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]

Cyclone Separator -

Cyclonic separation is a means of separating different liquid phases (different liquid densities), or, separating particles from a gas stream. Cyclone separators often form part of a pre-cleaning stage prior to a gas or liquid being discharged. This article focuses on the gas cyclone separator.

A cyclone separator has several colloquial names. These names include 'dust separator', 'dust collector', 'dust extractor', 'cyclone extractor' and 'cyclone separator'. Generally, smaller units are referred to as 'dust' separators or extractors, whilst large scale industrial separators are referred to as 'cyclone separators'.

Gas cyclone separators are grouped into two main categories, reverse-flow and axial-flow. In this project we use a reverse flow cyclone separator because this type of separator is the most common in use today.

Reverse flow cyclone separators are cone shaped. Gas enters the top of the separator body, flows downwards, then flows back upwards and is discharged.

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 are shown in the Figure below.

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.

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.

Efficiency –

Cyclone separators are generally able to remove somewhere between 50-99% of all particulate matter in the 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 particles 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 of 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.

Formulae’s Used –

Separation Efficiency –

`η_s=" Nos.of Particles Trapped " /" Nos.of Particles Tracked "`

Pressure Drop –

Pressure Drop = Inlet Pressure - Outlet Pressure

Four Empirical Models Used For Cyclone Separator Efficiency Calculation –

1.) lozia 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 `η_i` of particle diameter `d_(pI)` can be calculated from

`η_i=1/(1+(d_(pc)/d_(pI) )^β )`

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

`β=0.62-0.87ln⁡(d_(pc)/100)+5.21ln⁡((ab)/D^2 )+1.05[ln⁡((ab)/D^2 )]^2`

`d_(pI)` = Particle diameter.
`d_(pc)` = 50% cut size given by Barth.

2.) Li and Wang Model –

The Li and Wang 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 cyclone.
• Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are

`C=C_0,` at `θ=0`

`D_r*(∂C)/(∂r)=(1-α)ωc,` at `r=D/2`

The tangential velocity is related to the radius of cyclone by `uR^n=` constant.

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

`η_i=1-exp⁡{-λθ_1 }`

where,

`θ_1=2π ((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 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 a constant.

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

`η_i=1-exp⁡{-2[(Gτ_i Q)/D^3 (n+1)]^(0.5/(n+1)) }`

where,

`G=(8K_c)/(K_a^2 *K_b^2 )`

`η=1-{1-((12D)^0.14)/2.5} {(T+460)/530}^0.3`

`τ_i=(ρ_p d_(pI)^2)/(18μ)`

G is a factor related to the configuration of the cyclone, is related to the vortex and 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 efficiency. The semiempirical relationship developed by Lapple to calculate a cut diameter, `d_(pc)`, is

`d_(pc)=[(9μb)/(2πN_e v_i (ρ_p-ρ_g ) )]^(1/2)`

where `N_e` is the number of revolutions

`N_e=1/a [h+(H-h)/2]`

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

`η_i=1/(1+(d_(pc)/d_(pI) )^2 )`

CASE 1 - Varying the particle diameter from 1 μm to 5 μm while keeping both the velocities as 3m/s and also calculating the separation efficiency in each case -

Geometry -

We import the cyclone separator model into the SpaceClaim and extract the required volume for the analysis as shown below.

Cyclone separator model -

Edges Selected for Volume extraction -

Extracted Volume -

MESH -

As structural mesh gives the best results, we can use cutcell meshing approach available in Ansys Meshing to mesh our geometry. As the number of particles is the number of cells on the inlet face, we'll use the face sizing method to refine the inlet face as shown below.

Generated Mesh -

Now we can move on to the name selection. The inlets, outlet (top) and outlet(bottom) are named. The inlet is through which the particles enter the lighter impurities escape through the top, and the heavier impurities are trapped in the bottom.

Inlet -

Outlet (Top) -

Oulet (Bottam) -

In order to see if the mesh we have generated is accurate or not, we'll check a quantity known as orthogonal mesh quality which tells us about the quality of our mesh.

Element Quality -

SETUP -

Setting up the physics for analysis of cyclone separator in ANSYS fluent.

• For this case we are using pressure-based steady state solver.
• Gravity is turned on.
• Velocity formulation - Absolute

Model setup

• Viscous Model - k-epsilon (RNG) with swirl dominated flow.
• Discrete Phase Modeling (DPM)

Viscous Model -

Discrete Phase Modeling (DPM) -

Injection -

BOUNDARY CONDITIONS -

Inlet -

• Air is used as a inlet fluid
• Velocity =3 m/s
• DPM - Reflect

Outlet 1 (Top) -

• DPM - Reflect

Outlet 2 (Bottom) -

• DPM - Trap

1.1) Particle Size = 5μm

The first thing we'll do is set the particle size as 5μm in the injection-0 as shown below.

Now we can initialize the solution and run the analysis.

RESULT -

Residuals -

Particle Time -

Pressure -

Velocity -

Velocity Vortex Region - (swirling strength = 0.2010)

DPM particle results -

Separation Efficiency –

Efficiency = Number of particles Trapped / Number of particles Tracked.

Efficiency - 394/394 = 100%

1.2) Particle Size = 3μm

The first thing we'll do is set the particle size as 3μm in the injection-0 as shown below.

Now we can initialize the solution and run the analysis.

RESULT -

Residuals -

Particle Time -

Pressure -

Velocity -

Velocity Vortex Region - (swirling strength = 0.2010)

DPM particle results -

Separation Efficiency –

Efficiency = Number of particles Trapped / Number of particles Tracked.

Efficiency - 281/394 = 71.32%

1.3) Particle Size = 1μm

The first thing we'll do is set the particle size as 1μm in the injection-0 as shown below.

Now we can initialize the solution and run the analysis.

RESULT -

Residuals -

Particle Time -

Pressure -

Velocity -

Velocity Vortex Region - (swirling strength = 0.2010)

DPM particle results -

Separation Efficiency –

Efficiency = Number of particle Trapped / Number of particle Tracked.

Efficiency - 241/394 = 61.16%

CASE 2 - Varying both the particle and the flow velocity from 1 m/s to 5 m/s while keeping the particle diameter as 5 μm and also calculating the separation efficiency in each case -

Almost everything in this case is same as in the case 1 with the only difference is that this time we'll vary the both the velocities while keeping the particle diameter constant to 5 μm.

2.1) Particle and Flow Velocity = 1m/s

The first thing we'll do is set the particle and flow velocity as 1m/s in the injection-0 as shown below.

Now we can initialize the solution and run the analysis.

RESULT -

Residuals -

Particle Time -

Pressure -

Velocity -

Velocity Vortex Region - (swirling strength = 0.2010)

DPM particle results -

Separation Efficiency –

Efficiency = Number of particles Trapped / Number of particles Tracked.

Efficiency - 82/394 = 20.81%

2.2) Particle and Flow Velocity = 3m/s

This case is same as case 1.2 and hence we don't need to analyse this case again.

2.3) Particle and Flow Velocity = 5m/s

The first thing we'll do is set the particle and flow velocity as 5m/s in the injection-0 as shown below.

Now we can initialize the solution and run the analysis.

RESULT -

Residuals -

Particle Time -

Pressure -

Velocity -

Velocity Vortex Region - (swirling strength = 0.2010)

DPM particle results -

Separation Efficiency –

Efficiency = Number of particles Trapped / Number of particles Tracked.

Efficiency - 395/394 = 100%

Conclusion -

Table for result comparison -

• the separation efficiency increases with increase in particle size. because the particle with more mass will have more gravitational force to get settle down at the outlet 2.
  
  
• the pressure drops remains constant for the particles with same velocity, because the pressure drop is a function of velocity of the particles.
  
  
• the separation efficiency increases with increase in velocity of particle.
  
  
• the pressure drop increases with increase in particle velocity, because the pressure drop is a function of velocity of the particles.