Numerical Simulation Study of an Artificial Percolation Riverbed and Its Hydraulic Characteristics under Different Reynolds Numbers

Abstract

The direct extraction of clear water from a sandy river is a difficult task and can only be achieved through specific engineering measures. This paper proposes an artificial percolation riverbed structure for extracting clean water from sandy rivers, using a numerical simulation to study the flow field distribution characteristics of the structure under clean water conditions. The main conclusions are as follows: When the percolation vortex tube opening rate is 1.4%, the vortex tube with or without opening the percolation hole has little influence on the distribution characteristics of the flow field in the artificial riverbed, and the purpose of water extraction can be achieved while constructing a helical flow field. The axial flow velocity and circumferential flow velocity of the vortex tube cross-section under different Reynolds numbers show the distribution of a low-flow velocity close to the center of the vortex tube, and a high-flow velocity close to the vortex tube side-wall area. The average axial flow velocity and average circumferential flow velocity of the vortex tube show a trend of increasing and then decreasing distribution along the axial axis of the vortex tube in the direction of the sediment transport flume. The mean axial flow velocity of the vortex tube along the axis of the vortex tube toward the sediment transport flume and the mean circumferential flow velocity both show a distribution trend of increasing and then decreasing. At the junction of the vortex tube and the sediment transport flume, there are obvious pressure changes, and the pressure changes drastically under the same horizontal line. Along the direction of the bottom line of the vortex tube, the pressure at the vortex tube is obviously greater than that at the sediment transport flume. The vortex of the artificial percolation riverbed is mainly concentrated in the vicinity of the vortex tube, and the maximum value of the vortex intensity generally occurs at the junction of the vortex tube and the sediment transport flume. With the increase in the Reynolds number, the vortex intensity has an overall increasing trend, and the distribution of the vortex is more complex. This study helps to elucidate the distribution characteristics of the flow field in the artificial percolation riverbed, and it provides a reference basis for the future study of the flow field of artificial percolation riverbeds of sandy rivers.

1. Introduction

Most rivers in northern China are sandy. As a result, for the utilization of river water, sand must be extracted from the water. It is difficult to meet the water quality requirements of industrial and agricultural water users with direct water extraction, and at the same time, the presence of sediment may have a negative impact on water conservancy facilities and the environment. Therefore, different methods of water and sand separation must be used for the utilization of water from northern rivers. The current techniques for removing sand from rivers mainly include the following: interception of subsurface flow, infiltration wells [1,2], sand discharge swirl tubes [3,4], sand separation channels with swirling flow [5], sedimentation tanks [6], gill separators [7], and reverse osmosis water purifiers [8], among others. However, these techniques all have limitations to varying degrees, such as poor sand removal efficiency and high costs.

Therefore, in response to the various problems of existing techniques for removing sand from rivers with high sediment content, the author proposes an artificial infiltration riverbed water intake structure that allows for water intake without sand intake during water diversion from such rivers. Its advantages lie in its direct installation on the natural riverbed, small footprint, minimal impact on the ecological environment, ability to be unaffected by fine sediment particles during water and sand separation, high separation efficiency, direct discharge of sediment downstream, elimination of the cost of sediment handling, reduced project investment, and minimal energy consumption by utilizing the natural hydraulic head of the river.

However, currently, for complex structures like artificial infiltration riverbeds, the usual approach is to first study the flow field characteristics under clean water conditions. Once a thorough understanding of the flow field characteristics is obtained, subsequent research can be conducted by introducing sediment. Numerical simulation, with its high flexibility and scalability, allows for the simulation of different flow fields by changing model parameters and conditions. This approach saves a significant amount of time and cost compared to physical experiments and enables the completion of research that is currently not feasible under certain conditions. Therefore, numerical simulation methods are commonly used to study the complex internal flow characteristics of complex water treatment facilities. For example, Tian [9] utilized the Volume of Fluid (VOF) method to conduct three-dimensional numerical simulations of sand discharge swirl tubes under clean water conditions, analyzing the influence of various parameters on the flow velocity distribution inside the swirl tubes. Kirpa, H. [10] summarized the application of different Computational Fluid Dynamics (CFDs) methods in the design and analysis of sedimentation tanks. Tao [11] used the Euler model in Fluent to simulate the flow field of separation gills at different inclinations, obtaining the optimal combination of gill inclinations. Narasimha, M. [12] employed Large Eddy Simulation (LES) models to numerically simulate hydrocyclone and compared them with other models, ultimately demonstrating the accuracy of the LES model. K. U. Bhaskar [13] established a numerical simulation method for simulating hydrocyclone. Marvin. D. Cogollo [14] conducted a study on the complex dynamic characteristics of hydrocyclone using numerical simulations, proposing an improved computational model for assessing and enhancing the performance of hydrocyclone. Due to cost constraints, current research on the hydraulic characteristics of hydraulic machinery such as water pumps [15,16] and turbines [17,18,19] is mostly based on numerical simulations. These simulations study the effects of different structural parameters on the flow field of water pumps and turbines, and optimize their structures based on the numerical simulation results. Therefore, this paper mainly focuses on the numerical simulation research of the hydraulic characteristics of artificial infiltration riverbed water intake structures under clean water conditions. This study aims to prepare for future simulations of water and sediment transport and the optimization of structural parameters of artificial infiltration riverbeds.

2. Artificial Percolation Riverbed Water Extraction Methods

Aiming at the problems of the existing water extraction technologies for sandy rivers, we propose a new type of structure that is not restricted by the geological conditions or longitudinal slopes of the river, can achieve the purpose of extracting only water and not sand from sandy rivers, and at the same time, can save costs. The proposed invention can help realize efficient water extraction from sandy rivers.

The artificial percolation riverbed consists of percolation vortex tubes on both sides of the river, with a sediment transport flume at the center; the setup is shown in Figure 1. The main role of the artificial percolation riverbed is to artificially construct a spiral flow field to separate the water and sand, and at the same time, to percolate the water. The principle of the structure is that water enters the percolation vortex tube along the diagonal tangential direction and generates impact momentum, which forms momentum at the center of the vortex tube. This makes the water in the percolation vortex tube generate rotational movement, which combines with the longitudinal flow in the vortex tube to form a vortex tube spiral flow. The vortex tube is the main facility for water–sand separation, and the sediment in the water moves from the percolation vortex tube to the sediment transport flume under the action of the vortex tube spiral flow to ensure that the sediment does not accumulate in the percolation vortex tube. The sediment transport flume is connected to the end of the vortex tube, and its bottom is lower than the bottom of the end of the vortex tube. Its function is to discharge the water and sand in the vortex tube and transport them to lower reaches of the river. At the same time, under the premise of not affecting the cyclonic field of the vortex tube, percolation holes are added around the circumference of the vortex tube. This allows the water in the vortex tube to filter through the anti-filtration material layer to the underground catchment area, and then exit through the water pipeline, thus realizing the seepage of water.

There is a lack of research on the hydraulic characteristics of artificial percolation riverbeds because it is a new technology for water extraction from sandy rivers. Therefore, we adopted a numerical simulation supplemented by a physical test to study and compare the flow velocity, pressure, and vortex distribution of the vortex tube and its connection with the sediment transport flume of an artificial percolation riverbed (a vortex tube with open holes) with that of an artificial non-percolation riverbed (a vortex tube without open holes) under the conditions of clear water. The results of this study can help elucidate the flow field characteristics of the artificial percolation riverbed and provide a reference basis for future research on the optimization of artificial percolation riverbed structures and water–sand separation characteristics in sandy rivers.

3. Numerical Modeling and Experimental Validation

3.1. Geometric Modeling and Meshing

The dimensions and coordinate arrangement of the geometric model created for this study are shown in Figure 2.

In the case of a fixed riverbed longitudinal slope of 0.5%, the Reynolds number Re is the main control variable in this study, according to the commonly used diversion flow rate on small-scale diversion projects as well as the consideration of the measurement range of the laboratory measuring instruments, with which it is determined that the Reynolds number of the test is set to be 9817, 18,552, 34,341, 60,555, and 82,776 in total of five, respectively. A total of 10 models with different Reynolds numbers were established, including an artificial percolation riverbed (a vortex tube with open holes) and an artificial non-percolation riverbed (a vortex tube without open holes).

The meshing was performed using Polyhedra in Ansys Meshing. Polyhedra mesh combines many advantages of tetrahedral mesh and hexahedral mesh, while the mesh quality is better optimized compared to tetrahedral mesh, and it has higher accuracy and convergence compared to hexahedral mesh. Additionally, polyhedral mesh has many advantages, such as strong adaptability, high computational efficiency, small memory occupation, etc., which are great advancements in meshing technology. Meshing requires encryption of the vortex tube fluid region. Three sets of meshes were designed for this simulation, with their specific dimensions shown in

Table 1. Mesh design.

Division Parameters	Maximum Vortex Tube Encryption Size (mm)	Maximum Overall Grid Size (mm)	Total Number of Grids
First grids	2	5	703,529
Second grids	1	3	2,903,036
Third grids	0.5	1	11,612,144

.

Taking the artificial percolation riverbed with a Reynolds number of 34,341 under clear water conditions as an example, and comparing the simulated values with the experimental values in the test section of the flume in the profile between the measurement point (0, 0.065, 0.085) and the measurement point (0.120, 0.065, 0.085) along the measuring line of the pressure change, three different sets of grids and experimental values were compared, as shown in Figure 3.

As can be seen in Figure 3, the maximum deviation between the first set of grids and the experimental values is 2.7%. The second and third sets of grids are in good agreement with the experimental values, and the maximum deviation is not more than 1.2%. Considering the accuracy and computational efficiency, the second set of grids was selected for the simulation. Figure 4 presents a schematic diagram of the second set of grids.

3.2. Governing Equations

Since there is a free surface for air and water flow in open channels, the VOF model was used to calculate the liquid–gas two-phase flow. The model is based on the Eulerian method and introduces the variable of the volume fraction of the phase to track the interface of each computational unit so that the VOF model is highly accurate and effective for simulating an open-channel flow where there is a free surface. The volume fraction equation of the VOF model can be solved by implicit or explicit time formulation. The implicit time formulation was used in this simulation due to its numerical stability and better accuracy. When the implicit formula is used, the volume fraction discretization equation is

$${\displaystyle \frac{{\alpha }_q^{n+1}{P}_q^{n+1}-{\alpha }_q^n{P}_q^n}{\Delta t}}V+{\displaystyle \sum _f\left(P_q^{n+1}{U}_f^{n+1}{\alpha }_{q,f}^{n+1}\right)}=\left[S_{{\alpha }_q}+{\displaystyle \sum _{p=1}^n\left(m_{pq}-m_{qp}\right)}\right]V$$

(1)

where $m_{qp}$ is the mass transfer from phase q to phase p, and $m_{pq}$ is the mass transfer from phase p to phase q. By default, the source of $S_{{\alpha }_q}$ is 0; n + 1 is the index of the current time step; n is the index of the previous time step; ${\alpha }_q^{n+1}$ is the cell value of the volume fraction at the n + 1st time step; ${\alpha }_q^n$ is the cell value of the volume fraction at the nth time step; ${\alpha }_{q,f}^{n+1}$ is the face value of the volume fraction at step n + 1; $U_f^{n+1}$ is the volume flux through the surface at step n + 1; and V is the unit volume.

For the artificial percolation riverbed water flow, there are two different forms. The water flow in the diversion channel is free flowing under the effect of gravity, and the water flow in the percolation vortex tube is rotating, with a strong centrifugal force. Therefore, the viscous model used for this simulation was the realizable k-ε model. Compared to the RNG k-ε model and standard k-ε model, the realizable k-ε model corrects the vortex viscosity coefficients in each direction, and at the same time, it is highly applicable to the free flow of the mixed flow. Therefore, the computational results of the realizable k-ε model have the best fit with the experimental measured results.

3.3. Boundary Conditions

The model boundary conditions are shown in Figure 5 and Figure 6. For the artificial non-percolation riverbed boundary condition setup, the upstream channel flow inlet was set as a velocity inlet. The air inlet above the water surface line and the free surface of the open-channel flow were set as pressure inlets with an air volume fraction of 1. The downstream channel flow outlet was set as a pressure outlet with a return volume fraction of 1. The vortex tube and the rest of the boundaries were set as no-slip wall boundary conditions. For the artificial percolation riverbed model boundary conditions, the vortex tube opening outlet was set as a pressure outlet, and the return flow volume fraction was 1. The rest of the boundary conditions were the same as those of the artificial non-percolation riverbed model boundary conditions. The finite volume method was used to iteratively solve in the hidden format, the velocity–pressure coupling method was used in the coupled algorithm, the discrete format was used in the QUICK format, and the wall function was used in the Enhanced Wall Treatment wall function.

4. Results and Discussion

In this study, a numerical simulation was carried out to analyze the distribution of the flow field in artificial riverbed structures with and without percolation under different Reynolds numbers. The longitudinal section of the vortex tube and the cross-section of the vortex tube were selected for analysis, among which the transverse section of the vortex tube was selected to analyze the infiltration vortex tube cross-section 1, cross-section 2, and cross-section 3, because these three sections are located in the inlet, middle, and outlet sections of the vortex tube, respectively, which embody the overall development of the helical flow field in the vortex tube, and they have a very good representativeness. The results were analyzed as follows: the velocity distribution, pressure distribution, and eddy distribution of the flow field.

4.1. Analysis of Vortex Tube Flow Velocities in Artificial Riverbeds

4.1.1. Vortex Tube Axial Flow Velocity Analysis

Taking the distribution of the axial flow velocity in the vortex tube cross-section as an example, the positive direction of the axial flow velocity along the axis of the vortex tube toward the sediment transport flume was determined. The distribution of the axial flow velocity in the cross-section of the vortex tube at different Reynolds numbers and the distribution of the average axial flow velocity in the cross-section of the vortex tube in the histogram are shown in Figure 7 and Figure 8.

(1)

As can be seen in Figure 7, the distribution of the axial flow velocity in the cross-section of the vortex tube was between −0.20 m/s and 0.70 m/s, and the presence or absence of percolation had lesser influence on the distribution of the axial flow velocity in the cross-section of the vortex tube. The distribution of the axial flow velocity in the cross-section of the vortex tube shows a trend of a low axial flow velocity in the center region of the vortex tube and a high axial flow velocity in the region near the vortex tube side wall. This was due to the existence of forced vortices with higher vortex strength near the vortex tube side-wall region and free vortices with lower vortex strength in the center region of the vortex tube. Under the action of the vortex tube wall, the strength of the large, forced vortex pushed the axial water flow in the direction of the sediment transport flume. This increased the degree of influence of the forced vortex on the axial flow rate, so it was relatively large. The free vortex near the center of the vortex tube was smaller, and the axial flow rate was mainly affected by the gravity force in the direction of the vortex tube axis, making the axial flow rate relatively small. Near the center of the vortex tube, the axial flow velocity had a negative value, which indicates that the water flow in the vortex tube area did not move in the vortex tube axial direction to the sediment transport flume. However, some of the water flowed in the negative direction, forming a vortex, which overall moved in the form of a spiral flow in the positive direction. As the Reynolds number increased, the axial flow velocity in the vortex tube cross-section showed a significant increasing trend. This is because, under the premise that the other conditions remained unchanged, with the increase in the Reynolds number, the overall flow velocity of the flow field increased, and the corresponding axial flow velocity also increased.

(2)

As can be seen in Figure 8, at the same Reynolds number, the mean value of the axial flow velocity shows an increasing and then decreasing distribution from cross-section 1 to cross-section 3 of the vortex tube. This is because the development of the axial flow velocity from cross-section 1 to cross-section 2 was mainly influenced by the partial force of gravity along the axial direction of the vortex tube and the boundary conditions, which continually promoted the development of the axial flow velocity. Additionally, the axial flow velocity became larger due to the acute angle between the partial force of gravity and the direction of the axial flow velocity. From cross-section 2 to cross-section 3, the position was constantly close to the junction of the vortex tube and the sediment transport flume due to the strong turbulence of the water flow at the junction. This was accompanied by a high amount of energy exchange and mixing of the water flow, resulting in the phenomenon of localized reflux, which decreased the axial flow velocity of the vortex tube. As the Reynolds number increased, the overall axial flow velocities in cross-section 1, cross-section 2, and cross-section 3 increased. Taking the mean axial flow velocity value of the vortex tube cross-section of the artificial percolation riverbed as an example (the distribution law of the mean axial flow velocity value of the vortex tube cross-section of the artificial non-percolation riverbed was basically the same), when the Reynolds number transitioned from 9817 to 18,552, from 18,552 to 34,341, from 34,341 to 60,555, and from 60,555 to 82,776, the mean axial flow velocity value of the vortex tube in cross-section 1 increased by 20.1%, 30.0%, 41.0%, and 54.0%, respectively. In cross-section 2, the mean axial flow velocity increased by 21.4%, 29.4%, 45.5%, and 50.0%, respectively. In cross-section 3, it increased by 21.7%, 31.5%, 45.8%, and 51.4%, respectively. These results indicate that the mean axial flow velocity values of the vortex tubes increased as the Reynolds number increased.

4.1.2. Vortex Tube Circumferential Flow Analysis

Taking the clockwise direction as the positive direction of the vortex tube circumferential flow velocity, cloud plots of the distribution of the circumferential flow velocity across the vortex tube cross-section at different Reynolds numbers and histograms of the distribution of the average circumferential flow velocity values of the vortex tubes at different cross-sections are shown in Figure 9 and Figure 10.

(1)

As can be seen in Figure 9, the distribution of the vortex tube circumferential flow velocity was almost the same between the non-percolation condition and the percolation condition under the same working conditions. The distribution of the vortex tube circumferential flow velocity ranged from 0.01 m/s to 0.50 m/s. The distribution of the vortex tube circumferential flow velocity at different Reynolds numbers was close to that of the vortex tube and shows a trend of high circumferential flow velocity near the vortex tube side wall and low circumferential flow velocity near the vortex tube center. This is because the vortex tube circumferential flow velocity was mainly formed by the vortex tube upper water flow in the direction tangential to the vortex tube and by moving along the vortex tube side wall. In the region near the vortex tube side wall, an obvious forced vortex appeared, and a free vortex appeared in the vortex tube center region. Since the free vortex was derived from the viscous effect of the water due to the forced vortex rotation, the intensity of the forced vortex near the side wall was obviously greater than the intensity of the free vortex near the center, so the circumferential flow rate near the side-wall area of the vortex tube was high, while the circumferential flow rate near the center area of the vortex tube was low.

(2)

As can be seen in Figure 10, the maximum difference between the average circumferential flow velocity values of the vortex tubes with and without holes was not more than 4.2%, the maximum difference in the circumferential flow velocities was not more than 6.8%, and the difference in the minimum values was not more than 5.9%. This indicates that the effect of the opening rate of 1.4% on the vortex tube flow field was very small and did not disturb the distribution of the velocity of the vortex tube’s original flow field. The main reason for the differences is that the percolation seepage still produced a certain diversion effect, resulting in a localized water flow disturbance near the vortex tube openings, but the disturbance was so small that it was basically negligible. As the Reynolds number increased, the vortex tube circumferential flow velocity had a tendency to increase as a whole. From cross-section 1 to cross-section 2, the average circumferential flow velocity value of the vortex tube gradually became larger because the average circumferential flow velocity value of the vortex tube in cross-section 1 was not sufficiently developed. With the movement of the vortex tube in the axial direction toward the sediment transport flume, the spiral flow of the vortex tube continuously developed under the joint action of gravity and the conditions of the vortex tube boundary, and the average circumferential flow velocity value continuously increased. From cross-section 2 to cross-section 3, the average circumferential flow velocity value of the vortex tube gradually became smaller. This was because the vortex tube water flow met the main stream of the sand channel near the junction of the vortex tube and the sediment transport flume, which led to violent turbulence and energy dissipation. The kinetic energy was reduced, and the average circumferential flow velocity value of the vortex tube had a tendency to decrease accordingly.

4.2. Pressure Analysis of Artificial Riverbed Vortex Tube

The vortex tube pressure distribution was studied by taking the vortex tube cross-section and the vortex tube longitudinal-section pressure clouds as an example. The vortex tube cross-section and vortex tube longitudinal-section pressure clouds are shown in Figure 11 and Figure 12.

The following can be seen in Figure 11 and Figure 12:

(1)

The cloud plots of the overall pressure distribution are basically the same for the percolation and non-percolation conditions. With the increase in the Reynolds number, the pressure increased overall. This is because in the case of the constant width and slope of the artificial percolation riverbed, as the Reynolds number increases, the water depth increases, and the corresponding pressure increases.

(2)

As can be seen in Figure 11, the pressure distribution inside the vortex tube shows a “concave” distribution. This is due to the special structure of the vortex tube. The pressure in the vortex tube is redistributed, showing a “concave” distribution. The pressure on the center and the top of the vortex tube is low, and the pressure on the left and right sides, and bottom is high. This is because the water flow in the vortex tube is subject to the reaction force of the outer wall, which produces changes in pressure of different levels in different directions. Meanwhile, comparing the pressure distribution diagrams of cross-section 1, cross-section 2, and cross-section 3, it can be seen that the distributions of cross-section 2 and cross-section 3 are similar, while there is a difference in cross-section 1. The pressure upstream of the vortex tube in cross-sections 2 and 3 is greater than that downstream of the vortex tube, while the pressure upstream of the vortex tube in cross-section 1 is less than that downstream of the vortex tube. This is mainly due to the action of the artificial riverbed sidewall at cross-section 1, where a secondary flow is formed downstream at the junction of the vortex tube and the artificial riverbed sidewall, which, in turn, leads to relatively high pressure.

(3)

As can be seen in Figure 12, at the junction of the vortex tube and the sediment transport flume, there is a significant pressure change, and the pressure changes drastically along the same horizontal line. In the direction of the bottom line of the vortex tube, the pressure at the vortex tube is obviously greater than the pressure at the sediment transport flume, so under the action of pressure, the water flows from the vortex tube to the sediment transport flume in the direction of the bottom line of the vortex tube.

4.3. Volume Analysis of Artificial Riverbed Eddy

Since there are a large number of eddy structures with different scales and intensities in turbulent flows, they play a crucial role in the generation and maintenance of turbulence, and the generation and collapse of eddies are accompanied by the conversion and dissipation of energy [19]. Therefore, the study of the vortex characteristics of the artificial percolation riverbed is very meaningful for understanding its flow field structure. There are many ways to determine vortices [20,21,22,23], among which the Q criterion [24] is more computationally efficient. Its effect is remarkable, and it is an excellent method for vortex identification. The Q criterion is a decomposition of the velocity tensor into two parts.

$${\displaystyle \frac{\delta {\mathrm{u}}_{\mathrm{i}}}{\delta x_j}}=0.5\left[{\displaystyle \frac{\delta u_i}{\delta x_j}}+{\displaystyle \frac{\delta u_j}{\delta x_i}}\right]+0.5\left[{\displaystyle \frac{\delta u_i}{\delta x_j}}-{\displaystyle \frac{\delta u_j}{\delta x_i}}\right]$$

(2)

Here, the symmetric part, denoted by S, is often referred to as the strain rate tensor, and the antisymmetric part, denoted by Ω, is often referred to as the rotation rate or vortex tensor.

$$S=0.5\left[{\displaystyle \frac{\delta u_i}{\delta x_j}}+{\displaystyle \frac{\delta u_j}{\delta x_i}}\right]$$

(3)

$$\mathrm{\Omega }=0.5\left[{\displaystyle \frac{\delta u_i}{\delta x_j}}-{\displaystyle \frac{\delta u_j}{\delta x_i}}\right]$$

(4)

The inverse viscous stress tensor is defined as

$$\tau =\mu \left[{\displaystyle \frac{\delta u_i}{\delta x_j}}+{\displaystyle \frac{\delta u_j}{\delta x_i}}\right]$$

(5)

and it can be seen that the viscous stress tensor is only a specific function of the strain rate tensor. With this in mind, the Q value is defined as the second invariant of the velocity gradient tensor.

$$Q=0.5\left[{‖\mathrm{\Omega }‖}_F^2-{‖S‖}_F^2\right]$$

(6)

It can be seen that positive values of Q indicate regions of the flow field where vorticity dominates, and negative values indicate regions where the strain rate or viscous stress dominates. Figure 13 shows a 3D vortex volume map of the vortex tube using an identification method based on the Q criterion.

The following can be seen in Figure 13:

(1)

Regardless of the presence or absence of percolation, the vortex is mainly concentrated near the vortex tube, and its intensity ranges between 0 and 0.8. This is because at the junction of the vortex tube and the bed surface, the boundary conditions change dramatically, resulting in a sharp change in the flow velocity gradient there. This forms a strong vortex that moves forward in the axial direction of the vortex tube, forming a spiral flow. The vortex intensity in the middle of the vortex tube is relatively low, and the change in the vortex intensity is relatively stable. This is because of the special three-dimensional structure of the vortex; the main stream is mainly distributed near the side wall of the vortex tube and moves along the axis of the vortex tube toward the sediment transport flume. Therefore, the vortex intensity is relatively low in the center and higher near the sidewalls. The maximum vortex intensity generally occurs at the junction between the vortex tube and the bed surface, and between the vortex tube and the sediment transport flume. This is because this is where the vortex tube spiral flow meets the main flow of the sediment transport flume, which generates intense turbulence, accompanied by a large amount of energy exchange. This results in the maximum vortex intensity at this place.

(2)

As the Reynolds number increases, the vortex strength has an overall tendency to increase. Although the size of the vortex in the flow field depends mainly on the boundary conditions of the flow field rather than the size of the Reynolds number, the rate of the incoming velocity and its Reynolds number will not change the fixed boundary conditions to form a vortex size of an order of magnitude. However, based on turbulence-level string theory [25], it can be seen that as the Reynolds number increases, the dissipation scale of the vortex decreases, so the change in the vorticity from large to small in the flow field is more complex, and the vortex distribution increases. Therefore, as the flow rate increases, the vortex distribution becomes more complex with an overall increasing trend.

5. Conclusions

In this study, using a numerical simulation combined with a physical model test to validate the results, the flow field of an artificial non-percolation riverbed under clear water conditions and its characteristics were determined. The results show the following:

• The presence or absence of percolation has little effect on the flow velocity, pressure, and vortex characteristics of the flow field of the artificial riverbed when the percolation vortex tube opening rate is 1.4%, which shows that the special structure of the artificial percolation riverbed can achieve the purpose of water abstraction while constructing a spiral flow field.
• The axial flow velocity distribution of the vortex tube cross-section under different Reynolds numbers shows a distribution trend of a low axial flow velocity in the center region of the vortex tube and a high axial flow velocity in the region close to the side walls of the vortex tube. The circumferential flow velocity distribution of the vortex tube at different Reynolds numbers shows an overall distribution trend of high circumferential flow velocity near the vortex tube side-wall region and low circumferential flow velocity near the vortex tube center region. At the same Reynolds number, from cross-section 1 to cross-section 3 of the vortex tube, the mean axial flow velocity and the mean circumferential flow velocity of the vortex tube show a distribution that increases and then decreases. As the Reynolds number increases, the mean circumferential flow velocity and the mean axial flow velocity of the vortex tube have an overall increasing trend.
• With the increase in the Reynolds number, the pressure of the artificial percolation riverbed increases as a whole. The pressure distribution in the cross-section of the vortex tube shows a “concave” distribution. At the junction of the vortex tube and the sediment transport flume, there are obvious pressure changes, and the pressure changes drastically at the same level. Along the bottom line of the vortex tube, the pressure at the vortex tube is obviously greater than that at the sediment transport flume, so under the action of pressure, the water flows from the vortex tube to the sediment transport flume along the bottom line of the vortex tube.
• The vortex is mainly concentrated in the vicinity of the vortex tube, the vortex intensity in the middle of the vortex tube is relatively small, and the vortex intensity is relatively stable. The maximum value of vortex intensity generally occurs at the connection between the vortex tube and the bed surface and between the vortex tube and the sediment transport flume. With the increase in the Reynolds number, the vortex intensity has an overall increasing trend, and the distribution of the vortex becomes more complicated.