Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

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

B. 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.]
   1. 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]

C. Given Boundary Conditions:

• Inlet and wall:- Reflect
• Outlet (Top):- Escape
• Outlet (Bottom/dustbin):- Trap

D. Introduction:

[1] Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices known as precleaners 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 multicyclone.

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.

- How It Works:

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 Figure 2. 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.

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.

1. Any four empirical models [2] used to calculate the cyclone separator efficiency:

a. 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.

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 `η_i` of particle diameter dpi can be calculated from

`η_i = 1/(1+(d_(pc) / d_(pi))^β`

here `d_(pc)` is the 50% cut size given by Barth (1956)

`d_(pc) = [(9µQ)/ (πp_p z_c(v^2)_(tmax) )]^0.5`

where Core length `z_c`, and core diameter `d_c`

b. 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_0`, at θ = 0

`D_r d_c/d_r = (1- α)wc`, 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 my size is given as
`η_i` = 1 - exp {-λ`θ_1`}

where
`θ_1` = 2π (S + L) / a

c. 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:

• 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:
  `uR^n` = constant.

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

`η_i = 1-exp{-2[(Gτ_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`

`τ_i = (ρ_p(d_(p i))^2) /(18 µ)`

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

d. 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) = (9µb)/ (2πN_ev_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_(p i))^2`

2. 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. [Use both the velocity as 3m/sec.]

- Given Geometry of Cyclone Separator:

- Extracted Geometry:

2.1 CASE 1.1: Analysis on a given cyclone separator model with particle diameter 1 μm, inlet and particle velocity as 3 m/sec.

2.1.1 Meshing:

- Cartesian method :

• Mesh Type: Cartesian
• Element Size: 50 mm

- Inlet Face Sizing:

• Mesh Type: Cartesian
  • Element Size: 5 mm

> Mesh Statistics:

• Nodes: 92566
• Elements: 82750

2.1.2 Setup:

- General:

• Solver Type: Pressure Based
• Solver Time: Steady
• Gravitatonal Acceleration: -9.81 m/s in Y direction

- Viscous Model: k-epsilon (2 eqn)

• k-epsilon model: RNG
• RNG Options: Swirl Dominated Flow
• Near Wall Treatment: Standard Wall Functions

- Discrete Phase Model turned ON:

- Injection Properties:

• Particle Diameter = 1 μm

The trajectory is computed more than once if your input exceeds 1: two trajectory calculations are performed for input 2 as shown above.

- Material:

• Fluid: Air
• Solid: Aluminium
• Inert Particle: Anthracite

- Solution Methods:

Following default Solution methods autoset by the computation software are maintained to get accurate results.

- Initialization Method: Hybrid Initialization

- Boundary Conditions:

• Inlet Velocity: 3 m/s
• Particle Velocity: 3 m/s
• Inlet Discrete Phase BC Type: Reflect

• Outlet 1 Discrete Phase BC Type: Escape
• Outlet 2 Discrete Phase BC Type: Trap

2.1.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 1.1 Separation Efficiency in % = (174/320) X 100 = 54.37%

-Residuals Plot:

2.1.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

- Animation:

2.2. CASE 1.2: Analysis on a given cyclone separator model with particle diameter 3 μm, inlet and particle velocity as 3 m/sec.

2.2.1 Meshing and Setup details are maintained same as in CASE 1.1 except particle diameter = 3 μm

- Boundary Conditions:

• Inlet Velocity: 3 m/s
• Particle Velocity: 3 m/s
• Particle Diameter: 3 μm

2.2.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 1.2 Separation Efficiency in % = (217/320) X 100 = 67.81%

-Residuals Plot:

2.2.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

- Animation:

2.3. CASE 1.3: Analysis on a given cyclone separator model with particle diameter 5 μm, inlet and particle velocity as 3 m/sec.

2.3.1 Meshing and Setup details are maintained same as in CASE 1.1 except particle diameter = 5 μm

- Boundary Conditions:

• Inlet Velocity: 3 m/s
• Particle Velocity: 3 m/s
• Particle Diameter: 5 μm

2.3.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 1.3 Separation Efficiency in % = (261/320) X 100 = 81.56%

-Residuals Plot:

2.3.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

- Animation:

3. 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]

- Geometry and Mesh details remains same for all the cases below as considered in Case 1.

3.1. CASE 2.1: Analysis on a given cyclone separator model with particle diameter 5 μm, inlet and particle velocity as 1 m/sec.

3.1.1 Setup parameters remains same as above cases as considered in section 2 of the objective, except for particle diameter, inlet and particle velocity as mentioned below accordingly.

- Boundary Conditions:

• Inlet Velocity: 1 m/s
• Particle Velocity: 1 m/s
• Particle Diameter: 5 μm

3.1.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 2.1 Separation Efficiency in % = (217/320) X 100 = 67.81%

-Residuals Plot:

- Area Weighted Average Plot of Static Pressure at Inlet:

- Area Weighted Average Plot of Static Pressure at Outlet 2 at Bottom of the Cyclone Separator:

• Pressure Drop = Pressure at Inlet - Pressure at Outlet 2 = 3.356 - 0 = 3.356 Pa

The pressure distribution on two faces: outlet and circumferential side are having uniform atmospheric pressure. So the resultant pressure force will be zero on that faces. Further, there is only one face we have to consider for calculation of pressure at inlet because gauge pressure exist there.

Further the zero pressure outlet condition is considered where the flow exits into an ambient atmosphere i.e. its free surface is exposed to that atmosphere. Therefore the flow coming out will be at atmospheric pressure.

3.1.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

- Animation:

3.2. CASE 2.2: Analysis on a given cyclone separator model with particle diameter 5 μm, inlet and particle velocity as 3 m/sec.

3.2.1 Setup parameters remains same as above cases as considered in section 2 of the objective, except for particle diameter, inlet and particle velocity as mentioned below accordingly.

- Boundary Conditions:

• Inlet Velocity: 3 m/s
• Particle Velocity: 3 m/s
• Particle Diameter: 5 μm

3.2.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 2.2 Separation Efficiency in % = (261/320) X 100 = 81.56%

-Residuals Plot:

- Area Weighted Average Plot of Static Pressure at Inlet:

- Area Weighted Average Plot of Static Pressure at Outlet 2 at Bottom of the Cyclone Separator:

• Pressure Drop = 30.513 - 0 = 30.513 Pa

3.2.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

-Animation:

3.3. CASE 2.3: Analysis on a given cyclone separator model with particle diameter 5 μm, inlet and particle velocity as 5 m/sec.

3.3.1 Setup parameters remains same as above cases as considered in section 2 of the objective, except for particle diameter, inlet and particle velocity as mentioned below accordingly.

- Boundary Conditions:

• Inlet Velocity: 5 m/s
• Particle Velocity: 5 m/s
• Particle Diameter: 5 μm

3.3.2 Solution:

Separation Efficiency = (Number of particles trapped)/(Number of particles tracked)

Case 2.3 Separation Efficiency in % = (282/320) X 100 = 88.13%

-Residuals Plot:

- Area Weighted Average Plot of Static Pressure at Inlet:

- Area Weighted Average Plot of Static Pressure at Outlet 2 at Bottom of the Cyclone Separator:

• Pressure Drop = 86.509 - 0 = 86.509 Pa

3.2.3 Results:

- Anthracite Particle Time Contour:

- Votex Core Region at different levels:

- Animation:

4. Results and Discussions:

• Finer mesh leads to increase in number of particles being tracked which helps in improving the accuracy of the results.
• Solutions on Cartesian grids tend to converge better than those of body-fitted methods.
• Cartesian mesh fits perfectly with our geometry, reducing the number of inaccuracies that propagate through the rest of the domain.

• CASE 1:

• From CASE 1 results, we can conclude that as particle dia increases number of tracked particles increases in turn leading to increase in separation efficiency.

• CASE 2:

• Based on results obtained from CASE 2, we can understand higher the inlet and particle velocity, higher is the pressure drop.
• Also, higher the inlet and particle velocity, higher is the number of tracked particles and in turn leading to increase in separation efficiency.

References:

[1] https://energyeducation.ca/encyclopedia/Cyclone_separator

[2] A CFD Study on the Prediction of Cyclone Collection Efficiency; Jolius Gimbun1, Thomas S. Y. Choong2, T. G. Chuah2 and A. Fakhru’l-Razi2 (2014).