Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

AIM: -

A. To Perform the Analysis of the Given Cyclone separator for different particle sizes and different inlet speeds.

B. To Explain the relevant theories and to explain the generated results

Given and Assumed: -

A. The Geometry of the Given CAD Model: -

B. Material and their Properties: -

C. Conditions at Different Locations: -

     i. Inlet Velocities `->` 1 m/sec, 3 m/sec, 5 m/sec

     ii. Particle Traping Outlet `->` Bottom Outlet

     iii. Particle Escape Outlet `->` Top Outlet

Theories: -

A. Cyclone Separator: -

A Cyclone separator is a device used to separate particulate matter from the air. The working principle of the Cyclone Separator is based on inertia to remove particulate matter from gases, the gases are fed into the cyclone separator and the heavier particulate matter due to centrifugal forces gets pushed towards the walls of the Separator and due to gravity the particulate matter gets collected at the bottom exit and the air is escaped from the top exit.

Fig.1 Diagrammatic Representation of Cyclone Separator(This image is inspired/Re-created from A CFD Study on the Prediction of Cyclone Collector Efficiency, author Jolius Gimbun,Thomas S. Y. Choong,T. G. Chuah, and A. Fakhru’l-Razi for study purposes only and with no intention to infringe the Copyright of the original Author and/or the Publication)

There are some Empirical Relations that are used to compute the efficiency of the Cyclone Separator, Following are 4 Empirical Relations of the Cyclone Separator: -

     i. Lozia and Leith Model: -

 This Model was developed by modification of the Barth Model which was based on the Force Balance. This Model is based on the assumption that the Force Experienced by the Particle is Centrifugal Force and Flow Resistance. The Efficiency in this Model can be calculated through the following: -

      `eta_i = 1/(1+ (d_("pc") + d_("pi"))^beta)`

Where, `d_("pi") ->` Particle Diameter

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

              Here, `d_("pc") = [(9muQ)/(pirho_pz_c(v_t^2)_(max))]^0.5`

                        where, `z_c`(Cord Length) `= (H-S) - [(H-S)/((D/B) -1)] [(d_c/B) - 1]` for `d_c > B`

                                           `z_c = H-S` for `d_c < B`

                                           Here, `d_c = 0.47D((ab)/D^2)^(-0.25)(D_e/D)^1.4`

     ii. Li and Wang Model: -

The Li and Wang Model was developed by taking particle Bounce or re-entertainment and turbulence diffusion at Cyclone Wall. A 2D analytical expression of particle distribution in a cyclone is obtained. The Following are the Assumptions taken for this Model: -

        a. The Radial Particle Velocity and Radial Concentration profile are not constant for uncontrolled particles within the Cyclone.

        b. Boundary conditions with consideration of turbulence diffusion coefficient and particle bounce and re-entertainment on cyclone walls are.

     `c = c_o` at `theta = 0`

     `D_r(delc)/(delr) = (1 - alpha)wc` at `r = D/2`

        c. The tangential Velocity is related to the radius of the cyclone by `uR = "constant"`

The Concentration distribution in cyclones is given as: -

     `c(r,theta) = (c_o(r_w - r_n)e^({-lamda[1/(K(1+n))r^(1+n)]}))/(int_(r_n)^(r_w) e^({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))`

             `lamda = ((1-alpha)Kw_w)/(D_rr_w^n)`

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

         `eta_i = 1 - e^(-lamdatheta_1)`

          where, `theta = 2pi(S+L)/a`

     iii. Koch and Licht Model: -

Koch and Licht collection Theory recognized the inherently turbulent nature of the cyclones. Koch and Licht described particle motion in the entry and collection regions with the assumptions: -

        a. The tangential velocity of the particle is equal to the tangential velocity of the gas flow 

        b. The tangential Velocity is related to the radius of the cyclone by `uR = "constant"`

The Force balance and an equation on the particles collection yield the grade effeciency

     `eta_i = 1 - e^({-2[(Gtau_iQ)/D^3(n+1)]^(0.5/(n+1))}`

      Where, `G=(8K_c)/(K_a^2K_b^2)`

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

                    `tau_i = (rho_pd_("pi")^2)/(18mu)`

     iv. Lapple Model: -

The Lappel Model was developed using Force Balance without considering the flow resistance. Lapple assumed the following: -

        a. The particles entering the Cyclone are evenly distributed in the inlet

        b. The particles that travel from the inlet half-width to the wall in the cyclone is collected with 50% efficiency.

The semi-empirical formula developed by Lapple for 50% cut diameter `d_("pc")` is

        `d_("pc") = [(9mub)/(2piN_ev_i(rho_p - rho_g))]^(1/2)`

        where, `N_e = 1/a[h+(H-h)/2]`

The Efficiency of the Cyclone Collector is given as

         `eta_i = 1/(1+(d_("pc")/bar(d_("pi")))^2`

Steps to Setup the Cyclone Separator with Discrete Particles: -

A. Setting up the Ansys Workbench: -

Ansys Workbench `->` ToolBox `->` Analysis System `->` `ubrace("Fluid Flow(Fluent)")_("Selecting" -> "Holding" -> "Dragging and Drooping to Project Schematic")`

B. Opening SpaceClaim Geometry and Extracting Volume: -

     i. Steps to Open SpaceClaim: -

Ansys Workbench `->` Project Schematic `->` Project `->` Geometry `->` Right-Click `->` Select SpaceClaim Geometry

     ii. Steps to Load the Cyclone Separator Geometry: -

SpaceClaim `->` File `->` Open

     iii. Steps to Extract Volume: -

SpaceClaim `->` Prepare `->` Volume Extract `->` Select Edges `->` Enter

Extracted Fluid Volume	Solid Casing and Fluid Volumes

C. Opening Mechanical(Meshing) and Meshing the Geometry: -

     i. Steps to Open Meshing: -

Ansys Workbench `->` Project Schematic `->` Project `->` Mesh `->` Right-Click `->` Edit

     ii. Steps to Name the Boundary: -

Mechanical(Meshing) `->` Model Working Window `->` Select the Boundary `->` Click N `->` Give the desired Name `->` Enter

     iii. Steps to Create the Mesh: -

          a. Setting Base Mesh Size: Outline Window `->` Select Mesh `->` Details of Mesh Window `->` Defaults `->` Element Size is set to "8mm"

          b. Setting Capture Curvature: `ubrace("Select the Desired Geometry")_("Select the Fluid Volume")` `->` Mesh `->` Sizing `->` Set Capture Curvature to "Yes" `->` Set the desired Capture Curvature Parameter

Isometric View of Upper Meshed Fluid Volume	Isometric View of Upper Meshed Split Fluid Volume
View of Inlet Meshed Fluid Volume	View of Top Outlet Fluid Volume Edges

D. Setuping the Physics and Boundary Conditions: -

     i. Steps to Open Ansys Fluent: -

Ansys Workbench `->` Project Schematic `->` Project `->` Setup `->` Right-Click `->` Edit

     ii. Steps to Check Mesh: -

Fluent `->` Outline View Window `->` Setup `->` General `->` Mesh `->` Check

     iii. Steps to Set up the Physics: -

          a. Setting Gravity: Fluent `->` Outline View `->` General `->` Select Gravity `->` `ubrace("Select Desired Magnitude")_("In our case Set Y direction to -9.81")`

          b. Setting Viscous Model: Fluent `->` Physics `->` Models `->` Viscous `->` `ubrace("Select Desired Viscous Model")_("In our case Select K-Epsilon RNG Swirl Dominated Flow")`

          c. Setting Discrete Phase: Fluent `->` Physics `->` Models `->` Discrete Phases... `->` `ubrace("Select Desired Model")_("In our case Select Interaction with Continuous Phase and Update DPM Source Every Flow Iteration")` `->` Injections... `->` Create `->` `ubrace("Set the Desired Particles and their conditions")_("In this case Gave the Name, Selected Injection Type to Surface and Inlet, Set X-Velocity and Diameter of Particle")` `->` Ok

     iv. Steps to Set Boundary Conditions: -

Fluent `->` Physics `->` Zone `->` Boundaries `->` Select the desired Component `->` Select the Desired Type for that Component `->` Edit `->` Add the Values for the Component `->` Apply & Close

     v. Steps to Initialize and Run Calculations: -

          a. Initializing: Fluent `->` Solution `->` Initialization `->` Initialize

          b. Setting No. of Iterations: Fluent `->` Solution `->` Run Calculations `->` `ubrace("Setting Desired Iterations in No. of Iterations")_("In Our Case, No. of Iterations is set to 600")`

          c. Running Calculations: Fluent `->` Solution `->` Run Calculations `->` Calculate

Output/Results Generated after Analysis: -

A. For Inlet Velocity = 3 m/sec and Discrete Particle Diameter = 1 X `10^(-6)`

Pressure and Mass Flow Rate at Inlet and Outlets	Movement of Discrete Particles
Pressure Contour	Velocity Contour

B. For Inlet Velocity = 3 m/sec and Discrete Particle Diameter = 3 X `10^(-6)`

Pressure and Mass Flow Rate at Inlet and Outlets	Movement of Discrete Particles
Pressure Contour	Velocity Contour

C. For Inlet Velocity = 3 m/sec and Discrete Particle Diameter = 5 X `10^(-6)`

Pressure and Mass Flow Rate at Inlet and Outlets	Movement of Discrete Particles
Pressure Contour	Velocity Contour

D. For Inlet Velocity = 1 m/sec and Discrete Particle Diameter = 5 X `10^(-6)`

Pressure and Mass Flow Rate at Inlet and Outlets	Movement of Discrete Particles
Pressure Contour	Velocity Contour

D. For Inlet Velocity = 5 m/sec and Discrete Particle Diameter = 5 X `10^(-6)`

Pressure and Mass Flow Rate at Inlet and Outlets	Movement of Discrete Particles
Pressure Contour	Velocity Contour

Observations and their Reasons: -

A. Low-Pressure Region in the Center and High-Pressure Regions at the Walls and Its Effects on Solid Particles: -

Due to the Tangential inlet and the Circular Geometry, the Fluid within the Cyclone Separator starts to generate a Vortex which in turn causes Centripetal Forces to Act on the Fluid Molecules Which pushes the Molecules toward the Casing Walls causing a High-Pressure Region at the Casing walls, and a low-pressure region at the center of the Cyclone Separator.

Due to this the Solid Particles also experience a Centripetal Force which pushes the particles toward the Walls and due to gravity the Solid Particles fall towards the bottom of the Cyclone separator. But if the Pressure difference is too high the particles can also move towards the center of the Cyclone Separator and due to lift forces the particles can exit the Cyclone Separator from the top Outlet.

The Observed Pressures for different Velocities are as follows: -

B. Reasons for Some Particles to escape from Top Outlet: -

Due to the High-Pressure Difference between the Walls and the Center, there can be a sufficient lift that can be generated on the Particles which will lead to particles floating toward the Top Exit. The lift generated on the Following particles: -

     i. The mass of Particles

     ii. The Velocity of the Fluid

     iii. The Pressure Difference between the Central and Wall of the Cyclone Separator

     iv. The Surface Area of the Particles

The efficiency of the Cyclone Separator for different particle sizes and Inlet Velocity