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本文对任意旋成面叶栅的气动反命题及杂交型命题提出一个通用的新解法。为此,引入一组斜交流线座标系,并将它看作一个映射,然后在映象平面上求解。提出了四种求解方案:偏微分方程组法,偏微分方程法、微分-积分方程法和积分方程组法。 值得注意的是:①在本文对反命题的提法下,叶型封闭性可自动得到保证;②在映象平面上,质量守恒定律具有新的几何意义——映射的区域保持性:③这种流线座标系也可用于求解叶栅正命题及其它具有未定(自由)边界的问题。
In this paper, we propose a new universal solution to the aerodynamic inverse problem and hybrid type proposition of any spinneret cascade. To this end, a series of diagonal AC coordinate systems are introduced and treated as a map and then solved on the image plane. Four solutions are proposed: partial differential equation method, partial differential equation method, differential-integral equation method and integral equation method. It is noteworthy that: (1) In this article, the obturation of leaves can be automatically guaranteed; (2) On the image plane, the law of conservation of mass has a new geometric meaning - the regional retentivity of the map: (3) Streamline coordinate systems can also be used to solve cascade positive propositions and other problems with undetermined (free) boundaries.