NUMERICAL SIMULATIONS OF UNSTEADY CASCADE FLOWS

A time-accurate Navier-Stokes analysis is needed for understanding the relative importance of nonlinear and viscous effects on the unsteady flows associated with turbomachinery blade vibration and blade-row noi se generation. For this purpose an existing multi-blade-row Navier-Sto kes analysis has been modified and applied to predict unsteady flows e xcited by entropic, vortical, and acoustic disturbances through isolat ed, two-dimensional blade rows. In particular, time-accurate, nonrefle cting inflow and outflow conditions have been implemented to allow spe cification of vortical, entropic, and acoustic excitations at the inle t, and acoustic excitations at the exit, of a cascade. To evaluate the nonlinear analysis, inviscid and viscous numerical simulations were p erformed for benchmark unsteady flows and the predicted results were c ompared with analytical and numerical results based on linearized invi scid flow theory. For small-amplitude unsteady excitations, the unstea dy pressure responses predicted with the nonlinear analysis show very good agreement, both in the field and along the blade surfaces, with l inearized inviscid solutions. Based on a limited range of parametric s tudies, it was also found that the unsteady responses to inlet vortica l and acoustic excitations are linear over a surprisingly wide range o f excitation amplitudes, but acoustic excitations from downstream prod uce responses with significant nonlinear content.