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$$\mu m$to $5$$\mu m$ 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 $\mu m\; for\; all\; cases\; \&\; keep\; flow\; velocity\; same\; as\; particle\; velocity$]

Empirical Models used to calculate the cyclone separator efficiency :-

1. Barth Model :

Barth proposed a simple model based on a force balance. This model enables to obtain the cut-size and the pressure drop values. The principle of calculation consists on the fact that a particle carried by the vortex endures the influence of two forces: a centrifugal force Z and a flow resistance W. They are expressed at the outlet radius Ri where the highest tangential velocity occurs:

`W = c underset(w)() pi/4 (dunderset(pc)() ^2)rho/2 (wunderset(r)())^2`...............(1)

`Z = pi/6 (dunderset(pc)())^3 (rho underset(p)() - rho)u^2/r`................(2)

`Cunderset(w)() = 24/Reunderset(p)() = (24mu)/(dunderset(pc)() wunderset(r)()(Runderset(i)())rho)` ...........(3)

the tangential velocity at `R underset(i)()` equals:

`wunderset(r)() (Runderset(i)()) = (Vunderset(0)())/(2 pi R underset(i)() (H-L))`  .........(4)

The radial velocity `u (Runderset(i)())` equals:

`u(R underset(i)()) = ( (Vunderset(0)())/(pi R underset(i)()^2))/((S underset(e)() )/S alpha/((R underset(alpha)())/ R underset(i)()) + lamda (h underset(eq)())/R underset(i)()`  .......(5)

where 

`h underset(eq)() = (S underset(sf"tot")())/ (2 pi sqrt((R underset(c)())/(R underset(i)()))`     ...........(5.1)

`alpha = 1 - (0.54 - 0.153/((S underset(e)())/S )) (b/ (R underset(c)()))^(1/3)`     ......(5.2)

`lamda = 0.05 + 287.4/(Re underset(w)())` .....(5.3)

`Re underset(w)() = ( D underset(c)(). rho)/ mu . (V underset(0)())/(ab (0.089 - 0.204 b/( R underset(c)()))`      ......(5.4)

`alpha` is a correction factor for contraction, expressed as a function of the inlet geometry (the equation presented shows the case of a rectangular tangential inlet) and `lamda`  a friction factor either equals to 0.02 or a function of the inlet geometry and the inlet flow rate

 

The pressure drop is resolved into two terms. The first term ζi reflects the contribution by inlet losses and friction losses. The second term ζe results from the flow losses through the outlet pipe.

`Delta P = (zeta underset(e)() + zeta underset(i)()) rho /2 w^2(R underset(i)())`       .........(6)

with: 

`zeta underset(e)() = (R underset(i)())/(R underset(c)()) ( 1/ ((1 - (u (R underset(i)()).h underset(eq)())/(w (R underset(i)()). R underset(i)() ))^2 )-1) ((u (R underset(i)()))/(w (R underset(i)())))^2`   ...........(6.1)

`zeta underset(i)() = f (2 +3 ((u (R underset(i)()))/(w (R underset(i)())))^(4/3) +((u (R underset(i)()))/(w (R underset(i)())))^2)`  ...............(6.2)

This model is relatively simple but it allows to obtain easily an approximation of the pressure drop and the cut diameter which are the two main parameters for an industrial approach.

 

2. Iozia and Leith Model :

Iozia and Leith (1990) logistic model is 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 force, Z, and a flow resistance, W. Core length, `z underset(c)()` , and core diameter, `d underset (c)()`, are given as

`z underset(c)() = ( H- S) - ((H-S)/((D/B) -1)) (((d underset(c)())/B )- 1)`             for `d underset(c)()` > B ............(7.1)

`z underset(c)() = H-S`  for `d underset(c)()`< B .......(7.2)

`d underset (c)() = 0.47 ((ab)/D ^2) ^(-0.25) ((D underset(e)())/D)^(1.4)`         ...............(8)

The addition made by Iozia and Leith on the original Barth (1956) model are the core length zc and slope parameter β expression which is derived based on the statistical analysis of experimental data of cyclone with D = 0.25 m. The collection efficiency ηi of particle diameter dpi can be calculated from

`eta underset(i)() = 1/ ( 1+ ((d underset(pc)())/(d underset(p i)()))^beta` ............(9)

where `d underset(pc)()` is the 50% cut size f=given by Barth (1956)

`d underset(pc)() = ((9 mu Q )/(pi punderset(p)() z underset(c)() nu underset(tmax)()^2))^0.5`................(10)

 

3. Li and Wang Model :

The Li and Wang (1989) model includes 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 underset(0)()` at `theta = 0` .......(11)
  `D underset(r)() (del c)/(del r) = (1 - alpha ) wc` ,  at `r = D/2` .....(12)
• The tangential velocity is related to the radius of cyclone by:
  `u R^n`= constant.

The concentration distribution in a cyclone is given as:

`c (r, theta) = (c underset(0)() ( r underset(w)() - r underset(n)()) exp ( - lamda ( 1/(K ( 1+n)) r^(1+n))))/( underset(r underset(n)())(int) overset(r underset(w)())() exp ( 1/ ( K (1+n))r^(1+n))dr`...............(13)

where 

`K = ((1-n)(rho underset(p)() - rho underset(g)())d^2 Q)/( 18 mu b ( r underset(w)() ^(1-n) - r underset(n)()^(1-n))` .............(14)

and

`lamda = ((1-alpha) k w underset(w)())/(D underset(r)() r underset(w)()^n)`         ..............(15)

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

`eta underset(i)() = 1 - exp (- lamda theta underset(1)())` .......(16)

where 

`theta underset(1)() = 2 pi (S+L )/ a` .........(17) 

 

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 a 50% cut diameter, `d underset(oc)()` , is

`d underset(pc)() = ( ( 9 mu b)/(2 pi N underset (e)() nu underset(i)() ( rho underset(p)() - rho underset(g)())))^(1/2)`   ............(18)

where `N underset(e)()` is the number of revolutions

`N underset(e)() = 1/a ( h + (H-h)/2)` .............(19)

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

`eta underset(i)() = 1/(1 +((d underset(pc)())/(bar (d underset(p i)())))^2`     .........(20)

 

Solving and Modeling Approch :-

1. Import the cyclone separator .STEP file into spaceclaim and prepare the required geometry using the volume extract tool. suppress the outer geometry that include the cyclone separator design and only keep the extracted fluid volume for the meshing 
2. Moving to meshing given appropiate named selection to the inlet and the two outlets at top and bottom
3. Generate the mesh with the global size of 10 mm. and check for the mesh qualtiy and the number of elements generated. Update this mesh to Fluent.
4. In fluent, set the solver to pressure based , time to steady and enable gravity(Y) = -9.81 .
5. the viscous model is set to K-epsilon RNG with swirl dominated flow and standard wall treatment. 
6. Enable Discrete Phase Modeling(DPM) with coupled interation between the phase. and update the DPM sources for every 10 iterations . For the tracking parameters set the maximum number of steps as 50000 and step length factor to 5 as they are the default values. Then add the injection of material anthracite that has properties similar to cement and given the velocity for this injection at the inlet and the diameter according to the simulation.
7. Now set the boundary conditions as:
   Inlet and Wall -  Reflect
   Outlet(top) - Escape
   Outlet(bottom) - Trap
8. Then initialise the soluiton using standard initialization form the inlet and run the calculation for about 600 iterations.
9. Finally see the results in the form of plot for the report definitions for the volume averaged presure and area weighted average pressure also we will post process the solution to see contour plots fo pressure and velocities, etc.

 

GEOMETRY:  

 To create the required geometry first load the .STEP file into the SpaceClaim.

Using the extract volume tool in the prepare tab select the edges as shown below 

click on the green check to extract volume .

Now suppress for physics the Cyclone Seperator from the structure and also uncheck the box before it  

 

The required geometry for meshing is ready

 

MESHING:

For Meshing we have used the structured mesh as it helps in obtaining better results in the Discrete Phase Modelling. 

We have used a global mesh size of 4 mm and added body fitted cartesian method to obtain structure mesh, also a face sizing was intriduced to get good inlet face mesh

 

the mesh has a good nuber of elements further reduction in the size may lead to limitaions for the acadamic liscence of ansys.

the body fitted cartesian method details are shown below

the face meshing was done on the inlet face and the details are shown below

now the generated mesh images are shown below

mesh near the inlet

mesh in the conical region

this mesh was used to perform the analysis of variation in the patricle velocity.

For the analysis of the variation of particel size we have used another mesh and the details for the same are given below.

here the mesh used is coarse and has a global sizing of 10 mm

here the number of elements is less but still while performing the simualtion good results were obtained

the details of the refinement are shown below

the gerenated mesh was as shown below

the element quality metrices show that the mesh is good and there are very few cell that have poor quality.

 

mesh near the inlet region

mesh near the conical region

now we will be usign the respective meshs for the analysis of varying particle velocity and partice size.

 

FLUENT Setup:

SETUP for the Analysis of particle velocity while keeping the size of particle as 5e-6 [m]. The analysis is performed for teh particle velocity of 1, 3 and 5 [m/s] .

now first add gravity in the general setting of -9.81 [m/s^2] and keep the slover as pressure based and time as steady

For the viscous we will be using the RNG K-epsilon model with swirl dominant flow

now to set up the Discrete Phase Model select the Discrete Phase tool in the model menu of the Physics tab and DPM Window will open up 

Now here check the box for the Interaction with continuous phase this will make the model couples with both the phases and also check the box for Udate DPM sources  every flow iterations and make sure the number of iterations is set to 10.

now select the injection button and give the injection according to the required particel velocity and partivel size here the image is shown for the particle velocity of 1[m/s] and the diameter of particle as 5e-6[m].

 

also make sure to select the injection type to surface and select the inlet for the injection.

set the solution method as the COUPLED scheme and keep the turbulent kinetic energy and turbutlent dissipation rate as second order upwind for both.

now initialse the solution from the inlet usign standard initialization and run the calculation for about 500 or 600 iteration until the residual reach a stable state.

 

RESULTS :

Analysis For Varying Particle Velocity:

1. Residuals:

velocity 1m/s

velocity 3 m/s

velocity 5m/s

2. Pressure Drop:

velocity 1m/s

velocity 3m/s

velocity 5m/s

Velocity	Pressrue at inlet	Pressure at outlet-top	Pressrue at outlet-bottom	Pressure drop
1 m/s	2.2203	-0.0006	-0.0004	2.2213
3 m/s	25.6226	-0.0197	-0.0111	25.7533
5 m/s	74.3905	-0.0677	-0.0434	74.5016

We can see the trend that as the velocity increases the pressure drop also increases

 

3. Separating Efficiency:

velocity 1m/s

velocity 3m/s

velocity 5m/s

Velocity	numbers tracked	Escaped	Traped	incomplete	Separating efficiency = trapped/number tracked
1m/s	378	109	8	261	0.0211
3m/s	378	77	242	59	0.6402
5m/s	378	70	305	3	0.8068

Here we can see the trend that as the velcoity is increasing the separating efficiency also increases ,

the more number of incomplete in the velocity 1m/s is beacuse it required more number of mesh elements but due to the limitation we can only get this results .

 

Analysis For Varying Particle Size:

1. Residuals:

Size = 1e-6 m

Size = 3e-6 m

Size = 5e-6 m

2. Pressure Drop:

Size = 1e-6 m

Size = 3e-6 m

SIze = 5e-6 m

 

Particel Size	Pressrue at inlet	Pressure at outlet-top	Pressrue at outlet-bottom	Pressure drop
1e-6 m	16.3956	-0.0006	0	19.3962
3e-6 m	18.3555	-0.0036	0	18.3591
5e-6 m	18.3555	-0.0036	0	18.3591

We can see as the particle size increase form 1 [um] to 3 [um] the ressure drop increases but for the size 3 and 5 [um] the pressure remains the same.

 

3. Separating Efficiency:

size = 1e-6 m

Size = 3e-6 m

Size = 5e-6 m

Velocity	numbers tracked	Escaped	Traped	incomplete	Separating efficiency = trapped/number tracked
1m/s	496	105	382	9	0.7702
3m/s	496	62	427	7	0.8609
5m/s	496	0	496	0	1.0000

Here we can see the trend that as the particle size is increasing the separating efficiency also increases

 

Conclusion -

1. As the Particle Size increases the separating efficiency of the cyclone separator increases.
2. As the particle size increases the Presure drop of the cyclone separator increases.
3. As the particle velocity increases the separating efficency of the cyclone separator increases.
4. As the particle velocity increases the pressure drop of the cyclone separator increases.
5. for better results smaller element size and high mesh quality is required which is beyond the limits of the adacamic version of the software so we have to stop our simulation here.

 

References -

Numerical study of gas–solid flow in a cyclone separator - ScienceDirect

(PDF) A CFD Study on the Prediction of Cyclone Collection Efficiency (researchgate.net)

S. Altmeyer et al. / Chemical Engineering and Processing 43 (2004) 511–522