Linear-Frequency-Domain Predictions of Dynamic-Response Data for Viscous Transonic Flows

Abstract

Determining the flutter boundaries for full aircraft configurations by time-accurately solving the Reynolds-averaged Navier–Stokes equations is prohibitive with respect to computational expense, as the unsteady aerodynamic loading must be predicted for a wide range of flight conditions, frequencies, and structural mode shapes. Nonetheless, there is an increasing demand to accurately predict flutter boundaries in the viscous transonic regime—a demand, which, until recently, could only be satisfied by high-fidelity Reynolds-averaged Navier–Stokes methods. Brought to application readiness over the last years, time-linearized/small-disturbance methods, however, have been shown to satisfy this demand as well. They retain the Reynolds-averaged Navier–Stokes method’s fidelity to a high degree, at a substantially reduced computational expense. Such a method is presented here on the basis of the TAU–Reynolds-averaged Navier–Stokes method. Denoted as the TAU linear-frequency-domain method, it is validated for both a standard transonic airfoil and a high-aspect-ratio-wing dynamic test case using rigid pitch modes. The response data obtained from the linear frequency domain are in good agreement with the experiment for a two-dimensional case. For the three-dimensional case, there are larger differences. More important, the linear-frequency-domain method is in excellent agreement to time-accurate Reynolds-averaged Navier–Stokes simulations. Depending on the linear-frequency-domain-employed-solution scheme, reductions in computational costs well beyond an order of magnitude are obtained. In addition, the limits of the so-called frozen-eddy-viscosity approach are established.