Fig. 1 Multi-physics phenomena in the laser-material interaction zone

COMPARISON BETWEEN GREEN AND
INFRARED LASER IN LASER POWDER BED
FUSION OF PURE COPPER THROUGH HIGH
FIDELITY NUMERICAL MODELLING AT MESOSCALE

316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

W.E. ALPHONSO1*, M. BAYAT1 and J.H. HATTEL1
*Corresponding author
1Technical University of Denmark (DTU), 2800, Kgs, Lyngby, Denmark

ABSTRACT

L-PBF(Laser Powder Bed Fusion)는 금속 적층 제조(MAM) 기술로, 기존 제조 공정에 비해 부품 설계 자유도, 조립품 통합, 부품 맞춤화 및 낮은 툴링 비용과 같은 여러 이점을 산업에 제공합니다.

전기 코일 및 열 관리 장치는 일반적으로 높은 전기 및 열 전도성 특성으로 인해 순수 구리로 제조됩니다. 따라서 순동의 L-PBF가 가능하다면 기하학적으로 최적화된 방열판과 자유형 전자코일을 제작할 수 있습니다.

그러나 L-PBF로 조밀한 순동 부품을 생산하는 것은 적외선에 대한 낮은 광 흡수율과 높은 열전도율로 인해 어렵습니다. 기존의 L-PBF 시스템에서 조밀한 구리 부품을 생산하려면 적외선 레이저의 출력을 500W 이상으로 높이거나 구리의 광흡수율이 높은 녹색 레이저를 사용해야 합니다.

적외선 레이저 출력을 높이면 후면 반사로 인해 레이저 시스템의 광학 구성 요소가 손상되고 렌즈의 열 광학 현상으로 인해 공정이 불안정해질 수 있습니다. 이 작업에서 FVM(Finite Volume Method)에 기반한 다중 물리학 중간 규모 수치 모델은 Flow-3D에서 개발되어 용융 풀 역학과 궁극적으로 부품 품질을 제어하는 ​​물리적 현상 상호 작용을 조사합니다.

녹색 레이저 열원과 적외선 레이저 열원은 기판 위의 순수 구리 분말 베드에 단일 트랙 증착을 생성하기 위해 개별적으로 사용됩니다.

용융 풀 역학에 대한 레이저 열원의 유사하지 않은 광학 흡수 특성의 영향이 탐구됩니다. 수치 모델을 검증하기 위해 단일 트랙이 구리 분말 베드에 증착되고 시뮬레이션된 용융 풀 모양과 크기가 비교되는 실험이 수행되었습니다.

녹색 레이저는 광흡수율이 높아 전도 및 키홀 모드 용융이 가능하고 적외선 레이저는 흡수율이 낮아 키홀 모드 용융만 가능하다. 레이저 파장에 대한 용융 모드의 변화는 궁극적으로 기계적, 전기적 및 열적 특성에 영향을 미치는 열 구배 및 냉각 속도에 대한 결과를 가져옵니다.

Laser Powder Bed Fusion (L-PBF) is a Metal Additive Manufacturing (MAM) technology which offers several advantages to industries such as part design freedom, consolidation of assemblies, part customization and low tooling cost over conventional manufacturing processes. Electric coils and thermal management devices are generally manufactured from pure copper due to its high electrical and thermal conductivity properties. Therefore, if L-PBF of pure copper is feasible, geometrically optimized heat sinks and free-form electromagnetic coils can be manufactured. However, producing dense pure copper parts by L-PBF is difficult due to low optical absorptivity to infrared radiation and high thermal conductivity. To produce dense copper parts in a conventional L-PBF system either the power of the infrared laser must be increased above 500W, or a green laser should be used for which copper has a high optical absorptivity. Increasing the infrared laser power can damage the optical components of the laser systems due to back reflections and create instabilities in the process due to thermal-optical phenomenon of the lenses. In this work, a multi-physics meso-scale numerical model based on Finite Volume Method (FVM) is developed in Flow-3D to investigate the physical phenomena interaction which governs the melt pool dynamics and ultimately the part quality. A green laser heat source and an infrared laser heat source are used individually to create single track deposition on pure copper powder bed above a substrate. The effect of the dissimilar optical absorptivity property of laser heat sources on the melt pool dynamics is explored. To validate the numerical model, experiments were conducted wherein single tracks are deposited on a copper powder bed and the simulated melt pool shape and size are compared. As the green laser has a high optical absorptivity, a conduction and keyhole mode melting is possible while for the infrared laser only keyhole mode melting is possible due to low absorptivity. The variation in melting modes with respect to the laser wavelength has an outcome on thermal gradient and cooling rates which ultimately affect the mechanical, electrical, and thermal properties.

Keywords

Pure Copper, Laser Powder Bed Fusion, Finite Volume Method, multi-physics

Fig. 1 Multi-physics phenomena in the laser-material interaction zone
Fig. 1 Multi-physics phenomena in the laser-material interaction zone
Fig. 2 Framework for single laser track simulation model including powder bed and substrate (a) computational domain with boundaries (b) discretization of the domain with uniform quad mesh.
Fig. 2 Framework for single laser track simulation model including powder bed and substrate (a) computational domain with boundaries (b) discretization of the domain with uniform quad mesh.
Fig. 3 2D melt pool contours from the numerical model compared to experiments [16] for (a) VED = 65 J/mm3 at 7 mm from the beginning of the single track (b) VED = 103 J/mm3 at 3 mm from the beginning of the single track (c) VED = 103 J/mm3 at 7 mm from the beginning of the single track. In the 2D contour, the non-melted region is indicated in blue, and the melted region is indicated by red and green when the VED is 65 J/mm3 and 103 J/mm3 respectively.
Fig. 3 2D melt pool contours from the numerical model compared to experiments [16] for (a) VED = 65 J/mm3 at 7 mm from the beginning of the single track (b) VED = 103 J/mm3 at 3 mm from the beginning of the single track (c) VED = 103 J/mm3 at 7 mm from the beginning of the single track. In the 2D contour, the non-melted region is indicated in blue, and the melted region is indicated by red and green when the VED is 65 J/mm3 and 103 J/mm3 respectively.
Fig. 4 3D temperature contour plots of during single track L-PBF process at time1.8 µs when (a) VED = 65 J/mm3 (b) VED = 103 J/mm3 along with 2D melt pool contours at 5 mm from the laser initial position. In the 2D contour, the non-melted region is indicated in blue, and the melted region is indicated by red and green when the VED is 65 J/mm3 and 103 J/mm3 respectively.
Fig. 4 3D temperature contour plots of during single track L-PBF process at time1.8 µs when (a) VED = 65 J/mm3 (b) VED = 103 J/mm3 along with 2D melt pool contours at 5 mm from the laser initial position. In the 2D contour, the non-melted region is indicated in blue, and the melted region is indicated by red and green when the VED is 65 J/mm3 and 103 J/mm3 respectively.

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Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

316-L 스테인리스강의 레이저 분말 베드 융합 중 콜드 스패터 형성의 충실도 높은 수치 모델링

M. BAYAT1,* , AND J. H. HATTEL1

  • Corresponding author
    1 Technical University of Denmark (DTU), Building 425, Kgs. 2800 Lyngby, Denmark

ABSTRACT

Spatter and denudation are two very well-known phenomena occurring mainly during the laser powder bed fusion process and are defined as ejection and displacement of powder particles, respectively. The main driver of this phenomenon is the formation of a vapor plume jet that is caused by the vaporization of the melt pool which is subjected to the laser beam. In this work, a 3-dimensional transient turbulent computational fluid dynamics model coupled with a discrete element model is developed in the finite volume-based commercial software package Flow-3D AM to simulate the spatter phenomenon. The numerical results show that a localized low-pressure zone forms at the bottom side of the plume jet and this leads to a pseudo-Bernoulli effect that drags nearby powder particles into the area of influence of the vapor plume jet. As a result, the vapor plume acts like a momentum sink and therefore all nearby particles point are dragged towards this region. Furthermore, it is noted that due to the jet’s attenuation, powder particles start diverging from the central core region of the vapor plume as they move vertically upwards. It is moreover observed that only particles which are in the very central core region of the plume jet get sufficiently accelerated to depart the computational domain, while the rest of the dragged particles, especially those which undergo an early divergence from the jet axis, get stalled pretty fast as they come in contact with the resting fluid. In the last part of the work, two simulations with two different scanning speeds are carried out, where it is clearly observed that the angle between the departing powder particles and the vertical axis of the plume jet increases with increasing scanning speed.

스패터와 denudation은 주로 레이저 분말 베드 융합 과정에서 발생하는 매우 잘 알려진 두 가지 현상으로 각각 분말 입자의 배출 및 변위로 정의됩니다.

이 현상의 주요 동인은 레이저 빔을 받는 용융 풀의 기화로 인해 발생하는 증기 기둥 제트의 형성입니다. 이 작업에서 이산 요소 모델과 결합된 3차원 과도 난류 ​​전산 유체 역학 모델은 스패터 현상을 시뮬레이션하기 위해 유한 체적 기반 상용 소프트웨어 패키지 Flow-3D AM에서 개발되었습니다.

수치적 결과는 플룸 제트의 바닥면에 국부적인 저압 영역이 형성되고, 이는 근처의 분말 입자를 증기 플룸 제트의 영향 영역으로 끌어들이는 의사-베르누이 효과로 이어진다는 것을 보여줍니다.

결과적으로 증기 기둥은 운동량 흡수원처럼 작용하므로 근처의 모든 입자 지점이 이 영역으로 끌립니다. 또한 제트의 감쇠로 인해 분말 입자가 수직으로 위쪽으로 이동할 때 증기 기둥의 중심 코어 영역에서 발산하기 시작합니다.

더욱이 플룸 제트의 가장 중심 코어 영역에 있는 입자만 계산 영역을 벗어날 만큼 충분히 가속되는 반면, 드래그된 나머지 입자, 특히 제트 축에서 초기 발산을 겪는 입자는 정체되는 것으로 관찰됩니다. 그들은 휴식 유체와 접촉하기 때문에 꽤 빠릅니다.

작업의 마지막 부분에서 두 가지 다른 스캔 속도를 가진 두 가지 시뮬레이션이 수행되었으며, 여기서 출발하는 분말 입자와 연기 제트의 수직 축 사이의 각도가 스캔 속도가 증가함에 따라 증가하는 것이 명확하게 관찰되었습니다.

Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
Fig 1. Two different views of the computational domain for the fluid domain. The vapor plume is simulated by a moving momentum source with a prescribed temperature of 3000 K.
Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles' movement along with their velocity magnitude and directions are shown.
Fig 2. (a) and (b) are two snapshots taken at an x-y plane parallel to the powder layer plane before and 0.008 seconds after the start of the scanning process. (c) Shows a magnified view of (b) where detailed powder particles’ movement along with their velocity magnitude and directions are shown.
Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.
Fig 3. Front view of the ejected powder particles due to the plume movement. Powder particles are colored by their respective temperature while trajectory colors show their magnitude at 0.007 seconds.

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Plunge pool scour and bank erosion: assessment of protection measures for Ilarion dam by physical and numerical modelling

Plunge pool scour and bank erosion: assessment of protection measures for Ilarion dam by physical and numerical modelling

Abstract

130m 높이의 Ilarion 댐은 그리스 북부의 Aliakmon 강에 건설되었습니다. 2개의 여수로에는 플런지 풀의 중심을 향해 고속 제트를 빗나가게 하는 스키 점프가 장착되어 있습니다. 최근 몇 년 동안 두 번의 주요 홍수 동안 수영장에서 상당한 수중 작업이 발생했습니다.

신뢰할 수 있는 보호 조치를 조사하기 위해 FLOW-3D®를 사용하여 1:55 스케일 물리적 모델과 수치 모델을 만들었습니다. 플런지 풀과 여수로에서의 유체역학적 거동과 제트의 궤적을 결정할 수 있었습니다.

수치 모델은 플런지 풀의 흐름이 고도로 비대칭이고 두 개의 배수로 중 하나만 있는 회전 흐름이 작동한다는 것을 보여주었습니다.

이 회전 흐름은 여수로의 흐름 속도보다 3배 더 큰 국부적으로 효과적인 흐름 속도를 초래합니다. 시뮬레이션을 통해 이 문제에 대한 한 가지 해결책은 두 방수로의 대칭 작동임을 확인했습니다.

The 130 m high Ilarion Dam is built on the Aliakmon River in northern Greece. Its two spillways are equipped with ski jumps to deflect high-velocity jets towards the centre of the plunge pool. Significant scouring occurred in the pool during two major floods in recent years. To investigate reliable protection measures, a 1:55 scale physical model and a numerical model with FLOW-3D® were created. The hydrodynamic behaviour of the flow in the plunge pool and in the spillways as well as the trajectory of the jets could be determined. The numerical model showed, that the flow in the plunge pool is highly asymmetric and a rotational flow forms with only one of the two spillways is operational. This rotational flow results in locally effective flow rates three times greater than the flow rate from the spillway. Simulations confirm, that one solution to this problem is the symmetrical operation of both spillways.

Details

TitlePlunge pool scour and bank erosion: assessment of protection measures for Ilarion dam by physical and numerical modelling

Author(s)Van Mol, Romain Nathan Hippolyte Merlin ; Mörtl, Christian ; Amini, Azin ; Siachou, Sofia Schleiss, Anton ; De Cesare, Giovanni

Published inProceedings of HYDRO 2022 Conference

Pagination9

PagesPaper 27.02

ConferenceHYDRO 2022 Conference, Strasbourg, France, April 25-27, 2022

Date2022

Keywords

scourplunge poolspillwaynumerical modellingFLOW-3D

Note[1390]

LaboratoriesLCH
PL-LCH

Record Appears inScientific production and competences > ENAC – School of Architecture, Civil and Environmental Engineering > IIC – Civil Engineering Institute > PL-LCH – Hydraulic Constructions Platform
Scientific production and competences > ENAC – School of Architecture, Civil and Environmental Engineering > IIC – Civil Engineering Institute > LCH – Hydraulic Constructions Laboratory
Peer-reviewed publications
Conference Papers
Work produced at EPFL

Record creation date2022-09-14

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

References

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Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)

2-D Dam-Break Flow Modeling Based on Weighted Average Flux Method

Iranian Journal of Science and Technology, Transactions of Civil Engineering volume 46, pages1515–1525 (2022)Cite this article

Abstract

천해 방정식을 기반으로 하는 2차원 흐름 모델은 댐 붕괴 흐름을 모델링하기 위해 개발되었습니다. 공간 이산화는 유한 체적 셀 중심 유형 방법에 의해 얻어집니다.

수치 시스템은 명시적인 방식으로 해결됩니다. 플럭스 모델링은 시간과 공간 모두에서 2차 정확도로 TVD WAF 방식으로 배포되었습니다. 로컬 리만 문제는 셀 인터페이스에서 HLLC 방법으로 해결됩니다. 수치 모델은 모델 결과와 해석 솔루션을 비교하여 검증합니다.

그런 다음 수치 모델의 결과는 90° 및 180° 편차 각도를 갖는 수로 및 삼각형 바텀 씰 위의 직선 수로에서 사용 가능한 실험 데이터와 비교됩니다. 결과는 댐 파괴파를 예측하는 현재 모델의 합리적인 성능을 확인합니다.

A two-dimensional flow model based on shallow water equations is developed for modeling dam-break flows. The spatial discretization is obtained by the finite volume cell centered type method. The numerical system is solved in explicit way. The flux modeling has been deployed by TVD WAF scheme with a second-order accuracy in both time and space. The local Riemann problem is solved by the HLLC method in the interface of the cells. The numerical model is verified by comparison of model results and analytical solutions. Then the results of numerical model are compared with available experimental data of dam-break waves in a channel with 90° and 180° deviation angle and in a straight channel over a triangular bottom sill. The results confirm the reasonable performance of the present model in predicting dam-break waves.

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Keywords

  • Finite volume
  • Shallow water equations
  • Dam-break
  • HLLC
  • TVD
  • WAF
Fig. 2 Generic control volume and notations
Fig. 2 Generic control volume and notations
Fig. 1 The generated grid for a channel with a 180° bend
Fig. 1 The generated grid for a channel with a 180° bend
Fig. 4 a Water surface profle and b velocity profle of dam-break problem with left dry bed
Fig. 4 a Water surface profle and b velocity profle of dam-break problem with left dry bed
Fig. 5 a Water surface profle and b velocity profle of appearance dry region
Fig. 5 a Water surface profle and b velocity profle of appearance dry region
Fig. 6 Comparison of the present model results and exact solution for transcritical fow over a bump with a shock
Fig. 6 Comparison of the present model results and exact solution for transcritical fow over a bump with a shock
Fig. 7 Geometry of the reservoir and L-shaped channel: plan view (Soares-Frazao et al. 2019)
Fig. 7 Geometry of the reservoir and L-shaped channel: plan view (Soares-Frazao et al. 2019)
Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)
Fig. 9 Test facility a plan view, b the bottom elevation of the reservoir to the channel (Bell et al. 1992)

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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]

References

[1] na, “Landslides 101,” [Online]. Available: https://landslides.usgs.gov/learn/ls101.php.
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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
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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.

/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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10 한국수자원공사 (2021). 댐관리 규정. 대전: 한국수자원공사.

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)

References

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Fig. 2- Experimental setup (Shamloo et al., 2012)

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

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

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.

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.

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
Fig. 2- Experimental setup (Shamloo et al., 2012)
Fig. 2- Experimental setup (Shamloo et al., 2012)
Fig. 3- Results of numerical model validation in determining a) mean flow depth, b) mean velocity, and c) static pressure in various discharges vs (Shamloo et al., 2012) research under a 6 degree ramp angle
Fig. 3- Results of numerical model validation in determining a) mean flow depth, b) mean velocity, and c) static pressure in various discharges vs (Shamloo et al., 2012) research under a 6 degree ramp angle
Fig. 4- Location of data extraction stations after aeration on a scale model of 1:50
Fig. 4- Location of data extraction stations after aeration on a scale model of 1:50
Fig.7- Changes in cavitation index in different discharges with changes in ramp angle: a) 6 degrees, b) 8 degrees and c) 10 degrees
Fig.7- Changes in cavitation index in different discharges with changes in ramp angle: a) 6 degrees, b) 8 degrees and c) 10 degrees

Keywords

Aeration system Ramp angle Aeration coefficient Two-phase flow Flow-3D model

참고문헌

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2- Bayon, A., Toro, JP, Bombardelli, FA, Matos, J., & López-Jiménez, PA(2018). VOF 기술, 난류 모델 및 이산화 방식이 계단식 배수로에서 폭기되지 않은 스키밍 흐름의 수치 시뮬레이션에 미치는 영향. 수력 환경 연구 저널 , 19 , 137–149. https://doi.org/10.1016/j.jher.2017.10.002

3- Brethour, JM, & Hirt, CW (2009). 2성분 흐름에 대한 드리프트 모델. Flow Science, Inc. , FSI – 09 – TN83Rev , 1–7.

4- Chanson, H. (1989). 공기 유입 및 폭기 장치 연구. 수력학 연구 저널 , 27 (3), 301–319. https://doi.org/10.1080/00221688909499166

5- Dong, Z., Wang, J., Vetsch, DF, Boes, RM, & Tan, G. (2019). 매우 높은 단위 배출에서 X자형 플레어링 게이트 교각 뒤의 계단식 배수로에서 공기-물 2상 흐름의 수치 시뮬레이션. 물(스위스) , 11 (10). https://doi.org/10.3390/w11101956

6- Flow-3D, V. 11. 2. (2017). 사용자 매뉴얼. Flow Science Inc.: Santa Fe, NM, USA;

7- Hirt, CW (2003). 자유 표면에서 공기의 난류 동반 모델링. Flow Science, Inc. , FSI – 03 – TN6 , 1–9.

8- Hirt, CW (2016). 드리프트 플럭스에 대한 동적 액적 크기. Flow Science, Inc. , 1–10.

9- Hirt, CW, & Nichols, BD (1981). 자유 경계의 역학에 대한 VOF(유체 체적) 방법. 전산 물리학 저널 , 39 (1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5

10- Kherbache, K., Chesneau, X., Zeghmati, B., Abide, S., & Benmamar, S. (2017). 계단식 배수로의 물 흐름에 대한 계단식 경사 및 공기 주입의 영향: 수치 연구. 유체 역학 저널 , 29 (2), 322–331. https://doi.org/10.1016/S1001-6058(16)60742-4

11- Kramer, M., & Chanson, H. (2019). 폭기된 여수로 흐름에서 광학 흐름 추정: 샘플링 매개변수에 대한 필터링 및 논의. 실험적 열 및 유체 과학 , 103 , 318–328. https://doi.org/10.1016/j.expthermflusci.2018.12.002

12- Mahmoudian, Z., Baharvand, S., & Lashkarara, B. (2019). Baffle Fishway Denil Type의 흐름 패턴 조사. 관개 과학 및 공학(JISE) , 42 (3), 179–196.

13- Meireles, IC, Bombardelli, FA 및 Matos, J. (2014). 가파른 계단식 배수로의 스키밍 흐름에서 공기 유입 시작: 분석. 수력학 연구 저널 , 52 (3). https://doi.org/10.1080/00221686.2013.878401

14- Parsaie, A., & Haghiabi, AH (2019). 1/4 원형 볏이 있는 계단식 배수로에서 흐름 폭기의 시작 지점. 유량 측정 및 계측 , 69 . https://doi.org/10.1016/j.flowmeasinst.2019.101618

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16- Shamloo, H., Hoseini Ghafari, S., & Kavianpour, M. (2012). 슈트 여수로의 폭기에 대한 유입구 흐름의 영향에 대한 실험적 연구(사례 연구: 이란 Jare Dam). 제10차 토목 공학 발전에 관한 국제 회의, 중동 기술 대학, 앙카라, 터키 .

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22- Yang, J., Teng, P., & Lin, C. (2019). 넓은 여수로 폭기장치의 통풍구 배치 및 물-기류 거동. Theoretical and Applied Mechanics Letters , 9 (2), 130–143. https://doi.org/10.1016/j.taml.2019.02.009

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Fig. 1. General view of the Ilarion Dam (image from YouTube https://www.youtube.com/watch?v=KKm203f0r_k)

프리즘 콘크리트 요소를 사용한 플런지 풀 재활 – 그리스 Ilarion 댐의 사례 연구 및 물리적 모델

Plunge pool rehabilitation with prismatic concrete elements – case study and physical model of Ilarion dam in Greece

Van Mol, Romain

130m 높이의 Ilarion 댐은 그리스 북부의 Aliakmon 강에 건설되었습니다. 댐에는 끝에 스키 점프가 있는 2개의 방수로와 제트기의 충격을 완충하는 플런지 풀이 있습니다. 이 수영장은 최근 몇 년 동안 상당한 수질을 겪었습니다. 신뢰할 수 있는 보호 조치를 결정하기 위해 1:55 스케일 모델과 FLOW-3D®를 사용한 수치 모델이 생성되었습니다. 플런지 풀과 여수로에서의 유체역학적 거동과 제트의 궤적을 결정할 수 있었습니다. 수치 모델링은 아마도 대부분의 정련을 일으킨 제트의 영향이 아니라 결과적인 재순환 전류임을 보여주었습니다. 따라서 플런지 풀의 흐름은 매우 비대칭적이며 두 개의 배수로 중 하나만 작동할 때 소용돌이가 형성됩니다. 이 와류는 배수로의 유량보다 3배 더 큰 유역의 유효 유량을 초래합니다. 이 문제에 대한 간단한 해결책은 양쪽 배수로를 대칭적으로 운영하는 것입니다. 제트기의 충돌 표면을 증가시키고 이에 따라 세척 가능성을 줄이기 위해 스키 점프 버킷의 기하학적 구조를 수정하는 것도 조사되었습니다.

The 130 m high Ilarion Dam is built on the Aliakmon River in northern Greece. The dam has two spillways with ski jumps at their ends and a plunge pool to cushion the impact of the jets. This pool has suered signicant scouring during several oods in recent years. In order to determine a reliable protection measure, a 1:55 scale model and a numerical model with FLOW-3D® were created. The hydrodynamic behaviour of the ow in the plunge pool and in the spillways as well as the trajectory of the jets could be determined. The numerical modelling showed that it was probably not the impact of the jet that caused the most of the scouring but the resulting recirculation current. The ow in the plunge pool is thus highly asymmetric and a vortex forms when only one of the two spillways is operating. This vortex results in an eective ow rate in the basin that is three times greater than the ow rate from the spillway. A simple solution to this problem is to operate both spillways symmetrically. A modication of the geometry of the ski jump bucket to increase the impact surface of the jet and thus reduce its scouring potential was also investigated.

Fig. 1. General view of the Ilarion Dam (image from YouTube https://www.youtube.com/watch?v=KKm203f0r_k)
Fig. 1. General view of the Ilarion Dam (image from YouTube
Fig. 2. Topography before the 2013 flood (left) and after the 2015 flood (right)
Fig. 2. Topography before the 2013 flood (left) and after the 2015 flood (right)
Fig. 3. Top view of the velocity vectors at 293.5 m.a.s.l. for a total discharge of 500 m3 /s with only one spillway operational (left) and with two spillways operational (right); the water is coloured according to its velocity in m/s
Fig. 3. Top view of the velocity vectors at 293.5 m.a.s.l. for a total discharge of 500 m3 /s with only one spillway operational (left) and with two spillways operational (right); the water is coloured according to its velocity in m/s

Conclusions

The two spillways of the Ilarion Dam in Greece were studied by numerical modelling with FLOW-3D®. The study focused on the hydrodynamic behaviour of the flow in the plunge pool. It was found that the recirculation current in the plunge pool is a problematic phenomenon. This creates an effective discharge more than 3 times larger than the one expected. A simple and cost-effective solution is to operate the spillways symmetrically. However, this may not always be possible for any given flood discharge. Indeed, the opening range of the gates may be limited for reasons of operability or vibration of the gates.

Figure 16: Velocity Vectors of Flow at Ghulmet

댐 붕괴 홍수파 및 범람 매핑 시뮬레이션: A
아타바드 호수 사례 연구

Simulation of Dam-Break Flood Wave and Inundation Mapping: A
Case study of Attabad Lake

Wasim Karam1, Fayaz A. Khan2, Muhammad Alam3, Sajjad Ali4
1Lab. Engineer, Department of Civil Engineering, University of Engineering and Technology Mardan, Pakistan,
wasim10karam@gmail.com
2Assistant Professor, National Institute of Urban Infrastructure Planning, University of Engineering and Technology Peshawar,
Pakistan, fayazuet@yahoo.com
3,4Assistant Professor, Department of Civil Engineering, University of Engineering and Technology Mardan, Pakistan,
emalam82@gmail.com, sajjadali@uetmardan.edu.pk

ABSTRACT

산사태 또는 제방 댐의 파손 연구는 구성이 불확실하고 자연적이며 재해에 대해 적절하게 설계되지 않았기 때문에 다른 자연적 사건에 대한 대응 지식이 부족하기 때문에 더 중요합니다. 이 논문은 댐 ​​파괴의 수력학적 모델링의 다양한 방법을 개선하는 것을 목표로 합니다.

현재 이 연구에서 Attabad 호수의 댐 붕괴는 전산 유체 역학 기술을 사용하여 시뮬레이션됩니다. 수치 모델(FLOW-3D)은 Reynolds 평균 Navier-Stoke 방정식을 완전히 3D로 풀어서 다양한 단면에서의 피크 유량 깊이, 피크 속도, 피크 방전, 피크 깊이까지의 시간 및 피크 방전까지의 시간을 예측하기 위해 개발되었습니다.

표준 RNG 난류 모델을 사용하여 난류를 시뮬레이션한 다음 마을의 흐름에 대한 홍수 범람 지도와 속도 벡터를 그립니다. 결과는 Hunza 강의 수로를 통해 모델링된 홍수파의 대부분이 Hunza 강의 범람원에 포함되지만 Hunza 강의 범람원 내부에 위치한 Miaun 및 chalat와 같은 일부 마을의 경우 더 높은 위험에 있음을 보여줍니다.

그러나 이들 마을의 예상 홍수 도달 시간은 각각 31분과 44분으로 인구를 안전한 지역으로 대피시키기에 충분한 시간인 반면, 알리 아바드에 인접한 하산 아바드와 같은 일부 마을의 경우 침수 위험이 더 높은 반면 마을의 예상 홍수 도착 시간은 12분으로 인구 대피에 충분하지 않으므로 홍수 억제를 위한 추가 홍수 보호 구조가 필요합니다.

최고속도의 추정치는 하천평야의 더 높은 전단응력, 심한 침식의 위험, 농경지 피해, 주거지 및 형태학적 변화가 예상됨을 의미한다. 댐 파손 분석(예: 최고 깊이, 최고 속도, 홍수 도달 시간 및 홍수 범람 지도)은 향후 위험 분석 및 홍수 관리의 지침으로만 사용해야 합니다.

Figure 2: Case Study Location on Map of Pakistan
Figure 2: Case Study Location on Map of Pakistan
Figure 3: Lake Condition 3 months after Landslide
Figure 3: Lake Condition 3 months after Landslide
Figure 5: 3D Model from the Merged DEM
Figure 5: 3D Model from the Merged DEM
Figure 7: Free Surface Elevation relative to local origin
Figure 7: Free Surface Elevation relative to local origin
Figure 8: Model of lake referenced over Google Earth Image
Figure 8: Model of lake referenced over Google Earth Image
Figure 9: Meshing in the 3D Terrain Model
Figure 9: Meshing in the 3D Terrain Model
Figure 10: Flow Depth Hydrographs of the downstream villages  (A) Karim Abad (B) Ghulmet (C) Thol (D) Chalat (E) Nomal
Figure 10: Flow Depth Hydrographs of the downstream villages (A) Karim Abad (B) Ghulmet (C) Thol (D) Chalat (E) Nomal
Figure 11: Flow Hydrograph at Karim Abad and Nomal Bridge
Figure 11: Flow Hydrograph at Karim Abad and Nomal Bridge
Figure 12: Flood Inundation Map of Karim Abad
Figure 12: Flood Inundation Map of Karim Abad
Figure 13: Flood Inundation Map of Ghulmet
Figure 13: Flood Inundation Map of Ghulmet
Figure 14: Flood Inundation Map of Chalat
Figure 14: Flood Inundation Map of Chalat
Figure 15: Velocity Vectors of flow at Karim Abad
Figure 15: Velocity Vectors of flow at Karim Abad
Figure 16: Velocity Vectors of Flow at Ghulmet
Figure 16: Velocity Vectors of Flow at Ghulmet
Figure 17: Velocity Vectors of Flow at Chalat
Figure 17: Velocity Vectors of Flow at Chalat

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Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation

Understanding dry-out mechanism in rod bundles of boiling water reactor

끓는 물 원자로 봉 다발의 건조 메커니즘 이해

Liril D.SilviaDinesh K.ChandrakercSumanaGhoshaArup KDasb
aDepartment of Chemical Engineering, Indian Institute of Technology, Roorkee, India
bDepartment of Mechanical Engineering, Indian Institute of Technology, Roorkee, India
cReactor Engineering Division, Bhabha Atomic Research Centre, Mumbai, India

Abstract

Present work reports numerical understanding of interfacial dynamics during co-flow of vapor and liquid phases of water inside a typical Boiling Water Reactor (BWR), consisting of a nuclear fuel rod bundle assembly of 7 pins in a circular array. Two representative spacings between rods in a circular array are used to carry out the simulation. In literature, flow boiling in a nuclear reactor is dealt with mechanistic models or averaged equations. Hence, in the present study using the Volume of Fluid (VOF) based multiphase model, a detailed numerical understanding of breaking and making in interfaces during flow boiling in BWR is targeted. Our work will portray near realistic vapor bubble and liquid flow dynamics in rod bundle scenario. Constant wall heat flux for fuel rod and uniform velocity of the liquid at the inlet patch is applied as a boundary condition. The saturation properties of water are taken at 30 bar pressure. Flow boiling stages involving bubble nucleation, growth, merging, local dry-out, rewetting with liquid patches, and complete dry-out are illustrated. The dry-out phenomenon with no liquid presence is numerically observed with phase fraction contours at various axial cut-sections. The quantification of the liquid phase fraction at different axial planes is plotted over time, emphasizing the progressive dry-out mechanism. A comparison of liquid-vapor distribution for inner and outer rods reveals that the inner rod’s dry-out occurs sooner than that of the outer rod. The heat transfer coefficient to identify the heat dissipation capacity of each case is also reported.

현재 작업은 원형 배열에 있는 7개의 핀으로 구성된 핵연료봉 다발 어셈블리로 구성된 일반적인 끓는 물 원자로(BWR) 내부의 물의 증기 및 액체상의 동시 흐름 동안 계면 역학에 대한 수치적 이해를 보고합니다.

원형 배열의 막대 사이에 두 개의 대표적인 간격이 시뮬레이션을 수행하는 데 사용됩니다. 문헌에서 원자로의 유동 비등은 기계론적 모델 또는 평균 방정식으로 처리됩니다.

따라서 VOF(Volume of Fluid) 기반 다상 모델을 사용하는 본 연구에서는 BWR에서 유동 비등 동안 계면의 파괴 및 생성에 대한 자세한 수치적 이해를 목표로 합니다.

우리의 작업은 막대 번들 시나리오에서 거의 사실적인 증기 기포 및 액체 흐름 역학을 묘사합니다. 연료봉에 대한 일정한 벽 열유속과 입구 패치에서 액체의 균일한 속도가 경계 조건으로 적용됩니다. 물의 포화 특성은 30bar 압력에서 취합니다.

기포 핵 생성, 성장, 병합, 국소 건조, 액체 패치로 재습윤 및 완전한 건조를 포함하는 유동 비등 단계가 설명됩니다. 액체가 존재하지 않는 건조 현상은 다양한 축 단면에서 위상 분율 윤곽으로 수치적으로 관찰됩니다.

다른 축 평면에서 액상 분율의 정량화는 점진적인 건조 메커니즘을 강조하면서 시간이 지남에 따라 표시됩니다. 내부 막대와 외부 막대의 액-증기 분포를 비교하면 내부 막대의 건조가 외부 막대보다 더 빨리 발생함을 알 수 있습니다. 각 경우의 방열 용량을 식별하기 위한 열 전달 계수도 보고됩니다.

Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
Fig. 1. A typical Boiling Water Reactor (BWR) and selected segment of study for simulation
Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
Fig. 2. (a-c) dimensions and mesh configuration for G = 6 mm; (d-f) dimensions and mesh configuration for G = 0.6 mm
Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
Fig. 3. Simulating the effect of spacer (a) Spacer configuration around rod bundle (b) Mesh structure in spacer zone (c) Distribution of vapor bubbles in a rod bundle with spacer (d) Liquid phase fraction comparison for geometry with and without spacer (e,f,g) Wall temperature comparison for geometry with and without spacer; WS: With Spacer, WOS: Without Spacer; Temperature in the y-axis is in (f) and (g) is same as (e).
Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
Fig. 4. Validation of the present numerical model with crossflow boiling over a heated cylindrical rod [40]
Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
Fig. 5. Grid-Independent study in terms of vapor volume in 1/4th of computational domain
Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
Fig. 6. Interface contour for G = 6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; they are showing nucleation, growth, merging, and pseudo-steady-state condition.
Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
Fig. 7. Interface contours for G = 0.6 mm; ul = 1.2 m/s; q˙ w = 396 kW/m2; It shows dry-out at pseudo-steady-state near the exit
Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
Fig. 8. Vapor-liquid distribution across various distant cross-sections (Black color indicates liquid; Gray color indicates vapor); Magnification factor: 1 × (for a and b), 1.5 × (for c and d)
Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.
Fig. 21. Two-phase flow mixture velocity (u¯z); for G = 6 mm, r = 5 means location at inner heated wall and r = 25 means location at outer adiabatic wall; for G = 0.66 mm, r = 5 means location at inner heated wall and r = 16.6 mm means location at outer adiabatic wall.

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Fig. 4. Meshed quarter aluminum model with HAZ regions and support steel plates.

Benchmark study on slamming response of flat-stiffened plates considering fluid-structure interaction

유체-구조 상호작용을 고려한 평판 보강판의 슬래밍 응답에 대한 벤치마크 연구

Dac DungTruongabBeom-SeonJangaCarl-ErikJansoncJonas W.RingsbergcYasuhiraYamadadKotaTakamotofYasumiKawamuraeHan-BaekJua
aResearch Institute of Marine Systems Engineering, Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, South Korea
bDepartment of Engineering Mechanics, Nha Trang University, Nha Trang, Viet Nam
cDivision of Marine Technology, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
dNational Maritime Research Institute, National Institute of Maritime, Port and Aviation Technology, Tokyo, Japan
eDepartment of Systems Design for Ocean-Space, Yokohama National University, Kanagawa, Japan
fDepartment of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Tokyo, Japan

ABSTRACT

이 논문은 해양구조물의 평보강판의 슬래밍 반응에 대한 벤치마크 연구를 제시합니다. 목표는 유체-구조 상호작용(FSI) 시뮬레이션 방법론, 모델링 기술 및 슬래밍 압력 예측에 대한 기존 연구원의 경험을 비교하는 것이었습니다.

수치 FSI 시뮬레이션을 위해 가장 일반적인 상용 소프트웨어 패키지를 사용하는 3개의 연구 그룹(예: LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX 및 Star-CCM+/ABAQUS)이 이 연구에 참여했습니다.

공개 문헌에서 입수할 수 있는 경량 선박과 같은 바닥 구조의 평평한 강화 알루미늄 판에 대한 습식 낙하 시험 데이터는 FSI 모델링의 검증에 활용되었습니다. 형상 모델 및 재료 속성을 포함한 실험 조건의 요약은 시뮬레이션 전에 참가자에게 배포되었습니다.

충돌 속도와 강판의 강성이 슬래밍 응답에 미치는 영향을 조사하기 위해 해양 설비에 사용되는 실제 치수를 갖는 평판 보강 강판에 대한 매개변수 연구를 수행했습니다. 보강판에 작용하는 전체 수직력에 대한 FE 시뮬레이션 결과와 이러한 힘에 대한 구조적 반응을 참가자로부터 획득하여 분석 및 비교하였다.

앞서 언급한 상용 FSI 소프트웨어 패키지를 사용하여 슬래밍 부하에 대한 신뢰할 수 있고 정확한 예측을 평가했습니다. 또한 FSI 시뮬레이션에서 관찰된 동일한 영구 처짐을 초래하는 등가 정적 슬래밍 압력을 보고하고 분류 표준 DNV에서 제안한 해석 모델 및 슬래밍 압력 계산을 위한 기존 실험 데이터와 비교했습니다.

연구 결과는 등가 하중 모델이 물 충돌 속도와 플레이트 강성에 의존한다는 것을 보여주었습니다. 즉, 등가정압계수는 충돌속도가 증가함에 따라 감소하고 충돌구조가 더 단단해지면 증가한다.

This paper presents a benchmark study on the slamming responses of offshore structures’ flat-stiffened plates. The objective was to compare the fluid-structure interaction (FSI) simulation methodologies, modeling techniques, and established researchers’ experiences in predicting slamming pressure. Three research groups employing the most common commercial software packages for numerical FSI simulations (i.e. LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX, and Star-CCM+/ABAQUS) participated in this study. Wet drop test data on flat-stiffened aluminum plates of light-ship-like bottom structures available in the open literature was utilized for validation of the FSI modeling. A summary of the experimental conditions including the geometry model and material properties, was distributed to the participants prior to their simulations. A parametric study on flat-stiffened steel plates having actual scantlings used in marine installations was performed to investigate the effect of impact velocity and plate rigidity on slamming response. The FE simulation results for the total vertical forces acting on the stiffened plates and their structural responses to those forces, as obtained from the participants, were analyzed and compared. The reliable and accurate predictions of slamming loads using the aforementioned commercial FSI software packages were evaluated. Additionally, equivalent static slamming pressures resulting in the same permanent deflections, as observed from the FSI simulations, were reported and compared with analytical models proposed by the Classification Standards DNV and existing experimental data for calculation of the slamming pressure. The study results showed that the equivalent load model depends on the water impact velocity and plate rigidity; that is, the equivalent static pressure coefficient decreases with an increase in impact velocity, and increases when impacting structures become stiffer.

Fig. 4. Meshed quarter aluminum model with HAZ regions and support steel plates.
Fig. 4. Meshed quarter aluminum model with HAZ regions and support steel plates.
Fig. 6. (a) Boundary conditions of water hitting case and (b) water jets at end of the simulation.
Fig. 6. (a) Boundary conditions of water hitting case and (b) water jets at end of the simulation.
Fig. 7. Comparison of prediction and test results for deflection time history of (a) D1 and (b) D2 for Vi = 2.3 m/s.
Fig. 7. Comparison of prediction and test results for deflection time history of (a) D1 and (b) D2 for Vi = 2.3 m/s.
Fig. 8. Comparison of prediction and test results for maximum deflection with different impact velocities.
Fig. 8. Comparison of prediction and test results for maximum deflection with different impact velocities.
Fig. 16. Boundary conditions applied to present FSI simulations (Sym. denotes symmetric, and Cons. denotes constrained)
Fig. 16. Boundary conditions applied to present FSI simulations (Sym. denotes symmetric, and Cons. denotes constrained)
Fig. 24. Distribution of deflections at moment of maximum deflection in: (a) LS-Dyna ALE, (b) Star-CCM+/ABAQUS, (c) ANSYS CFD, and (d) LSDyna ICFD (unit: m).

Keywords

Benchmark studyEquivalent static pressureFlat-stiffened plateFluid-structure interactionPermanent deflectionSlamming pressure coefficient

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Obrázek 44: Barevné rozlišení proudnic dle rychlosti

Abstract

졸업 논문의 목표는 보스코비체 댐의 계획된 방수로의 흐름을 수치적으로 모델링하는 것입니다. 이 졸업 논문은 유형과 프로필에 따라 기본 여수로를 설명하고 나눕니다. 비상용 배수로도 언급되어 있습니다. 그런 다음 논문에서는 범람량 계산에 대한 설명, 수학적 모델링 및 사용된 난류 모델에 대한 설명을 소개합니다. 다음 부분은 Boskovice 댐의 기술적 설명, AutoCAD 2020 소프트웨어에서 방수로 및 방수로 슈트의 가상 3D 모델 생성 및 Blender 소프트웨어에서 모델의 제어 및 수정과 관련되어 있습니다. 논문 말미에는 Flow-3D 소프트웨어를 통해 얻은 유동의 수치적 모델링 결과와 BUT 토목공학부 수구조연구소에서 시행한 수리학적 모델 연구와 비교한 결과를 언급하였다.

The goal of the diploma thesis is the numerical modelling of flow in planned spillway of the Boskovice dam. In the introduction of this diploma thesis are described and divided basic spillways according to their types and profiles. There are also mentioned emergency spillways. Then the thesis introduces the description of calculation of overflow quantity, the description of mathematic modelling and used turbulent models. The next part is concerned with the technical description of the Boskovice dam, the creation of virtual 3D model of spillway and spillway chute in the AutoCAD 2020 software and concerned with the control and revision of model in the Blender software. In the end of the thesis are mentioned results of numeric modelling of flow gained from the Flow-3D software and the comparison of results with the research of hydraulic model implemented at Water structures institute of Faculty of Civil Engineering of BUT.

AuthorSvoboda, Jiří
TitleNumerické modelování proudění v bezpečnostním přelivu: Numerical modeling of flow in spilway
URLhttp://hdl.handle.net/11012/195970
Publication Date2021
Date Accessioned2021-02-05 08:03:49
University/PublisherBrno University of Technology
AbstractThe goal of the diploma thesis is the numerical modelling of flow in planned spillway of the Boskovice dam. In the introduction of this diploma thesis are described and divided basic spillways according to their types and profiles. There are also mentioned emergency spillways. Then the thesis introduces the description of calculation of overflow quantity, the description of mathematic modelling and used turbulent models. The next part is concerned with the technical description of the Boskovice dam, the creation of virtual 3D model of spillway and spillway chute in the AutoCAD 2020 software and concerned with the control and revision of model in the Blender software. In the end of the thesis are mentioned results of numeric modelling of flow gained from the Flow-3D software and the comparison of results with the research of hydraulic model implemented at Water structures institute of Faculty of Civil Engineering of BUT.
Subjects/KeywordsBezpečnostní přeliv; numerický model; 3D model; FLOW-3D; VD Boskovice; sypaná kamenitá hráz.; Spillway; numerical model; 3D model; FLOW-3D; Boskovice dam; rockfill dam.
ContributorsJandora, Jan (advisor); Holomek, Petr (referee)
Languagecs
RightsStandardní licenční smlouva – přístup k plnému textu bez omezení
Country of Publicationcz
Record IDhandle:11012/195970
Repositorybrno-tech
Date Indexed2021-12-08
Note[mark] A;
Obrázek 18: Kašnový čelní bezpečnostní přeliv [24]
OFigure 18: Fountain front safety spillway [24]
Obrázek 20: Skluz a divergentní vývar bezpečnostního objektu VD Boskovice [24]
Figure 20: Slip and divergent broth of the security building VD Boskovice [24]
Obrázek 22: Půdorys bezpečnostního přelivu a části skluzu VD Boskovice [12]
Obrázek 22: Půdorys bezpečnostního přelivu a části skluzu VD Boskovice [12]
Obrázek 23: Podélný řez BP a spadiště v rovině symetrie [12]
Figure 23: Longitudinal section BP and drop in the plane of symmetry [12]
Obrázek 44: Barevné rozlišení proudnic dle rychlosti
Figure 44: Color resolution of jets according to speed
Obrázek 45: Průběh hladiny ve Flow-3D bez zobrazeného 3D modelu
Figure 45: Flow profile in Flow-3D without 3D model displayed
Figure 47: Level course on the physical model [22]
Figure 47: Level course on the physical model [22]

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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.

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Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) - (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.

MULTIPHYSICS SIMULATION OF THEMRAL AND FLUID DYNAMICS PHENOMENA DURING THE PULSED LASER POWDER BED FUSION PROCESS OF 316-L STEEL

M. Bayat* , V. K. Nadimpalli, J. H. Hattel
1Department of Mechanical Engineering, Technical University of Denmark (DTU), Produktionstorvet
425, Kgs. 2800, Lyngby, Denmark

ABSTRACT

L-PBF(Laser Powder Bed Fusion)는 다양한 산업 분야에서 많은 관심을 받았으며, 주로 기존 제조 기술을 사용하여 만들 수 없었던 복잡한 토폴로지 최적화 구성 요소를 구현하는 잘 알려진 능력 덕분입니다. . 펄스 L-PBF(PL-PBF)에서 레이저의 시간적 프로파일은 주기 지속 시간과 듀티 주기 중 하나 또는 둘 다를 수정하여 변조할 수 있습니다. 따라서 레이저의 시간적 프로파일은 향후 적용을 위해 이 프로세스를 더 잘 제어할 수 있는 길을 열어주는 새로운 프로세스 매개변수로 간주될 수 있습니다. 따라서 이 작업에서 우리는 레이저의 시간적 프로파일을 변경하는 것이 PL-PBF 공정에서 용융 풀 조건과 트랙의 최종 모양 및 형상에 어떻게 영향을 미칠 수 있는지 조사하는 것을 목표로 합니다. 이와 관련하여 본 논문에서는 CFD(Computational Fluid Dynamics) 소프트웨어 패키지인 Flow-3D를 기반으로 하는 316-L 스테인리스강 PL-PBF 공정의 다중물리 수치 모델을 개발하고 이 모델을 사용하여 열과 유체를 시뮬레이션합니다. 다양한 펄스 모드에서 공정 과정 중 용융 풀 내부에서 발생하는 유동 조건. 따라서 고정된 레이저 듀티 사이클(50%)이 있는 레이저 주기 지속 시간이 용융 풀의 모양과 크기 및 최종 트랙 형태에 미치는 영향을 연구하기 위해 매개변수 연구가 수행됩니다. 더 긴 주기 기간에서 더 많은 재료가 더 큰 용융 풀 내에서 변위됨에 따라 용융 풀의 후류에 더 눈에 띄는 혹이 형성되며, 동시에 더 심각한 반동 압력을 받습니다. 또한 시뮬레이션에서 50% 듀티 사이클에서 1000μs에서 형성된 보다 대칭적인 용융 풀과 비교하여 400μs 사이클 주기에서 더 긴 용융 풀이 형성된다는 것이 관찰되었습니다. 풀 볼륨은 1000μs의 경우 더 큽니다. 매개변수 연구는 연속 트랙과 파손된 트랙 PL-PBF 사이의 경계를 설명하며, 여기서 연속 트랙은 항상 소량의 용융 재료를 유지함으로써 유지됩니다.

English Abstract

Laser Powder Bed Fusion (L-PBF) has attracted a lot of attention from various industrial sectors and mainly thanks to its well-proven well-known capacity of realizing complex topology-optimized components that have so far been impossible to make using conventional manufacturing techniques. In Pulsed L-PBF (PL-PBF), the laser’s temporal profile can be modulated via modifying either or both the cycle duration and the duty cycle. Thus, the laser’s temporal profile could be considered as a new process parameter that paves the way for a better control of this process for future applications. Therefore, in this work we aim to investigate how changing the laser’s temporal profile can affect the melt pool conditions and the final shape and geometry of a track in the PL-PBF process. In this respect, in this paper a multiphysics numerical model of the PL-PBF process of 316-L stainless steel is developed based on the computational fluid dynamics (CFD) software package Flow-3D and the model is used to simulate the heat and fluid flow conditions occurring inside the melt pool during the course of the process at different pulsing modes. Thus, a parametric study is carried out to study the influence of the laser’s cycle duration with a fixed laser duty cycle (50 %) on the shape and size of the melt pool and the final track morphology. It is noticed that at longer cycle periods, more noticeable humps form at the wake of the melt pool as more material is displaced within bigger melt pools, which are at the same time subjected to more significant recoil pressures. It is also observed in the simulations that at 50 % duty cycle, longer melt pools form at 400 μs cycle period compared to the more symmetrical melt pools formed at 1000 μs, primarily because of shorter laser off-times in the former, even though melt pool volume is bigger for the 1000 μs case. The parameteric study illustrates the boundary between a continuous track and a broken track PL-PBF wherein the continuous track is retained by always maintaining a small volume of molten material.

Figure 1: Front and side views of the computational domain. Note that the region along z and from -100 μm to +50 μm is void.
Figure 1: Front and side views of the computational domain. Note that the region along z and from -100 μm to +50 μm is void.
Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) - (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.
Figure 2: Temperature contours and melt pool border lines at different times for the 50 % duty cycle case: (a) – (c) Δtcycle = 400 μs, (d) – (f) Δtcycle = 1000 μs and (g) – (i) Δtcycle = 3000 μs.
Figure 3: Plot of melt pool volume versus time for four cases including continuous wave laser as well as 50 % duty cycle at 400 μs, 1000 μs and 3000 μs.
Figure 3: Plot of melt pool volume versus time for four cases including continuous wave laser as well as 50 % duty cycle at 400 μs, 1000 μs and 3000 μs.

CONCLUSIONS

In this work a CFD model of the modulated PL-PBF process of stainless steel 316-L is developed in the commercial software package Flow-3D. The model involves physics such as solidification, melting, evaporation, convection, laser-material interaction, capillarity, Marangoni effect and the recoil pressure effect. In the current study, a parametric study is carried out to understand how the change in the cycle period duration affects the melt pool’s thermo-fluid conditions during the modulated PL-PBF process. It is observed that at the pulse mode with 50 % duty cycle and 400 μs cycle period, an overlapped chain of humps form at the wake of the melt pool and at a spatial frequency of occurrence of about 78 μm. Furthermore and as expected, it is noted that the melt pool volume, the size of the hump as well as the crater size at the end of the track, increase with increase in the cycle period duration, as more material is re-deposited at the back of the melt pool and that itself is caused by more pronounced recoil pressures. Moreover, it is noticed that due to the short off-time period of the laser in the 400 μs cycle period case, there is always an amount of liquid metal left from the previous cycle, at the time the new cycle starts. This is found to be the main reason why longer and elongated melt pools form at 400 μs cycle period, compared to the bigger, shorter and more symmetrical-like melt pools forming at the 1000 μs case. In this study PL-PBF single tracks including the broken track and the continuous track examples were studied to illustrate the boundary of this transition at a given laser scan parameter setting. At higher scan speeds, it is expected that the Plateau–Rayleigh instability will compete with the pulsing behavior to change the transition boundary between a broken and continuous track, which is suggested as future work from this study.

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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

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Figure 6. Circular section of the viscosity and shear-rate clouds.

Simulation and Visual Tester Verification of Solid Propellant Slurry Vacuum Plate Casting

Wu Yue,Li Zhuo,Lu RongFirst published: 26 February 2020 https://doi.org/10.1002/prep.201900411Citations: 3

Abstract

Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.

개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.

타설시간, 타설품질, 수치해석으로 예측된 ​​유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.

연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.

시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.

또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.

마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.

Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 1. The equipment used in the vacuum flower-plate pouring process.
Figure 2. Calculation model.
Figure 2. Calculation model.
Figure 3. Grid block division unit.
Figure 3. Grid block division unit.
Figure 4. Circular section of the speed cloud.
Figure 4. Circular section of the speed cloud.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 6. Circular section of the viscosity and shear-rate clouds.
Figure 7. Volume fraction cloud chart at different time.
Figure 7. Volume fraction cloud chart at different time.
Figure 8. Experimental program.
Figure 8. Experimental program.
Figure 9. Emulation experimental device.
Figure 9. Emulation experimental device.
Figure 10. Visualization of the flow state of the pulp inside the tester.
Figure 10. Visualization of the flow state of the pulp inside the tester.

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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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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

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

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

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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.
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Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.

스키밍 흐름 영역에서 계단형 여수로의 수리 성능에 대한 삼각형 프리즘 요소의 영향: 실험 연구 및 수치 모델링

The effect of triangular prismatic elements on the hydraulic performance of stepped spillways in the skimming flow regime: an experimental study and numerical modeling 

Kiyoumars RoushangarSamira AkhgarSaman Shahnazi

계단식 여수로는 댐의 여수로 위로 흐르는 큰 물의 에너지를 분산시키는 비용 효율적인 유압 구조입니다. 이 연구에서는 삼각주형 요소(TPE)가 계단식 배수로의 수력 성능에 미치는 영향에 초점을 맞췄습니다. 9개의 계단식 배수로 모델이 TPE의 다양한 모양과 레이아웃으로 실험 및 수치적으로 조사되었습니다. 적절한 난류 모델을 채택하려면 RNG k – ε 및 표준 k – ε모델을 활용했습니다. 계산 모델 결과는 계단 표면의 속도 분포 및 압력 프로파일을 포함하여 실험 사례의 계단 여수로에 대한 복잡한 흐름을 만족스럽게 시뮬레이션했습니다. 결과는 계단식 여수로에 TPE를 설치하는 것이 캐비테이션 효과를 줄이는 효과적인 방법이 될 수 있음을 나타냅니다. 계단식 여수로에 TPE를 설치하면 에너지 소실률이 최대 54% 증가했습니다. 계단식 배수로의 성능은 TPE가 더 가깝게 배치되었을 때 개선되었습니다. 또한, 실험 데이터를 이용하여 거칠기 계수( f )와 임계 깊이 대 단차 거칠기( yc / k )의 비율 사이의 관계를 높은 정확도로 얻었다.

Keywords

energy dissipationFlow-3Droughness coefficientstepped spillwaytriangular prismatic elements

에너지 소산 , Flow-3D , 거칠기 계수 , 계단식 배수로 , 삼각형 프리즘 요소

Figure 1 | General schematics of laboratory flume facilities.
Figure 1 | General schematics of laboratory flume facilities.
Figure 2 | Different layouts of the selected TPE in the experimental study (y1 and y2 are initial, and sequent depths of hydraulic jump).
Figure 2 | Different layouts of the selected TPE in the experimental study (y1 and y2 are initial, and sequent depths of hydraulic jump).
Figure 3 | Geometry and alignment of TPE in the numerical study.
Figure 3 | Geometry and alignment of TPE in the numerical study.
Figure 5 | Comparison of turbulence models in Flow-3D.
Figure 5 | Comparison of turbulence models in Flow-3D.
Figure 6 | Sequent water depths versus unit flow rate in standard stepped spillways and stepped spillways with triangular TPEs of types A and B.
Figure 6 | Sequent water depths versus unit flow rate in standard stepped spillways and stepped spillways with triangular TPEs of types A and B.
Figure 7 | Energy dissipation for the standard stepped spillway and the stepped spillway with TPEs.
Figure 7 | Energy dissipation for the standard stepped spillway and the stepped spillway with TPEs.
Figure 8 | Positions of measurement points to investigate the pressure and velocity distributions on the stepped spillway
Figure 8 | Positions of measurement points to investigate the pressure and velocity distributions on the stepped spillway
Figure 9 | Velocity distributions on the vertical surface of step number 4.
Figure 9 | Velocity distributions on the vertical surface of step number 4.
Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.
Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.
Figure 11 | Pressure distribution on the vertical surface of the fourth step.
Figure 11 | Pressure distribution on the vertical surface of the fourth step.
Figure 12 | Horizontal profile of the pressure distribution on the floor of step 4.
Figure 12 | Horizontal profile of the pressure distribution on the floor of step 4.
Figure 13 | Roughness coefficient changes with various unit discharges for stepped spillways.
Figure 13 | Roughness coefficient changes with various unit discharges for stepped spillways.
Figure 14 | Variations of sequent depth of downstream with various unit discharges for stepped spillways.
Figure 14 | Variations of sequent depth of downstream with various unit discharges for stepped spillways.
Figure 15 | Energy dissipation rate changes with various unit discharges for different stepped spillways.
Figure 15 | Energy dissipation rate changes with various unit discharges for different stepped spillways.
Figure 16 | Roughness coefficients (f ) versus the critical depth to the step roughness ratio (yc/K).
Figure 16 | Roughness coefficients (f ) versus the critical depth to the step roughness ratio (yc/K).

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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 2 Idea and details of T-shaped weir.

Introducing the T-shaped weir: a new nonlinear weir

Behzad NorooziJalal BazarganAkbar Safarzadeh

Abstract

본 연구에서는 LW(Labyrinth Weir)와 PKW(Piano Key Weir)가 결합된 T자형 웨어(TSW)라는 새로운 비선형 웨어를 도입하여 수압 성능을 비교하였다.

PKW. 입구 키, 출구 키 또는 두 키 모두에서 수직 벽의 존재에 따라 TSW 위어는 각각 A, B 또는 C 유형 웨어로 분류되었습니다. 다른 TSW 사례의 흐름 패턴을 분석하고 배출 계수 곡선을 제공했습니다. 또한 테스트된 둑의 유체역학을 정확하게 연구하기 위해 FLOW-3D 소프트웨어를 사용하여 3D 수치 시뮬레이션을 수행했습니다.

결과는 출구 키(C-TSW 유형)의 상류에 수직 벽을 삽입하는 것이 PKW의 유압 성능에 미미한 영향을 미치는 것으로 나타났습니다. B-TSW의 토출계수는 PKW 대비 최대 16% 증가하였으며, Ht/p 0.45까지 수직벽의 성능향상 효과 증가 B-TSW는 유지되었습니다.

실험적 및 수치적 실험을 통해 가장 높은 방전 용량을 갖는 B-TSW에서 수직벽의 최적 높이비(Pd/P)는 0.4로 결정되었다.

In the present study, a new nonlinear weir called the T-shaped weir (TSW), which is a combination of the labyrinth weir (LW) and the piano key weir (PKW), was introduced, and its hydraulic performance was compared with the PKW. Based on the presence of the vertical walls at the inlet key, outlet key, or both keys, the TSW weirs were classified as type A, B, or C weirs, respectively. The flow pattern of different TSW cases was analyzed, and the discharge coefficient curves were provided. Furthermore, to accurately study the hydrodynamics of the tested weirs, 3D numerical simulations were performed using the FLOW-3D software. The results showed that inserting a vertical wall at the upstream of the outlet keys (C-TSW type) has a negligible effect on the hydraulic performance of the PKW. A maximum increase of 16% occurred in the discharge coefficient of the B-TSW in comparison to the PKW, and up to a head to height ratio (Ht/p) of 0.45, the effect of the vertical wall on increasing the performance of the B-TSW was maintained. Based on the experimental and numerical tests, the optimal height ratio of the vertical wall (Pd/P) in B-TSW with highest discharge capacity was determined to be equal to 0.4.

HIGHLIGHTS

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  • A new nonlinear weir called the T-shaped weir (TSW), which is a combination of the labyrinth weir (LW) and the piano key weir (PKW), is introduced.
  • To investigate the hydrodynamics of the tested weirs in more detail, 3D numerical models are developed on the CFD-software FLOW-3D.
  • By testing different vertical wall sizes, the optimal size of the vertical wall is determined for B-TSW weir.

Keywords

discharge coefficientlabyrinth weirlocal submergencepiano key weirT-shaped weir

Figure 2 Idea and details of T-shaped weir.
Figure 2 Idea and details of T-shaped weir.

Figure 19. Water surface profile at the middle part of the inlet key for H/P = 0.4.
Figure 19. Water surface profile at the middle part of the inlet key for H/P = 0.4.
Figure 21 Transverse water surface profile in the outlet key of tested weirs  for H/P = 0.4.
Figure 21 Transverse water surface profile in the outlet key of tested weirs for H/P = 0.4.

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Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.

Interference of Dual Spillways Operations

Jai Hong Lee, Ph.D., P.E., M.ASCE; Pierre Y. Julien, Ph.D., M.ASCE; and Christopher I. Thornton, Ph.D., P.E., M.ASCE

Abstract

이중 여수로 간섭은 여수로가 서로 가깝게 배치될 때 수압 성능의 손실을 나타냅니다. 배수로 간섭은 물리적 실험과 수치 시뮬레이션을 모두 사용하여 조사됩니다.

이중 여수로 구성의 4개 물리적 모델의 단계 및 배출 측정값을 한국의 4개 댐 부지에서 Flow-3D 계산 결과와 비교합니다.

두 개의 배수로를 함께 사용하는 것을 각 배수로의 단일 작동과 비교합니다. 두 여수로를 동시에 운영할 경우 두 여수로를 통한 총 유량은 최대 7.6%까지 감소합니다.

간섭 계수는 단계 He가 설계 단계 Hd를 초과하고 두 배수로를 분리하는 거리 D가 배수로 너비 W에 비해 짧을 때 가장 중요합니다. 매개변수 DHd/WHe는 계산 및 측정된 간섭 계수와 매우 잘 관련됩니다.

안동댐 설계방류에 대한 홍수경로 예시는 간섭계수를 적용한 경우와 적용하지 않은 경우 저수지 수위의 차이가 42cm임을 보여줍니다. 결과적으로 댐 안전을 위해 추가 여수로의 너비(간섭 계수 포함)를 늘려야 합니다.

Dual spillway interference refers to the loss of hydraulic performance of spillways when they are placed close together. Spillway interference is examined using both physical experiments and numerical simulations. Stage and discharge measurements from four physical models with dual spillways configurations are compared to the Flow-3D computational results at four dam sites in South Korea. The conjunctive use of two spillways is compared with the singular operation of each spillway. When both spillways are operated at the same time, the total flow rate through the two spillways is reduced by up to 7.6%. Interference coefficients are most significant when the stage He exceeds the design stage Hd and when the distance D separating two spillways is short compared to the spillway width W. The parameter DHd/WHecorrelates very well with the calculated and measured interference coefficients. A flood routing example for the design discharge at Andong dam shows a 42 cm difference in reservoir water level with and without application of the interference coefficient. Consequently, the width of additional spillways (including the interference coefficient) should be increased for dam safety.

Fig. 1. Definition sketch for dual spillways
Fig. 1. Definition sketch for dual spillways
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 2. Stage-discharge rating curves for dual spillway operations.
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 3. Physical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; and (d) Juam-1
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. Numerical modeling of dual spillways: (a) Andong-1; (b) Andong-2; (c) Imha-1; (d) Juam-1; (e) Andong-3; (f) Imha-2; (g) Imha-3; and (h) Juam-3.
Fig. 4. (Continued.)
Fig. 4. (Continued.)
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 5. Meshes and calculation domain for numerical modeling of Andong dam.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 6. Stage-discharge rating curve for existing and additional spillways (Andong-1): (a) existing spillway; (b) additional spillway; and (c) dual spillway simulations.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 7. Discharge comparison of physical experiments and numerical simulations. The upper panel is the comparative result for the existing spillway (ES) and the lower panel is for the additional spillway (AS) at four dams.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 8. Interference coefficients for dual spillways simulations with various scenarios.
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 9. Regression model for the distance-width ratio (D=W) and head ratio (Hd=He) by dual spillway simulations
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 10. Physical and numerical model validation: (a) numerical modeling; (b) solids of overflow weir of the spillway; and (c) physical models of reservoir and spillway
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 11. Interference coefficients for dual spillways operations with various scenarios. The dashed lines indicate the results of the validation model with dual conditions of 1 þ 2, 1 þ 4, 1 þ 6, 3 þ 4, and 4 þ 5.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.
Fig. 12. Results of reservoir operations under the PMF at Andong dam.

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Investigation ofcavitation in stepped spillway of Siah-Bishe dam by using Flow-3D model

Investigation ofcavitation in stepped spillway of Siah-Bishe dam by using Flow-3D model

Author(s) : Daneshfaraz, R. ;  Zogi, N.

Author Affiliation : Civil Eng. & Hydraulics Dept., Faculty of Engineering, University of Maragheh, Maragheh, Iran.

Author Email : daneshfaraz@yahoo.com

Journal article : International Research Journal of Applied and Basic Sciences 2013 Vol.4 No.11 pp.3382-3388 ref.14

Abstract

캐비테이션은 고속 및 과난류 흐름에서 수리 구조물에 손상을 입히고 구멍을 만드는 현상입니다. 본 연구에서는 Siah-Bishe 배수로의 계단식 급수 공식을 Flow-3D 소프트웨어를 통해 시뮬레이션하고 물리적 모델과 비교합니다.

이 소프트웨어는 자유 표면과 복잡한 형상의 불안정한 3D 흐름 문제를 분석하는 정확한 도구입니다. 유한체적법을 통해 질량, 운동량, 에너지 보존 공식을 풀어 문제를 해결합니다.

본 연구에서는 여수로의 시작, 끝, 끝 부분의 압력 매개변수를 연구하고 일부 부분에서 음압이 관찰됩니다. 이 압력은 캐비테이션을 일으킬 수 있습니다. 본 연구는 Flow-3D로 모델링된 물리적 모델과 유한체적법 간의 대응 결과를 보여준다.

Cavitation is a phenomenon which damages and makes hole in hydraulic structure in high velocity and over-turbulent flows. In this research, stepped fast water formula of Siah-Bishe spillway is stimulated via Flow-3D software and compared with physical model. This software is an accurate tool in analyzing unsteady 3D flow problems with free surface and complex geometry. It solves problems by solving conservation of mass formulas, momentum and energy viafinite volume method. In this study, pressure parameter at the beginning, end and along the spillway is studied and negative pressure is observed in some parts. This pressure can make cavitation. The study shows the results of correspondence between physical model and finite volume method modeled by Flow-3D.

ISSN : 2251-838X

URL : http://irjabs.com/files_site/paperlis…

Record Number : 20133348057

Publisher : Science Explorer Publications

Location of publication : London

Country of publication : UK

Language of text : English

Indexing terms for this abstract:

Keywords

cavitation, computer simulation, dams, pressure, simulation models, spillways, water flow

3D Numerical Modeling of a Side-Channel Spillway

3D Numerical Modeling of a Side-Channel Spillway

Géraldine MilésiStéphane Causse

Abstract

Electricité de Tahiti(GDF Suez) 댐의 재건이라는 틀 내에서 Coyne et Bellier는 진단과 Tahiti 댐의 전반적인 연구를 수행했습니다.

Tahinu는 프랑스령 폴리네시아의 Tahiti 섬에 위치한 37m 높이의 수력 발전 댐입니다. 수문학적 연구의 검토와 프랑스 표준의 적용은 최대 설계 홍수를 500에서 644 m3/s(+30%)로 증가시켰습니다.

먼저 측수로 여수로(마루 길이 60m)의 1D 수치 모델링을 수행하여 배수 용량을 평가했습니다. 결론은 마루댐과 배수로 수로 측벽의 오버토핑을 유발할 수 있는 배수로의 용량이 충분하지 않다는 것이었습니다.

그런 다음 이러한 결과를 확인하고 배수로의 특정 구성(정원 아래의 접근 속도와 깊이의 불균일한 분포, 측면 채널 단면의 불규칙한 기하학, 잠긴 둑, 곡선 채널 배수로)을 고려하기 위해, 3D 수치 모델링은 Flow 3D®로 수행되었습니다.

시뮬레이션은 1D 모델(흐름의 일반적인 패턴, 상류 저수지 수위)보다 더 정확한 결과를 보여주었습니다. 이에 따라 댐 능선의 높이와 여수로 측벽을 설계 및 최적화하여 안전을 위한 충분한 freeboards을 확보하도록 하였습니다.

Within the framework of the rehabilitation of Electricité de Tahiti (GDF Suez) dams, Coyne et Bellier carried out a diagnosis and an overall study of the Tahinu dam. Tahinu is a 37-m-high earthfill hydroelectric dam, located in the island of Tahiti, French Polynesia. The review of the hydrological study and the application of French standards lead to increase the peak design flood from 500 to 644 m3/s (+30 %). First, a 1D numerical modeling of the side-channel spillway (crest length 60 m) was performed to assess its discharge capacity. The conclusion was an insufficient capacity of the spillway that might induce an overtopping of the crest dam and of the sidewalls of the spillway channel. Then, to confirm these results and to take into account the specific configuration of the spillway (non-uniform distribution of the approach velocity and depth below crest, irregular geometry of the side-channel cross section, submerged weir, curved channel spillway), a 3D numerical modeling was carried out with Flow 3D®. Simulations showed more accurate results than 1D model (general pattern of the flow, upstream reservoir level). Consequently, heightenings of the dam crest and the sidewalls of the spillway channel were designed and optimized to secure sufficient freeboards for safety.

Keywords

CFD, Dam, FLOW-3D, Hydraulics, Numerical simulation, Rehabilitation, Submergence, Weir, 저수지, 댐, 측수로, 여수로

References

  1. 1.Khatsuria, R. M. (2005). Hydraulics of spillways and energy dissipators. New York: Marcel Dekker.Google Scholar
  2. 2.USBR. (1987). Design of small dams (3rd ed.). Washington: US Government printing office.Google Scholar

Copyright information

© Springer Science+Business Media Singapore 2014

About this chapter

Cite this chapter as:Milési G., Causse S. (2014) 3D Numerical Modeling of a Side-Channel Spillway. In: Gourbesville P., Cunge J., Caignaert G. (eds) Advances in Hydroinformatics. Springer Hydrogeology. Springer, Singapore. https://doi.org/10.1007/978-981-4451-42-0_39

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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Fig. 2 Schematic diagram of the experimental Rijke tube

RIJKE 튜브 내부의 열음향 장에 대한 새로운 조사

A novel investigation of the thermoacoustic field inside a Rijke tube

B. EntezamW. Van Moorhem and J. MajdalaniPublished Online:22 Aug 2012 https://doi.org/10.2514/6.1998-2582

Abstract

이 논문에서는 Rijke 튜브 내부의 시간 종속 유동장의 실험 연구 및 계산 시뮬레이션에서 진행한 결과를 제시하고 해석합니다. 기존의 추측과 스케일링 분석을 기반으로 한 이론적 논의가 진행됩니다. 주요 결과에는 열 구동 진동에서 중요한 역할을 하는 것으로 보이는 유사성 매개변수가 포함됩니다. 이 매개변수는 열 섭동을 속도, 압력 및 특성 길이의 제곱과 관련시킵니다. 열 진동을 압력 및 속도 진동의 결합된 효과에 기인하는 간단한 이론은 계산, 실험 및 스케일링 고려 사항을 통해 논의됩니다. 이전의 분석 이론은 열 진동을 속도 또는 압력 진동에 연결했기 때문에 현재 분석 모델은 기존 추측에 동의하고 조정합니다. Rayleigh 기준에 따라 열원은 Rijke-tube 하단에서 1/4의 임계 거리에 위치해야 공명이 발생합니다. 이 관찰은 결합이 최대화되는 임계점이 음향 속도와 압력의 곱인 음향 강도가 가장 큰 공간 위치에 해당하기 때문에 제안된 해석을 확인합니다. 수치 시뮬레이션은 Rijke 튜브 내부의 압력 진동이 열 입력이 증가함에 따라 기하급수적으로 증가한다는 것을 보여줍니다. 충분히 작은 열 입력으로 음향 싱크가 소스를 초과하고 음향 감쇠가 발생합니다. 열 입력이 임계 임계값 이상으로 증가하면 음향 싱크가 불충분해져서 ​​내부 에너지 축적으로 인해 빠른 음향 증폭이 발생합니다.

In this paper, results proceeding from experimental studies and computational simulations of the time-dependent flowfield inside a Rijke tube are presented and interpreted. A theoretical discussion based on existing speculations and scaling analyses is carried out. The main results include a similarity parameter that appears to play an important role in the heat driven oscillations. This parameter relates heat perturbations to velocity, pressure, and the square of a characteristic length. A simple theory that attributes heat oscillations to the combined effects of pressure and velocity oscillations is discussed via computational, experimental, and scaling considerations. Since previous analytical theories link heat oscillations to either velocity or pressure oscillations, the current analytical model agrees with and reconciles between existing speculations. In compliance with the Rayleigh criterion, it is found that the heat source must be positioned at a critical distance of 1/4 from the Rijke-tube lower end for resonance to occur. This observation confirms our proposed interpretation since the critical point where coupling is maximized corresponds to a spatial location where the acoustic intensity, product of both acoustic velocities and pressures, is largest. Numerical simulations show that pressure oscillations inside the Rijke tube grow exponentially with increasing heat input With a sufficiently small heat input, the acoustic sinks exceed the sources and acoustic damping takes place. When the heat input is augmented beyond a critical threshold, acoustic sinks become insufficient causing rapid acoustic amplification by virtue of internal energy accumulation.

Fig. 2 Schematic diagram of the experimental Rijke tube
Fig. 2 Schematic diagram of the experimental Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube
A novel investigation of the thermoacoustic field inside a Rijke tube

References

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Fig. 2. Schematic indication of the separate parts comprising the rotary kiln model, together with the energy fluxes from Eq. (1).

화염 모델링, 열 전달 및 클링커 화학을 포함한 시멘트 가마에 대한 CFD 예측

E Mastorakos Massias 1C.D Tsakiroglou D.A Goussis V.N Burganos A.C Payatakes 2

Abstract

실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 방사선에 대한 Monte Carlo 방법, 가마 벽의 에너지 방정식에 대한 유한 체적 코드 및 클링커에 대한 화학 반응을 포함한 에너지 보존 방정식 및 종에 대한 새로운 코드. 기상의 온도 장, 벽으로의 복사 열유속, 가마 및 클링커 온도에 대한 예측 간의 반복적인 절차는 내부 벽 온도의 분포를 명시적으로 예측하는 데 사용됩니다. 여기에는 열 흐름 계산이 포함됩니다. 수갑. 가스와 가마 벽 사이의 주요 열 전달 모드는 복사에 의한 것이며 내화물을 통해 환경으로 손실되는 열은 입력 열의 약 10%이고 추가로 40%는 장입 가열 및 클링커 형성. 예측은 실제 규모의 시멘트 가마에서 경험과 제한된 측정을 기반으로 한 경향과 일치합니다.

키워드

산업용 CFD, 로타리 가마, 클링커 형성, 복사 열전달, Industrial CFD, Rotary kilns, Clinker formation, Radiative heat transfer

1 . 소개

시멘트 산업은 에너지의 주요 소비자이며, 미국에서 산업 사용자의 총 화석 연료 소비량의 약 1.4%를 차지하며 [1] 일반적인 비에너지 사용량은 제조된 클링커 1kg당 약 3.2MJ [2] 입니다. CaCO 3  →  CaO  +  CO 2 반응이 일어나기 때문입니다., 클링커 형성의 첫 번째 단계는 높은 흡열성입니다. 시멘트 가마에서 에너지를 절약하기 위한 현재의 경향은 일반적으로 길이가 약 100m이고 직경이 약 5m인 회전 실린더인 가마를 떠나는 배기 가스로부터 에너지를 보다 효율적으로 회수하는 것과 저열량 연료의 사용에 중점을 둡니다. 값. 2-5초 정도의 화염 체류 시간을 허용하고 2200K의 높은 온도에 도달하는 회전 가마의 특성은 또한 시멘트 가마를 유기 폐기물 및 용제에 대한 상업용 소각로에 대한 경쟁력 있는 대안으로 만듭니다 [3]. 클링커의 형성이 이러한 2차 액체 연료의 사용으로 인한 화염의 변화로부터 어떤 식으로든 영향을 받지 않도록 하고, 대기 중으로 방출되는 오염 물질의 양에 대한 현재 및 미래 제한을 준수할 수 있도록, 화염 구조의 세부 사항과 화염에서 고체 충전물로의 열 전달을 더 잘 이해할 필요가 있습니다.

최근 시멘트 가마 4 , 5 , 6 , 7 에서 유동장 및 석탄 연소의 이론적 모델링복사 열 전달을 포함한 전산 유체 역학(CFD) 코드를 사용하여 달성되었습니다. 이러한 결과는 시멘트 가마에 대한 최초의 결과였으며 화염 길이, 산소 소비 등과 관련하여 실험적으로 관찰된 경향을 재현했기 때문에 그러한 코드가 수용 가능한 정확도로 대규모 산업용 용광로에 사용될 수 있음을 보여주었습니다. 킬른과 클링커는 포함하지 않았고, 벽온도의 경계조건은 가스온도와 용액영역의 열유속에 영향을 미치므로 계산에 필요한 경계조건은 예측하지 않고 실험적 측정에 기초하였다. 기상에 대한 CFD 솔루션은 앞으로의 주요 단계이지만 회전 가마를 포괄적으로 모델링하는 데만으로는 충분하지 않습니다.

내화물의 열 전달과 전하에 대한 세부 사항은 다양한 저자 8 , 9 , 10 , 11에 의해 조사되었습니다 . 충전물(보통 잘 혼합된 것으로 가정)은 노출된 표면에 직접 복사되는 열 외에도 전도에 의해 가마 벽에서 가열됩니다. 가장 완전한 이론적 노력에서, 가마 벽 (내화물)에 대한 3 차원 열전도 방정식을 해결하고, 두 개 또는 세 개의 인접하는 영역으로 한정 한 좌표 축 방향에서 어느 방사선 방사선 열전달 영역 모델과 결합 [ 10] 또는 자세히 해결 [11]. 그러나 클링커 형성 중에 일어나는 화학 반응은 고려되지 않았고 기체 상이 균일한 온도로 고정되어 필요한 수준의 정확도로 처리되지 않았습니다.

최종적으로 연소에 의해 방출되는 에너지(일부)를 받는 고체 전하가 화학 반응을 거쳐 최종 제품인 클링커를 형성합니다. 이것들은 [12]에 설명된 주요 특징에 대한 단순화된 모델과 함께 시멘트 화학 문헌에서 광범위한 조사의 주제였습니다 . 그 작업에서, 고체 온도 및 조성의 축 방향 전개를 설명하는 odes가 공식화되고 해결되었지만, 전하에 대한 열유속 및 따라서 클링커 형성 속도를 결정하는 가스 및 벽 온도는 1차원으로 근사되었습니다. 자세한 화염 계산이 없는 모델.

화염, 벽 및 장입물에 대한 위의 이론적 모델 중 어느 것도 회전식 가마 작동을 위한 진정한 예측 도구로 충분하지 않다는 것이 분명합니다. 국부 가스 온도(CFD 계산 결과 중 하나)는 벽 온도에 크게 의존합니다. 클링커 형성은 에너지를 흡수하므로 지역 가스 및 벽 온도에 따라 달라지며 둘 다 화염에 의존합니다. 벽은 화염에서 클링커로의 순 열 전달에서 “중개자” 역할을 하며, 내화재 두께에 따라 환경으로 피할 수 없는 열 손실이 발생합니다. 이러한 상호 의존성은 가마의 거동에 중요하며 개별 프로세스를 개별적으로 계산하는 데 중점을 두었기 때문에 문헌에서 발견된 수학적 모델로는 다루기 어렵습니다.

본 논문에서 우리는 위에 설명된 유형의 세 가지 개별 모델을 결합하여 수행되는 회전식 시멘트 가마에서 발생하는 대부분의 공정에 대한 포괄적인 모듈식 모델을 제시합니다. 우리 작업은 4 , 5 , 6 , 7 에서와 같이 석탄 연소를 위한 다차원 CFD 코드로 기체 상태를 처리합니다 . 10 , 11 에서와 같이 가마 벽의 3차원 열전도 방정식을 풉니다 . 9 , 12 와 유사한 모델로 잘 혼합된 전하 온도 및 조성을 해결합니다.. 3개의 모듈(화염, 벽, 전하)은 내화물에 입사하는 열유속의 축 분포에 대해 수렴이 달성될 때까지 반복적으로 계산됩니다. 충전 온도 및 구성. 따라서 이전 작업에 비해 현재의 주요 이점은 완전성에 있습니다. 이는 가스-킬른-클링커 시스템의 다양한 부분에서 에너지 흐름의 정량화를 통해 킬른 작동에 대한 더 나은 이해를 가능하게 하고 여기에서 사용된 방법을 건조 및 소각과 같은 다른 회전 킬른 응용 분야에 적용할 수 있게 합니다.

이 문서의 특정 목적은 회전식 시멘트 가마에 대한 포괄적인 모델을 제시하고 화염에서 클링커로의 에너지 플럭스와 가마에서 열 손실을 정량화하는 것입니다. 이 문서의 나머지 부분은 다음과 같이 구성됩니다. 2장 에서는 다양한 모델과 해법을 제시하고 3장 에서는 그 결과를 제시하고 논의한다 . 여기에는 본격적인 회전식 시멘트 가마의 제한된 측정값과의 비교가 포함됩니다. 이 논문은 가장 중요한 결론의 요약으로 끝납니다.

2 . 모델 공식화

2.1 . 개요

Fig. 1 은 시멘트 로터리 킬른의 단면을 보여준다. 가마의 회전은 전하의 움직임을 유도하여 후자를 대략적으로 잘 혼합되도록 합니다 [10] , 여기에서 채택할 가정입니다. 우리는 이 코팅을 클링커와 유사한 물리적 특성의 고체 재료로 모델링하여 가마 내화물에 부착된 클링커의 존재를 허용할 것입니다. 우리는 이 층의 두께가 가마를 따라 균일하다고 가정합니다. 이것은 아마도 지나치게 단순화한 것일 수 있지만 관련 데이터를 사용할 수 없습니다. 모델 설명을 진행하기 전에 그림 2 에 개략적으로 표시된 회전식 가마의 다양한 에너지 흐름을 이해하는 것이 중요합니다 .

석탄 연소에 의해 방출되는 에너지(단위 시간당)( 석탄 )는 배기 가스(Δ 가스 )와 함께 가마 밖으로 흘러 가마 벽에 직접 복사( rad ) 및 대류( conv )됩니다. 공급 및 배기 덕트( rad,1  + rad,2 ) 에 대한 축 방향의 복사에 의해 작은 부분이 손실됩니다 . 전하 가마 시스템은 복사( rad ) 및 대류( conv )에 의해 가스로부터 에너지(Δ cl )를 흡수 하고 주변으로 열을 잃습니다( Q 손실 ). 전체 에너지 균형에서 개별 항의 계산, 즉(1a)큐석탄=ΔH가스-Q라드-Q전환-Q일, 1-Q일, 2,(1b)큐라드+Q전환=ΔH클+Q손실여기에서 다음 섹션에 설명된 대로 가스, 가마 및 클링커에 대한 이산화 에너지를 국부적으로 해결함으로써 수행됩니다.

2.2 . CFD 코드

가스 운동량, 종 농도 및 에너지의 Favre 평균 방정식은 표준 k – ε 모델을 사용하여 방사 모듈(RAD-3D)과 함께 상업적으로 이용 가능한 축대칭 CFD 코드(FLOW-3D)에 의해 해결됩니다. [13] . 기하학이 실제로 3차원이고 벽 온도의 각도 분포가 존재하지만 합리적인 시간과 현재 워크스테이션에서 완전한 3으로 솔루션을 얻을 수 있도록 기체상을 축대칭으로 취급합니다. -D를 요구하는 해상도로 계산하려면 슈퍼컴퓨터에 의존해야 합니다. FLOW-3D에서 사용되는 다양한 하위 모델의 일부 기능과 벽 경계 조건에 대한 특수 처리는 다음과 같습니다.

2.2.1 . 석탄 연소

Rossin-Rammler 크기 분포(45μm 평균 직경, 1.3 지수 [6] )를 따르는 석탄 입자 는 CPU 시간을 줄이기 위해 솔루션 영역(즉, 확률적 구성 요소 없이)에서 결정론적으로 추적되었지만 분산을 과소 평가하는 단점이 있습니다 . 14] . 입자는 2-반응 모델에 따라 휘발되도록 허용되었고 휘발성 연소는 무한히 빠른 것으로 간주되었습니다. 석탄 연소에 대한 설명의 세부 사항은 FLOW-3D에서 석탄 휘발 및 열분해의 “표준” 상수 집합이 합리적인 결과를 제공하고 Ref. [5] .

2.2.2 . 복사와 대류

가스의 복사 강도는 RAD-3D 모듈을 사용하여 80,000개의 입자로 Monte-Carlo 방법으로 계산되었습니다. 가마는 반경 방향으로 7개, 축 방향으로 19개(크기가 0.1  ×  1.0 m와 0.2  ×  5.0 m 사이)로 불균일한 구역으로 나뉘었으며 각 구역 에서 방사선 강도가 균일하다고 가정했습니다. 방사선 모듈의 출력은 내부적으로 FLOW-3D에 대한 유체 계산에 인터페이스되고 외부적으로 벽 및 클링커에 대한 코드에 인터페이스되었습니다( 섹션 2.3 섹션 2.4 참조). 방사선 패키지의 이산화된 구역은 CFD 그리드의 셀보다 훨씬 커야 하므로 구역에 온도 평균이 형성될 수 있는 많은 셀이 포함될 수 있다는 점을 이해하는 것이 중요합니다. 상대적으로 조잡한 복사 구역의 분해능과 Monte-Carlo 방법의 통계적 특성은 구역의 복사 열유속이 더 미세한 구역화 및 더 많은 입자로 몇 번의 실행에 의해 결정된 바와 같이 최대 약 10%까지 부정확할 수 있음을 의미합니다. 또한 경계면에 입사하는 열유속은 영역 크기보다 미세한 분해능으로 결정할 수 없으므로 복사 열유속은 벽에 인접한 19개 영역 각각의 중심에서만 계산됩니다. 0.15m -1 의 흡수 계수는 Ref.[11] . 엄밀히 말하면, 흡수 계수는 국부적 가스 조성과 온도의 함수이므로 균일하지 않아야 합니다. 그러나 가스 조성은 가마의 일부만 차지하는 화염 내에서만 변 하므로( 3절 참조 ) 균일한 흡수 계수를 가정하는 것이 합리적입니다. 또한, 현재 버전의 소프트웨어는 FLOW-3D의 반복 프로세스 동안 이 요소의 자동 재조정을 허용하지 않습니다. 여기서 로컬 가스 특성이 계산되므로 일정하고 균일한 흡수 계수가 필요합니다.

최종적으로, 벽에서 대류 열전달이 플로우 3D 패키지에서 표준 출력 표준 “벽 기능”제형에 혼입 난류 경계층에 대한 식에 기초하고,의 속도 경계 조건과 유사한 K – ε 모델. FLOW-3D 및 RAD-3D에서 입력으로 사용하고 출력으로 계산된 다양한 양은 그림 3에 개략적으로 표시 됩니다.

2.2.3 . 그리드

반경 방향 47개, 축 방향 155개 노드를 갖는 불균일한 격자를 사용하였으며 격자 독립성 연구를 수행한 결과 충분하다고 판단하였다. 유사한 크기의 그리드도 Refs에서 적절한 것으로 밝혀졌습니다. 4 , 5 , 6 , 7 . 매우 높은 축 방향 및 소용돌이 속도로 인해 석탄 버너 유정에 가까운 지역을 해결하기 위해 특별한 주의를 기울였습니다. HP 715/100MHz 워크스테이션에서 이 그리드의 일반적인 CPU 시간은 10시간이었습니다.

2.2.4 . 경계 조건

벽 온도에 대한 경계 조건은 기체상 및 복사 솔버 모두에 필요하다는 것을 인식하는 것이 중요합니다. 아래에서는 4 , 5 , 6 , 7 을 규정하기 보다는 축대칭 그리드에 대한 이 온도 분포를 예측하는 대략적인 방법을 설명합니다 .

내벽 온도 w ( in , x , ϕ ) 의 각도 분포 가 알려져 있다고 가정합니다 . 그런 다음 전체 3차원 문제를 “동등한” 축대칭 문제로 줄이기 위해 가상의 내벽 온도 RAD ( x )는(2)2πε에티4라드(x) = ε클∫0ㄷ티4클(엑스)디ϕ + ε에∫ㄷ2π티4에(아르 자형~에, x, ϕ)디ϕ”효과적인” 경계 조건으로 사용할 수 있습니다. RAD ( x )는 방위각으로 평균화된 “복사 가중” 온도입니다. 필요한 경계 조건으로 이 온도를 사용하는 것은 복사가 열 전달을 지배한다는 기대에 의해 동기가 부여됩니다(후반부 확인, 섹션 3.4 ). 따라서 전체 3차원 문제와 이 “유효한” 축대칭 문제에서 가스에서 가마로의 전체 에너지 흐름은 거의 동일할 것으로 예상됩니다.  의 사용 (2) 축대칭 코드로 기체상 및 복사장을 계산할 수 있으므로 엔지니어링 워크스테이션을 사용하여 문제를 다루기 쉽습니다.

고려되는 가마의 규모와 온도에서 가스는 광학적으로 두꺼운 것으로 간주될 수 있습니다. 솔루션(나중에 제시됨)은 평균 경로 길이(즉, “광자”의 모든 에너지가 흡수되기 전의 평균 길이)가 약 3.2m임을 보여주며, 이는 가마 내경 4.1m보다 작습니다. 이것은 내벽에 입사하는 복사 플럭스가 국부적 벽과 가스 온도에 강하게 의존하고 더 먼 축 또는 방위각 위치에서 벽의 온도에 약하게만 의존함을 의미합니다. 이것은 기체상에 사용된 축대칭 근사에 대한 신뢰를 줍니다. 그것은 또한 Refs의 “구역 방법”을 의미합니다. 8 , 9 , 10표면에 입사하는 방사선이 1-2 구역 길이보다 더 먼 축 위치와 무관한 것으로 간주되는 경우에는 충분했을 것입니다.

2.3 . 가마 온도

내부 소성로 표면 온도 w ( in , x , ϕ )는 Eq. 에서 필요합니다 (2) 및 가마 벽 에너지 방정식의 솔루션 결과의 일부입니다. 각속도 ω로 회전하는 좌표계 에서 후자는 [10] 이 됩니다 .(3)ω∂(ϱ에씨피티에)∂ϕ=1아르 자형∂∂아르 자형에게에아르 자형∂티에∂아르 자형+1아르 자형2∂∂ϕ에게에∂티에∂ϕ+∂∂엑스에게에∂티에∂엑스경계 조건에 따라(3a)r=R~에,Θ<ϕ⩽2π:에게∂티에∂아르 자형=q라드(x)+q전환(엑스),(3b)r=R~에, 0 <ϕ⩽Θ:에게∂티에∂아르 자형=qw–cl(x, ϕ) = hw–cl티클(x)-T에(아르 자형~에, x, ϕ),(3c)r=R밖, 0 <ϕ⩽2π:.케이∂티에∂아르 자형=h쉿티쉿-T∞+ ε쉿티4쉿-T4∞.

전도도, 밀도 및 비열용량에 대한 값은 실제 가마에 사용되는 내화물 재료에 대한 제조업체 정보에서 가져옵니다 [15] . 외부 쉘 온도 sh = w ( out , x , ϕ )는 x 및 ϕ 에 따라 달라질 수 있습니다 .

위 방정식에 대한 몇 가지 의견이 있습니다. 에서는 식. (3a) 에서 열유속의 방위각 의존성이 제거되었습니다. 이전에 언급했듯이 흐름은 광학적으로 두꺼운 것으로 간주됩니다. 즉, 화염이 너무 방사되고 너무 넓기 때문에 벽면 요소가 화염을 가로질러 반대쪽 벽을 “보지” 않습니다. 따라서 rad ( x , ϕ ) 의 계산은 다른 각도 위치로부터의 복사를 포함할 필요 없이 가스 ( r , x ) 및 로컬 w ( in , x , ϕ )를 기반으로 할 수 있습니다. 여기부터 qrad ( x )는 Eq. 의 방위각 평균 온도를 기반으로 하는 축대칭 RAD-3D 솔루션에서 가져옵니다 (2) , 결과적인 rad ( x )는 어떤 의미에서 방위각으로 평균된 열유속입니다. 식 따라서 (3a) 는 우리가 이 열유속을 모든 ϕ 에 등분포한다는 것을 의미합니다 . Eq 에서 rad 의 각도 변화를 무시한다는 점에 유의하십시오 . (3a) 는 Refs. [10] 또는 [11] 이 우선되어야 합니다.

소성로와 장입물 사이의 열전달 계수 w-cl 은 소성로의 에너지 흐름과 온도를 정확하게 예측하는 데 중요하지만 잘 알려져 있지 않습니다. 500 W / m의 전형적인 값  K는 여기에 제시된 결과 사용되고있다 [8] . 계산된 w ( r , x , ϕ ) 및 RAD ( x) 이 계수의 선택에 따라 달라지지만 예측은 질적으로 변하지 않습니다. 껍질에서 대기로의 열 전달은 복사와 별도로 강제 및 자연 대류를 통해 발생합니다. 자연 대류에 대한 열전달 계수는 Ref. [11] , 현재 조건에서 약 5 W/m 2 K의 일반적인 값 을 사용합니다. 그러나 쉘에 불어오는 외부 팬은 과열을 피하기 위해 산업에서 종종 사용되며 이러한 효과는 총 sh =30 W/m 2 K 를 사용하여 여기에서 모델링 되었습니다. 방사율에는 다음 값이 사용되었습니다. ε w = ε cl = 0.9 및 ε sh = 0.8.

식 (3) 은 가마의 방사형 기울기가 훨씬 더 가파르기 때문에 방위각 및 축 전도를 무시한 후 명시적 유한 체적 방법으로 해결되었습니다. 방사형으로 50개 노드와 축 방향으로 19개 노드가 있는 균일하지 않은 그리드가 사용되었으며 회전으로 인한 화염에 주기적으로 노출되는 표면으로 인해 발생하는 빠른 온도 변화를 따르기 위해 내부 표면에서 적절한 방사형 분해능이 사용되었습니다. 동일한 이유로 사용 된 작은 단계(Δ ϕ = π /100)는 가마의 큰 열 관성과 함께 가마 벽 온도가 수렴되도록 하기 위해 2시간 정도의 CPU 시간이 필요했습니다.

2.4 . 수갑

가마에 대한 모델의 마지막 부분은 클링커 온도 및 조성 보존 방정식에 관한 것으로, 축 방향 기울기만 고려하고 전도는 무시합니다.(4)씨피V클디(ϱ클티클)디엑스=−엘wclㄷㅏ클∫0ㄷ큐w–cl(x, ϕ)디ϕ +엘gclㅏ클큐라드(x)+q전환(엑스)−∑나Nsp아르 자형나시간0, 나는에프+씨피티,(5)V클디(ϱ클와이나)디엑스=r나,(6)V클디ϱ클디엑스=−r무엇2,여기서 cl 은 속도 cl 로 흐르는 전하가 덮는 단면적 이며 둘 다 일정하다고 가정하고 gcl =2 in sin( Θ /2) 전하로 덮인 섹터의 현( 그림 1 ) , WCL = Θ 에서는 , SP 화학 종의 수와 r에 난을 (kg / m의 형성 속도 순 3 종의) I를 . 전하의 밀도는 Eq를 감소시킵니다 (6) CO 2 에 대한 질량 손실로 인한하소하는 동안 초기 값은 총 질량 유량이 ϱ cl cl cl 과 같도록 선택되었습니다 . 참고 ρ (CL)이 있다 하지 전하 느슨하게 포장 된 입자로 이루어지는 것으로 생각 될 수있는 바와 같이, 충전 재료 밀도하지만 벌크 밀도. 우리는 또한 전하의 실제 입상 흐름 패턴을 조사하는 것보다 적은 것은 모델의 신뢰성에 크게 추가되지 않는 임시 설명 [10] 이라고 믿기 때문에 전하의 전도를 무시 합니다. 전하는 CaCO 3 , CaO, SiO 2 , Al 2 O 3 , Fe 로 구성된 것으로 가정합니다.2 O 3 , C2S, C3S, C3A 및 C4AF로, 마지막 4종은 클링커화 중에 형성된 복합 염에 대해 시멘트 화학자가 사용하는 특수 표기법으로 표시됩니다. 다음과 같은 화학 반응을 가정합니다 [12] .

(나)CaCO3→높은+무엇2k = 108특급(−175728/RT)
(Ⅱ)높은+2SiO2→C2Sk = 107특급(−240000/RT)
(Ⅲ)높은+C2S→C3Sk = 109특급(−420000/RT)
(IV)3높은+로2그만큼3→C3Ak = 108특급(−310000/RT)
(V)4높은+로2그만큼3+철2그만큼3→Q4AFk = 108특급(−330000/RT)

상기 시행 착오에 의해 선택되는 아 레니 우스 식에 사용되는 사전 지수 인자 및 활성화 온도는 카코에 대한 활성화 에너지를 제외하고, 가마의 출구에서의 전하의 예상 조성물을 얻었다 (3) 에서 촬영 한 분해 참조 [16] . 우리는 이러한 반응이 임시 모델임을 강조합니다. 실제로 고체상의 화학반응은 다양한 종의 결정들 사이의 계면에서 일어나며 확산이 제한적 이지만 [17] , 클링커 화학에 대한 상세한 처리는 본 연구의 범위를 벗어난다.

클링커 형성의 마지막 단계로 간주되는 반응 (III)은 고온에서 액상이 존재할 때만 발생합니다. 클링커의 용융은 액체 분획 fus 에 대해서도 해결함으로써 모델링되었습니다 .(7)엘소란V클디(ϱ클와이소란)디엑스=RHS의식(4)만약 T의 CL이 융해 온도와 같거나보다 커진다 T의 FUS 와 T의 FUS 의 = 1560 K. 상한 Y의 FUS = 0.3 수행 하였다 [17] 상기 식을. (7) 무시되었다.

상미분 방정식, , Gear 방식과 통합되었습니다. 가마 온도에 대한 유한 체적 코드( 2.3절 )와 클링커에 대한 코드는 반복적으로 해결되었으며( 그림 4 ), 이는 벽 클링커 열유속 w–cl ( x , ϕ ).

2.5 . 최종 커플링

전체 문제(가스, 가마, 장입)는 반복 방식으로 해결되었습니다. RAD 의 균일한 분포에서 시작 하여 기체상은 rad ( x ) 및 conv ( x ) 의 축 분포를 제공하도록 해결되었습니다 . 이것들은 다음에서 사용되었습니다., 그 솔루션의 새로운 추정 결과 RAD ( X 통해) 식. (2) . 그런 다음 FLOW3D-RAD3D 실행이 6차 다항식 피팅의 계수 형태로 프로그램에 도입된 새로운 경계 조건으로 반복되었습니다. 의 연속 추정치 사이에 0.5 미만의 밑에 이완 인자 RAD ( X)는 벽 온도에 대한 복사 열유속의 민감도가 크기 때문에 필요한 것으로 밝혀졌습니다. 일반적으로 HP 715 워크스테이션에서 10일 정도의 총 CPU 시간에 해당하는 내벽 온도(연속 반복이 40K 이상 변하지 않을 때 정의됨)의 수렴을 달성하기 위해 이러한 단계 사이에 약 10번의 반복이 필요했습니다. . 그림 5 는 균일한 값(1600K)에서 시작하여 최종 프로파일까지 RAD ( x ) 의 수렴 이력을 보여줍니다 .

2.6 . 가마 조건

사용된 일부 매개변수에 대한 작동 조건 및 값은 표 1 표 2 표 3에 나와 있습니다. 이 값은 시멘트 회전 가마의 전형입니다.

표 1 . 공기 및 석탄 입자 입구 조건

수송소용돌이중고등 학년석탄
m (kg/s)2.2531.7592.91045.9304.0
 (m/s)77.136.576.112.7336.5
V (m/s)−20.7063.900
W (m/s)00112.800
 (케이)3183833181273383

표 2 . 클링커 조성(질량 분율)

밀가루가마 입구가마 출구
m (kg/s)50.37439.81532.775
 (케이)11001785
CACO 30.79470.402180
높은00.338010.0229
그런가 20.14340.181430
알 2 O 30.03490.04420
철 2 O 30.02700.034160
C2S000.1808
C3S000.5981
C3A000.0731
Q4AF000.1242
소성 인자00.61.0

소성 계수 카코의 비율을 3 의 CaO로 변환 된 FARINE있다.

표 3 . 재료 속성 및 기타 매개변수

ω (래드/초)0.5
V의 CL (m / s)0.035
 (K)300
sh (W/m 2 K)30
w–cl (W/m 2 K)500
ε w , ε cl0.9
ε 0.8
C의 P (클링커) (킬로 / kg K)1.5
ϱ cl (kg/m 3 )1200
fus (kJ/kg)418.4
p (벽) (kJ/kg K)1.5
ϱ w (kg/m 3 )1600–3000
k는 w (W / m K)0.6–3.0
석탄 열 방출(kJ/kg)25475

3 . 결과 및 토론

이 섹션에서는 먼저 화염 구조에 대한 정보와 함께 예측된 공기역학적 패턴의 세부사항을 제시합니다. 소성로 내화물의 온도 분포와 클링커 조성의 변화를 설명합니다. 이 섹션은 가마의 전체 에너지 균형과 가능한 모델 개선에 대한 논의로 끝납니다.

3.1 . 화염 구조

그림 6 은 명확성을 위해 방사상 좌표가 과장된 온도의 등고선 플롯을 보여줍니다. 석탄은 주입 지점에서 약 1m 지점에서 약간 축에서 벗어나 점화되며 최대 화염 온도(약 2400K)는 경험에 따라 약 40m 하류에서 도달합니다 [15] . 완전한 입자 소진에 대한 가장 긴 시간은 버너에서 45m에 해당하는 약 1.4초였습니다. 방사형 온도 프로파일( 그림 7 ) 은 온도의 상당한 불균일성이 있음을 보여주지만 출구 프로파일이 본질적으로 평평해짐에 따라 하류에서 감소합니다. 또한 벽에 인접한 가스가 더 차가운 열 경계층이 존재한다는 것이 분명합니다.석탄 노즐에서 최대 30m까지 벽보다 이것은 이 영역에서 대류에 의한 열 전달이 음(즉, 기체 쪽으로)임을 의미하며, 3.4절 에서 더 자세히 논의된 지점 입니다.

버너 출구 바로 하류에 길이가 약 1 버너 직경인 재순환 구역이 있는데( 그림 8 ), 여기에서 화염이 더 하류에서 발화하기 때문에 소용돌이 안정화 화염 [7] 에서와 같이 화염 안정화에 기여하지 않습니다 . 그러나 액체 연료를 사용할 때는 중요할 수 있으므로 버너에 가까운 그리드의 세부 사항을 강조해야 합니다. 버너에서 처음 몇 미터는 매우 높은 전단력과 높은 난류 에너지 생산을 포함하며 이것이 그리드 미세 조정을 강조하는 또 다른 이유입니다. 휘발성 물질 연소 영역( x =10m, r =1m) 에서 k 및 ε 의 일반적인 예측 값 은 24.3 및 142m 2 /s입니다.3 , 각각. 대규모 난류 시간은 171ms이고 Kolmogorov 시간 규모는 1.1ms입니다. 휘발성 물질의 연소는 0.1ms(일반적인 탄화수소 연료) 정도의 시간 규모에서 발생하며, 이는 가마의 소규모 난류 시간보다 10배 더 짧습니다. 따라서 이 흐름에서 연소에 대한 유한 속도 동역학을 포함할 필요는 없으며 “혼합 연소” 근사가 합리적입니다.

3.2 . 가마 온도 분포

중심선에서 계산된 가스 온도, 온도 RAD ( x ) 및 클링커 온도는 그림 9 에서 비교됩니다 . 최고 가스 온도는 25~40m 사이에 위치하며 내화 내부 표면 온도도 최고점입니다. 클링커는 놀랍게도 가마에서 나오기 전 마지막 몇 미터 동안 벽보다 뜨겁 습니다. 복사에 의해 내화물에 입사하는 열유속은 대류에 의한 것보다 1-2 배 더 높으며( 그림 10 ) 가마의 처음 10m에 대한 총 열 전달 은 가스를  합니다. 이 관찰의 중요성은 나중에 논의됩니다.

대류로 인한 에너지 플럭스는 화염에서 가마까지의 전체 에너지 플럭스의 매우 작은 부분인 것으로 밝혀졌습니다( 그림 10 ). 여기서 예측된 대류의 작은 기여는 Ref. [11] . 그 작업에서 대류 열 전달 계산에 사용된 가스 온도는 가마 단면의 평균이었고 따라서 축 근처에 있는 화염의 기여로 인해 벽 부근의 온도보다 훨씬 높았습니다. . 여기에서 우리는 온도와 가스 속도 및 난류 운동 에너지의 국부적 값을 기반으로 하는 보다 정확한 열전달 계수를 사용했기 때문에 보다 정확한 결과를 기대합니다.

예측된 벽 온도는 모든 방향에서 불균일합니다. Fig. 11 은 가마가 회전함에 따라 화염에 노출되었을 때 벽이 가스에 의해 연속적으로 가열되고 클링커에 열을 공급하여 냉각되는 것을 보여준다. 이것은 약 100K의 일반적인 각도 온도 변화를 갖는 대부분의 가마 길이에 해당됩니다. 대조적으로 버너에 가까우면 벽 은 (0 < ϕ < π /2) 동안 클링커에서 열을 얻고 다음으로 열을  습니다. 노출될 때의 가스( π /2 < ϕ < 2 π ). 벽과 클링커 온도가 같으면서 방위각 변화가 없는 경우가 발생할 수 있습니다( 그림 11 ,        x = 17.5m). 이 온도 변화가 작은 것으로 간주될 수 있지만 벽에서 클링커까지의 열유속을 계산하는 위치에 있으려면 전체 3차원 내벽 온도 분포를 계산해야 합니다(0  < ϕ 범위에서 발생 < π /2).   

그림 12 는 ϕ에 독립적인 외부(쉘) 온도와 함께 고체의 큰 비열로 인해 각도 방향의 변화 영역이 벽으로 약 1cm만 확장됨을 보여줍니다( 그림 12b) .. 벽 온도 방사 분포는 가스 온도, 입사 방사선 및 내화 재료의 특성이 변하기 때문에 축 방향 거리에 따라 달라집니다. 정확한 예측을 위해서는 내화물에 부착된 클링커 코팅의 두께에 대한 정확한 지식이 필요합니다. 여기에서 우리는 이 코팅을 클링커와 유사한 물성을 가진 균일한 두께의 재료로 취급했습니다. 그러나 이 코팅층의 실제 물리적 특성과 두께 분포에 관한 실험 데이터를 사용하여 예측의 신뢰성이 향상될 것입니다.

마지막으로, 그림 13 은 외부 쉘 온도가 화염 영역에서 최고조에 달하고 대략적으로 실험 경향을 따른다는 것을 보여줍니다 [15] . 외부 가마 외피는 다양한 강철 두께, 방사율(외피 착색으로 인한) 및 열 전달 계수(송풍기 간격으로 인한)를 갖고 가마는 가변 내화 두께(에 의한 침식으로 인해)를 갖기 때문에 정확한 비교는 의미가 없습니다. 클링커), 여기에 사용된 가정과 반대입니다. 전체 규모 가마는 또한 차등 코팅 및 내화 침식으로 인한 최대 ±100K의 쉘 온도 각도 변동을 보여줍니다 [15] . 따라서 우리는 그림 13 의 일치 가 실제 가마의 복잡성을 고려할 때 예상할 수 있는 만큼 우수 하다고 믿습니다 .

이 섹션에 제시된 예측은 가마 내부의 열 전달 경로에 대한 다음 그림을 뒷받침합니다. 대부분의 가마 길이에서 장입물은 화염으로부터의 복사와 벽으로부터의 열 전도에 의해 가열되고 있습니다. 장입물이 내화물보다 더 차갑기 때문입니다. 가마가 회전함에 따라 내화물은 화염에 노출될 때 열을 얻고 이를 클링커에 공급합니다( 그림 11 ). 벽의 이 “재생” 작용은 Refs. 9 , 10 및 현재 결과에서 재현되었습니다. 그러나 버너 근처에서 반대 에너지 흐름이 발생합니다( 그림 11 , 작은 x). 여기의 가스는 아직 충분히 뜨겁지 않아 내화물이나 장입물에 에너지를 공급하지 않습니다. 이 영역에서 벽은 다가오는 전하에 의해 열을 얻으므로 고체가 없을 때보다 더 뜨겁게 유지됩니다. 벽과 전하가 대류와 복사에 의해 가스에 열을 공급합니다. 우리는 이것을 “음의 재생” 작용으로 식별할 수 있으며 가마의 더 높은 온도 영역( x  >  15m) 에서 클링커에 의해 흡수된 에너지에 의해 유지됩니다 . 전반적으로 클링커는 x  >  15 m 에서 열을 흡수 하고 0  < x < 15 m 에서 일부를 가스로 되돌려 줍니다.   

이 상호 작용은 간단하지 않으며 쉽게 예상할 수 없습니다. 이는 예를 들어 고체를 액체 연료로 대체하여 화염을 수정하면 열유속 분포를 변경하여 최종 클링커 온도에 중대한 영향을 미칠 수 있음을 의미합니다. 현재의 포괄적인 모델이 제공하는 세부 사항은 가마에서 이러한 변화를 평가하는 데 도움이 될 것입니다.

3.3 . 클링커 온도 및 조성

클링커 온도( 그림 9 )는 가장 높은 화염 온도에 도달하는 축 방향 위치에서 거의 최고조에 달하며 클링커는 약 1780K에서 킬른에 존재하며 이는 시멘트 킬른에서 실험 측정값에 가까운 값입니다 [15] . 초기 및 최종 클링커 조성은 표 2 에 나와 있으며 실제 가마에서 작동 값에 가깝습니다 [15] . 다양한 클링커 성분의 축방향 분포( 그림 14 )는 완전한 하소를 위해 고체 유입구에서 약 25m, C2S, C3A 및 C4AF 생성을 위해 추가로 10m가 소요됨을 보여줍니다. 첫 번째 액체상은 x 에서 발견됩니다.=50m이고 액화는 경험과 일치하는 예측인 매우 직후에 완료됩니다 [17] . 클링커화 반응(R-III)은 모델에서 액체가 나타날 때 시작되는 것으로 가정되었으며, 그림 14 에서 클링커화에는 나머지 길이의 거의 전체가 완료되어야 한다는 것이 분명 합니다. 예측은 전체적으로 시멘트 가마 운영의 경험과 일치하며 여기에 사용된 화학적 및 물리적 매개변수가 현실적인 값을 가지고 있음을 의미합니다.

3.4 . 글로벌 에너지 균형

전지구적 에너지 균형은 기체상(FLOW-3D 및 RAD-3D에 의한)과 소성로 장입 시스템에 대한 솔루션에서 쉽게 계산할 수 있으며 표 4 에 나와 있습니다. CFD 코드는 방사 모듈과 함께 에너지를 약 2%까지 절약합니다. 작은 것으로 간주되는 이 오류는 주로 RAD-3D의 영역 이산화와 Monte-Carlo 계산의 유한한 입자 수로 인해 발생하는 오류에 기인하며 CPU 시간을 희생하여 개선할 수 있습니다. 소성로-클링커 계산의 정확도는 더 나쁩니다. 소성로-클링커 시스템에 입력되는 에너지의 약 10% 오류( rad  + conv )입니다. 이는 수렴된 솔루션이 식 (3) , 그리고 보다 정확한 암시적 솔버에 의해 개선될 수 있습니다.

표 4 . CFD 그리드 및 가마-클링커 조합에 대한 글로벌 에너지 균형

가스(MW)
라드 , 1−2.47
라드 , 2−2.72
큐 라드−57.12
전환0.04
석탄101.2
Δ 가스41.25
균형2.32
가마 클링커
큐 라드57.12
전환−0.04
손실−10.45
Δ H의 CL40.99
균형5.64

에너지 흐름의 정의는 그림 2 를 참조하십시오 .

시멘트 회전식 가마의 에너지 사용에 관한 몇 가지 흥미로운 결론은 표 4 의 결과를 통해 얻을 수 있습니다 . 연소에 의해 방출되는 에너지의 약 40%는 전하 가열 및 클링커 형성에 필요하고 약 10%는 내화물을 통해 대기로 손실됩니다. 나머지의 대부분은 본질적으로 배기 가스와 함께 소성로 밖으로 흐릅니다. 이 중 일부는 소성로 외부의 예비 하소기 및 사이클론에서 회수됩니다. 내부 가마 벽과 장입 온도를 자세히 다루는 여기에 제시된 포괄적인 모델에 의존하지 않고는 국지적 가스 온도를 정확하게 예측하고 이에 따라 향후 연구에서 오염 물질 형성을 예측하는 것이 불가능하다는 것이 분명합니다.

3.5 . 논의

여기에 제시된 회전식 시멘트 가마 작동에 대한 포괄적인 모델의 결과는 합리적이며 실험적으로 관찰된 경향을 재현합니다. 이전 모델링 작업에 비해 이 작업의 주요 이점은 가마에서 발생하는 대부분의 물리적 프로세스를 포함한다는 점입니다. 특히, 가스 온도와 클링커로의 열유속 및 이에 따른 클링커 형성을 결정하는 데 가장 중요한 양인 내벽 온도는 실험 데이터를 사용하여 규정된 것이 아니라 예측되었습니다. 이 특정 기능은 현재 모델을 진정한 예측형으로 만듭니다.

우리는 전체 3차원 문제를 공기역학에 대한 “동등한” 축대칭 문제로 줄이는 방법을 포함했습니다( 식 (2) ). 이를 통해 현재 워크스테이션에서 솔루션을 얻을 수 있습니다. 모델의 모듈식 특성, 즉 공기역학, 복사, 가마 및 장입에 대한 별도의 코드는 해당 모듈만 수정하면 다른 회전 가마 응용 프로그램(예: 소각 및 건조)에도 사용할 수 있음을 의미합니다. 예를 들어, 고형 폐기물의 소각은 현재 코드로 모델링할 수 있지만 적절한 화학.

실험 데이터와의 상세한 비교는 이용 가능한 측정이 거의 없고 현지 시멘트 회사에서 제공한 경험적 데이터로 제한되어 매우 어렵습니다 [15] . 비교는 앞서 지적한 바와 같이 출구 클링커 조성과 온도가 산업적 경험( 표 2 ) 이내 이고, 배기 가스 조성은 공장 굴뚝에서 측정된 값에 가깝고(“가짜 공기” 희석을 허용한 후), 가마 외피 온도는 측정 범위 내에 있습니다( 그림 13 ). 이 동의는 모델이 프로세스의 정확한 표현임을 시사합니다.

더 높은 정확도의 예측을 달성하려면 모델의 다양한 부분에서 개선이 필요합니다. 내화물의 정확한 두께(즉, 내화물과 부착된 클링커)를 설정해야 합니다. 이는 가마 벽을 통해 주변으로 열 손실이 발생하여 외부 쉘 온도에 영향을 미치기 때문입니다. 새 내화물이 있는 가마에서 쉘 온도 측정과 자세한 비교가 이루어져야 합니다(불균일한 코팅 두께가 방지되도록). 벽 재료의 물리적 특성(열용량, 밀도, 전도도)의 적절한 값을 사용해야 합니다. 가장 큰 불확실성은 클링커 코팅의 가정된 특성에 관한 것입니다. 내벽 표면의 방사율과 가스의 흡수 계수를 더 자세히 조사해야 합니다. 가마에 입사하는 복사 열유속에 영향을 미치므로 벽 온도에 영향을 줄 수 있습니다. 클링커의 온도는 사용된 비열 용량에 따라 달라지므로 정확한 평가에 각별한 주의가 필요합니다. 화염의 국지적 온도와 종 구성에 대한 지식은 CFD 코드를 검증하는 데 매우 유용할 것이지만 그러한 적대적인 환경에서 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다. 그러한 적대적인 환경에서의 측정은 분명히 달성하기 매우 어렵습니다. 마지막으로 클링커 화학 및 전하 이동은 개선할 수 있는 영역입니다.

이러한 모든 잠재적 개선과 모델과 관련된 불확실성에도 불구하고 가마의 모든 에너지 경로가 적절한 세부 사항으로 모델링되었기 때문에 전체 동작은 최소한 질적으로 정확합니다. 클링커 출구 구성, 쉘 온도 및 배기 가스 구성과 같은 중요한 양은 허용 가능한 정확도로 예측됩니다. 이 모델은 버너, 연료 유형, 품질 및 수량, 예비 하소 수준( 표 2 ) 또는 고형물 유량 등의 변경과 같은 많은 상황에서 산업계에 매우 유용할 것으로 예상됩니다 . 소성로 운영자는 최종 클링커 구성이 여전히 허용 가능하고 현재의 포괄적인 모델이 이 방향에 도움이 될 수 있는지 확인해야 합니다.

4 . 결론

실제 작동 조건에서 석탄 연소 회전 시멘트 가마의 클링커 형성은 석탄 화염과 가마 사이의 열 교환, 가마와 역류 고체 사이의 열 교환, 고형물을 최종 제품(클링커)으로 변환합니다. 방사선에 대한 Monte-Carlo 방법을 포함하는 축대칭 CFD 코드(상용 패키지 FLOW-3D)가 기상에 사용되었습니다. 가마 벽의 온도는 유한 체적 열전도 코드로 계산되었으며 클링커에 대한 종 및 에너지 보존 방정식도 공식화 및 해결되었습니다. 기체 온도 필드에 대한 예측 사이의 반복적인 절차, 벽에 대한 복사 열 유속, 가마 및 클링커 온도는 실험에서 이러한 정보를 사용한 이전 모델링 노력과 달리 내벽 온도 분포를 명시적으로 계산하는 데 사용되었습니다. 접선 좌표에 대한 통합은 CFD 코드에 필요한 경계 조건으로 사용되는 “유효” 내벽 온도의 축 분포를 초래했습니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다. CFD 코드에 필요한 경계 조건으로 사용됩니다. 이 절차를 통해 클링커로의 열 흐름 계산이 가능하고 축대칭 CFD 코드로 3차원 문제를 대략적으로 처리할 수 있습니다.

결과는 복사가 가스와 가마 벽 사이의 대부분의 열 전달을 설명하는 반면 내화물을 통한 환경으로의 열 손실은 입력 열의 약 10%를 설명한다는 것을 보여줍니다. 화학 반응과 충전물의 가열은 연소 에너지의 약 40%를 흡수합니다. 따라서 이러한 사항을 반드시 고려해야 합니다. 예측은 실제 규모의 시멘트 가마에서 얻은 경험과 측정값을 기반으로 한 경향과 일치합니다.

감사의 말

이 작업은 과학 및 기술을 위한 그리스 사무국 프로젝트 EPET-II/649의 자금 지원을 받았습니다. Mr.P에게 진심으로 감사드립니다. 시멘트 가마에 관한 지침 및 데이터는 그리스 TITAN SA의 Panagiotopoulos에게 문의하십시오.

References
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2 Also at Department of Chemical Engineering, University of Patras, Greece.

Fig.(9) Turbulent dissipation for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s

실험적 및 수치적 계단식 배수로의 에너지 소산 연구

The energy dissipation of Stepped Spillways experimentally and numerically

계단식 여수로는 댐의 통합된 부분인 수압 구조로, 넘침 흐름의 안전한 통과를 허용합니다. 이 논문에서는 에너지 소산을 최대한 활용하기 위해 여수로의 상대적인 계단 높이가 다른 영향을 조사하기 위해 실험적 및 수치적 연구를 수행했습니다.

여수로 위의 흐름 모델링은 RANS(Reynolds Averaged Navier-Stokes) 방정식을 푸는 상용 3D CFD 모델인 FLOW-3D를 사용하여 수행되었습니다.

FLOW-3D는 에너지 소산율을 분석하고 얻기 위해 사용되었습니다. 최대 에너지 소산을 달성할 수 있는 계단의 최상의 기하학은 관련 문헌을 검토하고 FLOW-3D에서 제안된 모델을 발명하여 결정되었습니다.

결과는 배수로의 상대적 계단 높이(hs/H) = 0.25. FLOW-3D를 사용한 수치모델은 다양한 실험모델에 대한 측정 데이터와 잘 일치하는 것으로 나타났습니다.

A. ShawkyAwada ,T. Hemdan Nasr-Allah a , Y. Abdallah Mohamed , b G. Mohamed Abdel-Aalb.
a Benah University, Faculty of Engineering, Egypt
b Zagazig University, Faculty of Engineering, Egypt

KEYWORDS

Stepped spillway, FLOW-3D, energy dissipation

Photo (1) general view of laboratory apparatus and flow direction
Photo (1) general view of laboratory apparatus and flow direction
Photo (2) stepped spillways for (hs/H) =0.17,0.25
Photo (2) stepped spillways for (hs/H) =0.17,0.25
Fig.(6) Pressure contours for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s Fig.(7) Velocity magnitude for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s
Fig.(6) Pressure contours for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s Fig.(7) Velocity magnitude for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s
Fig.(8) Flow depth for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s
Fig.(8) Flow depth for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s
Fig.(9) Turbulent dissipation for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s
Fig.(9) Turbulent dissipation for (hs/H)= 0.5, 0.33, 0.25, 0.17and 0.11) for Q = 40 l/s

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Mesh conditions: a) mesh block; b) computational cells c) boundary conditions applied in simulation

FLOW-3D를 이용한 Λ자 단차가 있는 계단식 배수로의 에너지 소산 조건 연구

A Study of the Conditions of Energy Dissipation in Stepped Spillways with Λ-shaped step Using FLOW-3D

Authors:

Abbas Mansoori at Islamic Azad University

Abbas Mansoori

Shadi Erfanian

Abstract and Figures

본 연구에서는 특정 유형의 계단식 배수로에서 에너지 소산을 조사했습니다. 목적은 여수로 하류에서 최고 수준의 에너지 소산을 달성하는 것이었습니다.

큰 러프니스로 계단에 대한 특정 유형의 기하학을 제공하여 수행되었습니다. 여기에서 계단은 흐름에 대한 큰 거칠기로 인식되었습니다.

이 단계에서 최대 흐름 에너지가 최소화될 수 있도록 모양과 수를 설계했습니다. 따라서 하류의 구조에서 가장 높은 에너지 소산률을 얻을 수 있다고 말할 수 있습니다. 또한, 이에 따라 프로젝트에서 저유조를 설계하고 건설함으로써 부과되는 막대한 비용을 최소화할 수 있었습니다.

이 연구에서는 FLOW-3D를 사용하여 에너지 소산율을 분석하고 구했습니다. 최대 에너지 소산을 달성할 수 있는 계단의 최상의 기하학은 관련 문헌을 검토하고 FLOW-3D에서 제안된 모델을 발명하여 결정되었습니다.

제안된 방법을 평가하기 위해 앞서 언급한 방법들과 함께 시행착오를 통해 메쉬망 크기를 분석하고 그 결과를 다른 연구들과 비교하였습니다. 즉, 스무드 스텝에 비해 에너지 소산율이 25도 각도에서 Λ자 스텝으로 가장 최적의 상태를 얻었습니다.

In the present study, energy dissipation was investigated in a specific type of stepped spillways. The purpose was to achieve the highest level of energy dissipation in downstream of the spillway. It was performed by providing a specific type of geometry for step as a great roughness. Here, steps were recognized as great roughness against flow. Their shape and number were designed in such a way that the maximum flow energy can be minimized in this stage, i.e. over steps before reaching to downstream. Accordingly, it can be stated that the highest energy dissipation rate will be obtained in the structure at downstream. Moreover, thereby, heavy costs imposed by designing and constructing stilling basin on project can be minimized. In this study, FLOW-3D was employed to analyse and obtain energy dissipation rate. The best geometry of the steps, through which the maximum energy dissipation can be achieved, was determined by reviewing related literature and inventing the proposed model in FLOW-3D. To evaluate the proposed method, analyses were performed using trial and error in mesh networks sizes as well as the mentioned methods and the results were compared to other studies. In other words, the most optimal state was obtained with Λ-shaped step at angel of 25 degree with respect to energy dissipation rate compare to smooth step.

Figure 2. Three-dimensional design of the spillway using SolidWorks 2012
Figure 2. Three-dimensional design of the spillway using SolidWorks 2012
The results obtained from energy dissipation computation
Geometrical characteristics of the í µíº²-shaped stepped spillway To investigate flow filed and hydraulic conditions, boundary and initial conditions should be applied to each of the models in FLOW-3D. 
Mesh conditions: a) mesh block; b) computational cells; c) boundary conditions applied in simulation 
Figure 6. a) 3D Numerical modelling of flow over Spillway; b) 3D experimental modelling of flow over Spillway (with the discharge of  )
Figure 6. a) 3D Numerical modelling of flow over Spillway; b) 3D experimental modelling of flow over Spillway (with the discharge of  )
Figure 7. 2D model of flow depth for each angle of the-shaped steps
Figure 7. 2D model of flow depth for each angle of the-shaped steps

References

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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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여수로 방류에 따른 여수로 바닥 슬래브의 손상 메커니즘 검토

여수로 방류에 따른 여수로 바닥 슬래브의 손상 메커니즘 검토

Examinations of Damage Mechanism on the Chuteway Slabs of Spillway under Various Flow Conditions

  • Yoo, Hyung Ju ;
  • Shin, Dong-Hoon ;
  • Lee, Seung Oh
  • 유형주 (홍익대학교 공과대학 건설환경공학과) ;
  • 신동훈 (K-water연구원 물인프라안전연구소) ;
  • 이승오 (홍익대학교 공과대학 건설환경공학과)
  • Published : 2021.06.03

Abstract

최근 기후변화로 인한 집중호우의 영향으로 홍수 시 댐으로의 유입량이 설계 당시보다 증가하여 댐의 안전성 확보가 필요하다(감사원, 2003). 이에 건설교통부(2003)는 기후변화와 댐 노후화에 대비하여 치수능력증대사업을 추진하여 댐의 홍수배제능력을 확보하였고, 환경부(2020)에서는 40년 이상 경과된 댐을 대상으로 스마트 안전관리체계 구축을 통한 선제적 보수보강, 성능개선 및 자산관리로 댐의 장수명화를 목적으로 댐의 국가안전대진단을 추진하고 있다. 이에 본 연구에서는 댐 시설(여수로)의 노후도 평가 시 활용 될 수 있는 여수로 표면손상 원인규명에 대하여 3차원 수치모형(FLOW-3D 및 COMSOL Multiphysics)을 통해 검토하고자 한다. 연구대상 댐은 𐩒𐩒댐으로 지형 및 여수로를 구축하였으며, 계획방류량(200년 빈도) 및 최대방류량(PMF) 조건에서 모의를 수행하였다. 수치모의 계산의 정확도 검토를 위하여 Baffle의 설치를 통하여 시간에 따른 유량의 변화를 설계 값과 비교하였고 오차가 1.0% 이내를 만족하는 것을 확인하였다. 여수로 표면손상의 다양한 원인 중 기존연구(USBR, 2019)를 통하여 공동침식(Cavitation Erosion) 및 수력잭킹(Hydraulic Jacking)에 초점을 두었으며 방류조건 별 공동지수(Cavitation Index)산정을 통하여 공동침식 위험 구간을 확인하였다. 이음부의 균열 및 공동으로 인한 표층부 콘크리트의 탈락현상을 가속화시키는 수력잭킹 검토를 위하여 국부모형을 구축하였고 음압력(Negative Pressure), 정체압력(Stagnation Pressure), 양압력(Uplift Pressure)의 분포를 확인하였다. 최종적으로 COMSOL Multiphysics를 통하여 압력분포에 따른 구조해석을 수행하여 폰 미세스(Von Mises) 등가응력 및 변위를 검토하여 콘크리트의 탈락가능성을 확인하였다. 본 연구는 여수로 공동부 및 균열부에서의 손상메커니즘을 확인할 수 있는 기초적인 연구이지만 향후에는 다양한 지형조건 및 흐름조건에서의 압력분포 분석 및 유체-구조물 상호작용(Fluid-Structure Interaction, FSI)모의를 수행한다면 구조물 노후도 및 잔존수명 평가에 필요한 손상한계함수 도출이 가능할 것으로 기대된다.

Keywords

Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

지속 가능한 해안 보호 구조로서 굴절식 콘크리트 블록 매트리스의 손상 메커니즘의 수치적 모델링

Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure

Author

Ramin Safari Ghaleh(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Omid Aminoroayaie Yamini(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

S. Hooman Mousavi(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Mohammad Reza Kavianpour(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Abstract

해안선 보호는 전 세계적인 우선 순위로 남아 있습니다. 일반적으로 해안 지역은 석회암과 같은 단단하고 비자연적이며 지속 불가능한 재료로 보호됩니다. 시공 속도와 환경 친화성을 높이고 개별 콘크리트 블록 및 보강재의 중량을 줄이기 위해 콘크리트 블록을 ACB 매트(Articulated Concrete Block Mattress)로 설계 및 구현할 수 있습니다. 이 구조물은 필수적인 부분으로 작용하며 방파제 또는 해안선 보호의 둑으로 사용할 수 있습니다. 물리적 모델은 해안 구조물의 현상을 추정하고 조사하는 핵심 도구 중 하나입니다. 그러나 한계와 장애물이 있습니다. 결과적으로, 본 연구에서는 이러한 구조물에 대한 파도의 수치 모델링을 활용하여 방파제에서의 파도 전파를 시뮬레이션하고, VOF가 있는 Flow-3D 소프트웨어를 통해 ACB Mat의 불안정성에 영향을 미치는 요인으로는 파괴파동, 옹벽의 흔들림, 파손으로 인한 인양력으로 인한 장갑의 변위 등이 있다. 본 연구의 가장 중요한 목적은 수치 Flow-3D 모델이 연안 호안의 유체역학적 매개변수를 모사하는 능력을 조사하는 것입니다. 콘크리트 블록 장갑에 대한 파동의 상승 값은 파단 매개변수( 0.5 < ξ m – 1 , 0 < 3.3 )가 증가할 때까지(R u 2 % H m 0 = 1.6) ) 최대값에 도달합니다. 따라서 차단파라미터를 증가시키고 파괴파(ξ m − 1 , 0 > 3.3 ) 유형을 붕괴파/해일파로 변경함으로써 콘크리트 블록 호안의 상대파 상승 변화 경향이 점차 증가합니다. 파동(0.5 < ξ m − 1 , 0 < 3.3 )의 경우 차단기 지수(표면 유사성 매개변수)를 높이면 상대파 런다운의 낮은 값이 크게 감소합니다. 또한, 천이영역에서는 파단파동이 쇄도파에서 붕괴/서징으로의 변화( 3.3 < ξ m – 1 , 0 < 5.0 )에서 상대적 런다운 과정이 더 적은 강도로 발생합니다.

Shoreline protection remains a global priority. Typically, coastal areas are protected by armoring them with hard, non-native, and non-sustainable materials such as limestone. To increase the execution speed and environmental friendliness and reduce the weight of individual concrete blocks and reinforcements, concrete blocks can be designed and implemented as Articulated Concrete Block Mattress (ACB Mat). These structures act as an integral part and can be used as a revetment on the breakwater body or shoreline protection. Physical models are one of the key tools for estimating and investigating the phenomena in coastal structures. However, it does have limitations and obstacles; consequently, in this study, numerical modeling of waves on these structures has been utilized to simulate wave propagation on the breakwater, via Flow-3D software with VOF. Among the factors affecting the instability of ACB Mat are breaking waves as well as the shaking of the revetment and the displacement of the armor due to the uplift force resulting from the failure. The most important purpose of the present study is to investigate the ability of numerical Flow-3D model to simulate hydrodynamic parameters in coastal revetment. The run-up values of the waves on the concrete block armoring will multiply with increasing break parameter ( 0.5 < ξ m − 1 , 0 < 3.3 ) due to the existence of plunging waves until it ( R u 2 % H m 0 = 1.6 ) reaches maximum. Hence, by increasing the breaker parameter and changing breaking waves ( ξ m − 1 , 0 > 3.3 ) type to collapsing waves/surging waves, the trend of relative wave run-up changes on concrete block revetment increases gradually. By increasing the breaker index (surf similarity parameter) in the case of plunging waves ( 0.5 < ξ m − 1 , 0 < 3.3 ), the low values on the relative wave run-down are greatly reduced. Additionally, in the transition region, the change of breaking waves from plunging waves to collapsing/surging ( 3.3 < ξ m − 1 , 0 < 5.0 ), the relative run-down process occurs with less intensity.

Figure 1.  Armor  geometric  characteristics  and  drawing  three-dimensional  geometry  of  a  breakwater section  in SolidWorks software.
Figure 1. Armor geometric characteristics and drawing three-dimensional geometry of a breakwater section in SolidWorks software.
Figure  5.  Wave  overtopping on  concrete block  mattress in (a)  laboratory  and (b)  numerical  model.
Figure 5. Wave overtopping on concrete block mattress in (a) laboratory and (b) numerical model.
Figure  7.  Mesh  block  for  calibrated  numerical  model  with  686,625  cells  and  utilization  of  FAVOR  tab to assess figure geometry.
Figure 7. Mesh block for calibrated numerical model with 686,625 cells and utilization of FAVOR tab to assess figure geometry.
Figure  10.  How to place different layers  (core, filter,  and revetment)  of the structure on slope.
Figure 10. How to place different layers (core, filter, and revetment) of the structure on slope.

Suggested Citation

Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
Figure  15.  Localized  deformations  on  revetment  due  to  run-down  and  sliding  of  armor  from  body  laboratory  model  (left) and  numerical  modeling (right).
Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

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Figure 1- The experimental model [17]

와류형 우수 저류지의 수치 모델링에 대한 난류 슈미트 수의 영향 조사

Investigation of the Turbulent Schmidt Number Effects On Numerical Modelling Of Vortex-Type Stormwater Retention Ponds

S. M. Yamini1; H. Shamloo2; S. H. Ghafari3
1M.Eng., Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
smyamini@alumni.kntu.ac.ir
2Associate Professor, Dep. of Civil Engineering K.N. Toosi University of Technology, Valiasr St., Tehran, Iran.
hshamloo@kntu.ac.ir
3Ph.D., Dep. of Civil Engineering Univ. of Tehran, Enqelab St., Tehran, Iran. sarvenazghafari@ut.ac.ir

Abstract

정확하고 신뢰할 수 있는 CFD 모델링 결과를 얻는 것은 이러한 시뮬레이션에서 입력의 중요성 때문에 종종 정밀 조사의 대상입니다.

난류 모델링이 RANS(Reynolds-Averaged Navier-Stokes) 방정식을 기반으로 하는 경우 난류 스칼라 전송을 추정하려면 난류 흐름에서 질량 1에 대한 운동량 확산의 비율로 정의되는 난류 슈미트 수(Sct)의 정의가 필요합니다.

그러나 이 매개변수는 난류 흐름의 속성이므로 보편적인 값이 허용되지 않았습니다. 우수 저류지의 수치 연구에서 적절한 Sct를 설정하는 실제 역할은 수력 효율의 평가가 추적자 테스트의 출력 질량 농도를 기반으로 하기 때문에 가장 중요합니다.

본 연구에서는 FLOW-3D를 사용하여 와류형 우수 저류지의 여러 수치 시뮬레이션을 체계적으로 수행했습니다. 다양한 난류 슈미트 수의 범위는 메쉬 감도를 조사하기 위해 다른 수의 계산 셀에 의해 수행된 수치 시뮬레이션에 도입되었습니다.

또한 사용자 정의 또는 자동 계산 값으로 최대 난류 혼합 길이의 영향을 평가했습니다. 이 연구의 결과는 실험 결과와 밀접한 일치를 제공하는 Sct= 0.625와 함께 수리학적 직경의 7%와 동일한 최대 난류 혼합 길이의 일정한 값을 갖는 확립된 수치 모델입니다.

특히 수치적 무차원 RDT 곡선의 피크 값은 극적으로 감소하여 실험 결과와 거의 일치했습니다. 이것은 FLOW-3D가 난류 유동의 와류형 물리학에서 질량 확산도를 적절하게 예측하는 상당한 능력을 가지고 있다는 결론을 내립니다.

– Achieving accurate and reliable CFD modelling results often is the subject of scrutiny because of the importance of the inputs in those simulations. If turbulence modelling is based on Reynolds-Averaged Navier-Stokes (RANS) equations, estimating the turbulent scalar transport requires the definition of the turbulent Schmidt number (Sct), defined as the ratio of momentum diffusivity to mass one in a turbulent flow. However, no universal value has been accepted for this parameter as it is a property of turbulent flows.

The practical role of establishing a suitable Sct in numerical studies of stormwater retention ponds is of the utmost importance because the assessment of the hydraulic efficiency of them is based on output mass concentration of tracer tests. In this study, several numerical simulations of a vortex-type stormwater retention pond were systematically carried out using FLOW-3D. A range of various turbulent Schmidt numbers were introduced in numerical simulations performed by different number of computational cells to investigate mesh sensitivity.

Moreover, the effects of maximum turbulent mixing length as a user-defined or automatically computed value were assessed. The outcome of this study is an established numerical model with a constant value of maximum turbulent mixing length equal to 7% of the hydraulic diameter along with Sct= 0.625 which provides a close agreement with experimental results.

Noticeably, the peak values of numerical dimensionless RDT curves are dramatically decreased, resulted in a close match with experimental results. This concludes that FLOW-3D has a considerable ability to appropriately predict mass diffusivity in vortex-type physics of turbulent flows.

Keywords:

turbulent Schmidt number – maximum turbulent mixing length – CFD – mesh sensitivity – vortex-type
stormwater retention pond – environmental fluid mechanics

Figure 1- The experimental model [17]
Figure 1- The experimental model [17]
Figure 2- Schematic of boundary conditions in the numerical model
Figure 2- Schematic of boundary conditions in the numerical model
Figure 3- Positioning of mesh blocks
Figure 3- Positioning of mesh blocks

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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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Numerical investigation on effective parameters on hydraulic flows in a sluice gate with sill on free-flow condition

자유 흐름 조건에서 문턱이 있는 수문의 유압 흐름에 대한 유효 매개변수에 대한 수치적 조사

Numerical investigation on effective parameters on hydraulic flows in a sluice gate with sill on free-flow condition

Authors

1 Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran

2 Water Engineering Department, University of Tabriz, Tabriz, Iran

3 M.Sc. Student, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh, Iran

Abstract

The importance of water control and distribution in irrigation and behind dams requires the use of practical and modern methods. The presence of sill under sluice gate is one of the solutions to control the flow rate. Therefore, this study was conducted to numerically investigate the discharge coefficient (Cd) of sluice gate with different heights and widths of sills in free flow conditions. The simulations were performed using FLOW-3D software and finite volume method. The results of numerical study showed that the gate opening has a good effect on the Cd with sill and non-sill condition. In both cases, the gate opening is inversely related to the Cd. This means that the Cd increases as the gate opening decreases. Results showed that reducing the gate opening from 5 cm to 2 cm increases the Cd in the gate with sill by 9% compared to the non-sill gate. The results also indicate that the height of the sill is one of the parameters affecting the Cd. The minimum and maximum discharge coefficients in gate with sill compared to the non-sill condition were estimated at 1.5% and 18%, respectively. Examination of sill width changes showed that decreasing the width reduces the discharge coefficient by reducing the amount of velocity and flow pressure along the sill sides. The effect of three parameters of gate opening, sill height and sill width were compared. The results showed that increasing the sill width compared to the two mentioned parameters has the maximum increase in the Cd

관개 및 댐 뒤에서 물 관리 및 분배의 중요성은 실용적이고 현대적인 방법의 사용을 요구합니다. 수문 아래 문턱의 존재는 유량을 제어하는 ​​솔루션 중 하나입니다. 

따라서 본 연구는 자유유동 조건에서 문턱의 높이와 너비가 다른 수문의 토출계수(Cd)를 수치적으로 조사하기 위해 수행되었습니다. 시뮬레이션은 FLOW-3D 소프트웨어와 유한 체적 방법을 사용하여 수행되었습니다. 

수치 연구의 결과는 게이트 개방이 sill 및 non-sill 조건에서 Cd에 좋은 영향을 미치는 것으로 나타났습니다. 두 경우 모두 게이트 개방은 Cd와 반비례합니다. 이것은 게이트 개방이 감소함에 따라 Cd가 증가한다는 것을 의미합니다. 

결과에 따르면 게이트 개구부를 5cm에서 2cm로 줄이면 비문이 있는 게이트에 비해 씰이 있는 게이트의 Cd가 9% 증가합니다. 결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다. 

문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 

게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 

결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다. 문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 

게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수와 비교하여 문턱 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 

결과는 또한 문턱의 높이가 Cd에 영향을 미치는 매개변수 중 하나임을 나타냅니다. 문턱이 없는 문에 비해 문턱이 있는 문에서 최소 및 최대 배출 계수는 각각 1.5% 및 18%로 추정되었습니다. 

문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 

게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수에 비해 씰 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다. 문턱 너비 변화를 조사하면 너비를 줄이면 문턱 측면을 따라 유속과 흐름 압력의 양이 감소하여 배출 계수가 감소하는 것으로 나타났습니다. 

게이트 개방, 문턱 높이 및 문턱 너비의 세 가지 매개변수의 효과를 비교했습니다. 결과는 언급된 두 매개변수와 비교하여 문턱 너비를 늘리면 Cd가 최대로 증가한다는 것을 보여주었습니다.

Keywords

Figure 4. FLOW-3D model results for the preliminary and optimized layout of the proposed spillway at John Hart Dam.

Spillway Hydraulics Assessments

Spillway Hydraulics Assessments

이 기사는 BC Hydro의 Hydrotechnical부서의 전문 엔지니어인 M.A.Sc., P.Eng의 FaizalYusuf에 의해 기고되었다.

브리티시 콜롬비아의 공공 전력 회사인 BC Hydro는 FLOW-3D를 사용하여 현존하는 여러 댐의 복잡한 유압 문제를 조사하고 제안된 시설의 설계와 최적화를 지원합니다. 본 기사에서는 FLOW-3D를 다양한 유형의 드릴에 적용하는 방법과 신뢰할 수 있는 프로토 타입 또는 수치 모델 보정용 물리적 유압 모델 데이터의 중요성을 강조하는 세가지 사례가 제시됩니다.

W.A.C. Bennett Dam

Shock Waves in Spillway Chute

W.C. Bennett 댐에서는 1960년대 물리적 유압 모델과 프로토 타입 사이에 있었던 레일 궤도의 차이로 인해 충격파 형성에 대한 신뢰할 수 있는 결론을 도출하기 어렵습니다. 이 자료는 실제 모델 테스트 결과의 슈트 용량을 제공합니다. 콘크리트 라인 스풀 레이 슈트의 충격 파장의 크기는 헤드 워크에 있는 세 개의 방사형 게이트의 다운 스트림이 44% 감소되는데 크게 영향을 받습니다. 방사형 관문의 방사형 개구부의 충격파는 지역적으로 더 높은 수위로 이어져 특정 과거 작업에서 슈트 월의 과다 주입을 야기합니다.

2012년에 최대 2,865 m3/s 의 배출에 대한 프로토 타입 유출 테스트가 실행되어 슈트 벽, 슈트 내 물 표면에 대한 3D레이저 스캔 및 FLOW-3D model 보정을 위한 흐름 패턴. 수치 모델과 현장 관찰 간에, 특히 슈트 월의 첫번째 충격파의 위치와 높이 사이에 훌륭한 일치가 이루어졌습니다.

Figure 1. Comparison between prototype observations and FLOW-3D for a spill discharge of 2,865 m^3/s at Bennett Dam spillway
Figure 1. Comparison between prototype observations and FLOW-3D for a spill discharge of 2,865 m^3/s at Bennett Dam spillway

보정된 FLOW-3D모델은 기존에 규정된 바와 같이 3개의 방사형 관문이 모두 열리는 한, 유출되지 않고 설계 홍수를 안전하게 통과할 수 있음을 확인했습니다. 바깥쪽 문을 이용한 허가 명령은 안쪽 문보다 더 많이 열립니다.
CFD모델 또한 spillway 슈트의 콘크리트 손상에 대한 통찰력을 제공했습니다. FLOW-3D시뮬레이션 결과로부터 계산된 공동지수를 USBR의 경험적 데이터와 비교했고, spillway의 과거 성능과 일치하는 것으로 확인되었습니다. 수치 해석을 통해 현장 검사를 지원하였으며, 이를 통해 슈트의 콘크리트 상태의 악화가 캐비테이션 때문이 아니라는 결론을 내렸습니다.

Strathcona Dam

Poor Approach Conditions and Uncertainty of Spillway Rating Curves

FLOW-3D는 댐 우측 교대에 수직 리프트 게이트가 3개 포함된 Strathcona댐 배수로의 등급 곡선과 관련한 열악한 접근 조건 및 불확실성을 조사하는 데 사용되었습니다. Strathcona spillway의 등급 곡선은 경험적인 조정과 교각의 기하학적 구조가 포함되지 않은 flume의 제한적인 물리적 유압 모델 테스트의 조합으로부터 개발되었습니다.
수치 모델 테스트 및 보정은 세개의 게이트가 모두 열려 있었던 1982년부터의 프로토 타입 유출 관측치와 비교하여 이루어진 것입니다. 맨 왼쪽 베이의 streamline입니다. 최좌측 베이로의 흐름은 댐 축에 평행하게 흐르는 물과 지하수 댐의 상류 경사에 인접한 콘크리트 옹벽 위로 곤두박질쳐 왜곡됩니다. 이 흐름은 다른 두 베이로 훨씬 더 부드럽게 들어갑니다. 프로토 타입과 비교하여 수치 모델에서 생성된 매우 유사한 흐름 패턴 외에도, 게이트 섹션에서 시뮬레이션된 수위는 1982년의 현장 측정 값과 0.1m이내에 일치했습니다.

Figure 2. Prototype observations and FLOW-3D results for a Strathcona Dam spill in 1982 with all three gates fully open.
Figure 2. Prototype observations and FLOW-3D results for a Strathcona Dam spill in 1982 with all three gates fully open.