Linear Frequency Domain Prediction 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 (RANS) 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 increasing demand to accurately predict flutter boundaries in the viscous transonic regime - a demand which until recently could only be satisfied by high-fidelity RANS 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 RANS methods fidelity to a high degree, at substantially reduced computational expense. Such a method is presented here on basis of the TAU-RANS method. Denoted as the TAU linear frequency domain (LFD) 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 LFD is in good agreement with the experiment for a 2D case. For the 3D case there are larger differences. More important, the LFD method is in excellent agreement to time-accurate RANS simulations. Depending on the LFD-employed solution scheme, reductions in computational costs well beyond an order of magnitude are obtained. In addition, the Determining the flutter boundaries for full aircraft configurations by time-accurately solving the Reynolds-averaged Navier-Stokes (RANS) 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 increasing demand to accurately predict flutter boundaries in the viscous transonic regime - a demand which until recently could only be satisfied by high-fidelity RANS 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 RANS methods fidelity to a high degree, at substantially reduced computational expense. Such a method is presented here on basis of the TAU-RANS method. Denoted as the TAU linear frequency domain (LFD) 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 LFD is in good agreement with the experiment for a 2D case. For the 3D case there are larger differences. More important, the LFD method is in excellent agreement to time-accurate RANS simulations. Depending on the LFD-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.