A Three-Dimensional Linearized Euler Analysis of Classical Wake/Stator Interactions: Validation and Unsteady Response Predictions

Abstract

A comprehensive validation of the linearized Euler analysis, LINFLUX, for wake/blade row interaction is carried out. The flow configuration is that of the benchmark problem for rotor-stator interaction proposed at the Third Computational Aeroacoustics Workshop. It consists of an unstaggered, annular, flat-plate blade row excited by the vortical gusts associated with the wakes shed from an upstream rotor. The numerical results for the unsteady pressure responses of the stator are compared with semi-analytic lifting surface and lifting line solutions. The validation is first conducted for narrow-annulus flows, where the numerical results are shown to agree well with classical two-dimensional solutions over a range of frequencies. We then carry out a detailed comparison of the three-dimensional LINFLUX results with the lifting surface results of Namba and Schulten for a blade row with a hub-to-tip ratio of 0.5. This study encompasses gust excitation frequencies for which the stator responses vary from cut off to propagating, as well as gusts with varying degrees of spanwise variation. The numerical and semi-analytical analyses yield results for the stator pressure response, including the complex amplitudes of the propagating and least attenuated, evanescent, pressure modes that are in very good agreement. The effect of increasing the spanwise phase variation of the gust is generally, but not necessarily, to reduce the power associated with the acoustic response of the blade row. A comparison of the present numerical results with those obtained from a stripwise application of classical linear theory reveals that the latter approach can be erroneous and, therefore, of questionable applicability to realistic turbomachinery unsteady flows.