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 noise generation. For this purpose an existing multi-blade-row Navier-Stokes analysis has been modified and applied to predict unsteady flows excited by entropic, vortical, and acoustic disturbances through isolated, two-dimensional blade rows. In particular, time-accurate, nonreflecting inflow and outflow conditions have been implemented to allow specification of vortical, entropic, and acoustic excitations at the inlet, and acoustic excitations at the exit, of a cascade. To evaluate the nonlinear analysis, inviscid and viscous numerical simulations were performed for benchmark unsteady flows and the predicted results were compared with analytical and numerical results based on linearized inviscid flow theory. For small amplitude unsteady excitations, the unsteady pressure responses predicted with the nonlinear analysis show very good agreement, both in the field and along the blade surfaces, with linearized inviscid solutions. Based on a limited range of parametric studies, it was also found that the unsteady responses to inlet vortical and acoustic excitations are linear over a surprisingly wide range of excitation amplitudes, but acoustic excitations from downstream produce responses with significant nonlinear content.
Nonlinear Analysis of the Dynamics of Criminality and Victimisation: A Mathematical Model with Case Generation and Forwarding
