Yung-Huai Kuo

This report concerns the problem of constructing solutions for transonic flows over symmetric airfoils. The aspect of the problem emphasized is, of necessity, not how to form a solution for compressible flow but how to simplify the initial phase of the problem, namely, the mapping of the incompressible flow. In the case of symmetric Joukowski airfoil without circulation, the mapping is relatively simple, but the coefficients in the power series are difficult to evaluate. As a result, the problem requires simplification. Instead of the exact incompressible flow past the airfoil, an approximate flow is used, which is derived from a combination of source and sink. This flow differs only slightly from the exact one when the thickness is small. By the same method, the flow with circulation is also considered.

After the incompressible-flow functions are approximated in this fashion, the numerical calculation of the corresponding compressible flow, by the hodograph theory, does not present any essential difficulty.

绕翼型的二维跨声速流

郭永怀

本报告讨论绕对称翼型跨声速流动解的构造问题，强调的方面自然不是如何去构成可压缩流动的解、而是在于求解的第一步，即可压缩和不可压缩流动的映照问题。对于无环量的对称儒可夫斯基翼型，映照比较简单，但幂级数中的系数不易计算，因而需要把问题简化。我们利用叠加源和汇导出的近似流动来代替绕翼型的精确不可压缩流动，当翼型厚度不大时，近似流动与精确流动仅稍有不同。利用同样的方法也考虑了具有环量的流动。

按这种方式近似求解不可压缩流函数后，基于速度图理论，对应的可压缩流动的数值计算并无实质性的困难。

原文发表于：NACA, TN. No.2356（1951）.见《郭永怀文集》北京：科学出版社，pp. 265-312, 2009.