Inviscid and viscous flow modeling for fast transonic flutter calculations

Transonic aeroelastic analysis at the design level relies on linear panel methods, such as the Doublet Lattice approach, usually after application of transonic corrections. The results from these calculations cannot predict shock motion, shock-boundary layer interactions and the effects of such phenomena on flutter behavior, even after corrections are applied, since the latter are generally quasi-steady. This paper proposes a higher-fidelity approach that involves the solutions of the flow equations in order to obtain the unsteady flow response to relatively small amplitude periodic deformations of a structure over a large range of oscillation frequencies. The main idea is to perform a few high-fidelity CFD simulations, such as Euler or RANS simulations, with an imposed structural deformation at selected oscillation frequencies so as to capture the most dominant nonlinear dynamic modes of the flow response. These fluid dynamic modes are then interpolated to estimate the flow response for any other oscillation frequency. The methodology can then be used to obtain a frequency-domain generalized aerodynamic force matrix, and stability analysis can be performed using standard flutter calculation methods such as the p-k method. The present methodology provides a very good estimate of the flutter boundary for the 2D Isogai airfoil validation case, but at much lower computational cost than the traditional higher-fidelity Fluid-Structure Interaction (FSI) simulations.