Cyclone Separator Simulation

CYCLONE:-

1. Cyclone are device that employ a centrifugal force generated by a spinning gas stream to separate particle from the carrier gas.
2. Their simple design, low maintaince cost and adaptability to a wide range of operating condition such as size and flow rate make cyclone one of most widely used particle removed device.
3. By using suitable material and method of construction cyclone may be adapted for use in extreme operating condition; high temperature, high pressure and corrosive gas.
4. Cyclone are important particle removal device in both engineering and process operation.

FOUR EMPIRICAL MODEL USED FOR CYCLONE 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 assume that a particle carried by the vortex endure the influence of two forces, a centrifugal force Z and a flow resistance W, core length z and core diameter d are given as

`z_c = ( H - S) - [ frac{H-S}{(D/B)-1][(frac{d_c}{B})-1]` for `d_c` > B

`z_c=H-S` for `d_c`<B

`d_c=0.47*(frac{ab}{D^2})^0.25 (frac{D_c}{D})^1.4`

• The addition made by Iozia and Leith on the original Barth model are the core length `z_c` and slope parameter `beta`expression which is derived based on the statistical analysis of experimental data of cyclone with D = 0.25 m. The collection efficiency `eta_i` of particle diameter `dp_i` can be calculated from

`eta_i=frac{1}{1+(frac{dp_c}{bardp_i})^beta`

where `dp_c` is the 50% cut size given by Barth

`dp_c=[frac{9muQ}{pip_pz_cv_max^2}]^0.5`

2. Li and Wang Model:-

• The Li and Wang model include particle bounce or re-entrainment and turbulent diffusion at the cyclone wall.
• A 2D analytical expression of particle distribution in the cyclone is obtained.
• Li and Wang model was developed based on the following assumption.
• The radial particle velocity and the radial concentration profile are not constant, for uncollected particle within the cyclone.
• Boundary condition with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are

c = `c_theta` at `theta` = 0

`D_rfrac{partialc}{partialr}=(1-alpha)wc` at r =D/2

• The tangential velocity is related to the radius of cyclone by `muR^n` = constant

The concentration distribution in cyclone is given as

`c(r,theta)=frac{c_0(r_w-r_n)exp{-lamda[frac{1}{k(1+n)}*r^(1+n)]}}{int exp{frac{1}{k(1+n)}*r^(1+n)}dr`

integration between `r_n to r_w`

where

`k=frac{(1-n)(rho_p-rho_g)d^2Q}{18mub(r_w^(1-n)-r_n^(1-n))`

and lamda = `frac{(1-alpha)kw_w}{D_rr_w^n}`

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

`eta_i = 1- exp{-lamdatheta_1}`

where `theta_1=2pi(S+L)/a`

3. Koch and Leith Model:-

• Koch and Leith collection theory recognized the inherently turbulent nature of cyclone and the distribution of gas resistance times within the cyclone Koch and Licht describe particle motion in the entry and collection region with the additional following assumption.
• The tangential velocity of a particle is equal to the tangential velocity of the gas flow that is 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 `muR^n` = constant
• A force balance and an equation on the particle collection yield the grade efficiency `eta_i`

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

where `G=frac{8k_c}{k_a^2*k_b^2}`

`n=1-{1-frac{(12D)^0.14}{2.5}}{frac{T+460}{530}}^0.3`

`tau_i=frac{rho_pdp_i^2}{18mu}`

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

4. Lapple Model :-

• Lapple model wall 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 travel from inlet half width to the wall in the cyclone is collected with 50% efficiency.
• The semi empirical relationship developed by Lapple to calculate a 50% cut diameter, `dp_c`

`dp_c=[frac{9mub}{2piN_ev_i(rho_p-rho_g)}]^0.5`

where `N_e`is number of revolution

`N_e=frac{1}{a}(h+frac{H-h}{2})`

The efficiency of collection of any size of particle

`eta_i=frac{1}{1+(dp_c-bardp_i)^2`

DISCRETE PHASE MODELLING (DPM):-

• The Lagrangian discrete phase model follows the Euler Lagrange approach.
• The fluid phase is treated as a continuum by solving the Navier Stokes equation, while the dispered phase is solved by tracking a large number of particle, bubble or droplet through the calculated flow field.
• The dispersed phase can exchange momentum, mass and energy with fluid phase.

TYPES:-

1.Reflect:-

The particle rebound off the boundary in question with a change in its momentum as defined by the coefficient of restitution.

2. Trap:-

The trajectory calculation are terminated and the fate of the particle is recorded as \" trapped \". In the case of evaporating droplet, their entire mass instantaneously passes into the vapour phase and enter the cell adjacent to the boundary.

In case of a combusting particle, the remaining volatile mass is passed into the vapour phase.

3. Escape:-

The particle is reported as having \"escaped\" when it encounter the boundary in question. Trajectory calculated are terminated .

4. Wall jet:-

The direction and velocity of the droplet particle are given by the resulting momentum flux, which is a function of the impingement angle `phi`and weber number.

The \" wall jet\" type boundary condition is appropriate for high temperature walls where no significant liquid film is formed and in high Weber Number where the spray acts as jet.

GEOMETRY:-

Given Geometry

Fluid Volume extracted for analysis purpose

For different boundary condition type are as follow:-

MESH:-

Mesh of 18 mm for different boundary condition type

SET UP:-

General:-

1. Steady State
2. Pressure Based Solver
3. Gravity= -9.81 `m/s^2`

Model:-

1. Viscous Model :- k-epsilon model - RNG - swirl mode on

DPM:-

1. Interaction - Interaction with continuous Phase
2. Injection type :- Surface (inlet)
3. Diameter(m) :- 5e-6
4. Velocity inlet (m/s) :- 3 m/s
5. Total Mass flow rate :- 1e-20

Material :-

1. Air(Fluid)
2. Anthracite(Particle)

Boundary Condition:-

1. Inlet :- 3 m/s
2. Discrete Phase :- a) Reflect b)Trap c)Escape and d)wall

Numerical Schemes:-

1. Pressure Velocity Coupling:- Simple
2. Spatial discretization :- a) Gradient :- Least square cell based

b) Pressure:- Second Order

c) Momentum :- Second Order Upwind

d) Turbulent Kinetic energy :- Second Order Upwind

e) Turbulent dissipation energy :- Second Order Upwind

Solver:-

1. Standard:- Initialization
2. Compute:- Inlet

A) REFLECT:-

Residual Plot:-

Residual Plot for Reflect discrete

Anthracite Particle Time:-

Anthracite Particle Time for Reflect

Anthracite Particle ID:-

Anthracite Particle ID for Reflect

Particle Velocity Contour:-

Anthracite Velocity of Particle for Reflect

Vortex Velocity:-

Vortex diagram of cyclone for Reflect discrete at the core region

B)TRAP:-

Residual Plot:-

Residual Plot For Trap

Particle Time:-

Particle Time for Trap

Particle ID:-

Particle ID for Trap

Velocity Contour:-

Velocity Contour for Trap

Vortex:-

Vortex Core Region for Trap discrete

C)Escape:-

Residual Plot:-

Residual Plot for escape

Particle Time:-

Particle Time for escape

Particle ID:-

Particle ID for Escape

Velocity Contour:-

Velocity contour plot for escape

Vortex:-

Vortex core region for escape at swirl 0.125

4.Wall Jet:-

Residual Plot:-

Residual Plot for Wall-Jet

Particle Time:-

Particle Time for Wall-Jet

Particle ID:-

Particle ID for Wall-Jet

Velocity Contour:-

Velocity Plot for wall-Jet

Vortex:-

Vortex core region for wall-Jet at 0.125 swirl.

DPM ITERATION VALUE:-

The above image is DPM iteration for reflect, trap, escape and wall-jet injection for mesh 18mm

For Reflect case as per the challenge, in this three different size of mesh are used.

CASE 1:-

MESH:-

Element size :- 20 mm

Total number element :- 76549

SET UP:-(Remain same for futher two case)

General:-

1. Steady State
2. Pressure Based Solver
3. Gravity= -9.81 `m/s^2`

Model:-

1. Viscous Model :- k-epsilon model - RNG - swirl mode on

DPM:-

1. Interaction - Interaction with continuous Phase
2. Injection type :- Surface (inlet)
3. Diameter(m) :- 5e-6
4. Velocity inlet (m/s) :- 3 m/s
5. Total Mass flow rate :- 1e-20

Material :-

1. Air(Fluid)
2. Anthracite(Particle)

Boundary Condition:-

1. Inlet :- 3 m/s
2. Discrete Phase :- Reflect

Numerical Schemes:-

1. Pressure Velocity Coupling:- Simple
2. Spatial discretization :- a) Gradient :- Least square cell based

b) Pressure:- Second Order

c) Momentum :- Second Order Upwind

d) Turbulent Kinetic energy :- Second Order Upwind

e) Turbulent dissipation energy :- Second Order Upwind

Solver:-

1. Standard:- Initialization
2. Compute:- Inlet

Residual:-

Particle ID

Particle Time:-

Velocity contour:-

Vortex:-

DPM Iteration:-

Case 2:-

MESH

Element Size:- 15 mm

Number of Element :- 157268

Residual Plot

From above plot we can see that the solution get converge after 500 iteration

Particle ID

Particle time:-

Velocity Contour:-

Vortex:-

Vortex Core Region for 0.125 swirl

DPM Iteration:-

Case 3:-

Residual Plot

From above plot we can see that the solution get converge after 500 iteration.

Particle ID

Particle Time

Vortex

Vortex core region for swirl 0.125

DPM Iteration:-

Discussion:-

• By observing the DPM Iteration we can in Reflect we can say that as we refined the mesh size we get more accurate result.
• The mass flow rate at outlet shows negative rate due to functional calculator which indicate that the flow is outwards.
• At some point the particle gets trapped in the cyclone this due to high inertia.