The failure propagation of weakly stable sediment: A reason for the formation of high-velocity turbidity currents in submarine canyons

약한 안정 퇴적물의 실패 전파: 해저 협곡에서 고속 탁도 흐름이 형성되는 이유

Abstract

Abstract해저 협곡에서 탁도의 장거리 이동은 많은 양의 퇴적물을 심해 평원으로 운반할 수 있습니다. 이전 연구에서는 5.9~28.0m/s 범위의 다중 케이블 손상 이벤트에서 파생된 탁도 전류 속도와 0.15~7.2m/s 사이의 현장 관찰 결과에서 명백한 차이가 있음을 보여줍니다. 따라서 해저 환경의 탁한 유체가 해저 협곡을 고속으로 장거리로 흐를 수 있는지에 대한 질문이 남아 있습니다. 연구실 시험의 결합을 통해 해저협곡의 탁류의 고속 및 장거리 운동을 설명하기 위해 약안정 퇴적물 기반의 새로운 모델(약안정 퇴적물에 대한 파손 전파 모델 제안, 줄여서 WSS-PFP 모델)을 제안합니다. 및 수치 아날로그. 이 모델은 두 가지 메커니즘을 기반으로 합니다. 1) 원래 탁도류는 약하게 안정한 퇴적층의 불안정화를 촉발하고 연질 퇴적물의 불안정화 및 하류 방향으로의 이동을 촉진하고 2) 원래 탁도류가 협곡으로 이동할 때 형성되는 여기파가 불안정화로 이어진다. 하류 방향으로 약하게 안정한 퇴적물의 수송. 제안된 모델은 심해 퇴적, 오염 물질 이동 및 광 케이블 손상 연구를 위한 동적 프로세스 해석을 제공할 것입니다.

The long-distance movement of turbidity currents in submarine canyons can transport large amounts of sediment to deep-sea plains. Previous studies show obvious differences in the turbidity current velocities derived from the multiple cables damage events ranging from 5.9 to 28.0 m/s and those of field observations between 0.15 and 7.2 m/s. Therefore, questions remain regarding whether a turbid fluid in an undersea environment can flow through a submarine canyon for a long distance at a high speed. A new model based on weakly stable sediment is proposed (proposed failure propagation model for weakly stable sediments, WSS-PFP model for short) to explain the high-speed and long-range motion of turbidity currents in submarine canyons through the combination of laboratory tests and numerical analogs. The model is based on two mechanisms: 1) the original turbidity current triggers the destabilization of the weakly stable sediment bed and promotes the destabilization and transport of the soft sediment in the downstream direction and 2) the excitation wave that forms when the original turbidity current moves into the canyon leads to the destabilization and transport of the weakly stable sediment in the downstream direction. The proposed model will provide dynamic process interpretation for the study of deep-sea deposition, pollutant transport, and optical cable damage.

Keyword

  • turbidity current
  • excitation wave
  • dense basal layer
  • velocity
  • WSS-PFP model

References

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Acknowledgment

We thank Hanru WU from Ocean University of China for his help in thesis writing, and Hao TIAN and Chenxi WANG from Ocean University of China for their helps in the preparation of the experimental materials. Guohui XU is responsible for the development of the initial concept, processing of test data, and management of coauthor contributions to the paper; Yupeng REN for the experiment setup and drafting of the paper; Yi ZHANG and Xingbei XU for the simulation part of the experiment; Houjie WANG for writing guidance; Zhiyuan CHEN for the experiment setup.

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Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Qingdao, 266100, ChinaYupeng Ren, Yi Zhang, Guohui Xu, Xingbei Xu & Zhiyuan Chen
  2. Shandong Provincial Key Laboratory of Marine Environment and Geological Engineering, Ocean University of China, Qingdao, 266100, ChinaYupeng Ren & Houjie Wang
  3. Key Laboratory of Marine Environment and Ecology, Ocean University of China, Ministry of Education, Qingdao, 266100, ChinaYi Zhang, Guohui Xu, Xingbei Xu & Zhiyuan Chen

Corresponding author

Correspondence to Guohui Xu.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 41976049, 41720104001) and the Taishan Scholar Project of Shandong Province (No. TS20190913), and the Fundamental Research Funds for the Central Universities (No. 202061028)

Data Availability Statement

The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Ren, Y., Zhang, Y., Xu, G. et al. The failure propagation of weakly stable sediment: A reason for the formation of high-velocity turbidity currents in submarine canyons. J. Ocean. Limnol. (2022). https://doi.org/10.1007/s00343-022-1285-0

Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.

Numerical study of the dam-break waves and Favre waves down sloped wet rigid-bed at laboratory scale

WenjunLiuaBoWangaYakunGuobaState Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, ChinabFaculty of Engineering & Informatics, University of Bradford, BD7 1DP, UK

Highlights

경사진 습윤층에서 댐파괴유동과 FFavre 파를 수치적으로 조사하였다.
수직 대 수평 속도의 비율이 먼저 정량화됩니다.
유동 상태는 유상 경사가 큰 후기 단계에서 크게 변경됩니다.
Favre 파도는 수직 속도와 수직 가속도에 큰 영향을 미칩니다.
베드 전단응력의 변화는 베드 기울기와 꼬리물의 영향을 받습니다.

Abstract

The bed slope and the tailwater depth are two important ones among the factors that affect the propagation of the dam-break flood and Favre waves. Most previous studies have only focused on the macroscopic characteristics of the dam-break flows or Favre waves under the condition of horizontal bed, rather than the internal movement characteristics in sloped channel. The present study applies two numerical models, namely, large eddy simulation (LES) and shallow water equations (SWEs) models embedded in the CFD software package FLOW-3D to analyze the internal movement characteristics of the dam-break flows and Favre waves, such as water level, the velocity distribution, the fluid particles acceleration and the bed shear stress, under the different bed slopes and water depth ratios. The results under the conditions considered in this study show that there is a flow state transition in the flow evolution for the steep bed slope even in water depth ratio α = 0.1 (α is the ratio of the tailwater depth to the reservoir water depth). The flow state transition shows that the wavefront changes from a breaking state to undular. Such flow transition is not observed for the horizontal slope and mild bed slope. The existence of the Favre waves leads to a significant increase of the vertical velocity and the vertical acceleration. In this situation, the SWEs model has poor prediction. Analysis reveals that the variation of the maximum bed shear stress is affected by both the bed slope and tailwater depth. Under the same bed slope (e.g., S0 = 0.02), the maximum bed shear stress position develops downstream of the dam when α = 0.1, while it develops towards the end of the reservoir when α = 0.7. For the same water depth ratio (e.g., α = 0.7), the maximum bed shear stress position always locates within the reservoir at S0 = 0.02, while it appears in the downstream of the dam for S0 = 0 and 0.003 after the flow evolves for a while. The comparison between the numerical simulation and experimental measurements shows that the LES model can predict the internal movement characteristics with satisfactory accuracy. This study improves the understanding of the effect of both the bed slope and the tailwater depth on the internal movement characteristics of the dam-break flows and Favre waves, which also provides a valuable reference for determining the flood embankment height and designing the channel bed anti-scouring facility.

Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 1. Sketch of related variables involved in shallow water model.
Fig. 2. Flume model in numerical simulation.
Fig. 2. Flume model in numerical simulation.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 3. Grid sensitivity analysis (a) water surface profile; (b) velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 4. Sketch of experimental set-up for validating the velocity profile.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 5. Sketch of experimental set-up for validating the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 6. Model validation results (a) variation of the velocity profile; (b) error value of the velocity profile; (c) variation of the bed shear stress; (d) error value of the bed shear stress.
Fig. 7. Schematic diagram of regional division.
Fig. 7. Schematic diagram of regional division.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. Variation of water surface profile (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 8. (continued).
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 9. Froude number for α = 0.1 (a) variation with time; (b) variation with wavefront position.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 10. Characteristics of velocity distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 11. Average proportion of the vertical velocity (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. Bed shear stress distribution (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 12. (continued).
Fig. 12. (continued).
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 13. Variation of the maximum bed shear stress position with time (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 14. Time when the maximum bed shear stress appears at different positions (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. Movement characteristics of the fluid particles (a) α = 0.1; (b) α = 0.3; (c) α = 0.5; (d) α = 0.7.
Fig. 15. (continued).
Fig. 15. (continued).

Keywords

Dam-break flow, Bed slope, Wet bed, Velocity profile, Bed shear stress, Large eddy simulation

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Figure 9. Turbulent kinetic energy (TKE) contour map on different sections.

Numerical Simulation Research on the Diversion
Characteristics of a Trapezoidal Channel

Yong Cheng, Yude Song, Chunye Liu, Wene Wang * and Xiaotao Hu
Key Laboratory of Agricultural Soil and Water Engineering in Arid and Semiarid Areas, Ministry of Education, Northwest A&F University, Yangling 712100, China

  • Correspondence: wangwene@nwsuaf.edu.cn

Abstract

개방 채널 분기점은 관개 지역에서 가장 일반적인 물 전환 구조입니다. 관개용수 운반에서는 물 운반 효율과 침전이 주요 관심사입니다. 따라서 이 연구는 관개 지역의 물 공급에 대한 개방 채널 분기점의 영향을 분석합니다.

여기에서 FLOW-3D 소프트웨어를 사용하고 15 세트의 작업 조건을 포함하는 수치 시뮬레이션을 통해 개방 채널 분기점에서의 3차원 유동을 연구했습니다. 개수로 분기점 부근의 재순환 구역 및 유동 구조의 수리학적 특성을 분석하였다.

그런 다음 사다리꼴 채널에서 표면 및 바닥층의 흐름 전환 폭에 대한 방정식을 얻었습니다. 수심에 따른 흐름 전환 폭은 사다리꼴 채널과 직사각형 채널에서 다른 것으로 나타났습니다. 결과는 또한 개방 수로 분기점이 주 수로의 유속에 상당한 영향을 미친다는 것을 보여줍니다.

개방 채널 분기점의 재순환 영역에서의 유속은 작았지만 맥동 속도와 난류 운동 에너지는 컸다. 이 지역에서 소산되는 에너지는 상대적으로 커서 수로 물 전달에 도움이 되지 않았습니다.

이 연구는 관개구역의 수로 최적화 및 운영 관리에 대한 참고 자료를 제공합니다.

Open-channel bifurcations are the most common water diversion structures in irrigation districts. In irrigation water conveyance, water transport efficiency and sedimentation are primary concerns. This study accordingly analyzes the influence of open-channel bifurcations on water delivery in irrigation areas. Herein, the three-dimensional flow at an open-channel bifurcation was studied via numerical simulations using FLOW-3D software and including 15 sets of working conditions. The hydraulic characteristics of the recirculation zone and flow structures in the vicinity of the open-channel bifurcation were analyzed. Equations for the flow diversion width of the surface and bottom layers in the trapezoidal channel were then obtained. The flow diversion widths along the water depth were found to differ between trapezoidal and rectangular channels. The results also show that open-channel bifurcations considerably influence the flow velocity in the main channel. The flow velocity in the recirculation zone of open-channel bifurcations was small, but the pulsation velocity and the turbulent kinetic energy were large. The energy dissipated in this area was relatively large, which was not conducive to channel water delivery. This study provides a reference for channel optimization and operation management in irrigation districts.

Keywords

trapezoidal open channel; numerical simulation; the recirculation zone; flow diversion
width; turbulence kinetic energy

Figure 1. Experimental plan and section measurement layout. Note: Red points in the figure represent the measurement point arrangement, and Roman numerals represent measurement section numbers.
Figure 1. Experimental plan and section measurement layout. Note: Red points in the figure represent the measurement point arrangement, and Roman numerals represent measurement section numbers.
Figure 5. Froude number (Fr) contour map at different water depths. Note: Q1 = 40 L/s; b = 30 cm. X* and Y* are obtained by dimensionless processing of X-axis and Y-axis coordinates. (a) depth of water below the sill height; (b) depth of water above the sill height.
Figure 5. Froude number (Fr) contour map at different water depths. Note: Q1 = 40 L/s; b = 30 cm. X* and Y* are obtained by dimensionless processing of X-axis and Y-axis coordinates. (a) depth of water below the sill height; (b) depth of water above the sill height.
Figure 1 Mitochondrial Weir Dam

The Three-dimensional Simulation of Granular
Mixtures Weir

Shen Zhen-dong*1, 2, Zhang Yang1, 2
1Zhejiang Guangchuan Engineering Consultation Co., Ltd., Hangzhou, 310020,
Zhejiang, China
2Zhejiang Institute of Hydraulics &Estuary, Hangzhou 310020, Zhejiang, China
E-mail: zdshen1991@126.com

Abstract

최근 몇 년 동안 생태학적 수자원 보존 공학의 발전으로 많은 새로운 댐 디자인이 등장했습니다. 본 논문에서는 체계적인 소면보 연구와 조사를 바탕으로 새로운 종류의 입상 혼합물 위어를 제시하였습니다.

입상보의 수치해석은 Flow-3D를 이용하여 수행하였으며, 그 결과를 물리적 모델 실험결과와 비교하였습니다. 유속, 유속 분포 및 둑의 파손에 대한 수치 시뮬레이션 결과는 실험 결과와 잘 일치하며, 이는 3차원 수학적 모델이 물리적 모델 실험과 결합되어 모든 입상 혼합물 둑을 시뮬레이션할 수 있음을 나타냅니다.

이 방법을 이용하여 특성 및 수리학적 매개변수를 분석하면 생태보의 후속 연구를 위한 기술적 지원을 제공할 수 있습니다.

In recent years, with the development of ecological water conservancy engineering,
many new weir designs have also emerged. This paper has put forward a new kind of granular
mixtures weir based on the systematic carding weir researches, combined with investigation. The
numerical simulation of granular weir is carried out by using Flow-3D,and the results are
compared with the physical model experiment results. The numerical simulation results of the
flow velocity, flow distribution and the failure of the weir are in good agreement with the
experimental results, which indicates that the 3-D mathematical model can be combined with
physical model experiments to simulate the granular mixtures weir in all directions. Using this
method to analysis the characteristics and hydraulic parameters can provide technical support
for the follow-up research of ecological weir.

Figure 1 Mitochondrial Weir Dam
Figure 1 Mitochondrial Weir Dam
Table 1 Numerical simulation programme table
Table 1 Numerical simulation programme table
Figure 4 Final Damage of Weir in Different Projects
Figure 4 Final Damage of Weir in Different Projects

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Fig. 9. Simulated separation regions for surface mounted cylinder

Investigation on the Local Scour Beneath Piggyback Pipelines Under Clear-Water Conditions

China Ocean Engineering volume 35, pages422–431 (2021)Cite this article

Abstract

피기백 파이프라인은 2개의 파이프로 구성되어 2차 라인이 2개의 파이프 사이의 길이가 고정된 거리로 메인 파이프에 탑승합니다. 새로운 전략은 단일 흐름 라인 대신 연안 지역에서 활용됩니다.

이와 관련하여 정상 전류에서 피기백 파이프라인 아래의 세굴 효과를 조사하는 실험 및 수치 연구는 소수에 불과합니다. 따라서 본 연구에서는 수치모사 및 실험적 실험을 통해 관직경, 관간격 등 정류에 의한 세굴에 영향을 미치는 요인을 살펴보고자 합니다.

따라서 연구의 첫 번째 단계에서 단일 파이프를 설치하고 실험식의 결과와 결과를 비교하기 위해 실험실에서 테스트했습니다. 실험적 검증을 마친 후, 피기백 파이프라인도 조립하여 안정된 전류 조건에서 정련을 연구했습니다. 파이프 사이의 간격을 늘리면 최대 세굴 깊이가 감소한다는 결론이 내려졌습니다.

그러나 작은 파이프의 직경이 증가하면 최대 세굴 깊이가 커집니다. 둘째, 본 연구의 수치적 조사에 적합한 도구인 FLOW-3D 소프트웨어를 사용하여 수치해석을 수행하였습니다.

마지막으로, 수치 결과를 해당 실험 데이터와 비교했으며, 이들 사이에 비교적 좋은 일치가 달성되었습니다.

A piggyback pipeline consists of two pipes such that the secondary line rides on the main pipe with a fixed distance between two pipes in length. The novel strategy is utilized in offshore areas instead of a single flow line. In this regard, there are only a handful of experimental and numerical studies investigating the effect of scour below a piggyback pipeline under steady current. Hence, this study focuses on examining the influential factors on scouring due to steady current including the pipe diameter and the gap between pipes through numerical simulations and experimental tests. Accordingly, at the first phase of the research, a single pipe was established and tested in laboratory to compare the results with those of an empirical equation. After finishing experimental verifications, piggyback pipelines were also assembled to study the scouring under steady current conditions. It was concluded that by increasing the gap distance between the pipes, the maximum scour depth decreases; however, an increase in the small pipe’s diameter results in a larger maximum scour depth. Secondly, numerical simulations were carried out using the FLOW-3D software which was found to be a suitable tool for the numerical investigation of this study. Finally, the numerical results have been compared with the corresponding experimental data and a relatively good agreement was achieved between them.

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Fig. 1.   (a) Arrangement of piggyback pipeline, (b) Plan view of experimental flume.
Fig. 1. (a) Arrangement of piggyback pipeline, (b) Plan view of experimental flume.
Fig. 3.   Initial photos of two mounted piggyback pipelines in experimental setup for d/D=0.25.
Fig. 3. Initial photos of two mounted piggyback pipelines in experimental setup for d/D=0.25.
Fig. 9.     Simulated  separation  regions  for  surface  mounted  cylinder
Fig. 9. Simulated separation regions for surface mounted cylinder

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Flow Field in a Sloped Channel with Damaged and Undamaged Piers: Numerical and Experimental Studies

Flow Field in a Sloped Channel with Damaged and Undamaged Piers: Numerical and Experimental Studies

Ehsan OveiciOmid Tayari & Navid Jalalkamali
KSCE Journal of Civil Engineering volume 25, pages4240–4251 (2021)Cite this article

Abstract

본 논문은 경사가 완만한 수로에서 손상되거나 손상되지 않은 교각 주변의 유동 패턴을 분석했습니다. 실험은 길이가 12m이고 기울기가 0.008인 직선 수로에서 수행되었습니다. Acoustic Doppler Velocimeter(ADV)를 이용하여 3차원 유속 데이터를 수집하였고, 그 결과를 PIV(Particle Image Velocimetry) 데이터와 분석하여 비교하였습니다.

다중 블록 옵션이 있는 취수구의 퇴적물 시뮬레이션(SSIIM)은 이 연구에서 흐름의 수치 시뮬레이션을 위해 통합되었습니다. 일반적으로 비교에서 얻은 결과는 수치 데이터와 실험 데이터 간의 적절한 일치를 나타냅니다. 결과는 모든 경우에 수로 입구에서 2m 거리에서 기복적 수압 점프가 발생했음을 보여주었습니다.

경사진 수로의 최대 베드 전단응력은 2개의 손상 및 손상되지 않은 교각을 설치하기 위한 수평 수로의 12배였습니다. 이와 같은 경사수로 교각의 위치에 따라 상류측 수위는 수평수로의 유사한 조건에 비해 72.5% 감소한 반면, 이 감소량은 경사면에서 다른 경우에 비해 8.3% 감소하였다. 채널 또한 두 교각이 있는 경우 최대 Froude 수는 수평 수로의 5.7배였습니다.

This paper analyzed the flow pattern around damaged and undamaged bridge piers in a channel with a mild slope. The experiments were carried out on a straight channel with a length of 12 meters and a slope of 0.008. Acoustic Doppler velocimeter (ADV) was employed to collect three-dimensional flow velocity data, and the results were analyzed and compared with particle image velocimetry (PIV) data. Sediment Simulation in Intakes with Multiblock option (SSIIM) was incorporated for the numerical simulation of the flow in this study. Generally, the results obtained from the comparisons referred to the appropriate agreement between the numerical and the experimental data. The results showed that an undular hydraulic jump occurred at a distance of two meters from the channel entrance in every case; the maximum bed shear stress in the sloped channel was 12 times that in a horizontal channel for installing two damaged and undamaged piers. With this position of the piers in the sloped channel, the upstream water level underwent a 72.5% reduction compared to similar conditions in a horizontal channel, while the amount of this water level decrease was equal to 8.3% compared to the other cases in a sloped channel. In addition, with the presence of both piers, the maximum Froude number was 5.7 times that in a horizontal channel.

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References

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Figure 2.1: Types of Landslides[2]

Landslide flow path modelling
A Case Study on Aranayaka
Landslide

산사태 유로 모델링 : Aranayaka 산사태 사례 연구

Authors:

Malithi De Silva at University of Kelaniya

Malithi De Silva : University of Kelaniya

N.M.T De Silva
University of Colombo School of Computing
2018

Abstract

산사태가 발생하기 쉬운 구릉 지역 근처에서 발생하는 최근 인구 증가 및 개발은 취약성을 증가시킵니다. 기후 변화의 영향은 산사태 위험의 가능성을 더욱 높입니다. 따라서 인명 및 재산 피해를 방지하기 위해서는 불안정한 경사면 거동에 대한 적절한 관찰과 분석이 중요합니다.

산사태 흐름 경로 예측은 산사태 흐름 경로를 결정하는 데 중요하며 위험 매핑의 필수 요소입니다. 그러나 현상의 복잡한 특성과 관련 매개변수의 불확실성으로 인해 흐름 경로 예측은 어려운 작업입니다. 이 작업에서는 Kegalle 지역의 Aranayaka 지역의 주요 산사태 사고를 흐름 경로를 모델링하기 위한 사례 연구로 사용합니다.

위치에서 디지털 고도 모델을 기반으로 잠재적 소스 영역이 식별되었습니다. 확산 영역 평가는 D8 및 다중 방향 흐름 알고리즘이라는 두 가지 흐름 방향 알고리즘을 기반으로 했습니다. 이 프로토타입 모델을 사용하여 사용자는 슬라이드의 최대 너비, 런아웃 거리 및 슬립 표면적과 같은 산사태 관련 통계를 대화식으로 얻을 수 있습니다.

모델에서 얻은 결과는 실제 Aranayaka 산사태 데이터 세트와 해당 지역의 산사태 위험 지도와 비교되었습니다. D8 알고리즘을 사용하여 구현된 도구에서 생성된 산사태 흐름 경로는 65% 이상의 일치를 나타내고 다중 방향 흐름 알고리즘은 실제 흐름 경로 및 기타 관련 통계와 69% 이상의 일치를 나타냅니다.

또한, 생성된 유동 경로 방향과 예상되는 산사태 시작 지점이 실제 산사태 경계 내부에 잘 일치합니다.

Recent population growth and developments taking place close to landslides prone
hilly areas increase their vulnerability. Climate change impacts further raise the
potential of landslide hazard. Therefore, to prevent loss of lives and damage to
property, proper observation and analysis of unstable slope behavior is crucial.
Landslide flow path forecasting is important for determining a landslide flow route and
it is an essential element in hazard mapping. However, due to the complex nature of
the phenomenon and the uncertainties of associated parameters flow path prediction is
a challenging task.
In this work, the major landslide incident at Aranayaka area in Kegalle district is taken
as the case study to model the flow path. At the location, potential source areas were
identified on the basis of the Digital Elevation Model. Spreading area assessment was
based on two flow directional algorithms namely D8 and Multiple Direction Flow
Algorithm. Using this prototype model, a user can interactively get landslide specific
statistics such as the maximum width of the slide, runout distance, and slip surface area.
Results obtained by the model were compared with the actual Aranayaka landslide data
set the landslide hazard map of the area.
Landslide flow paths generated from the implemented tool using D8 algorithm shows
more than 65% agreement and Multiple Direction Flow Algorithm shows more than
69% agreement with the actual flow paths and other related statistics. Also, the
generated flow path directions and predicted possible landslide initiation points fit
inside the actual landslide boundary with good agreement.

Figure 2.1: Types of Landslides[2]
Figure 2.1: Types of Landslides[2]
Figure 2.2: Landslide Glossary [2]
Figure 2.2: Landslide Glossary [2]

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하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

The Optimal Operation on Auxiliary Spillway to Minimize the Flood Damage in Downstream River with Various Outflow Conditions

하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

Hyung Ju Yoo1, Sung Sik Joo2, Beom Jae Kwon3, Seung Oh Lee4*

유 형주1, 주 성식2, 권 범재3, 이 승오4*

1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University
2Director, Water Resources & Environment Department, HECOREA
3Director, Water Resources Department, ISAN
4Professor, Dept. of Civil & Environmental Engineering, Hongik University

1홍익대학교 건설환경공학과 박사과정
2㈜헥코리아 수자원환경사업부 이사
3㈜이산 수자원부 이사
4홍익대학교 건설환경공학과 교수

ABSTRACT

최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다. 그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다. 이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류력 산정 결과를 호안 설계허용 기준과 비교하였다. 수문 완전 개도 조건으로 가정하고 계획홍수량 유입 시 다양한 보조 여수로 활용방안에 대하여 수치모의를 수행한 결과, 보조 여수로 단독 운영 시 기존 여수로 단독운영에 비하여 최대유속 및 최대 수위의 감소효과를 확인하였다. 다만 계획홍수량의 45% 이하 방류 조건에서 대안부의 호안 안정성을 확보하였고 해당 방류량 초과 경우에는 처오름 현상이 발생하여 월류에 대한 위험성 증가를 확인하였다. 따라서 기존 여수로와의 동시 운영 방안 도출이 중요하다고 판단하였다. 여수로의 배분 비율 및 총 허용 방류량에 대하여 검토한 결과 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 흐름이 중심으로 집중되어 대안부의 유속 저감 및 수위 감소를 확인하였고, 계획 홍수량의 77% 이하의 조건에서 호안의 허용 유속 및 허용 소류력 조건을 만족하였다. 이를 통하여 본 연구에서 제안한 보조 여수로 활용방안으로는 기존 여수로와 동시 운영 시 총 방류량에 대하여 보조 여수로의 배분량이 기존 여수로의 배분량보다 크게 설정하는 것이 하류하천의 영향을 최소화 할 수 있는 것으로 나타났다. 그러나 본 연구는 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토한다면 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출이 가능할 것으로 기대 된다.

키워드 : 보조 여수로, FLOW-3D, 수치모의, 호안 안정성, 소류력

1. 서 론

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로 유입되는 홍수량이 설계 홍수량보다 증가하여 댐 안정성 확보가 필요한 실정이다(Office for Government Policy Coordination, 2003). MOLIT & K-water(2004)에서는 기존댐의 수문학적 안정성 검토를 수행하였으며 이상홍수 발생 시 24개 댐에서 월류 등으로 인한 붕괴위험으로 댐 하류지역의 극심한 피해를 예상하여 보조여수로 신설 및 기존여수로 확장 등 치수능력 증대 기본계획을 수립하였고 이를 통하여 극한홍수 발생 시 홍수량 배제능력을 증대하여 기존댐의 안전성 확보 및 하류지역의 피해를 방지하고자 하였다. 여기서 보조 여수로는 기존 여수로와 동시 또는 별도 운영하는 여수로로써 비상상황 시 방류 기능을 포함하고 있고(K-water, 2021), 최근에는 기존 여수로의 노후화에 따라 보조여수로의 활용방안에 대한 관심이 증가하고 있다. 따라서 본 연구에서는 3차원 수치해석을 수행하여 기존 및 보조 여수로의 방류량 조합에 따른 하류 영향을 분석하고 하류 호안 안정성 측면에서 최적 방류 시나리오를 검토하고자 한다.

기존의 댐 여수로 검토에 관한 연구는 주로 수리실험을 통하여 방류조건 별 흐름특성을 검토하였으나 최근에는 수치모형 실험결과가 수리모형실험과 비교하여 근사한 것을 확인하는 등 점차 수치모형실험을 수리모형실험의 대안으로 활용하고 있다(Jeon et al., 2006Kim, 2007Kim et al., 2008). 국내의 경우, Jeon et al.(2006)은 수리모형 실험과 수치모의를 이용하여 임하댐 바상여수로의 기본설계안을 도출하였고, Kim et al.(2008)은 가능최대홍수량 유입 시 비상여수로 방류에 따른 수리학적 안정성과 기능성을 3차원 수치모형인 FLOW-3D를 활용하여 검토하였다. 또한 Kim and Kim(2013)은 충주댐의 홍수조절 효과 검토 및 방류량 변화에 따른 상·하류의 수위 변화를 수치모형을 통하여 검토하였다. 국외의 경우 Zeng et al.(2017)은 3차원 수치모형인 Fluent를 활용한 여수로 방류에 따른 흐름특성 결과와 측정결과를 비교하여 수치모형 결과의 신뢰성을 검토하였다. Li et al.(2011)은 가능 최대 홍수량(Probable Maximum Flood, PMF)조건에서 기존 여수로와 신규 보조 여수로 유입부 주변의 흐름특성에 대하여 3차원 수치모형 Fluent를 활용하여 검토하였고, Lee et al.(2019)는 서로 근접해있는 기존 여수로와 보조여수로 동시 운영 시 방류능 검토를 수리모형 실험 및 수치모형 실험(FLOW-3D)을 통하여 수행하였으며 기존 여수로와 보조 여수로를 동시운영하게 되면 배수로 간섭으로 인하여 총 방류량이 7.6%까지 감소되어 댐의 방류능력이 감소하였음을 확인하였다.

그러나 대부분의 여수로 검토에 대한 연구는 여수로 내에서의 흐름특성 및 기능성에 대한 검토를 수행하였고. 이에 기존 여수로와 보조 여수로 방류운영에 따른 하류하천의 흐름특성 변화 및 호안 안정성 평가에 관한 추가적인 검토가 필요한 실정이다. 따라서 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류하천의 흐름특성 및 호안 안정성분석을 3차원 수치모형인 FLOW-3D를 이용하여 검토하였다. 또한 다양한 방류 배분 비율 및 허용 방류량 조건 변화에 따른 하류하천의 흐름특성 및 소류력 분석결과를 호안 설계 허용유속 및 허용 소류력 기준과 비교하여 하류하천의 영향을 최소화 할 수 있는 최적의 보조 여수로 활용방안을 도출하고자 한다.

2. 본 론

2.1 이론적 배경

2.1.1 3차원 수치모형의 기본이론

FLOW-3D는 미국 Flow Science, Inc에서 개발한 범용 유체역학 프로그램(CFD, Computational Fluid Dynamics)으로 자유 수면을 갖는 흐름모의에 사용되는 3차원 수치해석 모형이다. 난류모형을 통해 난류 해석이 가능하고, 댐 방류에 따른 하류 하천의 흐름 해석에도 많이 사용되어 왔다(Flow Science, 2011). 본 연구에서는 FLOW-3D(version 12.0)을 이용하여 홍수 시 기존 여수로의 노후화에 대비하여 보조 여수로의 활용방안에 대한 검토를 하류하천의 호안 안정성 측면에서 검토하였다.

2.1.2 유동해석의 지배방정식

1) 연속 방정식(Continuity Equation)

FLOW-3D는 비압축성 유체에 대하여 연속방정식을 사용하며, 밀도는 상수항으로 적용된다. 연속 방정식은 Eqs. (1)(2)와 같다.

(1)

∇·v=0

(2)

∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

여기서, ρ는 유체 밀도(kg/m3), u, v, w는 x, y, z방향의 유속(m/s), Ax, Ay, Az는 각 방향의 요소면적(m2), RSOR는 질량 생성/소멸(mass source/sink)항을 의미한다.

2) 운동량 방정식(Momentum Equation)

각 방향 속도성분 u, v, w에 대한 운동방정식은 Navier-Stokes 방정식으로 다음 Eqs. (3)(4)(5)와 같다.

(3)

∂u∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂x+Gx+fx-bx-RSORρVFu

(4)

∂v∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂y+Gy+fy-by-RSORρVFv

(5)

∂w∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂z+Gz+fz-bz-RSORρVFw

여기서, Gx, Gy, Gz는 체적력에 의한 가속항, fx, fy, fz는 점성에 의한 가속항, bx, by, bz는 다공성 매체에서의 흐름손실을 의미한다.

2.1.3 소류력 산정

호안설계 시 제방사면 호안의 안정성 확보를 위해서는 하천의 흐름에 의하여 호안에 작용하는 소류력에 저항할 수 있는 재료 및 공법 선택이 필요하다. 국내의 경우 하천공사설계실무요령(MOLIT, 2016)에서 계획홍수량 유하 시 소류력 산정 방법을 제시하고 있다. 소류력은 하천의 평균유속을 이용하여 산정할 수 있으며, 소류력 산정식은 Eqs. (6)(7)과 같다.

1) Schoklitsch 공식

Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

(6)

τ=γRI=γC2V2

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), I는 에너지경사, C는 Chezy 유속계수, V는 평균유속(m/s)을 의미한다.

2) Manning 조도계수를 고려한 공식

Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

(7)

τ=γn2V2R1/3

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), n은 Manning의 조도계수, V는 평균유속(m/s)을 의미한다.

FLOW-3D 수치모의 수행을 통하여 하천의 바닥 유속을 도출할 수 있으며, 본 연구에서는 Maning 조도계수롤 고려하여 소류력을 산정하고자 한다. 소류력을 산정하기 위해서 여수로 방류에 따른 대안부의 바닥유속 변화를 검토하여 최대 유속 값을 이용하였다. 최종적으로 산정한 소류력과 호안의 재료 및 공법에 따른 허용 소류력과 비교하여 제방사면 호안의 안정성 검토를 수행하게 된다.

2.2 하천호안 설계기준

하천 호안은 계획홍수위 이하의 유수작용에 대하여 안정성이 확보되도록 계획하여야 하며, 호안의 설계 시에는 사용재료의 확보용이성, 시공상의 용이성, 세굴에 대한 굴요성(flexibility) 등을 고려하여 호안의 형태, 시공방법 등을 결정한다(MOLIT, 2019). 국내의 경우, 하천공사설계실무요령(MOLIT, 2016)에서는 다양한 호안공법에 대하여 비탈경사에 따라 설계 유속을 비교하거나, 허용 소류력을 비교함으로써 호안의 안정성을 평가한다. 호안에 대한 국외의 설계기준으로 미국의 경우, ASTM(미국재료시험학회)에서 호안블록 및 식생매트 시험방법을 제시하였고 제품별로 ASTM 시험에 의한 허용유속 및 허용 소류력을 제시하였다. 일본의 경우, 호안 블록에 대한 축소실험을 통하여 항력을 측정하고 이를 통해서 호안 블록에 대한 항력계수를 제시하고 있다. 설계 시에는 항력계수에 의한 블록의 안정성을 평가하고 있으나, 최근에는 세굴의 영향을 고려할 수 있는 호안 안정성 평가의 필요성을 제기하고 있다(MOLIT, 2019). 관련된 국내·외의 하천호안 설계기준은 Table 1에 정리하여 제시하였고, 본 연구에서 하천 호안 안정성 평가 시 하천공사설계실무요령(MOLIT, 2016)과 ASTM 시험에서 제시한 허용소류력 및 허용유속 기준을 비교하여 각각 0.28 kN/m2, 5.0 m/s 미만일 경우 호안 안정성을 확보하였다고 판단하였다.

Table 1.

Standard of Permissible Velocity and Shear on Revetment

Country (Reference)MaterialPermissible velocity (Vp, m/s)Permissible Shear (τp, kN/m2)
KoreaRiver Construction Design Practice Guidelines
(MOLIT, 2016)
Vegetated5.00.50
Stone5.00.80
USAASTM D’6460Vegetated6.10.81
Unvegetated5.00.28
JAPANDynamic Design Method of Revetment5.0

2.3. 보조여수로 운영에 따른 하류하천 영향 분석

2.3.1 모형의 구축 및 경계조건

본 연구에서는 기존 여수로의 노후화에 대비하여 홍수 시 보조여수로의 활용방안에 따른 하류하천의 흐름특성 및 호안안정성 평가를 수행하기 위해 FLOW-3D 모형을 이용하였다. 기존 여수로 및 보조 여수로는 치수능력 증대사업(MOLIT & K-water, 2004)을 통하여 완공된 ○○댐의 제원을 이용하여 구축하였다. ○○댐은 설계빈도(100년) 및 200년빈도 까지는 계획홍수위 이내로 기존 여수로를 통하여 운영이 가능하나 그 이상 홍수조절은 보조여수로를 통하여 조절해야 하며, 또한 2011년 기존 여수로 정밀안전진단 결과 사면의 표층 유실 및 옹벽 밀림현상 등이 확인되어 노후화에 따른 보수·보강이 필요한 상태이다. 이에 보조여수로의 활용방안 검토가 필요한 것으로 판단하여 본 연구의 대상댐으로 선정하였다. 하류 하천의 흐름특성을 예측하기 위하여 격자간격을 0.99 ~ 8.16 m의 크기로 하여 총 격자수는 49,102,500개로 구성하였으며, 여수로 방류에 따른 하류하천의 흐름해석을 위한 경계조건으로 상류는 유입유량(inflow), 바닥은 벽면(wall), 하류는 수위(water surface elevation)조건으로 적용하도록 하였다(Table 2Fig. 1 참조). FLOW-3D 난류모형에는 혼합길이 모형, 난류에너지 모형, k-ϵ모형, RNG(Renormalized Group Theory) k-ϵ모형, LES 모형 등이 있으며, 본 연구에서는 여수로 방류에 따른 복잡한 난류 흐름 및 높은 전단흐름을 정확하게 모의(Flow Science, 2011)할 수 있는 RNG k-ϵ모형을 사용하였고, 하류하천 호안의 안정성 측면에서 보조여수로의 활용방안을 검토하기 위하여 방류시나리오는 Table 3에 제시된 것 같이 설정하였다. Case 1 및 Case 2를 통하여 계획홍수량에 대하여 기존 여수로와 보조 여수로의 단독 운영이 하류하천에 미치는 영향을 확인하였고 보조 여수로의 방류량 조절을 통하여 호안 안정성 측면에서 보조 여수로 방류능 검토를 수행하였다(Case 3 ~ Case 6). 또한 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천의 영향 검토(Case 7 ~ Case 10) 및 방류 배분에 따른 허용 방류량을 호안 안정성 측면에서 검토를 수행하였다(Case 11 ~ Case 14).

수문은 완전개도 조건으로 가정하였으며 하류하천의 계획홍수량에 대한 기존 여수로와 보조여수로의 배분량을 조절하여 모의를 수행하였다. 여수로는 콘크리트의 조도계수 값(Chow, 1959)을 채택하였고, 댐 하류하천의 조도계수는 하천기본계획(Busan Construction and Management Administration, 2009) 제시된 조도계수 값을 채택하였으며 FLOW-3D의 적용을 위하여 Manning-Strickler 공식(Vanoni, 2006)을 이용하여 조도계수를 조고값으로 변환하여 사용하였다. Manning-Strickler 공식은 Eq. (8)과 같으며, FLOW-3D에 적용한 조도계수 및 조고는 Table 4와 같다.

(8)

n=ks1/68.1g1/2

여기서, kS는 조고 (m), n은 Manning의 조도계수, g는 중력가속도(m/s2)를 의미한다.

시간에 따라 동일한 유량이 일정하게 유입되도록 모의를 수행하였으며, 시간간격(Time Step)은 0.0001초로 설정(CFL number < 1.0) 하였다. 또한 여수로 수문을 통한 유량의 변동 값이 1.0%이내일 경우는 연속방정식을 만족하고 있다고 가정하였다. 이는, 유량의 변동 값이 1.0%이내일 경우 유속의 변동 값 역시 1.0%이내이며, 수치모의 결과 1.0%의 유속변동은 호안의 유속설계기준에 크게 영향을 미치지 않는다고 판단하였다. 그 결과 모든 수치모의 Case에서 2400초 이내에 결과 값이 수렴하는 것을 확인하였다.

Table 2.

Mesh sizes and numerical conditions

MeshNumbers49,102,500 EA
Increment (m)DirectionExisting SpillwayAuxiliary Spillway
∆X0.99 ~ 4.301.00 ~ 4.30
∆Y0.99 ~ 8.161.00 ~ 5.90
∆Z0.50 ~ 1.220.50 ~ 2.00
Boundary ConditionsXmin / YmaxInflow / Water Surface Elevation
Xmax, Ymin, Zmin / ZmaxWall / Symmetry
Turbulence ModelRNG model
Table 3.

Case of numerical simulation (Qp : Design flood discharge)

CaseExisting Spillway (Qe, m3/s)Auxiliary Spillway (Qa, m3/s)Remarks
1Qp0Reference case
20Qp
300.58QpReview of discharge capacity on
auxiliary spillway
400.48Qp
500.45Qp
600.32Qp
70.50Qp0.50QpDetermination of optimal division
ratio on Spillways
80.61Qp0.39Qp
90.39Qp0.61Qp
100.42Qp0.58Qp
110.32Qp0.45QpDetermination of permissible
division on Spillways
120.35Qp0.48Qp
130.38Qp0.53Qp
140.41Qp0.56Qp
Table 4.

Roughness coefficient and roughness height

CriteriaRoughness coefficient (n)Roughness height (ks, m)
Structure (Concrete)0.0140.00061
River0.0330.10496
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F1.jpg
Fig. 1

Layout of spillway and river in this study

2.3.2 보조 여수로의 방류능 검토

본 연구에서는 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천 대안부의 유속분포 및 수위분포를 검토하기 위해 수치모의 Case 별 다음과 같이 관심구역을 설정하였다(Fig. 2 참조). 관심구역(대안부)의 길이(L)는 총 1.3 km로 10 m 등 간격으로 나누어 검토하였으며, Section 1(0 < X/L < 0.27)은 기존 여수로 방류에 따른 영향이 지배적인 구간, Section 2(0.27 < X/L < 1.00)는 보조 여수로 방류에 따른 영향이 지배적인 구간으로 각 구간에서의 수위, 유속, 수심결과를 확인하였다. 기존 여수로의 노후화에 따른 보조 여수로의 방류능 검토를 위하여 Case 1 – Case 6까지의 결과를 비교하였다.

보조 여수로의 단독 운영 시 기존 여수로 운영 시 보다 하류하천의 대안부의 최대 유속(Vmax)은 약 3% 감소하였으며, 이는 보조 여수로의 하천 유입각이 기존 여수로 보다 7°작으며 유입하천의 폭이 증가하여 유속이 감소한 것으로 판단된다. 대안부의 최대 유속 발생위치는 하류 쪽으로 이동하였으며 교량으로 인한 단면의 축소로 최대유속이 발생하는 것으로 판단된다. 또한 보조 여수로의 배분량(Qa)이 증가함에 따라 하류하천 대안부의 최대 유속이 증가하였다. 하천호안 설계기준에서 제시하고 있는 허용유속(Vp)과 비교한 결과, 계획홍수량(Qp)의 45% 이하(Case 5 & 6)를 보조 여수로에서 방류하게 되면 허용 유속(5.0 m/s)조건을 만족하여 호안안정성을 확보하였다(Fig. 3 참조). 허용유속 외에도 대안부에서의 소류력을 산정하여 하천호안 설계기준에서 제시한 허용 소류력(τp)과 비교한 결과, 유속과 동일하게 보조 여수로의 방류량이 계획홍수량의 45% 이하일 경우 허용소류력(0.28 kN/m2) 조건을 만족하였다(Fig. 4 참조). 각 Case 별 호안설계조건과 비교한 결과는 Table 5에 제시하였다.

하류하천의 수위도 기존 여수로 운영 시 보다 보조 여수로 단독 운영 시 최대 수위(ηmax)가 약 2% 감소하는 효과를 보였으며 최대 수위 발생위치는 수충부로 여수로 방류시 처오름에 의한 수위 상승으로 판단된다. 기존 여수로의 단독운영(Case 1)의 수위(ηref)를 기준으로 보조 여수로의 방류량이 증가함에 따라 수위는 증가하였으나 계획홍수량의 58%까지 방류할 경우 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보되었다(Fig. 5 참조). 그러나 계획홍수량 조건에서는 월류에 대한 위험성이 존재하기 때문에 기존여수로와 보조여수로의 적절한 방류량 배분 조합을 도출하는 것이 중요하다고 판단되어 진다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F2.jpg
Fig. 2

Region of interest in this study

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F3.jpg
Fig. 3

Maximum velocity and location of Vmax according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F4.jpg
Fig. 4

Maximum shear according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F5.jpg
Fig. 5

Maximum water surface elevation and location of ηmax according to Qa

Table 5.

Numerical results for each cases (Case 1 ~ Case 6)

CaseMaximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation
in terms of Vp
Evaluation
in terms of τp
1
(Qa = 0)
9.150.54No GoodNo Good
2
(Qa = Qp)
8.870.56No GoodNo Good
3
(Qa = 0.58Qp)
6.530.40No GoodNo Good
4
(Qa = 0.48Qp)
6.220.36No GoodNo Good
5
(Qa = 0.45Qp)
4.220.12AccpetAccpet
6
(Qa = 0.32Qp)
4.040.14AccpetAccpet

2.3.3 기존 여수로와 보조 여수로 방류량 배분 검토

기존 여수로 및 보조 여수로 단독운영에 따른 하류하천 및 호안의 안정성 평가를 수행한 결과 계획홍수량 방류 시 하류하천 대안부에서 호안 설계 조건(허용유속 및 허용 소류력)을 초과하였으며, 처오름에 의한 수위 상승으로 월류에 대한 위험성 증가를 확인하였다. 따라서 계획 홍수량 조건에서 기존 여수로와 보조 여수로의 방류량 배분을 통하여 호안 안정성을 확보하고 하류하천에 방류로 인한 피해를 최소화할 수 있는 배분조합(Case 7 ~ Case 10)을 검토하였다. Case 7은 기존 여수로와 보조여수로의 배분 비율을 균등하게 적용한 경우이고, Case 8은 기존 여수로의 배분량이 보조 여수로에 비하여 많은 경우, Case 9는 보조 여수로의 배분량이 기존 여수로에 비하여 많은 경우를 의미한다. 최대유속을 비교한 결과 보조 여수로의 배분 비율이 큰 경우 기존 여수로의 배분량에 의하여 흐름이 하천 중심에 집중되어 대안부의 유속을 저감하는 효과를 확인하였다. 보조여수로의 방류량 배분 비율이 증가할수록 기존 여수로 대안부 측(0.00<X/L<0.27, Section 1) 유속 분포는 감소하였으나, 신규여수로 대안부 측(0.27<X/L<1.00, Section 2) 유속은 증가하는 것을 확인하였다(Fig. 6 참조). 그러나 유속 저감 효과에도 대안부 전구간에서 설계 허용유속 조건을 초과하여 제방의 안정성을 확보하지는 못하였다. 소류력 산정 결과 유속과 동일하게 보조 여수로의 방류량이 기존 여수로의 방류량 보다 크면 감소하는 것을 확인하였고 일부 구간에서는 허용 소류력 조건을 만족하는 것을 확인하였다(Fig. 7 참조).

따라서 유속 저감효과가 있는 배분 비율 조건(Qa>Qe)에서 Section 2에 유속 저감에 영향을 미치는 기존 여수로 방류량 배분 비율을 증가시켜 추가 검토(Case 10)를 수행하였다. 단독운영과 비교 시 하류하천에 유입되는 유량은 증가하였음에도 불구하고 기존 여수로 방류량에 의해 흐름이 하천 중심으로 집중되는 현상에 따라 대안부의 유속은 단독 운영에 비하여 감소하는 것을 확인하였고(Fig. 8 참조), 호안 설계 허용유속 및 허용 소류력 조건을 만족하는 구간이 발생하여 호안 안정성도 확보한 것으로 판단되었다. 최종적으로 각 Case 별 수위 결과의 경우 여수로 동시 운영을 수행하게 되면 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 9 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 6에 제시하였다.

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F6.jpg
Fig. 6

Maximum velocity on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F7.jpg
Fig. 7

Maximum shear on section 1 & 2 according to Qa

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F8.jpg
Fig. 8

Velocity results of FLOW-3D (a: auxiliary spillway operation only , b : simultaneous operation of spillways)

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F9.jpg
Fig. 9

Maximum water surface elevation on section 1 & 2 according to Qa

Table 6.

Numerical results for each cases (Case 7 ~ Case 10)

Case (Qe &amp; Qa)Maximum Velocity (Vmax, m/s)Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
7
Qe : 0.50QpQa : 0.50Qp
8.106.230.640.30No GoodNo GoodNo GoodNo Good
8
Qe : 0.61QpQa : 0.39Qp
8.886.410.610.34No GoodNo GoodNo GoodNo Good
9
Qe : 0.39QpQa : 0.61Qp
6.227.330.240.35No GoodNo GoodAcceptNo Good
10
Qe : 0.42QpQa : 0.58Qp
6.394.790.300.19No GoodAcceptNo GoodAccept

2.3.4 방류량 배분 비율의 허용 방류량 검토

계획 홍수량 방류 시 기존 여수로와 보조 여수로의 배분 비율 검토 결과 Case 10(Qe = 0.42Qp, Qa = 0.58Qp)에서 방류에 따른 하류 하천의 피해를 최소화시킬 수 있는 것을 확인하였다. 그러나 대안부 전 구간에 대하여 호안 설계조건을 만족하지 못하였다. 따라서 기존 여수로와 보조 여수로의 방류 배분 비율을 고정시킨 후 총 방류량을 조절하여 허용 방류량을 검토하였다(Case 11 ~ Case 14).

호안 안정성 측면에서 검토한 결과 계획홍수량 대비 총 방류량이 감소하면 최대 유속 및 최대 소류력이 감소하고 최종적으로 계획 홍수량의 77%를 방류할 경우 하류하천의 대안부에서 호안 설계조건을 모두 만족하는 것을 확인하였다(Fig. 10Fig. 11 참조). 각 Case 별 대안부에서 최대 유속결과 및 산정한 소류력은 Table 7에 제시하였다. 또한 Case 별 수위 검토 결과 처오름으로 인한 대안부 전 구간에서 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보하였다(Fig. 12 참조).

Table 7.

Numerical results for each cases (Case 11 ~ Case 14)

Case (Qe &amp; Qa)Maximum Velocity
(Vmax, m/s)
Maximum Shear
(τmax, kN/m2)
Evaluation in terms of VpEvaluation in terms of τp
Section 1Section 2Section 1Section 2Section 1Section 2Section 1Section 2
11
Qe : 0.32QpQa : 0.45Qp
3.634.530.090.26AcceptAcceptAcceptAccept
12
Qe : 0.35QpQa : 0.48Qp
5.745.180.230.22No GoodNo GoodAcceptAccept
13
Qe : 0.38QpQa : 0.53Qp
6.704.210.280.11No GoodAcceptAcceptAccept
14
Qe : 0.41QpQa : 0.56Qp
6.545.240.280.24No GoodNo GoodAcceptAccept
/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F10.jpg
Fig. 10

Maximum velocity on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F11.jpg
Fig. 11

Maximum shear on section 1 & 2 according to total outflow

/media/sites/ksds/2021-014-02/N0240140207/images/ksds_14_02_07_F12.jpg
Fig. 12

Maximum water surface elevation on section 1 & 2 according to total outflow

3. 결 론

본 연구에서는 홍수 시 기존 여수로의 노후화로 인한 보조 여수로의 활용방안에 대하여 하류하천의 호안 안정성 측면에서 검토하였다. 여수로 방류로 인한 하류하천의 흐름특성을 검토하기 위하여 3차원 수치모형인 FLOW-3D를 활용하였고, 여수로 지형은 치수능력 증대사업을 통하여 완공된 ○○댐의 제원을 이용하였다. 하류하천 조도 계수 및 여수로 방류량은 하천기본계획을 참고하여 적용하였다. 최종적으로 여수로 방류로 인한 하류하천의 피해를 최소화 시킬 수 있는 적절한 보조 여수로의 활용방안을 도출하기 위하여 보조 여수로 단독 운영과 기존 여수로와의 동시 운영에 따른 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다.

수문은 완전 개도 상태에서 방류한다는 가정으로 계획 홍수량 조건에서 보조 여수로 단독 운영 시 하류하천 대안부의 유속 및 수위를 검토한 결과 기존 여수로 단독운영에 비하여 최대 유속 및 최대 수위가 감소하는 것을 확인할 수 있었으며, 이는 보조 여수로 단독 운영 시 하류하천으로 유입각도가 작아지고, 유입되는 하천의 폭이 증가되기 때문이다. 그러나 계획 홍수량 조건에서 하천호안 설계기준에서 제시한 허용 유속(5.0 m/s)과 허용 소류력(0.28 kN/m2)과 비교하였을 때 호안 안정성을 확보하지 못하였으며, 계획홍수량의 45% 이하 방류 시에 대안부의 호안 안정성을 확보하였다. 수위의 경우 여수로 방류에 따른 대안부에서 처오름 현상이 발생하여 월류에 대한 위험성을 확인하였고 이를 통하여 기존 여수로와의 동시 운영 방안을 도출하는 것이 중요하다고 판단된다. 따라서 기존 여수로와의 동시 운영 측면에서 기존 여수로와 보조 여수로의 배분 비율 및 총 방류량을 변화시켜가며 하류 하천의 흐름특성 및 소류력의 변화를 검토하였다. 배분 비율의 경우 기존 여수로와 보조 여수로의 균등 배분(Case 7) 및 편중 배분(Case 8 & Case 9)을 검토하여 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 중심부로 집중되어 대안부의 최대유속, 최대소류력 및 최대수위가 감소하는 것을 확인하였다. 이를 근거로 기존 여수로의 방류 비율을 증가(Qe=0.42Qp, Qa=0.58Qp)시켜 검토한 결과 대안부 일부 구간에서 허용 유속 및 허용소류력 조건을 만족하는 것을 확인하였다. 이를 통하여 기존 여수로와 보조 여수로의 동시 운영을 통하여 적절한 방류량 배분 비율을 도출하는 것이 방류로 인한 하류하천의 피해를 저감하는데 효과적인 것으로 판단된다. 그러나 설계홍수량 방류 시 전 구간에서 허용 유속 및 소류력 조건을 만족하지 못하였다. 최종적으로 전체 방류량에서 기존 여수로의 방류 비율을 42%, 보조 여수로의 방류 비율을 58%로 설정하여 허용방류량을 검토한 결과, 계획홍수량의 77%이하로 방류 시 대안부의 최대유속은 기존여수로 방류의 지배영향구간(section 1)에서 3.63 m/s, 기존 여수로와 보조 여수로 방류의 영향구간(section 2)에서 4.53 m/s로 허용유속 조건을 만족하였고, 산정한 소류력도 각각 0.09 kN/m2 및 0.26 kN/m2로 허용 소류력 조건을 만족하여 대안부 호안의 안정성을 확보하였다고 판단된다.

본 연구 결과는 기후변화 및 기존여수로의 노후화로 인하여 홍수 시 기존여수로의 단독운영으로 하류하천의 피해가 발생할 수 있는 현시점에서 치수증대 사업으로 완공된 보조 여수로의 활용방안에 대한 기초자료로 활용될 수 있고, 향후 계획 홍수량 유입 시 최적의 배분 비율 및 허용 방류량 도출에 이용할 수 있다. 다만 본 연구는 여수로 방류에 따른 제방에 작용하는 수충력은 검토하지 못하고, 허용 유속 및 허용소류력은 제방과 유수의 방향이 일정한 구간에 대하여 검토하였다. 또한 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토하여 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출하고자 한다.

Acknowledgements

본 결과물은 K-water에서 수행한 기존 및 신규 여수로 효율적 연계운영 방안 마련(2021-WR-GP-76-149)의 지원을 받아 연구되었습니다.

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Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators

2상 유동 해석을 통한 슈트 폭기 시스템 효율에 대한 램프 각도의 영향 조사

Investigation of the Effect of Ramp Angle on Chute Aeration System Efficiency by Two-Phase Flow Analysis

Authors

1 Associate Professor, Civil Engineering Department, Jundi-Shapur University of Technology, Dezful, Iran

2 Instructor in Civil Engineering Department Jundi-Shapur University of Technology, Dezful,Iran.

 10.22055/JISE.2021.37743.1980

Abstract

Flow aeration in chute spillway is one of the most effective and economic ways to prevent cavitation damage. Surface damage is significantly reduced when very small values of air are scattered in a water prism. A structure known as an aerator may be used for this purpose. Besides, ramp angle is one of the factors influencing aerator efficiency. In this research, the value of air entraining the flow through the Jarreh Dam’s spillway at the ramp angles of 6, 8 and 10 degrees, as three different scenarios, was simulated using the Flow-3D software. In order to validate the results of the inlet air into the flowing fluid at a ramp angle of 6 degrees, the observational results of the dam spillway physical model from the laboratory of TAMAB Company in Iran were used. According to the results, raising the ramp angle increases the inlet air to the water jet nappe, and a ten-degree ramp angle provides the best aeration efficiency. The Flow-3D model can also simulate the two-phase water-air flow on spillways, according to the results.

슈트 여수로의 흐름 폭기는 캐비테이션 손상을 방지하는 가장 효과적이고 경제적인 방법 중 하나입니다. 수중 프리즘에 아주 작은 양의 공기가 흩어지면 표면 손상이 크게 줄어듭니다. 이를 위해 폭기 장치로 알려진 구조를 사용할 수 있습니다. 또한, 램프 각도는 폭기 효율에 영향을 미치는 요인 중 하나입니다. 이 연구에서는 FLOW-3D 소프트웨어를 사용하여 3가지 다른 시나리오인 6, 8 및 10도의 램프 각도에서 Jarreh 댐의 방수로를 통해 흐름을 동반하는 공기의 값을 시뮬레이션했습니다. 6도의 경사각에서 유동 유체로 유입되는 공기의 결과를 검증하기 위해이란 TAMAB Company의 실험실에서 댐 방수로 물리적 모델의 관찰 결과를 사용했습니다. 결과에 따르면 램프 각도를 높이면 워터제트 기저귀로 유입되는 공기가 증가하고 10도 램프 각도는 최고의 폭기 효율을 제공합니다. Flow-3D 모델은 결과에 따라 여수로의 2단계 물-공기 흐름을 시뮬레이션할 수도 있습니다.

Keywords

Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
Fig. 1- Schematic of the general pattern of flow and aeration process in the aerators
(a) The full-scale map of the Jarreh spillway’s plan and profile.
(a) The full-scale map of the Jarreh spillway’s plan and profile.
Fig. 2- Experimental setup (Shamloo et al., 2012)
Fig. 2- Experimental setup (Shamloo et al., 2012)

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Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)

고정 베드의 불침투성 토양에서 흐름 패턴의 수치 시뮬레이션

NUMERICAL SIMULATION OF FLOW PATTERN IN SERIES OF IMPERMEABLE GROYNES IN FIXED BED

Kafle, Mukesh Raj1
1Asst. Professor, Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, Nepal
Email: mkafle@pcampus.edu.np

Abstract

This paper presents a numerical simulation of recirculating flow patterns in groyne fields. Moreover, it entails the concept determination of proper spacing of vertical unsubmerged and impermeable groynesin seriesto control the bank erosion. Flow pattern between the groynes varies along their space. The flow in groyne field may significantly affect the flow change, bed change, bank erosion and condition of habitat. In this regard, an assessment of flow along the space of groynes will yield important data needed to diversify the object of groyne installation. So, knowledge about determination of the proper spacing of groynes in groyne field is important. Space of vertical groynes was set from 1.5 to 10 times the length of groynes. The velocity field between groynes was simulated by using Computational Fluid Dynamics (CFD) model Nays 2D. Simulated velocity field was compared with existing experimentaldata for the same parameter, which agreed satisfactorily. Based on simulated results,the optimal spacing of vertical groynes to control the bank erosion was recommended.

이 논문은 groyne 필드에서 재순환 흐름 패턴의 수치 시뮬레이션을 제공합니다. 더욱이, 그것은 제방 침식을 제어하기 위해 수직 비침수 및 불침투성 그로이네신 시리즈의 적절한 간격의 개념 결정을 수반합니다. groynes 사이의 흐름 패턴은 공간에 따라 다릅니다. groyne field의 흐름은 흐름 변화, 하상 변화, 제방 침식 및 서식지 상태에 중대한 영향을 미칠 수 있습니다. 이와 관련하여, groyne 공간을 따른 흐름의 평가는 groyne 설치 대상을 다양화하는 데 필요한 중요한 데이터를 산출할 것입니다. 따라서, groyne field에서 groyne의 적절한 간격 결정에 대한 지식이 중요합니다. 수직 여백의 간격은 여아 길이의 1.5배에서 10배 사이로 설정하였다. groyne 사이의 속도장은 CFD(Computational Fluid Dynamics) 모델 Nays 2D를 사용하여 시뮬레이션되었습니다. 시뮬레이션된 속도장은 동일한 매개변수에 대해 기존 실험 데이터와 비교되었으며 만족스럽게 일치했습니다. 모의 결과를 바탕으로 제방 침식을 억제하기 위한 최적의 수직 제방 간격을 제안하였다.

  1. Introduction
    Spur dikes or groynes are used to protect river banks from erosion and also keep the channel
    navigable.Depending upon the flow characteristics, spur-dikes may be classified as submerged and unsubmerged. Also, based on the permeability, spur dikes are further classified as permeable and
    impermeable. Herein, un-submerged !impermeable spur dikes are dealt. These structures are built from the river bank into the stream flow and usually built in group. Construction of groyne against the flow causes significant changes in flow pattern in channel. Those changes may result in scour phenomenon around groynes which may lead structure instability and changes in river morphology. Moreover, in series of groynes, spacing of groynes leads different types of recirculating flow patterns.Therefore, investigating the characteristics of flow pattern around groynes have been a great interest in river engineering. Numerous researchers like Sukhodolov et al. (2002), Hao Zhang et al.(2009), Beheshti (2010), Duan (2009), Naji(2010), Karami(2011) made a variety of experiments in order to determine the flow pattern around groynes. Most of these researchers studied effect of single groyne, while using series of groynes is more effective in protection of rivers. Besides experimental studies, variety of CFD models have been developed for computing flow pattern around hydraulic structures; like Fluent, Flow 3D, Nays 2D, Nays CUBE and SSIIM. In this study, Nays 2D numerical modelling has been used to investigate flow and recirculating pattern around a series of groynes and streamlines including components of velocities.
  1. Flow pattern in groyne fields
    Under conditions where the groynes are not submerged, the groyne fields are not really part of the wetted cross section of a river. Because of that, the flow pattern in the groyne-field is not directly the result of the discharge in the main channel. Reducing the main stream velocity has no effect on the flow pattern itself, whereas lowering the water level does (Uijttewaal et al.2001). Moreover, the flow pattern inside a groyne field may change with the change of its geometry, location along the river (inner curve, outer curve, or straight part), and/ or the groynes orientation( Przedwojski et al.1995). However, there is an indirect effect of the discharge on the flow pattern in the groyne field. Because of the flow that is diverted from the main channel into the groyne fields, water flows into the groyne field with low velocity through the downstream half of the interfacial section between the groyne field and the main channel. This water flows back to the main channel through a small width of, just downstream the upstream groyne of the groyne field ( Termes et al.1991). Flow separates on a groyne head and forms a secondary flow represented by a large scale vortex with a vertical axis of rotation called primary gyre. Deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre. Location, mutual interactions, and energy exchange between gyres are the factors that create a specific recirculation pattern, and, consequently assuming correspondence with sedimentation processes, they define deposition patterns.
  2. Model Formulation
    The CFD model selected for this study is the publically available software NAYS 2D (iRIC 2.0), which is an analytical solver for calculation of unsteady two-dimensional plane flow and riverbed deformation using boundary-fitted coordinates within general curvilinear coordinates. A numerical channel of length 8.0m and width 0.9m was created with grid size of 0.01m im stream wise and 0.03m in cross stream directions. Groynes or spur dikes of length 0.15 and width 0.01m were chosen in series. Groyne field with various aspect ratio (b/x) 0.7, 0.25, 0.17, 0.125 and 0.10, where b=length of spur dike, x=spacing of two dikes. Discharge of 0.0175 m3 /s was applied. For boundary conditions, water surface at downstream and velocity at upstream were considered as uniform flow. Relaxation coefficient for water surface calculation was considered as 0.8. For the finite-difference method, the CIP method was applied to the advection terms in equations of motion. For the turbulent field calculation, Constant eddy viscosity, Zero-equation model and k-G models were applied and compared. The model!s accuracy in predicting the velocity magnitudes is evaluated using statistical parameters- mean absolute error (MAE), mean square error(MSE), and root mean square error (RMSE). The comparison of results shows the importance of selecting an appropriate turbulence model in simulating flow field around a spur dike. From the comparison, k-I model is found superior over zero energy model and eddy viscosity model. So, k-I model is chosen as appropriate turbulence closure model.
  3. Model!s Validation
    The capability of CFD model Nays 2D to simulate the velocity field and recirculation pattern in groyne field was compared with experimental data of laboratory experiments by Sukhodolov et al. (2002). The numerical simulation was validated for aspect ratio (R=b/x=0.7) and R=0.25. For aspect ratio R=0.7, one gyre system occupies the whole area of the groyne field. The areas with lower-than-average velocity values are clearly seen in the central part of the gyre and near its corners. Velocities increase towards the margins of the gyre. For aspect ratio R=0.25, two gyre velocity fields were observed in the groyne field. In the downstream part of the groyne field a large gyre, covering two-thirds of the area is clearly visible. The left part(upstream) contains second gyre rotating much more slowly and in the direction opposed to the primary gyre. The simulated and observed velocity field pattern and gyre found satisfactorily agreed. Now, after validation, the model was used for further analysis of velocity field for various aspect ratios.
Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
  1. Results and Discussions
    The calibrated model was applied to five different cases of un-submerged and impermeable groyne fields with aspect ratios R=0.70,0.25,0.17,0.125 & 0.10 and flow pattern was numerically simulated. For aspect ratio R=0.7 i.e x/b=1.5, Fig 1(a) only one lateral primary gyre was formed inside the groyne field. The circulation pattern in this case is distinguished by the main flow that is deflected outside the groyne field. The developed primary gyre prevents the main flow from penetrating the groyne field. Therefore, this pattern is desirable for navigation purposes as a continuous deep channel is maintained along the face of the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 1(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R= 0.25 i. e x/b=4 Fig 2(a) and flow pattern inside the groyne field was simulated. In this case, in the downstream part of the groyne field, a primary gyre occupying almost two-third area was formed. In addition, deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre covering almost one-third part of the groyne field. Likewise in the first case, the main current is maintained deflected outside the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 2(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R=0.17 i.e x/b=6. In this case the flow pattern was similar to the aspect ratio R=0.25. The spacing of the groynes was further increased maintaining aspect ratio R=0.125 i. e x/b=8. In this case, similar to the previous scenarios two longitudinal gyres but with different positions are formed. The main current is directed in to the groyne field (Fig 3) creating a much more stronger eddy near the upstream groyne and greater turbulence along the upstream face and at the groyne lower head. As the spacing between groynes increased maintaining aspect ratio R=0.10 i. e x/b=10 (Fig 4), still primary and secondary gyres are generated. The formed gyres deflect the main flow thus preventing to enter in to the groyne field in upstream part. However, in the downstream of the primary gyre and just upstream of the second groyne, the flow attacks the bank directly. The resultant velocity profiles at the deflected region y/b=3 were plotted and how the spacing of second groyne affect the result was analyzed. Spacing of groynes makes little change in upstream resultant velocity. However, in the deflected region, its effect is significant. Higher value of spacing of groyne leads higher average deviation in resultant velocity. For aspect ratio R=0.7, the average deviation estimated as 0.02%. In the case of aspect ratio R=0.25, this value was reached to 1.57%. Further increment of spacing i. e decreasing the aspect ratio R=0.17, average deviation was found 3.82%. For the aspect ratio R=0.125, that value was estimated as 4.16%.
  2. Conclusions
    Geometry of the groyne fields; width and length of the groyne field mainly cause the specific flow patterns including number and shape of eddies or gyres. Eddies developed inside the groyne field deflects the main flow preventing it entering into the dead zone. An aspect ratio close to unity gives rise to a single eddy. A smaller aspect ratio (higher spacing between groynes) gives room to two stationary eddies, a large one called primary eddy, in the downstream part of the groyne field, and a smaller secondary eddy emerges near the upstream groyne. The extreme long groyne field -case of length to width ratio of larger thaneight shows penetration of main flow into the groyne field. The two eddies remain in a relatively stable position, while the main flow zone starts to penetrate into groyne field further downstream. In all cases, there is an eddy detaches from the upstream groyne tip that travels along the main channel groyne field interface and eventually merges with the primary eddy. The simulated results indicate that the spacing of groynes or spur dikes from the controlling of bank erosion point of view should be limited within six times the length of groyne.
Fig 3 Computed velocity field for aspect ratio 0.125
Fig 3 Computed velocity field for aspect ratio 0.125
Fig 4 Computed velocity field for aspect ratio 0.10
Fig 4 Computed velocity field for aspect ratio 0.10
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3
Fig 5 Resultant velocity profiles at y/b=3

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Computational Fluid Dynamics, 온실

CFD 사용: 유압 구조 및 농업에서의 응용

USO DE CFD COMO HERRAMIENTA PARA LA MODELACIÓN Y  PREDICCIÓN NUMÉRICA DE LOS FLUIDOS: APLICACIONES EN  ESTRUCTURAS HIDRÁULICAS Y AGRICULTURA

Cruz Ernesto Aguilar-Rodriguez1*; Candido Ramirez-Ruiz2; Erick Dante Mattos Villarroel3 

1Tecnológico Nacional de México/ITS de Los Reyes. Carretera Los Reyes-Jacona, Col. Libertad. 60300.  Los Reyes de Salgado, Michoacán. México. 

ernesto.ar@losreyes.tecnm.mx – 3541013901 (*Autor de correspondencia) 

2Instituto de Ciencias Aplicadas y Tecnología, UNAM. Cto. Exterior S/N, C.U., Coyoacán, 04510, Ciudad  de México. México.  3Riego y Drenaje. Instituto Mexicano de Tecnología del Agua. Paseo Cuauhnáhuac 8532, Progreso,  Jiutepec, Morelos, C.P. 62550. México.

Abstract

공학에서 유체의 거동은 설명하기에 광범위하고 복잡한 과정이며, 유체역학은 유체의 거동을 지배하는 방정식을 통해 유체 역학 현상을 분석할 수 있는 과학 분야이지만 이러한 방정식에는 전체 솔루션이 없습니다. . 전산유체역학(Computational Fluid Dynamics, 이하 CFD)은 수치적 기법을 통해 방정식의 해에 접근할 수 있는 도구로, 신뢰할 수 있는 계산 모델을 얻기 위해서는 물리적 모델의 실험 데이터로 평가해야 합니다. 수력구조물에서 선형 및 미로형 여수로에서 시뮬레이션을 수행하고 배출 시트의 거동과 현재의 폭기 조건을 분석했습니다. 침강기에서 유체의 특성화를 수행하고 필요한 특성에 따라 사체적, 피스톤 또는 혼합의 분수를 수정하는 것이 가능합니다. 농업에서는 온실 환경을 특성화하고 환경에 대한 재료의 디자인, 방향 및 유형 간의 관계를 찾는 데 사용할 수 있습니다. 발견된 가장 중요한 결과 중 온실의 길이와 설계가 환기율에 미칠 수 있는 영향으로 온실의 길이는 높이의 6배 미만인 것이 권장됩니다.

키워드: Computational Fluid Dynamics, 온실,

Spillway, Settler 기사: COMEII-21048 소개 

CFD는 유체 운동 문제에 대한 수치적 솔루션을 얻어 수리학적 현상을 더 잘 이해할 수 있게 함으로써 공간 시각화를 가능하게 하는 수치 도구입니다. 예를 들어, 수력 공학에서 벤츄리(Xu, Gao, Zhao, & Wang, 2014) 워터 펌핑(ȘCHEAUA, 2016) 또는 개방 채널 적용( Wu et 알., 2000). 

문헌 검토는 실험 연구에서 검증된 배수로의 흐름 거동에 대한 수리학적 분석을 위한 CFD 도구의 효율성을 보여줍니다. 이 검토는 둑의 흐름 거동에 대한 수리학적 분석을 위한 CFD의 효율성을 보여줍니다. Crookston et al. (2012)는 미로 여수로에 대해 Flow 3D로 테스트를 수행했으며, 배출 계수의 결과는 3%에서 7%까지 다양한 오류로 실험적으로 얻은 결과로 허용 가능했으며 연구 결과 측면에 저압 영역이 있음을 발견했습니다. 익사 방식으로 작업할 때 위어의 벽. Zuhair(2013)는 수치 모델링 결과를 Mandali weir 원형의 실험 데이터와 비교했습니다.  

최근 연구에서는 다양한 난류 모델을 사용하여 CFD를 적용할 가능성이 있음을 보여주었습니다. 그리고 일부만이 음용수 처리를 위한 침적자의 사례 연구를 제시했으며, 다른 설계 변수 중에서 기하학적인 대안, 수온 변화 등을 제안했습니다. 따라서 기술 개발로 인해 설계 엔지니어가 유체 거동을 분석하는 데 CFD 도구를 점점 더 많이 사용하게 되었습니다. 

보호 농업에서 CFD는 온실 환경을 모델링하고 보조 냉방 또는 난방 시스템을 통해 온실의 미기후 관리를 위한 전략을 제안하는 데 사용되는 기술이었습니다(Aguilar Rodríguez et al., 2020).  

2D 및 3D CFD 모델을 사용한 본격적인 온실 시뮬레이션은 태양 복사 모델과 현열 및 잠열 교환 하위 모델의 통합을 통해 온실의 미기후 분포를 연구하는 데 사용되었습니다(Majdoubi, Boulard, Fatnassi, & Bouirden, 2009). 마찬가지로 이 모델을 사용하여 온실 설계(Sethi, 2009), 덮개 재료(Baxevanou, Fidaros, Bartzanas, & Kittas, 2018), 시간, 연중 계절( Tong, Christopher, Li, & Wang, 2013), 환기 유형 및 구성(Bartzanas, Boulard, & Kittas, 2004). 

CFD 거래 프로그램은 사용자 친화적인 플랫폼으로 설계되어 결과를 쉽게 관리하고 이해할 수 있습니다.  

Figura 1. Distribución de presiones y velocidades en un vertedor de pared delgada.
Figura 2. Perfiles de velocidad y presión en la cresta vertedora.
Figura 3. Condiciones de aireación en vertedor tipo laberinto. (A)lámina adherida a la pared del
vertedor, (B) aireado, (C) parcialmente aireado, (D) ahogado.
Figura 4. Realización de prueba de riego.
Figura 5. Efecto de la posición y dirección de los calefactores en un invernadero a 2 m del suelo.
Figura 5. Efecto de la posición y dirección de los calefactores en un invernadero a 2 m del suelo.
Figura 6. Indicadores ambientales para medir el confort ambiental de los cultivos.
Figura 6. Indicadores ambientales para medir el confort ambiental de los cultivos.
Figura 7. Líneas de corriente dentro del sedimentador experimental en estado estacionario  (Ramirez-Ruiz, 2019).
Figura 7. Líneas de corriente dentro del sedimentador experimental en estado estacionario (Ramirez-Ruiz, 2019).

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Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

Investigating the peak outflow through a spatial embankment dam breach

공간적 제방댐 붕괴를 통한 최대 유출량 조사

Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

Abstract

Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.

유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.

다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.

위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.

Keywords

Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

1. Introduction

There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generationEmbankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.

The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.

Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].

The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8][9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point [11].

Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.

Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0

where: Qp = peak outflow discharge.

Qin = inflow discharge.

hc = critical flow depth.

d50 = mean sediment diameter.

Ho = initial dam height.

Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.

Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.

The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.

Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.

2. Numerical simulation

The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

2.1. Geometric presentations

A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.

2.2. Governing equations

The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).

The continuity equation:(2)∂ui∂xi=0

The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯

where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0

where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (AxAyAz) are the area fractions.

2.3. Boundary and initial conditions

To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.

2.4. Numerical method

FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.

2.5. Turbulent models

Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.

models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT

where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.

2.6. Sediment scour model

The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50

where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf

where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i

where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213

where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi

where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312

where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i

where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i

where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36

where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.

2.7. Grid type

Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.

2.8. Time step

The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.

2.9. Numerical model validation

The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:

(1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,

(5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3(9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.

By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.

3. Analysis and discussions

The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.

This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.

All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.

(Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).

3.1. Dam breaching process evolution

The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.

According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.

3.2. The effect of initial breach shape

To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.

Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.

3.3. The effect of initial breach dimensions

The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.

The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.

3.4. The effect of initial breach location

The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.

The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.

3.5. The effect of upstream and downstream dam slopes

The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.

The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.

According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.

Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr

4. Conclusions

A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.

The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.

The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.

The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.

The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.

The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.

The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.

Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.

The upstream slope has a negligible effect on the dam breaching process.

References

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Effect of roughness on separation zone dimensions.

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

조도 계수 및 역전 수준 변화가 개선된 90도 측면 분출구에서의 유동에 대한 실험적 및 수치적 연구

Maryam BagheriSeyed M. Ali ZomorodianMasih ZolghadrH. Md. AzamathullaC. Venkata Siva Rama Prasad

Abstract

측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 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%.

HIGHLIGHTS

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  • Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance.
  • Installation of 7 types of roughening elements at the turnout entrance and 3 different bed level inverts were investigated.
  • Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow.
  • Combining both methods can reduce the separation zone dimensions by up to 63%.
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

Keywords

discharge ratioflow separation zoneintakethree dimensional simulation

INTRODUCTION

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Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.

The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.

Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).

Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).

Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011)Nikbin & Borghei (2011)Seyedian et al. (2008).

Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.

Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE

Laboratory channel dimensions.

Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.

The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.

METHOD

Experimental setup

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The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.

Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE

Roughness plates.

The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).

The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).

Numerical simulation

ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:

formula

(1)where uv, and w represent the velocity components in the x, y, and z directions, respectively; AxAy, and Az are the surface flow fractions in the xy, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in xy and z dimensions respectively :

formula

(2)

formula

(3)

formula

(4)where GxGy, and Gz are the accelerations caused by gravity in the xy, and z directions, respectively; and fxfy, and fz are the accelerations caused by viscosity in the xy, and z directions, respectively.

The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.

Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.

The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1

Hydraulic conditions of the flow

Q(L/s)FrY1 (m)Q2/Q1
16 0.449 0.09 0.22 
18 0.335 0.09 0.61 
21 0.242 0.09 0.71 
23 0.180 0.09 1.04 

RESULTS AND DISCUSSION

Experimental results

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During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.

At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.Figure 4VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions.

It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE

Comparison of separation zone for n=0.023 and n=0.032.

Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.

The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.

In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2

Decrease percentage of separation zone area in 5 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.08 10.56 11.06 25.27 33.03 35.57 36.5 
0.121 7.66 11.14 11.88 15.93 34.59 36.25 
0.353 1.38 2.63 8.17 14.39 31.20 31.29 
0.362 11.54 19.56 25.73 37.89 38.31 

Table 3

Decrease percentage of separation zone area in 10 cm drop

Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
0.047 4.30 8.75 23.47 31.22 34.96 35.13 
0.119 11.01 13.16 15.02 21.48 39.45 40.68 
0.348 3.89 5.71 9.82 16.09 29 30.96 
0.354 2.84 10.44 18.42 25.45 35.68 35.76 

Figure 6VIEW LARGEDOWNLOAD SLIDE

Effect of drop implementation on separation zone dimensions.

The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4

Reduction in percentage of combined effect of roughness and 10 cm drop

Qin=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
16 32.3 35.07 37.2 45.7 58.01 59.1 
18 44.5 34.15 36.18 48.13 54.2 56.18 
21 43.18 32.33 42.30 37.79 57.16 63.2 
23 40.56 34.5 34.09 46.25 50.12 57.2 

Figure 7VIEW LARGEDOWNLOAD SLIDE

Combined effect of roughness and drop on separation zone dimensions.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.

Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE

Velocity profiles for various roughness coefficients along turnout width.

A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE

Effect of roughness on separation zone dimensions in numerical study.

Numerical results

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This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,

formula

where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.

Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE

Velocity vector for flow condition Q1/422 l/s, near surface.

The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE

Exprimental and numerical measured velocity.

CONCLUSION

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This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.

This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.

DATA AVAILABILITY STATEMENT

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All relevant data are included in the paper or its Supplementary Information.

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).Google Scholar 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.Google Scholar 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).Google Scholar 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.Google Scholar 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).Google Scholar 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.Google ScholarCrossref  Kasthuri B. & Pundarikanthan N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering 113 (4), 543–548.Google ScholarCrossref  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.Google ScholarCrossref  Kirkgöz M. S. & Ardiçlioğlu 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).Google Scholar 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).Google Scholar 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).Google ScholarCrossref  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.Google Scholar Odgaard J. A. & Wang Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.Google ScholarCrossref  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).Google Scholar 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.Google Scholar 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.Google Scholar Zolghadr M., Zomorodian S. M. A., Shabani R. & Azamatulla H.Md. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944.Google Scholar © 2022 The AuthorsThis is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.

Hybrid modeling on 3D hydraulic features of a step-pool unit

Chendi Zhang1
, Yuncheng Xu1,2, Marwan A Hassan3
, Mengzhen Xu1
, Pukang He1
1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China. 2
College of Water Resources and Civil Engineering, China Agricultural University, Beijing, 100081, China.
5 3Department of Geography, University of British Columbia, 1984 West Mall, Vancouver BC, V6T1Z2, Canada.
Correspondence to: Chendi Zhang (chendinorthwest@163.com) and Mengzhen Xu (mzxu@mail.tsinghua.edu.cn)

Abstract

스텝 풀 시스템은 계류의 일반적인 기반이며 전 세계의 하천 복원 프로젝트에 활용되었습니다. 스텝 풀 장치는 스텝 풀 기능의 형태학적 진화 및 안정성과 밀접하게 상호 작용하는 것으로 보고된 매우 균일하지 않은 수력 특성을 나타냅니다.

그러나 스텝 풀 형태에 대한 3차원 수리학의 자세한 정보는 측정의 어려움으로 인해 부족했습니다. 이러한 지식 격차를 메우기 위해 SfM(Structure from Motion) 및 CFD(Computational Fluid Dynamics) 기술을 기반으로 하이브리드 모델을 구축했습니다. 이 모델은 CFD 시뮬레이션을 위한 입력으로 6가지 유속의 자연석으로 만든 인공 스텝 풀 장치가 있는 침대 표면의 3D 재구성을 사용했습니다.

하이브리드 모델은 스텝 풀 장치에 대한 3D 흐름 구조의 고해상도 시각화를 제공하는 데 성공했습니다. 결과는 계단 아래의 흐름 영역의 분할, 즉 수면에서의 통합 점프, 침대 근처의 줄무늬 후류 및 그 사이의 고속 제트를 보여줍니다.

수영장에서 난류 에너지의 매우 불균일한 분포가 밝혀졌으며 비슷한 용량을 가진 두 개의 에너지 소산기가 수영장에 공존하는 것으로 나타났습니다. 흐름 증가에 따른 풀 세굴 개발은 점프 및 후류 와류의 확장으로 이어지지만 이러한 증가는 스텝 풀 실패에 대한 임계 조건에 가까운 높은 흐름에서 점프에 대해 멈춥니다.

음의 경사면에서 발달된 곡물 20 클러스터와 같은 미세 지반은 국부 수력학에 상당한 영향을 주지만 이러한 영향은 수영장 바닥에서 억제됩니다. 스텝 스톤의 항력은 가장 높은 흐름이 사용되기 전에 배출과 함께 증가하는 반면 양력은 더 큰 크기와 더 넓은 범위를 갖습니다. 우리의 결과는 계단 풀 형태의 복잡한 흐름 특성을 조사할 때 물리적 및 수치적 모델링을 결합한 하이브리드 모델 접근 방식의 가능성과 큰 잠재력을 강조합니다.

Step-pool systems are common bedforms in mountain streams and have been utilized in river restoration projects around the world. Step-pool units exhibit highly non-uniform hydraulic characteristics which have been reported to closely 10 interact with the morphological evolution and stability of step-pool features. However, detailed information of the threedimensional hydraulics for step-pool morphology has been scarce due to the difficulty of measurement. To fill in this knowledge gap, we established a hybrid model based on the technologies of Structure from Motion (SfM) and computational fluid dynamics (CFD). The model used 3D reconstructions of bed surfaces with an artificial step-pool unit built by natural stones at six flow rates as inputs for CFD simulations. The hybrid model succeeded in providing high-resolution visualization 15 of 3D flow structures for the step-pool unit. The results illustrate the segmentation of flow regimes below the step, i.e., the integral jump at the water surface, streaky wake vortexes near the bed, and high-speed jets in between. The highly non-uniform distribution of turbulence energy in the pool has been revealed and two energy dissipaters with comparable capacity are found to co-exist in the pool. Pool scour development under flow increase leads to the expansion of the jump and wake vortexes but this increase stops for the jump at high flows close to the critical condition for step-pool failure. The micro-bedforms as grain 20 clusters developed on the negative slope affect the local hydraulics significantly but this influence is suppressed at pool bottom. The drag forces on the step stones increase with discharge before the highest flow is used while the lift force has a larger magnitude and wider varying range. Our results highlight the feasibility and great potential of the hybrid model approach combining physical and numerical modeling in investigating the complex flow characteristics of step-pool morphology.

Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with 265 lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.

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Numerical study of the effect of flow velocity and flood roughness components on hydraulic flow performance in composite sections with converging floodplains

Numerical study of the effect of flow velocity and flood roughness components on hydraulic flow performance in composite sections with converging floodplains

Authors

1 Civil Enigneering Department, Lahijan Branch.Islamic Azad University.Lahijan.Iran

2 Department of Civil Engnieering, University of Qom,Qom,Iran

3 Civil Engineering Department, Lahijan Branch,Islamic Azad Univeristy,Lahijan,Iran

Abstract

홍수와 그 위험을 통제해야 할 필요성은 누구에게도 숨겨져 있지 않습니다. 또한 이 현상으로 인해 다양한 경제, 사회 및 환경 문제가 영향을 받습니다. 홍수 제어 방법의 설계 및 최적 관리의 첫 번째 단계는 홍수 중 하천 거동을 올바르게 식별하는 것입니다.

홍수 경로 지정, 하상 및 하천 면적 결정 등과 같은 대부분의 하천 엔지니어링 프로젝트에서 하천 단면의 수리학적 매개변수의 평균값을 계산하는 것으로 충분합니다. 오늘날 유체 환경 연구에서 수치 및 분석 방법의 사용이 성장하고 발전했습니다.

신뢰할 수 있는 결과 생성으로 인해 물리적 모델에 대한 좋은 대안이 될 수 있었습니다. 오늘날 수치 모델의 급속한 발전과 컴퓨터 계산 속도의 증가로 인해 3D 수치 모델의 사용이 선호되며 또한 강의 속도 분포 및 전단 응력을 측정하는 데 시간이 많이 걸리고 비용이 많이 들기 때문에 결과 3D 수치 모델의 가치가 있을 것입니다.

한편, 본 연구에서는 복합단면에 대해 FLOW-3D 모델을 이용한 종합적인 수치연구가 이루어지지 않았음을 보여주고 있어 적절한 연구기반을 제공하고 있습니다.

따라서 본 연구의 혁신은 발산 및 수렴 범람원을 동반하는 비 각형 복합 단면에서 흐름의 상태 및 수리 성능에 대한 거칠기와 같은 매개 변수의 영향에 대한 수치 연구입니다.

수치해석 결과를 검증하기 위해 Younesi(2013) 연구를 이용하였습니다. 이 실험에서는 먼저 고정층이 있는 복합 프리즘 및 비 프리즘 단면의 수리 흐름을 조사한 다음 조건을 유지하면서 프리즘 및 비 프리즘 모드에서 퇴적물 이동 실험을 수행했습니다.

실험은 15미터 길이의 연구 채널에서 수행되었습니다. 이 운하는 초당 250리터의 시스템에서 재순환을 위해 제공될 수 있는 유속과 0.0088 000의 종경사를 가진 폭 400mm의 두 개의 대칭 범람원이 있는 합성 운하입니다. 범람원의 가장자리는 0.18미터와 같고 주요 운하의 너비는 0.4미터와 같습니다(그림 1).

본수로의 바닥과 벽을 거칠게 하기 위해 평균직경 0.65mm의 퇴적물을 사용하였으며, 각 단계에서 범람원의 벽과 바닥은 평균직경 0.65, 1.3, 1.78의 퇴적물로 거칠게 하였습다. (mm). 삼각형 오버플로는 운하 상류에서 운하로의 유입량을 측정하는 데 사용됩니다.

상대깊이 0.15와 0.25, 직경 14mm의 마이크로몰리나 실험과 상대깊이 0.35의 실험에서는 유속을 측정하기 위해 3차원 속도계(ADV)를 사용하였습니다. 수위는 0.1mm의 정확도로 깊이 게이지로 측정 되었습니다.

본 연구에서는 수면 프로파일의 수치적 모델을 검증하기 위해 실험 0.25-2에서 발산대의 시작, 중간 및 끝에서 세 단면의 평균 깊이 속도 분포 및 경계 전단 응력) -11.3-NP 및 0.25-2-5.7-NP 및 또한 각형 복합 단면의 0.25-2-2 P 테스트가 평가되었습니다.

각형 합성 단면의 P.20-2-2-P 테스트와 관련된 RMSE 및 NRMSE 지수 값 및 표 (2) 실험 11.3에서 RMSE 및 NRMSE 지수 값 -2-0.25-NP 및 -0.25. 2-5.7-NP가 제공됩니다. 실험 0.25-2-5.7-NP-11.3-2-0.25, NP 및 P.2.0-2-2-P의 평균 깊이 속도의 검증과 관련된 결과가 표시됩니다. 0.25-2-5.7-NP 실험에서 초, 중, 기말 NRMSE의 양은 각각 5.7, 11.8, 10.3%로 계산되었으며, 이는 초급이 우수, 중급이 양호, 최종 성적. 배치. 보시다시피, RMSE 값은 각각 0.026, 0.037 및 0.026으로 계산됩니다.

실험 11.3-2-0.25, NP에서 초급, 중급 및 최종 수준의 NRMSE 값은 각각 7, 11.2 및 15.4%로 계산되었으며, 이는 초급에서 우수 범주 및 우수 범주에서 중간 및 최종 수준. 가져 가다. 보시다시피, RMSE 값은 각각 0.032, 0.038, 0.04로 계산됩니다. 0.25-2-P 실험에서 NRMSE 값은 1.7%로 계산되어 우수 범주에 속한다. 보시다시피 RMSE 값도 0.004로 계산됩니다. 중간 깊이의 속도 분포와 관련하여 수치 모델은 실험실 결과에 적합하며 접합 영역에 작은 오류만 입력되었다고 말할 수 있습니다. 이는 2차 전지의 이동 결과로 간주될 수 있습니다. 모서리를 향해.
결론: 본 연구에서는 3차원 유동 해석이 가능한 Flow 3D 소프트웨어를 사용하여 각형 및 비각형 단면이 복합된 수로의 유동 패턴을 조사했습니다. 3개의 다른 상대 거칠기(1, 2 및 2.74)와 3개의 상대 깊이(0.15, 0.25 및 0.35) 및 5.7 및 11.3도의 발산 각도에 대해 속도의 세로 성분 변화, 평균 깊이 속도 분포, 경계 범람원에 의해 전달되는 유속뿐만 아니라 전단 응력 분포를 조사했습니다.

결과는 수로를 따라 범람원의 폭이 증가함에 따라 유속량이 감소함을 보여주었다. 또한 조도가 유동패턴에 미치는 영향에 대한 연구는 일반적으로 벽의 거칠기에 따라 모든 구간에서 유속량이 감소하는 것으로 나타났으며, 또한 본관과 범람원의 교차점에서의 유동패턴은 벽의 거칠기 영향을 더 많이 받는 것으로 나타났습니다. 결과는 또한 상대 깊이가 증가하거나 상대 거칠기가 감소함에 따라 주 수로와 범람원 사이의 속도 구배가 감소함을 보여주었습니다.

Intrpduction: The need to control floods and their dangers is not hidden from anyone. In addition, a wide range of economic, social and environmental issues are affected by this phenomenon. The first step in the design and optimal management of flood control methods is the correct identification of river behavior during floods. In most river engineering projects such as flood routing, determining the bed and river area, etc., calculating the average values of hydraulic parameters of the river section is sufficient. Today, the use of numerical and analytical methods in the study of fluid environment have grown and developed. Due to the production of reliable results, they have been able to be a good alternative to physical models. Today, with the rapid development of numerical models and increasing the speed of computer calculations, the use of 3D numerical models is preferred and also due to the fact that measuring the velocity distribution and shear stress in rivers is very time consuming and expensive, the results of 3D numerical models It will be valuable. On the other hand, the present studies show that comprehensive numerical research using FLOW-3D model has not been performed on composite sections, so a suitable ground for research is provided. Therefore, the innovation of the present study is the numerical study of the effects of parameters such as roughness on the status and hydraulic performance of the flow in non-prismatic composite sections, which are accompanied by divergent and convergent floodplains, which have received less attention numerically.

Methodology: Younesi (2013) research has been used to validate the results of numerical simulation. In these experiments, first the hydraulic flow in composite prismatic and non-prismatic sections with fixed bed was examined and then, while maintaining the conditions, sediment transfer experiments were performed in prismatic and non-prismatic mode. The experiments were performed in a research channel 15 meters long. This canal is a composite canal with two symmetrical floodplains with a width of 400 mm with a flow rate that can be provided for recirculation in the system of 250 liters per second and a longitudinal slope of 0.0088 000. The depth of the main canal to the edge of the floodplain is equal to 0.18 meters and the width of the main canal is equal to 0.4 meters (Figure 1). In order to roughen the bed and walls of the main canal, sediments with an average diameter of 0.65 mm have been used and at each stage, the walls and bed of floodplains have been roughened by sediments with an average diameter of 0.65, 1.3 and 1.78 (mm). A triangular overflow is used to measure the inflow to the canal, upstream of the canal. In order to measure the flow velocity in experiments with relative depth of 0.15 and 0.25, a micromolina with a diameter of 14 mm and in experiments with relative depth of 0.35, a three-dimensional speedometer (ADV) was used. The water level was also taken by depth gauges with an accuracy of 0.1 mm.
Result and Diccussion: In the present study, in order to validate the numerical model of water surface profile, average depth velocity distribution and boundary shear stress in the three sections at the beginning, middle and end of the divergence zone) in experiments 0.25-2-11.3-NP and 0.25-2-5.7-NP and Also, the 0.25-2-2 P test of the prismatic composite section has been evaluated. In Table (1) the values of RMSE and NRMSE indices related to the P.20-2-2-P test of the prismatic composite section, and also in Table (2) the values of the RMSE and NRMSE indices in the experiments 11.3-2-0.25-NP and -0.25. 2-5.7-NP is provided. The results related to the validation of the average depth velocity of the experiments 0.25-2-5.7- NP-11.3-2-0.25, NP and P.2.0-2-2-P are shown. In 0.25-2-5.7-NP experiment, the amount of NRMSE in elementary, middle and final grades was calculated to be 5.7, 11.8 and 10.3%, respectively, which is in the excellent grade in the elementary grade and good in the middle and final grades. Placed. As can be seen, the RMSE values are calculated as 0.026, 0.037 and 0.026, respectively. In the experiment 11.3-2-0.25, NP, the NRMSE values in the primary, middle and final levels were calculated as 7, 11.2 and 15.4%, respectively, which are in the excellent category in the primary level and in the good category in the middle and final levels. Take. As can be seen, the RMSE values are calculated as 0.032, 0.038 and 0.04, respectively. In the 0.25-2-P experiment, the NRMSE value was calculated to be 1.7%, which is in the excellent category. As can be seen, the RMSE value is also calculated to be 0.004. Regarding the medium-depth velocity distribution, it can be said that the numerical model has an acceptable compliance with the laboratory results and only a small error has been entered in the junction area, which can be considered as a result of the movement of secondary cells towards the corners.
Conclusion: in this research The flow pattern in waterways with composite prismatic and non-prismatic sections was investigated using Flow 3D software that is capable of three-dimensional flow analysis. For three different relative roughnesses (1, 2 and 2.74) as well as three relative depths (0.15, 0.25 and 0.35) and divergence angles of 5.7 and 11.3 degrees, changes in the longitudinal component of velocity, The average depth velocity distribution, the boundary shear stress distribution as well as the flow rate transmitted by the floodplains were investigated. The results showed that with increasing the width of floodplains along the canal, the amount of velocity decreases. Also, the study of the effect of roughness on the flow pattern showed that in general, with wall roughness, the amount of velocity has decreased in all sections and also the flow pattern at the junction of the main canal and floodplain is more affected by wall roughness. The results also showed that with increasing relative depth or decreasing relative roughness, the velocity gradient between the main channel and floodplains decreases

Keywords

그림 1 하천횡단구조물 하류부 횡단구조물 파괴

유입조건에 따른압력변이로 인한하천횡단구조물 하류물받이공 및 바닥보호공설계인자 도출최종보고서

주관연구기관 / 홍익대학교 산학협력단
공동연구기관 / 한국건설기술연구원
공동연구기관 / 주식회사 지티이

연구의 목적 및 내용

하천횡단구조물이 하천설계기준(2009)대로 설계되었음에도 불구하고, 하류부에서 물받이공 및 바닥보호공의 피해가 발생하여, 구조물 본체에 대한 안전성이 현저하 게 낮아지고 있는 실정이다. 하천설계기준이 상류부의 수리특성을 반영하였다고 하나 하류부의 수리특성인 유속의 변동 성분 또는 압력의 변동성분까지 고려하고 있지는 않다. 현재 많은 선행연구에서 이러한 난류적 특성이 구조물에 미치는 영 향에 대해 제시하고 있는 실정이며, 국내 하천에서의 피해 또한 이와 관련이 있다 고 판단된다. 이에 본 연구에서는 난류성분 특히 압력의 변동성분이 물받이공과 바닥보호공에 미치는 영향을 정량적으로 분석하여, 하천 횡단구조물의 치수 안전 성 증대에 기여하고자 한다. 물받이공과 바닥보호공에 미치는 압력의 변동성분 (pressure fluctuation) 영향을 분석하기 위해 크게 3가지로 연구내용을 분류하였 다. 첫 번째는 압력의 변동으로 순간적인 음압구배(adversed pressure gradient) 가 발생할 경우 바닥보호공의 사석 및 블록이 이탈하는 것이다. 이를 확인하기 위 해 정밀한 압력 측정장치를 통해 압력변이를 측정하여, 사석의 이탈 가능성을 검 토할 것이며, 최종적으로 이탈에 대한 한계조건을 도출할 것이다. 두 번째는 압력 의 변동이 물받이공의 진동을 유발시켜 이를 지지하고 있는 지반에 다짐효과를 가 져와 물받이공과 지반사이에 공극이 발생하는 경우이다. 이러한 공극으로 물받이 공은 자중 및 물의 압력을 받게 되어, 결국 휨에 의한 파괴가 발생할 가능성이 있 게 된다. 본 연구에서는 실험을 통하여 압력의 변동과 물받이공의 진동을 동시에 측정하여, 진동이 발생하지 않을 최소 두께를 제시할 것이다. 세 번째는 압력변이 로 인한 물받이공의 진동이 피로파괴로 연결되는 경우이다. 이 현상 또한 수리실 험을 통해 압력변이-피로파괴의 관계를 정량적으로 분석하여, 한계 조건을 제시할 것이다. 본 연구는 국내 보 및 낙차공에서 발생하는 다양한 Jet의 특성을 수리실 험으로 재현해야 하며, 이를 위해 평면 Jet 분사기(plane Jet injector)를 고안/ 제작하여, 효율적인 수리실험을 수행할 것이다. 또한 3차원 수치해석을 통해 실제 스케일에 적용함으로써 연구결과의 활용도 및 적용성을 높이고자 한다.

Keywords

압력변이, 물받이공, 바닥보호공, 난류, 진동

 그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 2. 시간에 따른 압력의 변동 양상 및 정의
그림 2. 시간에 따른 압력의 변동 양상 및 정의
 그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
 그림 4. 파괴 개념
그림 4. 파괴 개념
그림 6. PIV 측정 원리(www.photonics.com)
그림 6. PIV 측정 원리(www.photonics.com)
그림 7. LED회로판 및 BIV기법 기본개념
그림 7. LED회로판 및 BIV기법 기본개념
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 9. 감세공의 분류
그림 9. 감세공의 분류
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 18 수리실험 개요도
그림 18 수리실험 개요도
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 128 RNG 모형을 이용한 수치모의 결과
그림 128 RNG 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 130 압력 Data의 필터링
그림 130 압력 Data의 필터링
그림 134 Case 1의 흐름특성 분포도 및 그래프
그림 134 Case 1의 흐름특성 분포도 및 그래프

참고문헌

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감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태.

국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서. 국토해양부 (2010). 낙동강 살리기 사업 24공구(성주칠곡지구) 실시설계보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인.

국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기준. 류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999).

류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.

배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.

우효섭 (2001). 하천수리학. 청문각.

한국수자원학회 (2009). 하천설계기준해설.

한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발

한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
기법에 대한 원천기술개발

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태. 국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인. 국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기

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류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.
배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.
우효섭 (2001). 하천수리학. 청문각. 한국수자원학회 (2009). 하천설계기준해설. 한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발
한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
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Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.

Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes

조도 계수 및 역 고도 변화가 향상된 90도 측면 회전에서 유동의 실험 및 수치 연구

Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. MD. Azamathulla d,*
and C. Venkata Siva Rama Prasade
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

Flow separation at the upstream side of the lateral turnouts (intakes) is a critical issue causing eddy currents at the turn-out entrance. It reduces the effective width of flow, turn-out 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 turn-out entrance and 3 different bed level inverts, with 4 different discharges (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%.

측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 턴아웃 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.

이 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 4가지 다른 배출(총 84개 실험)과 함께 7가지 유형의 조면화 요소를 출구 입구에 설치하고 3가지 서로 다른 베드 레벨 반전 장치를 조사했습니다.

또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다.

두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.

Key words

discharge ratio, flow separation zone, intake, three dimensional simulation

Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes
Experimental and numerical study of flow at a 90 degree lateral turn-out with enhanced roughness coefficient and invert elevation changes
Figure 2 | Roughness plates.
Figure 2 | Roughness plates.
Figure 3 | Effect of roughness on separation zone dimensions
Figure 3 | Effect of roughness on separation zone dimensions
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 5 | Comparison of separation zone for n¼0.023 and n¼0.032.
Figure 5 | Comparison of separation zone for n¼0.023 and n¼0.032.
Figure 6 | Effect of drop implementation on separation zone dimensions
Figure 6 | Effect of drop implementation on separation zone dimensions
Figure 7 | Combined effect of roughness and drop on separation zone dimensions
Figure 7 | Combined effect of roughness and drop on separation zone dimensions
Figure 8 | Non- dimensional Length of separation zone (Lr) variations against relative unit discharge per width (qr) in present study compared with other methods.
Figure 8 | Non- dimensional Length of separation zone (Lr) variations against relative unit discharge per width (qr) in present study compared with other methods.
Figure 9 | Velocity profiles for various roughness coefficients along turn-out width.
Figure 9 | Velocity profiles for various roughness coefficients along turn-out width.
Figure 10 | Effect of roughness on sepration zone dimensions in numerical study
Figure 10 | Effect of roughness on sepration zone dimensions in numerical study
Figure 11 | Comparision of the vortex area (software output) with three roughness (0.009, 0.023 and 0.032).
Figure 11 | Comparision of the vortex area (software output) with three roughness (0.009, 0.023 and 0.032).
Figure 12 | Comparison of vortex area in 3D mode (tecplot output) with two roughness (a) 0.009 and (b) 0.032
Figure 12 | Comparison of vortex area in 3D mode (tecplot output) with two roughness (a) 0.009 and (b) 0.032
Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.
Figure 13 | Velocity vector for flow condition Q¼22 l/s, Near surface.
Figure 14 | Exprimental and numerical measured velocity.
Figure 14 | Exprimental and numerical measured velocity.

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Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

다공성 미디어 및 나노유체에 의해 강화된 수집기로 태양광 CCHP 시스템의 최적화

Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid


Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4

Abstract

태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.

다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.

본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.

나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.

본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.

The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.

1. Introduction

Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability [1]. Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) [2]. Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system [3].

Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption [4].

Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered [5]. Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors [6]. One of the major problems of solar collectors is their low efficiency [7]. Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.

There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors [8]. A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al. [9] reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.

Abbasi et al. [10] proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.

Jiang et al. [11] combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [21215].

Wang et al. [16] optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% [17]. Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [1819].

Hirasawa et al. [20] investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid [21]. In the experimental study done by Jouybari et al. [22], the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al. [23] analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.

Shojaeizadeh et al. [24] investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al. [25] researched on the thermal performance of solar flat plate collectors for working fluid water with different nanofluids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanofluid as an absorbing medium causes the thermal efficiency to enhance up to 31.64%.

The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.

2. Cycle Description

CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water [26].

For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1 The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.

According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.

2.1. System Analysis Equations

An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic

Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.

Figure 1 Schematic shape of the cogeneration cycle.Table 2 Temperature and humidity of different points of system.

Based on the first law of thermodynamic, energy analysis is based on the following steps.

First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.

Collector efficiency is going to be calculated by the following equation [9]:

Total energy received by the collector is given by [9]

Also, the auxiliary boiler heat load is [2]

Energy consumed from vapor to expander is calculated by [2]

The power output form by the screw expander [9]:

The efficiency of the expander is 80% in this case [11].

In this step, cooling and heating loads were calculated and then, the required heating load to reach sanitary hot water will be calculated as follows:

First step: calculating the cooling load with the following equation [9]:

Second step: calculating heating loads [9]:

Then, calculating the required loud for sanitary hot water will be [9]

According to the above-mentioned equations, efficiency is [9]

In the third step, calculated exergy analysis as follows.

First, the received exergy collector from the sun is calculated [9]:

In the previous equation, f is the constant of air dilution.

The received exergy from the collector is [9]

In the case of using natural gas in an auxiliary heater, the gas exergy is calculated from the following equation [12]:

Delivering exergy from vapor to expander is calculated with the following equation [9]:

In the fourth step, the exergy in cooling and heating is calculated by the following equation:

Cooling exergy in summer is calculated [9]:

Heating exergy in winter is calculated [9]:

In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads [9]:

3. Porous Media

The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.

Figure 2 Copper foam with a porosity of 95%.Table 3 Thermophysical parameters and dimensions of copper foam.

In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.

Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method [27]. Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.

Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

3.1. Nano Fluid

In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4 Properties of the nanoparticles [9].

System constant parameters for input in the software are shown in Table 5.Table 5 System constant parameters.

The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).

The density of the mixture is shown in the following equation [28]:where ρ is density and ϕ is the nanoparticles volume fraction.

The specific heat capacity is calculated from the following equation [29]:

The thermal conductivity of the nanofluid is calculated from the following equation [29]:

The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.

The mixture viscosity is calculated as follows [30]:

In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.

4. Results and Discussion

In the present study, relations were written according to Wang et al. [16] and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.

Figure 4 Verification charts of energy analysis results.

Figure 5 Verification charts of exergy analysis results.

We may also investigate the application of machine learning paradigms [3141] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [4255], and intelligent model studies [5661] as well, for example, methods such as particle swarm optimizer (PSO) [6062], differential search (DS) [63], ant colony optimizer (ACO) [616465], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [5367], differential evolution (DE) [6869], and other fusion and boosted systems [4146485054557071].

At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [922263072]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6 Collectors with different percentages of nanofluids and porous media.

In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.

Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.

Figure 6 Energy and exergy efficiencies of the PTC with porous media and nanofluid.

Figure 7 Energy and exergy efficiency of the SCCHP.

Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.

In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe [73]. According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges [74]. One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.

5. Conclusion and Future Directions

In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.

In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.

In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.

Nomenclature

:Solar radiation
a:Heat transfer augmentation coefficient
A:Solar collector area
Bf:Basic fluid
:Specific heat capacity of the nanofluid
F:Constant of air dilution
:Thermal conductivity of the nanofluid
:Thermal conductivity of the basic fluid
:Viscosity of the nanofluid
:Viscosity of the basic fluid
:Collector efficiency
:Collector energy receives
:Auxiliary boiler heat
:Expander energy
:Gas energy
:Screw expander work
:Cooling load, in kilowatts
:Heating load, in kilowatts
:Solar radiation energy on collector, in Joule
:Sanitary hot water load
Np:Nanoparticle
:Energy efficiency
:Heat exchanger efficiency
:Sun exergy
:Collector exergy
:Natural gas exergy
:Expander exergy
:Cooling exergy
:Heating exergy
:Exergy efficiency
:Steam mass flow rate
:Hot water mass flow rate
:Specific heat capacity of water
:Power output form by the screw expander
Tam:Average ambient temperature
:Density of the mixture.

Greek symbols

ρ:Density
ϕ:Nanoparticles volume fraction
β:Ratio of the nanolayer thickness.

Abbreviations

CCHP:Combined cooling, heating, and power
EES:Engineering equation solver.

Data Availability

For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.

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.

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Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China

Barrier Lake의 홍수 침수 진행 및 평가지역 생태 시공간 반응 사례 연구 (쓰촨-티베트 지역)

Flood Inundation Evolution of Barrier Lake and Evaluation of Regional Ecological Spatiotemporal Response — A Case Study of Sichuan-Tibet Region

Abstract

중국 쓰촨-티베트 지역은 댐 호수의 발생과 붕괴를 동반한 지진 재해가 빈번한 지역이었습니다. 댐 호수의 붕괴는 하류 직원의 생명과 재산 안전을 심각하게 위협합니다.

동시에 국내외 학자들은 주변의 댐 호수에 대해 우려하고 있으며 호수에 대한 생태 연구는 거의 없으며 댐 호수가 생태에 미치는 영향은 우리 호수 건설 프로젝트에서 매우 중요한 계몽 의의를 가지고 있습니다.

이 기사의 목적은 방벽호의 댐 붕괴 위험을 과학적으로 예측하고 생태 환경에 대한 영향을 조사하며 통제 조치를 제시하는 것입니다. 본 논문은 쓰촨-티베트 지역의 Diexihaizi, Tangjiashan 댐호, Hongshihe 댐의 4대 댐 호수 사건을 기반으로 원격 감지 이미지에서 수역을 추출하고 HEC-RAS 모델을 사용하여 위험이 있는지 여부를 결정합니다.

댐 파손 여부 및 댐의 경로 예측; InVEST 모델을 이용하여 1990년부터 2020년까지 가장 작은 행정 구역(군/구)이 위치한 서식지를 평가 및 분석하고, 홍수 침수 결과를 기반으로 평가합니다. 결과는 공학적 처리 후 안정적인 댐 호수(Diexi Haizi)가 서식지 품질 지수에 안정화 효과가 있음을 보여줍니다.

댐 호수의 형성은 인근 토지 이용 유형과 지역 경관 생태 패턴을 변화 시켰습니다. 서식지 품질 지수는 사이 호수 주변 1km 지역에서 약간 감소하지만 3km 지역과 5km 지역에서 서식지 품질이 향상됩니다. 인공 홍수 방류 및 장벽 호수의 공학적 보강이 필요합니다.

이 논문에서 인간의 통제가 강한 지역은 다른 지역의 서식지 질 지수보다 더 잘 회복될 것입니다.

The Sichuan-Tibet region of China has always been an area with frequent earthquake disasters, accompanied by the occurrence and collapse of dammed lakes. The collapse of dammed lakes seriously threatens the lives and property safety of downstream personnel.

At the same time, domestic and foreign scholars are concerned about the surrounding dammed lake there are few ecological studies on the lake, and the impact of the dammed lake on the ecology has very important enlightenment significance for our lake construction project. It is the purpose of this article to scientifically predict the risk of dam break in a barrier lake, explore its impact on the ecological environment and put forward control measures.

Based on the four major dammed lake events of Diexihaizi, Tangjiashan dammed lake, and Hongshihe dammed lake in the Sichuan-Tibet area, this paper extracts water bodies from remote sensing images and uses the HEC-RAS model to determine whether there is a risk of the dam break and whether Forecast the route of the dam; and use the InVEST model to evaluate and analyze the habitat of the smallest administrative district (county/district) where it is located from 1990 to 2020 and make an evaluation based on the results of flood inundation.

The results show that the stable dammed lake (Diexi Haizi) after engineering treatment has a stabilizing effect on the habitat quality index. The formation of the dammed lake has changed the nearby land-use types and the regional landscape ecological pattern.

The habitat quality index will decrease slightly in the 1 km area around Sai Lake, but the habitat quality will increase in the 3 km area and the 5 km area. Artificial flood discharge and engineering reinforcement of barrier lakes are necessary. In this paper, the areas with strong human control will recover better than other regions’ habitat quality index.

Fengshan Jiang (  florachaing@mail.ynu.edu.cn )
Yunnan University https://orcid.org/0000-0001-6231-6180
Xiaoai Dai
Chengdu University of Technology https://orcid.org/0000-0003-1342-6417
Zhiqiang Xie
Yunnan University
Tong Xu
Yunnan University
Siqiao Yin
Yunnan University
Ge Qu
Chengdu University of Technology
Shouquan Yang
Yunnan University
Yangbin Zhang
Yunnan University
Zhibing Yang
Yunnan University
Jiarui Xu
Yunnan University
Zhiqun Hou
Kunming institute of surveying and mapping

Keywords

dammed lake, regional ecology, flood simulation, habitat quality

Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
Figure 1 Location map of barrier lakes, Sichuan-Tibet region, China
Figure 8 Habitat quality changes in Maoxian County
Figure 8 Habitat quality changes in Maoxian County
Figure 9 Habitat quality changes in Beichuan County
Figure 9 Habitat quality changes in Beichuan County
Figure 10 Habitat quality change map of Qingchuan County
Figure 10 Habitat quality change map of Qingchuan County

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Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

CFD 모델링을 이용한 침수 배수로 흐름의 수리학적 해석 및 슈트 폭기장치 성능 평가: Mangla Dam 배수로 사례 연구

Hydraulic Analysis of Submerged Spillway Flows and Performance Evaluation of Chute Aerator Using CFD Modeling: A Case Study of Mangla Dam Spillway

Muhammad Kaleem SarwarZohaib NisarGhulam NabiFaraz ul HaqIjaz AhmadMuhammad Masood & Noor Muhammad Khan 

Abstract

대용량 배출구가 있는 수중 여수로는 일반적으로 홍수 처리 및 침전물 세척의 이중 기능을 수행하기 위해 댐 정상 아래에 제공됩니다. 이 방수로를 통과하는 홍수 물은 난류 거동을 나타냅니다. 

게다가 이러한 난류의 수력학적 분석은 어려운 작업입니다. 

따라서 본 연구는 파키스탄 Mangla Dam에 건설된 수중 여수로의 수리학적 거동을 수치해석을 통해 조사하는 것을 목적으로 한다. 또한 다양한 작동 조건에서 화기의 유압 성능을 평가했습니다. 

Mangla Spillway의 흐름을 수치적으로 모델링하는 데 전산 유체 역학 코드 FLOW 3D가 사용되었습니다. 레이놀즈 평균 Navier-Stokes 방정식은 난류 흐름을 수치적으로 모델링하기 위해 FLOW 3D에서 사용됩니다. 

연구 결과에 따르면 개발된 모델은 최대 6%의 허용 오차로 흐름 매개변수를 계산하므로 수중 여수로 흐름을 시뮬레이션할 수 있습니다. 

또한, 여수로 슈트 베드 주변 모델에 의해 계산된 공기 농도는 폭기 장치에 램프를 설치한 후 6% 이상으로 상승한 3%로 개발된 모델도 침수형 폭기 장치의 성능을 평가할 수 있음을 보여주었습니다.

Submerged spillways with large capacity outlets are generally provided below the dam crest to perform the dual functions of flood disposal and sediment flushing. Flood water passing through these spillways exhibits turbulent behavior. Moreover; hydraulic analysis of such turbulent flows is a challenging task. Therefore, the present study aims to use numerical simulations to examine the hydraulic behavior of submerged spillways constructed at Mangla Dam, Pakistan. Besides, the hydraulic performance of aerator was also evaluated at different operating conditions. Computational fluid dynamics code FLOW 3D was used to numerically model the flows of Mangla Spillway. Reynolds-averaged Navier–Stokes equations are used in FLOW 3D to numerically model the turbulent flows. The study results indicated that the developed model can simulate the submerged spillway flows as it computed the flow parameters with an acceptable error of up to 6%. Moreover, air concentration computed by model near spillway chute bed was 3% which raised to more than 6% after the installation of ramp on aerator which showed that developed model is also capable of evaluating the performance of submerged spillway aerator.

Keywords

  • Aerator
  • CFD
  • FLOW 3D
  • Froude number
  • Submerged spillway
  • Fig. 1extended data figure 1Fig. 2extended data figure 2Fig. 3extended data figure 3Fig. 4extended data figure 4Fig. 5extended data figure 5Fig. 6extended data figure 6Fig. 7extended data figure 7Fig. 8

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Fig. 11. Velocity vectors along x-direction through the center of the box culvert for B0, B30, B50, and B70 respectively.

Numerical investigation of scour characteristics downstream of blocked culverts

막힌 암거 하류의 세굴 특성 수치 조사

NesreenTahabMaged M.El-FekyaAtef A.El-SaiadaIsmailFathya
aDepartment of Water and Water Structures Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt
bLab Manager, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt

Abstract

횡단 구조물을 통한 막힘은 안정성을 위협하는 위험한 문제 중 하나입니다. 암거의 막힘 형상 및 하류 세굴 특성에 미치는 영향에 관한 연구는 거의 없습니다.

이 연구의 목적은 수면과 세굴 모두에서 상자 암거를 통한 막힘의 작용을 수치적으로 논의하는 것입니다. 이를 위해 FLOW 3D v11.1.0을 사용하여 퇴적물 수송 모델을 조사했습니다.

상자 암거를 통한 다양한 차단 비율이 연구되었습니다. FLOW 3D 모델은 실험 데이터로 보정되었습니다. 결과는 FLOW 3D 프로그램이 세굴 다운스트림 상자 암거를 정확하게 시뮬레이션할 수 있음을 나타냅니다.

막힌 경우에 대한 속도 분포, 최대 세굴 깊이 및 수심을 플롯하고 비차단된 사례(기본 사례)와 비교했습니다.

그 결과 암거 높이의 70% 차단율은 상류의 수심을 암거 높이의 2.3배 증가시키고 평균 유속은 기본 경우보다 3배 더 증가시키는 것으로 입증되었다. 막힘 비율의 함수로 상대 최대 세굴 깊이를 추정하는 방정식이 만들어졌습니다.

Blockage through crossing structures is one of the dangerous problems that threaten its stability. There are few researches concerned with blockage shape in culverts and its effect on characteristics of scour downstream it.

The study’s purpose is to discuss the action of blockage through box culvert on both water surface and scour numerically. A sediment transport model has been investigated for this purpose using FLOW 3D v11.1.0. Different ratios of blockage through box culvert have been studied. The FLOW 3D model was calibrated with experimental data.

The results present that the FLOW 3D program was capable to simulate accurately the scour downstream box culvert. The velocity distribution, maximum scour depth and water depths for blocked cases have been plotted and compared with the non-blocked case (base case).

The results proved that the blockage ratio 70% of culvert height makes the water depth upstream increases by 2.3 times of culvert height and mean velocity increases by 3 times more than in the base case. An equation has been created to estimate the relative maximum scour depth as a function of blockage ratio.

1. Introduction

Local scour is the removal of granular bed material by the action of hydrodynamic forces. As the depth of scour hole increases, the stability of the foundation of the structure may be endangered, with a consequent risk of damage and failure [1]. So the prediction and control of scour is considered to be very important for protecting the water structures from failure. Most previous studies were designed to study the different factors that impact on scour and their relationship with scour hole dimensions like fluid characteristics, flow conditions, bed properties, and culvert geometry. Many previous researches studied the effect of flow rate on scour hole by information Froude number or modified Froude number [2][3][4][5][6]. Cesar Mendoza [6] found a good correlation between the scour depth and the discharge Intensity (Qg−.5D−2.5). Breusers and Raudkiv [7] used shear velocity in the outlet-scour prediction procedure. Ali and Lim [8] used the densimetric Froude number in estimation of the scour depth [1][8][9][10][11][12][13][14]. “The densimetric Froude number presents the ratio of the tractive force on sediment particle to the submerged specific weight of the sediment” [15](1)Fd=uρsρ-1gD50

Ali and Lim [8] pointed to the consequence of tailwater depth on scour behavior [1][2][8][13]. Abida and Townsend [2] indicated that the maximum depth of local scour downstream culvert was varying with the tailwater depth in three ways: first, for very shallow tailwater depths, local scouring decreases with a decrease in tailwater depth; second, when the ratio of tailwater depth to culvert height ranged between 0.2 and 0.7, the scour depth increases with decreasing tailwater depth; and third for a submerged outlet condition. The tailwater depth has only a marginal effect on the maximum depth of scour [2]. Ruff et al. [16] observed that for materials having similar mean grain sizes (d50) but different standard deviations (σ). As (σ) increased, the maximum scour hole depth decreased. Abt et al. [4] mentioned to role of soil type of maximum scour depth. It was noticed that local scour was more dangerous for uniform sands than for well-graded mixtures [1][2][4][9][17][18]. Abt et al [3][19] studied the culvert shape effect on scour hole. The results evidenced that the culvert shape has a limited effect on outlet scour. Under equivalent discharge conditions, it was noted that a square culvert with height equal to the diameter of a circular culvert would reduce scour [16][20]. The scour hole dimension was also effected by the culvert slope. Abt et al. [3][21] showed that the culvert slope is a key element in estimating the culvert flow velocity, the discharge capacity, and sediment transport capability. Abt et al. [21][22] tested experimentally culvert drop height effect on maximum scour depth. It was observed that as the drop height was increasing, the depth of scour was also increasing. From the previous studies, it could have noticed that the most scour prediction formula downstream unblocked culvert was the function of densimetric Froude number, soil properties (d50, σ), tailwater depth and culvert opening size. Blockage is the phenomenon of plugging water structures due to the movement of water flow loaded with sediment and debris. Water structures blockage has a bad effect on water flow where it causes increasing of upstream water level that may cause flooding around the structure and increase of scour rate downstream structures [23][24]. The blockage phenomenon through was studied experimentally and numerical [15][25][26][27][28][29][30][31][32][33]. Jaeger and Lucke [33] studied the debris transport behavior in a natural channel in Australia. Froude number scale model of an existing culvert was used. It was noticed that through rainfall event, the mobility of debris was impressed by stream shape (depth and width). The condition of the vegetation (size and quantities) through the catchment area was the main factor in debris transport. Rigby et al. [26] reported that steep slope was increasing the ability to mobilize debris that form field data of blocked culverts and bridges during a storm in Wollongong city.

Streftaris et al. [32] studied the probability of screen blockage by debris at trash screens through a numerical model to relate between the blockage probability and nature of the area around. Recently, many commercial computational fluid programs (CFD) such as SSIIM, Fluent, and FLOW 3D are used in the analysis of the scour process. Scour and sediment transport numerical model need to validate by using experimental data or field data [34][35][36][37][38]. Epely-Chauvin et al. [36] investigated numerically the effect of a series of parallel spur diked. The experimental data were compared by SSIIM and FLOW 3D program. It was found that the accuracy of calibrated FLOW 3D model was better than SSIIM model. Nielsen et al. [35] used the physical model and FLOW 3D model to analyze the scour process around the pile. The soil around the pile was uniform coarse stones in the physical models that were simulated by regular spheres, porous media, and a mixture of them. The calibrated porous media model can be used to determine the bed shear stress. In partially blocked culverts, there aren’t many studies that explain the blockage impact on scour dimensions. Sorourian et al. [14][15] studied the effect of inlet partial blockage on scour characteristics downstream box culvert. It resulted that the partial blockage at the culvert inlet could be the main factor in estimating the depth of scour. So, this study is aiming to investigate the effects of blockage through a box culvert on flow and scour characteristics by different blockage ratios and compares the results with a non-blocked case. Create a dimensionless equation relates the blockage ratio of the culvert with scour characteristics downstream culvert.

2. Experimental data

The experimental work of the study was conducted in the Hydraulics and Water Engineering Laboratory, Faculty of Engineering, Zagazig University, Egypt. The flume had a rectangular cross-section of 66 cm width, 65.5 cm depth, and 16.2 m long. A rectangular culvert was built with 0.2 m width, 0.2 m height and 3.00 m long with θ = 25° gradually outlet and 0.8 m fixed apron. The model was located on the mid-point of the channel. The sediment part was extended for a distance 2.20 m with 0.66 m width and 0.20 m depth of coarse sand with specific weight 1.60 kg/cm3, d50 = 2.75 mm and σ (d90/d50) = 1.50. The particle size distribution was as shown in Fig. 1. The experimental model was tested for different inlet flow (Q) of 25, 30, 34, 40 l/s for different submerged ratio (S) of 1.25, 1.50, 1.75.

3. Dimensional analysis

A dimensional analysis has been used to reduce the number of variables which affecting on the scour pattern downstream partial blocked culvert. The main factors affecting the maximum scour depth are:(2)ds=f(b.h.L.hb.lb.Q.ud.hu.hd.D50.ρ.ρs.g.ls.dd.ld)

Fig. 2 shows a definition sketch of the experimental model. The maximum scour depth can be written in a dimensionless form as:(3)dsh=f(B.Fd.S)where the ds/h is the relative maximum scour depth.

4. Numerical work

The FLOW 3D is (CFD) program used by many researchers and appeared high accuracy in solving hydrodynamic and sediment transport models in the three dimensions. Numerical simulation with FLOW 3D was performed to study the impacts of blockage ratio through box culvert on shear stress, velocity distribution and the sediment transport in terms of the hydrodynamic features (water surface, velocity and shear stress) and morphological parameters (scour depth and sizes) conditions in accurately and efficiently. The renormalization group (RNG) turbulence model was selected due to its high ability to predict the velocity profiles and turbulent kinetic energy for the flow through culvert [39]. The one-fluid incompressible mode was used to simulate the water surface. Volume of fluid (VOF) method was employed in FLOW 3D to tracks a liquid interface through arbitrary deformations and apply the correct boundary conditions at the interface [40].1.

Governing equations

Three-dimensional Reynolds-averaged Navier Stokes (RANS) equation was applied for incompressible viscous fluid motion. The continuity equation is as following:(4)VF∂ρ∂t+∂∂xρuAx+∂∂yρvAy+∂∂zρwAz=RDIF(5)∂u∂t+1VFuAx∂u∂x+vAy∂u∂y+ωAz∂u∂z=-1ρ∂P∂x+Gx+fx(6)∂v∂t+1VFuAx∂v∂x+vAy∂v∂y+ωAz∂v∂z=-1ρ∂P∂y+Gy+fy(7)∂ω∂t+1VFuAx∂ω∂x+vAy∂ω∂y+ωAz∂ω∂z=-1ρ∂P∂z+Gz+fz

ρ is the fluid density,

VF is the volume fraction,

(x,y,z) is the Cartesian coordinates,

(u,v,w) are the velocity components,

(Ax,Ay,Az) are the area fractions and

RDIF is the turbulent diffusion.

P is the average hydrodynamic pressure,

(Gx, Gy, Gz) are the body accelerations and

(fx, fy, fz) are the viscous accelerations.

The motion of sediment transport (suspended, settling, entrainment, bed load) is estimated by predicting the erosion, advection and deposition process as presented in [41].

The critical shields parameter is (θcr) is defined as the critical shear stress τcr at which sediments begin to move on a flat and horizontal bed [41]:(8)θcr=τcrgd50(ρs-ρ)

The Soulsby–Whitehouse [42] is used to predict the critical shields parameter as:(9)θcr=0.31+1.2d∗+0.0551-e(-0.02d∗)(10)d∗=d50g(Gs-1ν3where:

d* is the dimensionless grain size

Gs is specific weight (Gs = ρs/ρ)

The entrainment coefficient (0.005) was used to scale the scour rates and fit the experimental data. The settling velocity controls the Soulsby deposition equation. The volumetric sediment transport rate per width of the bed is calculated using Van Rijn [43].2.

Meshing and geometry of model

After many trials, it was found that the uniform cell size with 0.03 m cell size is the closest to the experimental results and takes less time. As shown in Fig. 3. In x-direction, the total model length in this direction is 700 cm with mesh planes at −100, 0, 300, 380 and 600 cm respectively from the origin point, in y-direction, the total model length in this direction is 66 cm at distances 0, 23, 43 and 66 cm respectively from the origin point. In z-direction, the total model length in this direction is 120 cm. with mesh planes at −20, 0, 20 and 100 cm respectively.3.

Boundary condition

As shown in Fig. 4, the boundary conditions of the model have been defined to simulate the experimental flow conditions accurately. The upstream boundary was defined as the volume flow rate with a different flow rate. The downstream boundary was defined as specific pressure with different fluid elevation. Both of the right side, the left side, and the bottom boundary were defined as a wall. The top boundary defined as specified pressure with pressure value equals zero.

5. Validation of experimental results and numerical results

The experimental results investigated the flow and scour characteristics downstream culvert due to different flow conditions. The measured value of maximum scour depth is compared with the simulated depth from FLOW 3D model as shown in Fig. 5. The scour results show that the simulated results from the numerical model is quite close to the experimental results with an average error of 3.6%. The water depths in numerical model results is so close to the experimental results as shown in Fig. 6 where the experiment and numerical results are compared at different submerged ratios and flow rates. The results appear maximum error percentage in water depths upstream and downstream the culvert is about 2.37%. This indicated that the FLOW 3D is efficient for the prediction of maximum scour depth and the flow depths downstream box culvert.

6. Computation time

The run time was chosen according to reaching to the stability limit. Hydraulic stability was achieved after 50 s, where the scour development may still go on. For run 1, the numerical simulation was run for 1000 s as shown in Fig. 7 where it mostly reached to scour stability at 800 s. The simulation time was taken 500 s at about 95% of scour stability.

7. Analysis and discussions

Fig. 8 shows the study sections where sec 1 represents to upstream section, sec2 represents to inside section and sec3 represents to downstream stream section. Table 1 indicates the scour hole dimensions at different blockage case. The symbol (B) represents to blockage and the number points to blockage ratio. B0 case signifies to the non-blocked case, B30 is that blockage height is 30% to the culvert height and so on.

Table 1. The scour results of different blockage ratio.

Casehb cmB = hb/hQ lit/sSFdd50 mmds/h measuredls/hdd/hld/hds/h estimated
B000351.261.692.50.581.500.275.000.46
B3060.30351.261.682.50.481.250.274.250.40
B50100.50351.221.742.50.451.100.244.000.37
B70140.70351.231.732.50.431.500.165.500.33

7.1. Scour hole geometry

The scour hole geometry mainly depends on the properties of soil of the bed downstream the fixed apron. From Table 1, the results show that the maximum scour depth in B0 case is about 0.58 of culvert height while the maximum deposition in B0 is 0.27 culvert height. There is a symmetric scour hole as shown in Fig. 9 in B0 case. An asymmetric scour hole is created in B50 and B70 due to turbulences that causes the deviation of the jet direction from the center of the flume where appear in Fig. 11 and Fig. 19.

7.2. Flow water surface

Fig. 10 presents the relative free surface water (hw/h) along the x-direction at center of the box culvert. From the mention Figure, it is easy to release the effect of different blockage ratios. The upstream water level rises by increasing the blockage ratio. Increasing upstream water level may cause flooding over the banks of the waterway. In the 70% blockage case, the upstream water level rises to 2.3 times of culvert height more than the non-blocked case at the same discharge and submerged ratio. The water surface profile shows an increase in water level upstream the culvert due to a decrease in transverse velocity. Because of decreasing velocity downstream culvert, there is an increase in water level before it reaches its uniform depth.

7.3. Velocity vectors

Scour downstream hydraulic structures mainly affects by velocities distribution and bed shear stress. Fig. 11 shows the velocity vectors and their magnitude in xz plane at the same flow conditions. The difference in the upstream water level due to the different blockage ratios is so clear. The maximum water level is in B70 and the minimum level is in B0. The inlet mean velocity value is about 0.88 m/s in B0 increases to 2.86 m/s in B70. As the blockage ratio increases, the inlet velocity increases. The outlet velocity in B0 case makes downward jet causes scour hole just after the fixed apron in the middle of the bed while the blockage causes upward water flow that appears clearly in B70. The upward jet decreases the scour depth to 0.13 culvert height less than B0 case. After the scour hole, the velocity decreases and the flow becomes uniform.

7.4. Velocity distribution

Fig. 12 represents flow velocity (Vx) distribution along the vertical depth (z/hu) upstream the inlet for the different blockage ratios at the same flow conditions. From the Figure, the maximum velocity creates closed to bed in B0 while in blocked case, the maximum horizontal velocity creates at 0.30 of relative vertical depth (z/hu). Fig. 13 shows the (Vz) distribution along the vertical depth (z/hu) upstream culvert at sec 1. From the mentioned Figure, it is easy to note that the maximum vertical is in B70 which appears that as the blockage ratio increases the vertical ratio also increases. In the non-blocked case. The vertical velocity (Vz) is maximum at (z/hu) equals 0.64. At the end of the fixed apron (sec 3), the horizontal velocity (Vx) is slowly increasing to reach the maximum value closed to bed in B0 and B30 while the maximum horizontal velocity occurs near to the top surface in B50 and B70 as shown in Fig. 14. The vertical velocity component along the vertical depth (z/hd) is presented in Fig. 15. The vertical velocity (Vz) is maximum in B0 at vertical depth (z/hd) 0.3 with value 0.45 m/s downward. Figs. 16 and 17 observe velocity components (Vx, Vz) along the vertical depth just after the end of blockage length at the centerline of the culvert barrel. It could be noticed the uniform velocity distribution in B0 case with horizontal velocity (Vx) closed to 1.0 m/s and vertical velocity closed to zero. In the blocked case, the maximum horizontal velocity occurs in depth more than the blockage height.

7.5. Bed velocity distribution

Fig. 18 presents the x-velocity vectors at 1.5 cm above the bed for different blockage ratios from the velocity vectors distribution and magnitude, it is easy to realize the position of the scour hole and deposition region. In B0 and B30, the flow is symmetric so that the scour hole is created around the centerline of flow while in B50 and B70 cases, the flow is asymmetric and the scour hole creates in the right of flow direction in B50. The maximum scour depth is found in the left of flow direction in B70 case where the high velocity region is found.

8. Maximum scour depth prediction

Regression analysis is used to estimate maximum scour depth downstream box culvert for different ratios of blockage by correlating the maximum relative scour by other variables that affect on it in one formula. An equation is developed to predict maximum scour depth for blocked and non-blocked. As shown in the equation below, the relative maximum scour depth(ds/hd) is a function of densimetric Froude number (Fd), blockage ratio (B) and submerged ratio (S)(11)dsh=0.56Fd-0.20B+0.45S-1.05

In this equation the coefficient of correlation (R2) is 0.82 with standard error equals 0·08. The developed equation is valid for Fd = [0.9 to 2.10] and submerged ratio (S) ≥ 1.00. Fig. 19 shows the comparison between relative maximum scour depths (ds/h) measured and estimated for different blockage ratios. Fig. 20 clears the comparison between residuals and ds/h estimated for the present study. From these figures, it could be noticed that there is a good agreement between the measured and estimated relative scour depth.

9. Comparison with previous scour equations

Many previous scour formulae have been produced for calculation the maximum scour depth downstream non-blockage culvert. These equations have been included the effect of flow regime, culvert shape, soil properties and the flow rate on maximum scour depth. Two of previous experimental studies data have been chosen to be compared with the present study results in non-blocked study data. Table 2 shows comparison of culvert shape, densmetric Froude number, median particle size and scour equations for these previous studies. By applying the present study data in these studies scour formula as shown in Fig. 21, it could be noticed that there are a good agreement between present formula results and others empirical equations results. Where that Lim [44] and Abt [4] are so closed to the present study data.

Table 2. Comparison of some previous scour formula.

ResearchersFdCulvert shaped50(mm)Proposed equationSubmerged ratio
Present study0.9–2.11square2.75dsh=0.56Fd-0.20B+0.45S-1.051.25–1.75
Lim [44]1–10Circular1.65dsh=0.45Fd0.47
Abt [4]Fd ≥ 1Circular0.22–7.34-dsh=3.67Fd0.57∗D500.4∗σ-0.4

10. Conclusions

The present study has shown that the FLOW 3D model can accurately simulate water surface and the scour hole characteristics downstream the box culvert with error percentage in water depths does not exceed 2.37%. Velocities distribution through and outlets culvert barrel helped on understanding the scour hole shape.

The blockage through culvert had caused of increasing of water surface upstream structure where the upstream water level in B70 was 2.3 of culvert height more than non-blocked case at the same discharge that could be dangerous on the stability of roads above. The depth averaged velocity through culvert barrel increased by 3 times its value in non-blocked case.

On the other hand, blockage through culvert had a limited effect on the maximum scour depth. The little effect of blockage on maximum scour depth could be noticed in Fig. 11. From this Figure, it could be noted that the residual part of culvert barrel after the blockage part had made turbulences. These turbulences caused the deviation of the flow resulting in the formation of asymmetric scour hole on the side of channel. This not only but in B70 the blockage height caused upward jet which made a wide far scour hole as cleared from the results in Table 1.

An empirical equation was developed from the results to estimate the maximum scour depth relative to culvert height function of blockage ratio (B), submerged ratio (S), and densimetric Froude number (Fd). The equation results was compared with some scour formulas at the same densimetric Froude number rang where the present study results was in between the other equations results as shown in Fig. 21.

Declaration of Competing Interest

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.

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Peer review under responsibility of Faculty of Engineering, Alexandria University.

Figure 7 | Variation of flow field of elliptical bridge pier with different axis ratios under multi-year average flow. (a) Axis ratio ¼ 1. (b) Axis ratio ¼ 0.85. (c) Axis ratio ¼ 0.75. (d) Axis ratio ¼ 0.5. (e) Axis ratio ¼ 0.25. (f) Axis ratio ¼ 0.15. (continued.)

교각의 형태학적 변화가 물의 이동 특성에 미치는 영향에 관한 연구

Study on the effect of morphological changes of bridge piers on water movement properties

Xianqi Zhanga,b,c, Tao Wanga,* and Bingsen Duana
a Water Conservancy College, North china University of Water Resources and Electric Power, Zhengzhou 450046, China
b Collaborative Innovation Center of Water Resources Efficient Utilization and Protection Engineering, Zhengzhou 450046, China c Technology Research Center of Water Conservancy and Marine Tra

ABSTRACT

하천을 가로지르는 교각의 다른 형태는 하천의 유동에 큰 영향을 미치며, 교각의 형태 변화가 물의 유동 특성에 미치는 영향에 대한 연구는 교량 설계 및 하천 범람에 큰 가치가 있습니다.

유체 역학 모델은 하천 흐름 패턴의 변화를 효과적으로 시뮬레이션하고 예측할 수 있으므로 하천 관리에 대한 과학적 데이터 지원을 제공할 수 있습니다.

본 논문은 Mike21을 기반으로 유체역학 모델을 구축하고 이를 황하 하류의 하천 유체역학 수치해석에 적용하고, 타원 교각을 예로 들어 교각 형태 변화가 유속에 미치는 영향을 모사한다. 강의 수위와 흐름장. 결과는 하천의 흐름 특성에 대한 타원형 교각 형태의 영향이 중요하다는 것을 보여줍니다.

동일한 유량에서 최대 축 비율에서 교각의 혼잡 값은 최소 축 비율의 1.65배이며 축 비율이 클수록 혼잡이 심각합니다. 최대 축 비율에서 유속의 차이는 최소 축 비율의 2.33배에 달할 수 있습니다.

The different shapes of bridge piers across rivers have a great influence on the river water movement, and the study of the influence of pier morphology changes on the water movement characteristics is of great value for bridge design and river flooding. The hydrodynamic model can effectively simulate and predict the changes of river flow patterns, which can provide scientific data support for river management. This paper constructs a hydrodynamic model based on Mike21 and applies it to the numerical simulation of river hydrodynamics in the lower reaches of the Yellow River, taking elliptical piers as an example, and simulates the effect of the change of pier morphology on the flow velocity, water level and flow field of the river. The results show that the effect of elliptical pier morphology on the flow characteristics of the river channel is significant; under the same flow rate, the congestion value of the pier at the maximum axis ratio is 1.65 times of the minimum axis ratio, and the larger the axis ratio, the more serious the congestion; the difference in flow velocity at the maximum axis ratio can reach 2.33 times of the minimum axis ratio.

Key words

bridge pier axial ratio, flow regime, MIKE21 flow model, numerical simulation, yellow river

Figure 2 | Location map of the study area.
Figure 2 | Location map of the study area.
Figure 7 | Variation of flow field of elliptical bridge pier with different axis ratios under multi-year average flow. (a) Axis ratio ¼ 1. (b) Axis ratio ¼ 0.85. (c) Axis ratio ¼ 0.75. (d) Axis ratio ¼ 0.5. (e) Axis ratio ¼ 0.25. (f) Axis ratio ¼ 0.15. (continued.)
Figure 7 | Variation of flow field of elliptical bridge pier with different axis ratios under multi-year average flow. (a) Axis ratio ¼ 1. (b) Axis ratio ¼ 0.85. (c) Axis ratio ¼ 0.75. (d) Axis ratio ¼ 0.5. (e) Axis ratio ¼ 0.25. (f) Axis ratio ¼ 0.15. (continued.)

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

Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves

무작위 파동에서 우산 흡입 앵커 기초 주변의 세굴 특성 및 평형 세굴 깊이 예측

Ruigeng Hu 1
, Hongjun Liu 2
, Hao Leng 1
, Peng Yu 3 and Xiuhai Wang 1,2,*

1 College of Environmental Science and Engineering, Ocean University of China, Qingdao 266000, China;
huruigeng@stu.ouc.edu.cn (R.H.); lh4517@stu.ouc.edu.cn (H.L.)
2 Key Lab of Marine Environment and Ecology (Ocean University of China), Ministry of Education,
Qingdao 266000, China; hongjun@ouc.edu.cn
3 Qingdao Geo-Engineering Survering Institute, Qingdao 266100, China; yp6650@stu.ouc.edu.cn

Abstract

무작위 파동 하에서 우산 흡입 앵커 기초(USAF) 주변의 국부 세굴을 연구하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 본 연구에서는 먼저 본 모델의 정확성을 검증하기 위해 검증을 수행하였다.

또한, 세굴 진화와 세굴 메커니즘을 각각 분석하였다. 또한 USAF 주변의 평형 세굴 깊이 Seq를 예측하기 위해 두 가지 수정된 모델이 제안되었습니다. 마지막으로 Seq에 대한 Froude 수 Fr과 Euler 수 Eu의 영향을 연구하기 위해 매개변수 연구가 수행되었습니다.

결과는 현재 수치 모델이 무작위 파동에서 세굴 형태를 묘사하는 데 정확하고 합리적임을 나타냅니다.

수정된 Raaijmaker의 모델은 KCs,p < 8일 때 본 연구의 시뮬레이션 결과와 잘 일치함을 보여줍니다. 수정된 확률적 모델의 예측 결과는 KCrms,a < 4일 때 n = 10일 때 가장 유리합니다. Fr과 Eu가 높을수록 둘 다 더 집중적 인 말굽 소용돌이와 더 큰 결과를 초래합니다.

Figure 1. The close-up of umbrella suction anchor foundation (USAF).
Figure 1. The close-up of umbrella suction anchor foundation (USAF).
Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wvwave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.
Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wvwave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.
Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].
Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].
Figure 9. Scour morphology under different times for case 7.
Figure 9. Scour morphology under different times for case 7.

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Fig. 1  Layout of spillway tunnel

Experimental study and numerical simulation of hydraulic characteristics of ogee spillway tunnel

WU Jingxia1
, ZHANG Chunjin2,3
(1. Xi’an Water Conservancy Survey Design Institute, Xi’an  710054, Shaanxi, China; 2. Key Laboratory of
Yellow River Sediment Research, M. W. R. , Yellow River Institute of Hydraulic Research, Zhengzhou 
450003, Henan, China; 3. State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, Nanjing  210098, Jiangsu, China)

수치 시뮬레이션을 통해 오지 여수로 터널의 수리적 특성 연구의 타당성을 탐색하기 위해 황하 Xiaolangdi 수질 관리 프로젝트의 2번 오지 여수로 터널을 연구 대상으로 취한 다음 오지의 수리 특성 설계 및 점검 홍수 수준 조건에서 여수로 터널은 RNG k-ε 난류 모델을 사용하여 배출 용량, 터널 크라운 잔류 공간, 단면 유속, 압전 수두, 유동 캐비테이션 수, 제트 흐름 범위 및 1 ∶ 40의 일반 수리 모델과 결합된 세굴 구덩이 깊이, 시뮬레이션 값과 실험 값 모두 비교됩니다.

연구결과 모의실험값이 실험값과 일치하여 오지 여수로터널의 수리적 특성을 수치모사를 통해 탐색할 수 있음을 확인하였다. 여수로터널 내부의 흐름은 안정적이고 터널 크라운 잔류 공간은 개방 흐름과 완전 흐름의 교대 흐름 패턴이 없는 25% 이상입니다.

체크 홍수 수위에서 시뮬레이션 값과 유량 계수의 실험 값은 모두 설계에서보다 높으므로 배출 용량은 홍수 제어 관련 설계 요구 사항을 충족할 수 있습니다. 오지 단면과 플립 단면의 유동 캐비테이션 수는 캐비테이션 손상이 발생할 가능성이 작기 때문에 캐비테이션 침식을 줄이기 위한 적절한 적절한 조치가 채택될 필요가 있습니다.

유압 모델의 고르지 않은 표면에 부압이 발생하면 표면 구조에 관련주의를 기울일 필요가 있습니다. 연구 결과는 여수로 터널의 설계 및 건설에 대한 관련 참고 및 이론적 근거를 제공할 수 있습니다.

Keywords

Xiaolangdi Water Control Project; ogee spillway tunnel; simulative calculation; hydraulic characteristics; turbulent
model

Fig. 1  Layout of spillway tunnel
Fig. 1  Layout of spillway tunnel
Fig. 4  Hydraulic modeling
Fig. 4  Hydraulic modeling
Fig. 6  Sectional surface profile distributions
Fig. 6  Sectional surface profile distributions
Fig. 7  Comparison between simulated results and experimental results for flow velocity of section-cross
Fig. 7  Comparison between simulated results and experimental results for flow velocity of section-cross

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Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s.

Optimization Algorithms and Engineering: Recent Advances and Applications

Mahdi Feizbahr,1 Navid Tonekaboni,2Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4Show moreAcademic Editor: Mohammad YazdiReceived08 Apr 2021Revised18 Jun 2021Accepted17 Jul 2021Published11 Aug 2021

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.


강의 식생은 거칠기를 증가시키고 평균 유속을 감소시키며, 유속 에너지를 감소시키고 강의 단면에서 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받으므로 홍수시 유동저항에 큰 영향을 미칩니다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건 및 식물에 따라 다르므로 모델은 유속, 흐름 깊이 및 운하를 따라 식생 유형의 영향을 고려하여 현재 속도를 시뮬레이션해야 합니다. 근관의 거칠기의 영향을 조사하기 위해 총 48개의 모델이 시뮬레이션되었습니다. 결과는 유속을 높임으로써 유속을 감소시키는 식생의 영향은 무시할 수 있는 반면, 해류가 더 낮은 유속일 때 유속을 감소시키는 식생의 영향은 분명히 상당함을 나타냈다.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [114]. 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 [1527]. Consequently, it is necessary to study the effects of the passive factors on the active domain [2836]. 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 [3841].

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 [4345]. 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 [4748].

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 nf, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn 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, Ks = 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 [4555].

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 [475758] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [455961]. 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 [496366] 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, S0 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 xyz and  are viscosity accelerations in the directions xyz 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 [7077]. Determination and true implementation of such parameters is one of the key steps of any simulation [237881] and computing procedure [8286]. 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 [8788]. 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 414 ). The total number of experiments in this study was 48 due to the limitations of modeling.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 4 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.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 9 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.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 14 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 510, 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 58 and 1011), 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.(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 19 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.(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 20 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 [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 21 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
S0: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.

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Watershed area

Analysis on inundation characteristics by compound external forces in coastal areas

연안 지역의 복합 외력에 의한 침수 특성 분석

Taeuk KangaDongkyun SunbSangho Leec*
강 태욱a선 동균b이 상호c*
aResearch Professor, Disaster Prevention Research Institute, Pukyong National University, Busan, KoreabResearcher, Disaster Prevention Research Institute, Pukyong National University, Busan, KoreacProfessor, Department of Civil Engineering, Pukyong National University, Busan, Korea
a부경대학교 방재연구소 전임연구교수b부경대학교 방재연구소 연구원c부경대학교 공과대학 토목공학과 교수*Corresponding Author

ABSTRACT

연안 지역은 강우, 조위, 월파 등 여러가지 외력에 의해 침수가 발생될 수 있다. 이에 이 연구에서는 연안 지역에서 발생될 수 있는 단일 및 복합 외력에 의한 지역별 침수 특성을 분석하였다. 연구에서 고려한 외력은 강우와 폭풍 해일에 의한 조위 및 월파이고, 분석 대상지역은 남해안 및 서해안의 4개 지역이다. 유역의 강우-유출 및 2차원 지표면 침수 분석에는 XP-SWMM이 사용되었고, 폭풍 해일에 의한 외력인 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 모형과 FLOW-3D 모형이 각각 활용되었다. 단일 외력을 이용한 분석 결과, 대부분의 연안 지역에서는 강우에 의한 침수 영향보다 폭풍 해일에 의한 침수 영향이 크게 나타났다. 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 지역의 침수 피해 저감을 위해서는 복합 외력을 고려한 분석이 요구되는 것으로 판단되었다.키워드연안 지역 침수 분석 강우 폭풍 해일 복합 외력

The various external forces can cause inundation in coastal areas. This study is to analyze regional characteristics caused by single or compound external forces that can occur in coastal areas. Storm surge (tide level and wave overtopping) and rainfall were considered as the external forces in this study. The inundation analysis were applied to four coastal areas, located on the west and south coast in Republic of Korea. XP-SWMM was used to simulate rainfall-runoff phenomena and 2D ground surface inundation for watershed. A coupled model of ADCIRC and SWAN (ADCSWAN) was used to analyze tide level by storm surge and the FLOW-3D model was used to estimate wave overtopping. As a result of using a single external force, the inundation influence due to storm surge in most of the coastal areas was greater than rainfall. The results of using compound external forces were quite similar to those combined using one external force independently. However, a case of considering compound external forces sometimes created new inundation areas that didn’t appear when considering only a single external force. The analysis considering compound external forces was required to reduce inundation damage in these areas.KeywordsCoastal area Inundation analysis Rainfall Storm surge Compound external forces

MAIN

1. 서 론

우리나라는 반도에 위치하여 삼면이 바다로 둘러싸여 있는 지리적 특성을 가지고 있다. 이에 따라 해양 산업을 중심으로 부산, 인천, 울산 등 대규모의 광역도시가 발달하였을 뿐만 아니라, 창원, 포항, 군산, 목포, 여수 등의 중․소규모 도시들도 발달되어 있다. 또한, 최근에는 연안 지역이 바다를 전망으로 하는 입지 조건을 가지고 있어 개발 선호도가 높고, 이에 따라 부산시 해운대의 마린시티, 엘시티와 같은 주거 및 상업시설의 개발이 지속되고 있다(Kang et al., 2019b).

한편, 최근 기후변화에 따른 지구 온난화 현상으로 평균 해수면이 상승하고, 해수면 온도도 상승하면서 태풍 및 강우의 강도가 커지고 있어 전 세계적으로 자연 재해로 인한 피해가 증가하고 있다(Kim et al., 2016). 실제로 2020년에는 최장기간의 장마가 발생하여 부산, 울산은 물론, 전국에서 50명의 인명 피해와 3,489세대의 이재민이 발생하였다1). 특히, 연안 지역은 강우, 만조 시 해수면 상승, 폭풍 해일(storm surge)에 의한 월파(wave overtopping) 등 복합적인 외력(compound external forces)에 의해 침수될 수 있다(Lee et al., 2020). 일례로, 2016년 태풍 차바 시 부산시 해운대구의 마린시티는 강우와 폭풍 해일에 의한 월파가 발생함에 따라 대규모 침수를 유발하였다(Kang et al., 2019b). 또한, 2020년 7월 23일에 부산에서는 시간당 81.6 mm의 집중호우와 약최고고조위를 상회하는 만조가 동시에 발생하였고, 이로 인해 감조 하천인 동천의 수위가 크게 상승하여 하천이 범람하였다(KSCE, 2021).

연안 지역의 복합 외력을 고려한 침수 분석에 관한 사례로서, 우선 강우와 조위를 고려한 연구 사례는 다음과 같다. Han et al. (2014)은 XP-SWMM을 이용하여 창원시 배수 구역을 대상으로 침수 모의를 수행하였는데, 연안 도시의 침수 모의에는 조위의 영향을 반드시 고려해야 함을 제시하였다. Choi et al. (2018a)은 경남 사천시 선구동 일대에 대하여 초과 강우 및 해수면 상승 시나리오를 조합하여 침수 분석을 수행하였다. Choi et al. (2018b)은 XP-SWMM을 이용하여 여수시 연등천 및 여수시청 지역에 대하여 강우 시나리오와 해수위 상승 시나리오를 고려한 복합 원인에 의한 침수 모의를 수행하여 홍수예경보 기준표를 작성하였다. 한편, 강우, 조위, 월파를 고려한 연구 사례로서, Song et al. (2017)은 부산시 해운대구 수영만 일원에 대하여 XP-SWMM으로 월파량의 적용 유무에 따른 침수 면적을 비교하였다. Suh and Kim (2018)은 부산시 마린시티 지역을 대상으로 태풍 차바 때 EurOtop의 경험식을 ADSWAN에 적용하여 월파량을 반영하였다. Chen et al. (2017)은 TELEMAC-2D 및 SWMM을 기반으로 한 극한 강우, 월파 및 조위를 고려하여 중국 해안 원자력 발전소의 침수를 예측하고 분석하기 위한 결합 모델을 개발한 바 있다. 한편, Lee et al. (2020)은 수리‧수문학 분야와 해양공학 분야에서 사용되는 물리 모형의 기술적 연계를 통해 연안 지역의 침수 모의의 재현성을 높였다.

상기의 연구들은 공통적으로 연안 지역에 대하여 복합 외력을 고려했을 때 발생되는 침수 현상의 재현 또는 예측을 목적으로 수행되었다. 이 연구는 이와 차별하여 복합 외력을 고려하는 경우 나타날 수 있는 연안 지역의 침수 특성 분석을 목적으로 수행되었다. 이를 위해 단일 외력을 독립적으로 고려했을 때 발생되는 침수 양상과 동시에 고려하는 경우의 침수 현상을 비교, 분석하였다. 복합 외력에 의한 지역적 침수 특성 분석은 우리나라 남해안과 서해안에 위치한 4개 지역에 대하여 적용되었다.

1) 장연제, 47일째 이어진 긴 장마, 50명 인명피해… 9년만에 최대, 동아닷컴, 2020년 8월 9일 수정, 2021년 3월 4일 접속, https://www.donga.com/news/article/all/20200809/102369692/2

2. 연구 방법

2.1 연안 지역의 침수 영향 인자

연안 지역의 침수는 크게 세 가지의 메카니즘으로 발생될 수 있다. 우선, 연안 지역은 바다와 인접하고 있기 때문에 그 영향을 직접적으로 받는다. Kim (2018)에 의하면, 연안 지역의 침수는 폭풍 해일에 의해 상승한 조위와 월파로 인해 발생될 수 있다(Table 1). 특히, 경상남도의 창원과 통영, 인천광역시의 소래포구 어시장 등 남해안 및 서해안 지역의 일부는 백중사리, 슈퍼문(super moon) 등 만조 시 조위의 상승으로 인한 침수가 발생하는 지역이 존재한다(Kang et al., 2019a). 두 번째는 강우에 의한 내수 침수 발생이다. ME (2011)에서는 도시 지역의 우수 관거를 10 ~ 30년 빈도로 계획하도록 지정하고 있고, 펌프 시설은 30 ~ 50년 빈도의 홍수를 배수시킬 수 있도록 정하고 있다. 하지만 최근에는 기후변화의 영향으로 도시 지역 배수시설의 설계 빈도를 초과하는 강우가 빈번하게 나타나고 있다. 실제로 2016년의 태풍 차바 시 울산 기상관측소에 관측된 시간 최대 강우량은 106.0 mm로서, 이는 300년 빈도 이상의 강우량에 해당하였다(Kang et al., 2019a). 따라서 배수시설의 설계 빈도 이상의 강우는 연안 도시 지역의 침수를 유발할 수 있다. 세 번째, 하천이 인접한 연안 도시에서는 하천의 범람으로 인해 침수가 발생할 수 있다. 하천의 경우, 기본계획이 수립되기는 하지만, 설계 빈도를 상회하는 강우의 발생, 제방, 수문 등 홍수 방어시설의 기능 저하, 예산 등의 문제로 하천기본계획 이행의 지연 등에 의해 범람할 가능성이 존재한다.

Table 1.

Type of natural hazard damage in coastal areas (Kim, 2018)

ItemRisk factor
Facilities damage∙ Breaking of coastal facilities by wave
– Breakwater, revetment, lighters wharf etc.
∙ Local scouring at the toe of the structures by wave
∙ Road collapse by wave overtopping
Inundation damage∙ Inundation damage by wave overtopping
∙ Inundation of coastal lowlands by storm surge
Erosion damage∙ Backshore erosion due to high swell waves
∙ Shoreline changes caused by construction of coastal erosion control structure
∙ Sediment transport due to the construction of artificial structures

상기의 내용을 종합하면, 연안 지역은 조위 및 월파에 의한 침수, 강우에 의한 내수 침수, 하천 범람에 의한 침수로 구분될 수 있다. 이 연구에서는 폭풍 해일에 의한 조위 상승 및 월파와 강우를 연안 지역의 침수 유발 외력으로 고려하였다. 하천 범람의 경우, 상대적으로 사례가 희소하여 제외하였다.

2.2 복합 외력을 고려한 침수 모의 방법

이 연구에서는 조위 및 월파와 강우를 연안 지역의 침수 발생에 관한 외력 조건으로 고려하였다. 따라서 해당 외력 조건을 고려하여 침수 분석을 수행할 수 있어야 한다. 이와 관련하여 Lee et al. (2020)은 Fig. 1과 같이 수리‧수문 및 해양공학 분야에서 사용되는 물리 기반 모형의 연계를 통해 조위, 월파, 강우를 고려한 침수 분석 방법을 제시하였고, 이 연구에서는 해당 방법을 이용하였다.

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Fig. 1.

Connection among the models for inundation analysis in coastal areas (Lee et al., 2020)

우선, 태풍에 의해 발생되는 폭풍 해일의 영향을 분석하기 위해서는 태풍에 의해 발생되는 기압 강하, 해상풍, 진행 속도 등을 고려하여 해수면의 변화 양상 및 조석-해일-파랑을 충분히 재현 가능해야 한다. 이 연구에서는 국내․외에서 검증 및 공인된 폭풍 해일 모형인 ADCIRC 모형과 파랑 모형인 UnSWAN이 결합된 ADCSWAN (coupled model of ADCIRC and UnSWAN)을 이용하였다. 정수압 가정의 ADCSWAN은 월파량 산정에 단순 경험식을 적용하는 단점이 있지만 넓은 영역을 모의할 수 있고, FLOW-3D는 해안선의 경계를 고해상도로 재현이 가능하다. 이에 연구에서는 먼 바다 영역에 대해서는 ADCSWAN을 이용하여 분석하였고, 연안 주변의 바다 영역과 월파량 산정에 대해서는 FLOW-3D 모형을 이용하였다. 한편, 연안 지역의 침수 모의를 위해서는 유역에서 발생하는 강우-유출 현상과 우수 관거 등의 배수 체계에 대한 분석이 가능해야 한다. 또한, 배수 체계로부터 범람한 물이 지표면을 따라 흘러가는 현상을 해석할 수 있어야 하고, 바다의 조위 및 월파량을 경계조건으로 반영할 수 있어야 한다. 이 연구에서는 이러한 현상을 모의할 수 있고, 도시 침수 모의에 활용도가 높은 XP-SWMM을 이용하였다.

2.3 침수 분석 대상지역

연구의 대상지역은 조위 및 월파에 의한 침수와 강우에 의한 내수 침수의 영향이 복합적으로 발생할 수 있는 남해안과 서해안에 위치한 4개 지역이다. Table 2는 침수 분석 대상지역을 정리하여 나타낸 표이고, Fig. 2는 각 지역의 유역 경계를 나타낸 그림이다.

Table 2.

Target region for inundation analysis

ClassificationAdministrative districtTarget regionArea
(km2)
Main cause of inundationPump
facility
Number of
major outfall
The south
coast
Haundae-gu, BusanMarine City area0.53Wave overtopping9
Haundae-gu, BusanCentum City area4.76Poor interior drainage at high tide level12
The west
coast
GunsanJungang-dong area0.79Poor interior drainage at high tide level23
BoryeongOcheon Port area0.41High tide level5

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Fig. 2.

Watershed area

남해안의 분석 대상지역 중 부산시 해운대구의 마린시티는 바다 조망을 중심으로 조성된 주거지 및 상업시설 중심의 개발지역이다. 마린시티는 2016년 태풍 차바 및 2018년 태풍 콩레이 등 태풍 내습 시 월파에 의한 해수 월류로 인해 도로 및 상가 일부가 침수를 겪은 지역이다. 부산시 해운대구의 센텀시티는 과거 수영만 매립지였던 곳에 조성된 주거지 및 상업시설 중심의 신도시 지역이다. 센텀시티 유역의 북쪽은 해발고도 El. 634 m의 장산이 위치하는 등 산지 특성도 가지고 있어 상대적으로 유역 면적이 넓고, 배수시설의 규모도 크고 복잡하다. 하지만 수영강 하구의 저지대 지역에 위치함에 따라 강우 시 내수 배제가 불량하고, 특히 만조 시 침수가 잦은 지역이다.

서해안 분석 대상지역 중 전라북도 군산시의 중앙동 일원은 군산시 내항 내측에 조성된 구도시로서, 금강 및 경포천 하구에 위치하는 저지대이다. 이에 따라 군산시 풍수해저감종합계획에서는 해당 지역을 3개의 영역으로 구분하여 내수재해 위험지구(영동지구, 중동지구, 경암지구)로 지정하였고, 이 연구에서는 해당 지역을 모두 고려하였다. 한편, 군산시 중앙동 일원은 특히, 만조 시 내수 배제가 매우 불량하여 2개의 펌프시설이 운영되고 있다. 충청남도 보령시의 오천면에 위치한 오천항은 배후의 산지를 포함한 소규모 유역에 위치한다. 서해안의 특성에 따라 조석 간만의 차가 크고, 특히 태풍 내습 시 폭풍 해일에 의한 침수가 잦은 지역이다. 산지의 강우-유출수는 복개된 2개의 수로를 통해 바다로 배제되고, 상가들이 위치한 연안 주변 지역에는 강우-유출수 배제를 위한 3개의 배수 체계가 구성되어 있다.

3. 연구 결과

3.1 침수 모의 모형 구축

XP-SWMM을 이용하여 분석 대상지역별 침수 모의 모형을 구축하였다. 적절한 침수 분석 수행을 위해 지역별 수치지형도, 도시 공간 정보 시스템(urban information system, UIS), 하수 관망도 등의 수치 자료와 현장 조사를 통해 유역의 배수 체계를 구성하였다. 그리고 2차원 침수 분석을 위해 무인 드론 및 육상 라이다(LiDAR) 측량을 수행하여 평면해상도가 1 m 이하인 고해상도 수치지형모형(digital terrain model, DTM)을 구성하였고, 침수 모의 격자를 생성하였다.

Fig. 3은 XP-SWMM의 상세 구축 사례로서 부산시 마린시티 배수 유역에 대한 소유역 및 관거 분할 등을 통해 구성한 배수 체계와 고해상도 측량 결과를 이용하여 구성한 수치표면모형(digital surface model, DSM)을 나타낸다. Fig. 4는 각 대상지역에 대해 XP-SWMM을 이용하여 구축한 침수 모의 모형을 나타낸다. 침수 분석을 위해서는 침수 모의 영역에 대한 설정이 필요한데, 다수의 사전 모의를 통해 유역 내에서 침수가 발생되는 지역을 검토하여 결정하였다.

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Fig. 3.

Analysis of watershed drainage system and high-resolution survey for Marine City

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Fig. 4.

Simulation model for inundation analysis by target region using XP-SWMM

한편, 이 연구에서는 월파량 및 조위의 산정 과정과 침수 모의 모형의 보정에 관한 내용 등은 다루지 않았다. 관련된 내용은 선행 연구인 Kang et al. (2019b)와 Lee et al. (2020)을 참조할 수 있다.

3.2 침수 모의 설정

3.2.1 분석 방법

복합 외력에 의한 침수 영향을 검토하기 위해서는 외력 조건에 대한 빈도와 지속기간의 설정이 필요하다. 이 연구에서는 재해 현상이 충분히 나타날 수 있도록 강우와 조위 및 월파의 빈도를 모두 100년으로 설정하였다. 이때, 조위와 월파량의 산정에는 만조(약최고고조위) 시, 100년 빈도에 해당하는 태풍 내습에 따른 폭풍 해일의 발생 조건을 고려하였다.

지역별 강우 발생 특성과 유역 특성을 고려하기 위해 MOIS (2017)의 방재성능목표 기준에 따라 임계 지속기간을 결정하여 대상지역별 강우의 지속기간으로 설정하였다. 이때, 강우의 시간 분포는 MLTM (2011)의 Huff 3분위를 이용하였다. 그리고 조위와 월파의 경우, 일반적인 폭풍 해일의 지속기간을 고려하여 5시간으로 결정하였다. 한편, 침수 모의를 위한 계산 시간 간격, 2차원 모의 격자 등의 입력자료는 분석 대상지역의 유역 규모와 침수 분석 대상 영역을 고려하여 결정하였다. 참고로 침수 분석에 사용된 수치지형모형은 1 m 급의 고해상도로 구성되었지만, 2차원 침수 모의 격자의 크기는 지역별로 3 ~ 4 m이다. 이는 연구에서 사용된 XP-SWMM의 격자 수(100,000개) 제약에 따른 설정이나, Sun (2021)은 민감도 분석을 통해 2차원 침수 분석을 위한 적정 격자 크기를 3 ~ 4.5 m로 제시한 바 있다.

Table 3은 이 연구에서 설정한 침수 모의 조건과 분석 방법을 정리하여 나타낸 표이다.

Table 3.

Simulation condition and method

ClassificationTarget regionSimulation conditionSimulation method
RainfallStorm surgeSimulation time interval2D
grid size
Return
period
DurationTemporal
distribution
Return
period
DurationWatershed
routing
Channel
routing
2D
inundation
The south coastMarine City area100 yr1 hr3rd quartile
of Huff’s
method
1005 hr5 min10 sec1 sec3 m
Centum City area1 hr1005 min10 sec1 sec4 m
The west coastJungang-dong area2 hr1005 min10 sec1 sec3.5 m
Ocheon Port area1 hr1001 min10 sec1 sec3 m

3.2.2 복합 재해의 동시 고려

이 연구의 대상지역들은 모두 소규모의 해안가 도시지역이고, 이러한 지역에 대한 강우의 임계지속기간은 1시간 ~ 2시간이나, 이 연구에서 분석한 폭풍 해일의 지속기간은 5시간으로 강우의 지속기간과 폭풍 해일의 지속기간이 상이하다. 이에 이 연구에서는 서로 다른 지속기간을 가진 강우와 폭풍 해일 또는 조위를 고려하기 위해 강우의 중심과 폭풍 해일의 중심이 동일한 시간에 위치하도록 설정하였다(Fig. 5).

XP-SWMM은 폭풍 해일이 지속되는 5시간 전체를 모의하도록 설정하였고, 폭풍 해일이 가장 큰 시점에 강우의 중심이 위치하도록 강우 발생 시기를 결정하였다. 다만, 부산 마린시티의 경우, 폭풍 해일에 의한 피해가 주로 월파에 의해 발생되므로 강우의 중심과 월파의 중심을 일치시켰고(Fig. 5(a)), 상대적으로 조위의 영향이 큰 3개 지역은 강우의 중심과 조위의 중심을 맞추었다. Fig. 5(b)는 군산시 중앙동 지역의 복합 외력에 의한 침수 분석에 사용된 강우와 조위의 조합이다.

한편, 100년 빈도의 확률강우량만을 고려한 침수 분석에서는 유역 유출부의 경계조건으로 우수 관거의 설계 조건을 고려하여 약최고고조위가 일정하게 유지되도록 설정하였다.

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Fig. 5.

Consideration of external force conditions with different durations

3.2.3 XP-SWMM의 월파량 고려

XP-SWMM에 ADCSWAN 및 FLOW-3D 모형에 의해 산정된 월파량을 입력하기 위해 해안가 지역에 절점을 생성하여 월파 현상을 구현하였다. XP-SWMM에서 월파량을 입력하기 위한 절점의 위치는 FLOW-3D 모형에서 월파량을 산정한 격자의 중심 위치이다.

Fig. 6(a)는 마린시티 지역에 대한 월파량 입력 지점을 나타낸 것으로서, 유역 경계 주변에 동일 간격으로 원으로 표시한 지점들이 해당된다. Fig. 6(b)는 XP-SWMM에 월파량 입력 지점들을 반영하고, 하나의 절점에 월파량 시계열을 입력한 화면을 나타낸다.

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Fig. 6.

Considering wave overtopping on XP-SWMM

3.3 침수 모의 결과

3.3.1 단일 외력에 의한 침수 모의 결과

Fig. 7은 단일 외력을 고려한 지역별 침수 모의 결과이다. 즉, Fig. 7의 왼쪽 그림들은 지역별로 100년 빈도 강우에 의한 침수 모의 결과를 나타내고, Fig. 7의 오른쪽 그림들은 만조 시 100년 빈도 폭풍 해일에 의한 침수 모의 결과이다. 대체로 강우에 의한 침수 영역은 유역 중․상류 지역의 유역 전반에 걸쳐 발생하였고, 폭풍 해일에 의한 침수 영역은 해안가 전면부에 위치하는 것을 볼 수 있다. 이는 폭풍 해일에 의한 조위 상승과 월파의 영향이 상류로 갈수록 감소하기 때문이다.

한편, 4개 지역 모두에서 공통적으로 강우에 비해 폭풍 해일에 의한 침수 영향이 상대적으로 크게 분석되었다. 이러한 결과는 연안 지역의 경우, 폭풍 해일에 대비한 침수 피해 저감 노력이 보다 중요함을 의미한다.

/media/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F7.jpg
Fig. 7.

Simulation results by single external force (left: rainfall, right: storm surge)

3.3.2 복합 외력에 의한 침수 모의 결과

Fig. 8은 복합 외력을 고려한 지역별 침수 모의 결과이다. 즉, 강우 및 폭풍 해일을 동시에 고려함에 따라 발생된 침수 영역을 나타낸다. 복합 외력을 고려하는 경우, 단일 외력만을 고려한 분석 결과(Fig. 7)보다 침수 영역은 넓어졌고, 침수심은 깊어졌다.

복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였고, 이는 일반적으로 예상할 수 있는 결과이다. 주목할만한 결과는 군산시 중앙동의 침수 분석에서 나타났다. 즉, 군산시 중앙동의 경우, 단일 외력만을 고려한 침수 모의 결과에서 나타나지 않았던 새로운 침수 영역이 발생하였다(Fig. 8(c)). 이와 관련된 상세 내용은 3.4절의 고찰에서 기술하였다.

/media/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F8.jpg
Fig. 8.

Simulation results by compound external forces

3.4 결과 고찰

외력 조건별 침수의 영향을 정량적으로 비교하기 위해 침수 면적을 이용하였다. 이 연구에서는 강우만에 의해 유발된 침수 면적을 기준(기준값: 1)으로 하고, 폭풍 해일(조위+월파량)에 의한 침수 면적과 복합 외력에 의한 침수 면적의 상대적 비율로 분석하였다(Table 4).

Table 4.

Impact evaluation for inundation area by external force

ConditionMarine City, BusanCentum City, BusanJungang-dong area,
Gunsan
Ocheon Port area,
Boryeong
Inundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
RateInundation area
(km2)
Rate
Single
external force
Rainfall (①)0.01641.00.07591.00.04571.00.01751.0
Storm surge (②)0.03632.210.06850.900.14633.200.04122.35
Compound
external forces
Combination
(①+②)
0.05243.190.15051.980.26325.760.04732.70

분석 결과, 부산 센텀시티를 제외한 3개 지역은 모두 폭풍 해일에 의한 침수 면적이 강우에 의한 침수 면적에 비해 2.2 ~ 3.2배 넓은 것으로 분석되었다. 한편, 복합 외력에 의한 침수 면적은 마린시티와 센텀시티의 경우, 각각의 외력에 의한 침수 면적의 합과 유사하게 나타났다. 이는 각각의 외력에 의한 침수 영역이 상이하여 거의 중복되지 않음을 의미한다. 반면에, 오천항에서는 각각의 외력에 의한 침수 면적의 합이 복합 외력에 의한 면적보다 크게 나타났다. 이는 오천항의 경우, 유역면적이 작고 배수 체계가 비교적 단순하여 강우와 폭풍 해일에 의한 침수 영역이 중복되기 때문인 것으로 분석되었다(Fig. 7(d)).

군산시 중앙동 일대의 경우, 복합 외력에 의한 침수 면적이 각각의 독립적인 외력 조건에 의한 침수 면적의 합에 비해 37.1% 크게 나타났다. 이러한 현상의 원인을 분석하기 위해 복합 외력 조건에서만 나타난 우수 관거(Fig. 8(c)의 A 구간)에 대하여 종단을 검토하였다(Fig. 9). Fig. 9(a)는 강우만에 의해 분석된 우수 관거 내 흐름 종단을 나타내고, Fig. 9(b)는 폭풍 해일만에 의한 우수 관거의 종단이다. 그림을 통해 각각의 독립적인 외력 조건 하에서는 해당 구간에서 침수가 발생되지 않은 것을 볼 수 있다. 다만, 강우만을 고려하더라도 우수 관거는 만관이 된 상태를 확인할 수 있다(Fig. 9(a)). 반면에, 만관 상태에서 폭풍 해일이 함께 고려됨에 따라 해수 범람과 조위 상승에 의해 우수 배제가 불량하게 되었고, 이로 인해 침수가 유발된 것으로 분석되었다(Fig. 9(c)). 따라서 이러한 지역은 복합 외력에 대한 취약지구로 판단할 수 있고, 단일 외력의 고려만으로는 침수를 예상하기 어려운 지역임을 알 수 있다.

/media/sites/kwra/2021-054-07/N0200540702/images/kwra_54_07_02_F9.jpg
Fig. 9.

A part of drainage profiles by external force in Jungang-dong area, Gunsan

4. 결 론

이 연구에서는 외력 조건에 따른 연안 지역의 침수 특성을 분석하였다. 연구에서 고려된 외력 조건은 두 가지로서 강우와 폭풍 해일(조위와 월파)이다. 분석 대상 연안 지역으로는 남해안에 위치하는 2개 지역(부산시 해운대구의 마린시티와 센텀시티)과 서해안의 2개 지역(군산시 중앙동 일원 및 보령시 오천항)이 선정되었다.

복합 외력을 고려한 연안 지역의 침수 모의를 위해서는 유역의 강우-유출 현상과 바다의 조위 및 월파량을 경계조건으로 반영할 수 있는 침수 모의 모형이 요구되는데, 이 연구에서는 XP-SWMM을 이용하였다. 한편, 조위 및 월파량 산정에는 ADCSWAN (ADCIRC와 UnSWAN) 및 FLOW-3D 모형이 이용되었다.

연안 지역별 침수 모의는 100년 빈도의 강우와 폭풍 해일을 독립적으로 고려한 경우와 복합적으로 고려한 경우를 구분하여 수행되었다. 우선, 외력을 독립적으로 고려한 결과, 대체로 폭풍 해일만 고려한 경우가 강우만 고려한 경우에 비해 침수 영향이 크게 나타났다. 따라서 연안 지역의 경우, 폭풍 해일에 의한 침수 피해 방지 계획이 상대적으로 중요한 것으로 분석되었다. 두 번째, 복합 외력에 의한 침수 분석 결과는 대체로 단일 외력에 의한 침수 모의 결과를 중첩시켜 나타낸 결과와 유사하였다. 다만, 특정 지역에서는 복합 외력을 고려함에 따라 단일 외력만을 고려한 침수 모의에서 나타나지 않았던 새로운 침수 영역이 발생하기도 하였다. 이러한 결과는 독립적인 외력 조건에서는 우수 관거가 만관 또는 그 이하의 상태가 되지만, 두 가지의 외력이 동시에 고려됨에 따라 우수 관거의 통수능 한계를 초과하여 나타났다. 이러한 지역은 복합 외력에 대한 취약지구로 판단되었고, 해당 지역의 적절한 침수 방지 대책 수립을 위해서는 복합적인 외력 조건이 고려되어야 함을 시사하였다.

현행, 자연재해저감종합계획에서는 침수와 관련된 재해 원인 지역을 내수재해, 해안재해, 하천재해 등으로 구분하고 있다. 하지만 이 연구에서 검토된 바와 같이, 연안 지역의 침수 원인은 복합적으로 나타날 뿐만 아니라, 복합 외력을 고려함에 따라 추가적으로 나타날 수 있는 침수 위험 지역도 존재한다. 따라서 기존의 획일적인 재해 원인의 구분보다는 지역의 특성에 맞는 복합적인 재해 원인을 검토할 필요가 있음을 제안한다.

Acknowledgements

본 논문은 행정안전부 극한 재난대응 기반기술 개발사업의 일환인 “해안가 복합재난 위험지역 피해저감 기술개발(연구과제번호: 2018-MOIS31-008)”의 지원으로 수행되었습니다.

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The Optimal Operation on Auxiliary Spillway to Minimize the Flood Damage in Downstream River with Various Outflow Conditions

류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

Hyung Ju Yoo1 Sung Sik Joo2 Beom Jae Kwon3 Seung Oh Lee4*
유 형주1 주 성식2 권 범재3 이 승오4*
1Ph.D Student, Dept. of Civil & Environmental Engineering, Hongik University2Director, Water Resources & Environment Department, HECOREA3Director, Water Resources Department, ISAN4Professor, Dept. of Civil & Environmental Engineering, Hongik University
1홍익대학교 건설환경공학과 박사과정
2㈜헥코리아 수자원환경사업부 이사
3㈜이산 수자원부 이사
4홍익대학교 건설환경공학과 교수*Corresponding Author

ABSTRACT

최근 기후변화로 인해 강우강도 및 빈도의 증가에 따른 집중호우의 영향 및 기존 여수로의 노후화에 대비하여 홍수 시 하류 하천의 영향을 최소화할 수 있는 보조 여수로 활용방안 구축이 필요한 실정이다. 이를 위해, 수리모형 실험 및 수치모형 실험을 통하여 보조 여수로 운영에 따른 흐름특성 변화 검토에 관한 연구가 많이 진행되어 왔다.

그러나 대부분의 연구는 여수로에서의 흐름특성 및 기능성에 대한 검토를 수행하였을 뿐 보조 여수로의 활용방안에 따른 하류하천 영향 검토 및 호안 안정성 검토에 관한 연구는 미비한 실정이다.

이에 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류영향 분석 및 호안 안정성 측면에서 최적 방류 시나리오 검토를 3차원 수치모형인 FLOW-3D를 사용하여 검토하였다. 또한 FLOW-3D 수치모의 수행을 통한 유속, 수위 결과와 소류력 산정 결과를 호안 설계허용 기준과 비교하였다.

수문 완전 개도 조건으로 가정하고 계획홍수량 유입 시 다양한 보조 여수로 활용방안에 대하여 수치모의를 수행한 결과, 보조 여수로 단독 운영 시 기존 여수로 단독운영에 비하여 최대유속 및 최대 수위의 감소효과를 확인하였다. 다만 계획홍수량의 45% 이하 방류 조건에서 대안부의 호안 안정성을 확보하였고 해당 방류량 초과 경우에는 처오름 현상이 발생하여 월류에 대한 위험성 증가를 확인하였다.

따라서 기존 여수로와의 동시 운영 방안 도출이 중요하다고 판단하였다. 여수로의 배분 비율 및 총 허용 방류량에 대하여 검토한 결과 보조 여수로의 방류량이 기존 여수로의 방류량보다 큰 경우 하류하천의 흐름이 중심으로 집중되어 대안부의 유속 저감 및 수위 감소를 확인하였고, 계획 홍수량의 77% 이하의 조건에서 호안의 허용 유속 및 허용 소류력 조건을 만족하였다.

이를 통하여 본 연구에서 제안한 보조 여수로 활용방안으로는 기존 여수로와 동시 운영 시 총 방류량에 대하여 보조 여수로의 배분량이 기존 여수로의 배분량보다 크게 설정하는 것이 하류하천의 영향을 최소화 할 수 있는 것으로 나타났다.

그러나 본 연구는 여수로 방류에 따른 대안부에서의 영향에 대해서만 검토하였고 수문 전면 개도 조건에서 검토하였다는 한계점은 분명히 있다. 이에 향후에는 다양한 수문 개도 조건 및 방류 시나리오를 적용 및 검토한다면 보다 효율적이고, 효과적인 보조 여수로 활용방안을 도출이 가능할 것으로 기대 된다.

키워드

보조 여수로, FLOW-3D, 수치모의, 호안 안정성, 소류력

Recently, as the occurrence frequency of sudden floods due to climate change increased and the aging of the existing spillway, it is necessary to establish a plan to utilize an auxiliary spillway to minimize the flood damage of downstream rivers. Most studies have been conducted on the review of flow characteristics according to the operation of auxiliary spillway through the hydraulic experiments and numerical modeling. However, the studies on examination of flood damage in the downstream rivers and the stability of the revetment according to the operation of the auxiliary spillway were relatively insufficient in the literature. In this study, the stability of the revetment on the downstream river according to the outflow conditions of the existing and auxiliary spillway was examined by using 3D numerical model, FLOW-3D. The velocity, water surface elevation and shear stress results of FLOW-3D were compared with the permissible velocity and shear stress of design criteria. It was assumed the sluice gate was fully opened. As a result of numerical simulations of various auxiliary spillway operations during flood season, the single operation of the auxiliary spillway showed the reduction effect of maximum velocity and the water surface elevation compared with the single operation of the existing spillway. The stability of the revetment on downstream was satisfied under the condition of outflow less than 45% of the design flood discharge. However, the potential overtopping damage was confirmed in the case of exceeding the 45% of the design flood discharge. Therefore, the simultaneous operation with the existing spillway was important to ensure the stability on design flood discharge condition. As a result of examining the allocation ratio and the total allowable outflow, the reduction effect of maximum velocity was confirmed on the condition, where the amount of outflow on auxiliary spillway was more than that on existing spillway. It is because the flow of downstream rivers was concentrated in the center due to the outflow of existing spillway. The permissible velocity and shear stress were satisfied under the condition of less than 77% of the design flood discharge with simultaneous operation. It was found that the flood damage of downstream rivers can be minimized by setting the amount allocated to the auxiliary spillway to be larger than the amount allocated to the existing spillway for the total outflow with simultaneous operation condition. However, this study only reviewed the flow characteristics around the revetment according to the outflow of spillway under the full opening of the sluice gate condition. Therefore, the various sluice opening conditions and outflow scenarios will be asked to derive more efficient utilization of the auxiliary spillway in th future.KeywordsAuxiliary spillway FLOW-3D Numerical simulation Revetment stability Shear stress

1. 서 론

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로 유입되는 홍수량이 설계 홍수량보다 증가하여 댐 안정성 확보가 필요한 실정이다(Office for Government Policy Coordination, 2003). MOLIT & K-water(2004)에서는 기존댐의 수문학적 안정성 검토를 수행하였으며 이상홍수 발생 시 24개 댐에서 월류 등으로 인한 붕괴위험으로 댐 하류지역의 극심한 피해를 예상하여 보조여수로 신설 및 기존여수로 확장 등 치수능력 증대 기본계획을 수립하였고 이를 통하여 극한홍수 발생 시 홍수량 배제능력을 증대하여 기존댐의 안전성 확보 및 하류지역의 피해를 방지하고자 하였다. 여기서 보조 여수로는 기존 여수로와 동시 또는 별도 운영하는 여수로로써 비상상황 시 방류 기능을 포함하고 있고(K-water, 2021), 최근에는 기존 여수로의 노후화에 따라 보조여수로의 활용방안에 대한 관심이 증가하고 있다. 따라서 본 연구에서는 3차원 수치해석을 수행하여 기존 및 보조 여수로의 방류량 조합에 따른 하류 영향을 분석하고 하류 호안 안정성 측면에서 최적 방류 시나리오를 검토하고자 한다.

기존의 댐 여수로 검토에 관한 연구는 주로 수리실험을 통하여 방류조건 별 흐름특성을 검토하였으나 최근에는 수치모형 실험결과가 수리모형실험과 비교하여 근사한 것을 확인하는 등 점차 수치모형실험을 수리모형실험의 대안으로 활용하고 있다(Jeon et al., 2006Kim, 2007Kim et al., 2008). 국내의 경우, Jeon et al.(2006)은 수리모형 실험과 수치모의를 이용하여 임하댐 바상여수로의 기본설계안을 도출하였고, Kim et al.(2008)은 가능최대홍수량 유입 시 비상여수로 방류에 따른 수리학적 안정성과 기능성을 3차원 수치모형인 FLOW-3D를 활용하여 검토하였다. 또한 Kim and Kim(2013)은 충주댐의 홍수조절 효과 검토 및 방류량 변화에 따른 상·하류의 수위 변화를 수치모형을 통하여 검토하였다. 국외의 경우 Zeng et al.(2017)은 3차원 수치모형인 Fluent를 활용한 여수로 방류에 따른 흐름특성 결과와 측정결과를 비교하여 수치모형 결과의 신뢰성을 검토하였다. Li et al.(2011)은 가능 최대 홍수량(Probable Maximum Flood, PMF)조건에서 기존 여수로와 신규 보조 여수로 유입부 주변의 흐름특성에 대하여 3차원 수치모형 Fluent를 활용하여 검토하였고, Lee et al.(2019)는 서로 근접해있는 기존 여수로와 보조여수로 동시 운영 시 방류능 검토를 수리모형 실험 및 수치모형 실험(FLOW-3D)을 통하여 수행하였으며 기존 여수로와 보조 여수로를 동시운영하게 되면 배수로 간섭으로 인하여 총 방류량이 7.6%까지 감소되어 댐의 방류능력이 감소하였음을 확인하였다.

그러나 대부분의 여수로 검토에 대한 연구는 여수로 내에서의 흐름특성 및 기능성에 대한 검토를 수행하였고. 이에 기존 여수로와 보조 여수로 방류운영에 따른 하류하천의 흐름특성 변화 및 호안 안정성 평가에 관한 추가적인 검토가 필요한 실정이다. 따라서 본 연구에서는 기존 여수로 및 보조 여수로 방류 조건에 따른 하류하천의 흐름특성 및 호안 안정성분석을 3차원 수치모형인 FLOW-3D를 이용하여 검토하였다. 또한 다양한 방류 배분 비율 및 허용 방류량 조건 변화에 따른 하류하천의 흐름특성 및 소류력 분석결과를 호안 설계 허용유속 및 허용 소류력 기준과 비교하여 하류하천의 영향을 최소화 할 수 있는 최적의 보조 여수로 활용방안을 도출하고자 한다.

2. 본 론

2.1 이론적 배경

2.1.1 3차원 수치모형의 기본이론

FLOW-3D는 미국 Flow Science, Inc에서 개발한 범용 유체역학 프로그램(CFD, Computational Fluid Dynamics)으로 자유 수면을 갖는 흐름모의에 사용되는 3차원 수치해석 모형이다. 난류모형을 통해 난류 해석이 가능하고, 댐 방류에 따른 하류 하천의 흐름 해석에도 많이 사용되어 왔다(Flow Science, 2011). 본 연구에서는 FLOW-3D(version 12.0)을 이용하여 홍수 시 기존 여수로의 노후화에 대비하여 보조 여수로의 활용방안에 대한 검토를 하류하천의 호안 안정성 측면에서 검토하였다.

2.1.2 유동해석의 지배방정식

1) 연속 방정식(Continuity Equation)

FLOW-3D는 비압축성 유체에 대하여 연속방정식을 사용하며, 밀도는 상수항으로 적용된다. 연속 방정식은 Eqs. (1)(2)와 같다.

(1)

∇·v=0

(2)

∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

여기서, ρ는 유체 밀도(kg/m3), u, v, w는 x, y, z방향의 유속(m/s), Ax, Ay, Az는 각 방향의 요소면적(m2), RSOR는 질량 생성/소멸(mass source/sink)항을 의미한다.

2) 운동량 방정식(Momentum Equation)

각 방향 속도성분 u, v, w에 대한 운동방정식은 Navier-Stokes 방정식으로 다음 Eqs. (3)(4)(5)와 같다.

(3)

∂u∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂x+Gx+fx-bx-RSORρVFu

(4)

∂v∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂y+Gy+fy-by-RSORρVFv

(5)

∂w∂t+1VF(uAx∂u∂x+vAy∂v∂y+wAz∂w∂z)=-1ρ∂p∂z+Gz+fz-bz-RSORρVFw

여기서, Gx, Gy, Gz는 체적력에 의한 가속항, fx, fy, fz는 점성에 의한 가속항, bx, by, bz는 다공성 매체에서의 흐름손실을 의미한다.

2.1.3 소류력 산정

호안설계 시 제방사면 호안의 안정성 확보를 위해서는 하천의 흐름에 의하여 호안에 작용하는 소류력에 저항할 수 있는 재료 및 공법 선택이 필요하다. 국내의 경우 하천공사설계실무요령(MOLIT, 2016)에서 계획홍수량 유하 시 소류력 산정 방법을 제시하고 있다. 소류력은 하천의 평균유속을 이용하여 산정할 수 있으며, 소류력 산정식은 Eqs. (6)(7)과 같다.

1) Schoklitsch 공식

Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

(6)

τ=γRI=γC2V2

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), I는 에너지경사, C는 Chezy 유속계수, V는 평균유속(m/s)을 의미한다.

2) Manning 조도계수를 고려한 공식

Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

(7)

τ=γn2V2R1/3

여기서, τ는 소류력(N/m2), R은 동수반경(m), γ는 물의 단위중량(10.0 kN/m3), n은 Manning의 조도계수, V는 평균유속(m/s)을 의미한다.

FLOW-3D 수치모의 수행을 통하여 하천의 바닥 유속을 도출할 수 있으며, 본 연구에서는 Maning 조도계수롤 고려하여 소류력을 산정하고자 한다. 소류력을 산정하기 위해서 여수로 방류에 따른 대안부의 바닥유속 변화를 검토하여 최대 유속 값을 이용하였다. 최종적으로 산정한 소류력과 호안의 재료 및 공법에 따른 허용 소류력과 비교하여 제방사면 호안의 안정성 검토를 수행하게 된다.

2.2 하천호안 설계기준

하천 호안은 계획홍수위 이하의 유수작용에 대하여 안정성이 확보되도록 계획하여야 하며, 호안의 설계 시에는 사용재료의 확보용이성, 시공상의 용이성, 세굴에 대한 굴요성(flexibility) 등을 고려하여 호안의 형태, 시공방법 등을 결정한다(MOLIT, 2019). 국내의 경우, 하천공사설계실무요령(MOLIT, 2016)에서는 다양한 호안공법에 대하여 비탈경사에 따라 설계 유속을 비교하거나, 허용 소류력을 비교함으로써 호안의 안정성을 평가한다. 호안에 대한 국외의 설계기준으로 미국의 경우, ASTM(미국재료시험학회)에서 호안블록 및 식생매트 시험방법을 제시하였고 제품별로 ASTM 시험에 의한 허용유속 및 허용 소류력을 제시하였다. 일본의 경우, 호안 블록에 대한 축소실험을 통하여 항력을 측정하고 이를 통해서 호안 블록에 대한 항력계수를 제시하고 있다. 설계 시에는 항력계수에 의한 블록의 안정성을 평가하고 있으나, 최근에는 세굴의 영향을 고려할 수 있는 호안 안정성 평가의 필요성을 제기하고 있다(MOLIT, 2019). 관련된 국내·외의 하천호안 설계기준은 Table 1에 정리하여 제시하였고, 본 연구에서 하천 호안 안정성 평가 시 하천공사설계실무요령(MOLIT, 2016)과 ASTM 시험에서 제시한 허용소류력 및 허용유속 기준을 비교하여 각각 0.28 kN/m2, 5.0 m/s 미만일 경우 호안 안정성을 확보하였다고 판단하였다.

Table 1.

Standard of Permissible Velocity and Shear on Revetment

Country (Reference)MaterialPermissible velocity (Vp, m/s)Permissible Shear (τp, kN/m2)
KoreaRiver Construction Design Practice Guidelines
(MOLIT, 2016)
Vegetated5.00.50
Stone5.00.80
USAASTM D’6460Vegetated6.10.81
Unvegetated5.00.28
JAPANDynamic Design Method of Revetment5.0

2.3. 보조여수로 운영에 따른 하류하천 영향 분석

2.3.1 모형의 구축 및 경계조건

본 연구에서는 기존 여수로의 노후화에 대비하여 홍수 시 보조여수로의 활용방안에 따른 하류하천의 흐름특성 및 호안안정성 평가를 수행하기 위해 FLOW-3D 모형을 이용하였다. 기존 여수로 및 보조 여수로는 치수능력 증대사업(MOLIT & K-water, 2004)을 통하여 완공된 ○○댐의 제원을 이용하여 구축하였다. ○○댐은 설계빈도(100년) 및 200년빈도 까지는 계획홍수위 이내로 기존 여수로를 통하여 운영이 가능하나 그 이상 홍수조절은 보조여수로를 통하여 조절해야 하며, 또한 2011년 기존 여수로 정밀안전진단 결과 사면의 표층 유실 및 옹벽 밀림현상 등이 확인되어 노후화에 따른 보수·보강이 필요한 상태이다. 이에 보조여수로의 활용방안 검토가 필요한 것으로 판단하여 본 연구의 대상댐으로 선정하였다. 하류 하천의 흐름특성을 예측하기 위하여 격자간격을 0.99 ~ 8.16 m의 크기로 하여 총 격자수는 49,102,500개로 구성하였으며, 여수로 방류에 따른 하류하천의 흐름해석을 위한 경계조건으로 상류는 유입유량(inflow), 바닥은 벽면(wall), 하류는 수위(water surface elevation)조건으로 적용하도록 하였다(Table 2Fig. 1 참조). FLOW-3D 난류모형에는 혼합길이 모형, 난류에너지 모형, k-ϵ모형, RNG(Renormalized Group Theory) k-ϵ모형, LES 모형 등이 있으며, 본 연구에서는 여수로 방류에 따른 복잡한 난류 흐름 및 높은 전단흐름을 정확하게 모의(Flow Science, 2011)할 수 있는 RNG k-ϵ모형을 사용하였고, 하류하천 호안의 안정성 측면에서 보조여수로의 활용방안을 검토하기 위하여 방류시나리오는 Table 3에 제시된 것 같이 설정하였다. Case 1 및 Case 2를 통하여 계획홍수량에 대하여 기존 여수로와 보조 여수로의 단독 운영이 하류하천에 미치는 영향을 확인하였고 보조 여수로의 방류량 조절을 통하여 호안 안정성 측면에서 보조 여수로 방류능 검토를 수행하였다(Case 3 ~ Case 6). 또한 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천의 영향 검토(Case 7 ~ Case 10) 및 방류 배분에 따른 허용 방류량을 호안 안정성 측면에서 검토를 수행하였다(Case 11 ~ Case 14).

수문은 완전개도 조건으로 가정하였으며 하류하천의 계획홍수량에 대한 기존 여수로와 보조여수로의 배분량을 조절하여 모의를 수행하였다. 여수로는 콘크리트의 조도계수 값(Chow, 1959)을 채택하였고, 댐 하류하천의 조도계수는 하천기본계획(Busan Construction and Management Administration, 2009) 제시된 조도계수 값을 채택하였으며 FLOW-3D의 적용을 위하여 Manning-Strickler 공식(Vanoni, 2006)을 이용하여 조도계수를 조고값으로 변환하여 사용하였다. Manning-Strickler 공식은 Eq. (8)과 같으며, FLOW-3D에 적용한 조도계수 및 조고는 Table 4와 같다.

(8)

n=ks1/68.1g1/2

여기서, kS는 조고 (m), n은 Manning의 조도계수, g는 중력가속도(m/s2)를 의미한다.

시간에 따라 동일한 유량이 일정하게 유입되도록 모의를 수행하였으며, 시간간격(Time Step)은 0.0001초로 설정(CFL number < 1.0) 하였다. 또한 여수로 수문을 통한 유량의 변동 값이 1.0%이내일 경우는 연속방정식을 만족하고 있다고 가정하였다. 이는, 유량의 변동 값이 1.0%이내일 경우 유속의 변동 값 역시 1.0%이내이며, 수치모의 결과 1.0%의 유속변동은 호안의 유속설계기준에 크게 영향을 미치지 않는다고 판단하였다. 그 결과 모든 수치모의 Case에서 2400초 이내에 결과 값이 수렴하는 것을 확인하였다.

Table 2.

Mesh sizes and numerical conditions

MeshNumbers49,102,500 EA
Increment (m)DirectionExisting SpillwayAuxiliary Spillway
∆X0.99 ~ 4.301.00 ~ 4.30
∆Y0.99 ~ 8.161.00 ~ 5.90
∆Z0.50 ~ 1.220.50 ~ 2.00
Boundary ConditionsXmin / YmaxInflow / Water Surface Elevation
Xmax, Ymin, Zmin / ZmaxWall / Symmetry
Turbulence ModelRNG model
Table 3.

Case of numerical simulation (Qp : Design flood discharge)

CaseExisting Spillway (Qe, m3/s)Auxiliary Spillway (Qa, m3/s)Remarks
1Qp0Reference case
20Qp
300.58QpReview of discharge capacity on
auxiliary spillway
400.48Qp
500.45Qp
600.32Qp
70.50Qp0.50QpDetermination of optimal division
ratio on Spillways
80.61Qp0.39Qp
90.39Qp0.61Qp
100.42Qp0.58Qp
110.32Qp0.45QpDetermination of permissible
division on Spillways
120.35Qp0.48Qp
130.38Qp0.53Qp
140.41Qp0.56Qp
Table 4.

Roughness coefficient and roughness height

CriteriaRoughness coefficient (n)Roughness height (ks, m)
Structure (Concrete)0.0140.00061
River0.0330.10496
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Fig. 1

Layout of spillway and river in this study

2.3.2 보조 여수로의 방류능 검토

본 연구에서는 기존 여수로와 보조 여수로의 방류량 배분에 따른 하류하천 대안부의 유속분포 및 수위분포를 검토하기 위해 수치모의 Case 별 다음과 같이 관심구역을 설정하였다(Fig. 2 참조). 관심구역(대안부)의 길이(L)는 총 1.3 km로 10 m 등 간격으로 나누어 검토하였으며, Section 1(0 < X/L < 0.27)은 기존 여수로 방류에 따른 영향이 지배적인 구간, Section 2(0.27 < X/L < 1.00)는 보조 여수로 방류에 따른 영향이 지배적인 구간으로 각 구간에서의 수위, 유속, 수심결과를 확인하였다. 기존 여수로의 노후화에 따른 보조 여수로의 방류능 검토를 위하여 Case 1 – Case 6까지의 결과를 비교하였다.

보조 여수로의 단독 운영 시 기존 여수로 운영 시 보다 하류하천의 대안부의 최대 유속(Vmax)은 약 3% 감소하였으며, 이는 보조 여수로의 하천 유입각이 기존 여수로 보다 7°작으며 유입하천의 폭이 증가하여 유속이 감소한 것으로 판단된다. 대안부의 최대 유속 발생위치는 하류 쪽으로 이동하였으며 교량으로 인한 단면의 축소로 최대유속이 발생하는 것으로 판단된다. 또한 보조 여수로의 배분량(Qa)이 증가함에 따라 하류하천 대안부의 최대 유속이 증가하였다. 하천호안 설계기준에서 제시하고 있는 허용유속(Vp)과 비교한 결과, 계획홍수량(Qp)의 45% 이하(Case 5 & 6)를 보조 여수로에서 방류하게 되면 허용 유속(5.0 m/s)조건을 만족하여 호안안정성을 확보하였다(Fig. 3 참조). 허용유속 외에도 대안부에서의 소류력을 산정하여 하천호안 설계기준에서 제시한 허용 소류력(τp)과 비교한 결과, 유속과 동일하게 보조 여수로의 방류량이 계획홍수량의 45% 이하일 경우 허용소류력(0.28 kN/m2) 조건을 만족하였다(Fig. 4 참조). 각 Case 별 호안설계조건과 비교한 결과는 Table 5에 제시하였다.

하류하천의 수위도 기존 여수로 운영 시 보다 보조 여수로 단독 운영 시 최대 수위(ηmax)가 약 2% 감소하는 효과를 보였으며 최대 수위 발생위치는 수충부로 여수로 방류시 처오름에 의한 수위 상승으로 판단된다. 기존 여수로의 단독운영(Case 1)의 수위(ηref)를 기준으로 보조 여수로의 방류량이 증가함에 따라 수위는 증가하였으나 계획홍수량의 58%까지 방류할 경우 월류에 대한 안정성(ηmax/ηref<0.97(=기설제방고))은 확보되었다(Fig. 5 참조). 그러나 계획홍수량 조건에서는 월류에 대한 위험성이 존재하기 때문에 기존여수로와 보조여수로의 적절한 방류량 배분 조합을 도출하는 것이 중요하다고 판단되어 진다.

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Fig. 2

Region of