Plasma models physically consistent from kinetic scale to hydrodynamic scale Thierry Magin Aeronautics and Aerospace Department von Karman Institute for Fluid Dynamics, Belgium Workshop on Moment Methods in Kinetic Theory II Fields Institute, Toronto, October 14-17, 2014 Thierry Magin (VKI) Plasma models 14-17 October 2014 1 / 58
von Karman Institute for Fluid Dynamics “With the advent of jet propulsion, it became necessary to broaden the field of aerodynamics to include problems which before were treated mostly by physical chemists . . . ” Theodore K´ arm´ an, 1958 “Aerothermochemistry” was coined by von K´ arm´ an in the 1950s to denote this multidisciplinary field of study shown to be pertinent to the then emerging aerospace era Thierry Magin (VKI) Plasma models 14-17 October 2014 2 / 58
Team Team Collaborators who contributed to the results presented here Mike Kapper, G´ erald Martins, Alessandro Munaf` o, JB Scoggins and Erik Torres (VKI) Benjamin Graille (Paris-Sud Orsay) Marc Massot (Ecole Centrale Paris) Irene Gamba and Jeff Haack (The University of Texas at Austin) Anne Bourdon and Vincent Giovangigli (Ecole Polytechnique) Manuel Torrilhon (RWTH Aachen University) Marco Panesi (University of Illinois at Urbana-Champaign) Rich Jaffe, David Schwenke, Winifred Huo (NASA ARC) Mikhail Ivanov and Yevgeniy Bondar (ITAM) Support from the E uropean R esearch C ouncil through Starting Grant #259354 Thierry Magin (VKI) Plasma models 14-17 October 2014 3 / 58
Team Outline 1 Introduction 2 Kinetic data 3 Atomic ionization reactions 4 Internal energy excitation in molecular gases 5 Translational thermal nonequilibrium in plasmas 6 Conclusion Thierry Magin (VKI) Plasma models 14-17 October 2014 4 / 58
Introduction Outline 1 Introduction 2 Kinetic data 3 Atomic ionization reactions 4 Internal energy excitation in molecular gases 5 Translational thermal nonequilibrium in plasmas 6 Conclusion Thierry Magin (VKI) Plasma models 14-17 October 2014 4 / 58
Introduction Motivation Thierry Magin (VKI) Plasma models 14-17 October 2014 5 / 58
Introduction Motivation Motivation: new challenges for aerospace science Design of spacecraft heat shields Modeling of the convective and radiative heat fluxes for: Robotic missions aiming at bringing back samples to Earth Manned exploration program to the Moon and Mars Intermediate eXperimental Vehicle of ESA Ballute aerocapture concept of NASA Hypersonic cruise vehicles Modeling of flows from continuum to rarefied conditions for the next generation of air breathing hypersonic vehicles Thierry Magin (VKI) Plasma models 14-17 October 2014 6 / 58
Introduction Motivation Motivation: new challenges for aerospace science Electric propulsion Today, 20% of active satellites operate with EP systems STO-VKI Lecture Series (2015-16) Electric Propulsion Systems: from recent research developments to industrial space applications EP system for ESA’s gravity mission GOCE ∼ 20,000 space debris > 10cm Space debris Space debris, a threat for satellite and space systems and for mankind when undestroyed debris impact the Earth STO-VKI Lecture Series (June 2015) Space Debris, In Orbit Demonstration, Debris Mitigation Thierry Magin (VKI) Plasma models 14-17 October 2014 7 / 58
Introduction Motivation Engineering design in hypersonics Two quantities of interest relevant to rocket scientists Heat flux Shear stress to the vehicle surface ⇒ Complex multiscale problem Chemical nonequilibrium (gas) Dissociation, ionization, . . . Internal energy excitation Thermal nonequilibrium Blast capsule flow simulation Translational and internal energy relaxation VKI COOLFluiD platform Radiation and Mutation library Gas / surface interaction Surface catalysis Ablation Rarefied gas effects Turbulence (transition) Thierry Magin (VKI) Plasma models 14-17 October 2014 8 / 58
Introduction Objective Physico-chemical models for atmospheric entry plasmas Earth atmosphere: S = { N 2 , O 2 , NO , N , O , NO + , N + , O + , e − , . . . } Fluid dynamics Kinetic theory ρ i ( x , t ), i ∈ S, v ( x , t ), E ( x , t ) f i ( x , c i , t ) , i ∈ S Fluid dynamical description Gas modeled as a continuum in terms of macroscopic variables e . g . Navier-Stokes eqs., Boltzmann moment systems Kinetic description Gas particles of species i ∈ S follow a velocity distribution f i in the phase space ( x , c i ) e . g . Boltzmann eq. ⇒ Constraint: descriptions with consistent physico-chemical models Thierry Magin (VKI) Plasma models 14-17 October 2014 9 / 58
Introduction Objective From microscopic to macroscopic quantities Mass density of species i ∈ S: R ρ i ( x , t ) = i m i d c i f Mixture mass density: ρ ( x , t ) = P j ∈ S ρ j ( x , t ) Hydrodynamic velocity: ρ ( x , t ) v ( x , t ) = P R f j m j c j d c j j ∈ S Total energy (point particles): 2 m j | c j | 2 d c j j 1 E ( x , t ) = P R f j ∈ S Thermal (translational) energy: Velocity distribution function for 1D Ar 2 m j | c j − v | 2 d c j j 1 R ρ ( x , t ) e ( x , t ) = P f shockwave (Mach 3.38) at different j ∈ S positions x ∈ [ − 1 cm , +1 cm ] [Munafo et al. 2013] ⇒ Suitable asymptotic solutions can be derived by means of the Chapman-Enskog perturbative solution method Thierry Magin (VKI) Plasma models 14-17 October 2014 10 / 58
Introduction Objective Objective of this presentation “Engineers use knowledge primarily to design, produce, and operate artifacts . . . Scientists, by contrast, use knowledge primarily to generate more knowledge.” Walter Vincenti ⇒ Enrich mathematical models by adding more physics ⇒ Derive mathematical structure and fix ad-hoc terms found in engineering models ⇒ Integrate quantum chemistry databases Thierry Magin (VKI) Plasma models 14-17 October 2014 11 / 58
Kinetic data Outline 1 Introduction 2 Kinetic data 3 Atomic ionization reactions 4 Internal energy excitation in molecular gases 5 Translational thermal nonequilibrium in plasmas 6 Conclusion Thierry Magin (VKI) Plasma models 14-17 October 2014 11 / 58
Kinetic data Transport collision integrals ⇒ Closure of the transport fluxes at a microscopic scale The transport properties are expressed in terms of collision integrals ∞ „ − E 2 ( l + 1) « Z Q ( l , s ) E s +1 Q ( l ) ¯ ( T ) = exp d E ij ij h 2 l + 1 − ( − 1) l i (k B T ) s +2 k B T ( s + 1)! 0 They represent an average over all possible relative energies of the relevant cross section ∞ Z Q ( l ) h 1 − cos l ( χ ) i ij ( E ) = 2 π b d b , 0 “Boltzmann impression”, Losa, Luzern 2004 Thierry Magin (VKI) Plasma models 14-17 October 2014 12 / 58
Kinetic data Deflection angle 2 b 1 5 2.4624 ij χ 0 ϕ e / ϕ 1 0 0 Dynamics of an elastic binary collision Effective potential -1 ϕ e ( E , b , r ) = ϕ ( r ) + E b 2 0 1 2 3 4 r 2 r / σ Deflection angle Effective Lennard-Jones potential ∞ d r � r 2 √ χ ( E , b ) = π − 2 b 1 − ϕ e / E r m Thierry Magin (VKI) Plasma models 14-17 October 2014 13 / 58
Kinetic data Neutral-neutral interactions: sewing method for potentials [M., Degrez, Sokolova 2004] 60 5 10 4 10 3 10 50 2 10 1 2 ] 10 (1,1) [A ϕ / ϕ 0 40 1.0 Q 0.5 0.0 30 -0.5 -1.0 I II III -1.5 20 0 2500 5000 7500 10000 12500 15000 0 1 2 T [K] r / σ Q (1 , 1) collision integral for the ¯ Potentials models for the O 2 − O 2 Tang-Toennies, −− Born-Mayer, CO 2 − CO 2 interaction: and −− (m,6) −− (m,6) potential, −− Born-Mayer potential, (experimental data of Brunetti) and − × − combined result Thierry Magin (VKI) Plasma models 14-17 October 2014 14 / 58
Kinetic data Ion-neutral interactions Q ( l , s ) Elastic collisions: ¯ el Born-Mayer potential: ϕ ( r ) = ϕ 0 exp ( − α r ) with parameters recovered from atom-atom model Q (1 , s ) Resonant charge-transfer: ¯ res , s ∈ { 1 , 2 , 3 } For l odd interaction where atom and ions are parent and child O − O + r [Stallcop, Partridge, Levin] W (release) U max C − C + W (no release) [Duman and Smirnov] Q exc = (7 . 071 − 0 . 3485 ln E ) 2 Q (1) res = 2 Q exc For l = 1 �� � 2 � 2 Q (1 , s ) = � ¯ Q (1 , s ) ¯ Q (1 , s ) ¯ + res el Thierry Magin (VKI) Plasma models 14-17 October 2014 15 / 58
Kinetic data Ion-neutral interactions 150 125 100 2 ] (1,1) [A 75 Q 50 25 0 0 2500 5000 7500 10000 12500 15000 T [K] Q (1 , 1) collision integrals: O − O + , ¯ Stallcop et al . ; C − C + , −− resonant charge transfer, · · · Born-Mayer, and × combined result Thierry Magin (VKI) Plasma models 14-17 October 2014 16 / 58
Kinetic data Charge-charge interactions 10000 Shielded Coulomb potential [Mason et al] 8000 and [Devoto] : 2 ] 6000 d − r (1,1) [A � � ϕ ( r ) = ± ϕ 0 r exp d Q 4000 2000 Debye length � 1 / 2 0 � ε 0 k B T e 5000 7500 10000 12500 15000 λ D = T [K] 2 n e q 2 e Q (1 , 1) for LTE carbon dioxide at 1 atm: ¯ −− attractive interaction and repulsive interaction Thierry Magin (VKI) Plasma models 14-17 October 2014 17 / 58
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