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Compressible Gas-particle Multiphase Flows: Computational Modeling Approaches
Akhil V. Marayikkottu∗, and Deborah A. Levin∗
Department of Aerospace Engineering∗, University of Illinois Urbana-Champaign, Illinois- 61801
Particle resolved study using Direct Simulation Monte Carlo (DSMC) method
v
v
nt
^^
r
i
!
∆"#$%
∆"#$%
∆"#$%
∆
ppan =Xncoll
k=1mg
vi−
vrk
Fnet =1
NsamXNsam
i=1"XNpan
p=1
1
∆t∆
ppan,p#i
where mgis the mass of the gas molecule, total
number of gas panel collisions are given by ncoll, in-
cident and reflected velocities are given by
viand
vr
respectively. Number of panels and number of sam-
ples are represented by Npan and Nsam respectively.
Model development for irregular particle geometries
Model
aggregates
Open aggregate
!
Dense aggregate
Resolved flow
Slip regime −→
Trans. regime −→
Particle drag lateral lift
yObtaining mobility parameters by momentum surface integration
yIrregular particles in a canonical Rankine-vortex using one-way coupled
Eulerian-Lagrangian approach
yThe mobility of the aggregates (b) and (c) is different from a sphere (a) due to
the modified drag force and lateral lift
Model development for aerodynamic interaction in dense particulate systems
yAerodynamic interaction between particles in dense particulate regimes modi-
fies the mobility of the constituents
yA: Force statistics within the dense particle distribution
yB: Mean force variation as a function of particle Re
RESEARCH OBJECTIVES : The blastwave-ground interaction
system has multiple length and time scales associated with it. To
efficiently study the system under consideration, accurate mobil-
ity models from particle scales should be coupled to lower-fidelity
continuum solvers that can simulate larger length-scales.
Large length scales are modeled using the Eulerian-
Lagrangian approach integrated to the FLASH research code
framework
Particle resolved simulations are performed in the in-house Di-
rect Simulation Monte Carlo (DSMC) code to develop accu-
rate particle mobility models
How does the Eulerian-Lagrangian code use the particle resolved data ?
ySimple functional form for the drag and lift generated on the irregular fractal
aggregate:
p=A1log(1+B1Ma)
q=A2log(1+B2Ma)/1+C2Ma2
where pand qare drag and lift parameters obtained by normalizing the drag
and lateral lift force with a monomer drag. A1,A2,B1,B2, and C2are non-
linear fit parameters.
Force
Torque
Neighbor list
Reynolds
number
Knudsen
number
ySince the aerodynamic interaction forces generated on a particulate within a
dense distribution is a highly non-linear function of multiple gas and particle
parameters, an artificial neural network will be trained from the high-fidelity
particle resolved DSMC data to predict the forces and torques on these
complex systems.
Publications
Vijayan, Akhil Marayikkottu, and Deborah A. Levin. ”Kinetic modeling of
fractal aggregate mobility.”Physics of Fluids 34, no. 4 (2022): 043315.
Marayikkottu, Akhil V., Saurabh S. Sawant, Deborah A. Levin, Ci Huang,
Mirko Schoenitz, and Edward L. Dreizin. ”Study of particle lifting mech-
anisms in an electrostatic discharge plasma.”International Journal of
Multiphase Flow 137 (2021): 103564.
V. Marayikkottu, Akhil, and Deborah A. Levin. ”Influence of particle non-
dilute effects on its dispersion in particle-laden blast wave systems.”
Journal of Applied Physics 130, no. 3 (2021): 034701.
Eulerian-Lagrangian (EL) method
1.) ε !"#θ$
2.)
& !
Governing equations for the Eulerian
sub-solver
∂(ερf)
∂t+∇.(ερfuf) = 0
∂(ερfuf)
∂t+∇.ερfufuf+∇P−ερfg=−Fs
∂(ερfE)
∂t+∇.(ερfE+P)uf+P∂ε
∂t−ερfuf.g=Es
where ρf,uf,P,Eand grepresents the gas density, gas velocity, pressure, en-
ergy, and the acceleration due to gravity, respectively. The momentum and energy
source terms are represented by Fsand Esrespectively. εrepresents the local
fluid volume fraction.
Governing equations for the Lagrangian
sub-solver
∂ϕ
∂t+∇.(ϕup) + ∇up.(ϕA) = 0
A=Drag +Pressure gradient force+
Saffman lift +Gravitational +Collisional
'
&
$
%
Source terms
Fs=Ztf
ti
mAdt
Es=Ztf
ti
mA.updt
where ϕ(x,up, ρp,t)is the probability distribution of particles. upand Aare the
particle velocity and the inter-phase acceleration terms respectively. The particle
resolved mobility models can be appended to the acceleration term A.
Moderately dense particle system modeling: Inelastic DSMC collisions
The particle system kinetic energy dissipates
through in-elastic collisions given by Haff et al.
Tgr (t) = Tgr (0)
(1+t/τ)2
τ−1=8
12(1−e2
n)D2
p¯
nqπTgr (0)
where Tgr (0)is the granular temperature at time
t=0 and ¯
nis the number density of particles in
the system. The relaxation time is indicated by
τ.
Dense particle system modeling: Harris & Crighton model
The force on the particulate distribution
due to the multiple inter-particle inter-
actions is given by Harris & Crighton
(1994) expressed as:
Fgran =1
ρpθp∇τp
τp=Psθβ
max[θcp −θ, ϵ(1−θ)]
where θcp is the closed packing fac-
tor, θis the particle volume fraction.
Ps∼ O(105), 1 ≤β≤5 and
ϵ∼ O(10−7)are constants in the
model. The scaling study by Ling(2012)
shows that the parametric space for Ps
and βgiven above models the interac-
tion of shock waves with dense parti-
cle distributions efficiently. The model
was tested against experimental stud-
ies with shock-particle curtain interac-
tions.
Preliminary numerical study: shockwave-particle curtain interaction (1/3)
4 mm 4 mm 2 mm 4 mm
4 mm
oParticle diameters = 100 micrometers, spherical, density = 2520 kg/m3, 2-dimensional
study
oParticles are assumed to be suspended with zero initial velocity, phi ~28%
oGas species : single species approximation for Air
oSecond-order accurate PPM scheme with shock steepening activated
Driver
Air at 7 atm
and 300K
Driven
Air at 1 atm
and 300K
x (m)
Preliminary numerical study: shockwave-particle curtain interaction (2/3)
† Samuel petter et al.``Early Experiments on Shock-Particle Curtain Interactions in the High-Temperature Shock Tube ’, Sandia National lab
report, SAND 2019-1484C, osti.gov, (2019).
Incident
shock
Incident
shock
Transmitted
shock
Reflected
shock
Reflected
shock
Contact
discontinuity
Particle
wake
Particle
wake
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