Week 8 - Simulating Cyclone separator with Discrete Phase Modelling

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

Introduction

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 large pieces of particulate matter. This prevents final filtration methods from having to deal with large, more abrasive particles later on. In addition, several cyclone separators can operate in parallel and this system is known as multi cyclone.

• It is important to note that cyclones can vary drastically in their size. 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 size can range from a relatively small 1.2 to 1.5 m tall (about4-5 feet) to around 9 meters (30 feet) which is about as tall as a three Storey building.

Remove components from cyclone separators

• Dust
• Particles: Abrasive, corrosive adhesive explosive.
  

Process description:

Working principle

Cyclone is a centrifugal separator in which particles, due to their mass are pushed to the outer edges as a result of centrifugal force. incoming air is automatically forced to adopt a fast-revolving spiral movement. The so-called double vertex. this double spiral movement consists of an outer stream, which flows downwards in spiral and inner stream, which flows upwards in a spiral. at the interchange between both streams, air passes from one stream to another. the particles which are present in air re-forced to the outer edges and leave the separator via collection device fitted to the bottom of the separator.

Airspeed of the cyclone lies between 10 to 20 m/s and the most common speed is 16 m/s. if there are fluctuation in speed (with lower speeds), separation yield falls quite drastically.

Most cyclones are built to control and remove particulate matter that is larger than 10 micrometers in diameter. However, there do exist high-efficiency cyclone 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.

Out of all of the particulate control devices. cyclone separators are the least expensive. they are often used as a pre-treatment before the flue gas enters more effective pollution control devices. Therefore, cyclone separators can be seen as “rough separators” before the flue gas reaches the filtration stage.

Effectiveness:

Cyclone separators are generally able to remove somewhere between 50-90% of all particulate matter in the flue gas. How well the cyclone separators are actually able to remove this matter depends largely on particle size. If there is a large amount of lighter particulate matter, less of these particles are able to be separated out. Because of this, cyclone separators work best on flue gases that contains large amount of big particulate matter.

There are several advantages and disadvantages of using cyclone separators. First, cyclone separators are beneficial because they are not expensive to install or maintain, and they have no moving parts. This keeps maintenance and operating costs low. Second, the removed particulate metal is collected when dry, which makes it easier to dispose of. Finally, these units take up very little space. Although effective, there are also advantages in using cyclone separators. Mainly because the standard models are not able to collect particulate matter that is smaller than 10 micrometers effectively and the machines are unable to handle sticky materials.

Empirical models for cyclone separator efficiency:

1. Iozia and Leith model
   Iozia and Leith logistic model is a modified version of Barth model (1956) 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.
   the collection efficiency `n_i` of particle diameter `d_(text(pi))` can be calculated by.
   `n_i=1/(1+(d_(pc)/d_text(pi ))^β )`
   `beta` is an expression for slope parameter derived based on the statistical analysis of experimental data of a cyclone with D=0.25m given as
   `β=0.62-0.87ln(d_(pc)/100)+5.12ln((ab)/D^2 )+1.05[ln((ab)/D^2 )]^2`
   and `d_pc` is the 50% cut size given by Birth
   
   `d_(pc)=[[9μQ]/(πρ_p z_c v_(t max )^2 )]^(0.5)`
   

   where, core length `z_c`, and core diameter `d_c` are given as:
   
   `z_c=(H-S)-[(H-S)/(D/B-1)][d_c/B-1]` for `d_c>B`
   
   `z_c=H-S` for `d_c<B`
   
   `d_c=0.47D([ab]/D^2 )^(-0.25) (D_e/D)^(1.4)`
   
   

Li and wang model:

The Li and wang model include 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:

1. The radial particle velocity and the radial concentration profile are not constant, for uncollected particles within the cyclones.
2. Boundary conditions with the consideration of turbulent diffusion coefficient and particle bounce re-entrainment on the cyclone wall are:
   `c=c_0` at `theta=0`
   `D_r (∂c)/(∂r)=(1-α)wc,` at r=D/2
   the tangential velocity is related to the radius of cyclone by:
   `uR^n=`constant
   the concentration distribution in a cyclone is given by
   `c(r,θ)=(c_0 (r_w-r_n ) exp⁡{-λ[1/[K(1+n)] r^(1+n) ]})/(∫_(r_n)^(r_w)exp⁡{ 1/(K(1+n)) r^(1+n)}dr)`
   
   `K=((1-n)(ρ_p-ρ_g ) d^2 Q)/(18μb(r_w^(1-n)-r_n^(1-n)))`
   `λ=((1-α)Kw_w)/(D_r r_w^n )`
   the resultant expression of the collection efficiency for particle of any size is given as
   
   `n_i=1-exp⁡{-λθ_1}`
   `θ_1=(2π(S+L))/a`
   
   
   

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:

1. 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 `uR^n=`constant
a force balance and an equation on the particle collection yields the grade efficiency `eta_i`

`η_i=1-exp⁡{-2[(Gτ_i Q)/D^3 (n+1)]^(0.5/(n+1))}`
`G=(8K_c)/(K_a^2 K_b^2 )`
`n=1-{1-(12D)^0.14/2.5} {(T+460)/530}^0.3`
`τ_i=(ρ_p d_pi^2)/[18μ]`
G is a factor related to the configuration of the cyclone, n is related to the vortex and `tau` is the relaxation term.

Lapple model
Lapple model was developed based on force balance without considering the flow resistance. Lapple assume that a particle entering the cyclone is evenly distributed across the inlet opening. A particle that travels from inlet of half-width to the wall in the cyclone is collected with 50% efficiency. The semi empirical relationships developed by Lapple to calculate a 50% cut diameter,`d_{pc}` is

`d_[pc]=[[9μb]/(2πN_e v_i (ρ_p-ρ_g ) )]^(1/2)`
where `N_e` is the number of revolutions

`N_e=1/a[h+(H-h)/2]`
the efficiency of collection of any size of particle is given by

`η_i=1/(1+([d_[pc]]/[bard_text[pi]] )^2 )`
Applications:

• Chemical and petroleum processes.
• Industrial, metallurgical and power generation.
• Food and pharmaceutical.
• Cement industry.

Case setup

• geometry
  • import geometry in SpaceClaim.
    
    imported geometry

extracted volume

• Meshing
  • create a baseline mesh
    Baseline mesh
    
  • refine the mesh.
    Refined mesh(5mm) setting
    

  • insert meshing method

    • select geometry
    • change method to cartesian
      
      Final mesh
      
• Setup
  
  • General setting
    
    • Solver type: pressure based
    • velocity formulation: Absolute
    • time: steady state
    • gravity enabled with the y-axis value -9.81`ms^-2`
      
  • viscous model
    
    • RNG K-epsilon with swirl dominated flow with standard wall function
      
  • Discrete phase model
    • Interaction with continuous phase enabled.
    • tracking parameters
      • max. no. of steps: 50000
      • step length factor: 5
        
    • Injections
      • create a injection
        • injection name: injection 0
        • injection type: surface
        • injection surface: inlet
        • particle type: inert
        • material: anthracite
        • diameter distribution: uniform
        • velocity inlet: as per case requirement (for case-1 we have 3 `ms^-1`)
        • diameter: as per case requirement ( for case-1 we have 1`mum`)
        • Total flow rate: `1e-20 kgsec^-1`
          
          
    • Boundary conditions
      • inlet type: velocity(3`m/sec`)
        
        
      • DPM: Reflect
        
        
      • Outlet-1 (Top): pressure outlet (0 Pa gauge pressure)
        
      • DPM: escape
        
        
      • Outlet-2(bottom): pressure outlet(0 Pa gauge pressure)
        
      • DPM: Trap
        
      • Wall type: wall
      • DPM: Reflect
        
        
  • Report definition
    • create a report definition for pressure at inlet, outlet-1 and outlet-2
      
    • Initialization
      
      • standard initialization from inlet.
        
      • Run simulation for 600 iterations

Result

Part-1

case 1( Velocity: 3`m/sec` Particle diameter:`1\mu m`)

case 2 ( Velocity: 3`m/sec` Particle diameter:`3\mu m`)

case 3( Velocity: 3`m/sec` Particle diameter:`5\mu m`)

Part-2

case 1 ( Velocity: 1`m/sec` Particle diameter:`5\mu m`)

case 2 ( Velocity: 3`m/sec` Particle diameter:`5\mu m`)

case 3 ( Velocity: 5`m/sec` Particle diameter:`5\mu m`)

Separation efficiency

it is defined as the fraction of particles of a given size collected in the cyclone, compared to those of that size going into the cyclone. Experience shows that the separation efficiency of the cyclone separator increases with increasing particle mean diameter and density, increasing gas tangential velocity, decreasing cyclone diameter, increasing cyclone length, extraction of gas along with solid through the cyclone legs.

In this case, 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. for this case ratio of the number of trapped particles to the total number of particles tracked.

`text[Separation Efficiency]=text[No. of Particles Trapped]/text[No. of Particles Tracked]`

Pressure drop

pressure drop across the cyclone is of much importance in a cyclone separator. The pressure drop significantly effects the performance parameters of a cyclone. the total pressure drop in a cyclone will be due to the entry and the 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.

`text[Pressure Drop]=text[Total inlet Pressure]-text[Total outlet pressure]`

As the 'escape" DPM condition is given to the Outlet-top in this case, So outlet-top is considered in pressure drop calculation.

Output Result Table

Part-1

S. No.	Particle size (`mu`m)	Velocity of particle `(m/sec)`	No. of particle tracked	No. of particle trapped	Separation Efficiency	Pressure inlet (Pa)	Pressure outlet (bottom) (Pa)	Pressure Drop (Pa)
1	1	3	378	230	0.61	25.63	-0.01	25.64
2	3	3	378	297	0.79	25.63	-0.01	25.64
3	5	3	378	364	0.96	25.63	-0.01	25.64

Part-2

S. No.	Particle size (`mu`m)	Velocity of particle `(m/sec)`	No. of particle tracked	No. of particle trapped	Separation Efficiency	Pressure inlet (Pa)	Pressure outlet (bottom) (Pa)	Pressure Drop (Pa)
1	5	1	378	221	0.58	1.89	-2.9e-4	1.89029
2	5	3	378	285	0.75	18.64	-4.39e-6	18.64
3	5	5	378	350	0.93	53.06	-0.01	53.07

• We can see from above tables that in part-1 cases, efficiency of separation increases with increasing particle diameter and in part-2 cases with increment of velocity.
• Also we can observe that in part-1 cases separation efficiency increases in casual manner with increase in particle diameter.
• But in part-2 cases separation efficiency increases rapidly with increase in velocity. it is because the pressure drop has more impact in cyclone separator efficiency.
• In part-1 cases particle residence time first increases then decreases with increase of diameter.
• In part-2 cases particle residence time first increases then decreases with increase of velocity.
  
  
  

Conclusion

• From the observations of part-1 and part-2 we can conclude that separation efficiency of cyclone separator depends on both particle diameter and velocity
• Efficiency of cyclone separator has direct effect on the pressure drop.
• Higher efficiency cyclones has highest pressure drops.
• higher the velocity, higher the pressure drop, highest the efficiency.
• with the increase of diameter of particle and velocity of particle , particle residence time decreases.
• So, when less resident time taken by the particles, efficiency of the cyclone separator can be high.