Surrogate Models of Electrical Conductivity in Air*
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62nd GEC10/20/2009
Slide 1
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)
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62nd GEC10/20/2009
Slide 2
Agenda
• Plasma-based Control of High Speed Air Vehicles
• Conductivity Models: Need for generality
• Surrogate (Design of Experiments) Modeling
• Base Case Approach
• Examples
• Concluding Remarks
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62nd GEC10/20/2009
Slide 3
Mach5 200
20
100
Alt
itu
de
[km
]
Near-Space
Q = 140 W
“Supersonic Plasma Flow Control Experiments,” AFRL-VA-WP-TR-2006-3006, Dec. 2005.
Net roll
Net pitch-up
Shock mitigation
Radio blackout
Virtual Cowl
MHD Power Generator
PLASMA CONTROL OF HYPERSONIC VEHICLES
Motivation/GoalsMotivation/Goals
Plasma-based Control• Affects boundary layers• No moving parts• Extremely rapid actuation • Minimal aerothermal penalty
when non-operational
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62nd GEC10/20/2009
Slide 4
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
Pressures from mTorr to many atm. Composition Temperature (ambient to many eV) Computationally tractable.
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62nd GEC10/20/2009
Slide 5
Motivation/GoalsMotivation/Goals
• Unstructured NS solver
• 2D/axisymmetric/3D grids
• Parallelized (MPI calls)
• Thermal non-equilibrium
• Non-equilibrium chemistry
LeMANS(Michigan Aerothermodynamic Navier-Stokes) code
Experiment: Nowlan (‘63)Experiment: Nowlan (‘63)
Mach 14 Air at 42 km
L = 0.2 mU∞ = 2185 m/s
T∞ = 60 KTw = 300 K
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62nd GEC10/20/2009
Slide 6
LeMANS-MHD
MeshMesh Input ConditionsInput Conditions
LeMANS (NS equations)LeMANS (NS equations)
MHDMHD
σ model
•Semi-empiric•Boltzmann
σ model
•Semi-empiric•BoltzmannIt
erat
e
• Nonequilibrium
• Parallelized
• Hall effect
• Nonequilibrium
• Parallelized
• Hall effect
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62nd GEC10/20/2009
Slide 7
• Several approximate models exist for various ranges.
• None fully capture the behavior.
• Several approximate models exist for various ranges.
• None fully capture the behavior.
Electrical Conductivity - Air
p = 1 atmp = 1 atm
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62nd GEC10/20/2009
Slide 8
• Charge quasineutrality• e-e collisions• Determine the electrical
conductivity from the electron mobility
• Computationally prohibitive direct coupling
• Charge quasineutrality• e-e collisions• Determine the electrical
conductivity from the electron mobility
• Computationally prohibitive direct coupling
MeshMesh Input ConditionsInput Conditions
LeMANS (NS equations)LeMANS (NS equations)
MHDMHD
Itera
te
Boltzmann Approach
Weng, & Kushner, Physical Review A, Vol. 42, No. 10.
σ model
•Semi-empiric•Boltzmann
σ model
•Semi-empiric•Boltzmann
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62nd GEC10/20/2009
Slide 9
Surrogate (DOE) Modeling
• ID Dimensions• Surrogates• Accuracy• CPU-Cost• Global Sensitivity
• Reduced Dimensions
• ID Dimensions• Surrogates• Accuracy• CPU-Cost• Global Sensitivity
• Reduced Dimensions
Surrogates Toolbox• Felipe Viana – U. of F.• Matlab library
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62nd GEC10/20/2009
Slide 10
Dimension in Surrogate Space
• E/N, n species• E/N, n species
• Transform species mole fractions dimensions into species angles
• Transform species mole fractions dimensions into species angles
Argon: Ar, Ar+
Air:N2, O2, NO, N, O, N2+, O2
+, NO+, N+, O+
• 1D reduction• 1D reduction
• Need a minimum of 2 x 2n points in DOE
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62nd GEC10/20/2009
Slide 11
Surrogates
Polynomial Response Surface Polynomial Response Surface
• (PRS)• Easy to implement• Minimal coefficients
1st Order PRS
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62nd GEC10/20/2009
Slide 12
Accuracy - Argon
• Standard error (E)
• Percent error (PE)
• Standard error (E)
• Percent error (PE)
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62nd GEC10/20/2009
Slide 13
CPU COST - IMPLEMENTABLE
• PRS models are comparable to semi-empirical models
• PRS models are comparable to semi-empirical models
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62nd GEC10/20/2009
Slide 14
Global Sensitivity
• Remove unnecessary dimensions and rerun.
• Reduced Order Methods (ROM)
• Ionic species appear more sensitive.
• Remove unnecessary dimensions and rerun.
• Reduced Order Methods (ROM)
• Ionic species appear more sensitive.
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62nd GEC10/20/2009
Slide 15
Air Surrogate Model
E/N, N2, O2, NO, N, O, N2
+, O2+, NO+, N+, O+
E/N, N2, O2, NO, N, O, N2
+, O2+, NO+, N+, O+ 11D 211 sub-domains
• 4096 learning pts• 3072 testing pts
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62nd GEC10/20/2009
Slide 16
3D Blunt Elliptic ConeMach 12.6 air at 40 km
• Dipole magnetic field to reduce heat transfer
Mach 12.6 Air at 42 km
L = 3 mU∞ = 4000 m/s
T∞ = 250 KTw = 300 K
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62nd GEC10/20/2009
Slide 17
3D Blunt Elliptic ConeMach 12.6 air at 40 km
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62nd GEC10/20/2009
Slide 18
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