Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

AIM : To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.  

OBJECTIVE : 

- To write a few words about any four empirical models used to calculate the cyclone separator efficiency. 

- To perform an analysis on a given cyclone separator model by varying the particle diameter from $1$$\mu m$to $10$$\mu m$ and calculate the separation efficiency in each case. Discuss the results. [Using velocity as 3m/sec].

- To perform an analysis on a  given cyclone separator model by varying the velocity from 1$m/sec\; to\; 5\; m/sec$ and calculate the separation efficiency and pressure drop in each case. Discuss the results. [Use particle diameter size as 5 $\mu m$].

THEORY :

Four empirical models used to calculate the cyclone separator efficiency :

1.Iozia and Leith Model :

Iozia and Leith  logistic model is a modified version of Barth Model, which is developed based on force balance. The model assumes that a particle carried by the vortex endures  the influence of two forces: a centrifugal force, Z and a flow resistance, W. The collection efficiency η_i of particle diameter d_pi can be calculated from

                                                        

β is an expression for slope parameter derived based on the statistical analysis of experimental data of a cyclone with D = 170 0.25 m given as

                                   

and dpc is the 50% cut size given by Barth

                            

2.Li and Wang Model :

The Li and Wang model includes particle bounce or reentrainment and turbulent diffusion at the cyclone wall. A twodimensional analytical expression of particle distribution in the cyclone is obtained. Li and Wang model was developed based on the following assumptions:

• The radial particle velocity and the radial concentration profile are not constant for uncollected particles within the cyclone.
• Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce reentrainment on the cyclone wall are:

                                                      

• The tangential velocity is related to the radius of cyclone by: uRⁿ = constant.

The concentration distribution in a cyclone is given as:

                                  

The resultant expression of the collection efficiency for particle of any size is given as

                                       

3.Koch and Licht Model

Koch and Licht  collection theory recognized the inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone. Koch and Licht described particle motion in the entry and collection regions with the additional following assumptions:

• The tangential velocity of a particle is equal to the tangential velocity of the gas flow, i.e. there is no slip in the tangential direction between the particle and the gas.
• The tangential velocity is related to the radius of cyclone by: uRⁿ = constant.

A force balance and an equation on the particles collection yields the grade efficiency η_i

                                 

G is a factor related to the configuration of the cyclone, n is related to the vortex and τ is the relaxation term.

4.Lapple Model

Lapple model was developed based on force balance without considering the flow resistance. Lapple assumed that a particle entering the cyclone is evenly distributed across the inlet opening. The particle that travels from inlet half width to the wall in the cyclone is collected with 50% efficiency. The semi empirical relationship developed by Lapple [1] to calculate a 50% cut diameter, d_pc, is

                                        

where N_e is the number of revolutions     

                                          

The efficiency of collection of any size of particle is given by

                                 

 Step1:Geometry creation

 

    Solid model:

 Fluid volume:

 

 

 

 

 STEP 2 :  MESHING

Method:Body fitted cartesian

Number of nodes : 456604

Number of elements : 427871

 

 

  Mesh Quality

  

 

 Boundaries

  Inlet :

Outlet 1  :

 

 

 

 Outlet 2 :

 

 

 

  STEP 3 : SET UP & SOLUTION 

1. In this problem, the max velocity attained by the particles and air is very less as compared to the speed of sound.
2. Hence, the Mach number is <<< 0.3. Hence, a pressure-based solver was used since density-based solvers are generally used for simulations with Mach no > 0.3.
3. In this particular simulation, a steady state solver was used since we do not require to observe each particle at every moment.
4. Observing the number of particles that have been trapped, escaped, and incomplete, is our main motive
5. Furthermore, a gravity value of 9.81 m/s^2 was added in the -ve Y direction.
6. The K-epsilon RNG model was used in this particular problem.
7. This model is an upgradation of the standard k-epsilon model and is used mainly for swirling flows.
8. Moreover, the “swirl dominated flow” option was turned on for this simulation.
9. Afterwards, the discrete phase model option was turned and the settings were changed.
10. Here, the air particles represent the continuous phase whereas the solid particles represent the discontinuous phase.
11. These two phases can exchange mass and momentum within the flow.
12. Coupled Flow – The discrete phase can influence the flow of the continuous phase
13. Uncoupled Flow – The discrete phase will not have any interaction with the continuous phase
14. In this particular case, the particle size is very small, it doesn’t matter which option we chose.
15. The DPM interval was chosen as 10 and thus, the particle tracking data will be updated and showed on the console every 10 iterations.
16. The tracking parameters and specify length scale was set to default.
17. Then a new injection was created with the following parameters –

• Material – anthracite
• Particle type – inert
• Diameter distribution – uniform
• Injection type – surface
• Release from - INLET
• Velocity – 1,3,5 m/s in the x direction
• Diameter of particles – 1,3,5 microns

18. Furthermore, the boundary conditions for DPM were set accordingly

• Inlet – Reflect
• Wall – Reflect
• Outlet top – escape
• Outlet Bottom – trap

19. The inlet was set to a velocity inlet and outlet to a pressure outlet
20. The coupled scheme with “second order upwind” was used for the turbulent kinetic energy and turbulent dissipation rate
21. The solution was initialised using standard initialisation and was computed from inlet.
22. The problem was then run for 600 iterations and the results were observed

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STEP 4 : RESULTS 

 1.Velocity = 3m/s, size = 5microns                                                            

    

 

 

 

 

 

 

 

 2.Velocity=3m/s,Size=3microns

 

 

 

 

 

 

 

 3.Velocity=3m/s,Size=1 micron

 

 

 

 

 

 

 

 

 4.Velocity=5m/s,Size=5microns

 

 

 

 

 

 

 

 

 5.Velocity=3m/s,Size=5microns

 

 

 

 

 

 

 6.Velocity=1m/s,Size=5 microns

 

 

 

 

 

 

 Tables of all cases:

 

	Velocity and diameter	Tracked	Escaped	Trapped	Incomplete	Collector Efficiency	pressure     drop(Pa)
1	3 m/s and 5 microns	378	56	322	-	85.18	1.045
2	3 m/s and 3 microns	378	66	312	-	82.53	5.584
3	3 m/s and 1 microns	378	78	300	-	79.36	8.821
4	5 m/s and 5 microns	378	89	286	3	75.66	10.125
5	3 m/s and 5 microns	378	104	274	-	72.48	13.156
6	1 m/s and 5 microns	378	117	260	1	68.78	17.178

 

Conclusion:

1.Collector efficiency depends on both particle diameter and velocity.

2.By keeping velocity constant and decreasing the particle diameter,collector efficiency decreases.

3.By keeping  particle diameter constant and decreasing the velocity,collector efficiency decreases.