zolghadr, M., Zomorodian, S. M. A., Shabani, R. & Azamatulla Md., H. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944

^{1} Institut für Wasserwirtschaft, Hydrologie und Konstruktiven Wasserbau, B.O.K.U. University, Muthgasse 18, 1190 Vienna, (actually Senior Process Engineer at the VTU Engineering in Vienna, Zieglergasse 53/1/24, 1070 Vienna, Austria).^{2} School of Pedagogical and Technological Education, Department of Civil Engineering Educators, ASPETE Campus, Eirini Station, 15122 Amarousio, Athens, Greece.

Abstract

이 논문은 최초의 아르키메데스 나사 터빈 CFD 모델링 결과에 대한 간략한 견해를 제시하며, 이는 “그리스에서 아르키메데스의 부활: 수리 역학 및 아르키메데스 달팽이관 물레방아의 유체역학적 거동 연구에 대한 기여”라는 제목의 최근 연구에서 수행되었습니다. 그리스 자연 및 기술 수로의 수력 잠재력”. Flow-3D 코드를 기반으로 하는 이 CFD 분석은 일반적인 TAST(Tubular Archimedean Screw Turbines)와 관련이 있으며 몇 TWh 정도의 그리스 자연 및 기술 수로의 중요한 미개발 수력 잠재력을 활용하는 연간 및 수천 MW 범위의 총 설치 용량인 소규모 수력 발전 시스템에 대한 몇 가지 유망한 성능을 보여줍니다.

This paper presents a short view of the first Archimedean Screw Turbines CFD modelling results, which were carried out within the recent research entitled “Rebirth of Archimedes in Greece: contribution to the study of hydraulic mechanics and hydrodynamic behavior of Archimedean cochlear waterwheels, for recovering the hydraulic potential of Greek natural and technical watercourses”. This CFD analysis, based to the Flow-3D code, concerns typical Tubular Archimedean Screw Turbines (TASTs) and shows some promising performances for such small hydropower systems harnessing the important unexploited hydraulic potential of natural and technical watercourses of Greece, of the order of several TWh / year and of a total installed capacity in the range of thousands MWs.

Keywords

CFD; Flow-3D; TAST; Small Hydro; Renewable Energy; Greek Watercourses.

Figure 1. Photorealistic view of an inclined axis TAST (photo A. Stergiopoulou).Figure 3. The spectrum of all the screw axis orientation cases.Figure 4. Creation of the 3bladed Archimedean Screw with SolidworksFigure 6. “Meshing & Geometry” tab Operations (Flow 3-D).Figure 7. Comparison of Archimedean screw power performances P(W) for Q = 0.15 m3
/s and 0.30m3
/s
and angles of orientation 22ο & 32ο
.Figure 12. Various performances of the Archimedean Screw (MKE/Mean Kinetic Energy, Torque,
Turbulent Kinetic Energy, Turbulent Dissipation) for flow discharge Q = 0.45 m3
/s and an angle of
orientation θ = 32ο

References

[1] A. Stergiopoulou, Computational and experimental investigation of the hydrodynamic behaviour of screw hydro turbine, Ph.D. Thesis, NTUA, 2017. [2] B. Pelikan, A. Lashofer, Verbesserung der Strömungseigenschaften sowie Planungs-und Betriebsoptimierung von Wasserkraftschnecken, Research Project, BOKU University, Vienna, 2012. [3] G. Müller, J. Senior, Simplified theory of Archimedean screws, Journal of Hydraulic Research 47 (5) (2009) 666-669. [4] C. Rorres, The turn of the screw: Optimal design of an Archimedes screw, Journal of Hydraulic Engineering, 80 (2000) 72-80. [5] A. Stergiopoulou, V. Stergiopoulos, Return of Archimedes: Harnessing with new Archimedean spirals the hydraulic potential of the Greek watercourses, in: Proceedings of the Conference for Climate Change, Thessaloniki, 2009. [6] A. Stergiopoulou, V. Stergiopoulos, from the old Archimedean screw pumps to the new Archimedean screw turbines for hydropower production in Greece, in: Proceedings of CEMEPE Conference, Mykonos, June 21-26, 2009.

[7] V. Stergiopoulos, A. Stergiopoulou, E. Kalkani, Quo Vadis Archimedes Nowadays in Greece? Towards Modern Archimedean Turbines for Recovering Greek Small Hydropower Potential, in: Proceedings of 3rd International Scientific “Energy and Climate Change” Conference, Athens, 2010. [8] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Greece beyond the horizon of the era of transition: Archimedean screw hydropower development terra incognita, International Journal of Energy and Development, v.6, Issue 6, pp. 627-536, 2015. [9] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Experimental and theoretical research of zero head innovative horizontal axis Archimedean screw turbines, Journal of Energy and Development, v.6, Issue 5, pp. 471-478, 2015. [10] A. Stergiopoulou, V. Stergiopoulos, E. Κalkani, Back to the Future: Rediscovering the Archimedean screws as modern turbines for harnessing Greek small hydropower potential, in: Proceedings of the Third International Conference CEMEPE 2011 & SECOTOX, Skiathos, 2011. [11] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439- 445, May 2018. [12] A. Stergiopoulou, V. Stergiopoulos, Educational Renewable Energy Screw Wheel Technologies for Pico Hydropower Generation, Modern Environmental Science and Engineering, v.4, No.5, pp. 439- 445, May 2018. [13] A. Stergiopoulou, V. Stergiopoulos, Towards an inventory of the archimedean small hydropower potential of Greece, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT Volume 11, Issue 2, 2020 pp.137-144. [14] Flow Science, FLOW-3D Manual, 2013. [15] K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, Pearson, 2007. [16] C. Hirsch, Numerical Computation of internal and external flows: The fundamentals of Computational Fluid dynamics, John Wiley & Sons, 2007. [17] A. Stergiopoulou, V. Stergiopoulos and E. Kalkani, An eagle’s CFD view of Studying Innovative Archimedean Screw Renewable Hydraulic Energy Systems, Proceedings of the 4th International Conference on Environmental Management, Engineering, Planning and Economics (CEMEPE) and SECOTOX Conference, Mykonos island, Greece, pp.454-460 June 24-28, 2013. [18] A. Stergiopoulou, V. Stergiopoulos, A., E. Kalkani, Computational Fluid Dynamics Study on a 3D Graphic Solid Model of Archimedean Screw Turbines, Fresenius Environmental Bulletin, vol.23- No1, 2014. [19] Α. Stergiopoulou, Kalkani E., “Towards a First C.F.D. Study of Innovative Archimedean Inclined Axis Hydropower Turbines”, International Journal of Engineering Research & Technology (IJERT), Vol. 2 Issue 9, September – 2013, pp. 193-199. [20] A. Stergiopoulou, V. Stergiopoulos, A first CFD study of small hydro energy recovery from the Attica water supply network, INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT, Volume 11, Issue 3, 2020 pp.157-166.

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

^{1}. ^{Introduction}

The increase in energy demand, the limitations of fossil fuels, as well as environmental crises, such as air pollution and global warming, are the leading causes of calling more attention to harvesting renewable energy recently [1], [2], [3]. While still in its infancy, ocean wave energy has neither reached commercial maturity nor technological convergence. In recent decades, remarkable progress has been made in the marine energy domain, which is still in the early stage of development, to improve the technology performance level (TPL) [4], [5]and technology readiness level (TRL) of wave energy converters (WECs). This has been achieved using novel modeling techniques [6], [7], [8], [9], [10], [11], [12], [13], [14] to gain the following advantages [15]: (i) As a source of sustainable energy, it contributes to the mix of energy resources that leads to greater diversity and attractiveness for coastal cities and suppliers. [16] (ii) Since wave energy can be exploited offshore and does not require any land, in-land site selection would be less expensive and undesirable visual effects would be reduced. [17] (iii) When the best layout and location of offshore site are taken into account, permanent generation of energy will be feasible (as opposed to using solar energy, for example, which is time-dependent) [18].

In general, the energy conversion process can be divided into three stages in a WEC device, including primary, secondary, and tertiary stages [19], [20]. In the first stage of energy conversion, which is the subject of this study, the wave power is converted to mechanical power by wave-structure interaction (WSI) between ocean waves and structures. Moreover, the mechanical power is transferred into electricity in the second stage, in which mechanical structures are coupled with power take-off systems (PTO). At this stage, optimal control strategies are useful to tune the system dynamics to maximize power output [10], [13], [12]. Furthermore, the tertiary energy conversion stage revolves around transferring the non-standard AC power into direct current (DC) power for energy storage or standard AC power for grid integration [21], [22]. We discuss only the first stage regardless of the secondary and tertiary stages. While Page 1 of 16 WECs include several categories and technologies such as terminators, point absorbers, and attenuators [15], [23], we focus on oscillating surge wave energy converters (OSWECs) in this paper due to its high capacity for industrialization [24].

Over the past two decades, a number of studies have been conducted to understand how OSWECs’ structures and interactions between ocean waves and flaps affect converters performance. Henry et al.’s experiment on oscillating surge wave energy converters is considered as one of the most influential pieces of research [25], which demonstrated how the performance of oscillating surge wave energy converters (OSWECs) is affected by seven different factors, including wave period, wave power, flap’s relative density, water depth, free-board of the flap, the gap between the tubes, gap underneath the flap, and flap width. These parameters were assessed in their two models in order to estimate the absorbed energy from incoming waves [26], [27]. In addition, Folly et al. investigated the impact of water depth on the OSWECs performance analytically, numerically, and experimentally. According to this and further similar studies, the average annual incident wave power is significantly reduced by water depth. Based on the experimental results, both the surge wave force and the power capture of OSWECs increase in shallow water [28], [29]. Following this, Sarkar et al. found that under such circumstances, the device that is located near the coast performs much better than those in the open ocean [30]. On the other hand, other studies are showing that the size of the converter, including height and width, is relatively independent of the location (within similar depth) [31]. Subsequently, Schmitt et al. studied OSWECs numerically and experimentally. In fact, for the simulation of OSWEC, OpenFOAM was used to test the applicability of Reynolds-averaged Navier-Stokes (RANS) solvers. Then, the experimental model reproduced the numerical results with satisfying accuracy [32]. In another influential study, Wang et al. numerically assessed the effect of OSWEC’s width on their performance. According to their findings, as converter width increases, its efficiency decreases in short wave periods while increases in long wave periods [33]. One of the main challenges in the analysis of the OSWEC is the coupled effect of hydrodynamic and geometric variables. As a result, numerous cutting-edge geometry studies have been performed in recent years in order to find the optimal structure that maximizes power output and minimizes costs. Garcia et al. reviewed hull geometry optimization studies in the literature in [19]. In addition, Guo and Ringwood surveyed geometric optimization methods to improve the hydrodynamic performance of OSWECs at the primary stage [14]. Besides, they classified the hull geometry of OSWECs based on Figure 1. Subsequently, Whittaker et al. proposed a different design of OSWEC called Oyster2. There have been three examples of different geometries of oysters with different water depths. Based on its water depth, they determined the width and height of the converter. They also found that in the constant wave period the less the converter’s width, the less power captures the converter has [34]. Afterward, O’Boyle et al. investigated a type of OSWEC called Oyster 800. They compared the experimental and numerical models with the prototype model. In order to precisely reproduce the shape, mass distribution, and buoyancy properties of the prototype, a 40th-scale experimental model has been designed. Overall, all the models were fairly accurate according to the results [35].

Inclusive analysis of recent research avenues in the area of flap geometry has revealed that the interaction-based designs of such converters are emerging as a novel approach. An initiative workflow is designed in the current study to maximizing the wave energy extrication by such systems. To begin with, a sensitivity analysis plays its role of determining the best hydrodynamic values for installing the converter’s flap. Then, all flap dimensions and characteristics come into play to finalize the primary model. Following, interactive designs is proposed to increase the influence of incident waves on the body by adding ribs on both sides of the flap as a novel design. Finally, a new bi-level metaheuristic method is proposed to consider the effects of simultaneous changes in ribs properties and other design parameters. We hope this novel approach will be utilized to make big-scale projects less costly and justifiable. The efficiency of the method is also compared with four well known metaheuristic algorithms and out weight them for this application.

This paper is organized as follows. First, the research methodology is introduced by providing details about the numerical model implementation. To that end, we first introduced the primary model’s geometry and software details. That primary model is later verified with a benchmark study with regard to the flap angle of rotation and water surface elevation. Then, governing equations and performance criteria are presented. In the third part of the paper, we discuss the model’s sensitivity to lower and upper parts width (we proposed a two cross-sectional design for the flap), bottom elevation, and freeboard. Finally, the novel optimization approach is introduced in the final part and compared with four recent metaheuristic algorithms.

2. Numerical Methods

In this section, after a brief introduction of the numerical software, Flow3D, boundary conditions are defined. Afterwards, the numerical model implementation, along with primary model properties are described. Finally, governing equations, as part of numerical process, are discussed.

^{2.1}. ^{Model Setup}

FLOW-3D is a powerful and comprehensive CFD simulation platform for studying fluid dynamics. This software has several modules to solve many complex engineering problems. In addition, modeling complex flows is simple and effective using FLOW-3D’s robust meshing capabilities [36]. Interaction between fluid and moving objects might alter the computational range. Dynamic meshes are used in our modeling to take these changes into account. At each time step, the computational node positions change in order to adapt the meshing area to the moving object. In addition, to choose mesh dimensions, some factors are taken into account such as computational accuracy, computational time, and stability. The final grid size is selected based on the detailed procedure provided in [37]. To that end, we performed grid-independence testing on a CFD model using three different mesh grid sizes of 0.01, 0.015, and 0.02 meters. The problem geometry and boundary conditions were defined the same, and simulations were run on all three grids under the same conditions. The predicted values of the relevant variable, such as velocity, was compared between the grids. The convergence behavior of the numerical solution was analyzed by calculating the relative L2 norm error between two consecutive grids. Based on the results obtained, it was found that the grid size of 0.02 meters showed the least error, indicating that it provided the most accurate and reliable solution among the three grids. Therefore, the grid size of 0.02 meters was selected as the optimal spatial resolution for the mesh grid.

In this work, the flume dimensions are 10 meters long, 0.1 meters wide, and 2.2 meters high, which are shown in figure2. In addition, input waves with linear characteristics have a height of 0.1 meters and a period of 1.4 seconds. Among the linear wave methods included in this software, RNGk-ε and k- ε are appropriate for turbulence model. The research of Lopez et al. shows that RNGk- ε provides the most accurate simulation of turbulence in OSWECs [21]. We use CATIA software to create the flap primary model and other innovative designs for this project. The flap measures 0.1 m x 0.65 m x 0.360 m in x, y and z directions, respectively. In Figure 3, the primary model of flap and its dimensions are shown. In this simulation, five boundaries have been defined, including 1. Inlet, 2. Outlet, 3. Converter flap, 4. Bed flume, and 5. Water surface, which are shown in figure 2. Besides, to avoid wave reflection in inlet and outlet zones, Flow3D is capable of defining some areas as damping zones, the length of which has to be one to one and a half times the wavelength. Therefore, in the model, this length is considered equal to 2 meters. Furthermore, there is no slip in all the boundaries. In other words, at every single time step, the fluid velocity is zero on the bed flume, while it is equal to the flap velocity on the converter flap. According to the wave theory defined in the software, at the inlet boundary, the water velocity is called from the wave speed to be fed into the model.

^{2.2}. ^{Verification}

In the current study, we utilize the Schmitt experimental model as a benchmark for verification, which was developed at the Queen’s University of Belfast. The experiments were conducted on the flap of the converter, its rotation, and its interaction with the water surface. Thus, the details of the experiments are presented below based up on the experimental setup’s description [38]. In the experiment, the laboratory flume has a length of 20m and a width of 4.58m. Besides, in order to avoid incident wave reflection, a wave absorption source is devised at the end of the left flume. The flume bed, also, includes two parts with different slops. The flap position and dimensions of the flume can be seen in Figure4. In addition, a wave-maker with 6 paddles is installed at one end. At the opposite end, there is a beach with wire meshes. Additionally, there are 6 indicators to extract the water level elevation. In the flap model, there are three components: the fixed support structure, the hinge, and the flap. The flap measures 0.1m x 0.65m x 0.341m in x, y and z directions, respectively. In Figure5, the details are given [32]. The support structure consists of a 15 mm thick stainless steel base plate measuring 1m by 1.4m, which is screwed onto the bottom of the tank. The hinge is supported by three bearing blocks. There is a foam centerpiece on the front and back of the flap which is sandwiched between two PVC plates. Enabling changes of the flap, three metal fittings link the flap to the hinge. Moreover, in this experiment, the selected wave is generated based on sea wave data at scale 1:40. The wave height and the wave period are equal to 0.038 (m) and 2.0625 (s), respectively, which are tantamount to a wave with a period of 13 (s) and a height of 1.5 (m).

Two distinct graphs illustrate the numerical and experi-mental study results. Figure6 and Figure7 are denoting the angle of rotation of flap and surface elevation in computational and experimental models, respectively. The two figures roughly represent that the numerical and experimental models are a good match. However, for the purpose of verifying the match, we calculated the correlation coefficient (C) and root mean square error (RMSE). According to Figure6, correlation coefficient and RMSE are 0.998 and 0.003, respectively, and in Figure7 correlation coefficient and RMSE are respectively 0.999 and 0.001. Accordingly, there is a good match between the numerical and empirical models. It is worth mentioning that the small differences between the numerical and experimental outputs may be due to the error of the measuring devices and the calibration of the data collection devices.

Including continuity equation and momentum conserva- tion for incompressible fluid are given as [32], [39]:(1)

where P represents the pressure, g denotes gravitational acceleration, u represents fluid velocity, and Di is damping coefficient. Likewise, the model uses the same equation. to calculate the fluid velocity in other directions as well. Considering the turbulence, we use the two-equation model of RNGK- ε. These equations are:

(3)��t(��)+����(����)=����[�eff�������]+��-��and(4)���(��)+����(����)=����[�eff�������]+�1�∗����-��2��2�Where �2� and �1� are constants. In addition, �� and �� represent the turbulent Prandtl number of � and k, respectively.

�� also denote the production of turbulent kinetic energy of k under the effect of velocity gradient, which is calculated as follows:(5)��=�eff[�����+�����]�����(6)�eff=�+��(7)�eff=�+��where � is molecular viscosity,�� represents turbulence viscosity, k denotes kinetic energy, and ∊∊ is energy dissipation rate. The values of constant coefficients in the two-equation RNGK ∊-∊ model is as shown in the Table 1[40].Table 2.

Table 1. Constant coefficients in RNGK-∊ model

Factors

�

�0

�1

�2

��

��

��

Quantity

0.012

4.38

1.42

1.68

1.39

1.39

0.084

Table 2. Flap properties

Joint height (m)

0.476

Height of the center of mass (m)

0.53

Weight (Kg)

10.77

It is worth mentioning that the volume of fluid method is used to separate water and air phases in this software [41]. Below is the equation of this method [40].(8)����+����(���)=0where α and 1 − _{α} are portion of water phase and air phase, respectively. As a weighting factor, each fluid phase portion is used to determine the mixture properties. Finally, using the following equations, we calculate the efficiency of converters [42], [34], [43]:(9)�=14|�|2�+�2+(�+�a)2(�n2-�2)2where �� represents natural frequency, I denotes the inertia of OSWEC, Ia is the added inertia, F is the complex wave force, and B denotes the hydrodynamic damping coefficient. Afterward, the capture factor of the converter is calculated by [44]:(10)��=�1/2��2����gw where �� represents the capture factor, which is the total efficiency of device per unit length of the wave crest at each time step [15], �� represent the dimensional amplitude of the incident wave, w is the flap’s width, and Cg is the group velocity of the incident wave, as below:(11)��=��0·121+2�0ℎsinh2�0ℎwhere �0 denotes the wave number, h is water depth, and H is the height of incident waves.

According to previous sections ∊,����-∊ modeling is used for all models simulated in this section. For this purpose, the empty boundary condition is used for flume walls. In order to preventing wave reflection at the inlet and outlet of the flume, the length of wave absorption is set to be at least one incident wavelength. In addition, the structured mesh is chosen, and the mesh dimensions are selected in two distinct directions. In each model, all grids have a length of 2 (cm) and a height of 1 (cm). Afterwards, as an input of the software for all of the models, we define the time step as 0.001 (s). Moreover, the run time of every simulation is 30 (s). As mentioned before, our primary model is Schmitt model, and the flap properties is given in table2. For all simulations, the flume measures 15 meters in length and 0.65 meters in width, and water depth is equal to 0.335 (m). The flap is also located 7 meters from the flume’s inlet.

Finally, in order to compare the results, the capture factor is calculated for each simulation and compared to the primary model. It is worth mentioning that capture factor refers to the ratio of absorbed wave energy to the input wave energy.

According to primary model simulation and due to the decreasing horizontal velocity with depth, the wave crest has the highest velocity. Considering the fact that the wave’s orbital velocity causes the flap to move, the contact between the upper edge of the flap and the incident wave can enhance its performance. Additionally, the numerical model shows that the dynamic pressure decreases as depth increases, and the hydrostatic pressure increases as depth increases.

To determine the OSWEC design, it is imperative to understand the correlation between the capture factor, wave period, and wave height. Therefore, as it is shown in Figure8, we plot the change in capture factor over the variations in wave period and wave height in 3D and 2D. In this diagram, the first axis features changes in wave period, the second axis displays changes in wave height, and the third axis depicts changes in capture factor. According to our wave properties in the numerical model, the wave period and wave height range from 2 to 14 seconds and 2 to 8 meters, respectively. This is due to the fact that the flap does not oscillate if the wave height is less than 2 (m), and it does not reverse if the wave height is more than 8 (m). In addition, with wave periods more than 14 (s), the wavelength would be so long that it would violate the deep-water conditions, and with wave periods less than 2 (s), the flap would not oscillate properly due to the shortness of wavelength. The results of simulation are shown in Figure 8. As it can be perceived from Figure 8, in a constant wave period, the capture factor is in direct proportion to the wave height. It is because of the fact that waves with more height have more energy to rotate the flap. Besides, in a constant wave height, the capture factor increases when the wave period increases, until a given wave period value. However, the capture factor falls after this point. These results are expected since the flap’s angular displacement is not high in lower wave periods, while the oscillating motion of that is not fast enough to activate the power take-off system in very high wave periods.

As is shown in Figure 9, we plot the change in capture factor over the variations in wave period (s) and water depth (m) in 3D. As it can be seen in this diagram, the first axis features changes in water depth (m), the second axis depicts the wave period (s), and the third axis displays OSWEC’s capture factor. The wave period ranges from 0 to 10 seconds based on our wave properties, which have been adopted from Schmitt’s model, while water depth ranges from 0 to 0.5 meters according to the flume and flap dimensions and laboratory limitations. According to Figure9, for any specific water depth, the capture factor increases in a varying rate when the wave period increases, until a given wave period value. However, the capture factor falls steadily after this point. In fact, the maximum capture factor occurs when the wave period is around 6 seconds. This trend is expected since, in a specific water depth, the flap cannot oscillate properly when the wavelength is too short. As the wave period increases, the flap can oscillate more easily, and consequently its capture factor increases. However, the capture factor drops in higher wave periods because the wavelength is too large to move the flap. Furthermore, in a constant wave period, by changing the water depth, the capture factor does not alter. In other words, the capture factor does not depend on the water depth when it is around its maximum value.

^{3}. ^{Sensitivity Analysis}

Based on previous studies, in addition to the flap design, the location of the flap relative to the water surface (freeboard) and its elevation relative to the flume bed (flap bottom elevation) play a significant role in extracting energy from the wave energy converter. This study measures the sensitivity of the model to various parameters related to the flap design including upper part width of the flap, lower part width of the flap, the freeboard, and the flap bottom elevation. Moreover, as a novel idea, we propose that the flap widths differ in the lower and upper parts. In Figure10, as an example, a flap with an upper thickness of 100 (mm) and a lower thickness of 50 (mm) and a flap with an upper thickness of 50 (mm) and a lower thickness of 100 (mm) are shown. The influence of such discrepancy between the widths of the upper and lower parts on the interaction between the wave and the flap, or in other words on the capture factor, is evaluated. To do so, other parameters are remained constant, such as the freeboard, the distance between the flap and the flume bed, and the wave properties.

In Figure11, models are simulated with distinct upper and lower widths. As it is clear in this figure, the first axis depicts the lower part width of the flap, the second axis indicates the upper part width of the flap, and the colors represent the capture factor values. Additionally, in order to consider a sufficient range of change, the flap thickness varies from half to double the value of the primary model for each part.

According to this study, the greater the discrepancy in these two parts, the lower the capture factor. It is on account of the fact that when the lower part of the flap is thicker than the upper part, and this thickness difference in these two parts is extremely conspicuous, the inertia against the motion is significant at zero degrees of rotation. Consequently, it is difficult to move the flap, which results in a low capture factor. Similarly, when the upper part of the flap is thicker than the lower part, and this thickness difference in these two parts is exceedingly noticeable, the inertia is so great that the flap can not reverse at the maximum degree of rotation. As the results indicate, the discrepancy can enhance the performance of the converter if the difference between these two parts is around 20%. As it is depicted in the Figure11, the capture factor reaches its own maximum amount, when the lower part thickness is from 5 to 6 (cm), and the upper part thickness is between 6 and 7 (cm). Consequently, as a result of this discrepancy, less material will be used, and therefore there will be less cost.

As illustrated in Figure12, this study examines the effects of freeboard (level difference between the flap top and water surface) and the flap bottom elevation (the distance between the flume bed and flap bottom) on the converter performance. In this diagram, the first axis demonstrates the freeboard and the second axis on the left side displays the flap bottom elevation, while the colors indicate the capture factor. In addition, the feasible range of freeboard is between -15 to 15 (cm) due to the limitation of the numerical model, so that we can take the wave slamming and the overtopping into consideration. Additionally, based on the Schmitt model and its scaled model of 1:40 of the base height, the flap bottom should be at least 9 (cm) high. Since the effect of surface waves is distributed over the depth of the flume, it is imperative to maintain a reasonable flap height exposed to incoming waves. Thus, the maximum flap bottom elevation is limited to 19 (cm). As the Figure12 pictures, at constant negative values of the freeboard, the capture factor is in inverse proportion with the flap bottom elevation, although slightly.

Furthermore, at constant positive values of the freeboard, the capture factor fluctuates as the flap bottom elevation decreases while it maintains an overall increasing trend. This is on account of the fact that increasing the flap bottom elevation creates turbulence flow behind the flap, which encumbers its rotation, as well as the fact that the flap surface has less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, the capture factor increases by raising the freeboard. This is due to the fact that there is overtopping with adverse impacts on the converter performance when the freeboard is negative and the flap is under the water surface. Besides, increasing the freeboard makes the wave slam more vigorously, which improves the converter performance.

Adding ribs to the flap surface, as shown in Figure13, is a novel idea that is investigated in the next section. To achieve an optimized design for the proposed geometry of the flap, we determine the optimal number and dimensions of ribs based on the flap properties as our decision variables in the optimization process. As an example, Figure13 illustrates a flap with 3 ribs on each side with specific dimensions.

Figure14 shows the flow velocity field around the flap jointed to the flume bed. During the oscillation of the flap, the pressure on the upper and lower surfaces of the flap changes dynamically due to the changing angle of attack and the resulting change in the direction of fluid flow. As the flap moves upwards, the pressure on the upper surface decreases, and the pressure on the lower surface increases. Conversely, as the flap moves downwards, the pressure on the upper surface increases, and the pressure on the lower surface decreases. This results in a cyclic pressure variation around the flap. Under certain conditions, the pressure field around the flap can exhibit significant variations in magnitude and direction, forming vortices and other flow structures. These flow structures can affect the performance of the OSWEC by altering the lift and drag forces acting on the flap.

^{4}. ^{Design Optimization}

We consider optimizing the design parameters of the flap of converter using a nature-based swarm optimization method, that fall in the category of metaheuristic algorithms [45]. Accordingly, we choose four state-of-the-art algorithms to perform an optimization study. Then, based on their performances to achieve the highest capture factor, one of them will be chosen to be combined with the Hill Climb algorithm to carry out a local search. Therefore, in the remainder of this section, we discuss the search process of each algorithm and visualize their performance and convergence curve as they try to find the best values for decision variables.

4.1. Metaheuristic Approaches

As the first considered algorithm, the Gray Wolf Optimizer (GWO) algorithm simulates the natural leadership and hunting performance of gray wolves which tend to live in colonies. Hunters must obey the alpha wolf, the leader, who is responsible for hunting. Then, the beta wolf is at the second level of the gray wolf hierarchy. A subordinate of alpha wolf, beta stands under the command of the alpha. At the next level in this hierarchy, there are the delta wolves. They are subordinate to the alpha and beta wolves. This category of wolves includes scouts, sentinels, elders, hunters, and caretakers. In this ranking, omega wolves are at the bottom, having the lowest level and obeying all other wolves. They are also allowed to eat the prey just after others have eaten. Despite the fact that they seem less important than others, they are really central to the pack survival. Since, it has been shown that without omega wolves, the entire pack would experience some problems like fighting, violence, and frustration. In this simulation, there are three primary steps of hunting including searching, surrounding, and finally attacking the prey. Mathematically model of gray wolves’ hunting technique and their social hierarchy are applied in determined by optimization. this study. As mentioned before, gray wolves can locate their prey and surround them. The alpha wolf also leads the hunt. Assuming that the alpha, beta, and delta have more knowledge about prey locations, we can mathematically simulate gray wolf hunting behavior. Hence, in addition to saving the top three best solutions obtained so far, we compel the rest of the search agents (also the omegas) to adjust their positions based on the best search agent. Encircling behavior can be mathematically modeled by the following equations: [46].(12)�→=|�→·��→(�)-�→(�)|(13)�→(�+1)=��→(�)-�→·�→(14)�→=2.�2→(15)�→=2�→·�1→-�→Where �→indicates the position vector of gray wolf, ��→ defines the vector of prey, t indicates the current iteration, and �→and �→are coefficient vectors. To force the search agent to diverge from the prey, we use �→ with random values greater than 1 or less than -1. In addition, C→ contains random values in the range [0,2], and �→ _{1} and �2→ are random vectors in [0,1]. The second considered technique is the Moth Flame Optimizer (MFO) algorithm. This method revolves around the moths’ navigation mechanism, which is realized by positioning themselves and maintaining a fixed angle relative to the moon while flying. This effective mechanism helps moths to fly in a straight path. However, when the source of light is artificial, maintaining an angle with the light leads to a spiral flying path towards the source that causes the moth’s death [47]. In MFO algorithm, moths and flames are both solutions. The moths are actual search agents that fly in hyper-dimensional space by changing their position vectors, and the flames are considered pins that moths drop when searching the search space [48]. The problem’s variables are the position of moths in the space. Each moth searches around a flame and updates it in case of finding a better solution. The fitness value is the return value of each moth’s fitness (objective) function. The position vector of each moth is passed to the fitness function, and the output of the fitness function is assigned to the corresponding moth. With this mechanism, a moth never loses its best solution [49]. Some attributes of this algorithm are as follows:

•It takes different values to converge moth in any point around the flame.

•Distance to the flame is lowered to be eventually minimized.

•When the position gets closer to the flame, the updated positions around the flame become more frequent.

As another method, the Multi-Verse Optimizer is based on a multiverse theory which proposes there are other universes besides the one in which we all live. According to this theory, there are more than one big bang in the universe, and each big bang leads to the birth of a new universe [50]. Multi-Verse Optimizer (MVO) is mainly inspired by three phenomena in cosmology: white holes, black holes, and wormholes. A white hole has never been observed in our universe, but physicists believe the big bang could be considered a white hole [51]. Black holes, which behave completely in contrast to white holes, attract everything including light beams with their extremely high gravitational force [52]. In the multiverse theory, wormholes are time and space tunnels that allow objects to move instantly between any two corners of a universe (or even simultaneously from one universe to another) [53]. Based on these three concepts, mathematical models are designed to perform exploration, exploitation, and local search, respectively. The concept of white and black holes is implied as an exploration phase, while the concept of wormholes is considered as an exploitation phase by MVO. Additionally, each solution is analogous to a universe, and each variable in the solution represents an object in that universe. Furthermore, each solution is assigned an inflation rate, and the time is used instead of iterations. Following are the universe rules in MVO:

•The possibility of having white hole increases with the inflation rate.

•The possibility of having black hole decreases with the inflation rate.

•Objects tend to pass through black holes more frequently in universes with lower inflation rates.

•Regardless of inflation rate, wormholes may cause objects in universes to move randomly towards the best universe. [54]

Modeling the white/black hole tunnels and exchanging objects of universes mathematically was accomplished by using the roulette wheel mechanism. With every iteration, the universes are sorted according to their inflation rates, then, based on the roulette wheel, the one with the white hole is selected as the local extremum solution. This is accomplished through the following steps:

Assume that

(16)���=����1<��(��)����1≥��(��)

Where ��� represents the jth parameter of the ith universe, Ui indicates the ith universe, NI(Ui) is normalized inflation rate of the ith universe, r1 is a random number in [0,1], and j x_{k} shows the jth parameter of the kth universe selected by a roulette wheel selection mechanism [54]. It is assumed that wormhole tunnels always exist between a universe and the best universe formed so far. This mechanism is as follows:(17)���=if�2<���:��+���×((���-���)×�4+���)�3<0.5��-���×((���-���)×�4+���)�3≥0.5����:���where Xj indicates the jth parameter of the best universe formed so far, TDR and WEP are coefficients, where Xj indicates the jth parameter of the best universelbjshows the lower bound of the jth variable, ubj is the upper bound of the jth variable, and r2, r3, and r4 are random numbers in [1], [54].

Finally, one of the newest optimization algorithms is WOA. The WOA algorithm simulates the movement of prey and the whale’s discipline when looking for their prey. Among several species, Humpback whales have a specific method of hunting [55]. Humpback whales can recognize the location of prey and encircle it before hunting. The optimal design position in the search space is not known a priori, and the WOA algorithm assumes that the best candidate solution is either the target prey or close to the optimum. This foraging behavior is called the bubble-net feeding method. Two maneuvers are associated with bubbles: upward spirals and double loops. A unique behavior exhibited only by humpback whales is bubble-net feeding. In fact, The WOA algorithm starts with a set of random solutions. At each iteration, search agents update their positions for either a randomly chosen search agent or the best solution obtained so far [56], [55]. When the best search agent is determined, the other search agents will attempt to update their positions toward that agent. It is important to note that humpback whales swim around their prey simultaneously in a circular, shrinking circle and along a spiral-shaped path. By using a mathematical model, the spiral bubble-net feeding maneuver is optimized. The following equation represents this behavior:(18)�→(�+1)=�′→·�bl·cos(2��)+�∗→(�)

Where:(19)�′→=|�∗→(�)-�→(�)|

X→_{(t}_{+ 1)} indicates the distance of the it h whale to the prey (best solution obtained so far),� is a constant for defining the shape of the logarithmic spiral, l is a random number in [−1_{,}_{1]}, and dot (.) is an element-by-element multiplication [55].

Comparing the four above-mentioned methods, simulations are run with 10 search agents for 400 iterations. In Figure 15, there are 20 plots the optimal values of different parameters in optimization algorithms. The five parameters of this study are freeboard, bottom elevations, number of ribs on the converter, rib thickness, and rib Height. The optimal value for each was found by optimization algorithms, naming WOA, MVO, MFO, and GWO. By looking through the first row, the freeboard parameter converges to its maximum possible value in the optimization process of GWO after 300 iterations. Similarly, MFO finds the same result as GWO. In contrast, the freeboard converges to its minimum possible value in MVO optimizing process, which indicates positioning the converter under the water. Furthermore, WOA found the optimal value of freeboard as around 0.02 after almost 200 iterations. In the second row, the bottom elevation is found at almost 0.11 (m) in all algorithms; however, the curves follow different trends in each algorithm. The third row shows the number of ribs, where results immediately reveal that it should be over 4. All algorithms coincide at 5 ribs as the optimal number in this process. The fourth row displays the trends of algorithms to find optimal rib thickness. MFO finds the optimal value early and sets it to around 0.022, while others find the same value in higher iterations. Finally, regarding the rib height, MVO, MFO, and GWO state that the optimal value is 0.06 meters, but WOA did not find a higher value than 0.039.

4.2. HCMVO Bi-level Approach

Despite several strong search characteristics of MVO and its high performance in various optimization problems, it suffers from a few deficiencies in local and global search mechanisms. For instance, it is trapped in the local optimum when wormholes stochastically generate many solutions near the best universe achieved throughout iterations, especially in solving complex multimodal problems with high dimensions [57]. Furthermore, MVO needs to be modified by an escaping strategy from the local optima to enhance the global search abilities. To address these shortages, we propose a fast and effective meta-algorithm (HCMVO) to combine MVO with a Random-restart hill-climbing local search. This meta-algorithm uses MVO on the upper level to develop global tracking and provide a range of feasible and proper solutions. The hill-climbing algorithm is designed to develop a comprehensive neighborhood search around the best-found solution proposed by the upper-level (MVO) when MVO is faced with a stagnation issue or falling into a local optimum. The performance threshold is formulated as follows.(20)Δ����THD=∑�=1�����TH��-����TH��-1�where BestTHDis the best-found solution per generation, andM is related to the domain of iterations to compute the average performance of MVO. If the proposed best solution by the local search is better than the initial one, the global best of MVO will be updated. HCMVO iteratively runs hill climbing when the performance of MVO goes down, each time with an initial condition to prepare for escaping such undesirable situations. In order to get a better balance between exploration and exploitation, the search step size linearly decreases as follows:(21)��=��-����Ma�iter��+1where iter and Maxiter are the current iteration and maximum number of evaluation, respectively. �� stands for the step size of the neighborhood search. Meanwhile, this strategy can improve the convergence rate of MVO compared with other algorithms.

Algorithm 1 shows the technical details of the proposed optimization method (HCMVO). The initial solution includes freeboard (�), bottom elevation (�), number of ribs (Nr), rib thickness (�), and rib height(�).

5. Conclusion

The high trend of diminishing worldwide energy resources has entailed a great crisis upon vulnerable societies. To withstand this effect, developing renewable energy technologies can open doors to a more reliable means, among which the wave energy converters will help the coastal residents and infrastructure. This paper set out to determine the optimized design for such devices that leads to the highest possible power output. The main goal of this research was to demonstrate the best design for an oscillating surge wave energy converter using a novel metaheuristic optimization algorithm. In this regard, the methodology was devised such that it argued the effects of influential parameters, including wave characteristics, WEC design, and interaction criteria.

To begin with, a numerical model was developed in Flow 3D software to simulate the response of the flap of a wave energy converter to incoming waves, followed by a validation study based upon a well-reputed experimental study to verify the accuracy of the model. Secondly, the hydrodynamics of the flap was investigated by incorporating the turbulence. The effect of depth, wave height, and wave period are also investigated in this part. The influence of two novel ideas on increasing the wave-converter interaction was then assessed: i) designing a flap with different widths in the upper and lower part, and ii) adding ribs on the surface of the flap. Finally, four trending single-objective metaheuristic optimization methods

Empty Cell

Algorithm 1:Hill Climb Multiverse Optimization

01:

procedure HCMVO

02:

�=30,�=5▹���������������������������������

03:

�=〈F1,B1,N,R,H1〉,…〈FN,B2,N,R,HN〉⇒lb1N⩽�⩽ubN

04:

Initialize parameters�ER,�DR,�EP,Best�,���ite��▹Wormhole existence probability (WEP)

05:

��=����(��)

06:

��=Normalize the inflation rate��

07:

for iter in[1,⋯,���iter]do

08:

for�in[1,⋯,�]do

09:

Update�EP,�DR,Black����Index=�

10:

for���[1,⋯,�]��

11:

�1=����()

12:

if�1≤��(��)then

13:

White HoleIndex=Roulette�heelSelection(-��)

14:

�(Black HoleIndex,�)=��(White HoleIndex,�)

15:

end if

16:

�2=����([0,�])

17:

if�2≤�EPthen

18:

�3=����(),�4=����()

19:

if�3<0.5then

20:

�1=((��(�)-��(�))×�4+��(�))

21:

�(�,�)=Best�(�)+�DR×�

22:

else

23:

�(�,�)=Best�(�)-�DR×�

24:

end if

25:

end if

26:

end for

27:

end for

28:

�HD=����([�1,�2,⋯,�Np])

29:

Bes�TH�itr=����HD

30:

ΔBestTHD=∑�=1�BestTII��-BestTII��-1�

31:

ifΔBestTHD<��then▹Perform hill climbing local search

32:

BestTHD=����-�lim��������THD

33:

end if

34:

end for

35:

return�,BestTHD▹Final configuration

36:

end procedure

The implementation details of the hill-climbing algorithm applied in HCMPA can be seen in Algorithm 2. One of the critical parameters isg, which denotes the resolution of the neighborhood search around the proposed global best by MVO. If we set a small step size for hill-climbing, the convergence speed will be decreased. On the other hand, a large step size reinforces the exploration ability. Still, it may reduce the exploitation ability and in return increase the act of jumping from a global optimum or surfaces with high-potential solutions. Per each decision variable, the neighborhood search evaluates two different direct searches, incremental or decremental. After assessing the generated solutions, the best candidate will be selected to iterate the search algorithm. It is noted that the hill-climbing algorithm should not be applied in the initial iteration of the optimization process due to the immense tendency for converging to local optima. Meanwhile, for optimizing largescale problems, hill-climbing is not an appropriate selection. In order to improve understanding of the proposed hybrid optimization algorithm’s steps, the flowchart of HCMVO is designed and can be seen in Figure 16.

Figure 17 shows the observed capture factor (which is the absorbed energy with respect to the available energy) by each optimization algorithm from iterations 1 to 400. The algorithms use ten search agents in their modified codes to find the optimal solutions. While GWO and MFO remain roughly constant after iterations 54 and 40, the other three algorithms keep improving the capture factor. In this case, HCMVO and MVO worked very well in the optimizing process with a capture factor obtained by the former as 0.594 and by the latter as 0.593. MFO almost found its highest value before the iteration 50, which means the exploration part of the algorithm works out well. Similarly, HCMVO does the same. However, it keeps finding the better solution during the optimization process until the last iteration, indicating the strong exploitation part of the algorithm. GWO reveals a weakness in exploration and exploitation because not only does it evoke the least capture factor value, but also the curve remains almost unchanged throughout 350 iterations.

Figure 18 illustrates complex interactions between the five optimization parameters and the capture factor for HCMVO (a), MPA (b), and MFO (c) algorithms. The first interesting observation is that there is a high level of nonlinear relationships among the setting parameters that can make a multi-modal search space. The dark blue lines represent the best-found configuration throughout the optimisation process. Based on both HCMVO (a) and MVO (b), we can infer that the dark blue lines concentrate in a specific range, showing the high convergence ability of both HCMVO and MVO. However, MFO (c) could not find the exact optimal range of the decision variables, and the best-found solutions per generation distribute mostly all around the search space.

Empty Cell

Algorithm 1:Hill Climb Multiverse Optimization

01:

procedure HCMVO

02:

Initialization

03:

Initialize the constraints��1�,��1�

04:

�1�=Mi�1�+���1�/�▹Compute the step size,�is search resolution

were utilized to illuminate the optimum values of the design parameters, and the best method was chosen to develop a new algorithm that performs both local and global search methods.

The correlation between hydrodynamic parameters and the capture factor of the converter was supported by the results. For any given water depth, the capture factor increases as the wave period increases, until a certain wave period value (6 seconds) is reached, after which the capture factor gradually decreases. It is expected since the flap cannot oscillate effectively when the wavelength is too short for a certain water depth. Conversely, when the wavelength is too long, the capture factor decreases. Furthermore, under a constant wave period, increasing the water depth does not affect the capture factor. Regarding the sensitivity analysis, the study found that increasing the flap bottom elevation causes turbulence flow behind the flap and limitation of rotation, which leads to less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, increasing the freeboard improves the capture factor. Overtopping hap