Modal analysis of the laminar boundary layer instability and tonal noise of an airfoil at Reynolds number 150,000

Abstract

A direct numerical simulation of the flow field around a controlled-diffusion airfoil within an anechoic wind-tunnel at $5°$ incidence and a high Reynolds number of $1.5\times {10}^5$ is performed for the first time using a lattice Boltzmann method. The simulation compares favorably with experimental measurements of wall-pressure, wake statistics, and far-field sound. The simulation noticeably captures experimentally observed high-amplitude acoustic tones that rise above a broadband hump. Both noise components are related to a breathing of a recirculation bubble formed around 65–70% of the chord, and to Kelvin-Helmholtz instabilities in the separated shear layer that yield rollers that break down into turbulent vortices whose diffraction at the trailing edge produces a strong dipole acoustic field. A wavelet analysis of the wall-pressure signals combined with some flow visualization has shown that the flow statistics are dominated by intense events caused by intermittent, large and intense bursting rollers. Several modal analyses of these events are performed on both the wall-pressure fluctuations and the span averaged flow field in order to analyse the boundary layer instability which triggers the typical sharp tones over a broadband hump in airfoil noise. A suction side Kelvin-Helmholtz instability is observed to be coupled with a pressure side vortex shedding induced by the sudden transition to turbulence and the blunt trailing edge.