Effect of the Discharging Flap on Particle Separation in a Cyclone

1 Introduction

Cyclone separators are widely used for particle separation from gases in many industrial applications, for instance, in fluidized catalytic cracking units, power generation, incineration plants, coking plants, and others. Particles are collected in the lower part of the cyclone and need to be discharged in order to allow continuous cyclone operation. For that, different types of underflow configurations are applied ¹. They allow collected particles to properly discharge out the underflow.

Several studies have been performed to investigate the influence of the main cyclone geometrical parameters on its performance, both experimentally and numerically. However, underflow configurations were very rarely explored. Elsayed and Lacor ² numerically examined the effect of the cone tip diameter on the flow field and performance of a cyclone separator and found that it has an insignificant influence on the collection efficiency (the cut-off diameter) and the pressure drop. Bryant et al. ³ based on his observations concluded that collection efficiency will be lower for cyclones with a small cone tip diameter.

Obermair and Staudinger ⁴ investigated five different dust outlet geometries, namely, a conventional dust hopper, a dust hopper with two cone inserts (apex cones) of different shape at various locations, a dust hopper with a downcomer tube (also referred to a dipleg), and a dust hopper with an additional step cone. They found that by changing the dust outlet geometry, separation efficiency can be improved significantly, due to a change of the flow pattern in the lower part of the cyclone. The geometry of the dust outlet has an effect on the re-entrainment of dust, on the turbulence, on the formation of deposits, and on agglomeration, and all these result in an improved separation as well. Elsayed et al. ⁵ also revealed that the dust outlet configuration, namely, the dipleg height, the dustbin height, and the dustbin diameter, affect the cyclone performance.

The effect of the apex cone (also referred to counter-cone) on the cyclone separation efficiency was also investigated by other researchers ^6-8. However, their results are somehow contradictory. Yoshida ⁶ reported that by use of the apex cone at the inlet of the dust hopper it is possible to decrease the fluid velocity in the dust hopper and reduce the re-entrainment of particles from the dust hopper. He stated the optimum apex cone angle is 70°.

Firdani et al. ⁷ computationally investigated a cyclone separator with a counter-cone with two different apex angles, 90° and 120°, and found that a counter-cone with an apex angle of 120° led to better cyclone performance. Wasilewski ⁸ computationally and numerically examined fifteen variants of geometric configurations of the counter-cone and concluded that not only the apex cone but also its location play a significant role. He deduced that the counter-cone should be located above the dust outlet of the cyclone, i.e., in the lower part of the cone section, and the apex cone angle should be 85°.

A flapper valve is one of the widely used industrial underflow configurations. During most of the operation time the flapper valve is in open position and only is closed when there is a need to discharge the dust hopper (Fig. 1).

The underflow configuration can significantly affect the cyclone performance. Flapper valves are one of the widely applied industrial underflow configurations. They allow collected particles to properly discharge out the underflow. Many investigations were performed to reveal the effects of operating and geometric parameters of cyclones on their performance, namely, on the separation efficiency and pressure drop. However, the underflow configuration such as a flapper valve remains mainly unresearched. Therefore, the main objective of this work is to determine the effect of the flapper valve on the flow field, pressure drop, and particle separation in an industrial cyclone. This was realized by computational fluid dynamics (CFD) simulations.

2 CFD Modeling

An Euler-Lagrange method has been applied to study the effects of a discharging flap on the flow field and cyclone performance. The continuous phase was treated in an Eulerian manner, where the flow variables are a function of space and time, thus mass and momentum conservation equations were solved for the continuous phase. The dispersed phase was treated in a Lagrangian fashion where individual particles are considered and the position and velocity of each particle were obtained from Newton's second law.

2.1 Governing Equations for the Continuous Phase

The Reynolds stress model (RSM), which is the most appropriate Reynolds-averaged Navier-Stokes (RANS) turbulence model for cyclonic flows ⁹, has been applied in this study to model the gas flow. Since the cyclone operates at low Mach numbers, the gas flow was modeled as incompressible and the following RANS equations were solved:

(1)

(2)

where is time-averaged (mean) gas velocity, represents fluctuating gas velocity, is the fluctuating Reynolds stress contribution, t is the time, ρ is the gas density, is the mean static (thermodynamic) pressure, and ν is the kinematic viscosity of the gas.

For swirling flows, the RSM model proposed by Speziale et al. ¹⁰, which uses a quadratic relation for the pressure-strain correlation, is more accurate than the other RSM models ¹¹ and has therefore been applied in this study. For the near-wall flow treatment, scalable wall functions were used. For that, the inflation layers near walls were created (Fig. 2) in order to get the wall parameter “y+” in the range of 30–300. The largest value of wall parameter “y+” was on the vortex finder wall and its area-averaged value on the vortex finder wall did not exceed 60. At all other walls, the “y+” was smaller.

The governing equations were solved using the commercial solver ANSYS CFX. The high-resolution advection scheme and the implicit time-stepping second-order backward Euler transient scheme were applied for continuity and momentum equations. For velocity-pressure coupling, the fourth-order strategy similar to the one proposed by Rhie and Chow ¹² and modified by Majumdar ¹³ was applied. Trilinear interpolation was used for interpolating nodal pressures to integration points for the pressure gradient term of the momentum equation and for interpolating nodal velocities to integration points for the velocity divergence term in the continuity equation.

Detailed information regarding the differential Reynolds stress transport equations and the model coefficients as well as scalable wall functions is given in ¹⁴.

2.2 Governing Equations for the Dispersed Phase

The dispersed phase was calculated using particle transport modeling where particles are tracked through the flow. The tracking was carried out by forming a set of ordinary differential equations in time for position and velocity of each particle.

Since the particle density is much higher than the air density, only the aerodynamic drag force and the gravitational force were considered in particle tracking and the following equation of motion for spherical particles was solved:

(3)

where d_p is the particle diameter, ρ_p is the particle density, u_p is the particle velocity, F_D is a drag force acting on the particle, and F_G is a net force due to gravity.

The aerodynamic drag force was computed as:

(4)

where the drag coefficient was calculated by using the Schiller-Naumann correlation modified by a Cunningham correction factor

(5)

where the particle Reynolds number is:

(6)

The Cunningham correction factor was calculated according to ¹⁵:

(7)

where λ is the mean free path of gas molecules.

2.4 Mesh Independence Study

In order to reveal the effect of the mesh resolution on the computational results, the mesh independence study was performed. For that, five meshes consisting of 0.48–3.90 million hexahedron elements were generated and tested (Tab. 1). The mesh near cyclone walls was refined with inflation layers to provide a proper near-wall modeling. Each mesh was characterized by the mean cell size:

(8)

where V is a cyclone volume and N is the number of mesh cells.

Table 1. Mesh size.

Mesh	Number of mesh elements, ×106 [–]	Average cell size [mm]
Coarsest	0.48	8.31
Coarse	0.84	6.87
Medium	1.36	5.85
Fine	2.29	4.92
Finest	3.90	4.12

The radial profiles of the mean tangential and axial velocity components at the cylinder-cone intersection plane obtained with different meshes are shown in Fig. 3. The mesh size slightly affects the axial velocities and the tangential velocities in the free vortex region. However, the effect on the inner vortex is more significant, namely, on the maximum tangential velocity. Therefore, the grid convergence index (GCI) proposed by Roache ¹⁸ was calculated for the maximum tangential velocity.

The GCI is a measure of how far the computed value deviates from the asymptotic numerical value and it is based upon a grid refinement error estimator derived from the theory of the generalized Richardson extrapolation. The GCI indicates how much the solution would change with a further refinement of the grid. The detail information on GCI calculation can be found in ¹⁹. Qualitative representation of the grid independence study for the maximum tangential velocity is shown in Fig. 4a.

The finer the mesh is, the higher maximum tangential velocity is predicted. The predicted maximum tangential velocity increases from 22.8 to 23.8 m s⁻¹ with decreasing average mesh cell size from 8 to 6 mm. Further decrease in mesh cell size insignificantly affects the maximum tangential velocity. The maximum tangential velocity (Fig. 4a) converges monotonically. The medium mesh with a mean cell size of 5.85 mm provides the maximum tangential velocity and the static pressure drop with an error below 1 %. Based on that, the grid-independent solution can be obtained with a mean cell size of 5.85 mm.

The effect of the mesh resolution on the particle tracking was also determined. The cyclone cut size, a diameter of particles which are collected in a cyclone with 50 % efficiency, was calculated for three different meshes and its asymptotic numerical value was obtained by the usage of Richardson extrapolation, as it was done for the maximum tangential velocity. A qualitative representation of the grid independence study for the cut size is depicted in Fig. 4b.

3 Results and Discussion

The static pressure drop across the cyclone was determined as a difference in mass flow-averaged static pressure between the inlet and outlet and is given in Tab. 2. Both cases, when the flapper valve is open and without a valve, showed practically the same results. The pressure drop is about 706 Pa. However, it increases up to 741 Pa when the valve is closed.

This can be explained by the tangential velocities created in the cyclone (Fig. 6). The mean tangential velocities in the cyclone body are almost the same when the flapper valve is open and in a cyclone without a valve. But switching the valve into a closed position leads to increased tangential velocities. This agrees with the earlier findings of Hoekstra ²⁰ and Hoffmann ¹ who experimentally found that the tangential velocities in a cyclone without a dust hopper are higher than in a cyclone with a dust hopper.

The cyclone separation efficiency was determined in the following way. When a particle reaches the dust hopper side or a bottom wall, it is assumed to be collected by applying zero coefficients of restitution. Particles which reach the gas outlet are considered as non-collected (penetrated) particles. The trajectories of collected and penetrated particles are shown in Fig. 7 as red and blue lines, respectively.

The separation efficiency is best characterized by a grade efficiency curve (GEC). The separation efficiency for each particle diameter was determined as a ratio of collected particles to the sum of collected and penetrated particles.

The determined grade efficiency curve was approximated by the following function ¹, which includes two characteristic parameters, i.e., the cyclone cut size and the slope of the GEC:

(9)

where d₅₀ is the cut size and m is a slope parameter.

Both grade efficiency curves, determined with LES simulations and the approximated by Eq. 9, are displayed in Fig. 8.

The cut size d₅₀ and a slope parameter m of the approximated grade efficiency curves (Eq. 9) were determined and are given in Tab. 3.

The highest separation efficiency is reached in a cyclone without a valve. The cut size is a bit lower than 2.8 µm. The flapper valve decreases the separation efficiency by increasing the cyclone cut size by 3.4 % when it is in the “closed” position and by 11.4 % when it is in the “open” position. The slope of the grade efficiency curve is almost the same for a cyclone without a valve and with a valve in position “closed”. When the valve is switched into open position the slope parameter increases. Such an effect of the flapper valve on the separation efficiency parameters can be explained by the flow field, namely, by the tangential velocities (Fig. 9) and the vortex structure (Fig. 10).

Despite the fact that the tangential velocities in a cyclone with a valve in closed position are slightly higher than in a cyclone without a valve (Fig. 9), the separation efficiency is lower. This can be explained by two mechanisms. First, the separation space in a cyclone with a closed valve is smaller than in a cyclone without a valve. In the latter, additional particle separation occurs in the dust hopper. Second, the particles in a cyclone with a closed valve are collected on the valve where the vortex is stronger and, as a result, an increased amount of the particles are entrained from the valve by a strong inner vortex and carried over by the air flow to the gas outlet.

In a cyclone without a valve, particles are collected on the bottom of the dust hopper where the vortex is weaker and particle re-entrainment is smaller. A more significant negative effect in a cyclone with a valve in an open position can be explained by a vortex breakdown (Fig. 10). The valve destroys the vortex in the dust hopper drastically, reducing velocities there. As a result, a lower amount of flow and particles enter the dust hopper and lower separation efficiency is expected.

Additionally, the cut size for a cyclone without a valve was calculated for the same operating conditions as in simulations according to the model most widely used by engineers, namely, the Muschelknautz model ²¹, and is given in Tab. 3. The deviation between the simulated and calculated according to the Muschelknautz model cut size is 2.1 %. Such a good agreement in a cut size can additionally prove a high accuracy of the performed simulations.

4 Conclusion

Symbols used

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