Application of a high-order CFD harmonic balance method to nonlinear aeroelasticity

Abstract

An Aeroelastic-Harmonic Balance (A-HB) formulation of the Euler flow equations using a high-order spatial discretization scheme coupled with structural dynamic equations is proposed. The main objective of this new approach is to dramatically reduce the computational cost required to predict unsteady, periodic problems such as limit cycle oscillations (LCO). To this end, a new solver based on the Monotonicity Preserving limiter together with the AUSM+-up flux function is developed for the harmonic balance equations. The use of high-order CFD schemes allows the reduction of the number of degrees of freedom required to achieve a given desired accuracy, with respect to lower order schemes. In this paper, the reduction in degrees of freedom of the fluid system is exploited in the context of a CFD based Harmonic-Balance framework using a frequency updating procedure to determine the limit cycle conditions. The standard A-HB methodology has shown over one order of magnitude speed-up over time-marching methods; by employing the proposed high-order scheme in conjunction with coarser grids, the LCO computational time is halved without compromising accuracy.