Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 1 — Description of the Method

An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi 3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multi-step Runge-Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.