Transonic aeroelastic instability searches using a hierarchy of aerodynamic models

The use of a hierarchy of high fidelity computational fluid dynamics models in routine aircraft aeroelastic stability analyses is investigated. An instability of the time– linearised aeroelastic system is predicted by a small nonlinear eigenvalue problem, with the normal mode structural problem corrected by an interaction matrix to represent the flow response which is simulated by different nonlinear aerodynamic models. These are given by the full potential, Euler, and Reynolds–averaged Navier–Stokes equations. The task of searching for aeroelastic instability over a flight envelope, which is a multidimensional parameter space, is accomplished by introducing searches for the approximation of the interaction matrix. This matrix is approximated by reconstruction based on true samples which are computed in the frequency or time domain. For the task of reconstruction, kriging interpolation is discussed. The kriging approach is derived and thoroughly investigated for two structural models describing the dynamics of two degrees–of–freedom aerofoil cases and realistic aircraft structures. It is demonstrated that the results from the approximation are in excellent agreement with the predictions of the exact full order eigenvalue solver for the stability analysis over the whole flight envelope. First, the stability results of the NACA 0012 aerofoil case are compared for all considered flow models discussing the influence of physical effects and numerical discretisation. Secondly, the kriging formulation for the symmetric Goland wing cases with and without tip store is shown to be equivalent to the aerofoil formulation with only minor modifications. Thirdly, the MDO wing case, fully accounting for the effects of static deformation, requires an expanded parameter space for the instability search including the response frequency, freestream Mach number and altitude. To search the flight envelope, while assuming little prior knowledge of the stability behaviour, several sampling techniques are considered for the aerofoil cases. Risk– based sampling is found to be efficient in detecting the instability points accurately in multidimensional parameter spaces. This is then shown for the statically deformed MDO wing using a four dimensional search space adding the freestream angle of attack. Finally, the stability analysis based on flow models of variable fidelity is demonstrated for the NACA 0012 aerofoil case and the Goland wing/store configuration using both an augmented set of samples and co–kriging for the task of reconstruction.