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Separation efficiency and pressure drop in a cyclone separator

Aim: To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop. Theory: Cyclone separators are separation devices that remove particulate matter from flue gases by using the principle of inertia. Cyclone separators are one of many air pollution control devices…

Shaloy Elshan Lewis
updated on 17 Dec 2020

Aim:

To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop.

Theory:

Cyclone separators are separation devices that remove particulate matter from flue gases by using the principle of inertia. Cyclone separators are one of many air pollution control devices known as pre-cleaners 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 multi-cyclone.

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. 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.

Some empirical models used to calculate the cyclone separator efficiency are:

1. Iozia and Leith Model:

Iozia and Leith logistic Model is a modified version of the 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 flow resistance, W.

The collection efficiency _i of particle diameter d_pi can be calculated by

$η_{i} = \frac{1}{1 + {(\frac{d_{p c}}{d_{p i}})}^{β}}$ $eta_i=frac{1}{1+(d_(pc)/d_(p i))^beta}$

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

$β = 0.62 - 0.87 \ln (\frac{d_{p c}}{100}) + 5.21 \ln (\frac{a b}{D^{2}}) + 1.05 {[\ln (\frac{a b}{D^{2}})]}^{2}$ $beta= 0.62-0.87ln (frac{d_(pc)}{100})+5.21 ln (frac{ab}{D^2})+1.05 [ln (frac{ab}{D^2})]^2$

$d_{p c}$ $d_(pc)$ is the 50% cut size given by Barth

$d_{p c} = {[\frac{9 μ Q}{π ρ_{p} Z_{c} {(v_{t max})}^{2}}]}^{0.5}$ $d_(pc)=[frac{9muQ}{pi rho_p Z_c (v_(tmax))^2}]^0.5$

`here core length $Z_{c}$ $Z_c$ and core diameter $d_{c}$ $d_c$ given as

$Z_{c} = (H - S) - [\frac{H - S}{(\frac{D}{B}) - 1}] [(\frac{d_{c}}{B}) - 1], d_{c} > B$ $Z_c = (H-S)-[frac{H-S}{(D/B)-1}][(d_c/B)-1], d_c>B$

$d_{c} = 0.47 D {(\frac{a b}{D^{2}})}^{- 0.25} {(\frac{D_{e}}{D})}^{1.4}$ $d_c=0.47D(frac{ab}{D^2})^(-0.25) (frac{D_e}{D})^1.4$

2. Li and Wang Model:

The Li and Wang model include 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:

$c = c_{o}, if θ = 0$ $c = c_o, if theta=0$

$D_{r} \frac{\partial c}{\partial r} = (1 - α) w c, a t, r = \frac{D}{2}$ $D_rfrac{delc}{delr) = (1-alpha)wc, at,r=D/2$

The tangential velocity is related to the radius of cyclone by: $μ R^{n} = c o n s \tan t$ $muR^n=constant$

$c (r, θ) = \frac{c_{0} (r_{w} - r_{n}) \exp {- λ [\frac{1}{K (1 + n)} r^{1 + n}]}}{\int_{r_{n}}^{r_{w}} \exp {\frac{1}{K (1 + n)} r^{1 + n}} d r}$ $c(r,theta)=frac{c_0(r_w-r_n)exp{-lamda[frac{1}{K(1+n)}r^(1+n)]}}{int_(r_n)^(r_w)exp{frac{1}{K(1+n)}r^(1+n)}dr$

Where

$K = \frac{(1 - n) (ρ_{p} - ρ_{g}) d^{2} Q}{18 μ b (r_{w}^{1 - n} - r_{n}^{1 - n})}$ $K= frac{(1-n)(rho_p-rho_g)d^2Q}{18mub(r_w^(1-n)-r_n^(1-n))}$

and

$λ = \frac{(1 - α) K w_{w}}{D_{r} r_{w}^{n}}$ $lamda=frac{(1-alpha)Kw_w}{D_rr_w^n}$

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

$η_{i} = 1 - \exp {- λ θ_{1}}$ $eta_i=1-exp{-lamdatheta_1}$

where

$θ_{1} = 2 π \frac{S + L}{a}$ $theta_1=2pi(S+L)/a$

3. 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.

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 uRⁿ =constant.

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

η_{i} = 1 - \exp {- 2 {[\frac{G τ_{i} Q}{D^{3}} (n + 1)]}^{\frac{0.5}{n + 1}}}

$eta_i=1-exp{-2[frac{Gtau_iQ}{D^3}(n+1)]^(0.5/(n+1)}}$

Where,

G = \frac{8 K_{c}}{K_{a}^{2} K_{b}^{2}}

$G=frac{8K_c}{K_a^2K_b^2}$

n = 1 - {1 - \frac{{(12 D)}^{0.14}}{2.5}} {\frac{(T + 460)}{530}}^{0.3}

$n=1-{1-frac{(12D)^(0.14)}{2.5}}{frac{(T+460)}{530}}^0.3$

τ_{i} = \frac{ρ_{p} d_{p i}^{2}}{18 μ}

$tau_i=frac{rho_pd_(p i)^2}{18mu}$

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

4. 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 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 to calculate a 50% cut diameter, d_pc, is

$d_{p c} = {[\frac{9 μ b}{2 π N_{e} v_{i} (ρ_{p} - ρ_{g})}]}^{\frac{1}{2}}$ $d_(pc)=[frac{9mub}{2pi N_ev_i(rho_p-rho_g)}]^(1/2)$

where $N_{e}$ $N_e$ is the number of revolutions

$N_{e} = \frac{1}{a} [h + \frac{H - h}{2}]$ $N_e =frac{1}{a}[h+frac{H-h}{2}]$

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

$η_{i} = \frac{1}{1 + {(\frac{d_{p c}}{d_{p i}})}^{2}}$ $eta_i=frac{1}{1+(d_(pc)/d_(p i))^2$

Geometry and mesh:

The cyclone separator efficiency consists of one inlet in the tangential direction through with the flue gas is fed, and 2 outlets, one at the top and the other at the bottom. The outlet at the top is to allow the smaller particles to escape from the domain, and the bottom outlet is to trap the larger particles.

Since we are stimulating the separation efficiency of the cyclone separator, the fluid volume is extracted, and the solid geometry suppressed. Once the resultant mesh is generated, a total of 66722 nodes and 64227 mesh elements were generated.

Structural mesh gives the best results, hence the cutcell meshing approach is used to mesh the resultant fluid geometry, which is available in Ansys Meshing.

The majority of the mesh elements have mesh element quality of greater than 80%, so it is suitable to perform simulations using the resultant mesh.

Setup:

1. All the test cases for the cyclone separator were solved using the steady-state equations. Acceleration due to gravity in the negative y-direction is 9.81m/s^2.

2. The simulations were solved using the K-epsilon, RNG, swirl dominated flow turbulence model

3. To introduce particles into the flow, the discrete phase model (DPM) is enabled. The interaction with the continuous phase is enabled. The DPM is updated after every 10 iterations, and a particle is tracked for a maximum of 50000 steps. An injection is created, of material anthracite, which is injected from the inlet of the cyclone separator, with the particle velocity being the same as the flow velocity. The particle diameter is specified as per the simulation case.

4. Next boundary conditions are given to different parts of the cyclone separator. The outlets are provided with pressure boundary conditions, with the gauge pressure being zero. The inlet is provided with the velocity inlet boundary condition with the velocity being set as per the simulation case. And the walls were provided with the no-slip wall boundary condition.

5. The DPM boundary condition for inlet and wall is 'reflect', for the bottom outlet is 'trap', and for the top outlet is 'escape'.

6. 'Second-order upwind' condition was set for the turbulent kinetic energy and turbulent dissipation ratio. This increases the accuracy of the obtained solution.

7. The area-weighted average of static pressure is calculated at the inlet.

8. The problem was initialized using 'standard initialization', and it is computed from the inlet. The problem is allowed to be solved for a certain number of iterations, and the particle history data is exported so that the results may be post-processed.

9. In the post-processor, particle history data is imported and is colored with velocity magnitude and pressure. Also, the animation of the particle path is simulated.

Results:

The simulations were run for two cases:

1. Case1

To perform an analysis on a given cyclone separator model by varying the particle diameter from 1-5 $μm$ and calculate the separation efficiency in each case with the fluid and particle velocity of 3m/s.

2. Case2

To perform an analysis on a given cyclone separator model by varying the particle and fluid velocity from $1 to$ $5m/s$ and calculate the separation efficiency in each case with the particle diameter of 5 $μm.$

Case1: fluid and particle velocity= 3m/s

1. Particle diameter= 1 $μm$

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{35}{98} \cdot 100 = 35.71 %$ $eta=35/98*100=35.71%$

Pressure contours

Velocity contours

2. Particle diameter= 3 $μm$

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{75}{98} \cdot 100 = 76.53 %$ $eta=75/98*100=76.53%$

Pressure contours

Velocity contours

3. Particle diameter= 5 $μm$

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{97}{98} \cdot 100 = 98.97 %$ $eta=97/98*100=98.97%$

Pressure contours

Velocity contours

Observations from the case1:

Particle diameter (1e-6m)	The pressure at the inlet	Particles tracked	Particles escaped	particles trapped	Path of particles incomplete	Separation efficiency (%)
1	28.4056	98	38	35	25	35.71
3	28.4056	98	23	75	0	76.53
5	28.4056	98	1	97	0	98.97

Case2: Particle diameter= 5 $μm$

1. Fluid and particle velocity= 1m/s

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{8}{98} \cdot 100 = 8.16 %$ $eta=8/98*100=8.16%$

Pressure contours

Velocity contours

2. Fluid and particle velocity= 3m/s

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{97}{98} \cdot 100 = 98.97 %$ $eta=97/98*100=98.97%$

Pressure contours

Velocity contours

3. Fluid and particle velocity= 5m/s

$Residuals plot$

An area-weighted average of static pressure at the inlet

Particle track data

The cyclone separation efficiency is given by the ratio of the total number of particles trapped to the total number of particles tracked

$η = \frac{90}{98} \cdot 100 = 91.83 %$ $eta=90/98*100=91.83%$

Pressure contours

Velocity contours

Observations from the case2:

Particle velocity (m/s)	The pressure at the inlet (Pa)	Particles tracked	Particles escaped	Particles trapped	Path of particles incomplete	Separation efficiency (%)
1	2.5415	98	24	8	66	8.16
3	28.4056	98	1	97	0	98.97
5	83.5763	98	8	90	0	91.83

Conclusions:

The separation efficiency of a cyclone separator at a particular velocity increases with the increase in the particle diameter, because the larger the particle diameter, the higher is its inertia, hence the chances of it escaping from the top outlet of the cyclone separator are reduced.
The inlet pressure of the cyclone separator remains the same for a given inlet velocity and the inlet pressure increases with the increase in the inlet velocity.
For particles with smaller diameter, and for particles with lesser velocity, it is more likely the major portion of particles do not complete the path in the cyclone separator to either get trapped or escape. That is if the flow velocity is less or the particle diameter is small or both, it will take more time to perform the separation.
For a particular particle diameter, the separation efficiency is the highest for a particular(optimal) inlet velocity. If the inlet velocity is lower than this then it will take more time for separation or the particles may endlessly revolve in the domain. If the inlet velocity is increased beyond this value, then these particles may get influenced by the vortex generated and may escape from the top outlet, hence reducing its separation efficiency.