Simulating Cyclone separator with Discrete Phase Modelling

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

Objective:

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

2) To perform analysis on a given cyclone separator model by varying particle diameter from 1e-6 m to 5e-6 m and calculate separation efficiency in each case. (for velocity equal to 3m/s)

3) To perform analysis on a given cyclone separator model by varying the particle velocity from 1m/s and 5 m/s and calculate separation efficiency and pressure drop in each case. (for particle diameter equal to 5e-6 m)

Introduction:

Cyclone separator is a device used to separate suspended particulate matter from the air stream with the help of centrifugal force. It consists of a cylindrical upper body with conical lower section and two outlets are provided on top of the cylinder and at the bottom. The air enters tangentialy through the inlet and then travels downwards towards the cone section forming a vortex. The increase in velocity of the air in vortex leads to increase in centrifugal force of the particles separating the heavy particulate matter from the air stream. Thus, the clean air stream leaves the cyclone separator through the top outlet and heavy particulate matter is collected at the bottom.

Emperical models used to calculate the separation efficiency of the cyclone separator:

1. Iozia and Leith model

This model assumes that the particle carried by the vortex is controlled by centrifugal force and flow resistance. The collection efficiency is calculated from the below formula,

dpc is the 50% cut size given by barth model

2. Li and Wong model

This model includes particle re-enrtainment and turbulent diffuesion at the cyclone wall. This model was developed based on the assumption that the radial particle velocity and radial concentration profile are not constant for uncollected particles within cyclone. Boundary conditions with turbulent diffuesion coefficient and particle re-entrainment on the cyclone wall are given below,

The concentration distribution in a cyclone is given,

The collection efficiency for any given particle size is,

3. Kocht and Licht model

This model describes the particle motion in the entry and collection regions with assumptions that the tangential velocity of the particle is equal to tangential velocity of the gas flow and the tangential velocity and radius of the cyclone are related by .

The collection efficiency is given by,

4. Lapple model

This model was developed based on the force balance with out considering flow resistance. It was assumed that the particle enetring the cyclone is evenly distributed across the inlet. Lappel developed an emperical relationship to calculate 50% cut diameter and it is given by,

The number of revolution is given by,

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

The geometry of the cyclone separator and mesh generated and solution setup up remains same for both analysis 1 (varying diameter of particle by keeping flow vlocity as 3 m/s) and analysis 2 (varying the flow velocity for particle diameter 5e-6 meter).

Geometry of the cyclone separator:

Fluid volume extracted:

The fluid volume is extracted in spaceclaim by selecting the edges of inlet and outlets at the top and bottom.

Mesh generated:

The mesh is generated using structural cutcell method. The cut cell method is prefered as it fits the geometry perfectly and reduces the number of inaccuracies which propagates throughout domain.The cutcell method also helps to speed up the run time calculations as it cuts the volume cells at the wall and the mesh resolution is then independent of the geometry resoution. The other benefict of this method is that it refines the mesh near wall which leads to increase in the accuracy of the solution.

Number of cells - 112565

Number of nodes - 22915

Solution setup:

Discrete phase model - interaction with continuous phase(on)

- injection type (surface)

- surface selected for injection (inlet)

- flow velocity ( velocity is varied from 1 m/s to 5 m/s at diameter 5 um.)

- particle diameter (diameter is varied from 1e-6 m to 5e-6 m ay 3m/s velocity )

- flow rate (0.018375 kg/s)

Viscous model - K epsilon model

- RNG

- swirl dominated flow

Gravity enabled - 9.81 (negative y-axis)

Boundary conditions - Varied based on velocity

Discrete phase boundary conditions - inlet (reflect)

- outlet top (escape)

- outlet bottom (trapped)

Solution methods - Pressure velocity coupling scheme (coupled)

- pressure (second order)

- momentum (second order upwind)

- turbulent kinetic energy (second order upwind)

- turbulent dissipation rate (second order upwind)

Initialization - standard

Number of iterations - 600

The discrete phase consists of the smaller particulate matter which is assumed to be interacting with the continuous phase (ie, the fliud domain) and hence in DPM the interaction with continous phase in enabled. The k-epsolin RNG model is selected because it helps in enhancing the accuracy of the solution with swirl dominated flow. The discrete phase boundary conditions for inlet is set to reflect and for top outlet escaped and for bottom outlet trapped. The second order upwind is prefered for calculating turbulent kinetic energy and the turbulent dissipation rate as it is more accurate spacial discretisation scheme for swirl flows.

Analysis 1: To perform analysis on given cyclone separator model by verying the particle diameter from 1e-6 m to 5e-6 m for flow velocity equal to 3 m/s and to calculate separation efficiency in each case.

Case 1 - particle diameter = 1e-6 m and flow velocity = 3 m/s

Residual

Anthracite particle time contour

Vortex:

Case 2 - particle diameter = 5e-6 m and flow velocity = 3 m/s

Residual

Anthracite particle time contour

Vortex:

Calculation of separation efficiency for each case of analysis 1:

The formula to calculate seperation efficiency of the cyclone separator is given by,

Separation efficiency = (particles trapped/total particles tracked) * 100

The below table gives the details of particle data obtained from the analysis and the separation efficiency calculated for each case.

Analysis 2: To perform analysis of given cyclone separator model by varying flow velocity from 1 m/s to 5 m/s for particle diameter equal to 5e-6 m and calculate separation efficiency and pressure drop.

Case 1: Flow velocity = 3 m/s and particle diameter = 5e-6 m

Residual

Case 2: Flow velocity 1 m/s and particle diameter = 5e-6 m

Residual

Case 3: Flow velocity = 5 m/s and particle diameter = 5e-6 m

Residual

Calculation of separation efficiency and pressure drop for each case of analysis 2:

The formula for calculating separation efficiency of the cyclone separator is given by the formula,

Separation efficiency = (particles trapped/total particles tracked) * 100

The formula for calculating pressure drop,

Pressure drop = pressure at inlet - pressure at outlet

The below table gives the detailes of particle data obtained from the analysis 2 and the separation efficiency and pressure drop calculated for each case.

Conclusion:-

• The anthracite time particle contour shows the change in location of the particles with respect to residence time of the particle. In analysis 1, it is observed that the particle with larger diameter takes less time to reach the outlet at bottom and vice versa. In analysis 2, it is observed that the particle with high flow velocity takes less time to reach the outlet at bottom.
• In both the analysis, it is observed that the particles expearince higher velocity near the barrel or middle cyclinder part of the cyclone separator and hence the particles face high pressure near the barrel or middle cylinder part of the cyclone separator.
• In analysis 1, it is observed that the separation efficiency increases as the particle diameter increases.
• In analysis 2, it is observed that the separation efficiency increases as the flow velocity of the particle increases and hence the pressure drop of the cyclone separator also increases.