A Viscous Transonic Inverse Design Method for Turbomachinery Blades: Part I — 2D Cascades

An inverse design methodology is presented for the design of turbomachinery blades using a cell-vertex finite volume time-marching algorithm in transonic viscous flow. In this method the blade shape is designed subject to a specified distribution of pressure loading (the difference in pressure across the blade) and thickness distribution. The difference between specified pressure loading and the pressures on the initial blade shape results in a normal velocity through the blade, which is then used to update the blade shapes. Viscous effects are represented by using a distributed body force. A simple and fast iterative scheme is proposed for automatically finding a suitable pressure loading that will provide a specified flow turning (or specific work). The method, therefore, can be applied to the design of new blade geometry without any need to supply information on the initial blade geometry or the blade loading corresponding to an existing design. The Euler solver is first validated by using experimental data for a turbine stage. The accuracy of the inverse procedure is then verified by designing the stator blade from the computed pressure loading. Finally the method is applied to the design of an axial transonic turbine stator and an axial compressor rotor and stator blade.