Application of SMILE++ Computational Tool to High-enthalpy Ionized Flows

Transcription

1 Application of SMILE++ Computational Tool to High-enthalpy Ionized Flows A. Shevyrin, P. Vashchenkov, A. Kashkovsky, Ye. Bondar Khristianovich Institute of Theoretical and Applied Mechanics Novosibirsk State University

2 DSMC method The most efficient numerical technique for high-speed rarefied flows is the Direct Simulation Monte Carlo (DSMC) method. The conventional treatment of the DSMC method is based on considering the rarefied gas flow as a set of particles (each of them represents a large number of gas molecules) and on the principle of splitting of permanent motion and collisions of gas molecules within a small time step Δt into two consecutive stages: - free-molecular transfer; - binary collisions in cells.

3 Master Kinetic Equation Accurate Collision Schemes Boltzmann Equation Linear MKE for N-particle DF fn (t,r,v) may be transformed into nonlinear BE for the one-particle DF f (t,r,v) when N => DSMC uses a finite number of simulated particles, which prompted M. Ivanov and S. Rogasinsky to construct DSMC schemes directly from MKE They also showed that one can use DSMC without splitting free molecular motion and collisions Starting from MKE also allows assessment of statistical errors and also provides connection between the N-particle gas model and the solution of BE Majorant Collision Frequency Schemes are mathematically strictly derived from the MKE, in contrast to traditional phenomenological DSMC schemes.

4 Mikhail Ivanov ( ) April 19, 1945 born in Moscow, USSR, to the family of a pharmacist Childhood in Saratov on the Volga river 1963 to 1968 earned a Master's of Sciences degree at the Department of Mechanics and Mathematics of the Moscow State University 1965 Married Ludmila, his wife of 48 years 1968 Moved to Siberia, joining research staff at the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences (ITAM) 1978 PhD in Fluid Mechanics at ITAM 1994 Doctor of Science 2011 AIAA Fellow Head of the Computational Aerodynamics Lab

5 Statistical Modeling In Low-density Environment (SMILE) Number of publications for most popular DSMC codes since 2010 Installed and used at RSC «Energia» (Russia) Makeev (Russia) MFTI (Russia) Penn State University (USA) AFRL (USA) Intel (USA) KARI (Korea) and other space institutions and universities

6 Examples: Re-entry Aerodynamics Soyuz Apollo Buran Clipper Kheops

7 SMILE++ software system Our experience achieved during development of the SMILE software system clearly demonstrates the fact that the greater the capabilities of the DSMC system are, the harder it is to modify the system by implementation of new models, methods and algorithms. The necessity of creation of the DSMC software system of the new generation based on the OOP approach became evident to us more than a decade ago. As a result the SMILE++ software system has been developed at the Computational Aerodynamics Lab of ITAM (the main developer: A.V. Kashkovsky). The SMILE++ is based on the OOP approach and completely written in C++. It is the descendant of SMILE and incorporates most of the capabilities of the latter. At the same time, it has new capabilities and significant advantages offered by OOP. The SMILE++ system provides a complete lifecycle of computations starting from a geometry model, pre-processing, going through the computation, and finishing with post-processing and presentation of results. M.S. Ivanov, A.V. Kashkovsky, P.V. Vashchenkov and Ye.A. Bondar. Parallel Object-Oriented Software System for DSMC Modeling of High-Altitude Aerothermodynamic Problems (INVITED), AIP Conference Proceedings Volume 1333, Proc. of RGD27, pp (2011).

8 Non-equilibrium Chemical Reactions in DSMC The Direct Simulation Monte Carlo (DSMC) method is traditionally used to study high-enthalpy flows with a significant level of thermochemical nonequilibrium. Recent efforts of the method development are mainly inspired by the need of effective and reliable modeling of nonequilibrium chemical reactions in hightemperature conditions of atmospheric reentry, in particular dissociation of N2 and O2. Due to the lack of suitable experimental data, validation of currently used DSMC chemical reaction models has not been finished yet and their applicability to high-enthalpy rarefied non-equilibrium flows is questionable. Below the results of the validation of the DSMC dissociation models against available experimental data are presented.

9 Dissociation Models For construction of a DSMC chemical model it is required to determine the cross sections (or probabilities) of chemical reactions. Let us consider dissociation of diatomic molecule AB resulting from a collision with molecule or atom M: AB+M A+B+M. TCE model, modified for discrete energy levels: uses Arrhenius input parameters, defined to match equilibrium reaction rate constant B K( T) AT exp kt QK model*: no assumed Arrhenius parameters but good match to measured ones; lots of recent attention KSS N.M. Kuznetsov-based State Specific**: like TCE, parameters defined to match given K(T) in equilibrium limit, but also incorporates vibrational favoring to match N.M. Kuznetsov 2T reaction rate for nonequilibirum conditions. * G.A. Bird, A Comparison of Collision Energy-Based and Temperature-Based Procedures in DSMC, 26th Int Symp on Rarefied Gas Dynamics, 2008 M.A. Gallis, R.B. Bond, J.R. Torcyznski, A Kinetic-theory Approach for Computing Chemical Reaction Rates in Upper Atmosphere Hypersonic Flows, J. Chem. Phys., 2009, Vol. 131, **Ye.A. Bondar and M.S. Ivanov, DSMC Dissociation Model Based on Two-Temperature Chemical Rate Constant, AIAA Paper , Ea

10 N.M. Kuznetsov-based State Specific (KSS) model Let us consider dissociation of diatomic molecule AB resulting from a collision with molecule or atom M: AB+M A+B+M. Vibrationally specific cross sections of the dissociation: σ n =σ n (E), n=0,,n max are assumed to be the functions of the sum E=E r +E t of the rotational energy E r and the relative translational energy of collision partners E t. Then rotational and translational energies being assumed in equilibrium at temperature T and Boltzmann distribution of vibrational energy with temperature T v the cross-sections can be found as a solution of the integral equation: r N 1 max C( T) E n E 2 E K( T, Tv ) exp n E de Q T v n kt ( ) exp ( ) 0 v kt kt Ed E n where 1 exp θv / T v 1 1 B E a K( T, Tv) Z( T, Tv) K ( T) exp E AT exp 0 1 exp θ / * v T ktv kt kt

11 Strong shock wave in oxygen M=9.3 M=13.4 Temperatures inside the shock-wave front in oxygen. Comparison with experiments of Ibragimova et al., 2012 I. Wysong, S. Gimelshein, Ye. Bondar, M. Ivanov. Phys. Fluids, 2014

12 Radio Attenuation Measurements (RAM-C II) RAM-C II capsule geometry and reflectometers stations (y1,y2, y3, y4) Complete energy and momentum accommodation at 1000K at the surface Flow composition: 78.3% N % O 2, V=7650 m/s Altitude, km Temperature, K Density, kg/m x x x10-5 Kn=λ/R α = 9º R = cm L = 1.3 m Isolines of electron density

13 Chemical reactions in air mixture The chemical kinetic mechanism (Park, 1994), which includes 19 dissociation and exchange reactions for 5 species: N, O, N2, NO, and O2 extended by associative ionization reactions which result in production of charged components N2 +, NO +, O2 +, e -. Discrete rotational and vibrational energy is assumed, Larsen-Borgnakke model is used for RT and VT. Three models are applied to dissociation reactions of molecular nitrogen and molecular oxygen, which exert the most pronounced effect on highaltitude aerothermodynamics: N 2 +M 2N+M O 2 +M 2O+M 1. Total collision energy (TCE) model 2. Quantum-kinetic (QK) model 3. Kuznetsov-based state specific (KSS) model

14 Chemical reactions in air mixture The other reactions are modeled in the similar manner in all cases. The TCE model modified for discrete rotational and vibrational energies of molecules is applied for 1. NO dissociation reactions NO+M N+O+M 2. Zel dovich reactions N2+O NO+N NO+O O2+N 3. Associative ionization reactions N + O NO + + e -, N + N N2 + + e -, O + O O2 + + e -. Plasma neutrality assumption is used to assess electron density. Ions are assumed to be not affected by the electric field and are neutralized at the vehicle surface. The dissociative recombination reactions AB + + e - A+B are modeled macroscopically, k(t v ) = AT vb.

15 81 km, translational temperature TCE KSS

16 DSMC Computations for 81 km KSS TCE QK

17 TCE 81km 77km 73 km KSS 81 km 77 km 73 km

18 Reflectometers locations in RAM-C II experiment: Calculated number density of electrons in four stations: 73 km 77 km 81 km

19 Dissociative recombination effect Station 1 Station 2 Electron density, m -3 Station 3 Station 4 1 TCE with dissociative recombination 2 TCE without dissociative recombination Altitude, km

20 Comparison of the DSMC with RAM-C II Altitude, km Station 1 2 Plasma density, m -3 - experiment 3 4

21 Comparison of the DSMC with RAM-C II (KSS model) 73 km 71 km Maximum electron density along the surface

22 Conclusions The comparisons of the DSMC computational results obtained with SMILE++ computational and results of the electron density measurements in the RAM C-II experiment were performed. The predicted values of plasma density in the shock layer is very sensitive to the N2 and O2 dissociation model. The differences between the results predicted by TCE, QK and KSS models decrease with decreasing altitude, which is explained by a lower degree of nonequilibrium of the flow. For altitudes lower than 73 km DSMC results are in good agreement with experimental data.

23 Thank you for your attention!

24 Aerodynamic Tools

25 Local heat transfer coefficient distribution Altitude 90 km Angle of attack 40 deg. Angle of attack 0. Heat transfer coefficient C h Q VS i Qr 3 ref /2

26 Translation temperature flowfields Altitude 90 km Temperature along stagnation line