Mitigation of Preferential Concentration due to electric charge in the dispersed phase I m going to talk about my work in last 2 years. I m going to keep this fairly simple bcos its only the simple thing tht I understood and the complex things, I have left for future work.

Overview Introduction Simplifying assumptions / Numerical method Measures of preferential accumulation Stokes number dependence Dependence on Re ? Charged particle simulations Conclusions Numerical method – I would focus on particle assumptions Lets put things in context: We sent a paper claiming that accumulation goes down with Re, and we got a review saying it doesn’t. So what is going on ? If you feel I am going back and forth between slides too much and you feel lost, don’t hesitate to stop me and ask whats going on

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

Dispersed phase flows Particles: Fluid: One-way coupling Particles do not influence fluid motion Point particles Particle wakes are not resolved Particle diameter << kolmogorov length scale Particle motion is governed only by “drag” Gravitational force not modelled Particle collisions not modelled (dilute suspension) Particle density >> fluid density Particles are “stochastic” for the purpose of charged particle simulations Incompressible, homogeneous, isotropic Stationarity obtained using artificial forcing Be confident about each of the particle assumptions

Governing equations Particles: Fluid: Modified Stokes drag law (Valid for Rep <= 800) Large-scale forcing function added to maintain stationary turbulence *Symbols have usual meanings

Numerical scheme (Fluid) Fluid (pseudo-spectral method): Particle: (suppose) Skip this fast ! 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

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 If using a school logo, make sure that if you have a long page title, it does not encroach on the logo. Allow about 2cm around the logo. Run the page title onto two lines if necessary.

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, γ = 0.05) space charge densities (μC/m3): 5, 10, 25, 50, 100 Emphasize the importance of Stokes number. St -> 0 tracer particles. St -> inf, particles not responding to turbulence

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

Evidence of preferential concentration Network of high particle number density regions. Showing here the 2 important parameters which govern this phenomenon. Reλ = 24.24, St = 0.25 Reλ = 24.24, St = 4.00 *S. Scott, Ph.D. thesis, Imperial College London, 2006

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. Mention sweep-stick mechanism

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 <n’e’>, correlation between number density and enstrophy ln, number density correlation length scale

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)

D2 – probability to find 2 particles at a distance less than a given r: P(r) ~ rD2 Range pictures to the left and place underneath the bullet point text. Range captions to the bottom right hand corner of the picture. The image shown here is 7cm x 5cm. D2 data for different cases compared to literature

Binning of particles h h – scale used for binning particles Some are going to be void h – scale used for binning particles n – number density i.e no. of particles / bin volume <nc> – mean number density i.e total particles / volume of cube

D, Dc : deviation from poisson distribution Dc*, D** : Deviation from poisson distribution D and dc have dependence on bin size which is annoying 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

‘D’ measure of accumulation Bin size used is corresponding to peak value of ‘D’.

<n’e’> – correlation between number density and enstrophy

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 <n’e’> and ‘ln’ capture distribution of particle number density Show dependence on Re

Destruction using Lorentz forces* Use divider pages to break up your presentation into logical sections and to provide a visual break for the viewer. The title can be one or two lines long. *A. Karnik and J. Shrimpton, ILASS 2008, Sept 8-10, 2008

Particle position, fluid velocity Network of high particle number density regions. Showing here the 2 important parameters which govern this phenomenon. Reλ = 24.24, St(k) = 1.0, Qv=5μC/m3 Reλ = 24.24, St(k) = 1.6, Qv=100μC/m3 *S. Scott, Ph.D. thesis, Imperial College London, 2006

Evidence of preferential concentration destruction Network of high particle number density regions. Showing here the 2 important parameters which govern this phenomenon. Reλ = 24.24, St(k) = 1.0, Qv=5μC/m3 Reλ = 24.24, St(k) = 1.6, Qv=100μC/m3 *S. Scott, Ph.D. thesis, Imperial College London, 2006

Evidence of preferential concentration destruction Network of high particle number density regions. Showing here the 2 important parameters which govern this phenomenon. Reλ = 24.24, St(k) = 1.0, Qv=5μC/m3 Reλ = 24.24, St(k) = 1.6, Qv=100μC/m3 *S. Scott, Ph.D. thesis, Imperial College London, 2006

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

Effect of Stokes Numbers Reλ = 24.2 Reλ = 81.1 Stokes number is defined differently – scaled by integral time scale Charged particle systems continue to exhibit same trends with Reynolds and Stokes numbers as the charge-free case.

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

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. If using a school logo, make sure that if you have a long page title, it does not encroach on the logo. Allow about 2cm around the logo. Run the page title onto two lines if necessary.