Surrogate Models of Electrical Conductivity in Air*
-
Upload
len-higgins -
Category
Documents
-
view
28 -
download
2
description
Transcript of Surrogate Models of Electrical Conductivity in Air*
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)
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
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
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.
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
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
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
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
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
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
62nd GEC10/20/2009
Slide 11
Surrogates
Polynomial Response Surface Polynomial Response Surface
• (PRS)• Easy to implement• Minimal coefficients
1st Order PRS
62nd GEC10/20/2009
Slide 12
Accuracy - Argon
• Standard error (E)
• Percent error (PE)
• Standard error (E)
• Percent error (PE)
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
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.
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
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
62nd GEC10/20/2009
Slide 17
3D Blunt Elliptic ConeMach 12.6 air at 40 km
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