Unstructured Shock-Fitting Calculations of the Transonic Flow in a Gas Turbine Cascade

Even though shock-capturing techniques are the de-facto standard in the CFD simulation of turbo-machinery flows, the accurate estimation of shock-induced losses in transonic flows can be severely hindered by the numerical errors that are generated along a captured shock and convected downstream. Indeed, and despite their widespread use, shock-capturing techniques are known to be plagued by a number of drawbacks that are inherent to the numerical details of the shock-capturing process. In recent works, the authors have developed a novel shock fitting technique for unstructured grids that has been applied to the computation of transonic, supersonic and hypersonic flows in both two and three space dimensions. In this paper, the proposed technique is applied to two-dimensional, transonic flows around an isolated profile and in a gas turbine cascade. It is shown that the use of unstructured meshes allows to relieve most of the algorithmic difficulties that have contributed to the dismissal of the shock-fitting technique in the framework of structured meshes. Moreover, it is confirmed that, in contrast to shock-capturing, shock-fitting allows to obtain very accurate solution on coarse meshes.