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.

Peer review under responsibility of Ain Shams University.

© 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

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

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

Abstract

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

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

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

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

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

Details

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

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

Published inProceedings of HYDRO 2022 Conference

Pagination9

PagesPaper 27.02

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

Date2022

Keywords

scourplunge poolspillwaynumerical modellingFLOW-3D

Note[1390]

LaboratoriesLCH
PL-LCH

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

Record creation date2022-09-14

Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).

Application of Computational Fluid Dynamics in Chlorine-Dynamics Modeling of In-Situ Chlorination Systems for Cooling Systems

Jongchan Yi 1, Jonghun Lee 1, Mohd Amiruddin Fikri 2,3, Byoung-In Sang 4 and Hyunook Kim 1,*

Abstract

염소화는 상대적인 효율성과 저렴한 비용으로 인해 발전소 냉각 시스템에서 생물학적 오염을 제어하는​​데 선호되는 방법입니다. 해안 지역에 발전소가 있는 경우 바닷물을 사용하여 현장에서 염소를 전기화학적으로 생성할 수 있습니다. 이를 현장 전기염소화라고 합니다. 이 접근 방식은 유해한 염소화 부산물이 적고 염소를 저장할 필요가 없다는 점을 포함하여 몇 가지 장점이 있습니다. 그럼에도 불구하고, 이 전기화학적 공정은 실제로는 아직 초기 단계에 있습니다. 이 연구에서는 파일럿 규모 냉각 시스템에서 염소 붕괴를 시뮬레이션하기 위해 병렬 1차 동역학을 적용했습니다. 붕괴가 취수관을 따라 발생하기 때문에 동역학은 전산유체역학(CFD) 코드에 통합되었으며, 이후에 파이프의 염소 거동을 시뮬레이션하는데 적용되었습니다. 실험과 시뮬레이션 데이터는 강한 난류가 형성되는 조건하에서도 파이프 벽을 따라 염소 농도가 점진적인 것으로 나타났습니다. 염소가 중간보다 파이프 표면을 따라 훨씬 더 집중적으로 남아 있다는 사실은 전기 염소화를 기반으로 하는 시스템의 전체 염소 요구량을 감소시킬 수 있었습니다. 현장 전기 염소화 방식의 냉각 시스템은 직접 주입 방식에 필요한 염소 사용량의 1/3만 소비했습니다. 따라서 현장 전기염소화는 해안 지역의 발전소에서 바이오파울링 제어를 위한 비용 효율적이고 환경 친화적인 접근 방식으로 사용될 수 있다고 결론지었습니다.

Chlorination is the preferred method to control biofouling in a power plant cooling system due to its comparative effectiveness and low cost. If a power plant is located in a coastal area, chlorine can be electrochemically generated in-situ using seawater, which is called in-situ electrochlorination; this approach has several advantages including fewer harmful chlorination byproducts and no need for chlorine storage. Nonetheless, this electrochemical process is still in its infancy in practice. In this study, a parallel first-order kinetics was applied to simulate chlorine decay in a pilot-scale cooling system. Since the decay occurs along the water-intake pipe, the kinetics was incorporated into computational fluid dynamics (CFD) codes, which were subsequently applied to simulate chlorine behavior in the pipe. The experiment and the simulation data indicated that chlorine concentrations along the pipe wall were incremental, even under the condition where a strong turbulent flow was formed. The fact that chlorine remained much more concentrated along the pipe surface than in the middle allowed for the reduction of the overall chlorine demand of the system based on the electro-chlorination. The cooling system, with an in-situ electro-chlorination, consumed only 1/3 of the chlorine dose demanded by the direct injection method. Therefore, it was concluded that in-situ electro-chlorination could serve as a cost-effective and environmentally friendly approach for biofouling control at power plants on coastal areas.

Keywords

computational fluid dynamics; power plant; cooling system; electro-chlorination; insitu chlorination

Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
Figure 1. Electrodes and batch experiment set-up. (a) Two cylindrical electrodes used in this study. (b) Batch experiment set-up for kinetic tests.
Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
Figure 2. Schematic diagram for pilot-scale cooling-water circulation system (a) along with a real picture of the system (b).
Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
Figure 3. Free chlorine decay curves in seawater with different TOC and initial chlorine concentration. Each line represents the predicted concentration of chlorine under a given condition. (a) Artificial seawater solution with 1 mg L−1 of TOC; (b) artificial seawater solution with 2 mg L−1 of TOC; (c) artificial seawater solution with 3 mg L−1 of TOC; (d) West Sea water (1.3 mg L−1 of TOC).
Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
Figure 4. Correlation between model and experimental data in the chlorine kinetics using seawater.
Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
Figure 5. Free chlorine concentrations in West Sea water under different current conditions in an insitu electro-chlorination system.
Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
Figure 6. Free chlorine distribution along the sampling ports under different flow rates. Each dot represents experimental data, and each point on the black line is the expected chlorine concentration obtained from computational fluid dynamics (CFD) simulation with a parallel first-order decay model. The red-dotted line is the desirable concentration at the given flow rate: (a) 600 L min−1 of flow rate, (b) 700 L min−1 of flow rate, (c) 800 L min−1 of flow rate, (d) 900 L min−1 of flow rate.
Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
Figure 7. Fluid contour images from CFD simulation of the electro-chlorination experiment. Inlet flow rate is 800 L min−1. Outlet pressure was set to 10.8 kPa. (a) Chlorine concentration; (b) expanded view of electrode side in image (a); (c) velocity magnitude; (d) pressure.
Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
Figure 8. Chlorine concentration contour in the simulation of full-scale in-situ electro-chlorination with different cathode positions. The pipe diameter is 2 m and the flow rate is 14 m3 s−1. The figure shows 10 m of the pipeline. (a) The simulation result when the cathode is placed on the surface of the pipe wall. (b) The simulation result when the cathode is placed on the inside of the pipe with 100 mm of distance from the pipe wall.
Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.
Figure 9. Comparison of in-situ electro-chlorination and direct chlorine injection in full-scale applications. (a) Estimated chlorine concentrations along the pipe surface. (b) Relative chlorine demands.

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

Numerical investigation of scour characteristics downstream of blocked culverts

막힌 암거 하류의 세굴 특성 수치 조사

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

Abstract

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

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

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

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

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

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

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

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

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

1. Introduction

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

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

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

2. Experimental data

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

3. Dimensional analysis

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

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

4. Numerical work

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

Governing equations

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

ρ is the fluid density,

VF is the volume fraction,

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

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

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

RDIF is the turbulent diffusion.

P is the average hydrodynamic pressure,

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

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

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

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

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

d* is the dimensionless grain size

Gs is specific weight (Gs = ρs/ρ)

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

Meshing and geometry of model

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

Boundary condition

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

5. Validation of experimental results and numerical results

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

6. Computation time

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

7. Analysis and discussions

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

Table 1. The scour results of different blockage ratio.

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

7.1. Scour hole geometry

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

7.2. Flow water surface

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

7.3. Velocity vectors

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

7.4. Velocity distribution

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

7.5. Bed velocity distribution

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

8. Maximum scour depth prediction

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

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

9. Comparison with previous scour equations

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

Table 2. Comparison of some previous scour formula.

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

10. Conclusions

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

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

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

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

Declaration of Competing Interest

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

References

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

Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

기계 학습 기술에 의한 불확실성 하에서 다중 이해 관계자 계단형 배수로 설계의 충돌 해결

Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

Mehrdad GhorbaniMooseluaMohammad RezaNikoobParnian HashempourBakhtiaribNooshin BakhtiariRayanicAzizallahIzadyd
aDepartment of Engineering Sciences, University of Agder, Norway
bDepartment of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran
cSchool of Engineering, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, IrandWater Research Center, Sultan Qaboos University, Muscat, Oman

Abstract

The optimal spillway design is of great significance since these structures can reduce erosion downstream of the dams. This study proposes a risk-based optimization framework for a stepped spillway to achieve an economical design scenario with the minimum loss in hydraulic performance. Accordingly, the stepped spillway was simulated in the FLOW-3D® model, and the validated model was repeatedly performed for various geometric states.

The results were used to form a Multilayer Perceptron artificial neural network (MLP-ANN) surrogate model. Then, a risk-based optimization model was formed by coupling the MLP-ANN and NSGA-II. The concept of conditional value at risk (CVaR) was utilized to reduce the risk of the designed spillway malfunctions in high flood flow rates, while minimizing the construction cost and the loss in hydraulic performance.

Lastly, given the conflicting objectives of stakeholders, the non-cooperative graph model for conflict resolution (GMCR) was applied to achieve a compromise on the Pareto optimal solutions. Applicability of the suggested approach in the Jarreh Dam, Iran, resulted in a practical design scenario, which simultaneously minimizes the loss in hydraulic performance and the project cost and satisfies the priorities of decision-makers.

Keywords

Stepped spillway, FLOW-3D® ,CVaR-based optimization model, GMCR-plus, NSGA-II

최적의 배수로 설계는 이러한 구조가 댐 하류의 침식을 줄일 수 있기 때문에 매우 중요합니다. 본 연구에서는 유압 성능 손실을 최소화하면서 경제적인 설계 시나리오를 달성하기 위해 계단형 여수로에 대한 위험 기반 최적화 프레임워크를 제안합니다. 따라서 FLOW-3D® 모델에서 계단식 배수로를 시뮬레이션하고 다양한 기하학적 상태에 대해 검증된 모델을 반복적으로 수행했습니다.

결과는 다층 퍼셉트론 인공 신경망(MLP-ANN) 대리 모델을 형성하는 데 사용되었습니다. 그런 다음 MLP-ANN과 NSGA-II를 결합하여 위험 기반 최적화 모델을 구성했습니다. 위험 조건부 값(CVaR)의 개념은 높은 홍수 유량에서 설계된 방수로 오작동의 위험을 줄이는 동시에 건설 비용과 수리 성능 손실을 최소화하기 위해 활용되었습니다.

마지막으로 이해관계자의 상충되는 목표를 고려하여 파레토 최적해에 대한 절충안을 달성하기 위해 갈등 해결을 위한 비협조적 그래프 모델(GMCR)을 적용하였다. 이란 Jarreh 댐에서 제안된 접근 방식의 적용 가능성은 수력 성능 손실과 프로젝트 비용을 동시에 최소화하고 의사 결정자의 우선 순위를 만족시키는 실용적인 설계 시나리오로 귀결되었습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

1Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
2William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, 151 W. Woodruff Ave., Columbus, OH 43210, USA
*Author to whom correspondence should be addressed.
Sensors 202020(11), 3030; https://doi.org/10.3390/s20113030
Received: 16 April 2020 / Revised: 21 May 2020 / Accepted: 25 May 2020 / Published: 27 May 2020
(This article belongs to the Special Issue Lab-on-a-Chip and Microfluidic Sensors)

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

Keywords: particle magnetophoresisCFDcross sectionchip fabrication

Korea Abstract

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를위한 기능화 된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드를 자기 적으로 회수하여 분석 또는 진단 테스트를 수행 할 수 있습니다. 연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 

따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다. 그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는 데있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜주의를 기울였습니다. 

여기에서 우리는 자기 비드가 혈액에서 분리되고 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 YY 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다. 

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증 된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다. 우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 

따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1. (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and U-shaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Numerical investigation of flow characteristics over stepped spillways

Güven, Aytaç
Mahmood, Ahmed Hussein
Water Supply (2021) 21 (3): 1344–1355.
https://doi.org/10.2166/ws.2020.283Article history

Abstract

Spillways are constructed to evacuate flood discharge safely so that a flood wave does not overtop the dam body. There are different types of spillways, with the ogee type being the conventional one. A stepped spillway is an example of a nonconventional spillway. The turbulent flow over a stepped spillway was studied numerically by using the Flow-3D package. Different fluid flow characteristics such as longitudinal flow velocity, temperature distribution, density and chemical concentration can be well simulated by Flow-3D. In this study, the influence of slope changes on flow characteristics such as air entrainment, velocity distribution and dynamic pressures distribution over a stepped spillway was modelled by Flow-3D. The results from the numerical model were compared with an experimental study done by others in the literature. Two models of a stepped spillway with different discharge for each model were simulated. The turbulent flow in the experimental model was simulated by the Renormalized Group (RNG) turbulence scheme in the numerical model. A good agreement was achieved between the numerical results and the observed ones, which are exhibited in terms of graphics and statistical tables.

배수로는 홍수가 댐 몸체 위로 넘치지 않도록 안전하게 홍수를 피할 수 있도록 건설되었습니다. 다른 유형의 배수로가 있으며, ogee 유형이 기존 유형입니다. 계단식 배수로는 비 전통적인 배수로의 예입니다. 계단식 배수로 위의 난류는 Flow-3D 패키지를 사용하여 수치적으로 연구되었습니다.

세로 유속, 온도 분포, 밀도 및 화학 농도와 같은 다양한 유체 흐름 특성은 Flow-3D로 잘 시뮬레이션 할 수 있습니다. 이 연구에서는 계단식 배수로에 대한 공기 혼입, 속도 분포 및 동적 압력 분포와 같은 유동 특성에 대한 경사 변화의 영향을 Flow-3D로 모델링 했습니다.

수치 모델의 결과는 문헌에서 다른 사람들이 수행한 실험 연구와 비교되었습니다. 각 모델에 대해 서로 다른 배출이 있는 계단식 배수로의 두 모델이 시뮬레이션되었습니다. 실험 모델의 난류 흐름은 수치 모델의 Renormalized Group (RNG) 난류 계획에 의해 시뮬레이션되었습니다. 수치 결과와 관찰 된 결과 사이에 좋은 일치가 이루어졌으며, 이는 그래픽 및 통계 테이블로 표시됩니다.

HIGHLIGHTS

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  • A numerical model was developed for stepped spillways.
  • The turbulent flow was simulated by the Renormalized Group (RNG) model.
  • Both numerical and experimental results showed that flow characteristics are greatly affected by abrupt slope change on the steps.

Keyword

CFDnumerical modellingslope changestepped spillwayturbulent flow

INTRODUCTION

댐 구조는 물 보호가 생활의 핵심이기 때문에 물을 저장하거나 물을 운반하는 전 세계에서 가장 중요한 프로젝트입니다. 그리고 여수로는 댐의 가장 중요한 부분 중 하나로 분류됩니다. 홍수로 인한 파괴 나 피해로부터 댐을 보호하기 위해 여수로가 건설됩니다.

수력 발전, 항해, 레크리에이션 및 어업의 중요성을 감안할 때 댐 건설 및 홍수 통제는 전 세계적으로 매우 중요한 문제로 간주 될 수 있습니다. 많은 유형의 배수로가 있지만 가장 일반적인 유형은 다음과 같습니다 : ogee 배수로, 자유 낙하 배수로, 사이펀 배수로, 슈트 배수로, 측면 채널 배수로, 터널 배수로, 샤프트 배수로 및 계단식 배수로.

그리고 모든 여수로는 입구 채널, 제어 구조, 배출 캐리어 및 출구 채널의 네 가지 필수 구성 요소로 구성됩니다. 특히 롤러 압축 콘크리트 (RCC) 댐 건설 기술과 더 쉽고 빠르며 저렴한 건설 기술로 분류 된 계단식 배수로 건설과 관련하여 최근 수십 년 동안 많은 계단식 배수로가 건설되었습니다 (Chanson 2002; Felder & Chanson 2011).

계단식 배수로 구조는 캐비테이션 위험을 감소시키는 에너지 소산 속도를 증가시킵니다 (Boes & Hager 2003b). 계단식 배수로는 다양한 조건에서 더 매력적으로 만드는 장점이 있습니다.

계단식 배수로의 흐름 거동은 일반적으로 낮잠, 천이 및 스키밍 흐름 체제의 세 가지 다른 영역으로 분류됩니다 (Chanson 2002). 유속이 낮을 때 nappe 흐름 체제가 발생하고 자유 낙하하는 낮잠의 시퀀스로 특징 지워지는 반면, 스키밍 흐름 체제에서는 물이 외부 계단 가장자리 위의 유사 바닥에서 일관된 흐름으로 계단 위로 흐릅니다.

또한 주요 흐름에서 3 차원 재순환 소용돌이가 발생한다는 것도 분명합니다 (예 : Chanson 2002; Gonzalez & Chanson 2008). 계단 가장자리 근처의 의사 바닥에서 흐름의 방향은 가상 바닥과 가상으로 정렬됩니다. Takahashi & Ohtsu (2012)에 따르면, 스키밍 흐름 체제에서 주어진 유속에 대해 흐름은 계단 가장자리 근처의 수평 계단면에 영향을 미치고 슈트 경사가 감소하면 충돌 영역의 면적이 증가합니다. 전이 흐름 체제는 나페 흐름과 스키밍 흐름 체제 사이에서 발생합니다. 계단식 배수로를 설계 할 때 스키밍 흐름 체계를 고려해야합니다 (예 : Chanson 1994, Matos 2000, Chanson 2002, Boes & Hager 2003a).

CFD (Computational Fluid Dynamics), 즉 수력 공학의 수치 모델은 일반적으로 물리적 모델에 소요되는 총 비용과 시간을 줄여줍니다. 따라서 수치 모델은 실험 모델보다 빠르고 저렴한 것으로 분류되며 동시에 하나 이상의 목적으로 사용될 수도 있습니다. 사용 가능한 많은 CFD 소프트웨어 패키지가 있지만 가장 널리 사용되는 것은 FLOW-3D입니다. 이 연구에서는 Flow 3D 소프트웨어를 사용하여 유량이 서로 다른 두 모델에 대해 계단식 배수로에서 공기 농도, 속도 분포 및 동적 압력 분포를 시뮬레이션합니다.

Roshan et al. (2010)은 서로 다른 수의 계단 및 배출을 가진 계단식 배수로의 두 가지 물리적 모델에 대한 흐름 체제 및 에너지 소산 조사를 연구했습니다. 실험 모델의 기울기는 각각 19.2 %, 12 단계와 23 단계의 수입니다. 결과는 23 단계 물리적 모델에서 관찰 된 흐름 영역이 12 단계 모델보다 더 수용 가능한 것으로 간주되었음을 보여줍니다. 그러나 12 단계 모델의 에너지 손실은 23 단계 모델보다 더 많았습니다. 그리고 실험은 스키밍 흐름 체제에서 23 단계 모델의 에너지 소산이 12 단계 모델보다 약 12 ​​% 더 적다는 것을 관찰했습니다.

Ghaderi et al. (2020a)는 계단 크기와 유속이 다른 정련 매개 변수의 영향을 조사하기 위해 계단식 배수로에 대한 실험 연구를 수행했습니다. 그 결과, 흐름 체계가 냅페 흐름 체계에서 발생하는 최소 scouring 깊이와 같은 scouring 구멍 치수에 영향을 미친다는 것을 보여주었습니다. 또한 테일 워터 깊이와 계단 크기는 최대 scouring깊이에 대한 실제 매개 변수입니다. 테일 워터의 깊이를 6.31cm에서 8.54 및 11.82cm로 늘림으로써 수세 깊이가 각각 18.56 % 및 11.42 % 증가했습니다. 또한 이 증가하는 테일 워터 깊이는 scouring 길이를 각각 31.43 % 및 16.55 % 감소 시킵니다. 또한 유속을 높이면 Froude 수가 증가하고 흐름의 운동량이 증가하면 scouring이 촉진됩니다. 또한 결과는 중간의 scouring이 횡단면의 측벽보다 적다는 것을 나타냅니다. 계단식 배수로 하류의 최대 scouring 깊이를 예측 한 후 실험 결과와 비교하기 위한 실험식이 제안 되었습니다. 그리고 비교 결과 제안 된 공식은 각각 3.86 %와 9.31 %의 상대 오차와 최대 오차 내에서 scouring 깊이를 예측할 수 있음을 보여주었습니다.

Ghaderi et al. (2020b)는 사다리꼴 미로 모양 (TLS) 단계의 수치 조사를 했습니다. 결과는 이러한 유형의 배수로가 확대 비율 LT / Wt (LT는 총 가장자리 길이, Wt는 배수로의 폭)를 증가시키기 때문에 더 나은 성능을 갖는 것으로 관찰되었습니다. 또한 사다리꼴 미로 모양의 계단식 배수로는 더 큰 마찰 계수와 더 낮은 잔류 수두를 가지고 있습니다. 마찰 계수는 다양한 배율에 대해 0.79에서 1.33까지 다르며 평평한 계단식 배수로의 경우 대략 0.66과 같습니다. 또한 TLS 계단식 배수로에서 잔류 수두의 비율 (Hres / dc)은 약 2.89이고 평평한 계단식 배수로의 경우 약 4.32와 같습니다.

Shahheydari et al. (2015)는 Flow-3D 소프트웨어, RNG k-ε 모델 및 VOF (Volume of Fluid) 방법을 사용하여 배출 계수 및 에너지 소산과 같은 자유 표면 흐름의 프로파일을 연구하여 스키밍 흐름 체제에서 계단식 배수로에 대한 흐름을 조사했습니다. 실험 결과와 비교했습니다. 결과는 에너지 소산 율과 방전 계수율의 관계가 역으로 실험 모델의 결과와 잘 일치 함을 보여 주었다.

Mohammad Rezapour Tabari & Tavakoli (2016)는 계단 높이 (h), 계단 길이 (L), 계단 수 (Ns) 및 단위 폭의 방전 (q)과 같은 다양한 매개 변수가 계단식 에너지 ​​소산에 미치는 영향을 조사했습니다. 방수로. 그들은 해석에 FLOW-3D 소프트웨어를 사용하여 계단식 배수로에서 에너지 손실과 임계 흐름 깊이 사이의 관계를 평가했습니다. 또한 유동 난류에 사용되는 방정식과 표준 k-ɛ 모델을 풀기 위해 유한 체적 방법을 적용했습니다. 결과에 따르면 스텝 수가 증가하고 유량 배출량이 증가하면 에너지 손실이 감소합니다. 얻은 결과를 다른 연구와 비교하고 경험적, 수학적 조사를 수행하여 결국 합격 가능한 결과를 얻었습니다.

METHODOLOGY

ListenReadSpeaker webReader: ListenFor all numerical models the basic principle is very similar: a set of partial differential equations (PDE) present the physical problems. The flow of fluids (gas and liquid) are governed by the conservation laws of mass, momentum and energy. For Computational Fluid Dynamics (CFD), the PDE system is substituted by a set of algebraic equations which can be worked out by using numerical methods (Versteeg & Malalasekera 2007). Flow-3D uses the finite volume approach to solve the Reynolds Averaged Navier-Stokes (RANS) equation, by applying the technique of Fractional Area/Volume Obstacle Representation (FAVOR) to define an obstacle (Flow Science Inc. 2012). Equations (1) and (2) are RANS and continuity equations with FAVOR variables that are applied for incompressible flows.

formula

(1)

formula

(2)where  is the velocity in xi direction, t is the time,  is the fractional area open to flow in the subscript directions,  is the volume fraction of fluid in each cell, p is the hydrostatic pressure,  is the density, is the gravitational force in subscript directions and  is the Reynolds stresses.

Turbulence modelling is one of three key elements in CFD (Gunal 1996). There are many types of turbulence models, but the most common are Zero-equation models, One-equation models, Two-equation models, Reynolds Stress/Flux models and Algebraic Stress/Flux models. In FLOW-3D software, five turbulence models are available. The formulation used in the FLOW-3D software differs slightly from other formulations that includes the influence of the fractional areas/volumes of the FAVORTM method and generalizes the turbulence production (or decay) associated with buoyancy forces. The latter generalization, for example, includes buoyancy effects associated with non-inertial accelerations.

The available turbulence models in Flow-3D software are the Prandtl Mixing Length Model, the One-Equation Turbulent Energy Model, the Two-Equation Standard  Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (Flow Science Inc. 2012).In this research the RNG model was selected because this model is more commonly used than other models in dealing with particles; moreover, it is more accurate to work with air entrainment and other particles. In general, the RNG model is classified as a more widely-used application than the standard k-ɛ model. And in particular, the RNG model is more accurate in flows that have strong shear regions than the standard k-ɛ model and it is defined to describe low intensity turbulent flows. For the turbulent dissipation  it solves an additional transport equation:

formula

(3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is

formula

(4)where uv and w are the x, y and z coordinates of the fluid velocity; ⁠, ⁠,  and ⁠, are FLOW-3D’s FAVORTM defined terms;  and  are turbulence due to shearing and buoyancy effects, respectively. R and  are related to the cylindrical coordinate system. The default values of RMTKE, CDIS1 and CNU differ, being 1.39, 1.42 and 0.085 respectively. And CDIS2 is calculated from turbulent production (⁠⁠) and turbulent kinetic energy (⁠⁠).The kinematic turbulent viscosity is the same in all turbulence transport models and is calculated from

formula

(5)where ⁠: is the turbulent kinematic viscosity.  is defined as the numerical challenge between the RNG and the two-equation k-ɛ models, found in the equation below. To avoid an unphysically large result for  in Equation (3), since this equation could produce a value for  very close to zero and also because the physical value of  may approach to zero in such cases, the value of  is calculated from the following equation:

formula

(6)where ⁠: the turbulent length scale.

VOF and FAVOR are classifications of volume-fraction methods. In these two methods, firstly the area should be subdivided into a control volume grid or a small element. Each flow parameter like velocity, temperature and pressure values within the element are computed for each element containing liquids. Generally, these values represent the volumetric average of values in the elements.Numerous methods have been used recently to solve free infinite boundaries in the various numerical simulations. VOF is an easy and powerful method created based on the concept of a fractional intensity of fluid. A significant number of studies have confirmed that this method is more flexible and efficient than others dealing with the configurations of a complex free boundary. By using VOF technology the Flow-3D free surface was modelled and first declared in Hirt & Nichols (1981). In the VOF method there are three ingredients: a planner to define the surface, an algorithm for tracking the surface as a net mediator moving over a computational grid, and application of the boundary conditions to the surface. Configurations of the fluids are defined in terms of VOF function, F (x, y, z, t) (Hirt & Nichols 1981). And this VOF function shows the volume of flow per unit volume

formula

(7)

formula

(8)

formula

(9)where  is the density of the fluid, is a turbulent diffusion term,  is a mass source,  is the fractional volume open to flow. The components of velocity (u, v, w) are in the direction of coordinates (x, y, z) or (r, ⁠).  in the x-direction is the fractional area open to flow,  and  are identical area fractions for flow in the y and z directions. The R coefficient is based on the selection of the coordinate system.

The FAVOR method is a different method and uses another volume fraction technique, which is only used to define the geometry, such as the volume of liquid in each cell used to determine the position of fluid surfaces. Another fractional volume can be used to define the solid surface. Then, this information is used to determine the boundary conditions of the wall that the flow should be adapted for.

Case study

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In this study, the experimental results of Ostad Mirza (2016) was simulated. In a channel composed of two 4 m long modules, with a transparent sidewall of height 0.6 m and 0.5 m width. The upstream chute slope (i.e. pseudo-bottom angle) Ɵ1 = 50°, the downstream chute slope Ɵ2 = 30° or 18.6°, the step heights h = 0.06 m, the total number of steps along the 50° chute 41 steps, the total number of steps along the 30° chute 34 steps and the total number of steps along the 18.6° chute 20 steps.

The flume inflow tool contained a jetbox with a maximum opening set to 0.12 meters, designed for passing the maximum unit discharge of 0.48 m2/s. The measurements of the flow properties (i.e. air concentration and velocity) were computed perpendicular to the pseudo-bottom as shown in Figure 1 at the centre of twenty stream-wise cross-sections, along the stepped chute, (i.e. in five steps up on the slope change and fifteen steps down on the slope change, namely from step number −09 to +23 on 50°–30° slope change, or from −09 to +15 on 50°–18.6° slope change, respectively).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).
Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Pressure sensors were arranged with the x/l values for different slope change as shown in Table 1, where x is the distance from the step edge, along the horizontal step face, and l is the length of the horizontal step face. The location of pressure sensors is shown in Table 1.Table 1

Location of pressure sensors on horizontal step faces

Θ(°)L(m)x/l (–)
50.0 0.050 0.35 0.64 – – – 
30.0 0.104 0.17 0.50 0.84 – – 
18.6 0.178 0.10 0.30 0.50 0.7 0.88 
Location of pressure sensors on horizontal step faces
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Numerical model set-up

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A 3D numerical model of hydraulic phenomena was simulated based on an experimental study by Ostad Mirza (2016). The water surcharge and flow pressure over the stepped spillway was computed for two models of a stepped spillway with different discharge for each model. In this study, the package was used to simulate the flow parameters such as air entrainment, velocity distribution and dynamic pressures. The solver uses the finite volume technique to discretize the computational domain. In every test run, one incompressible fluid flow with a free surface flow selected at 20̊ was used for this simulation model. Table 2 shows the variables used in test runs.Table 2

Variables used in test runs

Test no.Θ1 (°)Θ2 (°)h(m)d0q (m3s1)dc/h (–)
50 18.6 0.06 0.045 0.1 2.6 
50 18.6 0.06 0.082 0.235 4.6 
50 30.0 0.06 0.045 0.1 2.6 
50 30.0 0.06 0.082 0.235 4.6 
Table 2 Variables used in test runs

For stepped spillway simulation, several parameters should be specified to get accurate simulations, which is the scope of this research. Viscosity and turbulent, gravity and non-inertial reference frame, air entrainment, density evaluation and drift-flux should be activated for these simulations. There are five different choices in the ‘viscosity and turbulent’ option, in the viscosity flow and Renormalized Group (RNG) model. Then a dynamical model is selected as the second option, the ‘gravity and non-inertial reference frame’. Only the z-component was inputted as a negative 9.81 m/s2 and this value represents gravitational acceleration but in the same option the x and y components will be zero. Air entrainment is selected. Finally, in the drift-flux model, the density of phase one is input as (water) 1,000 kg/m3 and the density of phase two (air) as 1.225 kg/m3. Minimum volume fraction of phase one is input equal to 0.1 and maximum volume fraction of phase two to 1 to allow air concentration to reach 90%, then the option allowing gas to escape at free surface is selected, to obtain closer simulation.

The flow domain is divided into small regions relatively by the mesh in Flow-3D numerical model. Cells are the smallest part of the mesh, in which flow characteristics such as air concentration, velocity and dynamic pressure are calculated. The accuracy of the results and simulation time depends directly on the mesh block size so the cell size is very important. Orthogonal mesh was used in cartesian coordinate systems. A smaller cell size provides more accuracy for results, so we reduced the number of cells whilst including enough accuracy. In this study, the size of cells in x, y and z directions was selected as 0.015 m after several trials.

Figure 3 shows the 3D computational domain model 50–18.6 slope change, that is 6.0 m length, 0.50 m width and 4.23 m height. The 3D model of the computational domain model 50–30 slope changes this to 6.0 m length, 0.50 m width and 5.068 m height and the size of meshes in x, y, and z directions are 0.015 m. For the 50–18.6 slope change model: both total number of active and passive cells = 4,009,952, total number of active cells = 3,352,307, include real cells (used for solving the flow equations) = 3,316,269, open real cells = 3,316,269, fully blocked real cells equal to zero, external boundary cells were 36,038, inter-block boundary cells = 0 (Flow-3D report). For 50–30 slope change model: both total number of active and passive cells = 4,760,002, total number of active cells equal to 4,272,109, including real cells (used for solving the flow equations) were 3,990,878, open real cells = 3,990,878 fully blocked real cells = zero, external boundary cells were 281,231, inter-block boundary cells = 0 (Flow-3D report).

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.
Figure3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Figure 3VIEW LARGEDOWNLOAD SLIDE

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

When solving the Navier-Stokes equation and continuous equations, boundary conditions should be applied. The most important work of boundary conditions is to create flow conditions similar to physical status. The Flow-3D software has many types of boundary condition; each type can be used for the specific condition of the models. The boundary conditions in Flow-3D are symmetry, continuative, specific pressure, grid overlay, wave, wall, periodic, specific velocity, outflow, and volume flow rate.

There are two options to input finite flow rate in the Flow-3D software either for inlet discharge of the system or for the outlet discharge of the domain: specified velocity and volume flow rate. In this research, the X-minimum boundary condition, volume flow rate, has been chosen. For X-maximum boundary condition, outflow was selected because there is nothing to be calculated at the end of the flume. The volume flow rate and the elevation of surface water was set for Q = 0.1 and 0.235 m3/s respectively (Figure 2).

The bottom (Z-min) is prepared as a wall boundary condition and the top (Z-max) is computed as a pressure boundary condition, and for both (Y-min) and (Y-max) as symmetry.

RESULTS AND DISCUSSION

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The air concentration distribution profiles in two models of stepped spillway were obtained at an acquisition time equal to 25 seconds in skimming flow for both upstream and downstream of a slope change 50°–18.6° and 50°–30° for different discharge as in Table 2, and as shown in Figure 4 for 50°–18.6° slope change and Figure 5 for 50°–30° slope change configuration for dc/h = 4.6. The simulation results of the air concentration are very close to the experimental results in all curves and fairly close to that predicted by the advection-diffusion model for the air bubbles suggested by Chanson (1997) on a constant sloping chute.

Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.
Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure 4VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.
Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 5VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 6VIEW LARGEDOWNLOAD SLIDE

Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.
Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.
Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

Figure 7VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

But as is shown in all above mentioned figures it is clear that at the pseudo-bottom the CFD results of air concentration are less than experimental ones until the depth of water reaches a quarter of the total depth of water. Also the direction of the curves are parallel to each other when going up towards the surface water and are incorporated approximately near the surface water. For all curves, the cross-section is separate between upstream and downstream steps. Therefore the (-) sign for steps represents a step upstream of the slope change cross-section and the (+) sign represents a step downstream of the slope change cross-section.

The dimensionless velocity distribution (V/V90) profile was acquired at an acquisition time equal to 25 seconds in skimming flow of the upstream and downstream slope change for both 50°–18.6° and 50°–30° slope change. The simulation results are compared with the experimental ones showing that for all curves there is close similarity for each point between the observed and experimental results. The curves increase parallel to each other and they merge near at the surface water as shown in Figure 6 for slope change 50°–18.6° configuration and Figure 7 for slope change 50°–30° configuration. However, at step numbers +1 and +5 in Figure 7 there are few differences between the simulated and observed results, namely the simulation curves ascend regularly meaning the velocity increases regularly from the pseudo-bottom up to the surface water.

Figure 8 (50°–18.6° slope change) and Figure 9 (50°–30° slope change) compare the simulation results and the experimental results for the presented dimensionless dynamic pressure distribution for different points on the stepped spillway. The results show a good agreement with the experimental and numerical simulations in all curves. For some points, few discrepancies can be noted in pressure magnitudes between the simulated and the observed ones, but they are in the acceptable range. Although the experimental data do not completely agree with the simulated results, there is an overall agreement.

Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 8VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

The pressure profiles were acquired at an acquisition time equal to 70 seconds in skimming flow on 50°–18.6°, where p is the measured dynamic pressure, h is step height and ϒ is water specific weight. A negative sign for steps represents a step upstream of the slope change cross-section and a positive sign represents a step downstream of the slope change cross-section.

Figure 10 shows the experimental streamwise development of dimensionless pressure on the 50°–18.6° slope change for dc/h = 4.6, x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute compared with the numerical simulation. It is obvious from Figure 10 that the streamwise development of dimensionless pressure before slope change (steps number −1, −2 and −3) both of the experimental and simulated results are close to each other. However, it is clear that there is a little difference between the results of the streamwise development of dimensionless pressure at step numbers +1, +2 and +3. Moreover, from step number +3 to the end, the curves get close to each other.

Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.
Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 11 compares the experimental and the numerical results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute. It is apparent that the outcomes of the experimental work are close to the numerical results, however, the results of the simulation are above the experimental ones before the slope change, but the results of the simulation descend below the experimental ones after the slope change till the end.

Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.
Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

CONCLUSION

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In this research, numerical modelling was attempted to investigate the effect of abrupt slope change on the flow properties (air entrainment, velocity distribution and dynamic pressure) over a stepped spillway with two different models and various flow rates in a skimming flow regime by using the CFD technique. The numerical model was verified and compared with the experimental results of Ostad Mirza (2016). The same domain of the numerical model was inputted as in experimental models to reduce errors as much as possible.

Flow-3D is a well modelled tool that deals with particles. In this research, the model deals well with air entrainment particles by observing their results with experimental results. And the reason for the small difference between the numerical and the experimental results is that the program deals with particles more accurately than the laboratory. In general, both numerical and experimental results showed that near to the slope change the flow bulking, air entrainment, velocity distribution and dynamic pressure are greatly affected by abrupt slope change on the steps. Although the extent of the slope change was relatively small, the influence of the slope change was major on flow characteristics.

The Renormalized Group (RNG) model was selected as a turbulence solver. For 3D modelling, orthogonal mesh was used as a computational domain and the mesh grid size used for X, Y, and Z direction was equal to 0.015 m. In CFD modelling, air concentration and velocity distribution were recorded for a period of 25 seconds, but dynamic pressure was recorded for a period of 70 seconds. The results showed that there is a good agreement between the numerical and the physical models. So, it can be concluded that the proposed CFD model is very suitable for use in simulating and analysing the design of hydraulic structures.

이 연구에서 수치 모델링은 두 가지 다른 모델과 다양한 유속을 사용하여 스키밍 흐름 영역에서 계단식 배수로에 대한 유동 특성 (공기 혼입, 속도 분포 및 동적 압력)에 대한 급격한 경사 변화의 영향을 조사하기 위해 시도되었습니다. CFD 기술. 수치 모델을 검증하여 Ostad Mirza (2016)의 실험 결과와 비교 하였다. 오차를 최대한 줄이기 위해 실험 모형과 동일한 수치 모형을 입력 하였다.

Flow-3D는 파티클을 다루는 잘 모델링 된 도구입니다. 이 연구에서 모델은 실험 결과를 통해 결과를 관찰하여 공기 혼입 입자를 잘 처리합니다. 그리고 수치와 실험 결과의 차이가 작은 이유는 프로그램이 실험실보다 입자를 더 정확하게 다루기 때문입니다. 일반적으로 수치 및 실험 결과는 경사에 가까워지면 유동 벌킹, 공기 혼입, 속도 분포 및 동적 압력이 계단의 급격한 경사 변화에 크게 영향을받는 것으로 나타났습니다. 사면 변화의 정도는 상대적으로 작았지만 사면 변화의 영향은 유동 특성에 큰 영향을 미쳤다.

Renormalized Group (RNG) 모델이 난류 솔버로 선택되었습니다. 3D 모델링의 경우 계산 영역으로 직교 메쉬가 사용되었으며 X, Y, Z 방향에 사용 된 메쉬 그리드 크기는 0.015m입니다. CFD 모델링에서 공기 농도와 속도 분포는 25 초 동안 기록되었지만 동적 압력은 70 초 동안 기록되었습니다. 결과는 수치 모델과 물리적 모델간에 좋은 일치가 있음을 보여줍니다. 따라서 제안 된 CFD 모델은 수력 구조물의 설계 시뮬레이션 및 해석에 매우 적합하다는 결론을 내릴 수 있습니다.

DATA AVAILABILITY STATEMENT

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

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© 2021 The Authors
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Modeling of contactless bubble–bubble interactions in microchannels with integrated inertial pumps

Modeling of contactless bubble–bubble interactions in microchannels with integrated inertial pumps

통합 관성 펌프를 사용하여 마이크로 채널에서 비접촉식 기포-기포 상호 작용 모델링

Physics of Fluids 33, 042002 (2021); https://doi.org/10.1063/5.0041924 B. Hayesa) G. L. Whitingb), and  R. MacCurdyc)

ABSTRACT

In this study, the nonlinear effect of contactless bubble–bubble interactions in inertial micropumps is characterized via reduced parameter one-dimensional and three-dimensional computational fluid dynamics (3D CFD) modeling. A one-dimensional pump model is developed to account for contactless bubble-bubble interactions, and the accuracy of the developed one-dimensional model is assessed via the commercial volume of fluid CFD software, FLOW-3D. The FLOW-3D CFD model is validated against experimental bubble dynamics images as well as experimental pump data. Precollapse and postcollapse bubble and flow dynamics for two resistors in a channel have been successfully explained by the modified one-dimensional model. The net pumping effect design space is characterized as a function of resistor placement and firing time delay. The one-dimensional model accurately predicts cumulative flow for simultaneous resistor firing with inner-channel resistor placements (0.2L < x < 0.8L where L is the channel length) as well as delayed resistor firing with inner-channel resistor placements when the time delay is greater than the time required for the vapor bubble to fill the channel cross section. In general, one-dimensional model accuracy suffers at near-reservoir resistor placements and short time delays which we propose is a result of 3D bubble-reservoir interactions and transverse bubble growth interactions, respectively, that are not captured by the one-dimensional model. We find that the one-dimensional model accuracy improves for smaller channel heights. We envision the developed one-dimensional model as a first-order rapid design tool for inertial pump-based microfluidic systems operating in the contactless bubble–bubble interaction nonlinear regime

이 연구에서 관성 마이크로 펌프에서 비접촉 기포-기포 상호 작용의 비선형 효과는 감소 된 매개 변수 1 차원 및 3 차원 전산 유체 역학 (3D CFD) 모델링을 통해 특성화됩니다. 비접촉식 기포-버블 상호 작용을 설명하기 위해 1 차원 펌프 모델이 개발되었으며, 개발 된 1 차원 모델의 정확도는 유체 CFD 소프트웨어 인 FLOW-3D의 상용 볼륨을 통해 평가됩니다.

FLOW-3D CFD 모델은 실험적인 거품 역학 이미지와 실험적인 펌프 데이터에 대해 검증되었습니다. 채널에 있는 두 저항기의 붕괴 전 및 붕괴 후 기포 및 유동 역학은 수정 된 1 차원 모델에 의해 성공적으로 설명되었습니다. 순 펌핑 효과 설계 공간은 저항 배치 및 발사 시간 지연의 기능으로 특징 지어집니다.

1 차원 모델은 내부 채널 저항 배치 (0.2L <x <0.8L, 여기서 L은 채널 길이)로 동시 저항 발생에 대한 누적 흐름과 시간 지연시 내부 채널 저항 배치로 지연된 저항 발생을 정확하게 예측합니다. 증기 방울이 채널 단면을 채우는 데 필요한 시간보다 큽니다.

일반적으로 1 차원 모델 정확도는 저수지 근처의 저항 배치와 1 차원 모델에 의해 포착되지 않는 3D 기포-저수지 상호 작용 및 가로 기포 성장 상호 작용의 결과 인 짧은 시간 지연에서 어려움을 겪습니다. 채널 높이가 작을수록 1 차원 모델 정확도가 향상됩니다. 우리는 개발 된 1 차원 모델을 비접촉 기포-기포 상호 작용 비선형 영역에서 작동하는 관성 펌프 기반 미세 유체 시스템을 위한 1 차 빠른 설계 도구로 생각합니다.

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Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.

Continuous-Flow Separation of Magnetic Particles from Biofluids: How Does the Microdevice Geometry Determine the Separation Performance?

Cristina González Fernández,1 Jenifer Gómez Pastora,2 Arantza Basauri,1 Marcos Fallanza,1 Eugenio Bringas,1 Jeffrey J. Chalmers,2 and Inmaculada Ortiz1,*
Author information Article notes Copyright and License information Disclaimer

생체 유체에서 자성 입자의 연속 흐름 분리 : 마이크로 장치 형상이 분리 성능을 어떻게 결정합니까?

Abstract

The use of functionalized magnetic particles for the detection or separation of multiple chemicals and biomolecules from biofluids continues to attract significant attention. After their incubation with the targeted substances, the beads can be magnetically recovered to perform analysis or diagnostic tests. Particle recovery with permanent magnets in continuous-flow microdevices has gathered great attention in the last decade due to the multiple advantages of microfluidics. As such, great efforts have been made to determine the magnetic and fluidic conditions for achieving complete particle capture; however, less attention has been paid to the effect of the channel geometry on the system performance, although it is key for designing systems that simultaneously provide high particle recovery and flow rates. Herein, we address the optimization of Y-Y-shaped microchannels, where magnetic beads are separated from blood and collected into a buffer stream by applying an external magnetic field. The influence of several geometrical features (namely cross section shape, thickness, length, and volume) on both bead recovery and system throughput is studied. For that purpose, we employ an experimentally validated Computational Fluid Dynamics (CFD) numerical model that considers the dominant forces acting on the beads during separation. Our results indicate that rectangular, long devices display the best performance as they deliver high particle recovery and high throughput. Thus, this methodology could be applied to the rational design of lab-on-a-chip devices for any magnetically driven purification, enrichment or isolation.

생체 유체에서 여러 화학 물질과 생체 분자의 검출 또는 분리를 위한 기능화된 자성 입자의 사용은 계속해서 상당한 관심을 받고 있습니다. 표적 물질과 함께 배양 한 후 비드는 자기적으로 회수되어 분석 또는 진단 테스트를 수행 할 수 있습니다.

연속 흐름 마이크로 장치에서 영구 자석을 사용한 입자 회수는 마이크로 유체의 여러 장점으로 인해 지난 10 년 동안 큰 관심을 모았습니다. 따라서 완전한 입자 포획을 달성하기 위한 자기 및 유체 조건을 결정하기 위해 많은 노력을 기울였습니다.

그러나 높은 입자 회수율과 유속을 동시에 제공하는 시스템을 설계하는데 있어 핵심이기는 하지만 시스템 성능에 대한 채널 형상의 영향에 대해서는 덜 주의를 기울였습니다.

여기에서 우리는 자기 비드가 혈액에서 분리되어 외부 자기장을 적용하여 버퍼 스트림으로 수집되는 Y-Y 모양의 마이크로 채널의 최적화를 다룹니다. 비드 회수 및 시스템 처리량에 대한 여러 기하학적 특징 (즉, 단면 형상, 두께, 길이 및 부피)의 영향을 연구합니다.

이를 위해 분리 중에 비드에 작용하는 지배적인 힘을 고려하는 실험적으로 검증된 CFD (Computational Fluid Dynamics) 수치 모델을 사용합니다.

우리의 결과는 직사각형의 긴 장치가 높은 입자 회수율과 높은 처리량을 제공하기 때문에 최고의 성능을 보여줍니다. 따라서 이 방법론은 자기 구동 정제, 농축 또는 분리를 위한 랩 온어 칩 장치의 합리적인 설계에 적용될 수 있습니다.

Keywords: particle magnetophoresis, CFD, cross section, chip fabrication

Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 1 (a) Top view of the microfluidic-magnetophoretic device, (b) Schematic representation of the channel cross-sections studied in this work, and (c) the magnet position relative to the channel location (Sepy and Sepz are the magnet separation distances in y and z, respectively).
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 2. (a) Channel-magnet configuration and (b–d) magnetic force distribution in the channel midplane for 2 mm, 5 mm and 10 mm long rectangular (left) and U-shaped (right) devices.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 3. (a) Velocity distribution in a section perpendicular to the flow for rectangular (left) and Ushaped (right) cross section channels, and (b) particle location in these cross sections.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 4. Influence of fluid flow rate on particle recovery when the applied magnetic force is (a) different and (b) equal in U-shaped and rectangular cross section microdevices.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 5. Magnetic bead capture as a function of fluid flow rate for all of the studied geometries.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 6. Influence of (a) magnetic and fluidic forces (J parameter) and (b) channel geometry (θ parameter) on particle recovery. Note that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.
Figure 7. Dependence of bead capture on the (a) functional channel volume, and (b) particle residence time (tres). Note that in the curve fitting expressions V represents the functional channel volume and that U-2mm does not accurately fit a line.

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Figure 2.6 ESI apparatus for offline analysis with microscope imaging.

MODELING AND CHARACTERIZATION OF MICROFABRICATED EMITTERS: IN PURSUIT OF IMPROVED ESI-MS PERFORMANCE

미세 가공 방사체의 모델링 및 특성화 : 개선된 ESI-MS 성능 추구

by XINYUN WU

A thesis submitted to the Department of Chemistry in conformity with the requirements for the degree of Master of Science Queen’s University Kingston, Ontario, Canada December, 2011 Copyright © Xinyun Wu, 2011

Abstract

ESI (Electrospray ionization)는 특히 탁월한 감도, 견고성 및 단순성으로 대형 생체 분자를 분석하는 데있어 질량 분석 (MS)에 매우 귀중한 기술이었습니다. ESI 기술 개발에 많은 노력을 기울였습니다. 그 형태와 기하학적 구조가 전기 분무 성능과 추가 MS 감지에 중추적 인 것으로 입증 되었기 때문입니다.

막힘 및 낮은 처리량을 포함하여 전통적인 단일 홀 이미터의 본질적인 문제는 기술의 적용 가능성을 제한합니다. 이 문제를 해결하기 위해 현재 프로젝트는 향상된 ESI-MS 분석을위한 다중 전자 분무(MES) 방출기를 개발하는데 초점을 맞추고 있습니다.

이 논문에서는 스프레이 전류 측정을 위한 전기 분무와 오프라인 전기 분무 실험을 위한 전산 유체 역학 (CFD) 시뮬레이션의 공동 작업이 수행되었습니다. 전기 분무 성능에 대한 다양한 이미터 설계의 영향을 테스트하기 위해 수치 시뮬레이션이 사용되었으며 실험실 결과는 가이드 및 검증으로 사용되었습니다.

CFD 코드는 Taylor-Melcher 누설 유전체 모델(LDM)을 기반으로 하며 과도 전기 분무 공정이 성공적으로 시뮬레이션되었습니다.

이 방법은 750 μm 내경 (i.d.) 이미 터를 통해 먼저 검증되었으며 20 μm i.d.에 추가로 적용되었습니다. 모델. 전기 분무 공정의 여러 단계가 시각적으로 시연되었으며 다양한 적용 전기장 및 유속에서 분무 전류의 변화에 ​​대한 정량적 조사는 이전 시뮬레이션 및 측정과 잘 일치합니다.

단일 조리개 프로토 타입을 기반으로 2 홀 및 3 홀 이미터로 MES 시뮬레이션을 수행했습니다. 시뮬레이션 예측은 실험 결과와 유사하게 비교되었습니다. 이 작업의 증거는 CFD 시뮬레이션이 MES의 이미 터 설계를 테스트하는 효과적인 수치 도구로 사용될 수 있음을 입증했습니다.

이 작업에서 달성 된 마이크로 스케일 에미 터 전기 분무의 성공적인 시뮬레이션에 대한 벤치마킹 결과는 현재까지 발표 된 전기 분무에 대한 동적 시뮬레이션의 가장 작은 규모로 여겨집니다.

Co-Authorship

공동 저자: 이 논문에 대한 모든 연구는 Natalie M. Cann 박사와 Richard D. Oleschuk 박사의 지도하에 완료되었습니다. 다중 전자 분무에 관한 4 장에서 제시된 연구 작업의 일부는 Ramin Wright가 공동 저술했으며, 이 작업은 press에서 다음 논문에서 인용되었습니다.

ibson,G.T.T.; Wright, R.D.; Oleschuk, R.D. Multiple electrosprays generated from a single poly carbonate microstructured fibre. Journal of Mass Spectrometry, 2011, in press.

Chapter 1 Introduction

소프트 이온화 방법으로 ESI (electrospray ionization)의 도입은 질량 분석법 (MS)의 적용 가능성에 혁명을 일으켰습니다. 이 기술의 부드러운 특징은 상대적으로 높은 전하를 가진 이온을 생성하는 고유한 이점으로 인해 액상에서 직접 펩티드 및 단백질과 같은 큰 생체 분자를 분석 할 수 있게했습니다 [1].

지난 10 년 동안 ESI-MS는 놀라운 성장을 보였으며 현재는 단백질 체학, 대사 체학, 글리코 믹스, 합성 화학자를 위한 식별 도구 등 다양한 생화학 분야에서 광범위하게 채택되고 있습니다 [2-3].

ESI-MS는 겔 전기 영동과 같은 생물학적 분자에 대한 기존의 질량 측정 기술보다 훨씬 빠르고 민감하며 정확합니다. 또한, 액체상에서 직접 분석 할 수 있는 큰 비 휘발성 분자의 능력은 고성능 액체 크로마토 그래피 (HPLC) 및 모세관 전기 영동 (CE)과 같은 업스트림 분리 기술과의 결합을 가능하게합니다 [4].

일반적인 ESI 공정은 일반적으로 액적 형성, 액적 수축 및 기상 이온의 최종 형성을 포함합니다. 일렉트로 스프레이의 성능에 영향을 미치는 많은 요소 중에서 스프레이를 위한 이미터의 구조 (즉, 기하학, 모양 등)가 중요한 요소입니다.

전통적인 전기 분무 이미터는 일반적으로 풀링 또는 에칭 기술로 제작 된 단일 채널 테이퍼 형 또는 비 테이퍼 형입니다. 그러나 이러한 이미터는 종종 막힘, 부적절한 처리량 등과 같은 문제로 어려움을 겪습니다. [5]

향상된 감도 및 샘플 활용을 위해 다중 스프레이를 생성하는 새로운 이미터 설계 개발로 분명한 발전이 있었습니다. 새로운 ESI 이미터 설계에 대한 연구는 실험적으로나 이론적으로 큰 관심을 불러 일으켰습니다 [3]. 그러나 ESI의 복잡한 물리적 과정은 팁 형상 외에도 많은 다른 변수에 의존하기 때문에 연구간 직접 비교의 어려움은 장애물이 됩니다.

또한 새로운 나노 이미터 제조 및 테스트 비용이 상당히 높을 수 있습니다. 이 논문은 CFD 시뮬레이션 도구를 활용하여 가상 랩을 설정함으로써 이러한 문제를 해결합니다. 다른 매개 변수로 인해 상호 연결된 변경 없이 다양한 이미터 설계를 비교할 수 있도록 이상적으로 균일한 물리적 조건을 제공합니다.

맞춤 제작된 프로토 타입의 실험 측정 값도 수집되어 더 나은 계산 체계를 형성하는 데 도움이 되는 지침과 검증을 모두 제공합니다. 특히 이 분야의 주요 미래 플랫폼으로 여겨지는 다중 노즐 이미 터 설계에 중점을 둘 것입니다.

전기 분무 거동에 영향을 미치는 요인에 대한 추가 기본 연구는 다양한 기하학적 및 작동 매개 변수와 관련하여 수행됩니다. 이는 보다 효율적이고 견고한 이미터의 개발을 가능하게 할 뿐만 아니라 더 넓은 영역에서 ESI의 적용을 향상시킬 수 있습니다.

Figure 1.1Schematic setup for ESI-MS technique
Figure 1.1Schematic setup for ESI-MS technique
Figure 1.2 Schematic of major processes occurring in electrospray [5].
Figure 1.2 Schematic of major processes occurring in electrospray [5].
Figure 1.3 Illustration of detailed geometric parameters of a spraying Taylor cone wherera is the radius of curvature of the best fitting circle at the tip of the cone; re is the radius of the emission region for droplets at the tip of a Taylor cone;is the liquid cone angle.
Figure 1.3 Illustration of detailed geometric parameters of a spraying Taylor cone wherera is the radius of curvature of the best fitting circle at the tip of the cone; re is the radius of the emission region for droplets at the tip of a Taylor cone;is the liquid cone angle.
Figure 1.4 (A)Externally tapered emitter  (B) Optical image of a clogged tapered emitter with normal use [46].
Figure 1.4 (A)Externally tapered emitter (B) Optical image of a clogged tapered emitter with normal use [46].
Figure 1.5 (A)Three by three configuration of an emitter array made with polycarbonate using laser ablation; (B) Photomicrograph of nine stable electrosprays generated from the nine-emitter array [52]
Figure 1.5 (A)Three by three configuration of an emitter array made with polycarbonate using laser ablation; (B) Photomicrograph of nine stable electrosprays generated from the nine-emitter array [52]
Figure 1.6 SEM images of the distal ends of four multichannel nanoelectrospray emitters and a tapered emitter: (A) 30 orifice emitter; (B) 54 orifice emitter; (C) 84 orifice emitter; (D) 168 orifice emitter; Scale bars in A, B, and C represent 50 μm, and 100 μm in D[54]
Figure 1.6 SEM images of the distal ends of four multichannel nanoelectrospray emitters and a tapered emitter: (A) 30 orifice emitter; (B) 54 orifice emitter; (C) 84 orifice emitter; (D) 168 orifice emitter; Scale bars in A, B, and C represent 50 μm, and 100 μm in D[54]
Figure 1.7 Photomicrographs of electrospray from of a 168-hole MCN emitter at different flow rates. (A) A traditional integrated Taylor cone observed from offline electrospray of water with 0.1% formic acid at 300 nL/min; (B) A mist of coalesced Taylor cones observed from offline electrospray at 25 nL/min[54]
Figure 1.7 Photomicrographs of electrospray from of a 168-hole MCN emitter at different flow rates. (A) A traditional integrated Taylor cone observed from offline electrospray of water with 0.1% formic acid at 300 nL/min; (B) A mist of coalesced Taylor cones observed from offline electrospray at 25 nL/min[54]
Figure 1.8 Circular arrays of etched emitters for better electric field homogeneity [53].
Figure 1.8 Circular arrays of etched emitters for better electric field homogeneity [53].
Figure 2.6 ESI apparatus for offline analysis with microscope imaging.
Figure 2.6 ESI apparatus for offline analysis with microscope imaging.
Figure 3.9 Typical panel for displaying instant simulation result during simulation process.
Figure 3.9 Typical panel for displaying instant simulation result during simulation process.
Figure 5.3 Generation of a Taylor cone-jet mode (simulation) plotted with iso-potential lines at times    (Top to bottom panels correspond to 0.002 s, 0.012 s, 0.018 s, 0.08 s respectively).
Figure 5.3 Generation of a Taylor cone-jet mode (simulation) plotted with iso-potential lines at times (Top to bottom panels correspond to 0.002 s, 0.012 s, 0.018 s, 0.08 s respectively).
Figure 5.8 (A) Taylor cone-jet profiles with different contact angle of 30 degrees and 20 degrees (B) under the same physical conditions of 6 kV and 0.04 m/s. (C) Cone-jet profile generated from a tapered tip with a 20 degree contact angle at 6 kV and 0.04 m/s (as a comparison with (B)).
Figure 5.8 (A) Taylor cone-jet profiles with different contact angle of 30 degrees and 20 degrees (B) under the same physical conditions of 6 kV and 0.04 m/s. (C) Cone-jet profile generated from a tapered tip with a 20 degree contact angle at 6 kV and 0.04 m/s (as a comparison with (B)).

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Bibliography

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34. Wampler, F.M., A.T. Blades, and P. Kebarle, Negative-Ion Electrospray Mass-Spectrometry of Nucleotides – Ionization from Water Solution with Sf6 Discharge Suppression. Journal of the American Society for Mass Spectrometry, 1993. 4(4): p. 289-295. 35. Marginean, I., P. Nemes, and A. Vertes, Order-chaos-order transitions in electrosprays: The electrified dripping faucet. Physical Review Letters, 2006. 97(6): p. -. 36. Marginean, I., P. Nemes, and A. Vertes, Astable regime in electrosprays. Physical Review E, 2007. 76(2): p. -. 37. Nemes, P., I. Marginean, and A. Vertes, Spraying mode effect on droplet formation and ion chemistry in electrosprays. Analytical Chemistry, 2007. 79(8): p. 3105-3116. 38. Marginean, I., et al., Electrospray characteristic curves: In pursuit of improved performance in the nanoflow regime. Analytical Chemistry, 2007. 79(21): p. 8030-8036. 39. Page, J.S., et al., Subambient pressure ionization with nanoelectrospray source and interface for improved sensitivity in mass spectrometry. Analytical Chemistry, 2008. 80(5): p. 1800-1805. 40. Delamora, J.F. and I.G. Loscertales, The Current Emitted by Highly Conducting Taylor Cones. Journal of Fluid Mechanics, 1994. 260: p. 155-184. 41. Ganan-Calvo, A.M., On the general scaling theory for electrospraying. Journal of Fluid Mechanics, 2004. 507: p. 203-212. 42. Smith, D.R., G. Sagerman, and T.D. Wood, Design and development of an interchangeable nanomicroelectrospray source for a quadrupole mass spectrometer.Review of Scientific Instruments, 2003. 74(10): p. 4474-4477. 43. Barnidge, D.R., S. Nilsson, and K.E. Markides, A design for low-flow sheathless electrospray emitters. Analytical Chemistry, 1999. 71(19): p. 4115-4118. 44. Guzzetta, A.W., R.A. Thakur, and I.C. Mylchreest, A robust micro-electrospray ionization technique for high-throughput liquid chromatography/mass spectrometry proteomics using a sanded metal needle as an emitter. Rapid Communications in Mass Spectrometry, 2002. 16(21): p. 2067-2072. 45. Wilm, M. and M. Mann, Analytical properties of the nanoelectrospray ion source.Analytical Chemistry, 1996. 68(1): p. 1-8. 46. Covey, T.R. and D. Pinto, Practical Spectroscopy. Vol. 32. 2002. 47. Kelly, R.T., et al., Nanoelectrospray emitter arrays providing interemitter electric field uniformity. Analytical Chemistry, 2008. 80(14): p. 5660-5665. 48. Choi, Y.S. and T.D. Wood, Polyaniline-coated nanoelectrospray emitters treated with hydrophobic polymers at the tip. Rapid Communications in Mass Spectrometry, 2007. 21(13): p. 2101-2108. 49. Tojo, H., Properties of an electrospray emitter coated with material of low surface energy. Journal of Chromatography A, 2004. 1056(1-2): p. 223-228.

50. Liu, J., et al., Electrospray ionization with a pointed carbon fiber emitter. Analytical Chemistry, 2004. 76(13): p. 3599-3606. 51. Sen, A.K., et al., Modeling and characterization of a carbon fiber emitter for electrospray ionization. Journal of Micromechanics and Microengineering, 2006. 16(3): p. 620-630. 52. Tang, K.Q., et al., Generation of multiple electrosprays using microfabricated emitter arrays for improved mass spectrometric sensitivity. Analytical Chemistry, 2001. 73(8): p. 1658-1663. 53. Deng, W. and A. Gomez, Influence of space charge on the scale-up of multiplexed electrosprays. Journal of Aerosol Science, 2007. 38(10): p. 1062-1078. 54. Su, S.Q., et al., Microstructured Photonic Fibers as Multichannel Electrospray Emitters.Analytical Chemistry, 2009. 81(17): p. 7281-7287. 55. Sen, A.K., J. Darabi, and D.R. Knapp, Simulation and parametric study of a novel multi-spray emitter for ESI-MS applications. Microfluidics and Nanofluidics, 2007. 3(3): p. 283-298. 56. Hayati, I., A. Bailey, and T.F. Tadros, Investigations into the Mechanism of Electrohydrodynamic Spraying of Liquids .2. Mechanism of Stable Jet Formation and Electrical Forces Acting on a Liquid Cone. Journal of Colloid and Interface Science, 1987. 117(1): p. 222-230. 57. Glonti, G.A., On the Theory of the Stability of Liquid Jets in an Electric Field. Soviet Physics Jetp-Ussr, 1958. 7(5): p. 917-918. 58. Nayyar, N.K. and G.S. Murty, The Stability of a Dielectric Liquid Jet in the Presence of a Longitudinal Electric Field. Proceedings of the Physical Society of London, 1960. 75(483): p. 369-373. 59. Allan, R.S. and S.G. Mason, Particle Behaviour in Shear and Electric Fields .1. Deformation and Burst of Fluid Drops. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1962. 267(1328): p. 45-&. 60. Melcher, J.R. and G.I. Taylor, Electrohydrodynamics – a Review of Role of Interfacial Shear Stresses. Annual Review of Fluid Mechanics, 1969. 1: p. 111-&. 61. Saville, D.A., Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 1997. 29: p. 27-64. 62. Carretero Benignos, J.A. and Massachusetts Institute of Technology. Dept. of Mechanical Engineering., Numerical simulation of a single emitter colloid thruster in pure droplet cone-jet mode. 2005. p. 117 leaves. 63. Hartman, R.P.A., et al., The evolution of electrohydrodynamic sprays produced in the cone-jet mode, a physical model. Journal of Electrostatics, 1999. 47(3): p. 143-170. 64. Hartman, R.P.A., et al., Electrohydrodynamic atomization in the cone-jet mode physical modeling of the liquid cone and jet. Journal of Aerosol Science, 1999. 30(7): p. 823-849.

65. Yoon, S.S., et al., Modeling multi-jet mode electrostatic atomization using boundary element methods. Journal of Electrostatics, 2001. 50(2): p. 91-108. 66. Zeng, J., D. Sobek, and T. Korsmeyer, Electro-hydrodynamic modeling of electrospray ionization: Cad for a mu fluidic device – Mass spectrometer interface. Boston Transducers’03: Digest of Technical Papers, Vols 1 and 2, 2003: p. 1275-1278, 1938. 67. Lastow, O. and W. Balachandran, Numerical simulation of electrohydrodynamic (EHD) atomization. Journal of Electrostatics, 2006. 64(12): p. 850-859. 68. http://www.flow3d.com. 69. Valaskovic, G.A., et al., Attomole-Sensitivity Electrospray Source for Large-Molecule Mass-Spectrometry. Analytical Chemistry, 1995. 67(20): p. 3802-3805. 70. Kriger, M.S., K.D. Cook, and R.S. Ramsey, Durable Gold-Coated Fused-Silica Capillaries for Use in Electrospray Mass-Spectrometry. Analytical Chemistry, 1995. 67(2): p. 385-389. 71. Fang, L.L., et al., Online Time-of-Flight Mass-Spectrometric Analysis of Peptides Separated by Capillary Electrophoresis. Analytical Chemistry, 1994. 66(21): p. 3696-3701. 72. Cao, P. and M. Moini, A novel sheathless interface for capillary electrophoresis/electrospray ionization mass spectrometry using an in-capillary electrode. Journal of the American Society for Mass Spectrometry, 1997. 8(5): p. 561-564. 73. Fong, K.W.Y. and T.W.D. Chan, A novel nonmetallized tip for electrospray mass spectrometry at nanoliter flow rate. Journal of the American Society for Mass Spectrometry, 1999. 10(1): p. 72-75. 74. Emmett, M.R. and R.M. Caprioli, Micro-Electrospray Mass-Spectrometry – Ultra-High-Sensitivity Analysis of Peptides and Proteins. Journal of the American Society for Mass Spectrometry, 1994. 5(7): p. 605-613. 75. Gatlin, C.L., et al., Protein identification at the low femtomole level from silver-stained gels using a new fritless electrospray interface for liquid chromatography microspray and nanospray mass spectrometry. Analytical Biochemistry, 1998. 263(1): p. 93-101. 76. Aturki, Z., et al., On-line CE-MS using pressurized liquid junction nanoflow electrospray interface and surface-coated capillaries. Electrophoresis, 2006. 27(23): p. 4666-4673. 77. Edwards, J.L., et al., Negative mode sheathless capillary electrophoresis electrospray ionization-mass spectrometry for metabolite analysis of prokaryotes. Journal of Chromatography A, 2006. 1106(1-2): p. 80-88. 78. http://www.kiriama.com/kiriama%20single-mode%20polymer%20fibers_009.htm. 79. Wilm, M.S. and M. Mann, Electrospray and Taylor-Cone Theory, Doles Beam of Macromolecules at Last. International Journal of Mass Spectrometry, 1994. 136(2-3): p. 167-180.

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Sturgeon Navigate Fish Ladder

Sturgeon Navigate Fish Ladder

 

This material was provided by Jean-François Mercier, ing., Manager, hydraulics and hydrology at AECOM Tecsult inc.

AECOM Tecsult inc.은 FLOW-3D를 이용하여 물리적 모델링을 사용하지 않고 철갑상어가 Fish ladder를 탐색할 수 있는 물고기 사다리 설계를 개선했습니다. 실험은 현장구현의 제한과 비용때문에 배제되었고 FLOW-3D의 수치 모델링 결과로 정확한 정보를 제공하는 것이 중요했습니다.

Fish ladder는 James Bay, Quebec, Canada의 이스트 메인 강에 2005~2006년사이에 지어졌습니다. 2006년과 2007년에 실시된 후속 연구는, 다른 종의 물고기들이 이 사다리를 오를 수 있었던 반면, 철갑상어는 실패한 경우를 보여주었습니다. 기존의 Fish ladder에서 두 가지의 문제가 발견되었습니다. AECOM Tecsult inc에서의 물고기의 낮은 어획과 물의 빠른 속도가 문제가 되었습니다. 엔지니어들은 이러한 문제에 대한 해결책을 찾기 위해 FLOW-3D로 수치 모델링 연구를 수행하기로 결정했습니다.

 

Redesigning the fish ladder                          

AECOMTecsultinc. 엔지니어들은 물고기 사다리에 대한 최적의 설계 변경을 결정하기 위해 세가지 모델을 실행했습니다.

  • 유인을 극대화할 수 있는 강과 물고기 통로 사이의 흐름 분포를 평가하는 지역모델. 산란기 동안의 정상적인 조건에서 물고기 통로는 22m3/s의 유량흐름이 나타난다.
  • 슬롯 및 디플렉터의 개조를 위한 로컬 모델
  • 전체 길이에 걸쳐 수위 균형 유지를 위한 통로모델

Fish ladder specifications (before renovation)

Flow in fish passage before design optimization work

  • Length = 150 m
  • 17 basins
  • Drop = 3 m
  • Peak velocities of 2.6 m/s

Figure 1 – 45% of flow in fish passage shows velocities that are too high for the sturgeon to navigate

Figure 2 – 10% of flow in fish passage shows below the 1.8 m/s criteria required for sturgeon to navigate

Figure 3 – Tests were made with different additions of blocks (pink) and deflector plates (black) to find an optimum configuration

 

Validation of the numeric model

CFD모델을 실행한 후 엔지니어는 실험 데이터에 대해 숫자 결과를 검증했습니다. Flow-3D결과는 표면 높이를 비교하는 수문 기록과 비교되었습니다. 124개 중 80%가 유속이 일치했습니다.  동일한 위치 점에서 일치하지 않는 곳은 난류 영역이었습니다.

Velocity comparisons of measured data and FLOW-3D at specific locations

 

Meeting the criteria — modifications to flow rates

엔지니어들은 물고기가 곧장 바다로 가지 않도록 흐름을 15~20%로 줄이기 위해 Fish ladder를 개조하기로 결정했습니다. 그림 2는 그림과 비교하여 물고기 통로의 10% 유량으로 현저한 속도 감소를 보여 줍니다. 물고기 통로에 흐름의 45%를 가진 1. 그림 3은 흐름 속도를 늦추기 위한 블록 및 디플렉터를 보여 줍니다. 설정된 기준의 최대 속도는 1.8m/s 였습니다. 전체 흐름 조건은 그림 1과 2에서와 같이 모델로 잘 표현됩니다.

 

Conclusion

AECOM Tecsult inc 엔지니어들은 그들의 숫자 모델의 정확성을 검증할 수 있었고 FLOW-3D로부터 얻은 정보를 사용하였고 물고기 통로를 재설계하여 테스트와 관련된 높은 비용을 피할 수 있었습니다. 2008년 여름에 있었던 후속 연구에 따르면 철갑 상어가 높은 유량에도 불구하고 성공적으로 물고기 통로를 통과하고 있다는 것을 보여 주었습니다.

 

 

Sturgeon Navigate Fish Ladder

Sturgeon Navigate Fish Ladder

 

This material was provided by Jean-François Mercier, ing., Manager, hydraulics and hydrology at AECOM Tecsult inc.

AECOM Tecsult inc.은 FLOW-3D를 이용하여 물리적 모델링을 사용하지 않고 철갑상어가 Fish ladder를 탐색할 수 있는 물고기 사다리 설계를 개선했습니다. 실험은 현장구현의 제한과 비용때문에 배제되었고 FLOW-3D의 수치 모델링 결과로 정확한 정보를 제공하는 것이 중요했습니다.

Fish ladder는 James Bay, Quebec, Canada의 이스트 메인 강에 2005~2006년사이에 지어졌습니다. 2006년과 2007년에 실시된 후속 연구는, 다른 종의 물고기들이 이 사다리를 오를 수 있었던 반면, 철갑상어는 실패한 경우를 보여주었습니다. 기존의 Fish ladder에서 두 가지의 문제가 발견되었습니다. AECOM Tecsult inc에서의 물고기의 낮은 어획과 물의 빠른 속도가 문제가 되었습니다. 엔지니어들은 이러한 문제에 대한 해결책을 찾기 위해 FLOW-3D로 수치 모델링 연구를 수행하기로 결정했습니다.

 

Redesigning the fish ladder                          

AECOMTecsultinc. 엔지니어들은 물고기 사다리에 대한 최적의 설계 변경을 결정하기 위해 세가지 모델을 실행했습니다.

  • 유인을 극대화할 수 있는 강과 물고기 통로 사이의 흐름 분포를 평가하는 지역모델. 산란기 동안의 정상적인 조건에서 물고기 통로는 22m3/s의 유량흐름이 나타난다.
  • 슬롯 및 디플렉터의 개조를 위한 로컬 모델
  • 전체 길이에 걸쳐 수위 균형 유지를 위한 통로모델

Fish ladder specifications (before renovation)

Flow in fish passage before design optimization work

  • Length = 150 m
  • 17 basins
  • Drop = 3 m
  • Peak velocities of 2.6 m/s

Figure 1 – 45% of flow in fish passage shows velocities that are too high for the sturgeon to navigate

Figure 2 – 10% of flow in fish passage shows below the 1.8 m/s criteria required for sturgeon to navigate

Figure 3 – Tests were made with different additions of blocks (pink) and deflector plates (black) to find an optimum configuration

 

Validation of the numeric model

CFD모델을 실행한 후 엔지니어는 실험 데이터에 대해 숫자 결과를 검증했습니다. Flow-3D결과는 표면 높이를 비교하는 수문 기록과 비교되었습니다. 124개 중 80%가 유속이 일치했습니다.  동일한 위치 점에서 일치하지 않는 곳은 난류 영역이었습니다.

Velocity comparisons of measured data and FLOW-3D at specific locations

 

Meeting the criteria — modifications to flow rates

엔지니어들은 물고기가 곧장 바다로 가지 않도록 흐름을 15~20%로 줄이기 위해 Fish ladder를 개조하기로 결정했습니다. 그림 2는 그림과 비교하여 물고기 통로의 10% 유량으로 현저한 속도 감소를 보여 줍니다. 물고기 통로에 흐름의 45%를 가진 1. 그림 3은 흐름 속도를 늦추기 위한 블록 및 디플렉터를 보여 줍니다. 설정된 기준의 최대 속도는 1.8m/s 였습니다. 전체 흐름 조건은 그림 1과 2에서와 같이 모델로 잘 표현됩니다.

 

Conclusion

AECOM Tecsult inc 엔지니어들은 그들의 숫자 모델의 정확성을 검증할 수 있었고 FLOW-3D로부터 얻은 정보를 사용하였고 물고기 통로를 재설계하여 테스트와 관련된 높은 비용을 피할 수 있었습니다. 2008년 여름에 있었던 후속 연구에 따르면 철갑 상어가 높은 유량에도 불구하고 성공적으로 물고기 통로를 통과하고 있다는 것을 보여 주었습니다.

 

 

FSR-05-14_moisture drying model [수분/습기 건조 모델]

Introduction
In the manufacture of paper it is necessary to remove all water from the paper before it is rolled up. The majority of water is typically removed by squeezing the paper between large rollers. The remaining moisture can be removed by forcing hot air through the paper to accelerate its evaporation.
Using heated air can be an expensive process so there is interest in investigating optimum arrangements for achieving the fastest and least expensive means of removing the residual water from paper. A prototype arrangement using heated air is shown in the following figure: (그림은 첨부파일 참조)

Both the paper and the fabric backing are porous materials. The support blocks may not be porous. It is expected that the permeability of the fabric and paper will be a function of their water content.
This report describes a software development that allows for a realistic treatment of the drying process in porous media such as that shown in Fig. 1. A description is given of the new model, which has been validated with available data. This data does not cover the entire range of moisture content or airflow rates that are typically encountered in practice. Consequently, it may be found necessary to make some small model adjustments. It is hoped that the formulation of the model, which is based on simple physical principles, will be easy to adjust to fit a larger range of observations.
Before describing the new model, a better perspective of its capabilities can be appreciated by noting some of the ways that it differs from previous work on paper drying. Most importantly, the new model considers the paper as having finite thickness and properties such as moisture content, temperature and vapor concentration that vary through the thickness. Thus, the paper may have dried on the upstream side, but still be completely wet on the opposite side. Another difference is that air and water vapor constitute a two-component gas that is compressible. Compressibility means, for
example, that the gas velocity in the paper must increase in the direction of flow because of the decrease in pressure through the paper (i.e., density and/or temperature must decrease by expansion to give a pressure decrease). Since flow velocity has an important effect on drying rate, compressibility can influence local drying conditions in the paper.

Finally, by computing transient conditions throughout the paper, this model could be used to investigate arbitrary non-uniform initial conditions or paper with a non-uniform thickness and/or porosity distribution.

 

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FSR-05-14_moisture drying model

Water Rivers Bridge Piers

Bridge Piers

FLOW-3DSediment Scour Model 은 강이나 하천에서 수리학적으로 복잡한 교각과 지형에 따라 여러가지 퇴적물들의 높이 변화를 해석할 수 있습니다. 세굴 모델은 FLOW-3D 난류 모델들로 적분하여 3차원 분석이 가능합니다. FLOW-3D의 Shallow Water Model로 더 넓은 범위의 세굴 분석이 가능합니다.

Bridge piers scour simulation using FLOW-3D

교각 주위의 세굴 해석

세굴 모델은 deposition, packing, entrainment and drift-flux 메커니즘으로 되어있습니다. FLOW-3D v11 에서는 퇴적층의 형상을 FAVOR 하여 좀 더 정확하게 bed net 높이 변화를 시각화 할 수 있습니다. 시공간적으로 침전물의 변화뿐 아니라 유체의 부유물들, 바닥/유체 계면에서의 전단응력들을 분석할 수 있습니다.

Modeling Hydraulic Control Structures

In addition to the flow rates and detail of hydraulic behaviors associated with the control gate structures and powerhouse operation, FLOW-3D‘s sediment and scour model allows users to identify regions of high scour both near the control structure and further downstream in the vicinity of the bridge piers.

Bridge Pier Simulations

The first video shows a FLOW-3D simulation of the erosion that occurs around a group of three 2.4 m diameter piers as river water flows past at 1.5 m/s. The river depth is 15.8 m and the mean sediment size was presumed to be 0.35 mm.