Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Abstract

In the framework of unsteady aerodynamics, forced-harmonic-motion simulations can be used to compute unsteady loads.In this context, the present paper assesses two alternatives to the unsteady Reynolds-averaged Navier-Stokes approach, the linearized unsteady Reynolds-averaged Navier-Stokes equations method, and the harmonic balance approach.The test case is a NACA 64A006 airfoil with an oscillating flap mounted at 75% of the chord.Emphasis is put on examining the performances of the methods in terms of accuracy and computational cost over a range of physical conditions.It is found that, for a subsonic flow, the linearized unsteady Reynolds-averaged Navier-Stokes method is the most efficient one.In the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method remains the fastest approach, but with limited accuracy around shocks, whereas a oneharmonic harmonic balance solution is in closer agreement with the unsteady Reynolds-averaged Navier-Stokes solution.In the case of separation in the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method fails to converge, whereas the harmonic balance remains robust and accurate.