Transcript Numerical Simulations of Energy Deposition in Hypersonic Flows

Surrogate Models of Electrical
Conductivity in Air*
Nicholas Bisek, Mark J. Kushner, Iain Boyd
University of Michigan
Jonathan Poggie
US Air Force Research Laboratory
* Work supported by Collaborative Center in
Aeronautical Sciences (AFRL and Boeing)
62nd GEC
10/20/2009
Slide 1
Agenda
•
•
•
•
•
•
62nd GEC
10/20/2009
Plasma-based Control of High Speed Air Vehicles
Conductivity Models: Need for generality
Surrogate (Design of Experiments) Modeling
Base Case Approach
Examples
Concluding Remarks
Slide 2
PLASMA CONTROL OF
HYPERSONIC VEHICLES
Plasma-based Control
•
•
•
•
Q = 140 W
Affects boundary layers
No moving parts
Motivation/Goals
Extremely rapid actuation
Minimal aerothermal penalty
when non-operational
“Supersonic Plasma Flow Control Experiments,”
AFRL-VA-WP-TR-2006-3006, Dec. 2005.
Shock mitigation
100
Virtual Cowl
Net pitch-up
Radio blackout
20
Net roll
MHD Power Generator
62nd GEC
10/20/2009
Near-Space
0
5
Mach
20
Slide 3
PLASMA CONTROL OF
HYPERSONIC VEHICLES-MODELS
 Desire (and need) for general modeling tools that are applicable to
predict peformance, optimize design of re-entry vehicles and
hypersonic craft.




Wide range of geometries- 3D approach required.
Magnetic field capable
Altitudes, Mach speed
Composition (e.g., Earth vs Venus vs Mars)
 High performance computing (massively parallel, many weeks/case)
 Rate limiting step is properly representing conductivity in context of
vast dynamic range in conditions




62nd GEC
10/20/2009
Pressures from mTorr to many atm.
Composition
Temperature (ambient to many eV)
Computationally tractable.
Slide 4
LeMANS
(Michigan Aerothermodynamic Navier-Stokes) code
•
•
•
•
•
Unstructured NS solver
2D/axisymmetric/3D grids
Parallelized
(MPI calls)
Motivation/Goals
Thermal non-equilibrium
Non-equilibrium chemistry
Mach 14 Air at 42 km
L
U∞
T∞
Tw
= 0.2 m
= 2185 m/s
= 60 K
= 300 K
Experiment: Nowlan (‘63)
62nd GEC
10/20/2009
Slide 5
LeMANS-MHD
Input Conditions
Mesh
Iterate
LeMANS (NS equations)
σ model
•Semi-empiric
•Boltzmann
MHD
• Nonequilibrium
• Parallelized
• Hall effect
62nd GEC
10/20/2009
Slide 6
Electrical Conductivity - Air
• Several approximate
models exist for various
ranges.
• None fully capture the
behavior.
62nd GEC
10/20/2009
p = 1 atm
- degree of ionization
- collision cross-section
Slide 7
Boltzmann Approach
• Charge quasineutrality
• e-e collisions
• Determine the electrical
conductivity from the
electron mobility
• Computationally prohibitive
direct coupling
Input Conditions
Mesh
Iterate
LeMANS (NS equations)
σ model
•Semi-empiric
•Boltzmann
MHD
62nd GEC
10/20/2009
Slide
Weng, & Kushner, Physical Review A, Vol. 42, No.
10. 8
Surrogate (DOE) Modeling
•
•
•
•
•
ID Dimensions
Surrogates
Accuracy
CPU-Cost
Global Sensitivity
• Reduced Dimensions
Surrogates Toolbox
• Felipe Viana – U. of F.
• Matlab library
1st order PRS
62nd GEC
10/20/2009
Slide 9
Dimension in Surrogate
Space
• E/N, n species
• Need a minimum of
2 x 2n points in DOE
Argon: Ar, Ar+
Air:N2, O2, NO, N, O, N2+, O2+, NO+, N+, O+
• 1D reduction
• Transform species mole fractions
dimensions into species angles



62nd GEC
10/20/2009
Slide 10
Surrogates
Polynomial Response Surface
• (PRS)
• Easy to implement
• Minimal coefficients
1st Order PRS
62nd GEC
10/20/2009
Slide 11
Accuracy - Argon
• Standard error (E)
• Percent error (PE)
62nd GEC
10/20/2009
Slide 12
CPU COST IMPLEMENTABLE
• PRS models are comparable
to semi-empirical models
62nd GEC
10/20/2009
Slide 13
Global Sensitivity
• Remove unnecessary
dimensions and rerun.
• Reduced Order
Methods (ROM)
• Ionic species appear
more sensitive.
62nd GEC
10/20/2009
Slide 14
Air Surrogate Model
E/N, N2, O2, NO, N, O,
N2+, O2+, NO+, N+, O+
62nd GEC
10/20/2009
11D 
211
sub-domains
• 4096 learning pts
• 3072 testing pts
Slide 15
3D Blunt Elliptic Cone
Mach 12.6 air at 40 km
Mach 12.6 Air at 42 km
L
U∞
T∞
Tw
62nd GEC
10/20/2009
=3m
= 4000 m/s
= 250 K
= 300 K
• Dipole magnetic
field to reduce heat
transfer
Slide 16
3D Blunt Elliptic Cone
Mach 12.6 air at 40 km
62nd GEC
10/20/2009
Slide 17
Concluding Remarks
• High Performance Computing on massively parallel computers
becoming commonplace in aerospace plasma applications.
• Desire to incorporate fundamental, general techniques to
represent plasma transport which are computationally tractable.
• Surrogate-DOE techniques have captured these goals.
• Investment up-front to develop surrogate model but can be
automated and reused.
• Applicable to non-terrestrial atmospheres
• Improvements
• Real time adjustment of domain to refine surrogate model
62nd GEC
10/20/2009
Slide 18