Cyclone separator simulation using Discrete Phase Modelling

Cyclone seperators are one of the devices used in controlling air pollution, the cyclone seperators employ vortex seperation by using the force of inertia to remove larger particulate matter before sending the polluted air for further cleaning. One of the advantages of using a cyclone seperator is that there is no need for filters for their working. Cyclone seperators are only used for filtering larger particulate matter of size 20-30`mu`m their efficiency reduces if they are employed for filtering out small particulate matters. However, the dimensions of the cyclone seperator can be changed to improve the efficiency of smaller particulate matters.

Four empirical models are used for finding the cyclone seperator efficiency:

1) Iozia and Leith model:

Iozia and Leith model is based on force balance. The model assumes that the a particle carried by the vortex is influenced by two forces: centrifual force and flow resistance. This model is a improved version of Barth model. Here the efficiency is given as:

`eta_i = 1/(1+(d_(pc)/bar(d_(p i)))^beta`

where,

`d_(p i)` is the particle diameter and

`d_(pc)` 50% cut size by Barth.

2) Li and Wang model:

The Li and Wang model includes particle bounce and turbulent diffusion at the cyclone wall and relates tangential velocity to radius of cyclone. Here, a two-dimensional expression of particle distribution in the cyclone is obtained.

Here the efficiency is given as:

`eta_i=1-exp(-lamdatheta_1)`

3) Koch and Licht model:

Koch and Licht model takes into consideration inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone. This model assumes that there is no slip in the tangential direction between the particle and gas.

Here the efficiency is given as:

`eta_i=1-exp[-2((Gtau_iQ)/(D^3)(n+1))^(0.5/(n+1))]`

where,

G is afactor related to the configuration of the cyclone, n is related to vortex and `tau`is the relaxation term.

4) Lapple model:

Lapple model is force balance model that does not consider the flow resistance. Lapple model assumes that the particle is evenly distributed across inlet opening. Here, the particle that travels from inlet half width to the wall in thee cyclone is collected with 50% efficiency.

Here the efficiency is given as:

`eta_i = 1/(1+(d_(pc)/bar(d_(p i)))^2`

The simulation is carried out in steady state with operating conditions including a gravity acting along y-axis with a value of -9.81m/s^2. Turbulence is modelled by k-`epsilon`RNG models with swirl dominance. Discrete phase modelling is enabled with interaction with the continuous phase. DPM source is updated for every flow iteration and for the discrete phase anthracite particles of size 5e-06m is selected with surface type inject through the inlet boundary condition with 3m/s velocity given along x-axis. For the inlet boundary conditions of continuous phase a velocity of 3m/s is given normal to the inlet boundary and the DPM inlet boundary is set as required.

Geometry of cyclone seperator:

There are four different boundary conditions for a discrete phase modelling, the following results are obtained by changing the boundary conditions for the inlet and for the mesh element size of 10 mm:

Reflect:

If a boundary is set as reflect, a particle coming into contact with this boundary rebounds off with a change in momentum that is defined by coefficient of restitution. By default, the coefficient of restitution is set as 1.

For the simulation with this boundary condition the following results are obtained:

DPM Iteration ....
number tracked = 364, escaped = 169, aborted = 0, trapped = 0, evaporated = 0, incomplete = 195, incomplete_parallel = 0

Trap:

If a particle comes into contact with a boundary condition set as trap, its ttrajectory calculations are terminated and the particles is counted as trapped.

For the simulation with this boundary condition the following results are obtained:

DPM Iteration ....
number tracked = 364, escaped = 161, aborted = 0, trapped = 0, evaporated = 0, incomplete = 203, incomplete_parallel = 0

Escape:

When a particle hits a escape boundary, its trajectory calculation is stopped and it is considered escaped.

For the simulation with this boundary condition the following results are obtained:

DPM Iteration ....
number tracked = 364, escaped = 161, aborted = 0, trapped = 0, evaporated = 0, incomplete = 203, incomplete_parallel = 0

Wall-jet:

Wall-jet is a boundary is used only for high temperature walls and in high Weber number impacts where the spray act as jet. It is not an appropriate boundary condition where there is a formation of significant film of liquid e.g., port fuel injection and rain water runoff.

For the simulation with this boundary condition the following results are obtained:

DPM Iteration ....
number tracked = 364, escaped = 161, aborted = 0, trapped = 0, evaporated = 0, incomplete = 203, incomplete_parallel = 0

Boundary conditions	No. of tracked	Escaped	Aborted	Trapped	Evaporated	Incomplete	Incomplete parallel
Reflect	364	169	0	0	0	195	0
Trap	364	161	0	0	0	203	0
Escape	364	161	0	0	0	203	0
Wall-jet	364	161	0	0	0	203	0

It can be clearly observed that reflect condition increases the number of particles escaped while others boundary conditions have low number of escaped particles this is because the reflect boundary reflects the particles which then gets sucked in the vortex from which more particles might escape through outlet.

After analysing the changes caused by different boundary conditions we now change the mesh element size to change the number of particles injected and observe how it changes the result. For this purpose three element sizes 10 mm, 11 mm and 12 mm are selected and the simulations here are done taking inlet with reflect boundary condition.

10 mm element size mesh:

Number of nodes in this mesh is 79480 and the number of elements is 407130.

For the 10 mm element size with reflect boundary condition:

DPM Iteration ....
number tracked = 364, escaped = 169, aborted = 0, trapped = 0, evaporated = 0, incomplete = 195, incomplete_parallel = 0

11 mm element size mesh:

Number of nodes in the mesh is 65203 and the number of elements in the mesh is 333902.

For the 11mm element size with reflect boundary condition:

DPM Iteration ....
number tracked = 280, escaped = 153, aborted = 0, trapped = 0, evaporated = 0, incomplete = 127, incomplete_parallel = 0

12 mm element size mesh:

Number of nodes in the mesh is 53140 and the number of elements in the mesh is 270912.

For the 12mm element size with reflect boundary condition:

DPM Iteration ....
number tracked = 226, escaped = 109, aborted = 0, trapped = 0, evaporated = 0, incomplete = 117, incomplete_parallel = 0

Element size of mesh	No. of tracked	Escaped	Aborted	Trapped	Evaporated	Incomplete	Incomplete parallel
10mm	364	169	0	0	0	195	0
11mm	280	153	0	0	0	127	0
12mm	226	109	0	0	0	117	0

As we see here as the number of particles tracked increases so does number of escaped and incomplete particles. To reduce the number of incomplete particles the efficiency of the cyclone seperator need to be increased which can only be achieved by using reflect boundary condition in the inlet and adjusting the dimensions of the cyclone seperator.