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]

Boundary Conditions:-

Inlet and wall:- Reflect

Outlet(Top):- Escape

Outlet(Bottom/dustbin) - Trap

In this project we have performed two parts :-

# part - 1 -velocity -3m/s- 1microns.

# velocity - 3m/s - 3microns

# velocity - 3m/s - 5microns.

# In first part we have taken the velocity constant and different microns.

# part-2- velocity -1- 5microns

# velocity -3-5microns.

# velocity -5- 5microns.

# In part-2 velocity changes and microns will constant.

1. FOUR EMRICAL MODELS:-

1. Lapple :-

Lapple [1] 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 [1] to calculate a 50% cut diameter, dpcdpc, is

dpc=[9μb2πNevi(ρp−ρg)]12dpc=[9μb2πNevi(ρp-ρg)]12

Where NeNe is the number of revolutions

Ne=1α[h+H−h2]Ne=1α[h+H-h2]

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

ηi=11+(dpc¯dπ)2ηi=11+(dpcd¯π)2

2. Koch and Licht :-

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: uRn=uRn=constant.

A force balance and an equation on the particles collection yields the grade efficiency ηiηi

ηi=1−exp⎧⎨⎩−2[GτiQD3(n+1)]0.5n+1⎫⎬⎭ηi=1-exp{-2[GτiQD3(n+1)]0.5n+1}

where

G=8kck2aK2bG=8kcka2Kb2

n=1−{1−(12D)0.142.5}{T+460530}0.3n=1-{1-(12D)0.142.5}{T+460530}0.3

τi=ρpd2π18μτi=ρpdπ218μ

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

3. 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 are:

C=C0C0, at θθ=0

Dr∂c∂r=(1−α)ωcDr∂c∂r=(1-α)ωc, at r=D/2

• The tangential velocity is related to the radius of cyclone by: μRμR=constant.

The concentration distribution in a cyclone is given as:

c(r,θ)=c0(rω−rn)exp{−λ[1k(1+n)r1+n]}∫rωrnexp{[1k(1+n)r1+n}drc(r,θ)=c0(rω-rn)exp{-λ[1k(1+n)r1+n]}∫rnrωexp{[1k(1+n)r1+n}dr

C=C0C0, at θθ=0

Dr∂c∂r=(1−α)ωcDr∂c∂r=(1-α)ωc, at r=D/2

• The tangential velocity is related to the radius of cyclone by: μRμR=constant.

The concentration distribution in a cyclone is given as:

c(r,θ)=c0(rω−rn)exp{−λ[1k(1+n)r1+n]}∫rωrnexp{[1k(1+n)r1+n}drc(r,θ)=c0(rω-rn)exp{-λ[1k(1+n)r1+n]}∫rnrωexp{[1k(1+n)r1+n}dr

where

K=(1−n)(ρp−ρg)d2Q18μb(r1−nω−r1−nn)K=(1-n)(ρp-ρg)d2Q18μb(rω1-n-rn1-n)

and

λ=(1−α)KωωDrrnωλ=(1-α)KωωDrrωn

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

ηi=1−exp{−λθ1}ηi=1-exp{-λθ1}

where

θ1=2π(S+L)αθ1=2π(S+L)α

4. 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 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 efficiency ηiηi of particle diameter dpidpi can be calculated from

ηi=11+(dpcdpi)βηi=11+(dpcdpi)β

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

β=0.62−0.87ln(dpc100)+5.21ln(abD2)+1.05[ln(abD2)]2β=0.62-0.87ln(dpc100)+5.21ln(abD2)+1.05[ln(abD2)]2

and dpcdpc is the 50 % cut size.

2. PART-1

VELOCITY-3M/S- 1MICRON:-

1. GEOMETRY:- First we have import the geometry and select the volume extraction of each edges.

MESH:- in meshig we have used all triangualr method and given the named selection - inlet, outlet-1, outlet-2.

set-up:-

case-2 3m/s and 3 microns:-

case-3 velocity -3m/s and 5microns

PART-2:-

1M/S AND 5 MICRONS

CASE-2 3M/S 5 MICRONS

5M/S AND 5MICRONS

REPORTS;-

1. VELOCITY-3M/S - 1MICRON:-

NO Of tracked = 91

Trapped = 14

escaped = 40

incomplete = 37

# seperator efficiency = no of trapped/ no of tracked = 14/91 = 15.38%

# pressure drop = inlet - outlet = 30291.843-(-103.57917)

= 30.291+0.10357

= 30.39

2. velocity - 3m/s - 3 microns

= 54/91 = 59.3%

pressure drop = inlet-outlet = 2.54+0.946 = 3.48

3. velocity - 3m/s - 5microns

= trapped = 54

= tracked = 91

seperator effincy = 54/91 = 62.3%

# pressure drop = inlet-outlet = 8.7+0.0144

= 8.71

part-2 report:-

1. velocity -1m/s and 5 microns

number tracked = 91

escaped = 3

incomplete = 88

= inlet-outlet = 9.60

2. velocity - 3m/s

velocity - 3m/s - 5microns

= trapped = 54

= tracked = 91

seperator effincy = 54/91 = 62.3%

# pressure drop = inlet-outlet = 8.7+0.0144

= 8.71

3. velocity - 5m/s and 5 mic

tracked = 91

trapped = 12

incomplete = 79

=seperator efficiency = 12/91 = 13.18%

conclusions:-

# In this case we have performed the two cases

# case_1 constant velocities and different microns

# case_1 two cases results are betteer

# case_2 constant microns and different velocity

# some outputs are not given perfect results.

# especially vortex core region

# velocity 3m/s is better result 1micron and 3 micron.