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Temperature dependence of rotational relaxation in shock waves of nitrogen

Published online by Cambridge University Press:  26 April 2006

I. D. Boyd
I. D. Boyd
Affiliation:
Eloret Institute, NASA Ames Research Center, MS 230-2, CA 94035, USA Present address: School of Mechanical and Aerospace Engineering, Cornell University. Ithaca, NY 14853. USA.
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Abstract

Computations are presented for one-dimensional Shockwaves of diatomic nitrogen. The direct simulation Monte Carlo method (DSMC) is employed. A model which allows the use of the Sutherland viscosity model in the DSMC technique is further developed to include the modelling of rotational relaxation. This is achieved by employing a temperature-dependent expression for the rotational collision number to simulate the rate of relaxation, in contrast to earlier DSMC studies which employed a constant value for the collision number. The behaviour of the new model is first considered for rotational relaxation in a heat bath. Comparison is made with the more traditional DSMC collision model termed the variable hard sphere (VHS) model in which the viscosity has a fixed temperature exponent. These two models are then applied to a number of shock-wave cases for which experimental data exist. These have Mach numbers ranging from 1.5 to 26, yet the enthalpies involved are sufficiently low to allow omission of vibrational relaxation. It is found that both the VHS and Sutherland viscosity models give excellent agreement with the experimental data for shock-wave thickness, and for profiles of density, rotational temperature, and velocity. The most significant finding of the study is that the reciprocal shock thickness varies with the upstream temperature condition. This variation is observed in the experimental data, and is simulated numerically by employing the temperature-dependent expression for the rotational collision number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 343 - 360
Copyright
© 1993 Cambridge University Press

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References

ALSMEYER, H. 1976 Density profiles in argon and nitrogen shock waves measured by absorption of an electron beam. J. fluid Mech. 74, 497– 513.Google Scholar
Bird, G. A. 1976 Molecular Gas Dynamics. Clarendon.
Bird, G. A. 1981 Monte Carlo simulation in an engineering context. In Rarefied Gas Dynamics, Part 1, pp. 239– 255. AIAA.
Borgnakke, C. & Larsen, P.S. 1975 Statistical collision model for Monte Carlo simulation of polyatomic gas mixtures. J. Comput. Phys. 18, 405– 420.Google Scholar
Boyd, I.D. 1990a Rotational–translational energy transfer in rarefied nonequilibrium flows. Phys. Fluids A 2, 447– 452.Google Scholar
Boyd, I. D. 1990b Analysis of rotational nonequilibrium in standing shock waves of nitrogen. AIAA J. 28, 1997– 1999.Google Scholar
Boyd, I.D. 1992 Analysis of vibration-dissociation-recombination processes behind strong shock waves of nitrogen. Phys. Fluids A 4, 178– 185.Google Scholar
Brau, C.A. & Jonkman, R. M. 1970 Classical theory of rotational relaxation in diatomic gases. J. Chem. Phys. 52, 477– 484.Google Scholar
Butefisch, K.A. & Vennemann, U. 1974 Absolute velocity measurements in a rarefied gas flow by an ion time-of-flight technique. In Rarefied Gas Dynamics, pp. 245– 252. Academic.
Chapman, S. & Cowling, T.G. 1970 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Jacobsen, R.T., Stewart, R.B., McCarty, R.D. & Hanley, H.J. M. 1973 Thermophysical properties of nitrogen. Natl Bureau Stand. Tech. Note 648, 11– 15.Google Scholar
Kuscer, I, 1989 A model for rotational energy exchange in polyatomic gases. Physica A 158, 784– 800.Google Scholar
Lumpkin, F. E., Haas, B. L. & Boyd, I. D. 1991 Resolution of differences between collision number definitions in particle and continuum simulations. Phys, Fluids A 3, 2282– 2284.Google Scholar
MacPherson, A. K. 1971 Rotational temperature profiles of shock waves in diatomic gases. J. Fluid Mech. 49, 337– 351.Google Scholar
Melville, W. K. 1972 The use of the loaded-sphere molecular model for computer simulation of diatomic gases. J. Fluid Mech. 51, 571– 583.Google Scholar
Parker, J. G, 1959 Rotational and vibrational relaxation in diatomic gases. Phys. Fluids 2, 449– 462.Google Scholar
Robben, F. & Talbot, L. 1966 Measurement of shock wave thickness by the electron beam fluorescence method. Phys. Fluids 9, 633– 662.Google Scholar
Smith, R. B. 1972 Electron-beam investigation of a hypersonic shock wave in nitrogen. Phys. Fluids 15, 1010– 1017.Google Scholar