A Reduced-Order Modeling Approach to Enable Kinetic Simulations of Non-equilibrium Hypersonic Flows

Transcription

1 A Reduced-Order Modeling Approach to Enable Kinetic Simulations of Non-equilibrium Hypersonic Flows Marco Panesi AFOSR YIP Grant No: FA DEF Department of Aerospace Engineering University of Illinois at Urbana-Champaign 1

2 Outline Motivation and Background Master Equation Analysis Coarse Grained Model Conclusions 2

3 Standard Non-equilibrium Models Standard non-equilibrium models for hypersonic flows were mainly developed in the 1980 s and are correlation based: E.g., dissociation model of Park Multi-temperature model: Average temperature for fictitious Arrhenius rate coefficient 3

4 Motivation A large effort is underway at AIRFOCE which attempts to characterize the microscopic interaction of N2-N2, O2-O2 and N2-O2 from first-principles calculations. Ab initio calculations can provide the transition probabilities governing the transfer of energy between the flow and the internal energy modes of atoms and molecules in the gas. The large amount of information provided by ab initio calculations has great value, but it must be tailored to fulfill the needs of the problem that is being solved. Thus, it is imperative that reduced-order models be developed. 4

5 Objective METHODOLOGY: Developing non-equilibrium models for hypersonic flows based on microscopic theory and applying them to macroscopic scale. Work at the interface between computational chemistry, experimental data, and CFD. 5

6 Background: State-to-State Kinetics MT Models: Conventional methodologies rely on the assumption of Maxwell-Boltzmann distribution: James Clerk Maxwell Ludwig Eduard Boltzmann State to State Models: the internal states are treated as independent species governed by their own kinetics. Boltzmann Plot 6

7 High Fidelity Modeling: Roadmap Objectives: To assess the fundamental assumptions adopted in the modeling of hypersonic plasma flows. Key Relaxation Processes: 1. Energy Transfer: It is crucial to the understanding on the shock layer kinetics 2. Dissociation: critical process governing the redistribution of the kinetic energy within the internal energy modes and chemistry. 3. Recombination: critical in the boundary layer area, and in the expansion regions of the flow-field. Dissociation N 2 + N = N + N + N Rotational equilibrium (T = T rot ) Landau-Teller VT relaxation model Internal Energy Chemistry relaxation coupling (e.g., VC) Existence of a QSS rates Rovibrational State-to-state method 7

8 Analysis of Dissociating and Recombining Flows Test cases under consideration: 1. Master Equation 2. Flow Behind a normal shock wave 3. Quasi 1D nozzle flow 8

9 A Novel Approach to the Modeling of Non-equilibrium Flows First Principles Computation: 1. Quantum chemistry calculations to generate realistic nuclear interaction potentials (PES) 2. Quasi classical trajectory (QCT) method for the reaction cross-sections 9

10 Non-equilibrium Flow Behind a Normal Shock Wave 10

11 Flow-field Quantities Rovibrational STS model predicts larger relaxation distance with respect to the vibrational STS model 11

12 Post-Shock: Rovibrational Populations The distribution deviates from the Maxwell Boltzmann distribution Distribution is dissected into multiple strands for different v 12

13 1D Shock Tube Problem Left: rotational and vibrational temperatures Right: population of the first vibrational levels Assumption of fast rotational equilibrium is questionable Dissociation is better described by a unique temperature 13

14 Master Equation Solution QSS Rates Estimation 1. Rate Coefficient is in EXCELLENT agreement with Appleton data 2. Exchange reaction is important for correct estimation of reaction rate constant. 3. In the high temperature region the QSS assumption FAILS! 14

15 Comparison MT and STS Models Can we use QCT derived rate coefficients and relaxation parameters in the conventional MT models? NO! Using QCT derived rates based on the QSS assumption (or Boltzmann) are unable to reproduce the STS results. 15

16 Conclusions of the STS Analysis MT modeling (QSS based) Conventional MT models are unable to reproduce the STS results, because of the invalidity of the QSS assumption. 16

17 Model Reduction A c c u r a c y CGM State To State - RVC State To State - VC STS - EC MT T T, T R T, T R,T V T, T R,T V, T E Increasing Number of Assumptions Complexity 17

18 Coarse Grained Method The methodology of reduction consists of two distinct steps: 1. Local Representation and Reconstruction. It relies on the lumping of the internal energy levels in macroscopic energy groups and the reconstruction of the population of each grouped state, n i, using macroscopic quantities. The coefficients and are retrieved using constraints based on the maximum entropy principle and a variational method. 18

19 Coarse Grained Method 2. Macroscopic Moment Equations and Rate Coefficients. Macroscopic governing equations (referred to as macroscopic moment equations) are obtained by taking moments of the master equations and by using the reconstructed local representation. Governing Equations Zero Order Moment: Uniform Grouping (piece-wise reconstruction). First Order Moment: Boltzmann Grouping (linear reconstruction). 19

20 Coarse Grained Method Novel lumping scheme obtained by sorting the levels by energy and grouping in a bin all levels with similar energies 20

21 Coarse Grained Method reconstruction of the population of each grouped state, n i, using macroscopic quantities. 21

22 Considerations 1. Grouping strategy is crucial The choice of the grouping or grouping strategy should be guided by the physical intuition. For example, levels characterized by similar energies are likely to be in equilibrium between each other and should be grouped together. 2. State to state models and Multi-temperature models are a particular case of coarse grained approach. For example, conventional TTv model can be obtained by grouping the vibrational levels in a single bin and prescribing a Boltzmann distribution for each rotational level with T=T Rot 22

23 Conventional Model and Coarse Grain Modeling MT MT is a particular case of coarse grain model (1 Group) Boltzmann distribution (T Vib, T Rot ) Conventional TT Vib model if T Rot =T VCR(n) VCR is a particular case of coarse grain model (n Group) Boltzmann distribution (T rot ) Conventional Vib. STS model when T Rot = T 23

24 Novel Grouping Strategy Hyb(2,2) Two groups in the vibrational energy structure Two different rotational temperature for the two groups VCR(i) Vibrational specific model BC(3) VCR Three energy groups Three internal energy equations MT is a special case (1 internal temperature) 24

25 Evolution of the Vibrational Distribution MT models are unable to predict the distribution function 25

26 Evolution of the Vibrational Distribution BC(3) model is in good agreement with the STS model 26

27 Evolution of the Vibrational Distribution HyBVC shows excellent agreement with the STS model 27

28 Evolution of the Vibrational Distribution VCR2 shows excellent agreement with the STS model 28

29 Technical Challenges Remaining Diatom-Diatom Reactions Given the large number of possible channels the derivation of the exact rovibrational STS model is not feasible. Analysis of Recombining Flows Challenges are due to the strong deviation from the equilibrium distribution in expanding flows. Application to CFD (e.g., US3D) and Validation Validation data should include spatially resolved population measurements of the (ro-) vibrational population and atomic densities. (E.g., S.Sharma, et al. JTHT, Vol. 7, No. 4 (1993), pp ) Other systems, gas mixtures, higher order reconstruction 29

30 Publications and Honors Research Honors Air Force Summer Faculty Fellowship Program, California, USA. (2015) Award on Physical Modelling (8th Symposium on Aerothermodynamics for Space Vehicles - ESA) (2015) Air Force Young Investigator Award (YIP) (2015) Journal Publications 1. A., Munafo, Y. Liu, M. Panesi Physics of dissociation and energy transfer in shock heated nitrogen flows, Physics of Fluids, Under Review, (2015) 2. Y. Liu, M. Panesi, A. Sahai and M. Vinokur General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures J. Chem. Phys. 142, (2015); 3. Panesi, M., Munafo, A., Magin, T. E., and Jaffe, R. L., Study of the nonequilibrium shock heated nitrogen flows using a rovibrational state-to-state method, Phys. Rev. E, Vol. 90, (2014). 4. Panesi, M. Jaffe, R.L. Schwenke, D.W. Magin, T.E Rovibrational internal energy transfer and dissociation of N2-N system in hypersonic flows. J. Chem. 30 Phys. 138, (2013).

31 Conclusions Using the classical moment method, we introduced a general methodology for modeling thermal and chemical non-equilibrium processes. Based on the maximum entropy principle subject to a series of moment constraints, the logarithm of the distribution function in each energy group is expressed and reconstructed as a power series in internal energy. Conventional MT and STS models are only particular cases of the more general Coarse-Grain Method. These models have been applied to the study of rovibrational energy excitation and dissociation processes behind strong one-dimensional shock waves in nitrogen flow. 31

32 NEQRAD Group 32

33 Acknowledgments Special thanks to: AFOSR YIP Grant No: FA DEF UIUC Dr. A. Munafo (UIUC) Dr. R. Macdonald (UIUC) - NDSEG Dr. S. Venturi (UIUC) NASA Dr. R.L. Jaffe (NASA Ames Research Center) Dr. D.W. Schwenke (NASA Ames Research Center) Dr. Y. Liu (NASA Ames Research Center) AIRFORCE Dr. J.L. Cambier (USAF, AFOSR) Dr. E. Josyula (USAF, AFRL Wright Patterson) 33

34 Backup Slides 34

35 Summary (and Conclusions) 35

36 Summary (and Conclusions) Significant reduction of the CPU time is obtained with the Bin model N 2 -N System: CPU Time in function of the # of BINS 36

37 Convective Heating The MT model over-estimate the convective heating by 18 % if the parameters are calibrated using the RVC model Park Model over-predict by a factor 2 37

38 Detecting QSS Breakdown 38

39 Coarse Grained Method Novel lumping scheme obtained by sorting the levels by energy and grouping in a bin all levels with similar energies 39

40 Energy Transfer 40