Dimensionless numbers in the aerodynamics of low-density gases

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.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 140–144, January–February, 1981.