Week 8 - 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 μm to 5 μm 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 μm 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.

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 m tall (about 4-5 feet) to around 9 meters (30 feet)—which is about as tall as a three-story building.

Working of Cyclone Separator:

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. 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.

Empirical Model for Cyclone efficiency

Model 1: 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:

β is an expression for slope parameter derived based on the
statistical analysis of experimental data of a cyclone with D = 170
0.25 m given as:

and dpc is the 50% cut size given by Barth:

where core length, zc, and core diameter, dc, are given as

Model 2: Li and Wang Model

The Li and Wang [3] 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
• The profile is not constant for uncollected particles within the cyclone.

Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce entrainment on the cyclone wall are:

Model 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 described 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 the cyclone by u Rn = constant.

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

Model 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 [1] to calculate a 50% cut diameter, dpc, is:

PROCEDURE

the following procedure is followed in performing the simulation and extracting the results

Step 1 - Geometry setup:

• Import the given geometry in SpaceClaim
• Extract the fluid volume from the geometry. Prepare -> extract volume -> select edges
• Suppress the given geometry for physics.

Step 2 - Mesh:

Element size=5mm

No. of elements=427871

Named selections are assigned to identify the inlets and outlets of the domain

Step 3 - Setting up Physics:

• Pressure based, steady-state solver. Gravity = 9.81 m/s2
• Model: K-Epsilon -> RNG, Swirl Dominated Flow
• Model: Discrete Phase model -> Interaction with continuous phase, update DPM sources every flow iteration, Max no of steps -> Create Injections

• Boundary Conditions: Inlet -> velocity, DPM = reflect, Outlet top -> DPM = escape, Outlet bottom -> DPM = trap, walls -> DPM = reflect

Step 4 - Method:

Step 5 - Initialization: Standard initialization

Step 6 - Run the simulation: enter no of iterations, run the simulation

Step 7 - Extract the results: Check convergence from residuals, particle tracking

Results

Variations of Particle diamater

Case I: Particle vel= 3m/s, Particle diameter=5e-6 m

Pressure drop

Particle time

Case II

Particle vel= 3m/s, Particle diameter=3e-6 m

Pressure drop

Particle time

Case III

Particle vel= 3m/s, Particle diameter=1e-6 m

Pressure drop

Particle time

The table given below shows the effect of variations of particle size on the separation efficiency and pressure drop.

Sl no.	Size of Particle (m)	Velocity of Particle (m/s)	Particle tracked	Particle trapped	Particle escaped	Separation efficiency (%)	Pressure drop (Pa)
1	1e-6	3	378	243	135	64.3	26.86
2	3e-6	3	378	280	98	74	26.86
3	5e-6	3	378	304	74	80.42	26.86

Variations of Particle velocity:

Case I: Velocity= 1m/s, Diameter=5e-6 m

Residual

Pressure drop

Particle time

Case II: Velocity= 5m/s, Diameter=5e-6 m

Residual

Pressure drop

Particle time

The table given below shows the effect of variations of particle velocity on the separation efficiency and pressure drop.

Sl no.	Size of Particle (m)	Velocity of Particle (m/s)	Particle tracked	Particle trapped	Particle escaped	Separation efficiency (%)	Pressure drop (Pa)
1	5e-6	1	378	243	135	64.3	12.4
2	5e-6	3	378	250	128	66.1	26.86
3	5e-6	5	378	253	125	66.9	48.3

CONCLUSION

Based on the results obtained in the previous section, we can make the following conclusion

1. The efficiency of cyclone separators of the same size and configuration decreases as the particle size decreases.
2. The efficiency of the cyclone separator is directly proportional to the flow velocity of the particulate. i.e. high-velocity yields higher efficiency
3. Pressure drop only depends on the velocity of the particles. As the velocity increases the pressure difference between inlet and outlet pressure increases.
4. As the size of the particle decreases and the velocity of the flow decreases, the time taken for convergence also increases. So to overcome this, the maximum no of steps in tracking parameters need to be increased.