Extension of von Karman's Transonic Similarity Rule

概要

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An attempt is made to extend von Karman's transonic similarity theory so as to cover the whole range of Mach number from subsonic to supersonic. First, the equations for the two-dimensional compressible flow past a slender body are reduced to [numerical formula] by assuming that the perturbation velocity is small of order e and neglecting small quantities of O(ε^3). Here we have written [numerical formula], where 〓 is the stream function. U and M are respectively the free stream velocity and Mach number, γ is the ratio of specific heats, A is a constant of order O(ε), and G(ζ, ζ, 〓_1(ξ,η), x_1(ξ,η) are O(1). Then, it is shown that B=O(t) for M≠1, and that (v/u)t is an appropriate parameter for M≒1, where t is the thickness ratio of the body. For the ease M≠1, either subsonic or supersonic, the procedure of successive approximation can be applied to Eq. (1). It is to be noted that Eq . (2) is exact to the order O(ε^2) in contrast to the fact that the similar equation in the usual transonic approximation theory is correct only to the order O(ε). Hence it is suggested that the parameter (v/u)t may be used with advantage in place of the usual transonie parameter (γ+1)t/u^3 or (γ+1)t/(1-M^2)^<3/2>. Finally, Liepmann and Bryson's experimental data on the transonic flow past wedge sections are analyzed using the parameter (v/u)t.
社団法人日本物理学会の論文
1954-02-25