Cyclone Separator Challenge
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 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.]
- 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 Seperator
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.
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 sizes can range from a relatively small 1.2-1.5 meters tall (about 4-5 feet) to around 9 meters (30 feet)—which is about as tall as a three story 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.
Effectiveness:
Cyclone separators are generally able to remove somewhere between 50-99% of all particulate matter in flue gas. How well the cyclone separators are actually able to remove this matter depends largely on particle size. If there is a large amount of lighter particulate matter, less of these par0ticles are able to be separated out. Because of this, cyclone separators work best on flue gases that contain large amounts of big particulate matter.
There are several advantages and disadvantages in using cyclone separators. First, cyclone separators are beneficial because they are not expensive to install or maintain, and they have no moving parts. This keeps maintenance and operating costs low. Second, the removed particulate matter is collected when dry, which makes it easier to dispose of. Finally, these units take up very little space. Although effective, there are also disadvantages in using cyclone separators. Mainly because the standard models are not able to collect particulate matter that is smaller than 10 micrometers effectively and the machines are unable to handle sticky or tacky materials well.
Empirical models used for cyclone seperator efficiency:
1. IOZIA AND LEITH MODEL:
lozia and Leith (1990) logistic model N 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 form 2, and flow resistance, W. Core length, zc, and core diameter dc, 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<B'
`d_c = 0.47((ab)/D^2)^-0.25 (D_e/D)^1.4`
The addition made by lozia and Leith on the original Barth (1956) model is the core length zc and slope parameter `beta` expression which is derived based on the statistical analysis of experimental data of cyclone with D= 0.25 m, The collection efficiency `eta_i` of particle diameter dpi can be calculated from
`eta_i = 1/(1+(d_(pc)/(overlined_("pi")))^beta`
where `d_(pc)` is the 50% cut given by Barth (1956)
`d_(pc) = [(9muQ)/(piP_pz_cV_max^2)]^0.5`
2. Li AND WANG MODEL:
The Li and Wang (1989) model include particle bounce or re-entrainment and turbulent diffusion X the cyclone wall.
A two-dimensional analytical expression of pardcle distribution in the cyclone is obtained, and Wang rnodel 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 Me considerXion of turbulent diffusion coefficient and panicle bounce re-entrainment on the cyclone wall arc
`c=c_0` at `theta = 0`
`D_r(del_c)/(del_r) = (1-alpha)_(wc) 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^2Q)/(18mub(r_w^(1-n) - r_n^(1-n)) and lambda = ((1-alpha)kW_w)/(D_r r_w^n`
The resultant expression of the collection efficiency for a `theta_1 = 2π (S + L) / a` paticle of our size is given as:
`eta_i = 1 - exp {-lambda theta_1}`
where `theta_1 = 2π (S + L) / a`
3. KOCH AND LICHT MODEL :
Koch and Licht (1977) collection theory recognized the 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 particle collection yields the grade efficiency `eta_i`
`eta_i = 1-exp{-2[(Gtau_iQ)/D^3 (n+1)]^(0.5/(n+1))}`
where
`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_"pi"^2)/(18mu)`
G is a factor related to the configuration of the cyclone, n is related to the vortex and `tau_i`is the relaxation term
4. 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 50% cut diameter , `d_(pc)` is
`d_(pc) = [(9mub)/(2piN_iv_i(rho_p-rho_g))]^(1/2)`
Where `N_e` is the number of revolutions
`N_e = 1/a [h+(H-h)/2]`
The efficiency of collection of an average size of the particle is given by
`eta_i = 1/(1+(d_(pc)/overlined_"pi")^2`
ANALYSIS:
The analysis of cyclone seperator is performed in two parts:
- Keeping velocity constant and changing diameter of particle
- Keeping diameter constant and changing velocity
Model:
Extracted fluid volume:
Meshing:
Element size of 3.49 mm is given with cut-cell approach to capture geometry more accurately
Element quality:
Name selection:
One inlet and Two outlets . Top outlet is for lighter air while Bottom outlet is for heavier air.
Model setup:
- Solver : Pressure based
- Steady state
- With gravity enable along negative y direction
- Viscous model: K epsillon > RNG > Swirl dominated flow > Scalable wall functions
Discrete Phase Modelling(DPM):
Discrete Phase Modelling (DPM) is a method in which the flow of the discrete phase with a continuous flow is modeled. DPM is used to track individual particles through the continuum fluid. The Lagrangian discrete phase model follows Euler Lagrange approach. The fluid phase is treated as a continuum by solving the Navier Stokes equation while the dispersed phase is solved by tracking a large number of particle, bubble, or droplet through the calculated flow held. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.
In this case, solid particle size ranging from 1 `mum` to 10 `mum` being simulated as a discrete phase in a continuum.
- Enabled interaction with continuous phase-to enable coupled flow
- Enabled update DPM sources every flow iteration-Enabling this option gives chances to calculate particle source term at every iteration.
- Contour plots for DPM variables - unenabled -Allows cell averaged variable value.
- Tracking parameters - Max. No. of steps - 50000 - It is the no. of timesteps that is used to compute a single particle trajectory.
- Specify length scale- This option Is also used to control the timestep size
Injections:
- Injections type - Surface
- Release from surface - Inlet
- Material type - Anthracite
- x velocity(Particle velocity) - 3 m/s constant from Case 1
- Diameter varying from 1 to 10 micrometer
- Flow rate - 1e-20 kg/s
Boundary conditions:
- Inlet velocity - 3 m/s , DPM - Reflect
- Outlet Top pressure - 0 Pa , DPM - Escape
- Outlet Bottom pressure - 0 Pa , DPM - Trap
Solution method :
SIMPLE with Hybrid Initialisation
Solution:
Case 1(a): Fluid and Particle velocity = 3 m/s , Diameter = 1 micrometer
Particle tracking:
Separation efficiency- is defined as the fraction of particles of a given size collected in the cyclone, compared those of that size going into the cyclone. Experience shows that the separation efficiency of cyclone separator increases with increasing particle mean diameter and density increasing gas tangential velocity , decreasing cyclone diameter , increasing cyclone length , extraction of gas along with solids through the cyclone legs.
In this case, depending upon the particle history data Separation Efficiency is defined as the ratio of concentration that has been removed from the feed stream X the initial concentration in the feed stream. For this case ratio of the number of trapped particles to the total number of particles tracked.
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 206 / No. of particles tracked - 435
Seperation efficiency = 47.356%
Residual:
Solution is converged around 810 iterations
Anthracite particle time:
Velocity:
Pressure:
Vortex:
Animation of Particle tracking:
Case 1(b): Fluid and Particle velocity = 3 m/s , Diameter = 3 micrometer
Particle tracking:
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 258 / No. of particles tracked - 435
Seperation efficiency = 59.310%
Residual:
Solution is converged around 810 iterations
Anthracite particle time:
Velocity:
Pressure:
Vortex:
Animation of Particle tracking:
Case 1(c): Fluid and Particle velocity = 3 m/s , Diameter = 5 micrometer
Particle tracking:
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 325 / No. of particles tracked - 435
Seperation efficiency = 74.712%
Residual:
Solution is converged around 840 iterations
Anthracite particle time:
Velocity:
Pressure:
Vortex:
Animation of Particle tracking:
Case 2(a): Diameter = 5 micrometer , Fluid and Particle velocity = 1 m/s ,
Particle tracking:
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 117 / No. of particles tracked - 435
Seperation efficiency = 26.896%
Residual:
Solution is converged around 825 iterations
Anthracite particle time:
Velocity:
Pressure:
Pressure in and out:
Pressure inlet = 1.771 Pa and Pressure outlet at top = 0.180 Pa
Pressure drop = Press inlet - Press outlet = 1.771 - 0.180 = 1.591 Pa
Vortex:
Animation of Particle tracking:
Case 2(b): Diameter = 5 micrometer , Fluid and Particle velocity = 4 m/s ,
Particle tracking:
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 372 / No. of particles tracked - 435
Seperation efficiency = 85.517%
Residual:
Solution is converged around 840 iterations
Anthracite particle time:
Velocity:
Pressure:
Pressure in and out:
Pressure inlet = 33.490 Pa and Pressure outlet at top = 3.712 Pa
Pressure drop = Press inlet - Press outlet = 33.490 - 3.712 = 29.778 Pa
Vortex:
Animation of Particle tracking:
Case 2(c): Diameter = 5 micrometer , Fluid and Particle velocity = 5 m/s ,
Particle tracking:
Seperation efficiency = No. of particles trapped / No. of particles tracked
Seperation efficiency = No. of particles trapped - 406 / No. of particles tracked - 435
Seperation efficiency = 93.333%
Residual:
Solution is converged around 850 iterations
Anthracite particle time:
Velocity:
Pressure:
Pressure in and out:
Pressure inlet = 53.407 Pa and Pressure outlet at top = 5.972 Pa
Pressure drop = Press inlet - Press outlet = 53.407 - 5.972 = 47.435 Pa
Vortex:
Animation of Particle tracking:
Comparision table for case 1:
| Velocity m/s | Diameter in `mum` | Tracked particle | Escaped particle | Trapped particle | Pressure inlet Pa | Pressure Outlet Top Pa | Mass flow rate kg/s | Seperation Efficiency % |
| 3 | 1 | 435 |
221 |
206 | 18.258 | 2.003 | 0.01837 | 47.356 |
| 3 | 3 | 435 | 177 | 258 | 18.258 | 2.003 | 0.01837 | 59.31 |
| 3 | 5 | 435 | 110 | 325 | 18.258 | 2.003 | 0.01837 | 74.712 |
Comparision table for case 2:
| Diameter in `mum` | Velocity m/s | Tracked particle | Escaped particle | Trapped particle | Pressure inlet Pa | Pressure Outlet Top Pa | Pressure drop Pa | Mass flow rate kg/s | Seperation Efficiency % |
| 5 | 1 | 435 |
213 |
117 | 1.771 | 0.180 | 1.591 | 0.0061 | 26.896 |
| 5 | 4 | 435 | 63 | 372 | 33.490 | 3.712 | 29.778 | 0.0244 | 85.517 |
| 5 | 5 | 435 | 29 | 406 | 53.407 | 5.972 | 47.435 | 0.0306 | 93.333 |
Conclusion:
Comparing table 1 ,
- We can see that Pressure at inlet and outlet remains constant
- Also mass flow rate in case 1 remains constant as velocity is constant for all the three cases in table 1
- With increase in particle diameter , Number of trapped particles increases as a result Seperation efficiency increases.
Comparing table 2 ,
- We can see that Pressure at inlet and outlet increases with increase in velocity as a result pressure drop also increases
- Mass flow rate in case 2 increases with increase in velocity
- With increase in velocity and constant diameter , Number of trapped particles increases as a result Seperation efficiency increases.
- The efficiency of Cyclone seperator is related to pressure drop across the seperator. This is indirect measure of the energy required to move the gas through the system