Turbulence modulation by fully resolved particles using ...dutw1479.wbmt.tudelft.nl/~wim/euromech549/presentations/...Turbulence modulation by fully resolved particles using Immersed

Turbulence modulation by fully resolved particlesusing Immersed Boundary Methods

Abouelmagd Abdelsamie and Dominique Thevenin

Lab. of Fluid Dynamics & Technical FlowsUniversity of Magdeburg

”Otto von Guericke”

June 19th 2013

OUTLINE

1 MOTIVATIONS & OBJECTIVES

2 GOVERNING EQUATIONS & NUMERICAL APPROACHESPARTICLES COLLISION MODELS

3 RESULTSTURBULENCE STRUCTURE & PARTICLES’ MOTIONTURBULENCE STATISTICS

4 CONCLUSIONS

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 2/ 17

MOTIVATIONS

Considering

1 Isotropic incompressible turbulence modification by solid sphereparticles

2 Fully resolved particles released in the flow simulated using

Immersed Boundary Method-IBM (Particle-particle collision isemployed to prevent the over-lapping)

3 Direct numerical simulation (DNS)

Fourier pseudo-spectral solver

Objectives

1 Clarifying the effect of the fully resolved particles on two different nu-merical settings of the turbulence

Statistically stationary turbulenceDecaying turbulence

2 Test the effect of collision models on turbulence modulation.

3 Check the spectral solver compatibility with IBM (Uhlmann 2005).

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 3/ 17

GOVERNING EQUATIONS & NUMERICAL APPROACHES

Incompressible Navier-Stokes and continuity equations

∂ui∂t

= − ∂

∂xi

(p

ρ+

1

2ujuj

)+ εijkujωk + ν

∂2uixjxj

+ fi (1)

fi(x) =

Np∑m=1

NL∑l=1

Fi(Xml )δ(x−Xm

l )∆V ml ∀x ∈ gh (2)

∂ui∂xi

= 0 (3)

Numerical settings

Solver ⇒ Fourier pseudo-spectral (parallelized in one direction)

Domain ⇒ Box with volume=(2π)3, dimensionless code

Boundary conditions ⇒ Periodic in all directions

Computational nodes ⇒ 1283

Rλ (Taylor micro scale Reynolds number) ⇒ O (60)

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 4/ 17

CONTINUED

Particle motion governing equation

Fully resolved particles =⇒ method of Uhlmann (2005)

V mc

(ρmp − ρ

) dUi,m

dt= −ρ

∑l

F (Xml )∆V m

l +

Np∑j=1

j 6=m

F(m,j)R

ImcdΩ

dt= −ρ

∑l

(Xml −Xm

c )× F (Xml )∆V m

l

+ ρd

dt

∫gh

((x−Xmc )× u) dx (4)

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 5/ 17

COLLISION ALGORITHMRepulsive velocity barrier model (S. Dance, E. Climent and M. R. Maxey, 2003)

- Velocity barrier: added directly to particles velocity, reduces stiffness of the particleequation of motion

Vbarrier =

−Vref

dp

[d2ref − d

2(m,j)

d2ref − d2p

]2 (Xm

p −Xjp

)if d(m,j) < dref

0 otherwise

(5)

Repulsive potential force (Glowinski et al., 2001 and Lucci et al., 2010)- Repulsive force: added into particles linear momentum equation

F(m,j)R =

1

Cr

[dp + dR − d(m,j)

dR

]2 (Xm

p −Xjp

d(m,j)

), if d(m,j) < (dp + dR) ,

0 , elsewhere .(6)

Hard Sphere Model (Crowe et al., 1998)

mmp (Um(1)− Um(0)) = J , (7)

mjp(Uj(1)− Uj(0)) = −J , (8)

Imp (Ωm(1)− Ωj(0)) = dmp n× J , (9)

Ijp(Ωm(1)− Ωj(0)) = djp n× (−J) , (10)

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 6/ 17

PARALLELIZING COLLISION ALGORITHMS

OpenMp has been used to parallelize all the code including particlemotion.

The parallelization with collision needs additional treatment.

Visualizing particles motion without flow or in simple flows can showhow the parallelization and collision model are working

Animation: Test the collision model andtheir parallelization over 8 cores, using OpenMP

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 7/ 17

RESULTS

The particles properties are chosen as in the following tableThe Lagrangian points over the sphere surface are distributed uniformlyusing explicit spiral set (Saff & Kuijlaars, 1997 and Lucci et al., 2010),then the spherical coordinates (θk, φk, dp/2) are described as follows:

ck = −1 +2(k − 1)

(Nl − 1), 1 ≤ k ≤ Nl (11)

θk = arccos(ck), 1 ≤ k ≤ Nl (12)

φk = φk−1 +3.6√

Nl

(1− c2k

) , 1 < k < Nl (13)

Nl ≈π

3

(3d2p

∆x2+ 1

)Np = 350

Table: particle properties

φm φv d/η τp/τk ρp/ρ

0.00 0.00 0.00 0.00 0.000.13 0.10 20.6 35.67 1.510.25 0.10 20.6 59.54 2.520.35 0.10 20.6 83.23 3.520.50 0.10 20.6 118.9 5.00

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 8/ 17

RESULTS: Turbulence Structure and Particles Motion

Employing IBM (Uhlmann 2005) with spectral code introduces wrin-kling at small scale (around particles surface) due to the Gibbs phe-nomenon.

Other technique required with spectral solver or modification of Uhlmann(2005)’s version to be compatible with spectral solver.

Animation: 3-D iso-surface turbulence en-strophy and fully resolved particles in incom-pressible flow using IBM

Animation: fully resolved particles in incom-pressible flow, with particles velocity vectorusing IBM

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 9/ 17

RESULTS: No-Slip Conditions and Turbulence Statistics

Error regarding no-slip conditions(globally).

Turbulence kinetic energy and itsdissipation rate.

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 10/ 17

RESULTS: Temporal Decaying Turbulence Statistics

Temporal kinetic energy of decayingturbulence.

Temporal kinetic energy dissipation rate ofdecaying turbulence.

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 11/ 17

RESULTS:Collision Models Effect on Turbulence Statistics

Effect of the collision models (HSM orVBM) on temporal kinetic energy of

decaying turbulence

Effect of the collision models (HSM orVBM) on temporal kinetic energy

dissipation rate of decaying turbulence

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 12/ 17

COLLISION INCLUDING LUBRICATION EFFECTLubrication force model (Kempe and Frohlich, 2012)

- Lubrication subgrid model force

FLubm =

0 2∆x < S(m,j)

−6π ν ρd2

4S(m,j)

(xm − xj|xm − xj |

)[um − uj ] SLub

min ≤ S(m,j) ≤ 2∆x

0 S(m,j) < SLubmin

(14)

Activating the repulsive or lubrication models depends on the distancebetween binary particles’ surfaces.

Figure: Collision model ranges, Kempe and Frohlich, 2012

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 13/ 17

RESULTS: Lubrication force effect on Turbulence Statistics

Effect of the lubrication force ontemporal kinetic energy of decaying

turbulence

Effect of the lubrication force ontemporal kinetic energy dissipation rate

of decaying turbulence

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 14/ 17

RESULTS: SETTLING VELOCITY

On the way toward implement the discrete forcing IBM approach (wallor complex geometry) with contentious forcing IBM approach (movingparticles), we start as a preliminary step to check the settling velocityof a particle in 3-D tank.

The results will directly be compared with experimental and lattice-Boltzmann results (Cate et al. 2002)

Current results without wall yet (just periodic domain).

Animation: DNS of a particle settling velocity with fluid velocity magnitude contour

(spectral solver)

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 15/ 17

CONCLUSIONS

1 The impact of fully resolved particles on stationary and decaying tur-bulence are completely different.

2 The collision models affects directly particles’ concentration as it isexpected. Therefore, the dissipation rate of turbulence might be un-derestimated in that case, impacting the kinetic energy as well.

3 More realistic models are now being tested (Kempe and Frohlich, 2012).

4 IBM (following Uhlmann 2005) for moving bodies introduces (small)unphysical oscillations/wrinkling when combined with spectral tech-niques, so that an improved solver is needed.

OUTLOOK:

Implementing discrete forcing approach (complex geometry) and con-tinuous force approach (moving particles) together with Spectral meth-ods.

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 16/ 17

MANY THANKS FOR YOURATTENTION!

For more information:[email protected]

Abouelmagd Abdelsamie and Dominique Thevenin Lab. of Fluid Dynamics & Technical Flows, University of Magdeburg 17/ 17