Energy Transfer in Nonequilibrium Air (ETNA): Multidisciplinary Computation and Shock Tube Experiments

Transcription

1 Energy Transfer in Nonequilibrium Air (ETNA): Multidisciplinary Computation and Shock Tube Experiments Iain D. Boyd, University of Michigan Ronald K. Hanson, Stanford University Rigoberto Hernandez, Georgia Institute of Technology John F. Stanton, University of Texas AFOSR BRI Monitored By: John Luginsland, Jason Marshall 1

2 Project Background Hypersonic vehicles (Mach >> 5): - Produce very high temperatures (10,000 K) under conditions of thermochemical nonequilibrium - Significant uncertainty in rates, measured 40+ years ago - Effects of nonequilibrium on rates even more uncertain 2

3 Project Objectives Goal: Advance the modeling of thermochemical nonequilibrium processes in high temperature air that are relevant to flow around hypersonic vehicles with a focus on oxygen processes For each system of interest, e.g. O 2 (v,j) + M => O 2 (v,j )+M: Use best available potential surfaces (PESs) Evaluate transition cross sections (Quasi Classical Trajectory) Integrate to obtain temperature-dependent rates Use in state-resolved computation of nonequilibrium flows Develop reduced-order models Assess all modeling using shock tube measurements 3

4 Analysis of O 2 -Ar: Potential Energy Surface O 2 potential energy O-Ar potential energy Electronic excitation of O 2 (from X 3 Σ to a 1 Δ and b 1 Σ) occurs more readily in comparison to other atmospheric molecules Limited information on rovibrational relaxation for O 2 (X 3 Σ, a 1 Δ, and b 1 Σ) 4

5 Analysis of O 2 -Ar: Relatively Simple PES O 2 -Ar potential energy surface (PES): Simple potential energy surfaces used previously to construct PES for O 3 - Ar, H 2 -Ar, CO 2 -Ar or He O( 3 P)-O( 3 P) potential: - Hulburt-Hirschfelder (H-H) potential energy for O 2 (X 3 Σ, a 1 Δ, b 1 Σ) - Potential parameters of H-H potential obtained from semi-classical RKR potential energies O( 3 P)-Ar potential: - Buckingham equation - Potential parameters obtained from Kroes and Rettschnick (1991) and Gross and Billing (1997) 5

6 Analysis of O 2 -Ar: Rovibrational States Electronic+Rovibrational energy, cm X 3 Σ a 1 b 1 Σ O 2 (X,v=0,J) O 2 (X,v=1,J) Rotational J Rovibrational energy, ev v=0 v=1 v=2 X 3 Σ a 1 b 1 Σ Rotational J Rovibrational states and energies evaluated by solving Schrodinger Equation using the H-H potential energies 5115, 3851, and 3221 rovibrational states for O 2 (X 3 Σ, a 1 Δ, and b 1 Σ) 6

7 Analysis of O 2 -Ar: QCT and Master Equation Complete sets of rovibrational state-to-state transition cross sections and rates for O 2 (X 3 Σ, a 1 Δ, and b 1 Σ)+Ar at temperatures from 2,000 K to 14,000 K Three-body quasi-classical trajectory (QCT) method: - Collision energy ranges from 0.1 ev to 20 ev Systems of Master Equations for O 2 (X 3 Σ, a 1 Δ, and b 1 Σ)+Ar constructed using the state-to-state transition rates (5116, 3852, and 3222 equations) Master Equation studies for bound-bound and bound-free transitions are performed for various nonequilibrium conditions For bound-bound transitions: - Rovibrational relaxation parameters deduced For bound-free transitions: - Rovibrational quasi-steady state (QSS) exists - Nonequilibrium reaction rates in the QSS conditions deduced - Rotational and vibrational energy losses due to chemical reactions 7

8 Analysis of O 2 -Ar: Thermal Relaxation -2 Experiment, CAMAC (1962) Millikan-White (1963) Vib, VT master, O 2 (X 3 Σ )+Ar -3 ḡ Rot, RVT master, O 2 (X 3 Σ )+Ar Vib, RVT master, O ḡ 2 (X 3 Σ )+Ar ḡ -2-3 Experiment, CAMAC (1962) Millikan-White (1963) Vib, VT master, O 2 (a 1 g )+Ar Rot, RVT master, O 2 (a 1 g )+Ar Vib, RVT master, O 2 (a 1 g )+Ar -2-3 Experiment, CAMAC (1962) Millikan-White (1963) Vib, VT master, O 2 (b 1 Σ + g )+Ar Rot, RVT master, O 2 (b 1 Σ + g )+Ar Vib, RVT master, O 2 (b 1 Σ + g )+Ar Log(Pτ), atm-sec Log(Pτ), atm-sec Log(Pτ), atm-sec T -1/ T -1/ T -1/3 Rotational nonequilibrium exists above T=6,000K R-V-T energy transfer is important when rotational nonequilibrium exists Relaxation times for the electronic states of O 2 are significantly different 8

9 Analysis of O 2 -Ar: Dissociation Rates Log(K f ), cm -3 mol -1 sec Baulch et al. (1987) O 2 (X 3 Σ ḡ ), VT master O 2 (X 3 Σ ḡ ), RVT master Log(K f ), cm -3 mol -1 sec Baulch et al. (1987) O 2 (a 1 g ), VT master O 2 (a 1 g ), RVT master Log(K f ), cm -3 mol -1 sec Baulch et al. (1987) O 2 (b 1 Σ + g ), VT master O 2 (b 1 Σ + ), RVT master g Temperature, K Temperature, K Temperature, K O 2 dissociation in electronic excited states is faster than the ground state Rotational nonequilibrium effect on dissociation is weak enough to ignore Energy loss ratio values for O 2 are different for each electronic state 9

10 Analysis of O 2 -O: Vibrational Relaxation Time Potential for perpendicular approach (Varandas & Pais, 1988) Vibrational relaxation times (Park, 1989) O 2 -O molecular system: - Short vibrational relaxation time - Barrierless potential energy surface - Relatively fast dissociation 10

11 Analysis of O 2 -O: QCT Calculations Quasi Classical Trajectory (QCT) Method is used to generate rovibrational STS transition cross sections Large number of transitions even at small energies FHO model not applicable (energy transfer occurs via attraction) Fidelity study: two- and three-body potential energy surfaces WKB method: rovibrational ladder contains 46 vibrational states and a total of 6,245 states 2,000-8,000 trajectories per batch, 0.1 A step of impact parameter, stratified sampling, ev energy range, intermediate data is stored Computational cost: 150 cores/month (H-H PES) and 1,700 cores/month (Varandas PES) on FLUX cluster at ARC-TS University of Michigan A.J.C. Varandas, A.A.C.C. Pais, Molecular Physics, Vol. 65, No. 4, 1988 D. Steele, E.R. Lippincott, J.T. Vanderslice, DOE Technical report AROD

12 Analysis of O 2 -O: Collision Dynamics Example of O 2 -Ar trajectory (v=1, j=1) (v=1, j=13), 0.6 ev Example of O 2 -O trajectory (v=1, j=1) (v=0, j=33), 0.6 ev O atoms in O 2 -O system have strong interaction with each other Atom exchange, efficient VT energy transfer, multi-quantum jumps 12

13 Analysis of O 2 -O: Trajectory Analysis NESID: Number of Exchanges in the Shortest Interatomic Distance Describes efficiency of energy transfer (Lee, Kim, 1995) Applicable to molecular systems with an attractive potential Zero in systems with repulsive potential (e.g., O 2 -Ar) R AB B R BC C NESID equal to 50 A R AC Lee & Kim, Chemical Physics Letters, Vol. 233, pp ,

14 Analysis of O 2 -O: Effect of Collision Energy ( v j ) ( v j ) v = = 1, = 1 = 0, x Collision energies: 0.001, 0.02, 0.6, 3 ev 1 14

15 Analysis of O 2 -O: State-to-State Rates O 2 -O O 2 -Ar O 2 -O rates have much weaker temperature dependence compared to O 2 -Ar system O 2 -O rates are nearly independent of initial vibrational quantum number at high translational temperatures 15

16 Analysis of O 2 -O: Dissociation Rates Global dissociation rate State-specific dissociation rate, two- and three-body PESs State-specific rates are weakly affected by the three-body interaction term Good agreement with theoretical and experimental data Order of magnitude difference in cost 16

17 Summary of O 2 Data: Thermal Relaxation Times Anomalously fast O 2 -O vibrational relaxation Coupled O 2 -O vibrational and rotational relaxation Small variation with temperature Rotational relaxation in O 2 -Ar is faster Vibrational relaxation in O 2 -O is faster 17

18 Shock Tube Analysis Solve one-dimensional flow conservation equations coupled with thermochemical nonequilibrium equations Various experiments analyzed (Hanson, Shatalov, Matthews) Shatalov experiments: 100% O 2 freestream Test Case Shock Velocity [km/s] P 1 [torr] T 1 [K] T Post [K] C ,300 C ,620 C ,820 Vibrational temperature data (absorption spectroscopy) L.B. Ibraguimova, A.L. Sergievskaya, V.Yu. Levashov, O.P. Shatalov, Yu.V. Tunik, "Investigation of oxygen dissociation and vibrational relaxation at temperatures 4,000-10,800K, Journal of Chemical Physics, Vol. 139, p ,

19 O 2 -O Modeling Description Model Fidelity Model Type Vibrational Mode Equations Solved Rate source Title Low 2T Landau-Teller + Park Model T v 3 flow + 1 vib + n s species Millikan- White / Park QCT HH QCT - Varandas 2T-MW/Park 2T-QCT HH 2T-QCT Varandas High State-to-State n v 46 vib. state populations 3 flow + 46 vib + n s species QCT - Varandas STS-QCT Varandas Note: STS is an order of magnitude more computationally expensive 19

20 Overall Modeling Summary 2T O 2 -O 2 Relaxation: Millikan-White (matches experimental data) Dissociation: Arrhenius form (Park coefficients) O 2 -O Relaxation: Millikan-White, QCT-HH, QCT-Varandas Dissociation: Arrhenius form (Park; QCT-HH; QCT-Varandas) State-to-state (STS) O 2 -O 2 Bound-bound: Forced harmonic oscillator (FHO) rates Bound-free: Esposito rates corrected to dissociation rate O 2 -O QCT-Varandas for bound-bound and bound-free rates 20

21 Shock Tube Results: Comparison of 2T and STS C1: V=3.07 km/s, P=2.0 torr, T=295 K, T post =5,300 K STS and 2T models exhibit similar thermal relaxation, different dissociation 21

22 Shock Tube Results: Comparison of 2T and STS C2: V=3.95 km/s, P=1.0 torr, T=295 K, T post =8,620 K STS model follows experimental data much more closely STS dissociation is faster initially, then slower than 2T model 22

23 Shock Tube Results: Comparison of 2T and STS C3: V=4.44 km/s, P=0.8 torr, T=295 K, T post =10,820 K STS model captures experimental behavior more accurately Again, STS dissociation is faster initially, then slower than 2T model 23

24 Energy Distribution From STS Analysis C2: V=3.95 km/s, P=1.0 torr, T=295 K, T post =8,620 K Animation Time Span Boltzmann distribution is a temperature equivalent distribution 24

25 Future Plans Study additional oxygen interactions: - Repeat analyses for O 2 -N, O 2 -O 2, O 2 -N 2, O 2 -NO - Consider electronically excited states of O 2 and O Reduced order modeling: - Use results from STS master equation analysis - Consider various model forms (Landau-Teller, Park, Treanor, ) - Implement in a hypersonic CFD code, e.g., LeMANS Assessment: - Further shock tube analyses using Stanford data - Multi-dimensional flows (e.g., CUBRC test cases in O 2, air) 25

26 26

27 Modeling Issues In Hypersonic Oxygen Flow 100% O 2, 4MJ/kg M~ % O 2, 8MJ/kg M~12 Holden, M. S., Wadhams, T. P., and MacLean, M., AIAA

28 High-Fidelity Thermochemistry: Thermochemistry of O 2 -O Vibrational Relaxation Time Dissociation Rate Vibrational relaxation time has completely different temperature dependence Experiments inconclusive, our results agree with very high fidelity data Dissociation rate agrees with the literature 28

29 Reflected Shock Tube Gas Dynamics 5 2 Particle path 1 29

30 First Comparison To Stanford Data (Run 109) Composition: 98% Ar, 2% O 2 ; Shock: T 1 =298 K, P 1 =7.12 torr, M s =

31 Use of Simulations For Design of Experiments Identify interesting conditions that can be studied in the Stanford shock tube: - Composition: 99.9% Ar, 0.1% O 2 - Condition: T 1 =295 K, P 1 =1.0 torr (M s =5.9) QSS QSS Temperature Profiles Species Profiles 31

32 Non-Boltzmann Behavior: FHO model Deviation from Boltzmann distribution (small symbols are Boltzmann) SS QSS Initial State Vibrational State Distributions 32

33 Project Structure Potential Energy Surfaces (Stanton, Texas) Cross sections, Rate Coefficients (Hernandez, GaTech) CFD of Nonequilibrium Thermochemistry (Boyd, Michigan) Shock Tube Measurements (Hanson, Stanford) Model Validation Reduced Order Models Flow Around Hypersonic Vehicles 33

34 Analysis of O 2 -O: Thermal Relaxation Times Two- and three-body PESs Comparison with experiments Three-body PES predicts higher relaxation time Good description of experimental data (Kiefer et al., Breen et al.) Close description of Ibraguimova & Shatalov data Ibraguimova et al. J. Chem. Phys. 139, ,

35 Detailed Comparisons for O 2 -Ar and O 2 -O Single vs multi-quantum vibrational deactivation (black vs red lines) Temperature dependence Vibrational Rotational energy transfer O 2 -Ar O 2 -O 35