Time-linearized simulation of unsteady transonic flows with shock-induced separation

Abstract

During flutter analysis of a new aircraft a huge number of unsteady aerodynamic simulations is necessary in the parameter space consisting of Mach number, aeroelastic trim state, structural mode shape and frequency. For subsonic flow conditions fast potential methods like the Doublet Lattice Method can be applied. In the transonic regime unsteady flow perturbations depend on the mean flow state and CFD methods have to be employed. However, solving the nonlinear unsteady RANS equations for thousands of parameter combinations is not applicable. Hence, faster CFD methods are needed to reduce the computational costs. Assuming small time-harmonic perturbations, the RANS equations can be linearized around the steady mean solution. The latter are preferably solved in the frequency domain. This results in a large, sparse linear system for the perturbation of the fluid unknowns. In this paper an efficient time-linearized solver (LFD-TAU) is presented with special focus on 2-d external flows with strong shock-induced separation. The results are compared to small-amplitude pulse response and single-frequency RANS simulations, demonstrating good agreement over a wide frequency range. Even under pre-buffet flow conditions, showing aerodynamic resonance peaks, the resonance frequency is captured well, while the amplitudes are overestimated.