Title: Mitigation of Preferential Concentration due to electric charge in the dispersed phase
1Mitigation of Preferential Concentration due to
electric charge in the dispersed phase
2Overview
- Introduction
- Simplifying assumptions / Numerical method
- Measures of preferential accumulation
- Stokes number dependence
- Dependence on Re ?
- Charged particle simulations
- Conclusions
3The problem in physical space
- Dispersed phase flows
- continuous phase (fluid)
- dispersed phase (particles)
4Dispersed 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
5Governing 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
6Numerical 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
7Numerical 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
8Simulation 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
9Points 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
10Evidence of preferential concentration
Re? 24.24, St 4.00
Re? 24.24, St 0.25
S. Scott, Ph.D. thesis, Imperial College London,
2006
11Clustering 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.
12Measures 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
13D2 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)
14D2 probability to find 2 particles at a
distance less than a given r P(r) rD2
D2 data for different cases compared to literature
15Binning 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
16D, 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
17D measure of accumulation
Re 24
- Bin size used is corresponding to peak value of
D.
18ltnegt correlation between number density and
enstrophy
19Observations
- 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
20Destruction using Lorentz forces
A. Karnik and J. Shrimpton, ILASS 2008, Sept
8-10, 2008
21Particle 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
22Evidence 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
23Evidence 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
24Parametric 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
25Effect 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.
26Schematic 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
27Conclusions
- 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.