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Aim:- To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop. Objective:- To write a few words about any four empirical models used to calculate the cyclone separator efficiency. To perform an analysis on a given cyclone separator model by varying the particle…
Faizan Akhtar
updated on 25 May 2021
Aim:- To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.
Objective:-
Introduction
Cyclone separator: It is a device used for removing particulates from air, gas, or liquid stream, without the use of filters, through vortex separation. When removing particulate matter from the fluid a hydro cyclone is used, when removing particles from the gas a gas cyclone is used. Rotational effects and gravity are used to separate the mixture of solids and fluids.
Air is introduced into the cylinder exhibiting the vortex motion. The particulate matter having higher inertia do not follow the path prescribed by the air and thus hits the surface of the cyclone separator and falls at the bottom where it can be removed.
Application of cyclone separator
They are used in sawmills to remove sawdust from the extracted air. They are used in oil refineries to separate oils and gases, and in the cement industry as a component of kiln preheaters. They are also used as central vacuum cleaners in houses. They are also used in industrial and professional kitchen ventilation for separating the grease from the exhaust air in extraction hoods.
Empirical models used to calculate the cyclone separator efficiency
Cyclone Efficiency Empirical Models
IOZIA and LEITH model
The above model is the modified logistic model of Barth. The model assumes that the particle carried by the vortex endures the influence of two forces: a centrifugal force Z, and a flow resistance W, Core length,z, and core diameter, dc are given as
Equation 1(a)
for dc>B
zc=(H-S)-[H-S(DB)-1][(dcB)-1]
Equation 1(b)
for dc<B
zc=H-S
Equation 2
dc=0.47[abD2]-0.25∗[DeD]1.4
The addition made by the two scientists with respect to the Barth was core length zc and the slope parameter β. The collector efficiency on a particle diameter dpi for the cone diameter D=0.25m
Equation 3
ηi=11+(dpcd-pi)β
Equation 4
dpc is the 50% cut size given by Barth in 1956.
where dpc=[9μQπPpzcv2max]0.5
LI and WANG model
The above model includes particle bounce, re-entrainment, and turbulent diffusion at the cyclone wall. The model was developed on the following assumptions
Equation 5
c=c0, θ=0
Equation 6
Dr∂c∂r=(1-α)wc, at r=D2
The tangential velocity is related to the cyclone wall by uRn = constant.
The concentration distribution in a cyclone is given as
Equation 7
c(r,θ)=c0(rw-rn)exp{-λ[1K(1+n)r1+n]}∫rwrnexp{1K(1+n)r1+n}dr
Equation 8
where
k=(1-n)(ρp-ρg)d2Q18μb(r1-nw-r1-nn)
Equation 9
λ=(1-α)kwwDrrnw
The resultant expression of the collector efficiency of the particle is given as
Equation 10
η=1-exp{-λθ1}
Equation 11
where
θ1=2π(S+L)α
KOCH and LICHT model
The model recognized the inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone. The model is based on the following assumption
The grade efficiency of the particle is calculated as under
Equation 12
ηi=1-exp{-2[GτiQD3(n+1)]0.5n+1}
Equation 13
G=8kck2ak2b
Equation 14
n=1-{1-(12D)0.142.5}{T+460530}0.3
Equation 15
τi=ρpd2pi18μ
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 assumed that the particle entering the cyclone is evenly distributed across the inlet opening. The particle that travels 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, dpc, is
Equation 16
dpc=[9μb2πNevi(ρp-ρg)]12
Equation 17
where Ne is the number of revolutions
Ne=1a[h+H-h2]
Equation 18
The efficiency of the particle collection is given as
ηi=11+(dpcd-pi)2
Source: http://dspace.unimap.edu.my
Solving and Modeling approach
Preprocessing and Solver settings
The geometry is loaded into Spaceclaim
The fluid volume is extracted from the solid volume
The named selections are created for setting up the physics and the boundary condition
Inlet (Type Velocity inlet and Reflect)
Outlet_top (Type Pressure outlet and Escape)
Outlet_bottom (Type Pressure outlet and Trap)
Baseline mesh
Element size: 55.916mm
Mesh quality and attributes
Number of elements | Element quality | Aspect ratio | Skewness | Orthogonal quality |
20370 | 0.8201 | 1.9581 | 0.25021 | 0.74779 |
Refined mesh
Element size : 10mm
Mesh quality and attributes
Number of elements | Element quality | Aspect ratio | Skewness | Orthogonal quality |
112565 | 0.83691 | 1.8571 | 0.22862 | 0.76952 |
Element size: 9mm
Mesh quality and attributes
Number of elements | Element quality | Aspect ratio | Skewness | Orthogonal quality |
141918 | 0.83836 | 1.8508 | 0.22633 | 0.7718 |
Element size : 8mm
Mesh quality and attributes
Number of elements | Element quality | Aspect ratio | Skewness | Orthogonal quality |
185349 | 0.83779 | 1.8513 | 0.22746 | 0.77072 |
Set up
Turbulence model RNG k-ε
Setting up of boundary condition
Setting up of Discrete Phase Modelling
The discrete phase modelling consists of the dispersed phase and the fluid phase. The behaviour of the fluid phase (air) is being captured by the NS equation whereas the tracking of the dispersed phase (anthracite) is solved by tracking a large number of droplets, particles through the calculated flow field. The dispersed phase exchanges the momentum, mass flow rate, and energy within the fluid phase.
There are two types of coupling for the discrete phase modelling
The DPM is selected from the ribbon
The interaction with the continuous phase is selected as such it will be a coupled interaction the dispersed phase will transfer momentum to the fluid phase. The update DPM after every flow iteration is checked so that it calculates the source term of each particle so that the particles reaches their constant value, whereas the default values are retained for Max. number of steps, DPM iteration level, step length factor which is 50000 10 & 5 respectively. The particle size is varied accordingly to determine the efficiency of the cyclone separator.
The solution is standard initialized by hitting t=0 and the compute from inlet option is selected.
Case-1
Baseline mesh
Pressure-Velocity coupling schemes (SIMPLE)
Residual Plot
Inlet velocity 3msec-1
Area weighted average of pressure
Volume average of pressure
Pressure-Velocity coupling schemes (SIMPLEC)
Inlet velocity 3msec-1
Residual Plot
Area weighted average of pressure
Volume average of pressure
Pressure-Velocity coupling schemes (COUPLED)
Inlet velocity 3msec-1
Residual plot
Area weighted average of pressure
Volume average of pressure
Mesh | Element size | Number of elements | Pressure-velocity coupling scheme | Area weighted average of pressure (Pa) | Volume average of pressure (Pa) |
Baseline mesh | 55.916mm | 20370 | SIMPLE | 5.6146 | 4.4622 |
SIMPLEC | 5.4714 | 4.3152 | |||
COUPLED | 5.4741 | 4.3171 |
It can be inferred that the baseline mesh is run by using a particle size of 5e-6 m and the particle velocity having the value of 3 m/sec by using three different pressure-velocity coupling schemes (SIMPLE, SIMPLEC, COUPLED). It was observed that the most stable values of pressure were given by the COUPLED SCHEMES. It also takes less time for convergence because the pressure and velocity equations are solved instantaneously. It takes more space from segregated schemes (SIMPLE and SIMPLEC).The monitor plots for the COUPLED scheme took 100 iterations for convergence and after that it reaches to the steady-state, for the SIMPLEC scheme it took around 300 iterations for convergence and after that it reaches to the steady-state, for the SIMPLE scheme the graph is oscillating in nature.
For the COUPLED scheme, the gradient is selected as least square cell-based, pressure to the second-order scheme, momentum, turbulent kinetic energy, turbulent dissipation rate to second-order upwind. The least cell-based values are used to calculate the change in the value of the centroid of the two cells and offering comparable accuracy and is computationally less expensive to the node-based scheme. The second order scheme uses a central differencing scheme which is more accurate than standard and linear based schemes and is robust in the case of skewed schemes. Second-order upwind schemes make use of quantities at the cell face values to compute the cell centered solution of the at the cell centroid leading to a second order accurate solution.
Results
The particle size is varied from 1e-6m to 5e-6m keeping the velocity as 3msec-1 and accordingly cyclone separator efficiency is calculated for each case.
Case-2 Refined mesh
Element size: 10mm
Number of elements: 112565
Particle size: 1e-6m
Inlet velocity: 3msec-1
Residual Plot
Area weighted average of Pressure
Volume average of Pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Element size: 9mm
Number of elements: 141918
Particle size: 3e-6m
Inlet velocity: 3msec-1
Residual Plot
Area weighted average of Pressure
Volume average of Pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Element size: 8mm
Number of elements: 185349`
Particle size: 5e-6m
Inlet velocity: 3msec-1
Residual Plot
Area weighted average of Pressure
Volume average of Pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Comparison of all cases
Table-1
Mesh | Element size | Number of elements | Particle size |
Inlet velocity msec-1 |
Area weighted average of Pressure (Pa) | Volume average of Pressure (Pa) | Number of Particles tracked | Number of Particles trapped | Pressure drop (Pa) |
Cyclone Efficiency ηefficiency=NtrappedNtracked∗100 |
Refined mesh | 10mm | 112565 | 1e-6m | 3msec-1 | 11.8978 | 9.3656 | 124 | 31 | 18.3194 | 25% |
9mm | 141918 | 3e-6m | 12.6941 | 9.9649 | 142 | 125 | 19.4588 | 88.02% | ||
8mm | 185349 | 5e-6m | 13.5805 | 10.6312 | 172 | 165 | 20.706 | 95.93% |
Case-3
The velocity is varied from 1msec-1 to 5msec-1 keeping the particle size as 5e-6m, accordingly the cyclone separator efficiency is calculated.
Refined mesh
Element size: 10mm
Number of elements: 112565
Particle size: 5e-6m
Inlet velocity: 1msec-1
Residual Plot
Area weighted average of Pressure
Volume average of Pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Element size: 9mm
Number of elements: 141918
Particle size: 5e-6m
Inlet velocity: 3msec-1
Residual Plot
Area weighted average of Pressure
Volume average of Pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Element size: 8mm
Number of elements: 185349
Particle size: 5e-6m
Inlet velocity: 5msec-1
Residual Plot
Area weighted average of Pressure
Volume average of pressure
Static Pressure
Tangential Velocity
Radial Velocity
Axial Velocity
Anthracite Particle Time
Comparison of all cases
Table-2
Mesh | Element Size | Number of Elements | Particle size |
Inlet Velocity msec-1 |
Reynolds number Re=ρ∗v∗Dμ |
Area weighted average of Pressure (Pa) |
Volume average of Pressure (Pa) |
Pressure drop (Pa) |
Number of particles tracked
|
Number of particles trapped |
Cyclone efficiency ηefficiency=NtrappedNtracked∗100 |
Refined mesh | 10mm | 112565 | 5e-6m | 1 | 13691 | 1.037094 | 0.8208813 | 1.69251 | 124 | 11 | 8.87% |
9mm | 141918 | 3 | 41075 | 12.69416 | 9.964973 | 19.4588 | 142 | 142 | 100% | ||
8mm | 185349 | 5 | 68458 | 39.38731 | 30.77455 | 59.543 | 172 | 172 | 100% |
Cyclone separator efficiency for different particle diameter sizes and same input velocity 5msec-1.
Table-3
Mesh | Element Size | Number of Elements | Particle size |
Inlet Velocity msec-1 |
Reynolds number Re=ρ∗v∗Dμ |
Area weighted average of Pressure (Pa) |
Volume average of Pressure (Pa) |
Pressure drop (Pa) |
Number of particles tracked
|
Number of particles trapped |
Cyclone efficiency ηefficiency=NtrappedNtracked∗100 |
Refined mesh | 8mm | 185349 | 1e-6m | 5 | 68458 | 39.38731 | 30.77455 | 59.543 | 172 | 49 | 28.48% |
3e-6m | 39.38731 | 30.77455 | 172 | 169 | 98.25% | ||||||
5e-6m | 39.38731 | 30.77455 | 172 | 172 | 100% |
Conclusion
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