Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

Aim

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

Objectives

To write a few words about any four empirical models used to calculate the cyclone separator efficiency.

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.]

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]

Empirical models used to calculate the cyclone separator efficiency

1. IOZIA AND LEITH MODEL

Iozia and Leith’s logistic model is a modified version of Barth 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. Core length, z_c, and core diameter, d_c, are given as

The addition made by Iozia and Leith on the original Barth model are the core length z_c 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 d_pi can be calculated from

where d_pc is the 50% cut size given by Barth,

2. LI AND WANG MODEL

The Li and Wang 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:

• The tangential velocity is related to the radius of cyclone by: uRⁿ = constant.

The concentration distribution in a cyclone is given as:

Where

and

The resultant expression of the collection efficiency for particle of my size is given as

η_i = 1 - exp {-λθ1}

where

θ₁ = 2π (S + L) / a

3. KOCH AND LICHT MODEL

Koch and Licht 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: uRⁿ = constant.

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

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 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 to calculate a 50% cut diameter, d_pc, is

The efficiency of collection of any size of particle is given by

Geometry

First step is to import the 3D model into the Spaceclaim.

Fluid volume is extracted using volume extract tool.

Only the fluid volume is considered for analysis and other thickness of the geometry is set to suppress for physics.

Mesh

Base element size = 5 mm

Method = Body fitted cartesian

Total number of elements = 427871

After mesh generation Named selections such as inlet, outlet escape and outlet trap is specified.

Fluent setup

Setting up physics

Solver type = Pressure bases solver

Time = Steady

Gravitational acceleration is enabled in Y direction with -9.81 m/s²

Viscous model :

Model - K-epsilon

k-epsilon model - RNG

RNG Options - Swril Dominated Flow

Near-Wall Treatement - Standard Wall Functions

Discrete Phase Model :

In this case, solid particle size ranging from 1µm to 5µm being simulated as a discrete phase in a continuum.

Interaction - Intractions with continous phase is enabled.

Tracking parameters - Max. No. of steps - 50000 - It is the no. of timesteps that are used to compute a single particle trajectory.

Injections :

Injection Type - Surface

Injection surfaces choosen is Inlet

Particle Type - inert

Material - anthracite

Boundary conditions :

Inlet - Velocity inlet, Discrete Phase BC Type is reflect.

Outlet escape - Pressure outlet, Discrete Phase BC Type is escape.

Outlet trap - Pressure outlet, Discrete Phase BC Type is trap.

Standard initialization is opted.

Results

Case : 1 For Inlet velocity 3m/s and Particle diameter 1e^-06 m

Residuals

Flow contours

Pressure contours

Velocity contours

Animation

https://drive.google.com/file/d/130tlsmpwk_47uhKTBQOi0LKO_VEoW722/view?usp=share_link

Case : 2 For Inlet velocity 3m/s and Particle diameter 3e^-06 m

Residuals

Flow contours

Pressure contours

Velocity contours

Case : 3 For Inlet velocity 3m/s and Particle diameter 5e^-06 m

Residuals

Flow contours

Pressure contours

Velocity contours

Case : 4 For Inlet velocity 1m/s and Particle diameter 5e^-06 m

Residuals

Flow contours

Pressure contours

Velocity contours

Case : 5 For Inlet velocity 5m/s and Particle diameter 5e^-06 m

Residuals

Flow contours

Pressure contours

Velocity contours

Separation efficiency

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.

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, ΔP = 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.

Conclusion

Particles entering into the cyclone separator at different particle size and inlet velocity have different separation efficiency.

Particle diameter of 3e^-06 m entering at inlet velocity of 3 m/s have higher separation efficiency.

There is an increase in pressure drop in the system with the increase in inlet velocity.