Embankment Dams Overtopping Breach: A Numerical Investigation of Hydraulic Results

Embankment Dams Overtopping Breach: A Numerical Investigation of Hydraulic Results

Mahdi EbrahimiMirali MohammadiSayed Mohammad Hadi Meshkati & Farhad Imanshoar

Abstract

The overtopping breach is the most probable reason of embankment dam failures. Hence, the investigation of the mentioned phenomenon is one of the vital hydraulic issues. This research paper tries to utilize three numerical models, i.e., BREACH, HEC-RAS, and FLOW-3D for modeling the hydraulic outcomes of overtopping breach phenomenon. Furthermore, the outputs have been compared with experimental model results given by authors. The BREACH model presents a desired prediction for the peak flow. The HEC-RAS model has a more realistic performance in terms of the peak flow prediction, its occurrence time (5-s difference with observed status), and maximum flow depth. The variations diagram in the reservoir water level during the breach process has a descending trend. Whereas it initially ascended; and then, it experienced a descending trend in the observed status. The FLOW-3D model computes the flow depth, flow velocity, and Froude number due to the physical model breach. Moreover, it revealed a peak flow damping equals to 5% and 5-s difference in the peak flow occurrence time at 4-m distance from the physical model downstream. In addition, the current research work demonstrates the mentioned numerical models and provides a possible comprehensive perspective for a dam breach scope. They also help to achieve the various hydraulic parameters computations. Besides, they may calculate unmeasured parameters using the experimental data.

월류 현상은 제방 댐 실패의 가장 유력한 원인입니다. 따라서 언급된 현상에 대한 조사는 중요한 수리학적 문제 중 하나입니다.

본 연구 논문에서는 월류 침해 현상의 수리적 결과를 모델링하기 위해 BREACH, HEC-RAS 및 FLOW-3D의 세 가지 수치 모델을 활용하려고 합니다. 또한 출력은 저자가 제공한 실험 모델 결과와 비교되었습니다. BREACH 모델은 최대 유량에 대해 원하는 예측을 제시합니다.

HEC-RAS 모델은 최고유량 예측, 발생시간(관찰상태와 5초 차이), 최대유량수심 측면에서 보다 현실적인 성능을 가지고 있습니다. 위반 과정 중 저수지 수위의 변동 다이어그램은 감소하는 추세를 보입니다. 처음에는 상승했지만 그런 다음 관찰된 상태가 감소하는 추세를 경험했습니다.

FLOW-3D 모델은 물리적 모델 위반으로 인한 흐름 깊이, 흐름 속도 및 Froude 수를 계산합니다. 또한, 실제 모델 하류로부터 4m 거리에서 최대유량 발생시간이 5%, 5초 차이에 해당하는 최대유량 감쇠를 나타냈습니다.

또한, 현재 연구 작업은 언급된 수치 모델을 보여주고 댐 침해 범위에 대한 가능한 포괄적인 관점을 제공합니다. 또한 다양한 유압 매개변수 계산을 수행하는 데 도움이 됩니다. 게다가 실험 데이터를 사용하여 측정되지 않은 매개변수를 계산할 수도 있습니다.

Keywords

DOI

  • https://doi.org/10.1007/s40996-024-01387-9

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Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.

Conducting experimental and numerical studies to analyze theimpact of the base nose shape on flow hydraulics in PKW weirusing FLOW-3D

FLOW-3D를 사용하여 PKW 둑의 흐름 수력학에 대한 베이스 노즈 모양의 영향을 분석하기 위한 실험 및 수치 연구 수행

Behshad Mardasi 1
Rasoul Ilkhanipour Zeynali 2
Majid Heydari 3

Abstract

Weirs are essential structures used to manage excess water flow from behind dams to downstream areas. Enhancing discharge efficiency often involves extending the effective length of Piano Key Weirs (PKW) in dams or regulating flow within irrigation and drainage networks. This study employed both numerical and laboratory investigations to assess the impact of different base nose shapes installed beneath the outlet keys and varying Input to output key width ratios (Wi/Wo) on discharges ranging from 5 to 80 liters per second. Furthermore, the study aimed to achieve research objectives and compare the performance of Piano Key Weirs with Ogee Weir. For numerical simulation, the optimal number of cells for meshing was determined, and an appropriate turbulence model was selected. The results indicated that the numerical model accurately simulated the laboratory sample with a high degree of precision. Moreover, the numerical model closely approximated PKW for all parameters Q, H, and Cd compared to the laboratory sample. The findings revealed that in laboratory models with a maximum discharge area of 80 liters per second, the weir with Wi/Wo=1.2 and a flow head value of 285 mm exhibited the lowest value, whereas the weir with Wi/Wo=0.71 and a flow head value of 305 mm showed the highest, attributed to the higher discharge in the input-output ratio. Additionally, as the ratio of flow head to weir height H/P increased, the discharge coefficient Cd decreased. Comparing the flow conditions in weirs with different base nose shapes, it was observed that the weir with a spindle nose shape (PKW1.2S) outperformed the PKW with a flat (PKW1.2), semi-cylindrical (PKW1.2CL) and triangular base nose (PKW1.2TR). The results emphasized that models featuring semi-cylindrical and flat noses exhibited notable flow deviation and abrupt disruption upon impact with the nose. However, this effect was significantly reduced in models equipped with triangular and spindle-shaped noses. Also, the coefficient of discharge in PKW1.2S and PKW1.2TR weirs, compared to the PKW1.20 weir, increased by 27% and 20%, respectively.

웨어는 댐 뒤에서 하류 지역으로의 과도한 물 흐름을 관리하는 데 사용되는 필수 구조물입니다. 배출 효율을 높이는 데에는 댐의 피아노 키 위어(PKW) 유효 길이를 연장하거나 관개 및 배수 네트워크 내 흐름을 조절하는 것이 포함됩니다.

이 연구에서는 콘센트 키 아래에 설치된 다양한 베이스 노즈 모양과 초당 5~80리터 범위의 배출에 대한 다양한 입력 대 출력 키 너비 비율(Wi/Wo)의 영향을 평가하기 위해 수치 및 실험실 조사를 모두 사용했습니다. 또한 본 연구에서는 연구 목적을 달성하고 Piano Key Weir와 Ogee Weir의 성능을 비교하는 것을 목표로 했습니다.

수치 시뮬레이션을 위해 메시 생성을 위한 최적의 셀 수를 결정하고 적절한 난류 모델을 선택했습니다. 결과는 수치 모델이 높은 정밀도로 실험실 샘플을 정확하게 시뮬레이션했음을 나타냅니다. 더욱이, 수치 모델은 실험실 샘플과 비교하여 모든 매개변수 Q, H 및 Cd에 대해 PKW에 매우 근접했습니다.

연구 결과, 최대 배출 면적이 초당 80리터인 실험실 모델에서는 Wi/Wo=1.2, 플로우 헤드 값이 285mm인 웨어가 가장 낮은 값을 나타냈고, Wi/Wo=0.71 및 a인 웨어는 가장 낮은 값을 나타냈습니다. 플로우 헤드 값은 305mm로 가장 높은 것으로 나타났는데, 이는 입출력 비율의 높은 토출량에 기인합니다. 또한, 웨어 높이에 대한 유수두 비율 H/P가 증가함에 따라 유출계수 Cd는 감소하였다.

베이스 노즈 모양이 다른 웨어의 흐름 조건을 비교해 보면, 스핀들 노즈 모양(PKW1.2S)의 웨어가 평면(PKW1.2), 반원통형(PKW1.2CL) 및 삼각형 모양의 PKW보다 성능이 우수한 것으로 관찰되었습니다. 베이스 노즈(PKW1.2TR) 결과는 반원통형 및 편평한 노즈를 특징으로 하는 모델이 노즈에 충격을 가할 때 눈에 띄는 흐름 편차와 급격한 중단을 나타냄을 강조했습니다.

그러나 삼각형 및 방추형 노즈를 장착한 모델에서는 이러한 효과가 크게 감소했습니다. 또한 PKW1.20보에 비해 PKW1.2S보와 PKW1.2TR보의 유출계수는 각각 27%, 20% 증가하였다.

Keywords

Piano Key Weir, Base Nose Shape, Flow Hydraulics, Numerical Model, Triangular
Nose Shape, Flat Nose Shape, Semi-Cylindrical Nose Shape, Spindle Nose Shape

Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.
Figure (17): Stream Lines Indicating Average Flow Speed in the Model with Various Nose shapes, Measured at Mid-Depth and at the Flow Surface Level, at a Flow Rate of 78 Liters per Second.

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Discharge Coefficient of a Two-Rectangle Compound Weir combined with a Semicircular Gate beneath it under Various Hydraulic and Geometric Conditions

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

ABSTRACT

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

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

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

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

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

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

Keywords

combound weir; semicircular gates; discharge coefficient; combined structure; open channels;
discharge measurement

Fig. 2. The flume and hydraulic bench layout
Fig. 2. The flume and hydraulic bench layout

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Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.

On the hydraulic performance of the inclined drops: the effect of downstreammacro-roughness elements

경사 낙하의 수력학적 성능: 하류 거시 거칠기 요소의 영향

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

ABSTRACT

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

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

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

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

Key words

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

Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.
Figure 1 | Schematic of the present research model with dimensions and macro-roughnesses installed.
Figure 2 | Meshing, boundary condition, and solution field network
Figure 2 | Meshing, boundary condition, and solution field network

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Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Arash Ahmadi a, Amir H. Azimi b

Abstract

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

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

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

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

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

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

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

Introduction

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

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

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

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

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

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

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

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

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

Section snippets

Governing equations

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

Verification of numerical model

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

Conclusions

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

Author contributions

Arash Ahmadi: Software, Validation, Visualization, Writing – original draft. Amir Azimi: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Writing – review & editing

Uncited References

[30]; [31]; [32]; [33].

Declaration of competing interest

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

References (33)

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  • R. BaddourHead-discharge equation for the sharp-crested polynomial weirJ. Irrigat. Drain. Eng.(2008)
  • A.R. VatankhahHead-discharge equation for sharp-crested weir with piecewise-linear sidesJ. Irrigat. Drain. Eng.(2012)
  • A.H. Azimi et al.A note on sharp-crested weirs and weirs of finite crest lengthCan. J. Civ. Eng.(2012)
  • A.H. Azimi et al.Discharge characteristics of weirs of finite crest length with upstream and downstream rampsJ. Irrigat. Drain. Eng.(2013)
  • A.H. Azimi et al.Submerged flows over rectangular weirs of finite crest lengthJ. Irrigat. Drain. Eng.(2014)
  • A.H. Azimi et al.Water surface characteristics of submerged rectangular sharp-crested weirsJ. Hydraul. Eng.(2016)
  • M. Bijankhan et al.Experimental study and numerical simulation of inclined rectangular weirsJ. Irrigat. Drain. Eng.(2018)
  • A.H. AzimiAn Introduction to Hydraulic Structure” in Water Engineering Modeling and Mathematic Tools(2021)
Fig. 9 From: An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Abstract

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

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

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

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

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

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

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

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

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

1 Introduction

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

Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [12]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].

figure 1
Fig. 1

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

Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [79]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.

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

2 Materials and Methods

2.1 Physical Model Configuration

This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.

figure 2
Fig. 2

Table 1 Experimental conditions considered for calibration

Full size table

2.2 Numerical Models

Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.

figure 3
Fig. 3

2.3 Governing Equations

FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (xyzt). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [413]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (xyz) applicable to the model are as follows:

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

(1)

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

(2)

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

(3)

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

(4)

where (uvw) are the velocity components, (AxAyAz) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fxfyfz) are the viscous accelerations in the directions (xyz), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The kε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard kε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:

∂(��)∂�+∂(����)∂��=∂∂��[������∂�∂��]+��−�ε

(5)

∂(�ε)∂�+∂(�ε��)∂��=∂∂��[�ε�eff∂ε∂��]+�1εε��k−�2ε�ε2�

(6)

In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.

2.4 Meshing and the Boundary Conditions in the Model Setup

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

Full size table

The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.

figure 4
Fig. 4

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

�=ln⁡(�3−�2)(�2−�1)/ln⁡(�)

(7)

f1f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:

GCIfine=1.25|ε|��−1

(8)

Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:

GCI12=1.25|�2−�1�1|��−1

(9)

Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation

Full size table

figure 5
Fig. 5

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

figure 6
Fig. 6

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

figure 7
Fig. 7

3 Results

3.1 Verification of Numerical Results

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

MAPE(%)100×1�∑1�|�exp−�num�exp|

(10)

RMSE(−)1�∑1�(�exp−�num)2

(11)

Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].

figure 8
Fig. 8
figure 9
Fig. 9
figure 10
Fig. 10

3.2 Flow Regime and Discharge-Depth Relationship

Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [220]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:

��∗=���0���

(12)

Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].

figure 11
Fig. 11

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

�+=��ℎ�ℎ=23�d�

(13)

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

�d=0.57+0.075ℎ�

(14)

figure 12
Fig. 12

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

figure 13
Fig. 13

3.3 Depth-Averaged Velocity Distributions

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

figure 14
Fig. 14
figure 15
Fig. 15

On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.

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

figure 16
Fig. 16

On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.

figure 17
Fig. 17

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

figure 18
Fig. 18

3.4 Turbulence Characteristics

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

�=12(�x′2+�y′2+�z′2)

(15)

where uxuy, and uz are fluctuating velocities in the xy, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.

figure 19
Fig. 19

Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.

figure 20
Fig. 20
figure 21
Fig. 21

For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.

figure 22
Fig. 22

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

figure 23
Fig. 23

The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.

figure 24
Fig. 24
figure 25
Fig. 25

The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.

figure 26
Fig. 26

3.5 Energy Dissipation

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

�=����0��

(16)

where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.

figure 27
Fig. 27

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

ε=�1−�2�1

(17)

where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.

figure 28
Fig. 28
figure 29
Fig. 29

4 Discussion

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

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

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

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

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

5 Conclusions

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

  • The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
  • For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
  • In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
  • As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
  • The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
  • For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
  • For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
  • For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
  • Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.

Availability of data and materials

Data is contained within the article.

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Intrusion of fine sediments into river bed and its effect on river environment – a research review

미세한 퇴적물이 강바닥에 침투하고 하천 환경에 미치는 영향 – 연구 검토

Intrusion of fine sediments into river bed and its effect on river environment – a research review

Nilav Karna,K.S. Hari Prasad, Sanjay Giri & A.S. Lodhi

Abstract

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

Keywords: 

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

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Effects of surface roughness on overflow discharge of embankment weirs

표면 거칠기가 제방 둑의 오버플로 배출에 미치는 영향

Effects of surface roughness on overflow discharge of embankment weirs

Abstract

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

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

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

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

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

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

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Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

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

aMexican Institute of Water Technology, Mexico
bPostgraduate College, Hydrosciences, Carr. Mex-Tex Km 36.5, Texcoco, Mexico State, 56230, Mexico
cAgricultural Engineering Graduate Program, University of Chapingo, Mexicod
Inter-American Institute of Water Science and Technology, Mexico

https://doi.org/10.1016/j.flowmeasinst.2021.102031Get rights and content

Highlights

  • •Optimizing the geometric design of weirs can improve hydraulic performance.
  • •Labyrinth type weirs allow the discharge capacity to be increased compared to linear weirs.
  • •Hydraulic heads with ratio HT/P > 0.5 generated sub-atmospheric pressures on the side walls of the weir.
  • •Numerical simulation it is a strong tool to analyze and get optimized the weir function.

Abstract

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R2 = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with HT/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when HT/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.

Keywords

Labyrinth weir

Computational fluids dynamics (CFD)

Discharge coefficient

Apex shape

Crest profile

Figures (12)

  1. Fig. 1. Geometric parameters of a labyrinth weir
  2. Fig. 2. Crest profiles: (A) sharp-crest, (B) half-round, (C) quarter-round, (D) WES
  3. Fig. 3. Apex shapes
  4. Fig. 4. Weir and boundary conditions
  5. Fig. 5. Hydraulic head approach an asymptotic zero-grid spacing value
  6. Fig. 6. Percentage relative error of the discharge coefficient as a function of HT/P
  7. Fig. 7. Comparison of the discharge coefficients obtained numerically against the…
  8. Fig. 8. Pressure distribution in the downstream side walls of the labyrinth weir
  9. Fig. 9. Comparison of the discharge coefficient in trapezoidal apex labyrinth weirs
  10. Fig. 10. Comparison of the discharge coefficient in circular apex labyrinth weirs
  11. Fig. 11. Local drowning at the upstream apex
  12. Fig. 12. Ratio of the discharge coefficient of the circular apex weir with the…
원문보기
Study on Hydrodynamic Performance of Unsymmetrical Double Vertical Slotted Barriers

침수된 강성 식생을 갖는 개방 수로 흐름의 특성에 대한 3차원 수치 시뮬레이션

A 3-D numerical simulation of the characteristics of open channel flows with submerged rigid vegetation

Journal of Hydrodynamics volume 33, pages833–843 (2021)Cite this article

Abstract

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

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

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

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

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

Key words

  • Submerged rigid vegetation
  • longitudinal velocity
  • transverse velocity
  • vertical velocity
  • open channel

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Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)

Three-dimensional Numerical Evaluation of Hydraulic Efficiency and Discharge Coefficient in Grate Inlets

쇠창살 격자 유입구의 수리효율 및 배출계수에 대한 3차원 수치적 평가

Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González,
Wilson Enrique Amaya Tequia
Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202.
Tunja – Boyacá – Colombia

Abstract

홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.

Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.

Keywords

grate inlet, inlet efficiency, discharge coefficient, computational fluid dynamic, 3D modelling.

Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade
and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source:
made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source: made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface
configuration and flow regime, of some grating types (source: produced with FlowSight®)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface configuration and flow regime, of some grating types (source: produced with FlowSight®)

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측수로 물넘이 수위별 해석 결과

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저수지 정밀안전진단 수치해석 과업 예시

과업의 범위

  • 3차원 수치해석을 통한 OO저수지의 측수로부 수면 검토
  • 측수로 불완전 월류 발생 여부 및 제방 여유고 검토

수치해석 과업 세부내용

가능최대홍수량과 200년, 100년 빈도의 홍수량에 대해 각각의 측수로부 3차원 수치해석

경계조건

가. 수위

  • 만수위
  • 홍수위
    – 100년 빈도
    – 200년 빈도
    – 가능최대홍수량(PMF)

나. 홍수량

  • 100년 빈도의 홍수량
  • 200년 빈도의 홍수량
  • 가능최대홍수량(PMF)

저수지 수위별 방류량 검토 및 제방 여유고 검토

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  • 수위에 따른 물넘이 수위를 검토하여 제방 여유고 검토

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횡월류 위어 유입각 변화에 따른 유량계수 추정 기초 연구

국문초록

최근 이상기후의 영향으로 전 지구적 온난화 및 도시화로 인해 세계적으로 기상이변이 늘어나고 있다. 도시화 및 난개발로 인한 불투수 면적의 증가 같은 문제로 홍수량이 증가함에 따라 홍수피해를 줄이기 위한 다양한 방안이 제시되고 있다. 본 연구에서는 사행하천구간에 설치되는 횡월류 위어 유입각의 변화에 따라 3차원 CFD 모형인 FLOW-3D를 이용하여 흐름 특성과 월류량을 분석하여 횡월류 위어 유입각에 대한 수공구조물의 월류능력 평가 및 유량계수 산정을 위한 기초 연구를 수행하였다. 분석 결과, 횡월류 위어 유입각이 작을수록 횡월류부 통과 후 주수로 흐름의 수위가 감소하고 유속이 증가하였으며, 유입각이 증가할수록 수위가 상승하였고, 유속이 감소하는 경향을 보였다. 또한, 횡월류 위어 유입각이 40° 이상인 경우 직하류 유속이 상류 유속과 비교하여 감소하는 것을 확인할 수 있었다.

영문초록

Recently, due to global warming and urbanization due to the influence of abnormal weather, weather changes are increasing worldwide. Various measures have been proposed to reduce flood damage as flood volume increases due to problems such as an increase in impermeable area due to urbanization and reckless development. In this study, flow characteristics and overflow volume were analyzed using FLOW-3D, a three-dimensional CFD model, in accordance with changes in the cross-flow weir inlet angle installed in the meandering river section, and a basic study was conducted to evaluate the overflow capacity and calculate the flow coefficient. As a result of the analysis, the smaller the inflow angle of the transverse overflow, the lower the water level and flow rate of the main water flow after passing the transverse overflow, and the higher the inflow angle, the higher the water level and the flow rate. In addition, it was confirmed that the direct downstream flow rate decreased compared to the upstream flow rate when the inflow angle of the transverse overflow was 40° or higher.

Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment

by Hongbo Mi 1,2, Chuan Wang 1,3, Xuanwen Jia 3,*, Bo Hu 2, Hongliang Wang 4, Hui Wang 3 and Yong Zhu 5

1College of Mechatronics Engineering, Hainan Vocational University of Science and Technology, Haikou 571126, China

2Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

3College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China

4School of Aerospace and Mechanical Engineering/Flight College, Changzhou Institute of Technology, Changzhou 213032, China

5National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China

*Author to whom correspondence should be addressed.Sustainability202315(6), 5159; https://doi.org/10.3390/su15065159

Received: 30 January 2023 / Revised: 4 March 2023 / Accepted: 10 March 2023 / Published: 14 March 2023(This article belongs to the Special Issue Advanced Technologies of Renewable Energy and Water Management for Sustainable Environment

Abstract

Due to their high efficiency, low heat loss and associated sustainability advantages, impinging jets have been used extensively in marine engineering, geotechnical engineering and other engineering practices. In this paper, the flow structure and impact characteristics of impinging jets with different Reynolds numbers and impact distances are systematically studied by Flow-3D based on PIV experiments. In the study, the relevant state parameters of the jets are dimensionlessly treated, obtaining not only the linear relationship between the length of the potential nucleation zone and the impinging distance, but also the linear relationship between the axial velocity and the axial distance in the impinging zone. In addition, after the jet impinges on the flat plate, the vortex action range caused by the wall-attached flow of the jet gradually decreases inward with the increase of the impinging distance. By examining the effect of Reynolds number Re on the hydraulic characteristics of the submerged impact jet, it can be found that the structure of the continuous submerged impact jet is relatively independent of the Reynolds number. At the same time, the final simulation results demonstrate the applicability of the linear relationship between the length of the potential core region and the impact distance. This study provides methodological guidance and theoretical support for relevant engineering practice and subsequent research on impinging jets, which has strong theoretical and practical significance.

Keywords: 

PIVFlow-3Dimpinging jethydraulic characteristicsimpinging distance

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Figure 1. Geometric model.

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Figure 2. Model grid schematic.

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Figure 3. (a) Schematic diagram of the experimental setup; (b) PIV images of vertical impinging jets with velocity fields.

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Figure 4. (a) Velocity distribution verification at the outlet of the jet pipe; (b) Distribution of flow angle in the mid-axis of the jet [39].

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Figure 5. Along-range distribution of the dimensionless axial velocity of the jet at different impact distances.Figure 6 shows the variation of H

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Figure 6. Relationship between the distribution of potential core region and the impact height H/D.

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Figure 7. The relationship between the potential core length 

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Figure 8. Along-range distribution of the flow angle φ of the jet at different impact distances.

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Figure 9. Velocity distribution along the axis of the jet at different impinging regions.

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Figure 10. The absolute value distribution of slope under different impact distances.

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Figure 11. Velocity distribution of impinging jet on wall under different impinging distances.

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Figure 12. Along-range distribution of the dimensionless axial velocity of the jet at different Reynolds numbers.

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Figure 13. Along-range distribution of the flow angle φ of the jet at different Reynolds numbers.

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Figure 14. Velocity distribution along the jet axis at different Reynolds numbers.

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Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

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MDPI and ACS Style

Mi, H.; Wang, C.; Jia, X.; Hu, B.; Wang, H.; Wang, H.; Zhu, Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability 202315, 5159. https://doi.org/10.3390/su15065159

AMA Style

Mi H, Wang C, Jia X, Hu B, Wang H, Wang H, Zhu Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability. 2023; 15(6):5159. https://doi.org/10.3390/su15065159Chicago/Turabian Style

Mi, Hongbo, Chuan Wang, Xuanwen Jia, Bo Hu, Hongliang Wang, Hui Wang, and Yong Zhu. 2023. “Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment” Sustainability 15, no. 6: 5159. https://doi.org/10.3390/su15065159

Figure 2. Different PKW Types.

A review of Piano Key Weir as a superior alternative for dam rehabilitation

댐 복구를 위한 우수한 대안으로서의 Piano Key Weir에 대한 검토

Amiya Abhash &

K. K. Pandey

Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020

ABSTRACT

Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.

댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.

이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.

이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.

다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.

KEYWORDS: 

Figure 2. Different PKW Types.
Figure 2. Different PKW Types.

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Figure 4. Field gate discharge experiment.

FLOW-3D Model Development for the Analysis of the Flow Characteristics of Downstream Hydraulic Structures

하류 유압 구조물의 유동 특성 분석을 위한 FLOW-3D 모델 개발

Beom-Jin Kim 1, Jae-Hong Hwang 2 and Byunghyun Kim 3,*
1 Advanced Structures and Seismic Safety Research Division, Korea Atomic Energy Research Institute,
Daejeon 34057, Korea
2 Korea Water Resources Corporation (K-Water), Daejeon 34350, Korea
3 Department of Civil Engineering, Kyungpook National University, Daegu 41566, Korea

  • Correspondence: bhkimc@knu.ac.kr; Tel.: +82-53-950-7819

Abstract

Hydraulic structures installed in rivers inevitably create a water level difference between upstream and downstream regions. The potential energy due to this difference in water level is converted into kinetic energy, causing high-velocity flow and hydraulic jumps in the river. As a result, problems such as scouring and sloping downstream may occur around the hydraulic structures. In this study, a FLOW-3D model was constructed to perform a numerical analysis of the ChangnyeongHaman weir in the Republic of Korea. The constructed model was verified based on surface velocity measurements from a field gate operation experiment. In the simulation results, the flow discharge differed from the measured value by 9–15 m3/s, from which the accuracy was evaluated to be 82–87%. The flow velocity was evaluated with an accuracy of 92% from a difference of 0.01 to 0.16 m/s. Following this verification, a flow analysis of the hydraulic structures was performed according to boundary conditions and operation conditions for numerous scenarios. Since 2018, the ChangnyeongHaman weir gate has been fully opened due to the implementation of Korea’s eco-environmental policy; therefore, in this study, the actual gate operation history data prior to 2018 was applied and evaluated. The evaluation conditions were a 50% open gate condition and the flow discharge of two cases with a large difference in water level. As a result of the analysis, the actual operating conditions showed that the velocity and the Froude number were lower than the optimal conditions, confirming that the selected design was appropriate. It was also found that in the bed protection section, the average flow velocity was high when the water level difference was large, whereas the bottom velocity was high when the gate opening was large. Ultimately, through the reviewed status survey data in this study, the downstream flow characteristics of hydraulic structures along with adequacy verification techniques, optimal design techniques such as procedures for design, and important considerations were derived. Based on the current results, the constructed FLOW-3D-based model can be applied to creating or updating flow analysis guidelines for future repair and reinforcement measures as well as hydraulic structure design.

하천에 설치되는 수력구조물은 필연적으로 상류와 하류의 수위차를 발생시킨다. 이러한 수위차로 인한 위치에너지는 운동에너지로 변환되어 하천의 고속유동과 수압점프를 일으킨다. 그 결과 수력구조물 주변에서 하류의 세굴, 경사 등의 문제가 발생할 수 있다.

본 연구에서는 대한민국 창녕함안보의 수치해석을 위해 FLOW-3D 모델을 구축하였다. 구축된 모델은 현장 게이트 작동 실험에서 표면 속도 측정을 기반으로 검증되었습니다.

시뮬레이션 결과에서 유량은 측정값과 9~15 m3/s 차이가 나고 정확도는 82~87%로 평가되었다. 유속은 0.01~0.16m/s의 차이에서 92%의 정확도로 평가되었습니다.

검증 후 다양한 시나리오에 대한 경계조건 및 운전조건에 따른 수리구조물의 유동해석을 수행하였다. 2018년부터 창녕함안보 문은 한국의 친환경 정책 시행으로 전면 개방되었습니다.

따라서 본 연구에서는 2018년 이전의 실제 게이트 운영 이력 데이터를 적용하여 평가하였다. 평가조건은 50% open gate 조건과 수위차가 큰 2가지 경우의 유수방류로 하였다. 해석 결과 실제 운전조건은 속도와 Froude수가 최적조건보다 낮아 선정된 설계가 적합함을 확인하였다.

또한 베드보호구간에서는 수위차가 크면 평균유속이 높고, 수문개구가 크면 저저유속이 높은 것으로 나타났다. 최종적으로 본 연구에서 검토한 실태조사 자료를 통해 적정성 검증기법과 함께 수력구조물의 하류 유동특성, 설계절차 등 최적 설계기법 및 중요 고려사항을 도출하였다.

현재의 결과를 바탕으로 구축된 FLOW-3D 기반 모델은 수력구조 설계뿐만 아니라 향후 보수 및 보강 조치를 위한 유동해석 가이드라인 생성 또는 업데이트에 적용할 수 있습니다.

Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.
Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.
Figure 2. Changnyeong-Haman weir depth survey results (June 2015)
Figure 2. Changnyeong-Haman weir depth survey results (June 2015)
Figure 4. Field gate discharge experiment.
Figure 4. Field gate discharge experiment.
Figure 16. Analysis results for Case 7 and Case 8
Figure 16. Analysis results for Case 7 and Case 8

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Sketch of approach channel and spillway of the Kamal-Saleh dam

CFD modeling of flow pattern in spillway’s approach channel

Sustainable Water Resources Management volume 1, pages245–251 (2015)Cite this article

Abstract

Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.

댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.

Introduction

Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015ab; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characteristics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.

Materials and methods

Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.

figure 1
Fig. 1
figure 2
Fig. 2

Review of the governing equations in software Flow 3D

Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).

vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,

(1)

where uvz are velocity component in the x, y, z direction; A xA yA z cross-sectional area of the flow; ρ fluid density; PSOR the source term; v f is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).

∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,

(2)

where P is the fluid pressure; G xG yG z the acceleration created by body fluids; f xf yf z viscosity acceleration in three dimensions and v f is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.

∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0

(3)

Turbulence models

Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.

Steps of solving a problem in Flow 3D software

(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.

Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.

Model calibration

Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.

Results and discussion

The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested

Full size table

Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.

figure 3
Fig. 3

For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.

figure 4
Fig. 4
figure 5
Fig. 5

With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.

figure 6
Fig. 6

Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.

figure 7
Fig. 7
figure 8
Fig. 8

As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.

figure 9
Fig. 9

The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.

figure 10
Fig. 10
figure 11
Fig. 11
figure 12
Fig. 12

The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.

figure 13
Fig. 13

As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.

figure 14
Fig. 14

More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.

figure 15
Fig. 15

Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.

figure 16
Fig. 16

Conclusion

Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.

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Authors and Affiliations

  1. Department of Water Engineering, Lorestan University, Khorram Abad, IranAbbas Parsaie, Amir Hamzeh Haghiabi & Amir Moradinejad

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Correspondence to Abbas Parsaie.

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Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag. 1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9

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  • Received28 April 2015
  • Accepted28 August 2015
  • Published15 September 2015
  • Issue DateSeptember 2015
  • DOIhttps://doi.org/10.1007/s40899-015-0020-9

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Keywords

  • Approach channel
  • Kamal-Saleh dam
  • Guide wall
  • Flow pattern
  • Numerical modeling
  • Flow 3D software
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    Arabian Journal of Geosciences volume 15, Article number: 1614 (2022) Cite this article

    Abstract

    이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.

    In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.

    Keywords

    • Numerical modeling
    • Spillway
    • Hydraulic jump
    • Energy dissipation
    • FLOW 3D

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    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    Effect of tailwater depth on non-cohesive earth dam failure due to overtopping

    범람으로 인한 비점착성 흙댐 붕괴에 대한 테일워터 깊이의 영향

    ShaimaaAmanaMohamedAbdelrazek RezkbRabieaNasrc

    Abstract

    본 연구에서는 범람으로 인한 토사댐 붕괴에 대한 테일워터 깊이의 영향을 실험적으로 조사하였다. 테일워터 깊이의 네 가지 다른 값을 검사합니다. 각 실험에 대해 댐 수심 측량 프로파일의 진화, 고장 기간, 침식 체적 및 유출 수위곡선을 관찰하고 기록합니다.

    결과는 tailwater 깊이를 늘리면 고장 시간이 최대 57% 감소하고 상대적으로 침식된 마루 높이가 최대 77.6% 감소한다는 것을 보여줍니다. 또한 상대 배수 깊이가 3, 4, 5인 경우 누적 침식 체적의 감소는 각각 23, 36.5 및 75%인 반면 최대 유출량의 감소는 각각 7, 14 및 17.35%입니다.

    실험 결과는 침식 과정을 복제할 때 Flow 3D 소프트웨어의 성능을 평가하는 데 활용됩니다. 수치 모델은 비응집성 흙댐의 침식 과정을 성공적으로 시뮬레이션합니다.

    The influence of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. Four different values of tailwater depths are examined. For each experiment, the evolution of the dam bathymetry profile, the duration of failure, the eroded volume, and the outflow hydrograph are observed and recorded. The results reveal that increasing the tailwater depth reduces the time of failure by up to 57% and decreases the relative eroded crest height by up to 77.6%. In addition, for relative tailwater depths equal to 3, 4, and 5, the reduction in the cumulative eroded volume is 23, 36.5, and 75%, while the reduction in peak discharge is 7, 14, and 17.35%, respectively. The experimental results are utilized to evaluate the performance of the Flow 3D software in replicating the erosion process. The numerical model successfully simulates the erosion process of non-cohesive earth dams.

    Keywords

    Earth dam, Eroded volume, Flow 3D model, Non-cohesive soil, Overtopping failure, Tailwater depth

    Notation

    d50

    Mean partical diameterWc

    Optimum water contentZo

    Dam height (cm)do

    Tailwater depth (cm)Zeroded

    Eroded height of the dam measured at distance of 0.7 m from the dam heel (cm)t

    Total time of failure (sec)t1

    Time of crest width erosion (sec)Zcrest

    The crest height (cm)Vtotal

    Total volume of the dam (m3)Veroded

    Cumulative eroded volume (m3)RMSE

    The statistical variable root- mean- square errord

    Degree of agreement indexyu.s.

    The upstream water depth (cm)yd.s

    The downstream water depth (cm)H

    Water surface elevation over sharp crested weir (cm)Q

    Outflow discharge (liter/sec)Qpeak

    Peak discharge (liter/sec)

    1. Introduction

    Earth dams are compacted structures composed of natural materials that are usually mined or quarried from local locations. The failures of the earth dams have proven to be deadly, destructive, and costly. According to People’s Daily, two earthen dams, Yong’an Dam and Xinfa Dam located in Hulun Buir City in North China’s Inner Mongolia failed on 2021, due to a surge in the water level of the Nuomin River caused by heavy rain. The dam breach affected 16,660 people, flooded 325,622 mu of farmland (21708.1 ha), and destroyed 22 bridges, 124 culverts, and 15.6 km of roadways. Also, the failure of south fork dam (earth and rock fill dam) near Johnstown on 1889 is considered the worst U.S dam disaster in terms of loss of life. The dam was overtopped and washed away due to unexpected heavy rains, releasing 20 million tons of water which destroyed Johnstown and resulted in 2209 deaths, [1][2]. Piping or shear sliding, failure due to natural factors, and failure due to overtopping are all possible causes of earth dam failure. However, overtopping failure is the most frequent cause of dam failure. According to The International Committee on Large Dams (ICOLD, 1995), and [3], more than one-third of the total known dam failures were caused by dam overtopping.

    Overtopping occurs as the result of insufficient flood design or freeboard in some cases. Extreme rainstorms can cause floods which can overtop the dam and cause it to fail. The size and geometry of the reservoir or the dam (side slopes, top width, height, etc.), the homogeneity of the material used in the construction of the dam, overtopping depth, and the presence or absence of tailwater are all elements that influence this type of failure which will be illustrated in the following literature. Overtopping failures of earth dams may be divided into several failure mechanisms based on the material composition and the inner structure of the dam. For cohesive earth dams because of low permeability, no seepage exists on the slopes. Erosion often begins at the earth dam toe during turbulent erosion and moves upstream, undercutting the slope, causing the removal of large chunks of materials. While for non-cohesive earth dams the downstream face of the dam flattens progressively and is often said to rotate around a point near the downstream toe [4][5][6] In the last few decades, the study of failures due to overtopping has gained popularity among researchers. The overtopping failure, in fact, has been widely investigated in coastal and river hydraulics and morpho dynamic. In addition, several laboratory experimental studies have been conducted in this field in order to better understand different involved factors. Also, many numerical types of research have been conducted to investigate the process of overtopping failure as well as the elements that influence this type of failure.

    Tabrizi et al. [5] conducted a series of embankment overtopping tests to find the effect of compaction on the failure of a homogenous sand embankment. A plane breach process occurred across the flume width due to the narrow flume width. They measured the downstream hydrographs and embankment surface profile for every case. They concluded that the peak discharge decreased with a high compaction level, while the time to peak increased. Kansoh et al. [6] studied experimentally the failure of compacted homogeneous non-cohesive earthen embankment due to overtopping. They investigated the influence of different shape parameters including the downstream slope, the crest width, and the height of the embankment on the erosion process. The erosion process was initiated by carving a pilot channel into the embankment crest. They evaluated the time of embankment failure for different shape parameters. They concluded that the failure time increases with increasing the downstream slope and the crest width. Zhu et al. [7] investigated experimentally the breaching of five embankments, one constructed with pure sand, and four with different sand-silt–clay mixtures. The erosion pattern was similar across the flume width. They stated that for cohesive soil mixtures the head cut erosion was the most important factor that affected the breach growth, while for non-cohesive soil the breach erosion was affected by shear erosion.

    Amaral et al. [8] studied experimentally the failure by overtopping for two embankments built from silt sand material. They studied the effect of the degree of compaction of the embankment and the geometry of the pilot channel carved at the centre of the dam crest. They studied two shapes of pilot channel a rectangular shape and triangular shape. They stated that the breach development is influenced by a higher degree of compaction, however, the pilot channel geometry did not influence the breach’s final form. Bereta et al. [9] studied experimentally the breach formation of five dam models, three of them were homogenous clay soil while two were sandy-clay mixtures. The erosion process was initiated by cutting a pilot channel at the centre of the dam crest. They observed the initiation of erosion, flow shear erosion, sidewall bottom erosion, and distinguished the soil mechanical slope mass failure from the head cut vertically and laterally during these tests. Verma et al. [10] investigated experimentally a two-dimensional erosion phenomenon due to overtopping by using a wooden fuse plug model and five different soils. They concluded that the erosion process was affected mostly by cohesiveness and degree of compaction. For cohesive soils, a head cut erosion was observed, while for non-cohesive soils surface erosion occurred gradually. Also, the dimensions of fuse plug, type of fill material, reservoir capacity, and inflow were found to affect the behaviour of the overall breaching process.

    Wu and Qin [11] studied the effect of adding coarse grains to the downstream face of a non-cohesive dam as a result of tailings deposition. The process of overtopping during tailings dam failures is analyzed and its effect on delaying the dam-break process and disaster mitigation are investigated. They found that the tested protective measures decreased the breach area, the maximum breaching flow discharge and flow velocity, and the downstream inundated area. Khankandi et al. [12] studied experimentally the effect of reservoir geometry on dam break flow in case of dry and wet bed conditions. They considered four different reservoir shapes, a long reservoir, a wide, a trapezoidal shaped and one with a 90◦ bend all with identical water volume and horizontal bed. The dam break is simulated by the sudden gate removal using a pneumatic jack. They measured the variation of water level over time with ultrasonic sensors and flow velocity component with an acoustic Doppler velocimeter. Also, the experimental results of water level variation are compared with Ritters solution (1892) [13]. They stated that for dry bed condition the long and 90 bend reservoirs results are close to the analytical solution by ritter also in these two shapes a 1D flow is noticed. However, for wide and trapezoidal reservoirs a 2D effect is significant due to flow contraction at channel entrance.

    Rifai et al. [14] conducted a series of experiments to investigate the effect of tailwater depth on the outflow discharge and breach geometry during non-cohesive homogenous fluvial dikes overtopping failure. They cut an initial notch in the crest at 0.8 m from the upstream end of the dike to initiate overtopping. They compared their results to previous experiments under different main channel inflow discharges combined with a free floodplain. They divided the dike breaching process into three stages: gradual start of overtopping flow resulting in slow initiation of dike erosion, deepening and widening breach due to large flow depth and velocity, finally the flow depth starts stabilizing at its minimal level with or without sustained breach expansion. They stated that breach discharge has lower values than in free floodplain tests. Jiang [15] studied the effect of bed slope on breach parameters and peak discharge in non-cohesive embankment failure. An initial triangular breach with a depth and width of 4 cm was pre-set on one side of the dam. He stated that peak discharge increases with the increase of bed slope and then decreases.

    Ozmen-cagatay et al. [16] studied experimentally flood wave propagation resulted from a sudden dam break event. For dam-break modelling, they used a mechanism that permitted the rapid removal of a vertical plate with a thickness of 4 mm and made of rigid plastic. They conducted three tests, one with dry bed condition and two tests with tailwater depths equal 0.025 m and 0.1 m respectively. They recorded the free surface profile during initial stages of dam break by using digital image processing. Finally, they compared the experimental results with the with a commercially available VOF-based CFD program solving the Reynolds-averaged Navier –Stokes equations (RANS) with the k– Ɛ turbulence model and the shallow water equations (SWEs). They concluded that Wave breaking was delayed with increasing the tailwater depth to initial reservoir depth ratio. They also stated that the SWE approach is sufficient more to represent dam break flows for wet bed condition. Evangelista [17] investigated experimentally and numerically using a depth-integrated two-phase model, the erosion of sand dike caused by the impact of a dam break wave. The dam break is simulated by a sudden opening of an upstream reservoir gate resulting in the overtopping of a downstream trapezoidal sand dike. The evolution of the water wave caused from the gate opening and dike erosion process are recorded by using a computer-controlled camera. The experimental results demonstrated that the progression of the wave front and dike erosion have a considerable influence on each other during the process. In addition, the dike constructed from fine sands was more resistant to erosion than the one built with coarse sand. They also stated that the numerical model can is capable of accurately predicting wave front position and dike erosion. Also, Di Cristo et al. [18] studied the effect of dam break wave propagation on a sand embankment both experimentally and numerically using a two-phase shallow-water model. The evolution of free surface and of the embankment bottom are recorded and used in numerical model assessment. They stated that the model allows reasonable simulation of the experimental trends of the free surface elevation regardeless of the geofailure operator.

    Lots of numerical models have been developed over the past few years to simulate the dam break flooding problem. A one-dimensional model, such as Hec-Ras, DAMBRK and MIKE 11, ect. A two-dimensional model such as iRIC Nay2DH is used in earth embankment breach simulation. Other researchers studied the failure process numerically using (3D) computational fluid dynamics (CFD) models, such as FLOW-3D, and FLUENT. Goharnejad et al. [19] determined the outflow hydrograph which results from the embankment dam break due to overtopping. Hu et al. [20] performed a comparison between Flow-3D and MIKE3 FM numerical models in simulating a dam break event under dry and wet bed conditions with different tailwater depths. Kaurav et al. [21] simulated a planar dam breach process due to overtopping. They conducted a sensitivity analysis to find the effect of dam material, dam height, downstream slope, crest width, and inlet discharge on the erosion process and peak discharge through breach. They concluded that downstream slope has a significant influence on breaching process. Yusof et al. [22] studied the effect of embankment sediment sizes and inflow rates on breaching geometric and hydrodynamic parameters. They stated that the peak outflow hydrograph increases with increasing sediment size and inflow rates while time of failure decreases.

    In the present work, the effect of tailwater depth on earth dam failure during overtopping is studied experimentally. The relation between the eroded volume of the dam and the tailwater depth is presented. Also, the percentage of reduction in peak discharge due to tailwater existence is calculated. An assessment of Flow 3D software performance in simulating the erosion process during earth dam failure is introduced. The statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are used in model assessment.

    2. Material and methods

    The tests are conducted in a straight rectangular flume in the laboratory of Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexandria University, Egypt. The flume dimensions are 10 m long, 0.86 m wide, and 0.5 m deep. The front part of the flume is connected to a storage basin 1 m long by 0.86 m wide. The storage basin is connected to a collecting tank for water recirculation during the experiments as shown in Fig. 1Fig. 2. A sharp-crested weir is placed at a distance of 4 m downstream the constructed dam to keep a constant tailwater depth in each experiment and to measure the outflow discharge.

    To measure the eroded volume with time a rods technique is used. This technique consists of two parallel wooden plates with 10 cm distance in between and five rows of stainless-steel rods passing vertically through the wooden plates at a spacing of 20 cm distributed across flume width. Each row consists of four rods with 15 cm spacing between them. Also, a graph board is provided to measure the drop in each rod with time as shown in Fig. 3Fig. 4. After dam construction the rods are carefully rested on the dam, with the first line of rods resting in the middle of the dam crest and then a constant distance of 15 cm between rods lines is maintained.

    A soil sample is taken and tested in the laboratory of the soil mechanics to find the soil geotechnical parameters. The soil particle size distribution is also determined by sieve analysis as shown in Fig. 5. The soil mean diameter d50,equals 0.38 mm and internal friction angle equals 32.6°.

    2.1. Experimental procedures

    To investigate the effect of the tailwater depth (do), the tailwater depth is changed four times 5, 15, 20, and 25 cm on the sand dam model. The dam profile is 35 cm height, with crest width = 15 cm, the dam base width is 155 cm, and the upstream and downstream slopes are 2:1 as shown in Fig. 6. The dam dimensions are set as the flume permitted to allow observation of the dam erosion process under the available flume dimensions and conditions. All of the conducted experiments have the same dimensions and configurations.

    The optimum water content, Wc, from the standard proctor test is found to be 8 % and the maximum dry unit weight is 19.42 kN/m3. The soil and water are mixed thoroughly to ensure consistency and then placed on three horizontal layers. Each layer is compacted according to ASTM standard with 25 blows by using a rammer (27 cm × 20.5 cm) weighing 4 kg. Special attention is paid to the compaction of the soil to guarantee the repeatability of the tests.

    After placing and compacting the three layers, the dam slopes are trimmed carefully to form the trapezoidal shape of the dam. A small triangular pilot channel with 1 cm height and 1:1 side slopes is cut into the dam crest to initiate the erosion process. The position of triangular pilot channel is presented in Fig. 1. Three digital video cameras with a resolution of 1920 × 1080 pixels and a frame rate of 60 fps are placed in three different locations. One camera on one side of the flume to record the progress of the dam profile during erosion. Another to track the water level over the sharp-crested rectangular weir placed at the downstream end of the flume. And the third camera is placed above the flume at the downstream side of the dam and in front of the rods to record the drop of the tip of the rods with time as shown previously in Fig. 1.

    Before starting the experiment, the water is pumped into the storage basin by using pump with capacity 360 m3/hr, and then into the upstream section of the flume. The upstream boundary is an inflow condition. The flow discharge provided to the storage basin is kept at a constant rate of 6 L/sec for all experiments, while the downstream boundary is an outflow boundary condition.

    Also, the required tailwater depth for each experiment is filled to the desired depth. A dye container valve is opened to color the water upstream of the dam to make it easy to distinguish the dam profile from the water profile. A wooden board is placed just upstream of the dam to prevent water from overtopping the dam until the water level rises to a certain level above the dam crest and then the wooden board is removed slowly to start the experiment.

    2.2. Repeatability

    To verify the accuracy of the results, each experiment is repeated two times under the same conditions. Fig. 7 shows the relative eroded crest height, Zeroded / Zo, with time for 5 cm tailwater depth. From the Figure, it can be noticed that results for all runs are consistent, and accuracy is achieved.

    3. Numerical model

    The commercially available numerical model, Flow 3D is used to simulate the dam failure due to overtopping for the cases of 15 cm, 20 cm and 25 cm tailwater depths. For numerical model calibration, experimental results for dam surface evolution are used. The numerical model is calibrated for selection of the optimal turbulence model (RNG, K-e, and k-w) and sediment scour equations (Van Rin, Meyer- peter and Muller, and Nielsen) that produce the best results. In this, the flow field is solved by the RNG turbulence model, and the van Rijn equation is used for the sediment scour model. A geometry file is imported before applying the mesh.

    A Mesh sensitivity is analyzed and checked for various cell sizes, and it is found that decreasing the cell size significantly increases the simulation time with insignificant differences in the result. It is noticed that the most important factor influencing cell size selection is the value of the dam’s upstream and downstream slopes. For example, the slopes in the dam model are 2:1, thus the cell size ratio in X and Z directions should be 2:1 as well. The cell size in a mesh block is set to be 0.02 m, 0.025 m, and 0.01 m in X, Y and Z directions respectively.

    In the numerical computations, the boundary conditions employed are the walls for sidewalls and the channel bottom. The pressure boundary condition is applied at the top, at the air–water interface, to account for atmospheric pressure on the free surface. The upstream boundary is volume flow rate while the downstream boundary is outflow discharge.

    The initial condition is a fluid region, which is used to define fluid areas both upstream and downstream of the dam. To assess the model accuracy, the statistical variable root- mean- square error, RMSE, and the agreement degree index, d, are calculated as(1)RMSE=1N∑i=1N(Pi-Mi)2(2)d=1-∑Mi-Pi2∑Mi-M¯+Pi-P¯2

    where N is the number of samples, Pi and Mi are the models and experimental values, P and M are the means of the model and experimental values. The best fit between the experimental and model results would have an RMSE = 0 and degree of agreement, d = 1.

    4. Results of experimental work

    The results of the total time of failure, t (defined as the time from when the water begins to overtop the dam crest until the erosion reaches a steady state, when no erosion occurs), time of crest width erosion t1, cumulative eroded volume Veroded, and peak discharge Qpeak for each experiment are listed in Table 1. The case of 5 cm tailwater depth is considered as a reference case in this work.

    Table 1. Results of experimental work.

    Tailwater depth, do (cm)Total time of failure, t (sec)Time of crest width erosion, t1 (sec)cumulative eroded volume, Veroded (m3)Peak discharge, Qpeak (liter/sec)
    5255220.2113.12
    15165300.1612.19
    20140340.1311.29
    25110390.0510.84

    5. Discussion

    5.1. Side erosion

    The evolution of the bathymetry of the erosion line recorded by the video camera1. The videos are split into frames (60 frames/sec) by the Free Video to JPG Converter v.5.063 build and then converted into an excel spreadsheet using MATLAB code as shown in Fig. 8.

    Fig. 9 shows a sample of numerical model output. Fig. 10Fig. 11Fig. 12 show a dam profile development for different time steps from both experimental and numerical model, for tailwater depths equal 15 cm, 20 cm and 25 cm. Also, the values of RMSE and d for each figure are presented. The comparison shows that the Flow 3D software can simulate the erosion process of non-cohesive earth dam during overtopping with an RMSE value equals 0.023, 0.0218, and 0.0167 and degree of agreement, d, equals 0.95, 0.968, and 0.988 for relative tailwater depths, do/(do)ref, = 3, 4 and 5, respectively. The low values of RMSE and high values of d show that the Flow 3D can effectively simulate the erosion process. From Fig. 10Fig. 11Fig. 12, it can be noticed that the model is not capable of reproducing the head cut, while it can simulate well the degradation of the crest height with a minor difference from experimental work. The reason of this could be due to inability of simulation of all physical conditions which exists in the experimental work, such as channel friction and the grain size distribution of the dam soil which is surely has a great effect on the erosion process and breach development. In the experimental work the grain size distribution is shown in Fig. 5, while the numerical model considers that the soil is uniform and exactly 50 % of the dam particles diameter are equal to the d50 value. Another reason is that the model is not considering the increased resistance of the dam due to the apparent cohesion which happens due to dam saturation [23].

    It is clear from both the experimental and numerical results that for a 5 cm tailwater depth, do/(do)ref = 1.0, erosion begins near the dam toe and continues upward on the downstream slope until it reaches the crest. After eroding the crest width, the crest is lowered, resulting in increased flow rates and the speeding up of the erosion process. While for relative tailwater depths, do/(do)ref = 3, 4, and 5 erosion starts at the point of intersection between the downstream slope and tailwater. The existence of tailwater works as an energy dissipater for the falling water which reduces the erosion process and prevents the dam from failure as shown in Fig. 13. It is found that the time of the failure decreases with increasing the tailwater depth because most of the dam height is being submerged with water which decreases the erosion process. The reduction in time of failure from the referenced case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively.

    The relation between the relative eroded crest height, Zeroded /Zo, with time is drawn as shown in Fig. 14. It is found that the relative eroded crest height decreases with increasing tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref equals 3, 4, and 5, respectively. The time required for the erosion of the crest width, t1, is calculated for each experiment. The relation between relative tailwater depth and relative time of crest width erosion is shown in Fig. 15. It is found that the time of crest width erosion increases linearly with increasing, do /Zo. The percent of increase is 36.4, 54.5 and 77.3 % for relative tailwater depth, do /(do)ref = 3, 4 and 5, respectively.

    Crest height, Zcrest is calculated from the experimental results and the Flow 3D results for relative tailwater depths, do/(do)ref, = 3, 4, and 5. A relation between relative crest height, Zcrest/Zo with time from experimental and numerical results is presented in Fig. 16. From Fig. 16, it is seen that there is a good consistency between the results of numerical model and the experimental results in the case of tracking the erosion of the crest height with time.

    5.2. Upstream and downstream water depths

    It is noticed that at the beginning of the erosion process, both upstream and downstream water depths increase linearly with time as long as erosion of the crest height did not take place. However, when the crest height starts to lower the upstream water depth decreases with time while the downstream water depth increases. At the end of the experiment, the two depths are nearly equal. A relation between relative downstream and upstream water depths with time is drawn for each experiment as shown in Fig. 17.

    5.3. Eroded volume

    A MATLAB code is used to calculate the cumulative eroded volume every time interval for each experiment. The total volume of the dam, Vtotal is 0.256 m3. The cumulative eroded volume, Veroded is 0.21, 0.16, 0.13, and 0.05 m3 for tailwater depths, do = 5, 15, 20, and 25 cm, respectively. Fig. 18 presents the relation between cumulative eroded volume, Veroded and time. From Fig. 18, it is observed that the cumulative eroded volume decreases with increasing the tailwater depth. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative remained volume of the dam equals 0.18, 0.375, 0.492, and 0.8 for tailwater depths = 5, 15, 20, and 25 cm, respectively. Fig. 19 shows a relation between relative tailwater depth and relative cumulative eroded volume from experimental results. From that figure, it is noticed that the eroded volume decreases exponentially with increasing relative tailwater depth.

    5.4. The outflow discharge

    The inflow discharge provided to the storage tank is maintained constant for all experiments. The water surface elevation, H, over the sharp-crested weir placed at the downstream side is recorded by the video camera 2. For each experiment, the outflow discharge is then calculated by using the sharp-crested rectangular weir equation every 10 sec.

    The outflow discharge is found to increase rapidly until it reaches its peak then it decreases until it is constant. For high values of tailwater depths, the peak discharge becomes less than that in the case of small tailwater depth as shown in Fig. 20 which agrees well with the results of Rifai et al. [14] The reduction in peak discharge is 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively.

    The scenario presented in this article in which the tailwater depth rises due to unexpected heavy rainfall, is investigated to find the effect of rising tailwater depth on earth dam failure. The results revealed that rising tailwater depth positively affects the process of dam failure in terms of preventing the dam from complete failure and reducing the outflow discharge.

    6. Conclusions

    The effect of tailwater depth on earth dam failure due to overtopping is investigated experimentally in this work. The study focuses on the effect of tailwater depth on side erosion, upstream and downstream water depths, eroded volume, outflow hydrograph, and duration of the failure process. The Flow 3D numerical software is used to simulate the dam failure, and a comparison is made between the experimental and numerical results to find the ability of this software to simulate the erosion process. The following are the results of the investigation:

    The existence of tailwater with high depths prevents the dam from completely collapsing thereby turning it into a broad crested weir. The failure time decreases with increasing the tailwater depth and the reduction from the reference case is found to be 35.3, 45, and 57 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The difference between the upstream and downstream water depths decreases with time till it became almost negligible at the end of the experiment. The reduction in cumulative eroded volume is 23, 36.5, and 75 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The peak discharge decreases by 7, 14, and 17.35 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The relative eroded crest height decreases linearly with increasing the tailwater depth by 10, 41, and 77.6 % for relative tailwater depth, do /(do)ref = 3, 4, and 5, respectively. The numerical model can reproduce the erosion process with a minor deviation from the experimental results, particularly in terms of tracking the degradation of the crest height with time.

    Declaration of Competing Interest

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

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    Cited by (0)

    My name is Shaimaa Ibrahim Mohamed Aman and I am a teaching assistant in Irrigation and Hydraulics department, Faculty of Engineering, Alexandria University. I graduated from the Faculty of Engineering, Alexandria University in 2013. I had my MSc in Irrigation and Hydraulic Engineering in 2017. My research interests lie in the area of earth dam Failures.

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    Figure 3. Comparison of water surface profiles over porous media with 12 mm particle diameter in laboratory measurements (symbols) and numerical results (lines).

    다공층에 대한 돌발 댐 붕괴의 3차원 유동 수치해석 시뮬레이션

    A. Safarzadeh1*, P. Mohsenzadeh2, S. Abbasi3
    1 Professor of Civil Eng., Water Engineering and Mineral Waters Research Center, Univ. of Mohaghegh Ardabili,Ardabil, Iran
    2 M.Sc., Graduated of Civil-Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran
    3 M.Sc., Graduated of Civil -Hydraulic Structures Eng., Faculty of Eng., Univ. of Mohaghegh Ardabili, Ardabil, Iran Safarzadeh@uma.ac.ir

    Highlights

    유체 이동에 의해 생성된 RBF는 Ls-Dyna에서 Fluent, ICFD ALE 및 SPH 방법으로 시뮬레이션되었습니다.
    RBF의 과예측은 유체가 메인 도메인에서 고속으로 분리될 때 발생합니다.
    이 과잉 예측은 요소 크기, 시간 단계 크기 및 유체 모델에 따라 다릅니다.
    유체 성능을 검증하려면 최대 RBF보다 임펄스가 권장됩니다.

    Abstract

    Dam break is a very important problem due to its effects on economy, security, human casualties and environmental consequences. In this study, 3D flow due to dam break over the porous substrate is numerically simulated and the effect of porosity, permeability and thickness of the porous bed and the water depth in the porous substrate are investigated. Classic models of dam break over a rigid bed and water infiltration through porous media were studied and results of the numerical simulations are compared with existing laboratory data. Validation of the results is performed by comparing the water surface profiles and wave front position with dam break on rigid and porous bed. Results showed that, due to the effect of dynamic wave in the initial stage of dam break, a local peak occurs in the flood hydrograph. The presence of porous bed reduces the acceleration of the flood wave relative to the flow over the solid bed and it decreases with the increase of the permeability of the bed. By increasing the permeability of the bed, the slope of the ascending limb of the flood hydrograph and the peak discharge drops. Furthermore, if the depth and permeability of the bed is such that the intrusive flow reaches the rigid substrate under the porous bed, saturation of the porous bed, results in a sharp increase in the slope of the flood hydrograph. The maximum values of the peak discharge at the end of the channel with porous bed occurred in saturated porous bed conditions.

    댐 붕괴는 경제, 보안, 인명 피해 및 환경적 영향으로 인해 매우 중요한 문제입니다. 본 연구에서는 다공성 기재에 대한 댐 파괴로 인한 3차원 유동을 수치적으로 시뮬레이션하고 다공성 기재의 다공성, 투과도 및 다공성 층의 두께 및 수심의 영향을 조사합니다. 단단한 바닥에 대한 댐 파괴 및 다공성 매체를 통한 물 침투의 고전 모델을 연구하고 수치 시뮬레이션 결과를 기존 실험실 데이터와 비교합니다. 결과 검증은 강체 및 다공성 베드에서 댐 파단과 수면 프로파일 및 파면 위치를 비교하여 수행됩니다. 그 결과 댐파괴 초기의 동적파동의 영향으로 홍수수문곡선에서 국부첨두가 발생하는 것으로 나타났다. 다공성 베드의 존재는 고체 베드 위의 유동에 대한 홍수파의 가속을 감소시키고 베드의 투과성이 증가함에 따라 감소합니다. 베드의 투수성을 증가시켜 홍수 수문곡선의 오름차순 경사와 첨두방류량이 감소한다. 더욱이, 만약 층의 깊이와 투과성이 관입 유동이 다공성 층 아래의 단단한 기질에 도달하는 정도라면, 다공성 층의 포화는 홍수 수문곡선의 기울기의 급격한 증가를 초래합니다. 다공층이 있는 채널의 끝단에서 최대 방전 피크값은 포화 다공층 조건에서 발생하였다.

    Keywords

    Keywords: Dams Break, 3D modeling, Porous Bed, Permeability, Flood wave

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    Figure 1 Mitochondrial Weir Dam

    The Three-dimensional Simulation of Granular
    Mixtures Weir

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

    Abstract

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

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

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

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

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

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    Fig. 9. Simulated separation regions for surface mounted cylinder

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

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

    Abstract

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

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

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

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

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

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

    This is a preview of subscription content, access via your institution.

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

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    하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

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

    하류하천의 영향 최소화를 위한 보조 여수로 최적 활용방안 검토

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

    유 형주1, 주 성식2, 권 범재3, 이 승오4*

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

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

    ABSTRACT

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

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

    1. 서 론

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

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

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

    2. 본 론

    2.1 이론적 배경

    2.1.1 3차원 수치모형의 기본이론

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

    2.1.2 유동해석의 지배방정식

    1) 연속 방정식(Continuity Equation)

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

    (1)

    ∇·v=0

    (2)

    ∂∂x(uAx)+∂∂y(vAy)+∂∂z(wAz)=RSORρ

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

    2) 운동량 방정식(Momentum Equation)

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

    (3)

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

    (4)

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

    (5)

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

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

    2.1.3 소류력 산정

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

    1) Schoklitsch 공식

    Schoklitsch(1934)는 Chezy 유속계수를 적용하여 소류력을 산정하였다.

    (6)

    τ=γRI=γC2V2

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

    2) Manning 조도계수를 고려한 공식

    Chezy 유속계수를 대신하여 Manning의 조도계수를 고려하여 소류력을 산정할 수 있다.

    (7)

    τ=γn2V2R1/3

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

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

    2.2 하천호안 설계기준

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

    Table 1.

    Standard of Permissible Velocity and Shear on Revetment

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

    2.3. 보조여수로 운영에 따른 하류하천 영향 분석

    2.3.1 모형의 구축 및 경계조건

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

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

    (8)

    n=ks1/68.1g1/2

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

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

    Table 2.

    Mesh sizes and numerical conditions

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

    Case of numerical simulation (Qp : Design flood discharge)

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

    Roughness coefficient and roughness height

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

    Layout of spillway and river in this study

    2.3.2 보조 여수로의 방류능 검토

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

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

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

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

    Region of interest in this study

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

    Maximum velocity and location of Vmax according to Qa

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

    Maximum shear according to Qa

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

    Maximum water surface elevation and location of ηmax according to Qa

    Table 5.

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

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

    2.3.3 기존 여수로와 보조 여수로 방류량 배분 검토

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

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

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

    Maximum velocity on section 1 & 2 according to Qa

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

    Maximum shear on section 1 & 2 according to Qa

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

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

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

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

    Table 6.

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

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

    2.3.4 방류량 배분 비율의 허용 방류량 검토

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

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

    Table 7.

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

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

    Maximum velocity on section 1 & 2 according to total outflow

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

    Maximum shear on section 1 & 2 according to total outflow

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

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

    3. 결 론

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

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

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

    Acknowledgements

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

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    Computational Fluid Dynamics, 온실

    CFD 사용: 유압 구조 및 농업에서의 응용

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

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

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

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

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

    Abstract

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

    키워드: Computational Fluid Dynamics, 온실,

    Spillway, Settler 기사: COMEII-21048 소개 

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

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

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

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

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

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

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

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    13p

    Obrázek 44: Barevné rozlišení proudnic dle rychlosti

    Numerické modelování proudění v bezpečnostním přelivu: Numerical modeling of flow in spilway

    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.

    References

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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

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

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    기법에 대한 원천기술개발

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

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    원본 보기
    Fig. 1. Double-deck TBM tunnel example

    Flow 3D를 이용한 다목적 수로 터널의 마찰 손실 산정

    Friction loss of multi-purpose stormwater tunnel simulated by Flow 3D

    이두한1
    , 김정환2
    , 정건희2*
    1한국건설기술연구원 수자원하천연구소, 2호서대학교 토목공학과

    Abstract

    본 최근 지구의 온난화로 인하여 극한 홍수가 자주 발생하고 있으며, 기존 도시 유역의 우수배제시설 용량부족 등으로 도시홍수가 빈번하게 발생하고 있으므로, 주요 범람지역의 홍수량을 우회하거나 저류하여 홍수를 방지하기 위한 수로터널의 개발이 요구된다.

    본 연구에서는 교통기능과 수로기능을 동시에 갖춘 다기능 수로 터널의 설계 기준을 개발하기 위한 수리 실험 및 Flow3D를 이용한 수치모의을 수행하였다. 수치모의결과 동일한 수로 터널 구간 내 발생하는 마찰손실의 크기는 수치모의로 도출된 마찰손실이 이론적으로 계산한 마찰손실보다 더 크게 발생함을 관측하였으며, 이는 수로의 형상이 비원형인 경우에는 관의 기하학적 형상에 의한 흐름구조의 변화로 추가적인 마찰손실이 발생하는 것이 원인으로 판단된다.

    마찰손실의 증가는 난류보다 층류에서 두드러졌다. 따라서 터널의 홍수량 흐름 시 마찰손실계수가 터널의 형상에 좌우되며, 실무에서 정확한 설계를 위해 방수로 터널의 형상을 주의 깊게 고려해야 한다는 결론을 내렸다. 이는 실제 방수로 터널 설계에 활용될 수 있는 기본 정보를 제공할 수 있을 것으로 보인다.

    The extreme floods recently are have been attributed global warming, The development of a canal tunnel to prevent floods by making a bypass or undercurrent to flood discharge in a major flooding area is required because urban flooding in heavy rainfall occurs frequently, increasing the impermeability according to lack of capacity in sewage to urbanization by the existing urban basin. In this study, a numerical simulation was performed to support design standards for a multi-purpose waterway tunnel combined road tunnel of canal tunnel. The numerical simulation showed that the size of the friction loss occurring in the tunnel section of the same channel occurred more than the theoretically calculated frictional loss derived from the numerical simulations. This is probably due to the additional frictional loss caused by the change in the flow structure due to the geometry of the pipe when the shape of the channel is non-circular. The increase in friction loss was more pronounced in the laminar flow than in the turbulent flow. Depending on the shape of the conduit, the friction loss should be adjusted for accurate flow calculations. This result can provide the basin information about the design of flood by a pass conduit

    Fig. 1. Double-deck TBM tunnel example
    Fig. 1. Double-deck TBM tunnel example
    Table 1. Discharge cases
    Table 1. Discharge cases
    Fig. 3. Setup of geometry
    Fig. 3. Setup of geometry
    Table 2. Boundary applied model
    Table 2. Boundary applied model
    Fig. 4. Pressure value according to the 6 different discharges
    Fig. 4. Pressure value according to the 6 different discharges
    Fig. 5. Hydraulic grade line along the stormwater tunnel using FLOW-3D
    Fig. 5. Hydraulic grade line along the stormwater tunnel using FLOW-3D
    Fig. 6. Head loss compared hydraulic experiment with Flow 3D and assumed circular pipe
    Fig. 6. Head loss compared hydraulic experiment with Flow 3D and assumed circular pipe
    Table 3. Measured and calculated frictional loss coefficient in the discharge cases
    Table 3. Measured and calculated frictional loss coefficient in the discharge cases
    Fig. 7. Comparison of frictional loss coefficient according to the Reynolds number
    Fig. 7. Comparison of frictional loss coefficient according to the Reynolds number

    References

    [1] Kim, J.-H., Kwon, S.-H., Yoon, K.-S., Lee, L.-H., Chung, G.-H. Hydraulic Experiment for Friction Loss
    Coefficient in Non-circular Pipe, Procedia Engineering, Vol. 154, pp. 773-778, 2016.
    DOI: https://doi.org/10.1016/j.proeng.2017.02.354
    [2] Colebrook, C. F. and White, C. M. Experiments with fluid- friction in roughened pipes, Proc. Royal Soc.
    London, 161, 367-381, 1937.
    DOI: https://doi.org/10.1098/rspa.1937.0150
    [3] Flow Science Inc. FLOW-3D User’s Manual, 2015
    [4] Jeong, C.-S. Discharge coefficient of side weir for various curvatures simulated by FLOW-3D, Korea Water Resources Association, 2011.
    [5] Kang, S.-H. A comparison of hydraulic phenomenon in inlet and outlet point in retention reservoir using FLOW-3D model and hydraulic experiment, Donga University, 2012.
    [6] Seoul General planning for reducing traffic of surface road, 2015.
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    [8] Yen, Ben Chie. Channel flow resistance: centennial of Manning’s formula, Water Resources Publications, 1992.

    그림 1. 실험수로 평면도(Agaccioglu, 1998)

    FLOW-3D를 이용한 다양한 곡률에 대한 횡월류 위어의 유량계수 산정

    Discharge Coefficient of Side Weir for Various Curvatures Simulated
    by FLOW-3D

    Chang Sam Jeong*
    접수일자: 2015년 5월 15일/심사완료일: 2015년 6월 9일/게재일자: 2015년 6월 30일

    ABSTRACT

    본 연구는 수치모형을 이용하여 만곡수로 외측에 설치된 횡월류 위어의 곡률반경에 대한 횡월류 유량계수를 분석한 연구이다.

    곡률반경의 변화에 따른 만곡부의 중심각이 180°인 수로모형을 설계하였으며, FLOW-3D모형에 적용하여 유량계 수를 산정하고 직선 수로와 비교하는 방법으로 유량계수의 특성을 분석하였다. 모형의 적용성 검증을 위해 기존에 연구되었던 수리실험과 동일한 조건의 수치모의를 수행하였다.

    하폭(b)을 고정시키고 곡률반경(Rc)을 변화시킴으로써 Rc/b의 변화에 따른 유량계수(CM)의 변화를 분석하고, 만곡수로의 월류량(Qwc)에 대한 직선수로의 월류량(Qwc)의 비를 분석하였다.

    분석결과 유량 계수는 상류수심, 만곡수로의 곡률반경의 변화에 따라 유량계수는 변화하였으며, 직선과 만곡수로에 대해 분석을 수행하였기 때문에 직선수로의 영향인자를 이용하여 만곡수로에 설치된 횡월류 위어의 월류량과 유량계수를 추정 가능 할 것이라 판단된다.

    KEYWORDS

    discharge coefficient, side weir, curvature, meandering channel, FLOW-3D, 유량계수, 횡월류 위어, 곡률, 만곡수로

    서 론

    최근의 기상변화에 의한 이상홍수와 유역의 도시화로 인한 불투수면적의 증가는 홍수시 유출량을 증가시켜 기 존의 하도의 적정 소통량을 초과하는 홍수를 발생시키고 있다. 토지의 고도 이용으로 하도의 확폭이 제한된 도시유 역에서 초과 홍수에 대비할 수 있는 구조적 홍수관리 방안 은 제방 증고, 저류지 설치, 방수로 설치 등이 대표적이다. 저류지는 하천에 유입되는 홍수를 일시 조절하여 하도의 적정한 홍수 소통능력을 초과하는 유출을 억제하는 구조 물로 국내외에서 널리 이용되는 구조적 홍수대책의 하나 이다. 그러나 이러한 활용도에 비해서 예연위어, 광정위어,암거 등의 수리구조물에 비교할 때 횡월류 위어에 대한 연 구는 미진한 것이 현실이다. 횡월류 위어(side weir 또는 lateral weir)는 인공수로 또는 자연하천에서 흐름방향에 평행하게 수로측면에 설치된 수 공구조물이다.

    이는 본류의 수심이 횡월류 위어 월류부의 높이보다 높을 경우 위어를 통하여 물을 월류시켜 에너지 소산, 수위조절, 일정 유량의 취수 및 분배, 초과 홍수량 전 환 등의 목적으로 이용된다. 이러한 횡월류 유량의 취수 및 분배, 초과 홍수량 전환 등의 목적으로 이용된다. 이러한 횡월류 위어는 off-line저류지, 관계수로, 하수도 설비, 댐의 여수로 등에서 폭넓게 사용되고 있다.

    국내의 경우 개발에 따른 횡월류 위어 구조물의 사용이 증가하는 추세이나, 유입유량 결정이나 적용되는 유량계 수에 대한 신뢰할만한 평가가 이루어지지 않아서 설계에 어려움을 겪고 있다. 또한 지금까지 연구된 횡월류 위어는 직선수로에 국한되어있으며, 실험을 통해서 제안된 유량 계수식들은 제안자에 따라 편차가 커서 실무적으로 이용 되기에는 많은 한계를 가지고 있다. Cheong(1991)은 횡월류 위어의 단면을 사다리꼴로하여 상류 프루드수와 유량계수와의 관계를 정립하였다.

    Uyumaz (1997)는 U-모양 단면의 주수로의 횡월류 위어에서 사류와 상류시의 유량계수의 변화를 파악하였으며, Agaccioglu (1998)는 만곡수로의 사각형 단면에서 중심각에 따른 유량 계수와 무차원변수와의 관계를 정립하고, 퇴적이 발생하 는 지역의 크기는 상류 프루드수에 영향을 받는 다는 것을 확인 하였으며, Agaccioglu(2004)는 만곡수로에서 횡월류 위어의 단면을 삼각형으로 하여 중심각에 따른 유량계수 와 무차원 변수와의 관계를 정립하였다. 국내에서 윤세의 (1990)는 곡률반경에 대한 하폭의 비(Rc/b)의 변화에 따른 만곡수로에서의 흐름특성을 분석하였고, 이종태(1991)는 곡률반경의 증가, 감소는 만곡부 흐름특성인자에 많은 영 향을 끼치는 것을 확인 하였다.

    서일원 등(2004)이 실내 실 험을 수행하여 다중 만곡수로에서 이차류의 변화양상을 관찰하였고, 이두한 등(2005)은 복단면을 갖는 사행수로에 서 만곡부의 저수로와 홍수터에서 회전류가 발생함을 관 측하였으며, 홍수심이 증가 할수록 저수로와 고수로간의 유속 차이보다 사행의 영향이 지배적임을 분석하였다.

    본 연구에서는 기존에 연구된 만곡수로에 설치된 횡월류 위어를 상용 3차원 CFD모형인 FLOW-3D를 이용하여 횡 월류 위어의 흐름을 모의하여 그 적용성을 검증하고, 곡률 변화에 따른 만곡부 횡월류 위어에서의 유량계수와 여러 변수들과의 관계를 정립하고 특성을 분석하는데 목적이 있다.

    또한 만곡수로에 횡월류 위어를 설치하였을 때, 그 흐름 특성의 변화를 분석하여, 횡월류 위어 주변의 수심 및 유속변화, 월류량에 영향을 미치는 인자들을 관찰하고, 월 류량에 가장 직접적인 영향을 미치는 인자인 유량계수를 산정하여 영향인자들과의 관계를 무차원하여 분석하여 만 곡부에 설치된 횡월류 위어의 실용적인 기준으로 활용할 수 있는 자료를 제시하고자 한다.

    그림 1. 실험수로 평면도(Agaccioglu, 1998)
    그림 1. 실험수로 평면도(Agaccioglu, 1998)
    그림 2. Fr1에 따른 유량계수(Agaccioglu, 1998)
    그림 2. Fr1에 따른 유량계수(Agaccioglu, 1998)
    그림 3. Fr1에 따른 유량계수(3D 수치모의)
    그림 3. Fr1에 따른 유량계수(3D 수치모의)
    그림 4. 직선수로의 지오메트리와 mesh block
    그림 4. 직선수로의 지오메트리와 mesh block
    그림 5. 만곡 수로(Rc = 2.5 m)의 지오메트리와 mesh block
    그림 5. 만곡 수로(Rc = 2.5 m)의 지오메트리와 mesh block
    표 2. Case별 설계 수로의 제원
    표 2. Case별 설계 수로의 제원
    그림 6. 횡월류 위어에서의 수면형(0.04 m3 /sec)
    그림 6. 횡월류 위어에서의 수면형(0.04 m3 /sec)
    그림 7. 횡월류 위어에서의 수면형(0.06 m3 /sec)
    그림 7. 횡월류 위어에서의 수면형(0.06 m3 /sec)
    그림 8. 횡월류 위어에서의 수면형(0.1 m3 /sec)
    그림 8. 횡월류 위어에서의 수면형(0.1 m3 /sec)
    그림 9. Rc/b에 따른 CMC/CMS의 변화
    그림 9. Rc/b에 따른 CMC/CMS의 변화
    그림 10. 유량에 대한 CMC/CMS의 변화
    그림 10. 유량에 대한 CMC/CMS의 변화

    참고문헌

    1. 서일원, 성기훈, 백경오, 정성진(2004) 사행수로에서흐름특성에 관한 실험적 연구, 한국수자원학회논문집, 37(7), pp.527~540.
    2. 이두한, 이찬주, 김명환(2005) 복단면 사행 하도의 흐름 특성에 대한 실험 연구, 대한토목학회 논문집, 25(3B), pp.197~206.
    3. 이종태, 윤세의(1991) 만곡부 곡률의 연속적 변화와 흐름특성, 대한토목학회 학술발표회 개요집, pp.394~397.
    4. 윤세의, 이종태(1990) 만곡수로에서의 곡률반경 변화에 따른 흐름특성, 한국수문학회지, 23(4), pp.435~444.
    5. Agaccioglu, H., Yalcin, Y. (1998) Side-Weir Flow in Curved Channels, Journal of Irrigation and Drainage Engineering, 124(3), pp.163~175.
    6. Agaccioglu, H., Ali, C. (2004) Discharge Coefficient of a Triangular Side-Weir Located on a Curved Channels, Journal of Irrigation and Drainage Engineering, 130(5), pp.410~423.
    7. Cheong, H. F. (1991) Discharge coefficient of lateral diversion from trapezoidal channel, Journal of Irrigation and Drainage Engineering, 117(4), pp.461~475.
    8. Uyumaz, A. (1997) Side Weir in U-Shaped Channels Journal of Hydraulics Engineering. 123(7), pp.639~646.
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].

    Application of Numerical and Experimental Modeling to Improve the Efficiency of Parshall Flumes: A Review of the State-of-the-Art

    Parshall Flumes의 효율성 향상을 위한 수치 및 실험 모델링의 적용: 최신 기술 검토

    Mehdi Heyrani 1,* , Abdolmajid Mohammadian 1, Ioan Nistor 1 and Omerul Faruk Dursun 2

    Abstract

    열린 채널에서 흐름을 관리하는 기본 단계 중 하나는 속성을 결정하는 것입니다. 개방 수로의 흐름에 관한 추가 정보를 제공하기 위해 경험적 방정식이 개발되었습니다. 이러한 실험 방정식을 얻는 것은 비용과 시간이 많이 소요됩니다. 따라서 대체 솔루션이 모색되었습니다.

    지난 세기 동안 움직이는 부분이 없는 정적 측정 장치인 Parshall 수로가 개방 수로의 흐름을 측정하는 데 중요한 역할을 했습니다. 많은 연구자들이 관개 및 폐수 관리와 같은 다양한 분야에서 Parshall 수로의 적용을 연구하는 데 관심을 집중해 왔습니다.

    여러 학자들이 실험 결과를 사용하여 Parshall 수로의 등급 방정식을 향상시켰지만 다른 학자들은 수치 시뮬레이션을 사용하여 높이-방전 관계 방정식을 재보정하기 위해 대체 데이터 소스를 사용했습니다. 컴퓨팅 하드웨어가 지난 수십 년 동안 크게 발전하여 과거에 경험했던 제한된 해상도를 뛰어넘는 것이 가능해짐에 따라 CFD(Computational Fluid Dynamic) 소프트웨어가 오늘날 대중화되고 있습니다.

    여러 CFD 모델은 가용성에 따라 오픈 소스 또는 상업적으로 허가되어 수위 결과를 생성하기 위해 다양한 구성의 수로, 특히 Parshall 수로에 대한 수치 시뮬레이션을 수행하는 데 사용되었습니다.

    FLOW-3D, Ansys Fluent, OpenFOAM 등 지금까지 사용되어 온 다양한 CFD 도구에 대해 실험 데이터로 정밀 교정한 결과, 출력이 안정적이고 실제 시나리오에 구현할 수 있음이 확인되었습니다.

    결과를 생성하기 위해 이 기술을 사용하는 이점은 필요한 경우 유속 또는 구조적 형상과 같은 초기 조건을 조정하는 CFD 접근 방식의 능력입니다. 수로 크기와 수로가 위치한 부지의 조건과 관련하여 상황에 적합한 특정 Parshall 수로로 선택이 좁혀집니다.

    표준 Parshall 수로를 선택하는 것이 항상 가능한 것은 아닙니다. 따라서 엔지니어는 가장 가까운 수로 크기에 약간의 수정을 제공하고 정확한 유량을 생성하기 위해 새로운 등급 곡선을 제공합니다.

    이 검토는 기존 등급 방정식을 향상시키거나 구조의 기하학에 대한 추가 수정을 제안하기 위해 Parshall 수로에서 수치 시뮬레이션 및 물리적 실험 데이터의 적용을 목표로 하는 여러 학자의 작업에 대해 수행되었습니다.

    One of the primary steps in managing the flow in an open channel is determining its properties. Empirical equations are developed to provide further information regarding the flow in open channels. Obtaining such experimental equations is expensive and time consuming; therefore, alternative solutions have been sought. Over the last century, the Parshall flume, a static measuring device with no moving parts, has played a significant role in measuring the flow in open channels. Many researchers have focused their interest on studying the application of Parshall flumes in various fields like irrigation and wastewater management. Although various scholars used experimental results to enhance the rating equation of the Parshall flume, others used an alternative source of data to recalibrate the height–discharge relation equation using numerical simulation. Computational Fluid Dynamic (CFD) software is becoming popular nowadays as computing hardware has advanced significantly within the last few decades, making it possible to go beyond the limited resolution that was experienced in the past. Multiple CFD models, depending on their availability, either open-source or commercially licensed, have been used to perform numerical simulations on different configurations of flumes, especially Parshall flumes, to produce water level results. Regarding various CFD tools that have been used, i.e., FLOW-3D, Ansys Fluent, or OpenFOAM, after precise calibration with experimental data, it has been determined that the output is reliable and can be implemented to the actual scenarios. The benefit of using this technique to produce results is the ability of the CFD approach to adjust the initial conditions, like flow velocity or structural geometry, where necessary. With respect to channel size and the condition of the site where the flume is located, the choices are narrowed to the specific Parshall flume suitable to the situation. It is not always possible to select the standard Parshall flume; therefore, engineers provide some modification to the closest flume size and provide a new rating curve to produce accurate flowrates. This review has been performed on the works of a number of scholars who targeted the application of numerical simulation and physical experimental data in Parshall flumes to either enhance the existing rating equation or propose further modification to the structure’s geometry.

    Keywords

    Parshall flume; CFD; OpenFOAM; FLOW-3D; numerical simulation; turbulence model

    Figure 1. Parshall flume measuring structure, installed [2].
    Figure 1. Parshall flume measuring structure, installed [2].
    Figure 2. Parshall flume measuring structure, uninstalled [3]
    Figure 2. Parshall flume measuring structure, uninstalled [3]
    Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells; (b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].
    Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells; (b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].
    Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b) demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from Ref. [11]. 2020 ELSEVIER). ).
    Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b) demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from Ref. [11]. 2020 ELSEVIER). ).
    Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]
    Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]
    Figure 11. Experimental setup: contraction ratio used on each flume [23].
    Figure 11. Experimental setup: contraction ratio used on each flume [23].
    Figure 12. Entire flume geometry [25]
    Figure 12. Entire flume geometry [25]

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    1. Ribeiro, Á.S.; Sousa, J.A.; Simões, C.; Martins, L.L.; Dias, L.; Mendes, R.; Martins, C. Parshall Flumes Flow Rate Uncertainty
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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.