Cyclone Separator Challenge

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 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.

Effectiveness:

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.

Empirical models used for cyclone separator efficiency.

1. 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 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 Iozia and Leith on the original Barth (1956) model is 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_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 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:

1. The radial particle velocity and the radial concentration profile are not constant, for uncollected particles within the cyclones.
2. Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are:

`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`particle 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 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:

1. 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.
2. 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 ηi

`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 τ 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 a 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`

Part 1 - Analysis of the given cyclone separator model by varying the particle diameter from 1 µm to 10 µm and calculate the separation efficiency in each case. [Using both the velocity's as 3m/sec].

In this part of the challenge velocity of fluid and particles is kept constant as 3m/sec for all the cases in which varying the particle size starting from 1e-6 to 10e-6.

Therefore, Case Setup for Part-1

Case Setup:

1. Geometry:

a. Import Geometry into SpaceClaim:

Geometry is imported into SpaceClaim and further to carry out the analysis on the fluid volume, we need to extract fluid volume within the cyclone separator.

b. Extract Fluid Volume:

Edges for volume extraction Extracted Fluid volume

By selecting the highlighted edges of inlet and 2 outlets as shown in the left figure, we obtain the required fluid volume as shown in the right figure.

c. Suppressing for Physics:

As we need to analyze the extracted fluid volume, suppressing cyclone separator geometry for physics to avoid it from popping out into the analysis part.

2. Meshing:

a. Named Selection:

In cyclone separator there is one inlet and two outlets:

1st outlet is for lighter air.

2nd outlet is for heavier particles.

b. Mesh:

Mesh Element Size - 6.5mm

Number of Nodes - 155480

Number of Elements - 447521

3. Setup:

a. Physics:

Solver - Pressure based

Time - Steady time.

velocity Formulation - Absolute

Gravitational Acceleration - Enabled in y-direction = -9.81.

Viscous Model -

Model - k-Epsilon

k-epsilon Model - RNG

RNG Option - Swirl Dominated Flow

Near Wall Treatment - Standard 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 the 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 field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.

In this case, solid particle size ranging from 1µm to 10µm being simulated as a discrete phase in a continuum.

1. Enabled interaction with continuous phase - to enable coupled flow
2. Enabled update DPM sources every flow iteration - Enabling this option gives chances to calculate particle source term at every iteration.
3. Contour plots for DPM variables - unenabled - Allows cell averaged variable value.
4. Tracking parameters - Max. No. of steps - 50000 - It is the no. of timesteps that is used to compute a single particle trajectory.
5. Specify length scale - This option is also used to control the timestep size.

Injections -

Injection Type - Surface

Release From Surfaces - Inlet

Particle Type - Inert

Material Type - Anthracite

x- velocity - 3m/sec (In this part it constant for all the particle diameter size varying from 1e-6 to 10e-6)

Diameter - Varying from 1e-6 to 10e-6 for different cases

Flow Rate - 1e-20 kg/s.

Boundary Conditions -

i. Inlet - Velocity-Inlet

Velocity Magnitude - 3m/sec (In this part it constant for all the particle diameter size varying from 1e-6 to 10e-6)

DPM - Reflect

Reflect - The particle rebound off the boundary in question with a change in its momentum as defined by the coefficient of restitution.

ii. Outlet top - Pressure-Outlet

Pressure - 0 Pa

DPM - Escape

Escape - The particle is reported as having "escaped" when it encounters the boundary in question. Trajectory calculated are terminated.

iii. Outlet_Dustbin Bottom - Pressure-Outlet

Pressure - 0 Pa

DPM - Trap

Trap - The trajectory calculation are terminated and the fate of the particle is recorded as " trapped ". In the case of the evaporating droplet, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary. In the case of a combusting particle, the remaining volatile mass is passed into the vapor phase.

b. Solution

Solution Method:

Initialization:

Calculation:

With the above geometry, meshing, and solution setup, running 6 different cases with varying particle diameter sizes from 1 µm to 10 µm and obtaining the results.

Part 1 - Analysis of the given cyclone separator model by varying the particle diameter from 1 µm to 10 µm and calculate the separation efficiency in each case.

In this part of challenge Simulation

Part-1 Case - 1

Particle Diameter = 1e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency - is defined as the fraction of particles of a given size collected in the cyclone, compared to 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 to the initial concentration in the feed stream. For this case ratio of the number of trapped particles to the total number of particles tracked.

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-228"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 47.10%`

Global and User Specified Anthracite Particle Time

Animation

Part-1 Case - 2

Particle Diameter = 3e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency -

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-285"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 58.88%`

Global and User Specified Anthracite Particle Time

Animation:

Part-1 Case - 3

Particle Diameter = 5e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency -

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-347"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 71.69%`

Global and User Specified Anthracite Particle Time

Animation:

Part-1 Case - 4

Particle Diameter = 7e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency -

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-368"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 76.03%`

Animation:

Part-1 Case - 5

Particle Diameter = 9e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency -

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-401"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 82.85%`

Global and User Specified Anthracite Particle Time

Animation:

Part-1 Case - 6

Particle Diameter = 10e-6m

Fluid Velocity = 3 m/sec

Particle Velocity = 3 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency -

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-402"/"No.of Particles Tracked-484"`

`"Separation Efficiency" = 83.05%`

Animation:

Contours of Part 1 Cases

Pressure Contour

i. Static Pressure Contour

ii. Total Pressure Contour

Velocity Contour

Pressure and Velocity Streamlines of Part 2 Cases

Pressure Streamlines

Velocity Streamlines

Vortex Region of Part 2 Cases

Vortex Region - With Different Swirling Strength Level (Starting from [swirling strength level = 0.004,0.025 and 0.25 res])

Pressure Drop Calculation:

Pressure Report:

i. Inlet

ii. Outlet-top

Pressure Drop - Pressure drop across the cyclone is of much importance in a cyclone separator. The pressure drop significantly affects the performance parameters of a cyclone. The total pressure drop in a cyclone will be due to the entry and exit losses, and friction and kinetic energy losses in the cyclone. Normally the most significant pressure drop occurs in the body due to swirl and energy dissipation.

Pressure drop is defined as the difference in total pressure between two points of a fluid carrying network.

Pressure drop = Total inlet pressure - Total Outlet Pressure

As the escape DPM condition is given to the outlet-top in this case, so outlet-top is considered in pressure drop calculation.

For this case the obtained values from the inlet and outlet-top pressure reports-

Total Inlet Pressure - 25.135 Pa

Total Outlet-top Pressure - 3.270 Pa

Pressure Drop (`DeltaP`)

`DeltaP = "Total inlet pressure - Total Outlet Pressure"`

`DeltaP = 25.135 - 3.270`

`DeltaP = 21.865`Pa

The fluid velocity and particle velocity is 3m/sec for all particle sizes varied in part-1, Therefore the pressure drop remains constant.

Separation Efficiency of Part-1 Cases:

In all the below-given cases has both Fluid Velocity and Particle Velocity = 3m/sec

Part-1 Cases	Particle Size (m)	Particles Tracked	Particles Escaped	Particles Trapped	Separation Efficiency(`eta`)(%)
Case-1	1e-6	484	216	228	47.10
Case-2	3e-6	484	167	285	58.88
Case-3	5e-6	484	76	347	71.69
Case-4	7e-6	484	69	368	76.03
Case-5	9e-6	484	34	401	82.85
Case-6	10e-6	484	31	402	83.05

For all the varying particle sizes with the constant fluid velocity and particle velocity i.e. 3 m/sec. It can be observed that the cyclone efficiency increases as we increase the particle diameter.

Part-2 - Calculate the separation efficiency and pressure drop by varying the inlet velocity of both fluid and particle from 5 m/sec to 10 m/sec & Discuss the results. [Use particle diameter size as 5 µm.]

In this part of the challenge velocity of fluid and particles is kept constant as 3m/sec for all the cases in which varying the particle size starting from 1e-6 to 10e-6.

Therefore, Case Setup for Part-2

Case Setup:

1. Geometry:

a. Import Geometry into SpaceClaim:

Geometry is imported into SpaceClaim and further to carry out the analysis on the fluid volume, we need to extract fluid volume within the cyclone separator.

b. Extract Fluid Volume:

Edges for volume extraction Extracted Fluid volume

By selecting the highlighted edges of inlet and 2 outlets as shown in the left figure, we obtain the required fluid volume as shown in the right figure.

c. Suppressing for Physics:

As we need to analyze the extracted fluid volume, suppressing cyclone separator geometry for physics to avoid it from popping out into the analysis part.

2. Meshing:

a. Named Selection:

In cyclone separator there is one inlet and two outlets:

1st outlet is for lighter air.

2nd outlet is for heavier particles.

b. Mesh:

Mesh Element Size - 6.5mm

Number of Nodes - 155480

Number of Elements - 447521

3. Setup:

a. Physics:

Solver - Pressure based

Time - Steady time.

velocity Formulation - Absolute

Gravitational Acceleration - Enabled in y-direction = -9.81.

Viscous Model -

Model - k-Epsilon

k-epsilon Model - RNG

RNG Option - Swirl Dominated Flow

Near Wall Treatment - Standard Wall Functions

Boundary Conditions before Introducing DPM

i. Inlet - Velocity-Inlet

Velocity Magnitude - 3m/sec (In this part it constant for all the particle diameter size varying from 1e-6 to 10e-6)

Changing the x-velocity value according to different cases.

ii. Outlet top - Pressure-Outlet

Pressure - 0 Pa

iii. Outlet_Dustbin Bottom - Pressure-Outlet

Pressure - 0 Pa

After these settings, hybrid initialization is done and the solution ran for 100 iterations.

Once the calculation is completed introducing the DPM according to the cases. This is done in order to obtain better results.

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 the 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 field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.

In this case, solid particle size ranging from 1µm to 10µm being simulated as a discrete phase in a continuum.

1. Enabled interaction with continuous phase - to enable coupled flow
2. Enabled update DPM sources every flow iteration - Enabling this option gives chances to calculate particle source term at every iteration.
3. Contour plots for DPM variables - unenabled - Allows cell averaged variable value.
4. Tracking parameters - Max. No. of steps - 50000 - It is the no. of timesteps that are used to compute a single particle trajectory.
5. Specify length scale - This option is also used to control the timestep size.

Injections -

Injection Type - Surface

Release From Surfaces - Inlet

Particle Type - Inert

Material Type - Anthracite

x- velocity - 3m/sec (In this part it constant for all the particle diameter size varying from 1e-6 to 10e-6)

Diameter - Varying from 1e-6 to 10e-6 for different cases

Flow Rate - 1e-20 kg/s.

Changing the x-velocity value according to different cases and particle size will be the same for all the cases.

Boundary Conditions after introducing DPM -

i. Inlet - Velocity-Inlet

Velocity Magnitude - 3m/sec (In this part it constant for all the particle diameter size varying from 1e-6 to 10e-6)

DPM - Reflect

Reflect - The particle rebound off the boundary in question with a change in its momentum as defined by the coefficient of restitution.

ii. Outlet top - Pressure-Outlet

Pressure - 0 Pa

DPM - Escape

Escape - The particle is reported as having "escaped" when it encounters the boundary in question. Trajectory calculated are terminated.

iii. Outlet_Dustbin Bottom - Pressure-Outlet

Pressure - 0 Pa

DPM - Trap

Trap - The trajectory calculation is terminated and the fate of the particle is recorded as " trapped ". In the case of the evaporating droplet, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary. In the case of a combusting particle, the remaining volatile mass is passed into the vapor phase.

b. Solution

Solution Method:

Initialization:

Already Hybrid Initialization is done. Proceeding to calculation without initialization.

Calculation:

With the above geometry, meshing, and solution setup, running 5 different cases with varying particle velocity and fluid velocity from 1 m/sec to 5 m/sec with the same particle size i.e 5e-6 for all the cases and obtaining the results.

Part-2 - Calculate the separation efficiency and pressure drop by varying the inlet velocity of both fluid and particle from 5 m/sec to 10 m/sec

Part-2 Case - 1

Particle Diameter = 5e-6m

Fluid Velocity = 1 m/sec

Particle Velocity = 1 m/sec

Particle Tracking:

For this selecting option Export particle history data from file-

Separation efficiency - is defined as the fraction of particles of a given size collected in the cyclone, compared to 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 to the initial concentration in the feed stream. For this case ratio of the number of trapped particles to the total number of particles tracked.

`"Separation Efficiency" = "No. of Particles Trapped"/"No.of Particles Tracked"`

`"Separation Efficiency" = "No. of Particles Trapped-210"/"No.of Particles Tracked-540"`

`"Separation Efficiency" = 38.88%`

Pressure Drop Calculation:

Pressure Report:

i. Inlet

ii. Outlet-top

Pressure Drop - Pressure drop across the cyclone is of much importance in a cyclone separator. The pressure drop significantly affects the performance parameters of a cyclone. The total pressure drop in a cyclone will be due to the entry and exit losses, and friction and kinetic energy losses in the cyclone. Normally the most significant pressure drop occurs in the body due to swirl and energy dissipation.

Pressure drop is defined as the difference in total pressure between two points of a fluid carrying network.

Pressure drop = Total inlet pressure - Total Outlet Pressure

As the escape DPM condition is given to the outlet-top in this case, so outlet-top is considered in pressure drop calculation.

For this case the obtained values from the inlet and outlet-top pressure reports-

Total Inlet Pressure - 1.8355 Pa

Total Outlet-top Pressure - 0.1772 Pa

Pressure Drop (`DeltaP`)

`DeltaP = "Total inlet pressure - Total Outlet Pressure"`

`DeltaP = 1.8355 - 0.1772`

`DeltaP = 1.6583` Pa

Velocity Contour

Global and User Specified Anthracite Particle Time

Pressure Streamlines

Velocity Streamlines

Animation