Abstract
Various different dimensionless numbers are used to evaluate the experimental and theoretical data on the aerodynamics and heat transfer in low-density gases. They are obtained mainly in the analysis of simplified Navier—Stokes equations. In [1], the dimensionless number obtained from the Boltzmann equation is the Reynolds number Re0, in which the coefficient of viscosity is determined using the stagnation temperature. In the present paper, using the Boltzmann equation but different characteristic parameters from those in [1], we obtain the dimensionless number introduced for the first time by Cheng [2] in the analysis of the equations of a thin viscous shock layer. We show that for definite values of the characteristic temperature and dependences of the coefficient of viscosity on the temperature virtually all the dimensionless numbers used to evaluate the results of investigations into the aerodynamics and heat transfer in a low-density gas can be obtained.
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V. N. Gusev, M. N. Kogan, and V. A. Perepukhov, “On similitude and variation in the aerodynamic characteristics in the transition region at hypersonic flow velocities,” Uch. Zap. TsAGI,1, No. 1 (1970).
H. K. Cheng, “Hypersonic shock-layer theory of the stagnation region at low Reynolds number.” Proc. 1961 Heat Transfer and Fluid Mechanics Institute, Stanford Univ Press Stanford, Calif. (1961).
M. N. Kogan, Rarefied Gas Dynamics, New York (1969).
J. O. Hirschfelder, C. F. Curtis, and R. B. Bird, Molecular Theory of Gases and Liquids, New York (1965).
S. Chapman and T. G. Cowling, Mathematical Theory of Non-Uniform Gases, Cambridge (1952).
G. T. Coleman, S. C. Metcalf, and C. J. Berry, “Heat transfer to hemisphere cylinders and bluff cylinders between continuum and free molecular flow limits,” in: Rarefied Gas Dynamics, Progress in Astronautics and Aeronautics, Vol. 51, Pt. 1, Princeton Univ. Press, Princeton (1977).
R. D. Boettcher, G. Koppenwallner, and H. Legge, “Flat plate skin friction in the range between hypersonic continuum and free molecular flow,” in: Rarefied Gas Dynamics. Progress in Astronautics and Aeronautics, Vol. 51, Pt. 1, Princeton Univ. Press, Princeton (1977).
A. K. Artamonov and V. N. Arkhipov, “Hypersonic flow of rarefied gas over a sphere,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6 (1979).
V. N. Gusev and Yu. V. Nikol'skii, “Experimental investigation of heat transfer at the stagnation point of a sphere in a hypersonic stream of low-density gas,” Uch. Zap. TsAGI,2, No. 1 (1971).
Yu. A. Koshmarov and Yu. A. Ryzhov, Applied Dynamics of Low-Density Gases [in Russian], Mashinostroenie, Moscow (1977).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–144, January–February, 1981.
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Artamonov, A.K., Arkhipov, V.N. & Farafonov, V.G. Dimensionless numbers in the aerodynamics of low-density gases. Fluid Dyn 16, 110–114 (1981). https://doi.org/10.1007/BF01094822
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DOI: https://doi.org/10.1007/BF01094822