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Dynamic-Multi-Scale Modeling and Simulation of Immersed Granular Flows over Obstacles
Talib DBOUK
18 May 2016 Journée OpenFOAM® - Rouen
Institut Mines-TélécomÉcole des Mines de Douai Research Center
Industrial Engineering DepartmentDouai - FRANCE
(Assistant Professor)
Email : talib.dbouk@mines-douai.fr
Talib DBOUK Journée OpenFOAM® - Rouen 01
Dynamic-Multi-Scale Modeling and Simulationof Immersed Granular Flows over Obstacles
● Classical Modeling approaches of Immersed granular Flows
● A new Dynamic-Multi-Scale Modeling approach ( Last 7 years of personal R&D work accumulation in OpenFOAM)
● Some Results: Numerical Simulations in OpenFOAM vs Experiments
● Conclusion
Talib DBOUK Journée OpenFOAM® - Rouen 02
Classical Modeling approaches of Immersed granular Flows
Motivation ?
Talib DBOUK Journée OpenFOAM® - Rouen 03
Classical Modeling approaches of Immersed granular Flows
Motivation
Nature Industry
A concrete flow
Some applications
A blood flowA mud flow
Talib DBOUK Journée OpenFOAM® - Rouen 03
Classical Modeling approaches of Immersed granular Flows
Motivation
Nature Industry
A concrete flow
Some applications
A blood flowA mud flow
Different Scales ! Modeling ?
Talib DBOUK Journée OpenFOAM® - Rouen 04
Classical Modeling approaches of Immersed granular Flows
Non-Brownian Suspensions of rigid particles(Isothermal, incompressible, laminar)
Immersed Granular Media as :
Rigid Particles
( effective diameter ≥ 1 µm )
( density = )
Fluid
( density = )
( viscosity = )
ρ f
ρpη f
Assumption
Talib DBOUK Journée OpenFOAM® - Rouen 05
Classical Modeling approaches of Immersed granular Flows
Motivation (Physical phenomena)
Isodense Suspension of rigid spheres flow in a Channel
Flow direction
Talib DBOUK Journée OpenFOAM® - Rouen 05
Classical Modeling approaches of Immersed granular Flows
Motivation (Physical phenomena)
Isodense Suspension of rigid spheres flow in a Channel
Migration of particles from higher to lower shear rate zones ( Towards the centerline )
Mig
rati
on P
hen
omen
on
Flow direction
Flow direction
Talib DBOUK Journée OpenFOAM® - Rouen 06
Classical Modeling approaches of Immersed granular Flows
Scale
Mesoscopic
Macroscopic
Microscopic
Talib DBOUK Journée OpenFOAM® - Rouen 07
Classical Modeling approaches of Immersed granular Flows
Scale
Mesoscopic
Macroscopic
Microscopic
Advantages
Real Physics is enriched
Talib DBOUK Journée OpenFOAM® - Rouen 08
Classical Modeling approaches of Immersed granular Flows
Scale
Mesoscopic
Macroscopic
Microscopic
Disadvantages
But Computation time increases
Talib DBOUK Journée OpenFOAM® - Rouen 09
A new Dynamic-Multi-Scale Modeling approach (Last 7 years of research work accumulation )
Mesoscopic
Macroscopic
Microscopic
Dynamic-Multi-Scale Approach
Talib DBOUK Journée OpenFOAM® - Rouen 09
A new Dynamic-Multi-Scale Modeling approach (Last 7 years of research work accumulation )
Mesoscopic
Macroscopic
Microscopic
Dynamic-Multi-Scale Approach
A user's choice
Talib DBOUK Journée OpenFOAM® - Rouen 10
A new Dynamic-Multi-Scale Modeling approachT. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79, http://dx.doi.org/10.1016/j.jnnfm.2016.01.003.
Talib DBOUK Journée OpenFOAM® - Rouen 10
A new Dynamic-Multi-Scale Modeling approachT. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79, http://dx.doi.org/10.1016/j.jnnfm.2016.01.003.
Suspension flows Cotinuum Macroscopic Modeling
is coupled to
An Immersed Boundary Method
Talib DBOUK Journée OpenFOAM® - Rouen 11
Non-Brownian Suspensions of hard spheres
Suspension Balance Model (SBM)
Monodispersed Spheres
( diameter = 2a ≥ 1 µm )
( density = )
Newtonian Liquid
( density = )
( viscosity = = cst. )
ρ f
ρpη0
Suspension Concentration
=V s
V total
[]
0m 0.58⩽ϕm⩽0.68 ( for spheres)
Suspension Viscosity [ ]
η(ϕ)=η0 ηs(ϕ)
ηs(ϕ)=(1−ϕϕm)−2
(Maron & Pierce 1956)
Suspension flows Cotinuum Macroscopic Modeling
Nott and Brady (1994)Morris and Boulay (1999)
Talib DBOUK Journée OpenFOAM® - Rouen 12
Suspension Balance Model (SBM)
Suspension flows Cotinuum Macroscopic Modeling
Nott and Brady (1994)Morris and Boulay (1999)
Suspension Flow∇⋅1
p
∇⋅2p
∇⋅3p
∇⋅4p
Migration phenomenon is due to a flux J~∇⋅ p
Talib DBOUK Journée OpenFOAM® - Rouen 13
Suspension flows Cotinuum Macroscopic Modeling
Conservation Laws
p
f= f pSuspension stress
∇⋅U=0 1Continuity eqn. :
∇⋅ i g=0 2Momentum eqn. :
Transport eqn. : ∂∂ t U⋅∇=−∇⋅J total 3
The Flow● Incompressible and viscous● Re << 1 (non-inertial)● Pe >> 1 (non-Brownian)
The Suspension Balance Model (SBM)
Talib DBOUK Journée OpenFOAM® - Rouen 13
Suspension flows Cotinuum Macroscopic Modeling
Conservation Laws
p
f= f pSuspension stress
∇⋅U=0 1Continuity eqn. :
∇⋅ i g=0 2Momentum eqn. :
Transport eqn. : ∂∂ t U⋅∇=−∇⋅J total 3
SbmFoam Solver
OpenFOAM®
The Suspension Balance Model (SBM)
Talib DBOUK Journée OpenFOAM® - Rouen 14
Suspension flows Cotinuum Macroscopic Modeling
Viscous ReSuspension and 2D Mixing
ExperimentNMR imaging
Rao et al. (2002)
SBM solverOpenFOAM®
2D Mesh = 10000 cells | CFL << 1 | CPU time (single core Machine 1.8 GHz) ~ 5 h
● T. Dbouk, L. Lobry, E. Lemaire, and F. Moukalled “Shear-induced Particles Migration: Predictions From Experimental Determination of The Particle Stress Tensor ”, J. Non-Newtonian Fluid Mech. , Volume 198, P : 78–95, August (2013).
Talib DBOUK Journée OpenFOAM® - Rouen
A new Dynamic-Multi-Scale Modeling approachT. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79, http://dx.doi.org/10.1016/j.jnnfm.2016.01.003.
Suspension flows Cotinuum Macroscopic Modeling
An Immersed Boundary Method
is coupled to
Talib DBOUK Journée OpenFOAM® - Rouen 15
An Immersed Boundary Method coupled to the SBM● Peskin, C. S., (1972), (1977), (1982)
∇⋅U = 0
(1−ζ)∂ϕ
∂ t+ (1−ζ)[(U⋅∇ )ϕ ] = −(1−ζ)∇⋅J t + ζ
(ϕ−ϕB)
Δ t
● T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
ρ∂U∂ t
+ [ρ(U⋅∇)U − ∇⋅Σ − Δρi g ϕ ] = f
Talib DBOUK Journée OpenFOAM® - Rouen 15
An Immersed Boundary Method coupled to the SBM● Peskin, C. S., (1972), (1977), (1982)
∇⋅U = 0
(1−ζ)∂ϕ
∂ t+ (1−ζ)[(U⋅∇ )ϕ ] = −(1−ζ)∇⋅J t + ζ
(ϕ−ϕB)
Δ t
(ζ = 1−ϵ ∀ X (x , y , z ) ∈ ΩB
ζ = ϵ ∀ X ( x , y , z ) ∈ ΩS)(ϵ≪1)
ρ=ρp+ρ f with ρp= ϕρpi and ρ f= (1−ϕ)ρ f
i
● T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
ρ∂U∂ t
+ [ρ(U⋅∇)U − ∇⋅Σ − Δρi g ϕ ] = f
f = ζ [ρ ∂U∂ t
+ ρ(U⋅∇)U − ∇⋅Σ − Δρi g ϕ + ρ(U B − U )
Δ t ]Force of an immersedBody in a suspension
Immersed Body
Effect on Suspension dynamics
Talib DBOUK Journée OpenFOAM® - Rouen 16
An Immersed Boundary Method coupled to the SBM● Peskin, C. S., (1972), (1977), (1982)● T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
Rigid Body Dynamics in a Suspension FlowMobility of a immersed rigid bodies B in a suspension flow
Suspension Dynamics
Effect on Immersed Body
& Body/Body contacts
F SSI = ∫ΩB
(∇⋅Σ + Δρi g ϕ ) d Ω = − ∫
ΩB
ρ(1−ϵ)ϵ
(U B−U )Δ t
dΩ
Suspension/Structure Interaction Force
Talib DBOUK Journée OpenFOAM® - Rouen 17
An Immersed Boundary Method coupled to the SBM● Peskin, C. S., (1972), (1977), (1982)● T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
Rigid Body Dynamics laws
Suspension Dynamics
Effect on Immersed Body
& Body/Body contacts
FT = mB
∂U B
∂ t; T T = I B
∂ωB
∂ tFT = FSSI + FC + mBg ; T T = TSSI + TC
(U B=∂ X B
∂ t )
T SSI = r×F SSI
Rigid Body BLinear & Angular
Velocities
ωB;local position vector relative to
the immersed body centroid
Talib DBOUK Journée OpenFOAM® - Rouen 17
An Immersed Boundary Method coupled to the SBM● Peskin, C. S., (1972), (1977), (1982)● T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles",
Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
Rigid Body Dynamics laws
Suspension Dynamics
Effect on Immersed Body
& Body/Body contacts
FT = mB
∂U B
∂ t; T T = I B
∂ωB
∂ tFT = FSSI + FC + mBg ; T T = TSSI + TC
NSCD contact lawsM. Jean. The non-smooth contact dynamics method,
Computer Methods in Applied Mechanics and Engineering, 235–257, 177, (1999)
Talib DBOUK Journée OpenFOAM® - Rouen 18
Validations in OpenFOAM®
T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
S. Turek and M. Schäfer, Benchmark Computations of Laminar Flow around a Cylinder. In Flow Simulation with High-Performance Computers II, ed. E. H (1996)
t = 0
BC in OpenFOAM
Geometry
a=250 µm
Cx=Cy=0.2 m D = 0.1 m H=0.41m L=2.2 m
Isodense suspension flow over a stationary cylinder in a wide channel
Talib DBOUK Journée OpenFOAM® - Rouen 19
Validations in OpenFOAM®
T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
Re=ρ|U|D
η (ϕbulk )= 20
CD=F D
12
ρ (U−UB )2 D
;CL=FL
12
ρ (U−U B )2 D
FD=(−(FSSI )x ,0 ,0 ) ; FL=(0,−(FSSI ) y ,0 )
Example at
(Δp=p(Cx−D2
,Cy )−p (Cx+D2
,Cy))
Talib DBOUK Journée OpenFOAM® - Rouen 20
Validations in OpenFOAM®
S. Turek and M. Schäfer, Benchmark Computations of Laminar Flow around a Cylinder. In Flow Simulation with High-Performance Computers II, ed. E. H (1996)
OpenFOAM® results are in good agreement with the benchmark of
T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
Re=ρ|U|D
η (ϕbulk )= 20
CD=F D
12
ρ (U−UB )2 D
;CL=FL
12
ρ (U−U B )2 D
FD=(−(FSSI )x ,0 ,0 ) ; FL=(0,−(FSSI ) y ,0 )
(Δp=p(Cx−D2
,Cy )−p (Cx+D2
,Cy))
ϕbulk = 10−4 ; a=250 µmat
Example at
OpenFOAM® results for several valuesϕbulk
Isodense suspension flow over a stationary cylinder in a micro channel
H. Haddadi, S. Shojaei-Zadeh, K. Connington and J.F. Morris, Suspension flow past a cylinder: particle interactions with recirculating wakes. J. Fluid Mech. 760 (2014), R2. doi:10.1017/jfm.2014.613.
Re = 60 Re = 120 Re = 300
D = 200 μm ρs=ρ
f=1050 kg/m3 ϕbulk=8.4 % 2a=7 µm
OpenFOAM® 2D Results
; ; ;
Talib DBOUK Journée OpenFOAM® - Rouen 22
OpenFOAM® results for several valuesϕbulk
Isodense suspension flow over a stationary cylinder in a micro channel
OpenFOAM® 2D Results
Talib DBOUK Journée OpenFOAM® - Rouen 23
OpenFOAM® results for several valuesϕbulk
Isodense suspension flow over a stationary cylinder in a micro channel
Effect of Maximum packing volume fraction
Talib DBOUK Journée OpenFOAM® - Rouen 24
Op
enF
OA
M®
2D
Res
ult
s
T. DBOUK "A Suspension Balance Direct-Forcing Immersed Boundary Model for wet granular flows over obstacles", Journal of Non-Newtonian fluid Mechanics, 230 (2016), 68-79.
OpenFOAM® results for several valuesϕbulk
Isodense suspension flow over a stationary cylinder in a micro channel
Talib DBOUK Journée OpenFOAM® - Rouen 25
OpenFOAM® results are in good qualitative agreement with the experimental results of :
H. Haddadi, S. Shojaei-Zadeh, K. Connington and J.F. Morris, Suspension flow past a cylinder: particle interactions with recirculating wakes. J. Fluid Mech. 760 (2014), R2. doi:10.1017/jfm.2014.613.
Conclusions
Talib DBOUK Journée OpenFOAM® - Rouen 26
New Dynamic-Multi-Scale approach is introduced for the suspension flows of rigid particles over immersed obstacles
The new approach is developed, implemented andvalidated in the OpenFOAM® library
Successful coupling of the SBM to a DF-IBM
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