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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 : [email protected]

mailto:[email protected]

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


Classical Modeling approaches of Immersed granular Flows

Motivation ?



Motivation

Nature Industry

A concrete flow

Some applications

A blood flowA mud flow



Motivation

Nature Industry

A concrete flow

Some applications

A blood flowA mud flow

Different Scales ! Modeling ?



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



Motivation (Physical phenomena)

Isodense Suspension of rigid spheres flow in a Channel

Flow direction



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



Scale

Mesoscopic

Macroscopic

Microscopic



Scale

Mesoscopic

Macroscopic

Microscopic

Advantages

Real Physics is enriched



Scale

Mesoscopic

Macroscopic

Microscopic

Disadvantages

But Computation time increases


A new Dynamic-Multi-Scale Modeling approach (Last 7 years of research work accumulation )

Mesoscopic

Macroscopic

Microscopic

Dynamic-Multi-Scale Approach


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


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


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)


Nott and Brady (1994)Morris and Boulay (1999)


Suspension Balance Model (SBM)


Nott and Brady (1994)Morris and Boulay (1999)

Suspension Flow∇⋅1

p

∇⋅2p

∇⋅3p

∇⋅4p

Migration phenomenon is due to a flux J~∇⋅ p



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)



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)



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




An Immersed Boundary Method

is coupled to


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


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


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




Rigid Body Dynamics laws

Suspension Dynamics



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




Rigid Body Dynamics laws

Suspension Dynamics



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)


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




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))



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


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

; ; ;




OpenFOAM® 2D Results




Effect of Maximum packing volume fraction


Op

enF

OA

M®

2D

Res

ult

s





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


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

Thank you for your attention

Talib DBOUK Journée OpenFOAM® - Rouen

Dynamic-Multi-Scale Modeling and Simulation of Immersed Granular Flows over Obstacles

& special thanks to the OpenFOAM community

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Dynamic-Multi-Scale Modeling and Simulation of Immersed ...foam-u.fr/wp-content/uploads/2017/02/session1_1stOFDayFrance_Dbo… · Dynamic-Multi-Scale Modeling and Simulation of Immersed