Space-Time Mapping Analysis of Airfoil Nonlinear Interaction With Unsteady Inviscid Flow

Abstract

A new computational method of space-time mapping analysis is applied to nonlinear, inviscid computation of unsteady airfoil response to an upstream flow with a finite amplitude of a time-harmonic vortical perturbation. The unique feature of the method is that it solves the unsteady problem as a steady-state one, by treating the time coordinate identically to space directions. The periodic nature of the flow is used to design the mesh covering one period of the vortical gust in the time direction, with a periodic boundary condition applied at the time-inflow and time-outflow boundaries. The computed solution is, thus, driven directly to the final long-time periodic solution using a pseudotime marching with a high-order discretization scheme. Computed unsteady aerodynamic and aeroacoustic airfoil responses are compared against available numerical solutions. Results obtained for a high-amplitude impinging gust identify zones in the computational domain where nonlinear response effects appear most significant.