Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

 

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

• Theory:
• Cyclone Separator: 

Cyclone separators are separation devices that use the principle of inertia to remove particulate matter from flue gases. Cyclone separator is one of many air pollution control devices known as pre-cleaners 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 multi-cyclone.

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:

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 flow resistance, W. Core length, zc, and core diameter dc, are given as                

               $zc=(H-S)-H-S\left(\frac{D}{B}\right)-1[\left(\frac{dc}{B}\right)-1]$     for dc>B

               $zc=H-S$       for $dc<B$

               $dc=0.47D{\left(\frac{ab}{{}^{}}\right)}^{-0.25}\left(\frac{De}{D^{1.4}}\right)$

 

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=\frac{1}{1+{\left(\frac{dpc}{d\pi }\right)}^{\beta }}$$d_{pc}={\left[\frac{9\mu Q}{\pi {}_p{}_c{}^{}max}\right]}^{0.5}$

where, $d_{pc}$ is the 50% cut given by Barth (1956)

                               

 

b. 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:

                                        

                                    $Dr\frac{\partial c}{\partial r}=(1-\alpha )wc$ at 

The tangential velocity is related to the radius of cyclone by:

                                    $u{R}^n$= constant

The concentration distribution in a cyclone is given as:

The resultant expression of the collection efficiency for a $\theta 1=2\pi \frac{S+L}{a}$particle of our size is given as

                                 ${\eta }_i=1-\exp \{-\lambda {\theta }_1\}$

                        where,

                                  ${\theta }_1=2\pi \frac{S+L}{a}$

                              

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:

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 $u{R}^n=\text{constant}$

A force balance and an equation on the particle collection yields the grade efficiency ηi

 

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, dpc is   

              

 The separation efficiency based on this model is calculated at the result section and compared with the experimental data for 5 micrometre at 3 m/s. 

1. Geometry setup:

a. Choose Fluid flow fluent and start with editing geometry.

b. Import the step file of the model into spaceclaim.

Volume extract the model so that we can analyse the fluid flow of the cyclone separator.

 Hide the previous geometry and supress physics since we are only interested with the fluid flow and not the external surface.

Mesh setup:

Mesh stats:

1. Main element size: 9mm 

2. Method = Cartesian method

3. Cartesian element size= 5.2623mm

4. No. of elements= 140228

Mesh quality:

After up-streaming the model to meshing, choose generate mesh to generate the base mesh but since the number of particles entering the inlet depends on the refinement of the mesh, it's better to refine the mesh appropriately.

Assign the names by applying name selection for inlet and outlets accordingly.

 

• Fluent setup:

1. 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 5µm 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.

Material used: Anthracite

3. Boundary conditions:

a. Inlet: - Velocity-Inlet

Velocity Magnitude - 

Part 1- Constant velocity of 3m/s.

Part 2- Varying velocity from 1m/s - 5m/s

DPM - Reflect

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

b. Outlet 1- 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.

 Outlet 2 - 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 vapour phase and enters the cell adjacent to the boundary. In the case of a combusting particle, the remaining volatile mass is passed into the vapour phase.

 

Solution:

Solution method and solution control

Standard Initialisation:

 

Results and analysis:

• Part 1:  Analysis of a given cyclone separator model by varying the particle diameter from $1$$\mu m$to $5$$\mu m\; at\; 3m/s\; for\; both\; particle\; and\; flow\; velocity$ and calculate the separation efficiency in each case.

 

1. At 1 micrometre:

 a. Flow contour and vortex formation

Residuals:

Flow animation drive

link: https://drive.google.com/file/d/193mqx8-DArQxJXsd7ppNLhy9Dor3xlLo/view?usp=share_link

 

2. At 2 micrometre:

a. Flow contour and vortex formation:

Residuals:

Flow animation drive

link; https://drive.google.com/file/d/1Vyk8jwkHBytcqt3Qo7oZ9SrtwpfZt8eH/view?usp=share_link

 

3.At 3 micrometre:

a. Flow contour and vortex formation

Residuals:

Flow animation drive

link; https://drive.google.com/file/d/1sZ-rN0TqMDU7oh1oYK___1K_FiIR85YL/view?usp=share_link

 At 4 micrometre:

a. Flow contour and vortex

 

Residuals

Flow animation drive

link; https://drive.google.com/file/d/1sZ-rN0TqMDU7oh1oYK___1K_FiIR85YL/view?usp=share_link

 

At 5 micrometres

a. Flow contour and vortex

Residuals:

. Flow animation drive

link; https://drive.google.com/file/d/1WhCBA1tRmmH6gb95WJFijUGTvHHHiMBm/view?usp=share_link

 Part 2: Analysis of a  given cyclone separator model by varying the particle velocity from 1$m/sec\; to\; 5\; m/sec\; at\; 5\; micrometre$ and calculate the separation efficiency and pressure drop in each case.

 

1. At 1m/s

a. Flow contour and vortex

 Total pressure at inlet and escape ;

 Residuals:

Flow animation drive

 link;   https://drive.google.com/file/d/1k2ec4TPagueRLbJsRNPhHHlboMwKPBvz/view?usp=sharing

 

2. At 2 m/s

1. Flow contour and vortex

 

 

 

 

 Total pressure at inlet and escape ;

Residuals:

 Flow animation drive link: https://drive.google.com/file/d/1-EPKhW-IBQ96hwNJAto3eOHl8OvKZS1S/view?usp=sharing

 

3. At 3m/s

a. Flow contour and vortex

 

. Total pressure at inlet and escape:

 Residuals:

d. Flow animation drive

link: https://drive.google.com/file/d/1Fe5n136zRALfRk7Da87NozTsf-BgFokV/view?usp=sharing

 

4. At 4 m/s

a. Flow contour and vortex

Total pressure at inlet and escape:

  Residuals:

d. Flow animation drive

link: https://drive.google.com/file/d/1p_7mdH96z9MAbWjJntHGyk-aggVkmYUr/view?usp=sharing

 

5. At 5 m/s

a. Flow contour and vortex

 

Total pressure at inlet and escape

Residuals:

 

d. Flow animation drive link: https://drive.google.com/file/d/1tppMPeELDEdnaKfwaDqc9QjRB-ZdUdK1/view?usp=sharing

 

• Separation efficiency:

It 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

 

• 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, $\Delta P$  = Total inlet pressure - Total Outlet Pressure (escape)

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

 

• Analysis:

1. For varying particle diameter at 3m/s for both the velocities:

Part-1 Cases	Particle Size (m)	Particles Tracked	Particles Escaped	Particles Trapped	Particles incomplete	Separation Efficiency($\eta$)(%)
Case-1	1e-6	190	70	103	17	59.53
Case-2	2e-6	190	67	118	17	69.20
Case-3	3e-6	190	54	132	4	70.96
Case-4	4e-6	190	43	143	4	76.88
Case-5	5e-6	190	36	151	3	80.74

 

 2. For varying velocities at 5 micrometres: 

Part-1 Cases	Velocities (m/s)	Particles Tracked	Particles Escaped	Particles Trapped	Particles incomplete	Pressure drop ($\Delta P$)	Separation Efficiency($\eta$)(%)
Case-1	1	190	59	10	121	2.22	14.49
Case-2	2	190	46	26	118	9.64	36.11
Case-3	3	190	36	151	3	22.33	80.74
Case-4	4	190	37	151	2	40.39	80.31
Case-5	5	190	37	152	1	60.9	80.42

 

 

 Calculating separation efficiency with experimental data from Lapple model method:

The separation efficiency is given by,

$\eta i=\frac{1}{1+{\left(\frac{{}_{pc}}{{}_{\pi }}\right)}^2}$

Where, 

dpc- cut particle diameter collected with 50% efficiency(m)

dpi- diameter of particle in size range i(m)= 5 micrometre

dpc = $dpc={\left[\frac{9\mu b}{2\pi {}_e{}_i({}_p-{}_g)}\right]}^{\frac{1}{2}}$

Where,

$\mu$- Dynamic viscosity

b- cyclone inlet width (m)

Ne- number of revolutions Ne of gas spins through a in the outer vortex

$v_i$- inlet velocity (m/s)

${\rho }_p$- density of the particle(kg/m^3)- Anthracite(1550)

${\rho }_g$-density of the gas- Air(1.225)

 

Where,

a- cyclone Inlet height (m)

h- cylinder height (m)

H- cyclone height (m)

Efficiency obtained for 5 micrometre at 3m/s= 33.7%

•  Conclusion:

1. Both the parts simulated above show that Separation efficiency depends on both the diameter and velocity of the particles. As increased diameter and velocity gives increased separation efficiency.
2. Velocity has a greater impact as compared to the diameter of the particle.
3. Pressure drop is dependant on velocity. For constant velocity with varying diameter sizes, the pressure drop remains almost constant.
4. Increased velocity causes a higher pressure drop.

 Cyclone separator animation ; 

https://youtu.be/Ul0Fwy-JLcU