The Renaissance of Aeroelasticity and Its Future

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The Renaissance of Aeroelasticity and Its Future
Hybrid Particle-Continuum Computation of
Nonequilibrium Multi-Scale Gas Flows
Iain D. Boyd
Department of Aerospace Engineering
University of Michigan
Ann Arbor, MI 48109
Support Provided By:
MSI, AFOSR, NASA
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.
Gas Flows at the Micro–Scale
•
Examples:
– accelerometers (air-bags);
– micro-turbines (e.g. Karlsruhe);
– Knudsen pumps;
– Micro-Air-Vehicles (MAV’s).
•
Physical characteristics:
– atmospheric pressure;
– characteristic length ~ 10-6 m;
– Knudsen number ~ 0.01;
– non-continuum effects.
DSMC: Established
Particle Method for Gas Flows
• Direct simulation Monte Carlo (DSMC):
– developed by Bird (1960’s);
– 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.
  2RT  410 m s
'  
N  0.41m s N  1,000,000 
 ' s  0.41 s  1m s
{
u’, v’, w’
x, y, z
erot, evib
Subsonic Flow Over a 5% Flat Plate
Total sample size:760,000 particles/cell
Flat Plate
Density field
Pressure field
Information Preservation (IP)
• Relatively new method:
– first proposed by Fan and Shen (1998);
– further developed by Sun, Boyd, et al.;
– evolves alongside DSMC;
Dn
– particles and cells possess preserved D<u>
DT
information, e.g. n, <u>, T;
– Dn from mass conservation;
– D<u> from momentum conservation;
– DT from energy conservation;
– aims to reduce statistical fluctuations;
– may provide connection to CFD code.
}
{
u’, v’, w’
n, <u>, T
x, y, z
erot, evib
Outline of IP Algorithm
select collision pairs
perform binary collisions
Dt
Vi,1
1 C cos 
2
inject new particles
move particles, compute
boundary interactions
update information
sample cell information
dVi
1 p

dt
 x i
Vc  Vi
Vi,1 
1 C  cos 
2
Vi 
,2
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
Information Preservation Method:
Computational Performance
•
Numerically efficient implementation:
– only 20% overhead above DSMC;
– parallelized using domain decomposition.
Thermal Couette Flow
T=373K
y
1m
argon gas
T=173K
High Speed Couette Flow
V=300m/s, T=273K
y
1m
argon gas
V=0m/s, T=273K
Rayleigh Flow
argon gas V=0
T=273K
y
x
t=0: Vx=0, Tw=273K
Vx
t>0: Vx=10m/s, Tw=373K
Flow over flat plate
of zero thickness
M=0.2
Free-molecular theory: Cd=1.35/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)
Flow over a NACA-0012 Airfoil
Air: Ma = 0.8, Re = 73, Kn = 0.014, Lchord= 0.04m
DSMC
IP
Subsonic Flow Over a 5% Flat Plate
Air: Ma = 0.1, Re = 100, Kn = 0.01, L= 100 
Density field
Pressure field
Flow Over a 5% Flat Plate
Pressure contours (angle of attack 10o)
IP
NS
Flow Over a 5% Flat Plate
Surface properties
IP
pressure
NS
skin friction
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
Motivation for Hybrid Method
Flow
Regimes:
continuum
Kn
slip
transitional free-molecular
0.1
0.01
10
DSMC
Boltzmann Equation
Model
Accuracy:
Collisionless
Boltzmann Eqn
Navier-Stokes
Euler
Burnett
Numerical
Performance:
high
Kn
Accuracy +
Performance
}
DSMC
CFD
0.01
0.1
10
low
hybrid approach
Sometimes CFD Works Best
Sometimes DSMC Works Best
Hybrid Approach
MacCormack and Candler
Comp. Fluids, 17, 1989
Sun and Boyd
J. Comp. Phys., 179, 2002
Navier-Stokes solver
2nd order accurate modified
Steger-Warming flux-vector
splitting approach (FVM)
DSMC/IP method
interface
Macroscopic properties are
preserved as well as microscopic
particle information
Domain Coupling
Interface Location:
Continuum Breakdown Parameters
• Local Knudsen number, hypersonic flow (Boyd et al., 1995)
KnGLL Q 
l dQ
Q dx
 0.05
where Q= , 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?
Cut-off Value = 0.05
Hybrid CFD/DSMC-IP Process
CFD
Solution
Interface &
Particle Domain
Determined
Hybrid
Calculation
Final
Solution
Yes
End
No
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.
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.
Mach 5 Profiles
Reciprocal Shock Thickness
Numerical Performance
Method
CPU Time (sec)
Per Iteration
Pure CFD
0.032
Pure DSMC
0.48
Hybrid
0.29
• Hybrid simulation employed 57% particle cells
• DSMC time-step could be 20 times larger
Numerical Example (2)
Blunted Cone
Ma l (m)  (kg/m3) U (m/s) T (K) Tvib (K) Tw (K)
12.6 1.310-4 5.61810-4 2630.4 104.4 2680.2 297.2
Particle Domain (Knmax > 0.03)
Comparisons of Density Contours
Comparisons of
Temperature Contours
Comparisons of
Surface Properties
Detailed Comparisons
Along the Stagnation Streamline
Detailed Comparisons
at x = 2 cm
Detailed Comparisons
at x = 4 cm
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!
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).

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