Simulation of Transonic Buffet Using a Time-Spectral Method

Abstract

This paper extends the use of frequency-domain flow solvers to transonic buffet in turbulent flow regime. To do so, a time-spectral method with frequency adaptation is developed for the simulation of periodic flows of self-induced frequency. The time-spectral method is implemented into a cell-centered finite volume unsteady Reynolds-averaged Navier–Stokes (URANS) flow solver. This method uses the Fourier series to transform the URANS equations into a steady problem in the frequency domain, for a given frequency. This steady problem is recast in the time domain to allow the use of classic computational fluid dynamics techniques. Because transonic buffet is a self-induced phenomenon of unknown frequency before the computation, two algorithms are implemented in the time-spectral solver to determine its frequency. The first one relies on a gradient-based algorithm to minimize the residual of the system of equations. The second uses the phase shift per iteration of the frequency-domain solution. The accuracy of the time-spectral scheme for turbulent flows is first verified for the simulation of a pitching airfoil with a forced frequency. Then, the efficiency of the frequency-adaptation algorithms is assessed for the case of the laminar vortex shedding of a cylinder. Finally, the proposed method is applied to the solution of the transonic buffet over the OAT15A airfoil, and the results are compared to numerical and experimental results from the literature. It can be concluded that an accurate solution of the transonic buffet can be obtained with as few as five modes.