水力机械旋成面叶栅杂交命题的变域变分理论

本文通过对水力机械转轮叶片设计理论的研究,针对叶栅杂交命题求解域未定的特点,将叶栅未知边界位置坐标增设为自变量,利用反推法和泛函的变域变分公式建立了任意旋成面叶栅内不可压缩流动A,B,C,D和E类杂交命题的流函数型和势函数型变分原理与广义变分原理。将原来求偏微分方程组的边值问题转化为求一等价泛函的驻值问题,这样可以应用各种变分直接解法进行水力机械转轮叶片的设计、改型和流场分析。

A Theory of Variable Domain Variations for Hybrid Problems of Cascades on an Arbitrary Streamsheet of Revolution in Hydraulic Machinery

A theory for blades design of hydraulic machinery is discussed in this paper. The position coordinate of the unknown boundary of cascades is taken additionally as an independent variable of the functional to overcome the difficulties caused by undetermined solution region of hybrid problems of the cascades. By applying the inverse-deduction method and the formula for variable domain variations of functional, the variational principles and generalized variational principles in terms of the stream function and the potential function respectively have been derived for A,B,C,D and E type hybrid problems of an incompressible flow in cascades on an arbitrary streamsheet of revolution. As a result,the original boundary value problem of partial differential equations is changed into a stationary value problem of an equivalent functional. Thus the direct variational methods can be used for design, modification, and flow field analyses of runner blades of hydraulic machinery.