DOI QR코드

DOI QR Code

Rovibrational Nonequilibrium of Nitrogen Behind a Strong Normal Shock Wave

  • Kim, Jae Gang (Department of Aerospace System Engineering, Sejong University)
  • Received : 2016.05.09
  • Accepted : 2016.10.31
  • Published : 2017.03.30

Abstract

Recent modeling of thermal nonequilibrium processes in simple molecules like hydrogen and nitrogen has indicated that rotational nonequilibrium becomes as important as vibrational nonequilibrium at high temperatures. In the present work, in order to analyze rovibrational nonequilibrium, the rotational mode is separated from the translational-rotational mode that is usually considered as an equilibrium mode in two- and multi-temperature models. Then, the translational, rotational, and electron-electronic-vibrational modes are considered separately in describing the thermochemical nonequilibrium of nitrogen behind a strong normal shock wave. The energy transfer for each energy mode is described by recently evaluated relaxation time parameters including the rotational-to-vibrational energy transfer. One-dimensional post-normal shock flow equations are constructed with these thermochemical models, and post-normal shock flow calculations are performed for the conditions of existing shock-tube experiments. In comparisons with the experimental measurements, it is shown that the present thermochemical model is able to describe the rotational and electron-electronic-vibrational relaxation processes of nitrogen behind a strong shock wave.

Acknowledgement

Supported by : ADD

References

  1. Park, C., Nonequilibrium Hypersonic Aerothermodynamics, Wiley, New York, 1990.
  2. Gupta, R. N., Moss, J. N. and Price, J. M., "Assessment of Thermochemical Nonequilibrium and Slip Effects for Orbital Reentry Experiment(OREX)", NASA TM-111600, July 1996.
  3. Furudate, M., Nonaka, S. and Swada, K., "Calculation of Shock Shapes over Simple Geometries in Intermediate Hypersonic Air Flow", AIAA 1999-3686, 33rd AIAA Thermophysics Conference and Exhibit, Orlando, Florida, 1999.
  4. Kim, J. G., Kwon, O. J. and Park, C., "Master Equation Study and Nonequilibrium Chemical Reactions for $H+H_2$ and $He+H_2$", Journal of Thermophysics and Heat Transfer, Vol. 23, No. 3, 2009, pp. 443-453. https://doi.org/10.2514/1.41741
  5. Kim, J. G., Kwon, O. J. and Park, C., "Master Equation Study and Nonequilibrium Chemical Reactions for Hydrogen Molecule", Journal of Thermophysics and Heat Transfer, Vol. 24, No. 2, 2010, pp. 281-290. https://doi.org/10.2514/1.45283
  6. Kim, J. G. and Boyd, I. D., "State-Resolved Thermochemical Nonequilibrium Analysis of Hydrogen Mixture Flows", Physics of Fluids, Vol. 24, No. 8, Article 086102, 2012.
  7. Sharma, S. P. and Gillespie, W., "Nonequilibrium and Equilibrium Shock Front Radiation Measurements", Journal of Thermophysics and Heat Transfer, Vol. 5, No. 3, 1991, pp. 257-265. https://doi.org/10.2514/3.259
  8. Fujita, K., Sato, S., Abe, T. and Ebinuma, Y., "Experimental Investigation of Air Radiation Behind a Strong Shock Wave", Journal of Thermophysics and Heat Transfer, Vol. 16, No. 1, 2002, pp. 77-82. https://doi.org/10.2514/2.6654
  9. Sakurai, K., Bindu, V. H., Niinomi, S., Ota, M. and Maeno, K., "CARS Measurement of Vibrational/Rotational Temperatures with Total Radiation Visualization behind Strong Shock waves of 5-7km/s", 27th International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings, Vol. 1333, 2011, pp. 419-424.
  10. Hyun, S. Y., "Radiation Code SPRADIAN07 and its Applications", Ph. D. Dissertation, Dept. of Aerospace Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea, 2009.
  11. NIST atomic spectra database, http://www.nist.gov/pml/data/asd.cfm
  12. NIST molecular spectra database, http://webbook.nist.gov/chemistry
  13. Steele, D., Lippincott, E. R. and Vanderslice, J. T., "Comparative Study of Empirical Internuclear Potential Functions", Reviews of Modern Physics, Vol. 34 No. 2, 1962, pp. 239-251. https://doi.org/10.1103/RevModPhys.34.239
  14. Vanderslice, J. T., Mason, E. A., Maisch, W. G. and Lippincott, E. R., "Ground State of Hydrogen by the Rydberg- Kelein-Rees Method", Journal of Molecular Spectroscopy, Vol. 2, No. 1, 1959, pp. 17-29.
  15. Schwenke, D. W., "Calculations of Rate Constants for the Three-Body Recombination of $H_2$ in the Presence of $H_2$", Journal of Chemical Physics, Vol. 89, No. 4, 1988, pp. 2076- 2091. https://doi.org/10.1063/1.455104
  16. Jaffe, R., Schwenke, D., Chaban, G. and Huo, W., "Vibrational and Rotational Excitation and Relaxation of Nitrogen from Accurate Theoretical Calculation", AIAA 2008-1208, 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2008.
  17. Jaffe, R., Schwenke, D. and Chaban, G., "Theoretical Analysis of N2 Collisional Dissociation and Rotation- Vibration Energy Transfer", AIAA 2009-1569, 47th AIAA Aerospace Sciences Meeting and Exhibit, Orlando, Florida, 2009.
  18. Park, C., Jaffe, R. and Partridge, H., "Chemical- Kinetic Parameters of Hyperbolic Earth Entry", Journal of Thermophysics and Heat Transfer, Vol. 15, No. 1, 2001, pp. 76-90. https://doi.org/10.2514/2.6582
  19. Nishida, M. and Matsumoto, M., "Thermochemical Nonequilibrium in Rapidly Expanding Flows of High- Temperature Air", Zeitschrift fur Naturforschung, Teil A. Physik, Physikalische Chemie, Kosmophysik, Vol. 52, 1997, pp. 358-368.
  20. Gnoffo, P. A., Gupta, R. N. and Shinn, J. L., "Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Nonequilibrium", NASA TP-2867, Feb. 1989.
  21. Park, C. "Rotational Relaxation of N2 Behind a Strong Shock Wave", Journal of Thermophysics and Heat Transfer, Vol. 18, No. 4, 2004, pp. 527-533. https://doi.org/10.2514/1.11442
  22. Kim, J. G. and Boyd, I. D., "Master Equation Analysis of Post Normal Shock Waves of Nitrogen", Journal of Thermophysics and Heat Transfer, Vol. 29, No. 2, 2015, pp. 241-252. https://doi.org/10.2514/1.T4249
  23. Kim, J. G. and Boyd, I. D., "Thermochemical Nonequilibrium Analysis of $O_2+Ar$ Based on State-Resolved Kinetics", Chemical Physics, Vol. 446, 2015, pp. 76-85. https://doi.org/10.1016/j.chemphys.2014.11.009
  24. Parker, J. G., "Rotational and Vibrational Relaxation in Diatomic Gases", Physics of Fluids, Vol. 2, No. 4, 1959, pp. 449-462. https://doi.org/10.1063/1.1724417
  25. Rahn, L. A. and Palmer, R. E., "Studies of Nitrogen Self-Broadening at High Temperature with Inverse Raman Spectroscopy", Journal of Optical Society of America, Vol. 3, No. 9, 1986, pp. 1164-1169. https://doi.org/10.1364/JOSAB.3.001164
  26. Millikan, R. C. and White, D. R., "Systematics of Vibrational Relaxation", Journal of Chemical Physics, Vol. 39, No. 12, 1963, pp. 3209-3213. https://doi.org/10.1063/1.1734182
  27. Appleton, J. P., "Shock-Tube Study of the Vibrational Relaxation of Nitrogen Using Vacuum-Ultraviolet Light Absorption", Journal of Chemical Physics, Vol. 47, No. 9, 1967, pp. 3231-3240. https://doi.org/10.1063/1.1712381
  28. Allen, R. A., "Nonequilibrium Shock Front Rotational, Vibrational, and Electronic Temperature Measurements", AVCO Everett Research Lab., Everett, MA, Research Rept. 186, Aug. 1964.
  29. Matsuda, A., Ota, M., Arimura, K., Bater, S., Maeno, K. and Abe, T., "Assessment of Rotational and Vibrational Temperatures Behind Strong Shock Waves Derived from CARS Method", 26th International Symposium on Shock Waves, Vol. 1, Springer, Berlin, 2009, pp. 433-438.