An Inverse Time Marching Method for the Definition of Cascade Geometry

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Abstract
The article describes a so-called “inverse mode” calculation method, providing the geometry of a cascade corresponding to a given velocity distribution, and gives some examples of application. The velocity distribution may be assigned over the whole of the suction and pressure sides or over only a part of them, the remaining parts being already known. The closure condition of the profile is ensured by an iterative process on the solidity of the cascade. A second version allows the definition of the geometry of a profile with a given thickness evolution law and as assigned velocity distribution on the suction side. The method makes use of a pseudo-unsteady calculation, enabling one to treat the case of flows with shock waves in a two-dimensional stream with possible variations of cross section. This flexibility of use confers to the method a wide field of application, covering all possible configurations of flow in turbine and compressor cascades.

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