# Study of the Internal Cyclonic Flow Characteristics of Cyclones with Different Guide Vane Heights

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## Abstract

**:**

## 1. Introduction

## 2. Construction of a Mathematical Model of Guide Vane Cyclones

#### 2.1. Geometric Modelling

#### 2.2. Mesh Division

^{3}/h. Figure 3 shows the distribution of tangential velocity and axial velocity along the diameter for the three mesh−size models at the Z = 500 mm section. As can be seen from the graphs, the deviation of the results for the 2 mm and 3 mm mesh−size models was small, basically less than 1%, and the size of the mesh hardly affected the calculation results. It can be seen that a maximum mesh size of 3 mm is sufficient for accurate simulations, so the maximum mesh size was set to 3 mm for this simulation.

#### 2.3. Model Selection and Its Control Equations

_{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; $\mathsf{\mu}$ is the volume fraction weighted average molecular viscosity coefficient; ${\mathrm{a}}_{\mathrm{k}}$ and ${\mathrm{a}}_{\mathsf{\epsilon}}$ are the Prandtl number at turbulent kinetic energy k and the dissipation rate ε, respectively; ${\mathsf{\mu}}_{\mathrm{t}}$ is the turbulent viscosity coefficient; and G

_{k}is the turbulent kinetic energy generation term due to the average velocity gradient.

^{3}/h, corresponding to an initial velocity of 1.415 m/s. Due to the free outflow at the outlet, an atmospheric pressure of 101,000 Pa was chosen as the outlet pressure.

## 3. Research Programme

^{3}/h. The schematic diagram of the cyclone structure is shown in Figure 4.

## 4. Experimental Verification of Simulation Results

^{3}/h. Considering the masking effect of the guide vane, we selected a section with a horizontal diameter of Z = 500 mm for measurement and compared the measured results for tangential, radial and axial velocities with the simulated values. The results of the comparison are shown in Figure 10. It can be seen from the figure that the simulated values did not differ significantly from the measured values of the physical tests, and the trend of variation along the course was basically the same. The average absolute error of the axial velocity was calculated to be no more than 0.08 m/s, the average absolute error of the radial velocity was no more than 0.006 m/s and the average absolute error of the tangential velocity was no more than 0.008 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. The overall error remained within a plausible range, indicating that the results of the numerical simulations are credible and that it is feasible to use the numerical simulation approach to investigate the flow characteristics of spiral flows generated by cyclones.

## 5. Simulation Results and Analysis

#### 5.1. Analysis of the Internal Tangential Velocity Characteristics of Cyclones with Different Guide Vane Heights

^{3}/h. It can be seen that when the guide vane height was 25 mm, 30 mm and 35 mm, there were three obvious areas in the centre of the pipe where the tangential velocity was anticlockwise, while on both sides of the three guide vanes, there was a region where the tangential velocity was clockwise on each side. However, when the guide vane height was 20 mm and 40 mm, the distribution of these areas was not obvious. When the height of the guide vane was too low, the spiral flow formed is low, and when the height of the guide vane is too high, the central area of the pipe is small and the water flow guided by the guide vane interferes with each other, which is not conducive to the formation of a stable spiral flow. It can be seen that the height of the guide vane is either too high or too low for the formation of a spiral flow, and only when the height of the guide vane is moderate can a more stable spiral flow be formed quickly.

^{3}/h, the maximum anticlockwise tangential velocity of the same section inside the cyclone with different guide vane heights increased with the increase in the guide vane height and then decreased. The anticlockwise tangential velocity basically reached the maximum when the guide vane height was 30 mm and the height−to−diameter ratio was 0.6, while the maximum clockwise tangential velocity basically increased with the increase in the guide vane height.

#### 5.2. Analysis of the Internal Radial Velocity Characteristics of Cyclones with Different Guide Vane Heights

^{3}/h. It can be seen that as the height of the guide vane increased, the radial velocity area pointing to the tube wall increased, while the radial velocity area pointing to the tube axis decreased. When the height of the guide vane was 35 mm or 40 mm, there was a clear area of radial velocity pointing towards the tube wall on the waterward side of the outer edge of the guide vane, while at a guide vane height of 20 mm, 25 mm and 30 mm, the radial velocity pointing towards the tube wall was not obvious. This is due to the fact that with the deflection of the guide vane, the water tends to move in a circular motion under the action of the guide vane, which generates a centrifugal force in the outward direction, and under the action of this force, the water flow at some locations produces a flow velocity away from the centre of the circle. When the height of the guide vane is small, the outer edge of the guide vane produces little flow away from the centre of the circle. As the height of the guide vane increases, this deflecting effect becomes more pronounced, so the radial velocity region pointing towards the tube wall becomes larger as the height of the guide vane increases.

#### 5.3. Analysis of the Internal Axial Velocity Characteristics of Cyclones with Different Guide Vane Heights

^{3}/h. It can be seen that the overall distribution of the axial flow velocity varied similarly to the turbulent flow velocity distribution of a circular tube, due to the viscosity of the liquid. The axial flow velocity in the area near the axis of the pipe was large and the flow velocity gradient was small, while near the pipe wall and guide vane, the axial flow velocity dropped sharply and the flow velocity gradient was large.

## 6. Discussion and Conclusions

- The tangential velocity in the centre of the cyclone pipe is mainly in the anticlockwise direction, and the flow velocity increases with the increase in the guide vane height and then decreases. When the ratio between the height of the guide vane and the inner diameter of the cyclone is in the range of 0.5 to 0.7, it can produce a high−strength and more stable spiral flow. When the height of the guide vane is 30 mm and the height−to−diameter ratio is near 0.6, the tangential velocity reaches its maximum and the intensity of the spiral flow generated is the highest, which enables more particle of different sizes to enter the suspended flow at this time and provides a better sand removal effect.
- The radial velocity increases as the height of the guide vane increases, and the radial velocity region pointing towards the tube wall increases, while the radial velocity region pointing towards the tube axis decreases.
- The overall distribution of axial flow velocity is similar to that of turbulent flow in a circular tube. The axial flow velocity inside the cyclone increases gradually along the course due to the influence of the water−retaining area of the guide vane and increases accordingly when the height of the guide vane increases.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the geometric model of a guide vane cyclone: (

**a**) Front view and (

**b**) side view.

**Figure 2.**Schematic diagram of meshing: (

**a**) unstructured grid of the cyclone and (

**b**) structured grid of the downstream area.

**Figure 3.**Comparison of the results of numerical simulations of three mesh−size models: (

**a**) tangential velocity and (

**b**) axial velocity.

**Figure 10.**Comparison of measured and simulated values of the along—stream velocity inside a cyclone: (

**a**) H = 20 mm, (

**b**) H = 30 mm, and (

**c**) H = 40 mm.

**Figure 11.**Tangential velocity distribution of cyclone internal sections at different guide vane heights: (

**a**) h = 20 mm, (

**b**) h = 25 mm, (

**c**) h = 30 mm, (

**d**) h = 35 mm and (

**e**) h = 40 mm.

**Figure 12.**Plot of maximum tangential velocity with the height of the guide vane for each section: (

**a**) anticlockwise tangential velocity and (

**b**) clockwise tangential velocity.

**Figure 13.**Plot of maximum tangential velocity along the course for different guide vane heights: (

**a**) anticlockwise tangential velocity; (

**b**) Clockwise tangential velocity.

**Figure 14.**Radial velocity distribution of cyclone internal sections at different guide vane heights: (

**a**) h = 20 mm, (

**b**) h = 25 mm,(

**c**) h = 30 mm,(

**d**) h = 35 mm and (

**e**) h = 40 mm.

**Figure 15.**Variation curves along the course of radial velocity at characteristic positions inside the cyclone: (

**a**) feature position (0, 0°), (

**b**) feature position (20, 0°), (

**c**) feature position (30, 0°), and (

**d**) feature position (40, 0°).

**Figure 16.**Axial velocity distribution of cyclone internal sections at different guide vane heights: (

**a**) h = 20 mm, (

**b**) h = 25 mm, (

**c**) h = 30 mm, (

**d**) h = 35 mm and (

**e**) h = 40 mm.

**Figure 17.**Variation curves along the course of axial velocity at characteristic positions inside the cyclone: (

**a**) feature position (0, 0°), (

**b**) feature position (20, 0°), (

**c**) feature position (30, 0°), and (

**d**) feature position (40, 0°).

Computational Models | Advantages | Disadvantages |
---|---|---|

Standard k-ε | Wide range of application, economic and reasonable, with high accuracy; its convergence and calculation accuracy can meet general engineering calculation requirements; suitable for design selection and parameter study. | Poor simulation of complex flows with high curvature and sharp changes in pressure gradients; deficiencies in the simulation of cyclonic and bypass flows. |

RNG k-ε | Moderately complex flows, such as separation flows, secondary flows and cyclonic flows, can be simulated for complex shear flows involving fast strains and moderate vortices. | The strong cyclonic processes cannot be predicted due to the limitations of the vortex viscous homogeneity assumption. |

Realisable k-ε | Similar to the RNG, the calculation is more accurate than the RNG and allows for better simulation of circular jets. | Strong cyclonic processes cannot be predicted due to the limitations of the vortex viscous homogeneity assumption. Turbulent eddy viscosity coefficients are strain rate dependent and therefore less efficient to calculate. |

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**MDPI and ACS Style**

Tao, S.; Li, Y.; Song, X.; Zhang, J. Study of the Internal Cyclonic Flow Characteristics of Cyclones with Different Guide Vane Heights. *Water* **2023**, *15*, 78.
https://doi.org/10.3390/w15010078

**AMA Style**

Tao S, Li Y, Song X, Zhang J. Study of the Internal Cyclonic Flow Characteristics of Cyclones with Different Guide Vane Heights. *Water*. 2023; 15(1):78.
https://doi.org/10.3390/w15010078

**Chicago/Turabian Style**

Tao, Siyuan, Yongye Li, Xiaoteng Song, and Jiaxuan Zhang. 2023. "Study of the Internal Cyclonic Flow Characteristics of Cyclones with Different Guide Vane Heights" *Water* 15, no. 1: 78.
https://doi.org/10.3390/w15010078