Investigation of Fluid Structure Interaction in Vibrating Cascades Using a Time Domain Method

Flutter and forced response problems in turbomachine blade assemblies arre usually investigated in the frequency domain where we assume that the linearized unsteady aerodynamic forces are time-harmonic functions. These simplified analyses, however, may become doubtful as soon as nonlinear phenomena such as strong oscillating shocks or massive flow separation occur. Both phenomena may significantly influence the aerodynamic damping, hence causing a shift of stability boundaries or a change of response amplitudes. In order to investigate such aeroelastic effects, the governing equations of structural vibrations and fluid motion have to be simultaneously integrated in the time domain. In this paper a technique is presented which analyzes the flutter behaviour of an oscillating compressor cascade by a time domain method. The structural part of the governing aeroelastic equations is time-integrated according to the algorithm of Newmark, whereas the unsteady airloads are computed at every time step by an Euler or a Navier-Stoke code. The link between the two time integrations is an automatic grid generation in which the used mesh is dynamically deformed so that it conforms with the deflected blades at every time step. Time series were computed for a tunnel and a mistuned blade assembly of twenty compressor blades operating in transonic flow. It was found that the frequency domain results for subsonic flow are almost identical with the data obtained by a time domain method. However, for transonic flow, where vibrating shocks and a temporarily choked flow in the blade channel dominate the unsteady flow, the energy transfer between fluid and structure is no longer comparable to that of a linear system. It is demonstrated that here the application of the time domain method leads to a significantly different aeroelastic behaviour of the blade assembly including a shift of the stability boundary