Study on Internal Flow Characteristics of Hydrocyclone with Guide Vanes

Abstract

Hydrocyclone with guide vanes is one type of swirl flow launching device without energy input. For researching the flow characteristics of that hydrocyclone, the flow distribution of the sections and their variation along the flow were studied using numerical simulation and physical experiment. In addition, the flow field was convenient to be divided into three-dimensional velocities: axial velocity, circumferential velocity, radial velocity and the static pressure. The result showed that the water flow had obvious diversion by the effect of guide vanes. The axial velocity varied into the distribution of higher values emerging away from the pipe wall and the surfaces of guide vanes, and the value was higher on downstream surfaces than upstream surfaces of the guide vanes. The radial velocity’s direction pointed at the axis of pipe on upstream surfaces, and pointed at the pipe wall on the downstream surfaces of the guide vanes; the influenced range was larger in sections along the flow. The circumferential velocity increased along the flow, closing the distorted guide vanes; the value of that velocity was larger closer to the guide vanes, especially the downstream surfaces of the guide vanes. The static pressure decreased along the flow, and the value was larger on the upstream surfaces than the downstream surfaces of the guide vanes. The results can provide some theory references to improve the construction of the hydrocyclone.

1. Introduction

Many northern rivers in China have high sand content, and most of the reservoirs built on these rivers face more serious sedimentation problems. The large amount of sediment accumulation will reduce the reservoir capacity [1,2], shorten the service life of reservoirs and affect the safety of dams [3]; therefore, it is necessary to deploy sand discharge pipelines for sand discharge and transport [4]. It has been found that circular pipe hydrocyclone conveying can achieve higher concentration and lower flow rate of solid particle transport, and this is now widely used in sand dredging [5]. In order to further improve the efficiency of circular pipe hydrocyclone conveying, a lot of research has been carried out on the spiral flow generation device.

In the 1930s, Parshall [6] proposed the idea of arranging sand discharge vortex pipes at the bottom of the canal to generate spiral flow to reduce siltation, and Robinson then [7] investigated the spiral flow of vortex pipes for sand discharge in terms of theory and model tests. Rusak et al. [8] found that the peak circumferential velocity decayed and shifted toward the axis as the spiral flow moved downstream, while the axial velocity was very different in the low and high rotational fields, with the former showing a single peak at the axis and the latter showing a double peak on both sides of the axis. Parchen et al. [9,10] investigated the decay of swirl flow in a horizontal pipe and showed that the decay of the angular momentum component depends on the distribution of the initial velocity even downstream of the hydrocyclone. Granata et al. [11] investigated the swirl flow in pipes at large Reynolds number and revealed the theory of vortex dynamics at large Reynolds number. Ronald et al. [12] studied the nature of rotating flow in straight pipe cyclonic flow using the near-wall quadratic equation, evaluated the feasibility of three different near-wall quadratic equations, and improved the dissipation rate equation. Since the 1970s, experts and scholars in China have also begun to pay attention to the spiral flow sand discharge, which has been thoroughly studied and its structure has been optimized. Zhang Kaiquan [13] analyzed the principle of spiral flow sand discharge and considered that spiral flow can be regarded as a kind of large scale vortex, and calculated the flow coefficient and diversion ratio of the vortex pipe by measuring the flow rate in the vortex pipe and the water depth in the channel. Zhou Zhu [14,15] conducted a model test on the circulation chamber sand discharge facility invented by Sarakhov [16], optimized its structure form by analyzing the flow field and sand discharge mechanism, and came up with the structure form of “strong spiral flow sand discharge funnel”.

As a kind of spiral flow generating device, it is necessary to study the effect of the variation of its structural parameters on the spiral flow generated by the guided vane hydrocyclone. Lin Yu et al. [17,18] studied the circular pipe slurry spiral flow and revealed the flow velocity distribution law of the circular pipe spiral flow. Jiang Minghu et al. [19] used different types of turbulence models to simulate and analyze the single-phase fluid flow of spiral flow in the circular hollow pipe, and found that the general spiral flow can be calculated with reliable accuracy using the RNG k-ε model. Zhang Yu et al. [20] researched the flow velocity distribution characteristics of hydrocyclone with different guide vane placement angles using a self-circulating experimental device, and concluded that the flow conditions were better when the guide vane placement angle was 15° or 45°. Wu Penglin [21,22] studied the formation and decay process of spiral flow in horizontal circular pipe, analyzed the flow velocity distribution after the hydrocyclone and the decay process of downstream spiral flow. Sun Xihuan et al. [23,24,25] studied the characteristics of the spiral flow field generated by hydrocyclones with different structural parameters, analyzed the velocity loop quantity and vortex intensity of the vorticity field, calculated the pressure energy loss of the hydrocyclone and the rotational kinetic energy of the outlet section, and discussed the drag loss and loss coefficient of the hydrocyclone.

In summary, circular pipe hydrocyclone conveying can effectively improve the efficiency of sediment conveying, and the improved effect is related to the selection of guide vane parameters in the hydrocyclone. However, the concentric deflection of the guide vane will make the state of the water flow in the pipe redistributed, which is studied in this paper, mainly analyzing the distribution characteristics of the flow velocity and static pressure inside the hydrocyclone and discussing the reasons. Due to the occlusion of the guide vane structure, there are large experimental errors in both contact and optical measurement methods. Therefore, we used particle image velocimetry (PIV) to conduct visualization experiments on the unobstructed area of the hydrocyclone under the premise of ensuring the experimental accuracy and used the experimental data to verify the feasibility and credibility of the CFD method. The CFD results were used to resolve the complex flow field caused by the hydrocyclone, and the distribution of flow velocity and pressure inside the cyclone was examined. The clear flow field results in this study are beneficial to help interested scholars better understand the flow state inside the hydrocyclone and provide a reference for further research on the structural parameters of hydrocyclone.

2. Research Program

2.1. Selection of the Hydrocyclone Structure Parameters

The guide vane cyclone is a device that generates spiral flow by installing fixed twisted guide vanes on the pipe wall.

The guide vane hydrocyclone is a device that generates spiral flow by installing fixed twisted guide vanes on the pipe wall. In the test, the inner radius of the hydrocyclone pipe is R = 50 mm and the length is 550 mm. Three guide vanes are arranged at equal intervals on the inner wall of the hydrocyclone; the total length of the guide vanes is 400 mm, the distance from the inlet section of the hydrocyclone is 50 mm, the distance from the outlet section is 100 mm, the length of the straight section of the guide vanes is 100 mm and the length of the curved section is 300 mm. The guide vane is twisted 1° every 20 mm during the curved section; the guide vane wrap angle is 15°, the guide vane placement angle is 45.52°, and the guide vane thickness is 5 mm. The height of guide vane H is 30 mm, that is, the relative height of guide vane H/R is 0.6. Hydrocyclone guide vane arrangement and guide vane parameters are shown in Figure 1.

2.2. Arrangement of Characteristic Sections and Feature Points

When analyzing the overall distribution of the flow field inside the hydrocyclone, the distance from the inlet section of the model is Z. Seven sections are selected along the range of Z = 1000 mm, Z = 1050 mm, Z = 1150 mm, Z = 1250 mm, Z = 1350 mm, Z = 1450 mm, Z = 1550 mm for analysis. The sections are named Z1000, Z1050, Z1150, Z1250, Z1350, Z1450 and Z1550, respectively, and the locations of the sections are shown in Figure 2. Among them, Z1000 and Z1550 are the inlet section and outlet section of hydrocyclone respectively. The inlet section of hydrocyclone is 0.5 times the pipe diameter upstream of the leading edge of the guide vane, and the outlet section is twice the times of the pipe diameter downstream from the trailing edge of the guide vane. Z1050, Z1150, Z1250, Z1350, Z1450 are the five sections of the hydrocyclone internal guide vane section selected at equal intervals, and the distance between sections is 100 mm.

Feature points are arranged inside the hydrocyclone to extract the data of axial velocity, radial velocity, circumferential velocity and static pressure at the feature points to study their along-range variation trend. Since the water flow in the hydrocyclone is symmetrical regrading the pipe axis and the flow field in the area between the three guide vanes is similar, feature points are created only for the 120° fan-shaped region between two of the guide vanes. The fan-shaped region is enclosed by the upstream surfaces of one guide vane and downstream surfaces of the other guide vane, the pipe wall, and the extension line of the guide vane in the direction of the pipe axis. Seven polar axis are uniformly distributed in the fan-shaped region, with angles θ = 15°, θ = 30°, θ = 45°, θ = 60°, θ = 75°, θ = 90°, and θ = 105°, respectively, to the upstream surface of the guide vane. The feature points are arranged in four layers along the radial direction, and the distances from the tube axis are r = 0.6R, r = 0.7R, r = 0.8R, and r = 0.9R, respectively, and a total of 28 feature points are arranged in each section. Figure 3 shows the feature point arrangement of section at the front of guide vane. A total of nine layers of feature points are set from the leading edge of the guide vane to the trailing edge of the guide vane, and the expansion of the projected pipe wall at feature points is shown in Figure 4. The trajectory of the feature points is parallel to the projection of the guide vane surface on the pipe wall.

3. Construction of a Mathematical Model of Guided Vane Hydrocyclone

3.1. Geometric Modelling

The hydrocyclone model and pipe model established in this paper are shown in Figure 5. The model has a total length of 7000 mm, of which the hydrocyclone is 550 mm long, the upstream pipe section is 1000 mm long and the downstream pipe section is 5450 mm long.

3.2. Mesh Division

The model was imported into ICEM CFD to mesh the computational domain. In the meshing, unstructured tetrahedral mesh with a maximum size of 3 mm and 2.5 mm on the surface of the guide vane is generated because of the complex structure of the internal region of the hydrocyclone. While the upstream and downstream regions are standard cylinders with simple structure, structured hexahedral mesh with O-profile is used with a maximum size of 3 mm.

Since the k-ε model is used in this simulation, the wall function requires a restriction on Y+. If Y+ is too small, the wall function is not available, while if Y+ is too large, the viscous bottom layer cannot be solved. Therefore, the y+ needs to be estimated, and the calculation formula is as follows:

(1)

Estimating Reynolds number:

$$R_e=\frac{\rho uL}{\mu }$$

(1)

(2)

Estimating wall friction coefficient:

$$C_f=0.058R_e^{-0.2}$$

(2)

(3)

Calculating wall shear stress:

$${\tau }_w=0.5C_f\rho U_{\infty }$$

(3)

(4)

Using wall shear stress to estimate the speed:

$$U_{\tau }=\sqrt{\frac{{\tau }_w}{\rho }}$$

(4)

(5)

Calculating the height of the first mesh layer:

$$\mathrm{y}+=\frac{y{U}_{\tau }\rho }{\mu }$$

(5)

In the formula: $\rho$ is the fluid density; u is the flow characteristic speed; L is the characteristic size; μ is the dynamic viscosity, U_∞ is the incoming flow speed. The estimation result is 30 < y+ < 100 for the k-ε model at high Reynolds numbers. When setting the wall boundary layer mesh, the height of the first mesh layer of the pipe wall boundary is set to 0.2 mm, the growth rate is 1.2, and a total of 10 layers are set; the height of the first mesh layer of the guide vane boundary is set to 0.2 mm, the growth rate is 1.1, and a total of 10 layers are set.

After generating the mesh, the validity of the mesh was checked, and it was found that the quality of mesh was greater than 0.3 and minimum angle was greater than 18°; therefore, the quality of mesh was good. The schematic diagram of the meshing is shown in Figure 6.

3.3. Verification of Mesh Irrelevancy

In order to ensure the accuracy of the simulation and improve the efficiency of the calculation, the mesh size needs to be verified as irrelevant to ensure that the mesh size does not affect the results of the simulation calculation. Here, three mesh sizes were selected for verification, which are the models with maximum mesh sizes of 2 mm, 3 mm and 4 mm.

Table 1. Comparison of the number of mesh and related performance parameters under different mesh sizes.

Title	Value
Mesh Size (mm)	2	3	4
The number of mesh	16,658,422	4,935,829	2,082,303
Average static pressure difference between inlet and outlet sections (Pa)	361.3437	360.6469	359.8461
The deviation of results (%)	0.193	0.223

shows the comparison of the number of mesh and performance parameters under different mesh sizes. From the table, it can be seen that when the maximum mesh size is 2 mm and 3 mm, respectively, the deviation of the calculated average static pressure difference between the inlet and outlet sections is very small, less than 0.2%, and the mesh size almost does not affect the calculated results. It can be seen that a maximum mesh size of 3 mm is sufficient for accurate simulations; therefore, the maximum mesh size was set to 3 mm for this simulation.

3.4. Control Equations and Boundary Conditions

We use Fluent software to simulate the cyclonic flow characteristics inside the hydrocyclone. In choosing the calculation model, the RNG k-ε turbulence model was selected for the simulation considering the complex flow conditions inside the hydrocyclone. The basic control equations for this model are shown as follows.

Continuity equation:

$$\frac{\partial u_x}{\partial x}+\frac{\partial u_y}{\partial y}+\frac{\partial u_z}{\partial z}=0$$

(6)

Momentum equation:

$$\frac{\partial u_i}{\partial t}+\frac{\partial }{\partial x_j}\left(u_i{u}_j\right)=\frac{1}{\rho }\{-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}[(\mu +{\mu }_t)(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})]\}$$

(7)

Turbulent kinetic energy k equation:

$$\frac{\partial k}{\partial t}+\frac{\partial }{\partial x_i}\left(u_{i}k\right)=\frac{1}{\rho }\{\frac{\partial }{\partial x_i}[\left(a_k{\mu }_{eff}\right)\frac{\partial k}{\partial x_i}]+G_k-\rho \epsilon \}$$

(8)

Dissipation rate $\mathsf{\epsilon }$ equation:

$$\frac{\partial \epsilon }{\partial t}+\frac{\partial }{\partial x_i}\left(u_i\epsilon \right)=\frac{1}{\rho }\{\frac{\partial }{\partial x_i}[\left(a_{\epsilon }{\mu }_{eff}\right)\frac{\partial \epsilon }{\partial x_i}]+C_{1\epsilon }^{*}\frac{\epsilon }{k}{G}_k-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}\}$$

(9)

Among them,${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }, C_{\mu }=0.0845, {\mu }_{eff}=\mu +{\mu }_t, a_k=a_{\epsilon }=1.39, G_k={\mu }_t\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right)\frac{\partial u_i}{\partial x_j},$

$$C_{1\epsilon }^{*}=C_{1\epsilon }-\frac{\eta \left(1-\eta /{\eta }_0\right)}{1+\beta {\eta }^3},\hspace{1em} {\eta }_0=4.377,\hspace{1em} \beta =0.012,$$

$$\eta ={\left(2E_{ij}·E_{ij}\right)}^{\frac{1}{2}}\frac{k}{\epsilon },\hspace{1em} E_{ij}=\frac{1}{2}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i}\right),\hspace{1em} C_{1\epsilon }=1.68,\hspace{1em} C_{2\epsilon }=1.42$$

In the formula: t is time; i and j = 1, 2, 3; u_i is the velocity component in the x_i direction; ρ is the density of the volume fraction weighted average; p is the modified pressure; $\mu$ is the volume–fraction weighted average molecular viscosity coefficient; $a_k$ and $a_{\epsilon }$ are the Prandtl number at turbulent kinetic energy k and dissipation rate ε, respectively; ${\mu }_t$ is the turbulent viscosity coefficient; G_k is the turbulent kinetic energy generation term due to the average velocity gradient [26].

The boundary conditions of this model include velocity inlet boundary and pressure outlet boundary. Among them, the velocity inlet boundary is set by Reynolds numbers Re = 140,559 and Re = 175,699, that is, the model inlet velocity is 1.415 m/s and 1.768 m/s, respectively; the pressure outlet boundary sets the pressure to 0.

4. Experimental Verification of Simulation Results

In order to verify the simulation results of the flow characteristics of the spiral flow generated by the guide vane hydrocyclone, the hydrocyclone was selected to test the flow velocity at its outlet section at Re = 140,559. The test system mainly includes the PIV velocimetry system and the water circulation system. The PIV velocimetry system (particle image velocimetry system) can obtain the flow velocity of the measured section. In order to reduce the measurement error caused by laser refraction, a rectangular water tank is installed in the test section. The water circulation system mainly includes the water storage tank, centrifugal pump, electromagnetic flow meter, pipeline, and guide vane hydrocyclone. Figure 7 shows the layout of the test system and the diagram of the PIV system in use.

The results of axial, radial and circumferential flow velocity distribution on the horizontal diameter of the section 1600 mm from the model inlet section (50 mm from the cyclone outlet section) were selected for comparison, and the comparison results are shown in Figure 8. The horizontal coordinates of Figure 8 represent the x-coordinates of the points on the horizontal diameter of the comparison. From the figure, it can be seen that the simulated results agree well with the experimental results. The absolute error between the simulation results and the experimental results can be obtained by taking the absolute value after making the difference between them. The average absolute error of axial velocity is calculated to be less than 0.06 m/s, the average absolute error of radial velocity is less than 0.02 m/s, and the average absolute error of circumferential velocity is less than 0.02 m/s. The error may be due to the fact that the model applies the Reynolds averaging algorithm to obtain the flow velocity as a time-averaged quantity, while the presence of pulsating velocities during the test makes the two results deviate to a lesser extent. This shows that the numerical simulation method is feasible to study the flow characteristics of the spiral flow generated by the hydrocyclone.

5. Results and Analysis

This paper mainly analyzes the axial velocity, radial velocity, circumferential velocity and static pressure characteristics of the inner hydrocyclone under the condition of Reynolds number Re = 175,699, and studies the generation process of the spiral flow inside the hydrocyclone. The axial velocity is positive along the pipe axis in the direction of water flow, and negative against the direction of water flow; the radial velocity is positive when it departs from the pipe axis, and negative when it points to the pipe axis; the circumferential velocity is positive or negative according to the right-hand spiral rule, with the thumb pointing to the axial direction of water flow; the same direction as the four fingers is positive, and the opposite direction is negative.

5.1. Analysis of the Internal Axial Velocity Characteristics of Hydrocyclones

Seven sections of Z = 1000 mm, 1050 mm, 1150 mm, 1250 mm, 1350 mm, 1450 mm and 1550 mm were selected for the analysis of axial velocity. Figure 9 shows the distribution of axial velocity in the internal sections of the hydrocyclone. It can be seen from the figure that: influenced by the viscosity of the liquid, the overall distribution of axial velocity changes similarly to the distribution of turbulent flow in the circular pipe; the axial velocity in the area near the axis of the pipe is larger, and the flow velocity gradient is smaller; while in the area near the pipe wall and guide vane, the axial velocity drops sharply and the flow velocity gradient is large. The axial velocity is redistributed under the influence of the guide vane, and the distribution changes continuously with the deflection of the guide vane, and the axial velocity is lower on the downstream surfaces of the guide vane near the pipe wall and the inner edge of the guide vane.

In order to further study the axial velocity of the water flow in the guide vane section inside the hydrocyclone, the distribution of the axial velocity between two adjacent guide vanes along different polar axis angles in the cross section and the change of the axial velocity along the course of each section were analyzed, as shown in Figure 10. From the figure, it can be seen that: (1) In the same cross-section under the same polar diameter, with the region where the polar axis angle increases, the axial velocity is first increased and then decreased. This is due to the influence of the side wall in the area close to the surface of the guide vane, and the resistance of the guide vane to the upstream surfaces is greater than that of the downstream surfaces. (2) Under the same polar diameter, the difference of axial velocity between the regions with different angles of the polar axis increases along the range, and the angle of the polar axis where the maximum value of axial velocity is located also increases; after the section, Z = 1300 mm is obviously biased towards the region with larger polar axis. This is mainly due to the fact that in the area between two guide vanes, as the deflection angle of the guide vanes accumulates along the course, the difference between the influence of the upstream surfaces and the downstream surfaces on the water flow becomes larger, and the flow field is gradually deflected from symmetrical straight flow to spiral flow. (3) With the increase in the polar diameter, the axial velocity value has a tendency to decrease. This is because when the polar diameter increases, the water flow shear near the wall makes the velocity of the water flow near the pipe wall smaller than that of the water flow away from the pipe wall area.

5.2. Analysis of the Internal Radial Velocity Characteristics of Hydrocyclones

Similarly, seven sections of Z = 1000 mm, 1050 mm, 1150 mm, 1250 mm, 1350 mm, 1450 mm and 1550 mm were selected for the analysis of radial velocity. Figure 11 shows the distribution of radial velocity in the internal sections of the hydrocyclone. It can be seen from the figure that: (1) In the leading edge section of the guide vane, the water flow is influenced by the guide vane, and the radial velocity pointing to the pipe axis will be generated in the area near the inner edge of the guide vane when passing through the leading edge of the guide vane, and the radial velocity pointing to the pipe wall will be generated in the area far from the inner edge. (2) In the straight section of the guide vane, the radial velocity is very small, which indicates that the straight section of the guide vane causes almost no radial disturbance to the water flow. (3) In the twisted section of the guide vane, the water flow has the negative radial velocity near the upstream surfaces of the guide vane and tends to flow toward the center of the pipe; the water flow has the positive radial velocity near the downstream surfaces of the guide vane and tends to move away from the pipe axis. The area affected by the radial velocity gradually expands along the range, and the area with positive radial velocity appears together with the area with negative radial velocity.

In order to further study the radial velocity of the water flow in the guide vane section inside the hydrocyclone, the distribution of the radial velocity between two adjacent guide vanes along different polar axis angles in the cross section and the change of the radial velocity along the course of each section were analyzed, as shown in Figure 12. From the figure, it can be seen that:

In the straight section of the guide vane: In the leading edge section of the guide vane, when the polar diameters are the same, the absolute value of radial velocity is larger at the polar axis near the guide vane. Except for the leading edge of the guide vane, the radial velocity of the water flow in other areas is small.

In the twist section of the guide vane: (1) The radial velocity of the water flow at the upstream surfaces of the guide vane is negative, and the closer to the upstream surfaces of the guide vane, the smaller the radial velocity, and the water flow has the velocity pointing to the direction of the pipe axis. The radial velocity at the downstream surfaces of the guide vane is positive, and the closer to the downstream surfaces of the guide vane, the larger the radial velocity, and the water flow has the velocity pointing to the pipe wall. This is because in the process of guide vane twisting, the water flow is influenced by the guide vane, the pressure near the upstream surfaces is higher than in the mainstream area, while the pressure near the downstream surface is lower than in the mainstream area; the water flow is influenced by the pressure gradient to deflect the movement, and the flow velocity produces a radial component. (2) As the diameter of the polar increases, the radial velocity of the water flow has a tendency to decrease. This is because the closer the location of the pipe wall, the stronger the restraint of the pipe wall, and the more difficult it is to generate radial velocity. (3) The absolute value of the radial velocity tends to increase along the range, and the absolute value of the radial velocity of the water flow near the downstream surfaces of the guide vane is larger than that near the upstream surfaces of the guide vane.

5.3. Analysis of the Internal Circumferential Velocity Characteristics of Hydrocyclones

Similarly, seven sections of Z = 1000 mm, 1050 mm, 1150 mm, 1250 mm, 1350 mm, 1450 mm and 1550 mm were selected for the analysis of circumferential velocity. Figure 13 shows the distribution of circumferential velocity in the internal sections of the hydrocyclone. It can be seen from the figure that: (1) In the leading edge section of the guide vane, when the water flows in the axial direction, the water flows on both sides of the guide vane due to the blocking effect of the leading edge of the guide vane, there will be a symmetrical distribution of the circumferential velocity. (2) With the increase in the deflection angle of the guide vane, the area of the positive circumferential velocity increases, and the average value of the circumferential velocity increases. (3) At the inner edge of the guide vane, there is a small area of negative circumferential velocity. This is because the pressure is large at the upstream surfaces of the guide vane and small at the downstream surfaces, so the water flow near the upstream surfaces of the guide vane will flow to the center of the pipe and the downstream surfaces of the guide vane with less pressure, while the downstream surfaces will have the water flow from the pipe center and upstream surfaces, thus forming a region where the circumferential velocity is negative. (4) On both sides of the guide vane, there are regions with positive circumferential velocity and large values, and the circumferential velocity near the downstream surfaces of the guide vane is greater than that of the upstream surfaces.

In order to further study the circumferential velocity of the water flow in the guide vane section inside the hydrocyclone, the distribution of the circumferential velocity between two adjacent guide vanes along different polar axis angles in the cross section and the change of the circumferential velocity along the course of each section were analyzed, as shown in Figure 14. From the figure, it can be seen that:

In the straight section of the guide vane: (1) In the leading edge of the guide vane section, the circumferential velocity near the upstream surfaces of the guide vane is positive, and the circumferential velocity near the downstream surfaces of the guide vane is negative; the closer to the guide vane surface, the larger the absolute value of the circumferential velocity. This is because the leading edge of the guide vane is a surface: when the water inflows the guide vanes, it needs to bypass the guide vanes and a large deflection will happen, thus generating a large circumferential velocity. The closer the area to the guide vane, the larger the influence of the guide vane. (2) For the other areas of the straight section of the guide vane, the absolute value of the circumferential velocity is small, indicating that there is almost no circumferential movement of the water in the straight section of the guide vane.

In the twist section of the guide vane: (1) In the same section, the circumferential velocity of the water flow in the same area with the same polar diameter decreases and then increases with the increase in the angle of the polar axis, that is, the water flow near the guide vane surface has a larger circumferential velocity, and the circumferential velocity near the downstream surfaces of the guide vane is larger than that of the upstream surfaces. This is because the presence of the guide vane will have a direct effect on the flow of water, and the flow will then be transferred to the area farther away from the guide vane through compression and water viscosity. The circumferential velocity near the upstream surfaces is smaller than in the downstream surfaces, indicating that the effect of compression on the upstream surfaces of the guide vane to produce circumferential velocity is weaker than the circumferential velocity produced by adsorption of water on the downstream surfaces of the guide vane. (2) With the increase in the distance from the model inlet section, the overall circumferential velocity of the water flow has a tendency to increase. This is because as the twist of the guide vane increases along the course, the guide vane has a greater ability to rotate water; therefore, the circumferential velocity of the water also increases along the course.

5.4. Analysis of the Internal Static Pressure Characteristics of Hydrocyclones

When the guide vane inside the hydrocyclone deflects the water flow, it will have an effect on the static pressure distribution of the water flow. Figure 15 shows the distribution of static pressure in the internal sections of the hydrocyclone. It can be seen from the figure that: (1) The static pressure at the inlet section of the hydrocyclone is larger than the static pressure at the leading edge of the guide vane, and the static pressure at the outlet section is larger than the static pressure at the trailing edge of the guide vane. This is due to the reduction in the cross-sectional area of the guide vane section: the pressure energy is transformed into kinetic energy, the flow velocity increases and the static pressure decreases. (2) In the straight section of the guide vane, the difference in static pressure between the two sides of the guide vane is not large. In the twisted section of the guide vane, the static pressure on the upstream surfaces of the guide vane is larger than in the downstream surfaces, and the greater the degree of the twisting of the guide vane, the larger the difference in static pressure between the two sides of the guide vane. This is because when the guide vane is deflected, the upstream surfaces of the guide vane is forced to squeeze the water flow, and the static pressure is large, while the water flow on the downstream surfaces has the tendency to break away from the guide vane; therefore, the static pressure is small.

In order to further study the static pressure of the water flow in the guide vane section inside the hydrocyclone, the distribution of the static pressure between two adjacent guide vanes along different polar axis angles in the cross section and the change of the static pressure along the course of each section were analyzed, as shown in Figure 16. From the figure, it can be seen that:

In the straight section of the guide vane: (1) With the increase in the angle of the polar axis, the static pressure at the leading edge of the guide vane section first increases and then decreases, and the static pressure in the area near the surface of the guide vane is small. This is because when the water flows around the leading edge of the guide vane, the upstream water pressure mainly acts on the leading edge of the guide vane and is not transferred to the water flow, resulting in the smaller static pressure in the area near the guide vane. (2) The static pressure at the leading edge of the guide vane is significantly larger than in the other two sections of the straight section of the guide vane. This is because the leading edge of the guide vane section is at the critical section between the section without guide vane and the section with guide vane, and the static pressure in this section is in the transition process from upstream to downstream; therefore, it is larger than the static pressure in the last two sections.

In the twisted section of the guide vane: (1) In the same section of the same polar diameter of the region, the static pressure of the water flow decreases with the increase in the angle of the polar axis, that is, the closer the area to the upstream surfaces of the guide vane, the larger the static pressure, and the closer the area to the downstream surfaces of the guide vane, the smaller the static pressure. This is because the upstream surfaces of the guide vane has a squeezing effect on the water flow, and the downstream surfaces of the guide vane has a adsorption effect on the water flow, and the closer it is to the guide vane surface, the more it is affected. (2) In the region with the same polar diameter and the same angle of the polar axis, the static pressure decreases along the course and the static pressure decreases faster. This is due to the fact that there is energy loss during the flow of water along the course, and the energy lost is mainly pressure energy; thus, the static pressure along the course of the section decreases. As the degree of distortion of the guide vane increases, the rate of energy loss increases; thus, the rate of static pressure decrease also accelerates. (3) In the trailing edge section of the guide vane, with the increase in the polar axis angle, the static pressure shows a trend of increasing and then decreasing. This is because there is a low-pressure area downstream of the guide vane, and the closer the position to the guide vane, the greater the influence of the area, and the smaller the static pressure.

6. Conclusions

(1)

When the water flows through the hydrocyclone, the axial velocity of the water flow is redistributed under the action of the guide vane. In the straight section of the guide vane and the twisted section of the guide vane with less distortion, the axial velocity is small in the area near the surface of the guide vane, and large in the area near the center and far from the guide vane; in the twisted section of the guide vane with more distortion, the axial velocity tends to increase from the upstream surfaces to the downstream surfaces of the guide vanes.

(2)

The radial velocity of the water flow under the action of the guide vane is small in the straight section of the guide vane, while the absolute value of the radial velocity increases in the twisted section of the guide vane as the degree of twisting of the guide vane increases along the course. The radial velocity is pointing to the direction of the pipe axis near the upstream surfaces of the guide vane, and pointing to the direction of the pipe wall near the downstream surfaces of the guide vanes, and the area of radial velocity pointing to the pipe axis and the area pointing to the pipe wall appear together. The closer the area is to the pipe wall, the lower the radial velocity of the water flow; the further the area is from the guide vane surface, the lower the radial velocity of the water flow.

(3)

The circumferential velocity of the water flow in the straight section of the guide vane is small. In the twisted section of the guide vane, as the twist degree of the guide vane increases along the range, the area of the circumferential velocity in the counterclockwise direction increases, and the average circumferential velocity of the section increases along the range. The circumferential velocity near the upstream surfaces and the downstream surfaces of the guide vane is larger than that in the area away from the guide vane, and the circumferential velocity at the downstream surfaces of the guide vane is larger than that at the upstream surfaces of the guide vane.

(4)

In the guide vane section, the overall static pressure of the section shows a trend of decreasing along the course, and the static pressure of the straight section of the guide vane decreases less than that of the twisted section of the guide vane, and the static pressure of the twisted section of the guide vane decreases faster along the course. Influenced by the guide vane, in the same section, the static pressure in the area closer to the upstream surfaces of the guide vane is larger, and the static pressure in the area close to the downstream surfaces is smaller.