Cyclone Separator Challenge

1. Cyclone Separator:

Cyclone Separators or simply cyclones are devices that employ a centrifugal force generated by a spinning gas stream to separate particles from the carrier gas. Particles get separated basically due to their inertia in a vortex formed in the spinning gas stream. Low cost and minimum maintenance make them ideal for use as pre-cleaners for more expensive final control devices like baghouses or electrostatic precipitators.

Typically, a particulate-laden gas enters tangentially near the top of the cyclone, as shown schematically in figure 1.1. The gas flow is forced into a downward spiral simply because of the cyclone’s shape and the tangential entry.

Fig: 1.1: A cyclone separator

Centrifugal force and inertia cause the particles to move outward, collide with the outer wall, and then slide down to the bottom of the device. Near the bottom of the cyclone, the gas
reverses its downward spiral and moves upward in a smaller inner spiral. The cleaned gas exits from the top through a “vortex-finder” tube, and the particles exit from the bottom of the cyclone through a pipe sealed by a spring-loaded flapper valve or rotary valve.

Two important parameters are Collection Efficiency and Pressure Drop through the cyclone.

There are various designs available for cyclone separators. The basic design of the cyclone is as follows:

Fig: 1.2: A cyclone separator and various symbols used.

2. Empirical Models for calculation of collection efficiency:

2.1. Iozia and Leith Model:

It is a modified version of Barth Model which is developed on the basis of force balance. This model assumes that a particle carried by the gas stream is under the influence of two forces; Centrifugal Force and a Flow Resistance.

Following variables are defined for calculation of the collection efficiency:

• Core Diameter- (dc) = `0.47*D*((ab)/D^2)^-0.25*((De)/D)^1.`
• Core length- (Zc) = H-S ; if dc<B
• Core length- (Zc) = `(H-S)-{(H-S)/((D/B)-1)}*{((dc)/B)-1}`; if dc>B
• 50% cut size given by Barth -(dpc) = `((9muQ)/(pi rho*Zc*Vtmax))^0.5`; `mu`= viscosity of air, `rho`= particle mass density, Q= volumetric gas flow rate. Vt max= maximum tangential velocity.- it denotes the particle size for which cyclone will work with a collection efficiency of 50%.

`beta`- an expression for slope parameter derived based on the statistical analysis of experimental data of a cyclone with Dia of 0.25`

• `beta`= `0.62-0.87 ln ((dpc)/100)+5.21ln((ab)/D^2)+1.05(ln(ab/D^2)+1.05(ln((ab)/D^2))^2`

Based on these variables the collection efficiency is defined as follow

`eta i=1/(1+(dpc)/(dp))^beta` ; where dp is the particle size in the flow and the dpc is 50% cut size.

2.2 Li and Wang model:

This model includes particle bounce or re-entrainment and turbulent diffusion at the cyclone wall. A two-dimensional analytical expression of particle distribution in the polar coordinate system is obtained.

Assumptions used:

1. The radial particle velocity and the radial concentration profile are not constant for uncollected particles within the cyclone.

2. Boundary conditions with the consideration of the turbulent diffusion coefficient and the particle bounce re-entrainment on the cyclone wall are:

a. `C=Co`at `theta=0`

b. `Dr (delC)/(delr)= (1-alpha)*omega c`at `r=D/2`

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

Final expression for collection efficiency is given as:

`eta i = 1- exp(-lambda*theta1)`where `theta1 = 2*pi (S+L)/a`

2.3 Koch and Licht model:

Koch and Licht model recognizes the inherently turbulent nature of cyclones and the distribution of gas residence times within the cyclone.

They described the particle motion in entry and collection regions with the following assumptions:

1. The tangential velocity of a particle is equal to the tangential velocity of gas flow i.e. there is no slip between gas and particles in tangential direction.

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

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

`eta i = 1=exp{-2*((G*tau i *Q)/(D^3)*(n+1))^(0.5/(n+1))`

Where `G= (8Kc)/(Ka^2*Kb^2)`. It is a factor related to the configuration of the cyclone, n is related to the vortex, another parameter used is tau which is relaxation term `

2.4 Lapple Model:

It was developed based on force balance without considering the flow resistance. Lapple assumed that particles entering cyclone are evenly distributed across the inlet opening. A particle that travels from inlet half-width to the wall in the cyclone is collected with 50% efficiency.

The Semi Empirical formula developed by Lapple is:

`eta i= 1/(1+((dpc)/(dp i))^2`

Where dpc is the 50% cut diameter given by: `{(9*mu*b)/(2*pi*Ne*vi(rho p-rho g) )}^0.5`

and Ne is given as: `1/a{h+(H-h)/2}`

3. Analysis in Ansys Fluent for a given Cyclone model using particle diameter from 1 micro meter to 10 micro meter

The aim of this analysis was to compare the collection efficiency of the cyclone with respect to change in particle diameter.

A total of five simulations were done with particle sizes of 1 micrometer, 3micrometer, 5 micrometers, 8 micrometers and 10 micrometers.

3.1 Geometry

A step file of the cyclone model was imported in the SpaceClaim and fluid volume was extracted from it.

Fig: 3.1.1 Geometry used.

3.2 Meshing:

Named selections were made for avoiding errors in boundary condition allotment.

Fig: 3.2.1 Named selections used along with intended boundary conditions.

Default tetrahedron mesh was used with a body sizing of 10 mm.

Fig: 3.2.2 Meshed model and mesh quality.

Meshing resulted in 178232 cells and minimum quality was at 0.13 which is not so bad.

The meshed model was imported in ANSYS FLUENT

3.3 Simulation with particle sizes of 1 micro-meter to 10 micro-meters

Solver settings used: Pressure based solver with gravity in the negative Y direction.

K-epsilon turbulence model with RNG and swirling flow settings were used to capture the flow properly.

l

Fig 3.3.1 K-epsilon turbulence model used

Then to simulate the flow of fine dust particles the discrete phase model available in the FLUENT was used. Anthracite particles of inert nature were injected into the flow domain from inlet :

Fig:3.3.2 DPM settings used.

An injection was created in the DPM model with release from inlet and particle velocity set in the direction normal to wall surface. It creates a particle history file which can be used for post-processing the results.

Then boundary conditions were set as follows:

Standard initialization with compute from inlet option was used to initialize the solution. A total of 600 iterations were used for each case to get the solution.

Fig: 3.3.3 Scaled residuals

As clear from the residuals plot the solution has converged as all the parameters have become steady.

3.4 Results:

The results for all the four all the five simulations are compared and discussed in this section:

3.4.1

Table 3.4.1: Comparison of separation efficiency for various particle diameters.

Note the formula used for separation efficiency is: No. of Trapped particles/No. of tracked particles.

Graph 3.4.1: plot of particle dia vs separation efficiency.

Inference: For the currently used geometrical characteristics of the cyclone after particle dia of 5 micrometers the separation efficiency jumps above 90% reaching up to 99% for 10 micrometers which in accordance with the characteristics of cyclones that they are suitable for larger sized particles.

Fig: 3.4.1: Pressure contour on the cyclone outer surface.

Inference: the stepped pressure drop in the conical section is evident from the plot which is vital for achieving the spiral flow with flow reversal near the bottom so that particles drop due to their inertia and gas rises to exit through top outlet via the vortex finding tube.

Total pressure drop:

Fig:3.4.2: Calculated values at various locations.

The inlet pressure was 17 Pa and outlet pressure drops to almost zero. So the pressure drop is almost 17 Pa, further assuming the inlet to the cyclone is coming from an Induced Draft (ID) fan we can calculate the power rating of the motor for the case using the formula: Power= flow rate * pressure drop (neglecting effects of temperature changes and gas characteristics for simplification)

Fig:3.4.3: Particles track with colour scheme set to the time of residing inside the cyclone.

Note: the particles which escaped from the top outlet resided for the longest period of time and hence it can be concluded that the flow reversal happened and these particles were carried to the top outlet by the upward spiraling gas stream.

4. Simulation in Ansys Fluent with the variation of inlet velocity from 5 m/s to 10 m/s for carrier gas and the injected particles.

• For this part of the challenge, a case was set up in Ansys Fluent with the same geometry and meshing.
• The diameter of injected particles was fixed to 5 μm for all the 5 simulations.
• The velocity of the inlet for carrier gas and injected particles were varied from 5 m/s to 10 m/s in subsequent simulations keeping all the settings same.

Separation efficiency and pressure drop for all the five cases were calculated.

Table 4.1: The separation efficiency for simulations.

Graph 4.1: Velocity Vs Separation Efficiency.

From the obtained plot it is clear that the separation efficiency was maximum at 10 m/s velocity and was lowest for 6 m/s. It followed a downward trend in the intervals 5 to 6 m/s and 7 to 9 m/s while the trend was of rise in the intervals 6 to 7 m/s and 9 to 10 m/s.

4.1 Pressure drop against inlet velocities:

The pressure drop between inlet and outlet sections is a direct indication of motor power needed for driving the ID fan or blower used along with the cyclone separator for maintaining air flow. Funcion calculator was used in CFD post to determine the pressure at inlet and outlet sections. The results are as follows:

Table 4.1.1: Pressure drop against velocity variation.

Graph 4.1.1: pressure drop against inlet velocities.

The pressure drop was consistently rising except in the range 7 to 8 m/s. This trend can be attributed to the fact that friction losses increase with a rise in velocity.

5. Validation

In this section an attempt is made to validate the obtained results using Iozia and Leith Model:

• All the details as shown in fig 1.2 were obtained from the CAD model in Spaceclaim.
• Formulae from the model were used to calculate the theoretical 50% cut size (dpc) or the particle diameter for 50% separation efficiency.
• Then maximum tangential velocity (Vt max) was calculated from the CFD post for each simulation of section 4.
• Finally using the provided formulae theoretical efficiency was calculated in Excel.

Table:5.1: Iozia and Leith model theoretical and simulation values of the separation efficiency.

Graph 5.1: Theoretical Vs Simulation efficiency.

Conclusion: As clear from the above graph 5.1 the error is in the range of 5% which is acceptable as our simulation and calculations have lots of assumptions that caused error in the results.