Abstract
Predicted numerical distributions of the vibrational temperature of molecular oxygen behind a reflected shock wave are compared with experimental measurements in a shock tube. The computations are performed with the use of five two-temperature models (including models of Park, Kuznetsov, \(\beta\)-model, Marrone–Treanor model, and Macheret–Fridman model), five dissociation constants, and three variants of the source term that describes the rate of change of the vibrational energy due to chemical reactions. The Landau-Teller model is used to calculate the rate of translational-vibrational energy transfer, and the time of vibrational relaxation is calculated by the Millikan–White formula with Park’s high-temperature correction. The numerical and experimental results are found to be in reasonable agreement. The biggest difference between the numerical and experimental data is observed in the region of relaxation of the shock wave incident onto the wall.
REFERENCES
J. W. Streicher, A. Krish, and R. K. Hanson, “Coupled Vibration-Dissociation Time-Histories and Rate Measurements in Shock-Heated, Nondilute O2 and O2–Ar Mixtures from 6000 to 14 000 K," Phys. Fluids 33 (5) (2021); DOI: 10.1063/5.0048059.
L. B. Ibraguimova, A. L. Sergievskaya, V. Yu. Levashov, et al., “Investigation of Oxygen Dissociation and Vibrational Relaxation at Temperatures 4000–10800 K," J. Chem. Phys. 139 (3), 034317 (2013); DOI: 10.1063/1.4813070.
I. Wysong, S. Gimelshein, Ye. Bondar, and M. Ivanov, “Comparison of Direct Simulation Monte Carlo Chemistry and Vibrational Models Applied to Oxygen Shock Measurements," Phys. Fluids 26 (4), 043101 (2014); DOI: 10.1063/1.4871023.
Yu. Gorbachev, O. Kunova, and G. Shoev, “A Non-Equilibrium Dissociation and Vibrational Relaxation Model for Computational Fluid Dynamics Simulations of Flows with Shock Waves," Phys. Fluids 33 (12), 126105 (2021); DOI: 10.1063/5.0062628.
M. Yu. Plotnikov and E. V. Shkarupa, “Numerical Estimation of Heterogeneous Reaction Constant in the Flow of Rarefied Gas through a Cylindrical Channel," Prikl. Mekh. Tekh. Fiz. 58 (3), 30–38 (2017) [J. Appl. Mech. Tech. Phys. 58 (3), 402–409 (2017)].
Yu. N. Grigoryev and I. V. Ershov, “Influence of Vibrational Excitation of the Gas on the Position of the Laminar–Turbulent Transition Region on a Flat Plate," Prikl. Mekh. Tekh. Fiz. 62 (1), 14–21 (2021) [J. Appl. Mech. Tech. Phys. 62 (1), 11–17 (2021)].
A. N. Kudryavtsev, A. V. Kashkovsky, S. P. Borisov, and A. A. Shershnev, “A Numerical Code for the Simulation of Non-Equilibrium Chemically Reacting Flows on Hybrid CPU-GPU Clusters," AIP Conf. Proc. 1893 (1), 030054 (2017); DOI: 10.1063/1.5007512.
C. Wilke, “A Viscosity Equation for Gas Mixtures," J. Chem. Phys. 18 (4), 517–519 (1950); DOI: 10.1063/1.1747673.
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird (eds.), Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
C. Park, Nonequilibrium Hypersonic Aerothermodynamics (N. Y.; Chichester; Brisbane; Toronto; Singapore: John Wiley and Sons, 1990).
N. M. Kuznetsov, Kinetics of Monomolecular Reactions (Nauka, Moscow, 1982) [in Russian].
“Physical and Chemical Processes in Gas Dynamics: Computerized Reference Book, Vol. 1 of 3, Dynamics of Physical and Chemical Processes in Gases and Plasma," Eds. by G. G. Chernyi and S. A. Losev (Izd. Mosk. Gos. Univ., Moscow, 1995) [in Russian].
S. A. Losev and N. A. Generalov, “On Studying Excitation of Vibrations and Decomposition of Oxygen Molecules at High Temperatures," Dokl. Akad. Nauk SSSR 141 (5), 1072–1075 (1961).
P. Marrone and C. Treanor, “Chemical Relaxation with Preferential Dissociation from Excited Vibrational Levels," Phys. Fluids 6 (9), 1215–1221 (1963).
S. A. Losev, A. L. Sergievskaya, V. D. Rusanov, et al., “Coupling Factor in Two-Temperature Kinetics of Dissociation behind the Shock Wave Front," Dokl. Akad. Nauk 346 (2), 192–196 (1996).
S. Macheret, A. Fridman, I. Adamovich, et al., “Mechanisms of Nonequilibrium Dissociation of Diatomic Molecules," Williamsville, 1994. (Paper / AIAA; N 94-1984). DOI: 10.2514/6.1994-1984.
L. Landau and E. Teller, “To the Theory of Sound Dispersion," Phys. Z. Sowjet. Bd 10, 34–43 (1936).
R. C. Millikan and D. R. White, “Systematics of Vibrational Relaxation," J. Chem. Phys. 39 (12), 3209–3213 (1963); DOI: 10.1063/1.1734182.
P. A. Gnoffo, R. N. Gupta, and J. L. Shinn, “Conservation Equations and Physical Models for Hypersonic Air Flow in Thermal and Chemical Non-Equilibrium," S. l., 1989. (Paper / NASA; N 2867).
E. Nagnibeda and E. Kustova (eds.), Non-Equilibrium Reacting Gas Flows (Springer, Berlin; Heidelberg, 2009).
A. N. Kudryavtsev, “Computational Aerodynamics of Supersonic Flows with Strong Shock Waves," Doctor’s Dissertation in Physics and Mathematics (Novosibirsk, 2014).
H. C. Yee, “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods: Tech. Memorandum," NASA. No. 101088. S. l., (1989).
E. F. Toro, M. Spruce, and W. Speares, “Restoration of the Contact Surface in the HLL-Riemann Solver," Shock Waves 4 (1), 25–34 (1994); DOI: 10.1007/BF01414629.
P. Batten, M. A. Leschziner, and U. C. Goldberg, “Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows," J. Comput. Phys. 137 (1), 38–78 (1997). DOI: 10.1006/jcph.1997.5793.
D. S. Kravchenko, E. V. Kustova, and M. Yu. Melnik, “Modeling of State-to-State Oxygen Kinetics behind Reflected Shock Waves," Vestnik St. Petersburg University, Mathematics 9 (3), 426–439 (2022).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2023, Vol. 64, No. 3, pp. 137-151. https://doi.org/10.15372/PMTF20230314.
Rights and permissions
About this article
Cite this article
Shoev, G.V., Shershnev, A.A. VALIDATION OF TWO-TEMPERATURE MODELS OF OXYGEN DISSOCIATION IN THE PROBLEM OF SHOCK WAVE REFLECTION FROM THE WALL. J Appl Mech Tech Phy 64, 478–490 (2023). https://doi.org/10.1134/S0021894423030148
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894423030148