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