Project

Numerical Analysis of cyclone separator using discrete phase model DPM

GGirish S2 Apr 2020

Abstract: Cyclone separators are separation devices that use the principle of inertia to remove particulate matter from flue gases. Numerical analysis of cyclone separators are essential in determining the performance efficiency of cyclone separator by determining the percentage of particulate matter removed from carrier gases.

In present work, Discrete phase modelling(dpm) method is used to numerically simulate the cyclone separator which separates particulate matter anthracite(of diameter 5 micrometer) from carrier gas air. RNG `k-epsilon` turbulence model is implimented since the effect of swirl on turbulence is included in the RNG model, enhancing accuracy for swirling flows.

In analysis one, three different mesh configurations are adopted in order to vary the number of particles through the inlet.In analysis two, four different dpm boundary conditions i.e. reflect,trap,escape and wall-jet is being implimented at the inlet.

Cyclone separator:

Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices known as precleaners since they generally remove larger pieces of particulate matter.

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.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.

Cyclone efficiency empirical models:

1. Iozia and Leith Model

Iozia and Leith 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.

The collection efficiency `eta_i` of particle diameter `d_(p i)` can be calculated from

`eta_i=frac{1}{1+(d_(pc)/d_(p i))^beta}`

where, `beta` is an expression for slope parameter derived based on the statistical analysis of experimental data of a cyclone with D = 0.25 m

`d_(pc)` is the 50% cut size given by Barth

`d_(pc)=[frac{9muQ}{pirho_pz_cv_(tmax)^2}]^0.5`

where, `z_c` is the core length for core diameter `d_c`

For `d_c>B`, `z_c=(H-S)-[frac{H-S}{(D/B)-1}][(d_c/B)-1]`

For `d_c < B`, `z_c=H-S`

`d_c= 0.47D(frac{ab}{D^2})^-0.25(D_e/D)^1.4`

2. Li and Wang Model:

The Li and Wang model includes particle bounce or reentrainment and turbulent diffusion at the cyclone wall. A twodimensional analytical expression of particle distribution in the cyclone is obtained. Li and Wang model was developed based on the following assumptions:

i. The radial particle velocity and the radial concentration profile are not constant for uncollected particles within the cyclone.

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

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iii. The tangential velocity is related to the radius of cyclone by: `uR^n` = constant.

The concentration distribution in a cyclone is given as:

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

`eta_i= 1-exp{-lamdatheta_1}`

where, `theta_1=2pi(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 described particle motion in the entry and collection regions with the additional following assumptions:

i. The tangential velocity of a particle is equal to the tan- gential velocity of the gas flow, i.e. there is no slip in the tangential direction between the particle and the gas.

ii. The tangential velocity is related to the radius of cyclone by: `uR^n` = constant.

A force balance and an equation on the particles collection yields the grade efficiency ,`eta_i`,given by

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

where,

G is the factor related to configuration of cyclone

n is related to vortex

`tau` is relaxation term

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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, dpc, is

`d_(pc)=[(9mub)/(2piN_ev_i(rho_p-rho_g))]^0.5`

where,

`N_e` is the number of revolutions

`N_e=1/a[H+(H-h)/2]`

the collection efficiency for particle of any size is given as

`eta_i= 1/(1+(d_(pc)/bar(d)_(p i))^2`

Discrete Phase Model(DPM):

The discrete phase model follows the Euler-Lagrange approach.The fluid phase is treated as a continuum by solving the Navier-Stokes equations, while the dispersed phase is solved by tracking a large number of particles, bubbles, or droplets through the calculated flow field. The dispersed phase can exchange momentum, mass, and energy with the fluid phase.

A fundamental assumption made in this model is that the dispersed second phase occupies a low volume fraction, even though high mass loading is acceptable.This makes the model appropriate for the modeling of spray dryers, coal and liquid fuel combustion, and some particle-laden flows, but inappropriate for the modeling of liquid-liquid mixtures, fluidized beds, or any application where the volume fraction of the second phase cannot be neglected.

Geometry Preparation:

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1. above figure shows the solid model of cyclone separator fro which fluid volume has to be extracted in order to perform flow analysis. This is done by using volume extract option in spaceclaim by selecting edges of all the inlets and outlets of the fluid flow. The extracted fluid volume geometry is shown below

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Analysis I: Numerical analysis of cyclone separator by using three different mesh configurations in order to vary the number of particles inlet to cyclone separator.

Mesh:

Case 1:

Element size: 12 mm

Number of elements: 273012

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Case 2:

Element size: 10 mm

Number of elements: 411139

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Case 3:

Element size: 8 mm

Number of elements: 709527

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Setup:

I. General:

Solver: Pressure-based

Time: steady

Gravity(m/s2): -9.81 (Y-direction)

Pressure-based solver: The pressure-based solver employs an algorithm which belongs to a general class of methods called the projection method . In the projection method, wherein the constraint of mass conservation (continuity) of the velocity field is achieved by solving a pressure (or pressure correction) equation. The pressure equation is derived from the continuity and the momentum equations in such a way that the velocity field, corrected by the pressure, satisfies the continuity. Since the governing equations are nonlinear and coupled to one another, the solution process involves iterations wherein the entire set of governing equations is solved repeatedly until the solution converges.

II. Models:

Viscous: RNG `k-epsilon` turbulence model(swirl dominated flow enabled, swirl factor=0.07)

RNG `k-epsilon` turbulence model: RNG `k-epsilon` turbulence model was derived using a rigorous statistical technique (called renormalization group theory). It is similar in form to the standard `k-epsilon` model, but includes the following refinements:

The RNG model has an additional term in its `epsilon` equation that significantly improves the accuracy for rapidly strained flows.

The effect of swirl on turbulence is included in the RNG model, enhancing accuracy for swirling flows.

The RNG theory provides an analytical formula for turbulent Prandtl numbers, while the standard `k-epsilon` model uses user-specified, constant values..

Discrete phase Model:

Interaction- interaction with contnious phase

Injection: Anthracite (Inert)

Injection Type: surface(Inlet)

Diameter(m)= 5e-06 (uniform)

Velocity Magnitude(m/s)= 3 (Inject using face normal direction enabled)

Total mass flow rate: 1e-20

III. Materials:

1. Fluid: Air (acting as carrier gas)

Density(kg/m^3) : 1.225

Dynamic viscosity(kg/m-s) : 1.7894e-05

2. Inert : Anthracite (particulate matter)

Density(kg/m^3) : 1550

IV. Boundary conditions:

Appropriate boundary conditions haved been applied according to the physics of the flow.

1. At Inlet: (Inlet named to the inlet of the cyclone separator)

Velocity inlet of magnitude 20 m/s normal to boundary,

Discrete phase BC Type: Reflect

Turbulent intensity(%)= 5 and turbulent viscosity ratio= 10.

2. At outlet_upper: (outlet_upper named to the upper oulet of cyclone separator)

Pressure outlet at zero gauge pressure(atmospheric pressure),

Turbulent intensity(%)= 5 and turbulent viscosity ratio= 10.

Discrete phase BC Type: Trap (Trap BC is set in order to count the number of particles escaping through the upper outlet,which will help us to determine the effectiveness of the cyclone separator)

3. At outlet_lower: (outlet_lower named to the lower oulet of cyclone separator)

Pressure outlet at zero gauge pressure(atmospheric pressure),

Turbulent intensity(%)= 5 and turbulent viscosity ratio= 10.

Discrete phase BC Type: escape (the number of particles that escaped through the lower oulet can be determined, which will help us to determine the effectiveness of the cyclone separator)

V. Numerical schemes:

1. Pressure velocity coupling: SIMPLE

The SIMPLE algorithm uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field.

2. Spatial discretization:

Gradient: Least squares cell based

Pressure: Second order

Momemtum: Second order upwind

Turbulent kinectic energy: second order upwind

Turbulent dissipation energy : Second order upwind

VI. Initialization:

Initialization: Standard

Compute from: Inlet

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Residual plots:

Case 1:

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Case 2:

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Case 3:

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In case 1 and case 2, the residuals have dropped considerably and settled down at 900 iteration,hence assumed converged. In case 3, residuals show repeated pattern of fluctuations,hence considered converged.

Results:

Case 1:

1. Particle time contour:

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2. Particle tracking Information:

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3. Particle velocity contour:

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4. Velocity contour at centre plane:

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5. Particle flow animation:

Case 2:

1. Particle time contour:

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2. Particle tracking Information:

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3. Particle velocity contour:

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4. Velocity contour at centre plane:

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5. Particle flow animation:

Case 3:

1. Particle time contour:

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2. Particle tracking Information:

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3. Particle velocity contour:

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4. Velocity contour at centre plane:

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5. Particle flow animation:

Analysis I Discussions:

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1. From above table, we can observe that as the mesh element size decreases, The number of particles tracked in dpm model increases, (226 particles tracked in case of 12 mm,364 particles tracked in case of 10 mm and 498 particles tracked in case of 8 mm). When the mesh gets finer, the number of elements at inlet face increases, hence the number of particles entering throught inlet increases.

2. Note: Boundary outlet_upper has been given Trap boundary condition, in order to count the number of particles escaping through the upper outlet(which is undesired).

3. From above table and animation of cases, we can observe that in all three cases, Particles has escaped through lower outlet(which is desired) and particles escpaing throught upper outlet is zero. Therefore we can conclude that, For particle size of 5 micrometer, the cyclone separator has resulted in 100 percent efficiency in separating the particles,therefore the dimensions of cyclone separator is appropriate for particle size of 5 micro meter.

4. Comparing the number of Incomplete particles in case 1,case 2and case 3, Decrease in element size(finer mesh) has resulted in decrease in number of incomplete particles.

5. Comparing the particle time and velocity contours of particles, we can observe that the particles inlet the cyclone separator at 3 m/s.As the particles gets carried in the vortex flows, the velocity of the particles decrease as the particles reaches the lower outlet, hence higher particle time can be observed near the lower outlet of the flow.

6. Form velocity contour at centre plane, we can observe that the velocity at the centre of the swirl is close to zero,and the intensity of swirl is maximum at the centre of cyclone separator(since the low velocity region is thin), and diameter of low velocity region increases near the outlets.

Analysis II: To Analysis various dpm boundary conditions by implimenting on inlet boundary

DPM boundary conditions:

1. Reflect: The particle rebounds off the boundary in question with a change in its momentum as defined by the coefficient of restitution. The reflect type is assumed at wall, symmetry, and axis boundaries, with both coefficients of restitution equal to 1.0

2. Trap: The trajectory calculations are terminated and the fate of the particle is recorded as \"trapped\'\'.In the case of evaporating droplets, their entire mass instantaneously passes into the vapor phase and enters the cell adjacent to the boundary.In the case of combusting particles, the remaining volatile mass is passed into the vapor phase.

3. Escape: The particle is reported as having \"escaped\'\' when it encounters the boundary in question. Trajectory calculations are terminated. The escape type is assumed at all flow boundaries (pressure and velocity inlets, pressure outlets, etc.)

4. Wall-Jet: The direction and velocity of the droplet particles are given by the resulting momentum flux, which is a function of the impingement angle φ, and weber number. The \"wall-jet\" type boundary condition is appropriate for high-temperature walls where no significant liquid film is formed, and in high-Weber-number impacts where the spray acts as a jet.

5. Wall-film: This boundary condition consists of four regimes: stick, rebound, spread, and splash, which are based on the impact energy and wall temperature.

6. Interior: This boundary condition means that the particles will pass through the internal boundary. This option is available only for internal boundary zones, such as a radiator or a porous jump. The interior type is assumed at all internal boundaries (radiator, porous jump, etc.)

Mesh:

Element size: 10 mm

Number of elements: 411139

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Setup:

I. General:

Solver: Pressure-based

Time: steady

Gravity(m/s2): -9.81 (Y-direction)

II. Models:

Viscous: RNG `k-epsilon` turbulence model(swirl dominated flow enabled, swirl factor=0.07)

Discrete phase Model:

Interaction- interaction with contnious phase

Injection: Anthracite (Inert)

Injection Type: surface(Inlet)

Diameter(m)= 5e-06 (uniform)

Velocity Magnitude(m/s)= 3 (Inject using face normal direction enabled)

Total mass flow rate: 1e-20

III. Materials:

1. Fluid: Air (acting as carrier gas)

Density(kg/m^3) : 1.225

Dynamic viscosity(kg/m-s) : 1.7894e-05

2. Inert : Anthracite (particulate matter)

Density(kg/m^3) : 1550

IV. Boundary conditions:

Appropriate boundary conditions haved been applied according to the physics of the flow.

1. At Inlet: (Inlet named to the inlet of the cyclone separator)

Velocity inlet of magnitude 20 m/s normal to boundary,

Discrete phase BC Type: Reflect(for case 1), Trap(for case 2), escape (for case 3), Wall-jet(for case 4).