Numerical simulation study of particle self-rotation velocity in cyclone separator

Cyclone separators are widely used in petrochemical, environmental protection and other fields. Taking the cyclone separators with single volute inlet as the research object, in order to study the particle self-rotation velocity and motion trajectory in its internal flow field, the Reynolds stress model (RSM) was used for the gas phase and the discrete phase model (DPM) was used for the solid phase. The tangential velocity distribution and the particle motion trajectory were obtained through numerical simulation, and the tangential velocity was used to derive the formula for the particle self-rotation velocity, and self-rotation velocity distribution obtained by writing expressions in Fluent. The results show that: in the internal flow field of the cyclone separator, the place with large velocity gradient will present a larger self-rotation velocity; when the particle size is 14.44 μm and the inlet air intake is 212 m3/h, the particles can be stably suspended in a certain region of the cylindrical section.


Introduction.
Cyclone separator is widely used in petrochemical industry, environmental protection and other fields because of its simple structure with non-moving parts, low operating cost, and ease of maintenance, high separation efficiency and other technical advantages, its basic structure is shown in figure 1.The basic operating principle of the cyclone separator is to utilize the centrifugal force generated when the mixture is rotated at high speeds, so that the two phases with different densities are distributed in different positions inside the cyclone, the dense phase migrates to the wall and discharges from the underflow outlet, and the less dense phase migrates to the center and discharges from the vortex finder.
With the increasing application of cyclone, many scholars have conducted a lot of research on the structure, size, pressure drop, separation efficiency, etc. Yang et al. studied the influence of inlet crosssection size of the cyclone separator on natural cyclone length, and the results showed that the cyclone inlet size has an important effect on the performance of the cyclone separator [1]; Qian et al. used FLUENT to analyze the cyclone separator with different inlet angles, mainly to study its separation efficiency and pressure drop [2]; Kwon et al. designed and fabricated two single-entry and one doubleentry cyclone separator, and evaluated and compared the separation efficiency between them [3].Many studies have found that the strong centrifugal force generated in the cyclone field not only separates the mixture, but also generates a strong shear flow that drives the solid particles [4][5][6]; there is a high-speed rotation phenomenon of the particles in the cyclone, and the behavior of high-speed rotation of particles has a purifying effect on the porous pollutant particles [7].
At present, the research on centrifugal separation within the cyclone is relatively adequate, but the research on particle motion in the swirling turbulent flow field within the cyclone is very few, and the study of particle rotation in the cyclone field provides a new direction for cyclone separation performance enhancement and function expansion.Therefore, this paper addresses this problem, using numerical simulation methods, analyses the distribution of particle rotation velocity in the cyclone, which provides a certain basis for the separation of oil-sludge mixtures using cyclone separators in practical engineering.

Modelling.
ANSYS SCDM (SpaceClaim) was used for modelling.The key step in the numerical calculation is the mesh, which is also the pre-processing of the numerical simulation of the flow field, and the accuracy of the final calculation results will be directly affected by the quality of the mesh, and if the quality of the mesh is poor, it may lead to serious distortion in the final calculation results.ICEM was used for meshing, and in order to improve the mesh quality and calculation speed, hexahedral structured mesh was used.Due to the existence of a very thin boundary layer at the cyclone wall where the velocity changes drastically, the mesh near the cyclone wall was refined , setting the boundary layer to 15 layers, with a growth factor of 1.2, so as to make the computation of the flow field at the side wall more accurate, which is conducive to the subsequent analysis of the DPM model.From figure 2, it can be seen that the deviation of the pressure drop value is not significant when the number of grids is between 1.2 and 2 million, and in order to save computational resources, the number of grids is selected as 1.2 million.

Numerical methodology.
Given the accuracy of results and low computational cost, RSM was applied in this work to compute the gas flow field in the cyclone.We simulated the dispersed phase by tracking a large number of spherical dispersed particles through the converged flow field of continuous flow in the Lagrangian reference frame by using a two-way coupling method via discrete phase model (DPM).To get the optimization results quickly, steady calculation is used in this paper.The solution method of the CFD is set as follows: the pressure velocity coupling adopts the SIMPLE algorithm with fast convergence; there is a sudden pressure change in the cyclone separator, so the pressure difference format adopts PRESTO!; the momentum discretization and turbulent kinetic energy use the QUICK discrete format with thirdorder accuracy; the dissipation rate adopts the Second order upwind formula with higher accuracy.The simulation was carried out by the commercial software Fluent.
(1) Inlet boundary conditions: the inlet volume is 212m 3 /h, set the inlet type as velocity inlet, the density is 1.225kg/m 3 , the viscosity is 1.789 × 10 −5 Pa•s, the inlet velocity is 6.6m/s.
(2) Outlet boundary conditions: set the outlet type as pressure outlet, and the outlet pressure is 400Pa.
(3) Wall setting: The wall is adopted as no-slip boundary.
(4) Solid phase setting: the particle density is 1538.46kg/m 3 , the diameter is 14.44μm, and the inlet particle concentration is 1×10 -5 kg/s.The exit position of the vortex finder is "escape", the particles enter the underflow outlet is "capture", the wall is set to "rebound" reflect, the wall rebound coefficient according to the reference [8] is 0.8.

Velocity distribution.
In the three-dimensional gas motion inside the cyclone separator, the tangential velocity occupies the most important position, not only because the tangential velocity is numerically much larger than axial and radial velocity, but more importantly, the tangential velocity is the basic premise for generating centrifugal force.Therefore, the cyclone tangential velocity which is of great importance for the study of particle self-rotation velocity.The tangential velocity distribution basically consistent with the combined vortex motion model, which is sequentially divided into three regions along the radius of the cyclone, quasi-forced vortex region, quasi-free vortex region and boundary layer region.These three regions can be clearly seen on figure 4(b).In the radius of 0 to close to the radius of the vortex finder, the tangential velocity increases sharply, and its maximum value is close to 5 times of the inlet velocity, which is the quasi-forced vortex region, and the distribution of the tangential velocity is basically linear; in the quasi-free vortex region, the tangential velocity decreases slowly, and in the boundary layer region, the tangential velocity drops sharply to 0. The maximum tangential velocity in the vortex finder in the 0 ° ~ 180 ° face, greater than 90 ° ~ 270 ° face, this is because from 0 ° ~ 180 ° face, the radial width of the annular space of the cyclone separator with single volute is gradually narrowed to speed up the air flow, so that the tangential velocity increases; and from 180 ° face to 270 ° face, the radial width of the annular space is constant, but some of the air flow downward into the cylinder space, so that the tangential velocity decreases.As can be seen from figure 5, in the 0° to 90° surface, above vortex finder is affected by the reversed flow of the outside air, resulting in the asymmetry of the tangential velocity in the part from z = -50mm to z = -150mm, and the 90° to 270° surface is less affected by the reversed flow, which basically shows an axisymmetric distribution of the tangential velocity in this part.Below z = -150mm, with the air flowing downwards, the cylindrical space attenuates the non-axisymmetric rotational motion, the airflow inside the cyclone tends to be stable, and the tangential velocity shows an axisymmetric distribution as a whole.From the cyclone cylinder-cone interface downwards, the cyclone diameter decreases gradually, which leads to an increase in the air flow velocity, the tangential velocity also increases.The velocity gradient reaches its maximum in the boundary layer region, which is conducive to the enhancement of the rotational motion of the particles and the increase of the particle self-rotation velocity.

Particle self-rotation velocity.
In shear flow, particles are not only subjected to forces such as trailing force, buoyancy, gravity, etc., which induce macroscopic migratory motion of the particles, but also subjected to unbalanced shear stresses on the surface, which in turn generates rotational motion.The study of particle motion and its two-phase interaction in turbulent flow is of great significance for the study of two-phase mixing and other problems in industrial production.Best investigated the influence of rotational motion on particle wake stability for particles (spheres and ellipsoids) with fixed rotation axes at Reynolds numbers below 300 using an oil-filled flow channel [9].Kajishima carried out direct numerical simulations of a homogeneous flow containing a large number of settling particles in order to investigate the influence of particle rotation on the interaction between particle clusters and particle-induced turbulence [10].Mortensen et al. investigated the displacement and rotational motions of spherical particles in a turbulent channel.This study examined three different particles in the Euler-Lagrange system to determine the statistical effect of response time on particle motion [11].
In 2017, Huang Yuan et al. systematically derived the microsphere rotation model by solving the flow field theory [12].
where Uθ is the tangential velocity, r is the radius of rotation from the mass to the axis of the cyclone, n is the empirical index, and  is the particle self-rotation velocity.
The fluid and particle motion inside the cyclone is generally described in a column coordinate system, figure 8 shows the radial distribution of particle self-rotation velocity at four heights under the inlet velocity of 6.6m/s, the minus sign only indicates that its direction is opposite to the rotational velocity.
From figure 8, it can be seen that in the quasi-free vortex region the self-rotation velocity varies less with radial position, and in the boundary layer region the self-rotation velocity increases sharply along the radial direction, and the maximum rotational velocity in the boundary layer is directly proportional to the axial height.From the previous tangential velocity analysis, it can be seen that the velocity gradient in the boundary layer is much larger than the quasi-free vortex region, the tangential velocity decreases sharply at the same time as the maximum velocity gradient in the boundary layer increases with the axial height, according to equation (5), it can be concluded that the particles in the boundary layer have a larger rotational velocity, and the maximum rotational velocity is directly proportional to axial height.When the particles are in contact with the boundary layer of the wall, the closer they are to the wall, the stronger the fluid shear they are subjected to, and the greater the rotation speed.When the particles are in contact (collision) with the wall, the particles will reach the highest rotational speed.

Particle trajectory.
The study of particle motion is of great significance to improve reaction efficiency and reduce process energy consumption.A critical capacity of suspending particles in certain gas-solid swirl field is observed when the added amount reaches a certain degree.Particles change from the completely suspending state to the suspending rotation, that is, spiral dropout equilibrium state, which makes the particles drop out from the underflow.Suspending rotation extends the residence time of particle in cyclone and constantly updates contact among different phases, thereby improving the total separation efficiency of equipment when controlled reasonably.As can be seen from figure 9, the particles are suspended and rotated in the region of the column section of h = -220 ~ -240mm.In the swirl field, since the particle density is much larger than the gas density, the particles are less affected by the fluid pressure gradient, the particles move outward in the radial direction, and the particle movement is mainly concentrated near the wall surface.Combined with the previous section, because there is a large rotation speed within the boundary layer, so the longer the particles remain suspended near the wall, the better the separation of contaminants on the surface of the particles.

Conclusions.
In this research, numerical simulation was used to obtain the velocity distribution and particle trajectories in the cyclone separator.The tangential velocity of the cyclone separator basically conforms to the combined vortex motion, which is sequentially divided into three regions along the radius of the cyclone separator, quasi-forced vortex region, quasi-free vortex region and boundary layer region.The tangential velocity show a non-axisymmetric distribution in the vortex finder and are basically axisymmetric in the other regions.The velocity gradient in the boundary layer region is large, which is conducive to enhance the self-rotation velocity of the particle.The particle self-rotation velocity varies less with radial position in the quasi-free vortex region, and increases sharply in the boundary layer region, where the particles will reach their maximum velocity when they come into contact (collision) with the wall.When the particle size is 14.44μm and the inlet gas volume is 212m 3 /h, the particle can be stably suspended in a certain area near the wall of the cylindrical section.Because of the high selfrotation velocity near the wall, the longer the suspension time is, the more favorable to the separation of pollutants on the particle surface.

Figure 2 .
Figure 2. Cyclone separator pressure drop for different number of grids.

Figure 8 .
Figure 8. Radial distribution of rotational velocities at different height.