The Renaissance of Aeroelasticity and Its Future

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Hybrid Particle-Continuum Computation
of Nonequilibrium Multi-Scale Gas Flows
Iain D. BoydDepartment of Aerospace
EngineeringUniversity of MichiganAnn Arbor, MI
48109Support Provided ByMSI, AFOSR, NASA
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Overview

• Problems with DSMC for low-speed MEMS flows.
• The Information Preservation (IP) method
• basic ideas and algorithms
• validation studies.
• Use of IP in a hybrid CFD-DSMC method
• data communication and interface location
• hypersonic flow applications.
• Future directions.

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Gas Flows at the MicroScale

• Examples
• accelerometers (air-bags)
• micro-turbines (e.g. Karlsruhe)
• Knudsen pumps
• Micro-Air-Vehicles (MAVs).
• Physical characteristics
• atmospheric pressure
• characteristic length 10-6 m
• Knudsen number 0.01
• non-continuum effects.

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DSMC EstablishedParticle Method for Gas Flows

• Direct simulation Monte Carlo (DSMC)
• developed by Bird (1960s)
• particles move in physical space
• particles possess microscopic properties, e.g. u
  (thermal velocity)
• cell size l, time step 1/n
• collisions handled statistically
• ideal for supersonic/hypersonic flows
• statistical scatter for subsonic flow.

u, v, w x, y, z erot, evib
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Subsonic Flow Over a 5 Flat Plate
Total sample size760,000 particles/cell
Flat Plate
Density field
Pressure field
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Information Preservation (IP)

• Relatively new method
• first proposed by Fan and Shen (1998)
• further developed by Sun, Boyd, et al.
• evolves alongside DSMC
• particles and cells possess preserved
  information, e.g. n, ltugt, T
• Dn from mass conservation
• Dltugt from momentum conservation
• DT from energy conservation
• aims to reduce statistical fluctuations
• may provide connection to CFD code.

Dn Dltugt DT

u, v, w n, ltugt, T x, y, z erot, evib
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Outline of IP Algorithm
select collision pairs
perform binary collisions
inject new particles
Dt
move particles, compute boundary interactions
update information
sample cell information
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Information Preservation Method

• Statistical scatter (from a flow over a flat
  plate)

Time step 1 Sampling size 20 Time step
1000 Sampling size 20,000 Time step
100,000 Sampling size 2,000,000
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Information Preservation MethodComputational
Performance

• Numerically efficient implementation
• only 20 overhead above DSMC
• parallelized using domain decomposition.

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Thermal Couette Flow
T373K
1m
argon gas
y
T173K
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High Speed Couette Flow
V300m/s, T273K
1m
argon gas
y
V0m/s, T273K
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Rayleigh Flow
V0 T273K
y
argon gas
t0 Vx0, Tw273K
x
tgt0 Vx10m/s, Tw373K
Vx
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Flow over flat plateof zero thickness
M0.2
Free-molecular theory Cd1.35/M
Compressible experiment
Schaaf and Sherman (1954)
Slip Oseen-Stokes solution
Tamada and Miura (1978)
Incompressible N-S
Dennis and Dunwoody (1966)
Incompressible experiment
Janour (1951)
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Flow over a NACA-0012 Airfoil
Air Ma? 0.8, Re? 73, Kn? 0.014, Lchord
0.04m
DSMC
IP
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Subsonic Flow Over a 5 Flat Plate
Air Ma? 0.1, Re? 100, Kn? 0.01, L 100 m
Density field
Pressure field
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Flow Over a 5 Flat Plate
Pressure contours (angle of attack 10o)
IP
NS
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Flow Over a 5 Flat Plate
Surface properties
IP
NS
pressure
skin friction
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Hybrid Method for Hypersonic Flows

• Hypersonic vehicles encounter a variety of flow
  regimes
• continuum modeled accurately and efficiently
  with CFD
• rarefied modeled accurately and efficiently
  with DSMC.
• A hybrid DSMC-CFD method is attractive for mixed
  flows
• CFD Navier-Stokes finite-volume algorithm
• DSMC MONACO Information Preservation (DSMC/IP).

Rarefied DSMC approach based on kinetic
theory high altitude sharp edges
Continuum CFD approach solve NS
equations low altitude long length
scales
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Motivation for Hybrid Method
transitional
slip
free-molecular
Flow Regimes
continuum
Kn
0.1
0.01
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DSMC
Boltzmann Equation
Model Accuracy
Collisionless Boltzmann Eqn
Navier-Stokes
Euler
Burnett
high
Numerical Performance
DSMC
CFD
Kn
0.01
0.1
10
low
Accuracy

hybrid approach
Performance
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Sometimes CFD Works Best
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Sometimes DSMC Works Best
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Hybrid Approach
Sun and Boyd J. Comp. Phys., 179, 2002
MacCormack and Candler Comp. Fluids, 17, 1989
Navier-Stokes solver
DSMC/IP method
Macroscopic properties are preserved as well as
microscopic particle information
2nd order accurate modified Steger-Warming
flux-vector splitting approach (FVM)
interface
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Domain Coupling
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Interface Location Continuum Breakdown Parameters

• Local Knudsen number, hypersonic flow (Boyd et
  al., 1995)
• where Q r, T, V.
• Determined through detailed DSMC versus CFD
  comparisons
• Parameters also under investigation for use
  inside DSMC
• - failure of breakdown parameters at shock front
• - use DSMC to evaluate continuum onset parameter?

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Cut-off Value 0.05
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Hybrid CFD/DSMC-IP Process
CFD Solution
Interface Particle Domain Determined
Hybrid Calculation
Final Solution
No
Yes
End
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Summary of Hybrid Code

• Numerical methods
• 2d/axially symmetric, steady state
• CFD explicit, finite volume solution of NS Eqs.
• DSMC based on MONACO
• interface Information Preservation scheme
• implementation a single, parallel code.
• Physical modeling
• simple, perfect gas (rotation, but no vibration)
• walls slip / incomplete accommodation
• breakdown parameter local Knudsen number.

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Numerical Example (1) Normal Shock Waves of Argon

• Argon normal shocks investigated
• relatively simple hypersonic flow
• Alsmeyer experimental measurements
• well-known case for testing new algorithms.
• Simulations
• modeled in 2D (400 x 5 cells)
• initialized by jump conditions
• pure DSMC
• pure CFD (Navier-Stokes equations)
• hybrid code initialized by CFD solution.

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Mach 5 Profiles
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Reciprocal Shock Thickness
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Numerical Performance

• Hybrid simulation employed 57 particle cells
• DSMC time-step could be 20 times larger

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Numerical Example (2) Blunted Cone
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Particle Domain (Knmax gt 0.03)
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Comparisons of Density Contours
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Comparisons of Temperature Contours
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Comparisons of Surface Properties
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Detailed Comparisons Along the Stagnation
Streamline
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Detailed Comparisons at x 2 cm
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Detailed Comparisons at x 4 cm
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Summary

• Simulation of subsonic nonequilibrium gas flows
• difficulties caused by low speed and
  rarefaction
• DSMC not effective due to statistical
  fluctuations
• IP method developed and applied to several
  flows
• IP is effective at reducing statistical
  fluctuations
• IP provides a basis for creating a hybrid
  method.
• Simulation of hypersonic nonequilibrium gas
  flows
• vehicle analysis involves continuum/rarefied
  flow
• hybrid CFD-DSMC/IP method looks promising
• physical modeling must be improved
• numerical performance must be improved
• much work still to be done!

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Future Directions

• Algorithm development for hybrid method
• CFD parallel, implicit solver on unstructured
  mesh
• DSMC implicit and/or other acceleration schemes.
• Physics development for hybrid method
• vibrational relaxation
• chemically reacting gas mixture.
• Development of hybrid methodology
• refinement of breakdown parameters
• evaluation against data (measured, computed).