The object of this paper is to present a concise inverse inviscid target pressure theory for the design of turbomachinery stator blade sections lying on an arbitrary axisymmetric stream-surface with varying stream-surface width. The flow is considered irrotational and compressible. Introducing the potential (φ) and the streamfunction (ψ) as independent natural coordinates, a curvilinear coordinate transformation is performed, which expresses the governing flow equations in the natural coordinates space using differential geometry arguments. The flow equations are then solved on the (φ,ψ) plane using as Dirichlet conditions the imposed target pressure. Geometry is determined by integrating the generalized Frenet equations along the natural coordinate lines. Particular attention is given to the numerical implementation of the method. An auxiliary coordinate transformation permits the definition ofC-type computational grids on the (φ,ψ) plane resulting in a more accurate description of the leading edge region, where the natural coordinates transformation becomes singular. A two-parameter iterative scheme assures the trailing edge closure of the blade section. The method is validated through several comparisons of inverse calculation results with direct, ‘reproduction’, computational results. The design procedure of new sections is also discussed.
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机译：本文旨在提出一种简明的反粘性目标压力理论，用于设计位于任意轴对称流面和不同流面宽度的涡轮机械定子叶片截面上。流动被认为是非旋转和可压缩的。将势（φ）和流函数（ψ）作为独立的自然坐标，进行曲线坐标变换，利用微分几何参数表示自然坐标空间中的控制流动方程。然后，在（φ，ψ）平面上求解流动方程，使用狄利克雷条件施加的目标压力。几何形状是通过沿自然坐标线对广义弗雷内特方程进行积分来确定的。特别注意该方法的数值实现。辅助坐标变换允许在 （φ，ψ） 平面上定义 C 型计算网格，从而更准确地描述前缘区域，其中自然坐标变换变得奇异。双参数迭代方案确保了叶片截面的后缘闭合。该方法通过对逆向计算结果与直接的“再现”计算结果的多次比较来验证。还讨论了新部分的设计程序。
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