Predictive Engineering and Computational Sciences. Detailed and simplified kinetic mechanisms for high enthalpy flows

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Marco Panesi Non-equilibriumst ionization January 31 st, 211 1 / 22

simplified kinetic mechanisms for high enthalpy flows Application to

Bourdon, Arnaud Bultel, Thierry Magin Institute for Computational

1 Marco Panesi Non-equilibriumst ionization January 31 st, / 22 PECOS Predictive Engineering and Computational Sciences Detailed and simplified kinetic mechanisms for high enthalpy flows Application to the analysis of the Fire II flight experiment Marco Panesi, Anne Bourdon, Arnaud Bultel, Thierry Magin Institute for Computational Engineering and Sciences, The University of Texas at Austin, U.S.A. CNRS Research Fellow, EM2C Laboratory CORIA, CNRS UMR 6614, Université de Rouen von Karman Institute for Fluid Dynamics Symposium in Honor of Prof Mario Capitelli

2 Outline 1 Introduction 2 Atomic and Molecular Energy Levels 3 Coupled Fluid & Collisional Radiative models Kinetic Processes Radiative Processes Fluid Model and Radiation Transfer 4 Results FIRE II: non-equilibrium ionization EAST: Comparison with shock tube data. Grouping of the levels 5 Conclusions Marco Panesi Non-equilibrium ionization January 31 st, / 22

Introduction Motivations and Objectives of the Project Marginal PDF.2.15.1.5 Mode = 44.8 [W/cm 2 ] µ = 76.69 [W/cm 2 ] σ = 45.

3 Introduction Motivations and Objectives of the Project Marginal PDF Mode = 44.8 [W/cm 2 ] µ = [W/cm 2 ] σ = [W/cm 2 ] Goals Pecos 1 2 Radiative Heating [W/cm 2 ] Specair (Laux) Development of an accurate kinetic mechanism for earth entry applications. Determination of a reduced mechanism for CFD applications. Bultel, A. et al., Collisional-radiative model in air for earth re-entry problems Physics of Plasmas, 26, 13, 11 Marco Panesi Non-equilibrium ionization January 31 st, / 22

4 Atomic and Molecular Energy Levels Atomic Structure Atomic chemical components: N,O, N +, O + NITROGEN Normalized Population [m -3 ] NIST Abba N II ( 3 P ) Energy [ev] Nitrogen 46 lumped levels: Combination of real and lumped levels (NIST 381). Oxygen 4 lumped levels: Combination of real and lumped levels (NIST 614). Marco Panesi Non-equilibrium ionization January 31 st, / 22

5 Atomic and Molecular Energy Levels Molecular structure N 2 system.6.6 NO + system.5.5 V r,s a. u C B A V r,s a. u A.1 X R, a. u..1 X R, a. u Schwenke D. AIAA Molecular chemical components: N 2, NO, O 2, N + 2, NO+, O + 2 Electronic specific treatment of the electronic molecular systems (27 states). Boltzmann assumption for the ro-vibrational structure, except for NO +. T v,me = T v,n2 X T r,me = T r,n2 X Marco Panesi Non-equilibrium ionization January 31 st, / 22

6 Coupled Fluid & Collisional Radiative models Kinetic Processes Kinetic Processes Collisional excitation (/ionization) and de-excitation (heavy/light). Atomic processes: A(E i ) + C A (+) (E j ) + C(+e) C [e, H] Molecular processes, (Averaged over the ro-vibrational structure) Collisional dissociation (heavy/light) M(Ēi) + C M (+) (Ēj) + C(+e) C [e, H] Exchange reactions (Zeld ovich reactions) Charge exchange Dissociative recombination / Associative ionization NO + (X 1 Σ +, v) + e N + O, Motapon et al. O + 2, N+ 2, Boltzmann averaged values. (Not included in the present model) Over 1 K elementary processes included Bultel, A. et al., Collisional-radiative model in air for earth re-entry problems Physics of Plasmas, 26, 13, 11 Marco Panesi Non-equilibrium ionization January 31 st, / 22

7 Coupled Fluid & Collisional Radiative models Radiative Processes Line radiation The atomic bound-bound radiation N i (v, E i ) + hν (n, dω ν ) N j (v, E j ) (1) Detailed balance N j (v, E j ) + hν (n, dω ν ) N i (v, E i ) + 2hν (n, dω ν ) (2) B j,i,(ν) = c2 8πhν 3 A j,i,(ν) g j B j,i,(ν) = g i B i,j,(ν) The B coefficients defined originally by Einstein, and still sometimes used in literature, differ from the Einstein-Milne coefficients by a factor (c/4π). Marco Panesi Non-equilibrium ionization January 31 st, / 22

8 Coupled Fluid & Collisional Radiative models Radiative Processes Radiative Recombination and photo-ionization The atomic photoionisation corresponds to: N i (v, E i ) + hν (n, dω ν ) N + j (v, E+ j ) + e ( v e, d 3 v e ) (3) ( g Q (,+) + i,j,(ν) = 2 j gi ) m e (hν) 2 c2 E e Q (+,) j,i,(e e) We define the cross section for induced free-bound processes as follows Q (,+) j,i,(v e) Q (,+) j,i,(v e) ( ) c 2 = 2hν 3 Marco Panesi Non-equilibrium ionization January 31 st, / 22

9 Coupled Fluid & Collisional Radiative models Radiative Processes Transition Rates Bound-Bound rates [ ] dn(i,s) = dt j>i i>j [ A j,i n s,j (B i,j n s,i B j,i n s,j ) [ A i,j n s,i (B j,i n s,j B i,j n s,i ) ] G ν Φ i,j ν dν ] G ν Φ i,j ν dν (4) Bound-Free rates [ ] + dn(i,s) dt (i,s) = n + (j,s) n e v e + n + (j,s) n e v e Q (,+) j,i,(ɛ e) ɛ e exp ( ɛ e )dɛ e G ν Q(,+) j,i,(ɛ e) ɛ e exp ( ɛ e )dɛ e [ ] dn(i,s) dt (i,s) = n (i,s) G ν hν Q(,+) i,j,(ν) dν Marco Panesi Non-equilibrium ionization January 31 st, / 22

10 Coupled Fluid & Collisional Radiative models Radiative Processes Radiative Transfer Equation Incident Intensity: µ di λ(τ, µ) dτ λ + I λ (τ λ, µ) = η λ κ λ (τ λ ) = S λ (τ λ ) (5) [ τ G λ (τ) = 2π I + λ (τ λ,b)e 2 (τ λ ) + I λ (τ λ,s)e 2 (τ λ,s τ λ ) + S λ E 1 (τ λ τ λ) dτ λ τ b τs ] + S λ E 1 (τ λ τ λ ) dτ λ Radiative heating and its divergence [ q λ (τ) = 2π I + λ (τ λ,b)e 3 (τ λ ) + τ τ τ b S λ E 2 (τ λ τ λ)dτ λ τs ] I λ (τ λ,s)e 3 (τ λ,s τ λ ) S λ E 2 (τ λ τ λ )dτ λ τ Marco Panesi Non-equilibrium ionization January 31 st, / 22

11 Coupled Fluid & Collisional Radiative models Fluid Model and Radiation Transfer Modeling of non-equilibrium flows Euler eqs.: conservation of mass for species i, momentum and total energy ρ d i ρu + d ρ i u M i ω i ρu 2 + p = dt dx ρe ρuh q rad MultiT models: additional energy conservation eqs., e.g. vibrational energy eq. Radiation transport models d dt (ρe m) + d dx (ρue m) = Ω m qrad m + µ di λ(τ, µ) dτ λ + I λ (τ λ, µ) = S λ (τ λ ) Marco Panesi Non-equilibrium ionization January 31 st, / 22

12 Coupled Fluid & Collisional Radiative models Fluid Model and Radiation Transfer Radiation Coupling Loosely coupled (explicit coupling) strategy Flow quantities SHOCKING Ū = [N i, T i, p] T Spectral quantities HPC-RAD I λ = I λ (ɛ λ, κ λ ) Divergence and Intensity Ī = [ ω rad, q] HPC-RAD SHOCKING Spectral Properties RADIATION TRANSPORT P Ti Ni Marco Panesi Non-equilibrium ionization January 31 st, / 22

13 Results Results Fire II - Fully coupled EAST - Comparison with experiments Fire II - Reduction of the model References: Panesi, M. et al. Analysis of the Fire II Flight Experiment by means of a Collisional Radiative Model Journal of Thermophysics an Transfer, 29, 23, Panesi, M. et al. Electronic Excitation of atoms and molecules for the Fire II Flight Experiment Journal of Thermophysics an Transfer, 211, accepted Panesi, M. et al. Non-equilibrium ionization phenomena behind shock waves 27th International Symposium on Rarefied Gas Dynamics, 21 Marco Panesi Non-equilibrium ionization January 31 st, / 22

Results FIRE II: non-equilibrium ionization FIRE II Objective Study the behavior of the electronically excited states of atomic and molecular species in the post shock area.

14 Results FIRE II: non-equilibrium ionization FIRE II Objective Study the behavior of the electronically excited states of atomic and molecular species in the post shock area. Investigate the validity of the Q.S.S. assumption. Characterization of the ionization process. Time [s] 1634 p 1 [Pa] 2. T 1 [K] 195 u 1 [m/s] p 2 [Pa] 3827 T 2 [K] u 2 [m/s] 1899 Flow characteristic quantities Marco Panesi Non-equilibrium ionization January 31 st, / 22

15 Results FIRE II: non-equilibrium ionization Flowfield quantities Temperature [K] T T V Distance from the shock [m] Number Density [m 3 ] Thick limit Thin limit Coupled calculation Distance from the shock [m].1 Figure: Post-shock temperature (left) and electron number density (right) profiles for a fluid particle as a function of the distance from the shock Marco Panesi Non-equilibrium ionization January 31 st, / 22

16 Results FIRE II: non-equilibrium ionization Internal distribution functions Normalized Population [m -3 ] Thin Limit Boltzmann Thick Limit Coupled calculation Energy [ev] Normalized Population [m -3 ] Thin Limit Boltzmann Thick Limit Coupled calculation Energy [ev] Figure: Electronic energy distribution function for atomic nitrogen (left) and oxygen (right) at 1 cm from the shock front Marco Panesi Non-equilibrium ionization January 31 st, / 22

17 Results FIRE II: non-equilibrium ionization Atomic spectra Intensity [W/cm 2 -µm-sr] Intensity [W/cm 2 -µm-sr] Wavelength [nm] Wavelength [nm] Figure: Atomic spectra: non-equilibrium (left) and equilibrium (right) atomic line radiation at 1 cm from the shock front Marco Panesi Non-equilibrium ionization January 31 st, / 22

18 Results EAST: Comparison with shock tube data. EAST experiment: Simplified radiation P = 13 [P a] and V s = Km.s 1 2e+5 1.5e+5 EAST exp. Abba Modified Abba Park TT v λ (nm) = [7,83] [85,88] 1 8 EAST exp. Abba Modified Abba Park TT v λ (nm) = [7,83] [85,88] I / D 1e+5 I / I EQ Distance from the shock front [cm] Distance from the shock front [cm] ABSOLUTE MEASUREMENT RELATIVE MEASUREMENT Boltzmann results over-predict the radiative peak. by a factor 4 Marco Panesi Non-equilibrium ionization January 31 st, / 22

19 Results Grouping of the levels Grouping of the high-lying excited states Population/degeneracy CR ABBA Boltzmann Reduced ABBA Energy Levels [ev] GROUPING STRATEGY COMPARISON REDUCED/FULL MODEL Marco Panesi Non-equilibrium ionization January 31 st, / 22

20 Results Grouping of the levels Acknowledgments The author want to acknowledge: NASA Ames Research Center, USA Richard Jaffe Winifred Huo Yen Liu David Schwenke Alan Wray Duane Carbon for the very insightful discussions. Marco Panesi Non-equilibrium ionization January 31 st, / 22

21 Conclusions CONCLUSIONS: We have studied the departures of the electronic energy populations from Boltzmann distribution for one-dimensional air flows obtained in a shock-tube. Validation and improvement of the model is obtained comparing our results with shock tube experiments. The atomic (and molecular) excited species distribution are found to depart from Boltzmann. Importance of self-consistent coupling of collisional and radiative processes. FUTURE WORK: Improvement of dissociation model: Bin model (N 2 ). Modeling of diatomic and triatomic molecular radiation. Non-Boltzmann treatment of the free electrons (Colonna). Marco Panesi Non-equilibrium ionization January 31 st, / 22

22 Conclusions Happy Birthday!!! The Abba Group Marco Panesi Non-equilibrium ionization January 31 st, / 22

Elaboration of collisional-radiative models applied to Earth and Mars entry problems

Journal of Physics: Conference Series OPEN ACCESS Elaboration of collisional-radiative models applied to Earth and Mars entry problems To cite this article: Julien Annaloro et al 2014 J. Phys.: Conf. Ser.