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DSMC Simulation of Rarefied Flows

Ehsan RoohiEhsan Roohi

Mechanical Engineering Department, Faculty of Engineering,Ferdowsi University of Mashhad

January 2011

Ferdowsi University of Mashhad,Mashhad, Iran

January 2011Sofia, Bulgaria

Overview Micro-fluidics applications Numerical Method: DSMC-IP Results ResultsFlow in micro/nano geometriesP ll l iParallel processingViscosity coefficient modification dsmcFoam developmentHypersonic flow applicationHypersonic flow application

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Micro‐Fluidics Systems

Micro turbinesMicro-channel

Micro-turbines

Micro-Air-Vehicles (MAV’s) Micro-nozzles4

l hDSMC AlgorithmExample: Flow past a sphere

Initialize system with particles Loop over time steps

C   i l      

Example: Flow past a sphere

Create particles at open boundaries

Move all the particlesp Process any interactions of particle & boundariesS   i l  i   ll Sort particles into cells

Sample statistical values Select and execute random Select and execute random collisions

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Slide taken from Alejandro L. Garcia, Department of Physics, San Jose State University

Part 1: Micro‐Nano Flows Simulation Using g

DSMC‐IP Method

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Supersonic Flow: Effect of Knudsen p(Roohi et al, ICNMM08, AIAA Paper 2009)

Kn=0.062 Kn=0.35

Mach: 0.2 0.8 1.4 2 2.6 3.2 3.8

Kn 0.35

X5E-06 1E-05

Kn=0.740Mixed Supersonic‐Subsonic

Mach Number: 0.2 0.5 0.7 0.9 1.1 1.3

X1E-06 2E-06

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Subsonic Flow (Roohi et al JHT 2009)Subsonic Flow (Roohi et al, JHT, 2009)2.5

o

2

P/P

1.5 Grid 1Grid 2

0 0 2 0 4 0 6 0 8 11

Grid 2Grid 3Analytical (Arkilic et al.)DSMC (Liou and Fang)

X/L0 0.2 0.4 0.6 0.8 1

M a c h : 0 .1 5 0 .3 0 .4 5 0 .6 0 .7 5T: 60 100 140 180 220 260 300

1 E -0 6 2 E -0 6 3 E -0 6 1E 06 2E 06 3E 06

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X1 E 0 6 2 E 0 6 3 E 0 6

a) Mach contoursX

1E-06 2E-06 3E-06

b) Temperature contoursKnKn out= 0.0612out= 0.0612q  wall= q  wall= ‐‐55

Choked Flow: Role of Buffer ZoneM ach: 0 .1 0.25 0.4 0.55 0.7 0.85 1 1.15

X5E-07 1E-06 1.5E-06

H/2

InletSymmetry

Outlet

b) Mach contours, without buffer zone, Non‐physical  solution (Mout > 1)

L

Wall

Mach: 0.1 0.25 0.4 0.55 0.7 10.2

KnGLL-Density with BufferKnGLL-Density without Buffer

L

X5E-07 1E-06 1.5E-06

L-D

ensi

ty

0 1

0.15

y

a) Mach contours, with buffer zone, Correct physical simulation 

Kn G

LL

0.05

0.1

X/L0 0.2 0.4 0.6 0.8 1

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Step Flow

M a c h : 0 0 5 0 2 0 3 5 0 5 0 6 5 0 8 0 9 5

p

Y/S 1

2M a c h : 0 .0 5 0 .2 0 .3 5 0 .5 0 .6 5 0 .8 0 .9 5

Kn=0.01

X /S- 2 0 2 4 6

2M a c h : 0 .0 2 0 .1 2 0 .2 2 0 .3 2 0 .4 2 0 .5 2

X / S

Y/S

- 2 0 2 4 6

1Kn=0.10

X / S

S

2M a c h : 0 .0 5 0 .1 5 0 .2 5 0 .3 5 0 .4 5

X /S

Y/S

- 2 0 2 4 6

1Kn=1

10Rarefaction, Re reduction

DSMC with Unstructured Grid (joint work with V. Mirjalili, (Roohi et al, ICNMM09, MFNF J., 2011) 

4E 05

6E-05Inlet Pressure= 1 atm

Y

2E 05

0

2E-05

4E-05Inlet/Wall Temperature=300 K

Supersonic Outlet

I l t K d 0 0004

X0 5E-05 0.0001 0.00015 0.0002 0.00025

-4E-05

-2E-05Inlet Knudsen=0.0004

Throat Width=15 micron

2.5

Ma

1.5

2

Current workDSMC, LioN-S Slip Lio

1

N-S Slip, LioN-S No Slip, Lio

1111

X0.2 0.4 0.6 0.8 1

0.5

*10-4

DSMC‐NS (OpenFoam) ComparisonDSMC NS (OpenFoam) Comparison

m)

5E-05

(m)

5E-05

Y(m

)

0NS

DSMC

Y(m

0NS

DSMC

X (m)0 5E-05 0.0001 0.00015 0.0002

-5E-05T: 120 160 200 240 280

X (m)0 5E-05 0.0001 0.00015 0.0002

-5E-05Mach: 0.2 0.6 1 1.4 1.8 2.2 2.6

)

5E-05

X (m)X (m)

)

5E-05

Y(m

)

0NS

DSMC

Y(m

)

0NS

DSMC

0 5E-05 0.0001 0.00015 0.0002

-5E-05U: 50 150 250 350 450 550

X (m)0 5E-05 0.0001 0.00015 0.0002

-5E-05Density: 0.1 0.3 0.5 0.7 0.9 1.1

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X (m)0 5E-05 0.0001 0.00015 0.0002

X (m)0 5E-05 0.0001 0.00015 0.0002

Supersonic‐Subsonic Nozzle Flow0.5

1

Mach: 0.2 0.6 1 1.4 1.8 2.2

p

0 5

1

Mach: 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

Y/H

Out

0 5

0

Y/H

out

0

0.5

X/L0 0.2 0.4 0.6 0.8 1

-1

-0.5

X/L0 0.2 0.4 0.6 0.8 1

-1

-0.5

Back Pressure=15 kPaBack Pressure=7 kPa

0 5

1

Mach: 0.1 0.3 0.5 0.7 0.9 1.1

X/L

0 5

1

Mach: 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Y/H

out

0

0.5

Y/H

out

0

0.5

0 0 2 0 4 0 6 0 8 1-1

-0.5

Back Pressure=35 kPa0 0.2 0.4 0.6 0.8 1

-1

-0.5

Back Pressure=25 kPa

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X/L0 0.2 0.4 0.6 0.8 1X/L

Inviscid WallsInviscid Walls1 Mach: 0 2 0 6 1 1 4 1 8 2 2 2 6

1 Mach: 0.2 0.6 1 1.4 1.8 2.2

Y/H

out

0

0.5

Mach: 0.2 0.6 1 1.4 1.8 2.2 2.6

Y/H

out

0

0.5

Y

-1

-0.5

Y

-1

-0.5

Pb=7 kPa Pb=15 kPa

X/L0 0.2 0.4 0.6 0.8 1 1.2 X/L

0 0.2 0.4 0.6 0.8 1 1.2

out

0.5

1Mach: 0.2 0.6 1 1.4 1.8

ut

1.5

2Mach: 0.1 0.3 0.5 0.7 0.9 1.1 1.3

Y/H

o

-0.5

0Y

/Hou

0

0.5

1

Pb 25 kP Pb=35 kPa

14X/L0 0.2 0.4 0.6 0.8 1 1.2

-1

X/L0 0.2 0.4 0.6 0.8 1 1.2

0Pb=25 kPa Pb=35 kPa

Higher Knudsen Numbers2

Kn=0.025

Higher Knudsen Numbers Y

/Hin

0.5

1

Y/H

in

1

0

Mach: 0.1 0.3 0.5 0.7 0.9 1.10 Mach: 0.1 0.3 0.5 0.7 0.9

X/L0 0.2 0.4 0.6 0.8 1

X/L0 0.5 1

Without Buffer Zone, (Vacuum Discharge) Outlet Mach more than 1

With Buffer Zone, Acceleration in the Divergent Part of the Nozzle with Subsonic Flow

0.5

1Back Pressure=20 kPa1

Mach: 0.10.30.50.70.9

Y/H

in

0 5

0Y/H

in

1

0

X/L0 0.2 0.4 0.6 0.8 1

-1

-0.5

Mach: 0.05 0.15 0.25 0.35 0.45X/L0 0.2 0.4 0.6 0.8 1 1.2

-1

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Parallel DSMC (PDSMC) (joint work with V Mirjalili P d ti )(joint work with V. Mirjalili, Paper under preparation) 

High Performance Computing Clusters

Linux

Domain Decomposition

Si l P M lti l D t (A C f th P E h Single Program Multiple Data (A Copy of the Program on Each Node)

1TST

SEn

nT n

1200

1400

12

14

16

IdealPDSMC

Com

putin

gTi

me

800

1000

1200

Spe

edup

8

10

12

Tota

lC

400

600

2

4

6

16

Processors2 4 6 8 10 12 14 16

200

Processors2 4 6 8 10 12 14 16

2

Parallel DSMC

7

8

Ideal200*30 NM=123319

7

8

Ideal200*30, NM=123319100*30, NM=61659

Tim

e(S

ec)

5

6

200 30, NM 123319100*30, NM=123319100*15, NM=12331950*15, NM=123319

Tim

e(S

ec)

5

6 100*15, NM=3083150*15, NM=15414

SS

CPU

2

3

4

CPU

2

3

4

Number of Procs1 2 3 4 5 6 7 8

1

Number of Procs1 2 3 4 5 6 7 8

1

2

NM=cteNMPC=cte

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IP MethodU (m/s): 0.1 0.25 0.4 0.55 0.7AR=3000

Y(m

)0 001 0 002 0 003

05E-071E-06

( )AR=3000

X (m)0.001 0.002 0.003

0.04AR=100

PLi

near

)/PO

ut(P

- 0.02

IPAnalytical, 1storderAnalytical 2ndorder

18X/L0 0.2 0.4 0.6 0.8 1

0

Analytical, 2 order

Extending the NS to Transition Extending the NS to Transition (Roohi & Darbandi, 2009, POF, AIAA Paper 2009, ETH presentation)

o Slip B.C’s: either accurate 1) u or 2) mass flow

Case 1: 2/])1([ Case 1:

Case 2:

2/])1([ wvvs uuuu

,KnKn 2

22

21 yuC

yuCuu ws

o As Kn increases, stress-strain relation changes,

o more complicated relation than Stokes’

yy

o more complicated relation than Stokes ,

o Switch to Burnett, super Burnett, R13 Eq., etc

o Alternative solution: modification

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Viscosity modificationViscosity modificationAtVVmx s

Nrejt

injtIPw

s

/)()( ,,,

We suggest:

xIPw)(

)Kn( , s

jjtjtIPw

1,,,

We suggest: nVt

e /)Kn(

)Kn()()()()( 33)( OV

xKnOV

xx tNSe

Bw

tNSeIPw

0.9

IP b d d l)(B

)()()()()( ,,, nn NSewNSeIPw

0.8

IP-based modelNS-based modelKarniadakis et al. model, =2.2

)(Bw : negligible for low Mach isothermal flows

K11)Kn(

Karniadakis

0.6

0.7

2Kn6Kn62)Kn(

Kn10

NS-based

0 4

0.5

2Kn5.13Kn62

NSo

2Kn70.4Kn89.0)K(

20Kn (x)0.1 0.2 0.3 0.4 0.5

0.4

20 Kn98.19Kn75.02

2)Kn(

IP

Current IP

Velocity ProfilesVelocity Profiles1.2

1.21.2

1.1

1

1.2

1

1.1

11

1

U* 0.8 U

*

0.8

0.9

U*

0.8

U*

0.8

U*

08

0.9

0.4

0.6

SecondOrder (Kinetic)Ohwadaet al.BeskokIP Model 1 05

0.6

0.7

0.606

0.8

0.7

0.8

y*0 0.2 0.4

IP, Model 1IP, Model2DSMC

y*

0 0.2 0.40.4

0.5

y*

0 0.2 0.4

y*0 0.2 0.4

0.6

y*

0 0.2 0.40.6

Kn=0.113 Kn=0.226 Kn=0.451 Kn=0.667 Kn=1.13

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ValidationValidationVariation of the IP‐based slip coefficient expression with Knudsen number

0 6

0.7IP-based ModelSecond Order (Aubert & Colin)Beskok, =2.2

i (C li )

0.5

0.6 Experiment (Colin)HadjiconstantinouFirst OrderSecond Order (Kinetic theory)

1/S

0.4

0.3

Knout

0.1 0.2 0.3 0.4 0.5

0.2

22

out

)ln(07.34ln00.511Kn

1Kn

1 22

2

1 aammS outout

cIP

Part 2: Hypersonic Flowypwith dsmcFoamwith dsmcFoam

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Famous DSMC CodeThree Dimensional, Arbitrary Geometry Codes

d l ( l bl )DS2V, G. Bird, Australia (GUI Available)Monaco, I. D. Boyd, Michigan University (NA)

i ( )SMILE, M. S. Ivanov, Russia (NA)DAC, NASA, USA (NA)....dsmcFoam, OpenCFD, Open source

d l d d O F 1 5 (G hdeveloped under OpenFoam v. 1.5.x (Graham Macpherson (OpenCFD Ltd.), Ehsan Roohi (Sharif U i i ) T S l (U i i f S h l d )University), Tom Scanlon (University of Strathclyde)

freely released with newest version of OF, v 1.6, A 2009 d LiAug. 2009 , under Linux 

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Why OpenFOAM?Why OpenFOAM?

C++ code flexibility hierarchical structureC++ code flexibility, hierarchical structure, inheritance features

Solvers, utilities and libraries fully extensible

Advanced error checking at compile and runAdvanced error checking at compile and run times

R b l d ili bl Robust solver and utility executables

Unlimited parallel processing capabilityp p g p y

Open source

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dsmcFoam: current featuresdsmcFoam: current features Steady / transient solutions

Parallel solver

Arbitrary 2D/3D geometriesArbitrary 2D/3D geometries

Arbitrary number of gas species

VHS/LB collision model

New contributions:

Density B.C ImplementationsDensity B.C Implementations

Lacking:

Ch i l R ti V i bl ti t idChemical Reactions, Variable time step, grid adaptation, …. 26

How to Install and Use OF

Install Linux + updates (Preferably Ubuntu)p ( y )

Go to the OpenFoam homepage/download

Download the compiled version of the OF Download the compiled version of the OF v.1.7.1 for Ubuntu as directed

D l d d il OF f th Li Download and compile OF for other Linuxes

Start with UserGuide

Create the mesh file (I usually convert Fluent meshes))

Set the gas properties

Run the code

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Run the code

dsmcFoamdsmcFoam dsmcInitialise-

pre-processing utility to create initialconfigurations of DSMC particles in arbitraryg p ygeometries

dsmcFoam – solverdsmcFoam solver

All can be run in parallel and dsmcFields can beexecuted at runtime of solverexecuted at runtime of solver.

Post-processing with Paraview, Tecplot

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Arbitrary Volume/Area FillingArbitrary Volume/Area Filling Divide each cell to tetrahedral (basic constituent) Randomly distribute  particles in tetrahedral 

o Divide each free stream boundary face to triangleso Divide each free stream boundary face to triangleso Randomly distribute  incoming particles in trianglesF   ti l  t ki    M h  N di    o For particle tracking, see: Macpherson, Nordin, 2009, CNME

P ti l  t ki  i   t t d   bit   l h d l Particle tracking in unstructured, arbitrary polyhedral meshes for use in CFD and molecular dynamics

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relaxation to equilibriumq(Scanlon et al, DSMC workshop Sep. 2009, CAF 2010 Journal)

Argon gas in volume of side length 1 x 10‐6 mg g g Cyclic boundaries Initial U conditions random, T = 273 K

K   6 Kn = 0.067,

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Flat plate (Bird p.340)

Nitrogen, Ma = 4, Kn = 0.00143 Freestream(U,T,P)

Diffusive ReflectionSpecular Reflection

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2D flow over a cylinder Mach=10, Kn=0.01, d=0.3048 m

Geometry and mesh

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2D flow over a cylindery

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cylinder with Kn=0.25

Results compared with Lofthouse thesis(2008) Using MONACO 

High scatter possibly due to too fine mesh in wake region 34

3D Supersonic corner ( )(Bird p.394, run by Dr. T. Scanlon)

dsmcFoamBirdBirdBird

Comparison of skin friction coefficientComparison of skin friction coefficient

Nitrogen Ma = 6 Kn = 0 043 Bird (p 340)Nitrogen, Ma 6, Kn 0.043, Bird (p.340)

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3D Supersonic corner Bird

p

C i f M h fil d FComparison of Mach profiles dsmcFoam

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3D Complex geometryp g y(run by Dr. T. Scanlon)

Demonstrate dsmcFoam capability for arbitrary 3D p y ygeometries

Nitrogen, Ma = 3, Kn = 0.005

70 km altitude70 km altitude

Freestreaminlet/outlet/upper/lower/side boundariesboundaries

VHS collisions/ LB internal energy/ diffuse wall reflection

H M h d snappyHexMesh used.

200 x 65 x 75 = 975000 cells

dt = 1 x10‐7 s

31 million DSMC particles

1 cpu, 7 days compute time

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3D Complex geometry

Average velocity

Velocity vectors

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AcknowledgmentAcknowledgmentAcknowledgmentAcknowledgment Dr. Masoud Darbandi Mr. Vahid Mir‐JaliliJ

Thank You

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