dsmc - ferdowsi university of...
TRANSCRIPT
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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
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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
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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
5
Slide taken from Alejandro L. Garcia, Department of Physics, San Jose State University
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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
8
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
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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
09
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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
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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
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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
12
X (m)0 5E-05 0.0001 0.00015 0.0002
X (m)0 5E-05 0.0001 0.00015 0.0002
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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
13
X/L0 0.2 0.4 0.6 0.8 1X/L
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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
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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
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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
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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
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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
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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
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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
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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
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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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