Cyclone Separator Challenge

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

Objective:-

1. To write a few words about any four empirical models used to calculate the cyclone separator efficiency.
2. To perform an analysis on a given cyclone separator model by varying the particle diameter from 1 μm to 5 μm and calculate the separation efficiency in each case. Discuss the results. [Use both the velocity's as 3m/sec.]
3. To perform an analysis on a given cyclone separator model by varying the particle 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 μm for all cases & keep flow velocity same as particle velocity]

Cyclone Separator

Cyclonic separation is a method of removing particulates from an air, gas or liquid stream, without the use of filters, through vortex separation. When removing particulate matter from liquid, a hyrocyclone is used; while from gas, a gas cyclone is used. Rotational effects and gravity are used to separate mixtures of solids and fluids. The method can also be used to separate fine droplets of liquid from a gaseous stream.

A high speed rotating (air)flow is established within a cylindrical or conical container called a cyclone. Air flows in a helical 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 thus strike the outside wall, then fall 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, thus separating smaller and smaller particles. The cyclone geometry, together with volumetric flow rate, defines the cut point of the cyclone. This is the size of particle that will be removed from the stream with a 50% efficiency. Particles larger than the cut point will be removed with a greater efficiency, and smaller particles with a lower efficiency as they separate with more difficulty or can be subject to re-entrainment when the air vortex reverses direction to move in direction of the outlet.

Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices known as precleaners since they generally remove larger pieces of particulate matter. This prevents finer filtration methods from having to deal with large, more abrasive particles later on. In addition, several cyclone separators can operate in parallel, and this system is known as a multicyclone.

Cyclone efficiency empirical models

• Lozia and Lieth Model

Lozia and Lieth 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 effieciency `eta_i`of particel diameter `dp_i` can be calculated from

`eta_i=frac{1}{1+(frac{d_(pc)}{d_(PI)})^beta`

`beta` is an expression for slope parameter derived based on the statistical analysis of experiment data of a cyclone with D=0.25 m given as

`beta=0.62-0.87ln(frac{d_(pc)}{100})+5.21ln(frac{ab}{D^2})+1.05[ln(frac{(ab)}{D^2})]^2`

and `d_(pc)` is the 50% cut size given by Barth

`d_(pc)=[frac{9 mu Q}{pi rho_p z_c v_(tmax)^2}]^(0.5)`

Where core length, z_c, and core diameter, d_c, are given as

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

Z_c =H-S for d_c<B

d_c = 0.47 D(ab/D^2)^(-0.25) (D_e/D)^(1.4)

• Li and Wang Model

The Li and Wang model includes particle bounce or reenterainment 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 followibg assumptions:

• The radial particle velocity and 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:

`c=c_0`, at `theta=0`

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

• The tangebtial velocity is related to the radius of cyclone by:uR^(n) = constant.

The concentration distribution in a 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_(r_n)^(r_w)exp{[frac{1}{K(1+n)}r^(1+n)]}dr}`

`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 any size is given as

`eta_i=1-exp{-lamdatheta_1}`

Where

`theta_1= frac{2pi(S+L)}a`

• Koch and Licht Model

Koch and Licht collection theory recognized the inherently turbulent nature of cyclone 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 direction 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=1-exp{-2[frac{Gtau_iQ}{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_g d_(PI)^2}{18mu}`

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 with out 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% effeciency. The semi empirical relationship developed by Lapple to calculate a 50% cut diameter, `d_(pc)`, is

`d_(pc) =[frac{9 mub}{2piN_ev_i(rho_p-rho_g)}]^(1/2)`

where `N_e`is the number of revolutions

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

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

`eta_i = frac{a}{1+(d_p`

Geometry preparation

• In the step-1, we import the geometry in space claim.

• Then go to prepare and then go volume extraction and select the inlet, outlet(top) and outlet(bottm/dustbin) and then click on . we got the geometry in this form

• Then click on . we got the geometry in this form

• Then suppress the thickness of the geometry and only the fluid volume is remaining.

Meshing

Note:

Structural mesh gives the best results thats why i used the triangular mesh method to generate the results. I have also used the cutcell meshing approach available in Ansys Meshing for the genertion of mesh but results are not displayed here. I have used the hexa mesh method to generate the mesh but results are not displayed here.

Case setup

• Time: Steady state
• Solver type:pressure based
• Velocity formulation:absolute
• Gravity Accelerational: (Enable in y-direction) x=0, y=-9.81, z=0.
• Viscous model:

Model: K-epsilon

K-epsilon model: RNG

RNG option: Swirl dominated

Near wall treatment : standard wall function.

• Injections

Type: Surface injection

Release from surface: Inlet

Particle type: Inert

Material type: Anthracite

X-Velocity: 3(m/s) (varying velocity from 1 to 5 m/s)

Diameter: Varying from 1e-06 to 10e-06 from different case.

Flow Rate: 1e-20 kg/s

• Discrete phase model(DPM)

Fluent provides a model that is especially for spray simulations, or more general suspended particle trajectory simulations. This is the Discrete Phase Model (DPM) and it is based on the so-called Euler-Lagrange method. In the computational domain there are two separate phases present, namely, the continuous and the discrete phase (particles). The transport equations are solved for the continuous phase only and the motion of particles is dealt with particle trajectory calculations. Through an iterative solution procedure the mass, momentum and energy interaction between both phases can be realized.

In this solid particle size ranging from 1`mu` to 5`mu`being simulated as a discrete phase in a continuum.

• Enable interaction with continuous phase- To enable coupled flow
• Enable update DPM source every flow iteration: Enabling this option gives chances to calculate the particle source term at every flow iteration.
• Tracking parameters- Max No. of time steps-50000- It is the no.of timesteps that is used to compute the single particle trajectory.
• Specify length scale: This option is also used to control the time step.

• Boundary Conditions:

• Inlet: Velocity inlet
• Velocity magnitude: 3 m/s( In this part it constant for all particle diameter size varying from 1e-06 to 5e-06)
• DPM: Reflect
• Reflect: The particles rebound off the boundary in question with a change in its momentum as defined by the coefficient of restitution.

• Outlet_1: Pressure outlet
• Pressure: 0 Pa
• DPM: Escape
• Escape: The particle is reported as having escaped when it encountered the boundary in equation. Trajectoried calculated as terminied.

• Outlet_2(Dustbin Bottom): pressure outlet
• DPM: Trap
• Pressure: 0 Pa
• Trap: The trajectory calculation are terminied and the fate of the particle is termined as a "trapped". In the case of the evaprating droplet, their entire mass instantaneously passes into the vapor phase and enters the cells adjacent to the boundary. In the case of the combusting particle, the remaining volatile mass is passed into the vapor phase.

• Solution Method:

• Initialization:

• Run Calculation:

Results

• Part-1 Analysis of the given cyclone separator model by varying the diameter from 1`mu`to 5`mu`
• Part-1, Case-1

Residuals

• Particle Diameter: 1e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History

• Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)
• Separation Efficiency = 149/(226-31)=149/195=0.76410256
• Pressure drop

Pressure Drop = 33.71717-1.8814676= 31.8357024

Vertex Core region at 0.0047651 swirl factor

Vertex Core region at 0.025 swirl factor

Vertex Core region at 0.25 swirl factor

Animation

Pressure Contours

Velocity Contours

Mass flow rate calculation

• Part-1, Case-2

• Particle Diameter: 2e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 169/(226-24)=169/202=0.8366336

Pressure drop

Pressure Drop = 33.71717-1.8814676= 31.8357024

Core vortex region

Pressure contours Velocity contours

Mass flow rate

Animation

• Part-1, Case-3

• Particle Diameter: 3e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 185/(226-27)=185/199=0.92964824

Pressure drop

Pressure Drop = 33.71717-1.8814676= 31.8357024

Vortex Core region

Pressure contours Velocity contours

Mass flow rate

Animation

• Part-1, Case-4

• Particle Diameter: 4e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 212/(226-10)=212/216=0.98148148

Pressure drop

Pressure Drop = 33.71717-1.8814676= 31.8357024

Vortex core region

Pressure contours Velocity contours

Animation

Part-1, Case-5

• Particle Diameter: 5e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 184/(226-41)=184/185=0.99459

Pressure drop

Pressure Drop = 33.71717-1.8814676= 31.8357024

Vortex core region

Pressure contours Velocity contours

Mass Flow rate

Animation

Table:1 Separation Efficiency

Particle Diameter	Particle Velocity	Flow velocity	No of tracked	Escaped	Trapped	Incomplete	Separation efficiency
1`mu m`	3 m/s	3 m/s	226	46	149	31	0.76410256
2 `mu m`	3 m/s	3 m/s	226	33	169	24	0.8366336
3 `mu m`	3 m/s	3 m/s	226	14	185	27	0.92964824
4 `mu m`	3 m/s	3 m/s	226	4	212	10	0.98148148
5 `mu m`	3 m/s	3 m/s	226	1	184	41	0.99459

Table:2 Pressure Drop

Particle Diameter	Inlet pressure	Outlet pressure	Pressure drop
1 `mu m`	33.71717	1.8814676	31.8357024
2 `mu m	33.71717	1.8814676	31.8357024
3 `mu m	33.71717	1.8814676	31.8357024
4 `mu m	33.71717	1.8814676	31.8357024
5 `mu m	33.71717	1.8814676	31.8357024

• Part-II Analysis of the given cyclone separator model by varying the Velocity from 1`mu`to 5`mu`
• Part-1, Case-1

Residuals

• Particle Diameter: 5e-06
• Particle Velocity: 1 m/s
• Flow Velocity: 1 m/s
• Particle History

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 4/(226-221)=4/5=0.8

Pressure Drop

Pressure drop = Inlet_1-outlet_2=3.1786832-0.1840995=2.9945

Vortex Core region

Pressure contours Velocity contours

Mass Flow rate

Animation

• Part-II, Case-2

• Particle Diameter: 5e-06
• Particle Velocity: 2 m/s
• Flow Velocity: 2 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 5/(226-220)=5/6=0.8333

Pressure drop

Pressure drop = Inlet_1-Outlet_2= 14.626747-0.8155187= 13.8112283

Vortex core region

Pressure contours Velocity contours

Mass flow rate

Animation

• Part-II, Case-3

• Particle Diameter: 5e-06
• Particle Velocity: 3 m/s
• Flow Velocity: 3 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 184/(226-41)=184/185=0.9945945

Pressure drop

Pressure drop = inlet_1-Outlet_2=33.71717-1.8814676=31.835

Vortex core region

Pressure Velocity

Mass flow rate

Animation

• Part-II, Case-4
• Particle Diameter: 5e-06
• Particle Velocity: 4 m/s
• Flow Velocity: 4 m/s
• Particle History:

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 221/(226-3)=221/223=0.9910313

Pressure drop

Pressure drop = Inlet_1-Outlet_2= 61.150112-3.3707154= 57.779

Vortex core region

Pressure Velocity

Mass flow rate

Animation

• Part-II, Case-5
• Particle Diameter: 5e-06
• Particle Velocity: 5 m/s
• Flow Velocity: 5 m/s
• Particle History

Separation Efficiency = (no particle trapped particle)/(no of tracked particle- no of incomplete particle)

• Separation Efficiency = 183/(226-42)=183/184=0.99456521

Pressure drop

Pressure drop = Inlet_1-Outlet_2= 61.150112-3.3707154= 57.779

Vortex core region

Pressure Velocity

Mass flow rate

Table:3

Particle Diameter	Particle Velocity	Flow velocity	No of tracked	Escaped	Trapped	Incomplete	Separation efficiency
5`mu m`	1 m/s	1 m/s	226	1	4	221	0.8
5`mu m`	2 m/s	2 m/s	226	0	5	220	0.8333
5 `mu m`	3 m/s	3 m/s	226	1	184	41	0.9945945
5 `mu m`	4 m/s	4 m/s	226	2	221	3	0.9910313
5 `mu m`	5 m/s	5 m/s	226	1	183	42	0.99456521

Animation

Table:4 Pressure Drop

Particle Diameter	particle Velocity	Fluid velocity	Inlet pressure	Outlet pressure	Pressure drop
5 `mu m`	1 m/s	1 m/s	3.1786832	0.1840995	31.8357024
5 `mu m	2 m/s	2 m/s	14.626747	0.8155187	13.8112283
5`mu m	3 m/s	3 m/s	33.71717	1.8814676	31.835
5 `mu m	4 m/s	4 m/s	61.150112	3.3707164	57.779
5 `mu m	5 m/s	5 m/s	33.71717	1.8814676	57.779

Conclusions

• In this challenge we have analyzed the cyclone separator efficiency by varying the diameter and velocity.
• As we increased the diameter and velocity, it increase the cyclone efficiency.
• Velocity has a great impact as compared to the diameter variation.
• Pressure is also depend on the velocity change.
• For constant velocity, with varying the diameter sizes pressure drop remains same.
• Increases velocity causes a high pressure drop.