Yung-Huai Kuo
The method developed in NACA TN No.995 has been slightly modified and extended to include flows with circulation. The essential feature of the modified method is that in analytic continuation of the solution the alteration of the singularities of the incompressible solution due to the presence of the hypergeometric functions has been taken into account. It was found that for finite Mach number the only case in which the nature of the singularity of the incompressible solution can remain unchanged is for a ratio of specific heats equal to -1.
Two particular flows, one having a finite circulation and the other having zero circulation, have been studied. Both flows were derived from the incompressible flow about an elliptic cylinder of thickness ratio 0.60. The free-stream Mach number for both cases was taken to be 0.60 in order to avoid the appearance of limiting lines. The pressure distribution for the flow without circulation has been compared with that of incompressible flow over approximately the same body. The discrepancies between the exact results and those predicted by the approximate von Karman-Tsien and Glauert-Prandtl formulas are so wide as to show definitely that in this case the effect of geometry cannot be ignored, as is done in both approximate formulas. In general, it seems that the effect of geometry cannot be neglected and the conventional “pressure-correction” formulas are not valid, even in the subsonic region if the body is thick, especially if there is a supersonic region in the flow.
可压缩流体二维无旋跨声速流动
郭永怀
本文对NACA TN No.995 中提出的方法做了一些改进，并推广到包括有环量的流动，本方法的要点是：在解的解析延拓时考虑到超几何函数的出现，不可压缩解的奇异性会发生变化。可以看到，对于有限的马赫数，仅在比热比为-1的情况下不可压缩解的奇异性才能保持不变。
本文研究了两个具体流动，一个是环量为有限值的情况，另一个是环量为零的情况，他们都是从绕一个厚度比为0.60椭圆柱的不可压缩流动得来的。为了避免出现极限线，上述两种情况的来流马赫数都取为0.60。无环量的压力分布与物形近似相同的不可压缩流的结果做了比较，精确解与von Karman-钱公式及 Glauert-Prandtl近似公式所预计的结果相差很大。可以肯定，在这两种情况下，不能像两个近似公式那样来做，几何形状的影响是不能忽略的。一般来说，如果物体是厚的，那么甚至在亚声速区也不能忽略几何形状的影响，通常的压力修正公式是不正确的。如果在流动中有一个超声速区那就更是如此。
原文发表于：NACA TN No.1445(1948)，见《郭永怀文集》北京：科学出版社出版，pp.173-263, 2009.
