Cyclone separator challenge
Cyclone Separator:
Principle and Working:
A high speed rotating (air)flow is established within a cylindrical or conical container called a cyclone. Air flows in a spiral pattern, beginning at the top (wide end) of the cyclone and ending at the bottom (narrow) end before exiting the cyclone in a straight stream through the center of the cyclone and out the top. Larger (denser) particles in the rotating stream have too much inertia to follow the tight curve of the stream and strike the outside wall, falling then to the bottom of the cyclone where they can be removed. In a conical system, as the rotating flow moves towards the narrow end of the cyclone the rotational radius of the stream is reduced, separating smaller and smaller particles.
Applications:
General applications include:
- oil refineries to separate oils and gases
- cement industry
- vacuum cleaners
Features Required:
- High efficiency over a broad flow range
- Flow-optimized design
- Low pressure drop resulting in energy savings
- High safety during operation under pressure
- Long-term corrosion protection
CYCLONE EFFICIENCY EMPIRICAL MODELS:
Iozia and Leith Model:
Iozia and Leith logistic model 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 or drag force, W. The collection efficiency `eta_i` of particle diameter `d_(p i)` can be calculated from
`η_i = 1 /{1 + (d_(pc)/d_(p i))^ β}`
β is an expression for slope parameter
`β = 0.62 − 0.87 ln(d_(pc)/100 )+ 5.21 ln({ab}/{D^2} ) + 1.05 [ln({ab}/{D^2})]^2`
`d_(pc)` is cut particle diameter collected with 50% efficiency (m)
`d_(pc) = [{9µQ}/{πρ_p z_c(v _(t max))^2}]^0.5`
`d_(p i)`is diameter of particle in size range i(m)
where core length, zc, and core diameter, dc, are given as
`z_c = (H − S) − [ {H − S }/{(D/B) − 1}] [(d_c/B) − 1]` for `d_c> B`
`z_c = (H − S)` for `d_c< B`
`dc = 0.47D ( {ab}/ {D^2} )^(−0.25)(D_e/D)^1.4`
Li and Wang Model:
The Li and Wang model includes particle bounce or reentrainment and turbulent diffusion at the cyclone wall. A two dimensional 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
where
`K = {(1 − n)(ρ_p − ρ_g)d^2Q}/{18 µb (r_w^(1−n) − r_n^(1−n))}`
`λ = {(1 − α)Kw_w}/{D_r(r_w)^n`
The resultant expression of the collection efficiency for particle of any size is given as
`η_i = 1 − exp{−λθ_1}`
where
`θ_1 = {2π(S + L)}/a`
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:
`uR^n`= constant.
A force balance and an equation on the particles collection yields the grade efficiency `eta_i`
`η_i = 1 − exp{ −2[(Gtau_i Q)/ D^3 (n + 1)]^(0.5/(n+1))}`
`G = (8K_c)/{(K_a)^2 (K_b)^2}`
`n = 1 − { 1 − (12D) ^0.14 /2.5 }{{T + 460 }/530 }^0.3`
`tau_i = {ρ_p(d_(p i))^2}/{18µ}`
`K_a` = a/D
`K_b`= b/D
`K_c` is cyclone volume constant
a is cyclone inlet height (m)
b is cyclone inlet width (m)
T is absolute temperature (K)
D is cyclone body diameter (m)
G is a factor related to the configuration of the cyclone, n is related to the vortex and `tau` is the relaxation term.
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.It is mostly based on the terminal velocity of particles in the cyclone.
`d_(pc) = [{9 µb}/{2π N_ev_i(ρ_p − ρ_g)}] ^{1/2}`
where `N_e` is the number of revolutions
`N_e = 1/a[h + (H − h)/2]`
The efficiency of collection of any size of particle is given by
`η_i = 1 /{1 + (d_(pc)/d_(p i))^2}`
2Q. Perform an analysis on the given cyclone separator model and apply four different boundary condition types at the inlet i.e. reflect, trap, escape and wall-jet and submit images on your findings on the different conditions.
A) Boundary condition: reflect
Geometry:
3D Model of Cyclone separator
3D Model of Extracted Fluid volume:
Cyclone separator Mesh:
Element size = 30 mm
Number of nodes = 6686
Number of elements = 31317
Mesh Quality:
Mesh Metric:
SIMULATION SETUP DETAILS:
I. SETUP PHYSICS
SOLVER
Type --> pressure based
velocity Formulation --> Absolute
Time --> Steady
Gravity - Tick the check box
Gravitational Acceleration
X (m/s2) = 0
Y (m/s2) = -9.81
MODELS
Viscous --> k-epsilon
k-epsilon Model --> RNG
RNG options--> Swirl Dominated Flow
Near-wall Treatment --> Standard Wall Functions
press Ok.
Discrete Phase Model:
Tick - Interaction with Continous Phase
Tick - Update DPM Sources Every Flow Iteraction
click on Injections-->create
Injection type --> surface
Release from surfaces - inlet
Material --> anthracite
Point Properties - set the variables
X - Velocity (m/s) = 3
Diameter (m) = 5e-6
click on Ok.
close Injections wizard.
click on Ok.
Boundary conditions:
inlet -->Edit
Momentum
Velocity magnitude(m/s) = 3
DPM
Discrete Phase BC Type - reflect
II SOLUTION
SOLUTION METHODS
Turbulent kinetic Energy - Second Order Upwind
Turbulent Dissipation Rate - Second Order Upwind
INITIALIZATION
Method --> Standard
Options
Compute from --> inlet
Click on Initialize
RUN CALCULATON
Time scale Factor = 1
No. of Iterations = 600
Scaled Residuals: The solution is converged at 193 iterations.
After the simulation.
Export the Particle tracking History, save it in the appropriate folder.
close the fluent.
III RESULTS
Open the cfd post process by clicking on the Results.
Tick on wall.
Double click on wall.
Details of wall
Render
Transparency - set appropriate value.
Apply.
click on File.
Import--> Import the Fluent Particle File.
select the file, click on Ok.
Double click on FLUENT PT for Anthracite
Details of FLUENT PT for Anthracite
color
Mode --> variable
variable --> Anthracite Particle time
click on Apply
Anthracite Particle time(Reflect):
Insert vortex core Region and vary the swirling strength to see the vortex formation.
Vortex Core Region
Method: Swirling Strength
Level - 0.01
B) Boundary condition: trap
The Geometry, Mesh, are same as in previous case, but in simulation details, the
boundary conditions of DPM is to be changed to trap
scaled Residuals:The solution is converged at 193 iterations.
Anthracite Particle time(trap):
Vortex Core Region
Method: Swirling Strength
Level - 0.01
C) Boundary condition: escape
The Geometry, Mesh, are same as in previous case, but in simulation details, the
boundary conditions of DPM is to be changed to escape
scaled Residuals: The solution is converged at 281 iterations.
Anthracite Particle time(escape):
Vortex Core Region
Method: Swirling Strength
Level - 0.01
D) Boundary condition: wall-jet
The Geometry, Mesh, are same as in previous case, but in simulation details, the
boundary conditions of DPM is to be changed to wall-jet
scaled Residuals: The solution is converged at 193 iterations.
Anthracite Particle time(wall-jet):
Vortex Core Region
Method: Swirling Strength
Level - 0.01
Comparison of cyclone separator by varying the Discrete Phase Boundary condition:
|
Boundary Condition |
Number of Particle tracked |
Number of particle escaped |
Number of particle incomplete |
|
Reflect |
40 |
40 |
0 |
|
Trap |
40 |
40 |
0 |
|
escape |
40 |
40 |
0 |
|
Wall-jet |
40 |
40 |
0 |
3Q. Vary the number of particles through the inlet and run the simulation for 3 cases. Report the number of particles that pass through or remain in the cyclonic separator. Post images to show the same. For this question, use the “Reflect” option as the boundary condition for the Discrete Phase
Variation of number of particles through the inlet is done by varying Mesh size, Reflect option is used as the boundary condition.
Case 1 (Mesh size : 30 mm)
Geometry:
3D Model of Cyclone separator
3D Model of Extracted Fluid volume:
Cyclone separator Mesh:
Element size = 30 mm
Number of nodes = 6686
Number of elements = 31317
Mesh Quality:
SIMULATION SETUP DETAILS:
I. SETUP PHYSICS
SOLVER
Type --> pressure based
velocity Formulation --> Absolute
Time --> Steady
Gravity - Tick the check box
Gravitational Acceleration
X (m/s2) = 0
Y (m/s2) = -9.81
MODELS
Viscous --> k-epsilon
k-epsilon Model --> RNG
RNG options--> Swirl Dominated Flow
Near-wall Treatment --> Standard Wall Functions
press Ok.
Discrete Phase Model:
Tick - Interaction with Continous Phase
Tick - Update DPM Sources Every Flow Iteraction
click on Injections-->create
Injection type --> surface
Release from surfaces - inlet
Material --> anthracite
Point Properties - set the variables
X - Velocity (m/s) = 3
Diameter (m) = 5e-6
click on Ok.
close Injections wizard.
click on Ok.
Boundary conditions:
inlet -->Edit
Momentum
Velocity magnitude(m/s) = 3
DPM
Discrete Phase BC Type - reflect
II SOLUTION
SOLUTION METHODS
Turbulent kinetic Energy - Second Order Upwind
Turbulent Dissipation Rate - Second Order Upwind
INITIALIZATION
Method --> Standard
Options
Compute from --> inlet
Click on Initialize
RUN CALCULATON
Time scale Factor = 1
No. of Iterations = 600
Scaled Residuals: The solution is converged at 159 iterations
After the simulation.
Export the Particle tracking History, save it in the appropriate folder.
close the fluent.
III RESULTS
Open the cfd post process by clicking on the Results.
Tick on wall.
Double click on wall.
Details of wall
Render
Transparency - set appropriate value.
Apply.
click on File.
Import--> Import the Fluent Particle File.
select the file, click on Ok.
Double click on FLUENT PT for Anthracite
Details of FLUENT PT for Anthracite
color
Mode --> variable
variable --> Anthracite Particle time
click on Apply
Create Animation for Fluent PT for Anthracite (Mesh size 30 mm)
Insert vortex core Region and vary the swirling strength to see the vortex formation.
Case 2 (Mesh size : 20 mm)
The Geometry and the simulation details are same as the case 1, but the Mesh size is refined to 20 mm.
Element size = 20 mm
Number of nodes = 15843
Number of elements = 77335
Cyclone separator Mesh:
Mesh Quality:
scaled Residuals: The solution is converged at 202 iterations
Create Animation for Fluent PT for Anthracite (Mesh size 20 mm)
Case 3 (Mesh size : 10 mm)
The Geometry and the simulation details are same as the case 1, but the Mesh size is refined to 10 mm.
Element size = 10 mm
Number of nodes = 79513
Number of elements = 407290
Cyclone separator Mesh:
Mesh Quality:
scaled Residuals: The solution is converged at 238 iterations
Create Animation for Fluent PT for Anthracite (Mesh size 10 mm)
Comparison by varying Mesh size:
|
|
Case 1 |
Case 2 |
Case 3 |
|
Element size (mm) |
30 |
20 |
10 |
|
Number. of elements |
31317 |
77335 |
407290 |
|
Number of particles tracked |
40 |
94 |
364 |
|
Number of particles escaped |
39 |
94 |
290 |
|
Number of particles incomplete |
1 |
0 |
74 |
|
Anthracite.Particle Time(sec) |
4.745 |
3.971 |
14.80 |
|
Mass flow rate at inlet(kg/s) |
0.0569625 |
0.0569625 |
0.0569625 |
|
Mass flow rate at outlet 1(kg/s) |
-0.01851 |
-0.0176765 |
-0.0157922 |
|
Mass flow rate at outlet 2 (kg/s) |
-0.0384525 |
-0.0392863 |
-0.041171 |