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Title: Mitigation of Preferential Concentration due to electric charge in the dispersed phase


1
Mitigation of Preferential Concentration due to
electric charge in the dispersed phase
2
Overview
  • Introduction
  • Simplifying assumptions / Numerical method
  • Measures of preferential accumulation
  • Stokes number dependence
  • Dependence on Re ?
  • Charged particle simulations
  • Conclusions

3
The problem in physical space
  • Dispersed phase flows
  • continuous phase (fluid)
  • dispersed phase (particles)

4
Dispersed phase flows
Particles
Fluid
  • One-way coupling
  • Particles do not influence fluid motion
  • Point particles
  • Particle wakes are not resolved
  • Particle diameter ltlt kolmogorov length scale
  • Particle motion is governed only by drag
  • Gravitational force not modelled
  • Particle collisions not modelled (dilute
    suspension)
  • Particle density gtgt fluid density
  • Particles are stochastic for the purpose of
    charged particle simulations
  • Incompressible, homogeneous, isotropic
  • Stationarity obtained using artificial forcing

5
Governing equations
Particles
Fluid
Modified Stokes drag law (Valid for Rep lt 800)
Large-scale forcing function added to maintain
stationary turbulence
Symbols have usual meanings
6
Numerical scheme (Fluid)
Particle
Fluid (pseudo-spectral method)
(suppose)
  • dealiasing by 2/3rd rule
  • temporal discretization using RK3
  • stochastic forcing scheme to sustain kinetic
    energy

V. Eswaran and S.B. Pope, Computers and Fluids,
Vol. 16(3), pp. 257-278, 1988
7
Numerical Method (summary)
  • The turbulence is limited to homogeneous,
    isotropic case (HIT) in a periodic cube.
  • Particles are not resolved.
  • Force on particles is due to Stokes drag.
  • One way coupling between fluid and particles

8
Simulation parameters
Stokes Number
Rayleigh Number
where,
  • Mono-sized particles
  • number of particles (Np) 100000
  • particle stokes numbers
  • Stk 0.2 - 20
  • Same charge on all particles (Ra 0.8,
    ? 0.05)
  • space charge densities (µC/m3) 5, 10, 25,
    50, 100

9
Points to note -
  • All simulations for a given Re, are restarted
    from same fluid realisation.
  • Statistics are collected only after fluid has
    reached stationary state.
  • Particle distribution is assumed to reach
    stationary state when the positions are
    completely de-correlated from initial position.

Particle rms velocity
Turbulent kinetic energy
10
Evidence of preferential concentration
Re? 24.24, St 4.00
Re? 24.24, St 0.25
S. Scott, Ph.D. thesis, Imperial College London,
2006
11
Clustering at different scales
  • Clustering occurs broadly at 2 scales
  • Dissipative scales
  • particles are centrifuged out of coherent eddies
    and accumulate in low-vorticity regions.
  • Inertial range
  • clustering is a multi-scale phenomenon.
  • Eddies larger than Kolmogorov length scale play a
    part in clustering.

12
Measures of Accumulation
  • Dissipative range measures
  • D ( Fessler et al., 1994 )
  • Dc ( Wang and Maxey, 1993 )
  • Dn
  • Inertial (multi-scale) measures
  • RDF ( Sundaram and Collins, 1997 )
  • D2
  • Fluid-particle correlation measures
  • ltnegt, correlation between number density and
    enstrophy
  • ln, number density correlation length scale

13
D2 measure
r
  • Correlation integral, C(r) number of particles
    within range r of any given particle
  • D2 is slope of curve log( C(r) ) vs log( r )
  • D2 is equal to the spatial dimension for uniform
    distribution (equal to 3 for a 3D distribution)

14
D2 probability to find 2 particles at a
distance less than a given r P(r) rD2
D2 data for different cases compared to literature
15
Binning of particles
h
h scale used for binning particles
n number density i.e no. of particles / bin
volume
ltncgt mean number density i.e total particles /
volume of cube
16
D, Dc deviation from poisson distribution
  • Dc, D Deviation from poisson distribution

Pc probability of finding cells with given
number of particles k number of particles in
a cell
L.P. Wang and M.R. Maxey, J. Fluid Mech., Vol.
256, pp. 27-68, 1993
J.R. Fessler, J.D. Kulick and J.K. Eaton, Phys.
Fluids, Vol. 6(11), pp. 3742-3749, 1994
17
D measure of accumulation
Re 24
  • Bin size used is corresponding to peak value of
    D.

18
ltnegt correlation between number density and
enstrophy
19
Observations
  • D and Dc measures clearly depend on bin-size
  • Dependence of Re is attributed to less number of
    smaller particle structures at higher Re.
  • D2 measure looks at probability of finding
    particles in shells around a given particle
  • Shows nearly no dependence on Re
  • ltnegt and ln capture distribution of particle
    number density
  • Show dependence on Re

20
Destruction using Lorentz forces
A. Karnik and J. Shrimpton, ILASS 2008, Sept
8-10, 2008
21
Particle position, fluid velocity
Re? 24.24, St(k) 1.6, Qv100µC/m3
Re? 24.24, St(k) 1.0, Qv5µC/m3
S. Scott, Ph.D. thesis, Imperial College London,
2006
22
Evidence of preferential concentration destruction
Re? 24.24, St(k) 1.6, Qv100µC/m3
Re? 24.24, St(k) 1.0, Qv5µC/m3
S. Scott, Ph.D. thesis, Imperial College London,
2006
23
Evidence of preferential concentration destruction
Re? 24.24, St(k) 1.6, Qv100µC/m3
Re? 24.24, St(k) 1.0, Qv5µC/m3
S. Scott, Ph.D. thesis, Imperial College London,
2006
24
Parametric study of bulk charge density levels
St 0.25 for all plots
  • Space charge density of 25-50 µC/m3 is sufficient
    to destroy preferential accumulation
  • With increasing Reynolds number, greater charge
    density is required to significantly destroy
    accumulation

25
Effect of Stokes Numbers
Re? 24.2
Re? 81.1
  • Charged particle systems continue to exhibit same
    trends with Reynolds and Stokes numbers as the
    charge-free case.

26
Schematic of a spray released from a charged
injection atomizer
  • d0 500 µm, Q0 0.5 C/m3, ? 45o
  • The charge level found in this study (50 µC/m3)
    corresponds to an area about 2 cm from the nozzle
    tip

27
Conclusions
  • Preferential accumulation is maximum at St 1.0
    based on kolmogorov scale, for all the measures
    used in this study.
  • While ln shows clear dependence on Re, D2 is
    insensitive to Re.
  • Bulk charge density level of 50 µC/m3 is
    sufficient to significantly destroy preferential
    accumulation. This has been consistently observed
    using different sensors for preferential
    accumulation.
  • The required charge density level mentioned above
    is attainable within 2 cms from tip of a nozzle
    in practical charge injection atomizers.
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