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:-

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]

Introduction:- Cyclone separators are separation devices 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.

It is important to note that cyclones can vary drastically in their size. The size of the cyclone depends largely on how much flue gas must be filtered, thus larger operations tend to need larger cyclones. For example, several different models of one cyclone type can exist, and the size can range from a relatively small 1.2-1.5 meters tall to around 9 meters which is about as tall as a three storey building

Working

Cyclone separators work much like a centrifuge, but with a continuous feed of dirty air. In a cyclone separator, dirty flue gas is fed into a chamber. The inside of the chamber creates a spiral vortex, similar to a tornado. This spiral formation and the separation is shown in Figure 2. The lighter components of this gas have less inertia, so it is easier for them to be influenced by the vortex and travel up it. Contrarily, larger components of particulate matter have more inertia and are not as easily influenced by the vortex

Since these larger particles have difficulty following the high-speed spiral motion of the gas and the vortex, the particles hit the inside walls of the container and drop down into a collection hopper. These chambers are shaped like an upside-down cone to promote the collection of these particles at the bottom of the container. The cleaned flue gas escapes out the top of the chamber.

Most cyclones are built to control and remove particulate matter that is larger than 10 micrometers in diameter. However, there do exist high efficiency cyclones that are designed to be effective on particles as small as 2.5 micrometers. As well, these separators are not effective on extremely large particulate matter. For particulates around 200 micrometers in size, gravity settling chambers or momentum separators are a better option.

Out of all of the particulate-control devices, cyclone separators are among the least expensive. They are often used as a pre-treatment before the flue gas enters more effective pollution control devices. Therefore, cyclone separators can be seen as "rough separators" before the flue gas reaches the fine filtration stages.

Empirical models used to calculate the cyclone separator efficiency

IOZIA AND LEITH MODEL

Iozia and Leith (1990) logistic model is a modified version of Barth (1956) 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. Core length, `z_c` , and core diameter, `d_c` , 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

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

The addition made by Iozia and Leith on the original Barth (1956) model are the core length `z_c` and slope parameter β expression which is derived based on the statistical analysis of experimental data of cyclone with D = 0.25 m. The collection efficiency `η_i` of particle diameter `d_(pi)` can be calculated from

`eta_i = 1/(1+(d_(pc)/bard_(pi))^beta`

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

`d_(pc) = [(9*mu*Q)/(pi*p_p*z_c* v_max^2]^0.5]`

LI AND WANG MODEL

The Li and Wang (1989) model includes particle bounce or re-entrainment 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 cyclones.
• Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are:

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

`D_r*(delc)/(delr) = (1-alpha)*omega*c`, at `r = D/2`

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

The concentration distribution in a cyclone is given as:

`c(r,theta) = (c_0(r_w-r_n)*exp{-lambda*[1/(K*(1+n))*r^(1+n)]})/(int_(r_n)^(r_w) exp{1/(K*(1+n))*r^(1+n)}dr`

where

`k = ((1-n)*(rho_p-rho_g)*d^2*Q)/(18*mu*b*(r_w^(1-n)-r_n^(1-n))`

and

`lambda = ((1-alpha)*k*w_w)/(D_r*r_w^n)`

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

`eta_i = 1-exp{-lambda*theta_1}`

where,

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

KOCH AND LICHT MODEL

Koch and Licht (1977) collection theory recognized the inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone. Koch and Licht describe 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 `η_i` .

`eta_i = 1 – exp{-2*[(G*tau_i*Q)/D^3 *(n+1)]^(0.5/(n+1))}`

where

`G = (8*k_c)/(k_a^2*k_b^2)`

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

`tau_i = (rho_p*d_(p*i)^2)/(18*mu)`

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

LAPPLE MODEL

Lapple (1951) 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 (1951) to calculate a 50% cut diameter, `d_(pc)`, is

`d_(pc) = [(9*mu*b)/(2*pi*N_e*v_i*(rho_p-rho_g))]^0.2`

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

`eta_i = 1/(1+(d_(pc)/bard_(pi))^2`

Procedure:-

Geometry

Importing the geometry in SpaceClaim

After importing the geometry, now extracting the fluid volume as the simulation will be carried out on the volume part.

Meshing

Meshing is done with an element size of 8mm

Setup

Solver Type: Steady

Enabling the gravity in negative y-direction

Viscous model- k-epsilon RNG model with Scalable Wall Functions

RNG option – Swirl Dominated Flow

Boundary Conditions:-

Inlet and wall:- Reflect

Outlet(Top):- Escape

Outlet(Bottom/dustbin) - Trap

Discrete Phase modelling will be performed to track the flow of the particles

Number of step for particle tracking = 50000

Injection material : Anthracite

Particle type: Inert

Diameter of particle: 5 microns (5*10^-6)

Inlet velocity : 3 m/s

Injection type: Surface (will be normal to the surface of injection i.e Inlet)

Initializing the problem with standard Initialization and running it for about 500 iteration

Results:-

Case 1: Varying the particle diameter from 1 μm to 5 μm and calculate the separation efficiency in each case. Both velocities will be 3m/s

The solution gets converged in about 209 iterations for all the cases below

Particle diameter:- 1 μm

Particle diameter:- 2 μm

Particle diameter:- 3 μm

Particle diameter:- 4 μm

Particle diameter:- 5 μm

Particle Diameter(μm)	Velocity(m/s)	Efficiency(%)
1	3	70.93
2	3	79.069
3	3	94.186
4	3	100
5	3	100

Case 2: Varying the particle velocity from 1 m/sec to 5 m/sec and calculating the separation efficiency and pressure drop in each case. Particle diameter size is 5 μm

Below is the plot of Efficiency, Solution convergence, Residual and Pressure respectively

Velocity: 1m/s

Velocity: 2m/s

Velocity: 3m/s

Velocity: 4m/s

Velocity: 5m/s

Velocity(m/s)	Iterations	Efficiency(%)	Pressure (Pa)
			Inlet	Outlet above	Outlet below
1	177	85.46	2.3647	-0.00054	-2.558*10^-5
2	202	100	10.492	-0.00402	-0.001
3	209	100	24.59	-0.01071	-0.00492
4	213	100	44.730	-0.02015	-0.0102
5	216	100	71.017	-0.0348	-0.016

Conclusion:-

• The efficiency of separation depends on both diameter and velocity of particles
• For a larger diameter of particle if the velocity is increased then its separation efficiency increases
• As velocity increases the pressure drop also increases
• As seen in case 1 the efficiency decreases when particle diameter decreases for a given velocity
• And in case 2 the efficiency decreases when velocity is decreased for a particular given diameter of particle