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Surrogate Models of Electrical Conductivity in Air*

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). Agenda.

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Surrogate Models of Electrical Conductivity in Air*

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  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)

  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

  3. PLASMA CONTROL OF HYPERSONIC VEHICLES Shock mitigation • Plasma-based Control • Affects boundary layers • No moving parts • Extremely rapid actuation • Minimal aerothermal penalty when non-operational • Motivation/Goals Q = 140 W Virtual Cowl Radio blackout Net pitch-up Net roll “Supersonic Plasma Flow Control Experiments,” AFRL-VA-WP-TR-2006-3006, Dec. 2005. 100 Near-Space MHD Power Generator Altitude [km] 20 0 5 20 Mach

  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.

  5. LeMANS(Michigan Aerothermodynamic Navier-Stokes) code • Motivation/Goals • Unstructured NS solver • 2D/axisymmetric/3D grids • Parallelized (MPI calls) • Thermal non-equilibrium • Non-equilibrium chemistry Mach 14 Air at 42 km L = 0.2 m U∞ = 2185 m/s T∞ = 60 K Tw = 300 K Experiment: Nowlan (‘63)

  6. LeMANS-MHD Input Conditions Mesh LeMANS (NS equations) σ model • Semi-empiric • Boltzmann Iterate MHD • Nonequilibrium • Parallelized • Hall effect

  7. Electrical Conductivity - Air p = 1 atm • Several approximate models exist for various ranges. • None fully capture the behavior. • degree of ionization • collision cross-section

  8. Boltzmann Approach • Charge quasineutrality • e-e collisions • Determine the electrical conductivity from the electron mobility • Computationally prohibitive direct coupling Input Conditions Mesh LeMANS (NS equations) σ model • Semi-empiric • Boltzmann Iterate MHD Weng, & Kushner, Physical Review A, Vol. 42, No. 10.

  9. 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

  10. 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   

  11. Surrogates Polynomial Response Surface • (PRS) • Easy to implement • Minimal coefficients 1st Order PRS

  12. Accuracy - Argon • Standard error (E) • Percent error (PE)

  13. CPU COST - IMPLEMENTABLE • PRS models are comparable to semi-empirical models

  14. Global Sensitivity • Remove unnecessary dimensions and rerun. • Reduced Order Methods (ROM) • Ionic species appear more sensitive.

  15. Air Surrogate Model E/N, N2, O2, NO, N, O, N2+, O2+, NO+, N+, O+ • 4096 learning pts • 3072 testing pts 11D  211 sub-domains

  16. 3D Blunt Elliptic Cone Mach 12.6 air at 40 km Mach 12.6 Air at 42 km L = 3 m U∞ = 4000 m/s T∞ = 250 K Tw = 300 K • Dipole magnetic field to reduce heat transfer

  17. 3D Blunt Elliptic Cone Mach 12.6 air at 40 km

  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

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