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 ␣ap 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 ␣ow, the linearized unsteady Reynolds-averaged Navier–Stokes method is the most ef␣cient 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 one- harmonic 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.