Cyclone Seprator

The four efficiciency models used for the cyclone seprator are as follows:

A.Iozia and Leith Model.
1.This model is based on the force balancing and it is the modified form of the model given by the Barth.
2.The model makes the assumption that due to the formation of the vortex two forces act on the particle namely, centrifugal force (Z) and a flow resistance (W).
The efficiency η for the particle diameter (d`d_c`) can be given as

`η_i = 1 /(1 + (d_c/d_i )^β`


where,

β = expression for slope parameter given by.

`β = 0.62 - 0.87 ln(d_c/100) + 5.21 ln ((ab)/D^2) + 1.05[ln((ab)/D^2)]^2`

`d_c` = 50% Cut size given by Barth as follows.

`d_c = [(9 mu Q)/(pi rho_p z_c nu_(tmax)^2]`

`z_c` = core length

`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`

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

B.Li and Wang Model.

This model calculates the bounce and turbulent diffusion at the cylone wall to obtain the two dimensional analytical expression of particle distribution.

It makes following assumptions.

The radial particle velocity and the radial concentration profile are not constant for uncollected particles within the cyclone.

The tangential velocity is related to radius of the cylone which is given by.

`mu*R*n = Const.`

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

`η_i = 1 − exp{−λθ_1}`

`θ_1 = 2π.(S + L)/a`

`λ = (1 − α)(Kw_w )/(D_rr_w^n``K = ((1 − n)(ρ_p − ρ_g)d^2 Q)/ (18 µbr_w^1−n − r_n^(1−n))`

The boundary conditions are given as follows.
c = c0, at θ = 0.`D_r((∂c)/ (∂r)) = (1 − α)wc, r = D/2`.

C. 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.

The model is based on the 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.

u.Rn = constant.

The efficiency using force balance and the equation on the particle collection yields.

`η_i = 1 − exp {−2 [(Gτ_iQ)/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 = (rho_p.d_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.

D. 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 pening. 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 to calculate a 50% cut diameter.

`d_c = [(9µb)/(2 pi N_e v_i(rho_p - rho_g))]^(1/2)`

`Ne = (1/a)[ h + (H − h)/2 ]`

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

`η_i = 1 + (d_c/d_i )^2`

Here,

L natural length (m)
a cyclone inlet height (m)
b cyclone inlet width (m)
D cyclone body diameter (m)
D_e cyclone gas outlet diameter (m)
H cyclone height (m)
h cyclone cylinder height (m)
S cyclone gas outlet duct length (m)
B cyclone dust outlet diameter (m)
c0, c1 particle inlet and outlet concentration (kg/m3)
d_p particle diameter (m)
D_r radial turbulent diffusion coefficient
d_c cut particle diameter collected with 50% efficiency(m)
n cyclone vortex exponent (0.5 < n < 1)
Q volumetric gas flow rate (m3/s)
r radial dimension, rw = D/2 and rn = De/2(m)
R radius (m)
T absolute temperature (K)
w radial particle velocity (rad/s)
d_i diameter of particle in size range i(m)
g gravity acceleration (m/s2)
G cyclone configuration factor

Simulation Setup:

The analysis is performed for the following parameters.

The particle size is kept as 5 micrometer.

Mesh size is 10mm

Inlet velocity of air and particles is 3m/s.

Simulation was performed for the 4 different conditions using reflect, trap, Escape, wall-jet.

Number of Particles.

Particle Time.

Simulation using reflect condition and mesh sizing on input face is 12mm.

Number of Particles tracked

Particle Time.

Simulation using reflect condition and mesh sizing on input face is 5mm.

Meshing.

Number of Particles Tracked

Particle Time.

Simulation using reflect condition and mesh sizing on input face is 2mm.

Meshing.

Number of Particles Tracked

Particle Time.

Observations

DPM condition	Mesh Size on Inlet Face (mm)	Number of Particles Tracked	Max Particle Time (s)
Reflect	10	364	10.527
Trap	10	364	10.527
Escape	10	364	10.527
Wall-Jet	10	364	10.527
Reflect	12	229	11.723
Reflect	5	1297	15.255
Reflect	2	7916	14.478

1. No change in was observed using different boundary conditions such as trap, reflect, escape and wall jet boundary conditions.
2. Varying mesh size on inlet face, varies the number of particles injected.