Numerical Simulation of Cyclone Separator
Abstract:
A numerical simulation was undertaken to determine the overall efficiency of the given cyclone separator in ANSYS Fluent. The inlet conditions varied by changing the number of particles injected at the inlet and the overall efficiency in each case was determined. The flow inside the cyclone separator was modeled using the Discrete Phase Modelling (DPM) approach. The impact of different boundary conditions at the inlet on the simulation was studied and it was observed that the boundary conditions did not affect the results of the simulation.
Introduction:
A cyclonic separation is a method of removing particulates from gas or liquid stream, without the use of filters in equipment called cyclone. A cyclone is a conical vessel into which a dust-bearing gas-stream is passed tangentially. Because the rotating motion of the gas in the cyclone separator arising from its tangential entry, a free vortex is established. Rotational effects and gravity are used to separate mixtures of solids and fluids depending upon their densities. The method can also be used to separate fine droplets of liquid from a gaseous stream. Cyclone performance is determined by pressure drop and collection efficiency.
Cyclone collection efficiency, η, is defined as the fraction of particles of a given size that is retained by the cyclone. There are theoretical models that have been developed to predict efficiency. Separation of particles in the cyclone is due to the centrifugal force caused by the spinning gas stream; this force throws particles outward to the cyclone wall. Opposing this outward particle motion is an inward drag force caused by gas flowing toward the axis of the cyclone prior to discharge. All efficiency models set up a balance between these opposing forces.
The overall efficiency is usually the most important consideration in an industrial process [1]. Let’s consider the mass balance of solid particle in the cyclone. Then the mass balance of solid particle over the cyclone can be denoted by
Mf = Mc + Me
Mf – mass flow rate of the feed
Mc – Mass flow rate of particle collected
Me – Mass flow rate of the escaped particles
The overall separation efficiency can be calculated directly as the mass fraction of feed that is successfully collected.
The overall efficiency, though useful, does not specify anything about the effect of the particle on a cyclone. Hence, it does not provide us with any information that can be used in the future to design cyclone. The separation characteristics are best defined by grade efficiency.
There is a list of models that describe the grade efficiency of a cyclone separator. Some of the empirical models are listed below [2].
Critical Diameter: Timed Flight Approach:
The Lapple model:
It is the most widely used example of the timed flight approach. Lapple assumed that dust entering the cyclone was evenly distributed across the inlet opening. The particle size that travels from the inlet half-width to the wall during the time in the cyclone is collected with 50% efficiency. Lapple calculated this particle size, the cut diameter, as
The efficiency for a particle of any size can be determined from its ratio to the cut diameter
Critical Diameter: Static Particle Approach:
The static particle approach determines the particle diameter for which centrifugal force is exactly balanced by the drag force.
Barth's model:
It is widely cited in European literature, is an example of the static particle approach. Barth calculated the terminal settling velocity for the static particle and the collection velocity of any particle size is determined from the ratio of its settling velocity to the terminal settling velocity. The model predicts a sharp increase in cyclone efficiency from zero for particles smaller than the critical diameter to unity for larger particles. In practice, a sharp separation is never observed because of fluctuations in radial and tangential
Fractional Efficiency Approach:
It allows for the direct calculation of collection efficiency for particles of any size by cyclones of any design. The entire fractional efficiency curve can be determined without resorting to a generalized efficiency curve based on a critical diameter.
Leith-Licht model:
It is an example of this approach. It accounts for turbulence by assuming that at any height in the cyclone, uncollected dust is completely and uniformly mixed. Average residence time in the cyclone is determined from cyclone dimensions and gas throughput. The resultant expression for collection efficiency is
The Dietz model:
It represents a refinement of the Leith-Licht method. The model divides the cyclone into three regions: the entrance region (the annular space around the outlet duct at the top of the cyclone); the downflow region (corresponding to the vortex below the level of the outlet duct); and the core region (formed by the extension of the outlet duct to the bottom of the cyclone). Turbulence is assumed to produce a uniform radial concentration profile for uncollected particles with each region. To approximate distribution of particle residence times in the cyclone, the theory allows for the exchange of particles between the downflow and core regions. The Dietz model calculates cyclone collection efficiency as
Model Preparation:
The 3D model of the cyclone separator as shown in figure 1 is imported into SpaceClaim. Since the fluid volume is of interest in this simulation, the fluid volume inside the model is extracted with the volume extract option and the outer solid shell was suppressed from being included in the simulation. Then the model was meshed and the meshed model is displayed in figure 2. The mesh characteristics are summarized in table 1.
Then the model is imported into the solver, Fluent. A steady-state simulation was performed in a gravity enabled environment. The continuous medium used was air and the suspended particles were modeled using the Discrete Phase Model (DPM). The summary of the solver settings used is as follows.
Viscous Model: RNG k-ε model with standard wall function.
Discrete Phase Model: Interaction with the continuous flow.
Maximum number of steps = 50000
The injection was created with the following properties on the inlet.
Material: Anthracite with uniform diameter distribution.
Particle type: Inert.
Particle Diameter: 5e-6 m.
Total flow rate: 1e-20 kg/s.
Velocity: 3 m/s.
Density: 1550 kg/m3
The boundary conditions (BC) used are listed in table 2.
Results and Discussion:
The simulation is divided into two tasks, each concentrating on varying a specific parameter to investigate its effect on the results of the simulation. The first task of the simulation was conducted by running the simulation with different DPM boundary condition for the inlet and the results are compared. The meaning of the different boundary conditions was also reviewed [3]. The particle tracking data file was exported into CFD post to perform the post-processing. The particle residing time was considered the main component of comparison for the different cases. The mass flow rate on all the surface is calculated to determine the overall efficiency of the cyclone separator.
Task 1:
1. Reflect BC:
Meaning: The particle rebounds the off the boundary in question with a change in its momentum as defined by the coefficient of restitution.
The simulation was run for 600 iterations till convergence and the results are shown below. The particle tracking data was obtained as
|
number tracked = 94, |
trapped = 0 |
|
escaped = 85 |
evaporated = 0 |
|
aborted = 0, |
incomplete = 9 |
|
incomplete_parallel= 0 |
Overall efficiency: η = 65%
2. Trap BC:
Meaning: The trajectory calculations are terminated and the fate of the particle is recorded as "trapped''. In the case of evaporating droplets, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary.
|
number tracked = 94, |
trapped = 0 |
|
escaped = 85 |
evaporated = 0 |
|
aborted = 0, |
incomplete = 9 |
|
incomplete_parallel= 0 |
Overall Efficiency: η = 65%
3. Escape BC:
Meaning: The particle is reported as having "escaped'' when it encounters the boundary in question. Trajectory calculations are terminated
|
number tracked = 94, |
trapped = 0 |
|
escaped = 85 |
evaporated = 0 |
|
aborted = 0, |
incomplete = 9 |
|
incomplete_parallel= 0 |
Overall Efficiency: η = 65%
4. Wall-jet BC:
Meaning: The "wall-jet" type boundary condition assumes an analogy with an inviscid jet impacting a solid wall.
|
number tracked = 94, |
trapped = 0 |
|
escaped = 85 |
evaporated = 0 |
|
aborted = 0, |
incomplete = 9 |
|
incomplete_parallel= 0 |
Overall Efficiency: η = 65%
It can be observed on the comparison of the four cases, there is no significant change in the particle residing time or the velocity. The overall efficiency also remained constant in all cases. Hence, it can be concluded that the different DPM boundary conditions on application to the inlet surface have no significant impact.
Task 2:
In the second task of this simulation, the number of particles at the inlet are varied and overall efficiency is determined for each case. The number of particles can be varied by changing the number of mesh elements at the inlet which was achieved by varying the mesh size. The solver settings were retained from task 1 and the DPM boundary condition at the inlet was fixed at Reflect BC for all cases.
Case 1:
Number of particles:
Mesh size: 30 mm
No. elements: 31449
No. nodes: 6700
number tracked = 40, escaped = 38, aborted = 0, trapped = 0, evaporated = 0, incomplete = 2, incomplete_parallel = 0
Max time = 9.63 s
Mass Flow on inlet = 0.0569625 [kg/s]
Mass Flow on outlet_up = -0.018529 [kg/s]
Mass Flow on outlet_down = -0.0384151 [kg/s]
Therefore, the overall efficiency = Mf/Mc
= 0.0384151/0.0569625
= 67.4%
Case 2:
Number of Particles at the inlet: 94
Mesh size: 20 mm
No. Elements: 77163
No. Nodes: 15813
number tracked = 94, escaped = 85, aborted = 0, trapped = 0, evaporated = 0, incomplete = 9, incomplete_parallel = 0
Mass Flow on inlet (Mf) = 0.0569625 [kg/s]
Mass Flow on outlet_up (Me) = -0.0195865 [kg/s]
Mass Flow on outlet_down (Mc) = -0.0373406 [kg/s]
Therefore, the overall efficiency = Mf/Mc
= 0.0373406/0.0569625
= 65.5%
Case 3:
Number of particles: 364
Mesh size: 10 mm
No. elements: 411139
No. nodes: 80093
number tracked = 364, escaped = 347, aborted = 0, trapped = 0, evaporated = 0, incomplete = 17, incomplete_parallel = 0
Max residence tome = 18.15s
Mass Flow on inlet (Mf) = 0.0569625 [kg/s]
Mass Flow on outlet_up (Me) = -0.0213829 [kg/s]
Mass Flow on outlet_down (Mc) = -0.0355543 [kg/s]
Therefore, the overall efficiency = Mf/Mc
= 0.0355543/0.0569625
= 62.4%
Conclusion:
The results of the simulation in task 1 show that the simulation was not affected by the inlet DPM boundary condition. Although the overall efficiency is not a precise indicator of performance efficiency, it provides a basic understanding of the efficiency of the cyclone separator. It can be concluded from this simulation that as the number of particles being tracked increased, the overall efficiency of the cyclone separator decreased. The effect is due to a greater number of particles being escaped in the cyclone separator which is captured by simulating with a large number of particles.
References:
1. Tapkir, M.P., & Kamble, D.N. (2015). Analysis Of Cyclone Separator Using Empirical Models And CFD For Variation Of Dimensions.
2. John Dirgo & David Leith (1985) Cyclone Collection Efficiency: Comparison of Experimental Results with Theoretical Predictions, Aerosol Science and Technology, 4:4, 401-415, DOI: 10.1080/02786828508959066
3.https://www.sharcnet.ca/Software/Fluent6/html/ug/node852.htm