旋成面叶栅汽蚀绕流的变分原理

叶栅汽蚀绕流时所产生的汽穴不仅使流场发生了变化，而且其未知的形状使流场的求解变得十分困难。本文通过映射方法解决叶栅流场求解域的不定问题，分别以两个新型通用函数 （角函数和矩函数） 为泛函的自变量，建立了任意旋成面叶栅局部汽蚀绕流的变分原理，旨在为用有限元法和其它变分直接解法求解汽蚀汽穴及叶栅汽蚀绕流流场提供新的理论基础。

Variational Principles for the Cavitation Flow in a Cascade on an Arbitrary Streamsheet of Revolution

A cavitation bubble in a cascade not only changes the flow field of the cascade, but also makes it difficult to calculate the flow field because of its unknown shape. By introducing a mapping method to solve the problem of the undetermined boundary of the cascade and by taking the two general functions (i.e., the angular function and the momentum function) as the independent variables, the variational principles are derived for the cavitation flow in a cascade on a arbitrary streamsheet of revolution. The paper aims to provide a new theoretical basis for the calculation of both the shape of the bubble and the cavitation flow field.