Study on Characteristics of Water Flow Under Different Riverbed Structures in River Narrowing Section

In this paper, a numerical simulation research on the flow characteristics of dammed river under four kinds of riverbed structures is studied by using the turbulence model and the VOF model.The results show that: 1 Due to the influence of the riverbed structure, the water flow vortex area of different riverbed structures is obviously different. The backwater and the reflux are the most obvious in a simulated bucket basin model of step-pool structure. 2 The average velocity of the section of the bucket basin riverbed and the clustered riverbed is small, and the steady flow velocity is not large. Combined with the base pressure distribution of the riverbed, the pressure distribution of the bucket basin riverbed and ribbed riverbed is relatively regular.This shows that the bucket basin structure is of great help to improve the stability of riverbed. ○3 The bucket basin model has better effect of energy dissipation than the other three types. 1 Research Background The mountain rivers in the river valleys and bank slopes are affected by certain geological and geomorphological conditions to cause collapse, landslides, mudslides and other activities, forming deposits to block the original river channels, resulting in significant narrowing of the river channels and changing the characteristics of the water flow, and the riverbed slope becomes larger. In the narrowing river channel, various types of riverbed structure will be formed, which will affect the river flow characteristics and water and sediment movement. Some scholars have done related research. Wang Shuying[1] etc. studied the influence of geological conditions and river bed evolution in mountainous areas, and compared the model calculated value with the result of hydrodynamic SMS software to obtain the flow structure characteristics of the wide and narrow rivers. Zhou Sufen[2] etc. tested the calculated value of flow mathematical model and the water flow of wide and narrow flume. It is concluded that the wide and narrow river channel’s width gradation will cause the water depth and flow velocity to change. The water depth is the lowest where velocity is the largest at the narrowest section of the river. The water depth reaches the peak at the widest section of the river where velocity is the smallest. WANG[3] etc. studied the types of riverbed structures. Jong and Ergenzinger[4] etc. explored the influencing factors in the development of riverbed structures, such as hydraulics and topography, etc. Liu Huaixiang[5] etc. statistically analyzed the geomorphological characteristics and riverbed structure development of typical inferior river regions in China. The study shows that the riverbed structure is the embodiment of the self-regulation of the river system, forming a negative feedback mechanism of ‘downcutting collapse and landslide river structure development suppressing downcutting. It also discussed the energy dissipation effect of riverbed structure on water flow. Yu Guoan[6] etc. observed and analyzed the bed load particles motion of mountain rivers in three typical riverbed structures, and initially studied the restrictive relationship between bed load motion and riverbed structure development. It is an inevitable trend to study and solve the problem by generalizing the entity into a physical model and a mathematical model and combining the two in the study of the characteristics of river flow. However, in terms of the research content, the research on wide and narrow river channels in mountainous areas mainly focuses on the change of flow velocity and water level. There are not many studies on the pressure distribution at the bottom of riverbed. The understanding of the movement mechanism of the water flow characteristics in the narrowing river is not enough, and there are few studies on the use of engineering design. In this paper, a numerical simulation of four riverbed structures is carried out to study the characteristics of water flow movement in narrowing sections of mountain rivers under the conditions of right-angled stepped, bucket basin model, ribbed and clustered riverbed structures. 2 Theoretical basis of numerical simulation 2.1 Numerical Simulation Methods , 0 (2018) MATEC Web of Conferences https://doi.org/10.1051/matecconf/201824602044 2


Research Background
The mountain rivers in the river valleys and bank slopes are affected by certain geological and geomorphological conditions to cause collapse, landslides, mudslides and other activities, forming deposits to block the original river channels, resulting in significant narrowing of the river channels and changing the characteristics of the water flow, and the riverbed slope becomes larger. In the narrowing river channel, various types of riverbed structure will be formed, which will affect the river flow characteristics and water and sediment movement. Some scholars have done related research. Wang Shuying [1] etc. studied the influence of geological conditions and river bed evolution in mountainous areas, and compared the model calculated value with the result of hydrodynamic SMS software to obtain the flow structure characteristics of the wide and narrow rivers. Zhou Sufen [2] etc. tested the calculated value of flow mathematical model and the water flow of wide and narrow flume. It is concluded that the wide and narrow river channel's width gradation will cause the water depth and flow velocity to change. The water depth is the lowest where velocity is the largest at the narrowest section of the river. The water depth reaches the peak at the widest section of the river where velocity is the smallest. WANG [3] etc. studied the types of riverbed structures. Jong and Ergenzinger [4] etc. explored the influencing factors in the development of riverbed structures, such as hydraulics and topography, etc. Liu Huaixiang [5] etc. statistically analyzed the geomorphological characteristics and riverbed structure development of typical inferior river regions in China. The study shows that the riverbed structure is the embodiment of the self-regulation of the river system, forming a negative feedback mechanism of 'downcutting -collapse and landslide -river structure developmentsuppressing downcutting. It also discussed the energy dissipation effect of riverbed structure on water flow. Yu Guoan [6] etc. observed and analyzed the bed load particles motion of mountain rivers in three typical riverbed structures, and initially studied the restrictive relationship between bed load motion and riverbed structure development. It is an inevitable trend to study and solve the problem by generalizing the entity into a physical model and a mathematical model and combining the two in the study of the characteristics of river flow. However, in terms of the research content, the research on wide and narrow river channels in mountainous areas mainly focuses on the change of flow velocity and water level. There are not many studies on the pressure distribution at the bottom of riverbed. The understanding of the movement mechanism of the water flow characteristics in the narrowing river is not enough, and there are few studies on the use of engineering design.
In this paper, a numerical simulation of four riverbed structures is carried out to study the characteristics of water flow movement in narrowing sections of mountain rivers under the conditions of right-angled stepped, bucket basin model, ribbed and clustered riverbed structures. The motion of three-dimensional water flow is complicated, so it is important to choose a suitable numerical simulation method. After a lot of practice tests, it is found that the simulation accuracy and effect are better in the simulation of natural rivers by using the two-equation turbulence model of time-average Reynold equations. It is relatively a mature method. In this paper, a VOF model of water-air two-phase flow and twoequation turbulence model are combined to carry out numerical simulation; 3-D orthogonal curvilinear coordinate system with the finite volume method and SIMPLEC algorithm are adopted to have a coupling calculations of pressure and speed; A point implicit scheme Gauss-Seidel iterative method is used to solve the finite equations.

Numerical Simulation Methods
The VOF model used in this paper performs a simulation tracking of the free surface by solving the individual momentum equations and calculating the volume of the fluid in the grid cell; it is suitable for processing the steady and transient of the gas-liquid interface. The governing equation for this method consists of volume fraction equation and a conservation equation.

Governing Equation
The water flow movement changes with the river path, water depth and river width, and it is a three-dimensional problem. A combination of k-ε turbulence model and VOF model is used to perform a simulation in this study. In In the above formula: ρ and μ represent the density and molecular viscosity coefficient; P represents the pressure term under gravity condition; σk and σε represent the turbulent Prandtl number of k and ε, where σk=1.0， σε=1.3; C1 ε and C2 ε represent the constants of ε .92. The turbulent energy k and turbulence dissipation rate ε are put into equation (5) to obtained the turbulence viscosity coefficient μt. In equation (5), C μ represents the empirical constant, where C μ =0.09; G represents the turbulent energy caused by average velocity gradient which can be defined by equation (6); Equation (7) is the control differential equation for the water volume fraction αw. Solving this control differential equation is to perform a simulation tracking of air-water interface. ui and xi represent the velocity component and the coordinate component, and t represents time. As shown in figure 1, the model will be divided into 3 critical sections: the import section, the wide section and the narrow section, and the length of the simulated channel is 210m in total, the widest segment is 20m and the narrowest segment is 10m. the width of the narrow segment is unchanged and the wide segment is elliptic. The slope of the narrow segment is 13.5% and the wide segment is horizontal. Four models of right-angled stepped, bucket basin model, ribbed and clustered riverbed structures are set up as follows. As shown in Figure 2, it is a right-angled stepped model where the channel is stair-stepping on the narrow segment. In total, there are 5 steps, the height of each step is 1m and the length is 7.5m. When the water flows through the steps, there will be a vertical falling buffer, so as to reduce the flow rate and achieve the purpose of energy dissipation. As shown in figure 3, it is a bucket basin model which stimulates the step-pool structure. This model changes the general staircase shape to form the model of water cushion. The height difference between the exit and the lowest point is 2m, and the upper pick height is 1m. When water flows through, there will be a process of "up and down", so as to increase the turbulence. As shown in figure 4, it is a ribbed model. 5 stone rectangular clusters, which are 10m in length, 1.2m in width and 1m in height are set up on the narrow section. When water flows through the narrow section, it needs to continuously flow through five rectangular stone clusters, and the water speed will gradually slow down, so as to achieve the purpose of    The flow inlet is defined as the velocity inlet boundary, the upper boundary as the pressure inlet boundary, and the downstream outlet as the pressure outlet boundary. The wall surface adopts the non-slip condition, and the standard wall function method is used to simulate the near-wall surface, and the total number of dividing grids is controlled between 200,000 and 300,000 4 Numerical simulation results and analysis  Figure 8 is a velocity vector distribution profile of the narrow section (X=124m to X=128m) Y=0 profile of the four models, reflecting water movement on the Y=0 profile under different riverbed structures of narrow section. It can be seen from the figures that under the Model 1 riverbed structure, the falling water flow forms a local reflow; In model 2, the bucket forms a water cushion, which causes the reflow phenomenon to be more pronounced and plays a significant role in the energy consumption of the water flow；In model 3, due to the resistance of the ribbed slab, the water flow also begins to reflow; Model 4 has a larger contact area with the water flow along the flow direction, and has a greater blocking effect on the water flow, increasing the turbulence intensity of water flow. Model 1 utilizes a continuous step to create a horizontal roll at the starting position of each step of the drained water flow, and a strong mixing effect with the main flow of the step to increase the turbulence of the water flow；Model 2 is to let the water flow into each step, form a water cushion on the ladder, and consume the energy of the water flow；Model 3 and model 4 have similar mechanisms. By increasing the resistance of the riverbed, the water flow produces strong turbulence, and most of the kinetic energy is converted into turbulent kinetic energy to achieve energy dissipation.  Figure 9 below shows the distribution of the average flow velocity along the narrow section (X=86m to X=140m) under four different models. The overall trends of the average flow rate of modes 1, 2, 3, and 4 are roughly equal, all are increase -fluctuation -decrease, and finally stabilize. The average flow velocity of model 3 begins to decrease at X = 122 m, and models 1, 2, and 4 begin to decrease at X = 126 m. The outlet section flow velocity values are similar in model 2, 3, and 4, which is about 0.54 m/s, and the model 1 is 0.94 m/s, which is obviously higher than the others. Throughout the change process, the model 2 has a water cushion formed by the arc shaped of the riverbed, which makes the water body involved in more energy dissipation. Therefore, the overall fluctuation is more severe, the amplitude is larger, but the stability is better. The model 3 variable amplitude value reaches the highest of all models. Among the four models, the average flow velocity maximum appeared at 3.07 m/s when X = 102 m at model 3, and the minimum value appeared at 0.20 m/s when X = 98 m at model 2. In the step of model 1, the pressure at the bottom of the river bed changes very little, about 10 KPa, and the pressure at the bottom of the riverbed appears at X = 96 m with a peak of 12 KPa. From the cloud map of the narrow section of the model 2, it can be seen that the pressure value at the bottom of the riverbed at all levels are relatively regular, and the pressure value is around 14KPa, the most highest pressure region at the bottom of riverbed occurs at X=104m, which is 20KPa due to the large difference between the front and back of the bucket. The pressure distribution at the bottom of the riverbed in the narrow section of Model 3 is different from model 1. At the earliest stage, the pressure peak at the bottom of the riverbed is 20KPa at X=104m, and the pressure at the bottom of the riverbed at X=130m is increased compare to the upper part of the narrower section X=80m, and the distribution along each step is more regular. It can be seen from the figure that under the condition of model 4, the maximum pressure at the bottom of the riverbed appears at the X=98m upstream of the narrow section which is 18KPa.

Pressure Distribution at the Bottom of the Riverbed
In summary, riverbed structure varies accordingly with the pressure peak position at the bottom of the riverbed in the narrow section of the river channel, which change with a wide range, and the distribution is not evenly distributed at wide sections.

Estimation of Energy Dissipation
Due to its special riverbed structure, The water flows, the energy of water flow is consumed to varying degrees through the narrow sections of the models 1, 2, 3, and 4. The writer calculate the energy dissipation ratios under the four models by total flow energy equation. The comparison of energy dissipation ratios under the four models is shown in Figure 12. Selecting X=86m for the upper section of the river channel and X=140m for the downstream section of the river channel and listing the energy equations of the upstream and downstream sections and calculate the equation of energy dissipation ratio: In the equation, U 1 and U 2 are the average flow velocity of the upstream and downstream sections, respectively ； d 1 and d 2 are the water depths of the upstream and downstream sections ； H S is the step height, that is, the height difference of the bottom of the riverbed in the upstream and downstream sections；α 1 and α 2 are the kinetic energy correction coefficients of upstream and downstream；h f is the head loss; g is the acceleration of gravity,β is energy dissipation ratio.
After calculation, the energy dissipation ratio of model 1 is the lowest, which is 74.98% while model 2 is the highest, which is 79.01%, model 3 and model 4 is between the two. It proves that the energy dissipation effect of the bucket style of riverbed structure is better than the other three models.

Conclusions
(1) Influenced by the structure of the riverbed, the flow field distribution of different riverbed structures are quite different. For the model of the simulated step-pool and bucket basin structure, the reflux is most obvious and the turbulence is more severe (2) The variation amplitude of average velocity of the section of bucket basin and cluster riverbed structure is small. Combined with the pressure distribution at the bottom of the riverbed, the the bucket basin riverbed structure and the ribbed riverbed structure are more regular, which illustrates that bucket basin riverbed structure is of great help to improve the stability of the riverbed. Through comprehensive comparison, the structure of the bucket basin riverbed is more conducive to inhibiting the current scour of the riverbed surface and protecting the riverbed.
(3)The effect of energy dissipation of the bucket basin riverbed structure is better than the other three types, which reduces the requirements of the downstream energy dissipation facilities of the river channel, saving construction costs and improving efficiency.