Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

Abstract

An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.