Small disturbance navier-stokes computations employing the Wilcox K-omega turbulence model

Developed at Technische Universität München, the small disturbance Navier-Stokes method FLM-SD.NS has been substantiated as both an efficient and accurate means for providing unsteady air loads to the transonic aeroelastic analysis process. In an effort to extend its range of applicability, a dynamically linear instance of the Willcox k-ω eddy-viscosity closure is incorporated, complementing the original Spalart- Allmaras option. Harmonic pitching oscillations of a generic high-aspect-ratio wing are investigated. For the attached-flow cases, the k-ω incarnation of FLM-SD.NS delivers equally accurate predictions as the Spalart-Allmaras original. Reductions in computation time, up to half an order of magnitude, in relation to the comparative time-domain Reynolds-averaged Navier- Stokes method FLM-NS are again observed. For the detached-flow case, the primary benefit of the Wilcox k-ω eddy-viscosity closure is witnessed in the FLM-NS-supplied time-invariant mean solution about which FLM-SD.NS computes the dynamically linear perturbation: At localities of flow detachment, the supersonic-flowterminating shock is rendered distinctly closer to the measured physical position than for the Spalart-Allmaras instance. Limitations of the small disturbance approach, however, become apparent for both incarnations, as a substantial degree of nonlinear interaction physically exists.