Direct numerical simulation of turbulent flow past a trailing edge and the associated noise generation

Abstract

Direct numerical simulations (DNS) are conducted of turbulent flow passing an infinitely thin trailing edge. The objective is to investigate the turbulent flow field in the vicinity of the trailing edge and the associated broadband noise generation. To generate a turbulent boundary layer a short distance from the inflow boundary, high-amplitude lifted streaks and disturbances that can be associated with coherent outer-layer vortices are introduced at the inflow boundary. A rapid increase in skin friction and a decrease in boundary layer thickness and pressure fluctuations is observed at the trailing edge. It is demonstrated that the behaviour of the hydrodynamic field in the vicinity of the trailing edge can be predicted with reasonable accuracy using triple-deck theory if the eddy viscosity is accounted for. Point spectra of surface pressure difference are shown to vary considerably towards the trailing edge, with a significant reduction of amplitude occurring in the low-frequency range. The acoustic pressure obtained from the DNS is compared with predictions from two- and three-dimensional acoustic analogies and the classical trailing-edge theory of Amiet. For low frequencies, two-dimensional theory succeeds in predicting the acoustic pressure in the far field with reasonable accuracy due to a significant spanwise coherence of the surface pressure difference and predominantly two-dimensional sound radiation. For higher frequencies, however, the full three-dimensional theory is required for an accurate prediction of the acoustic far field. DNS data are used to test some of the key assumptions invoked by Amiet for the derivation of the classical trailing-edge theory. Even though most of the approximations are shown to be reasonable, they collectively lead to a deviation from the DNS results, in particular for higher frequencies. Moreover, because the three-dimensional acoustic analogy does not provide significantly improved results, it is suggested that some of the discrepancies can be attributed to the approach of evaluating the far-field sound using a Kirchhoff-type integration of the surface pressure difference.