Numerical Prediction of the Tonal Airborne Noise for a NACA 0012 Aerofoil at Moderate Reynolds Number Using a Transitional URANS Approach

Abstract

Tonal airborne noise of aerofoils appears in a limited range of moderate Reynolds numbers and angles of attack. In these specific conditions, the aerofoil is characterised by a large region of laminar flow over the aerodynamic surface, typically resulting in two-dimensional laminar instabilities in the boundary layer, generating one or more acoustic tones. The numerical simulation of such phenomenon requires, beside an accurate prediction of the unsteady flow field, a proper modelling of the laminar to turbulent transition of the boundary layer, which generally imposes the use of highly CPU demanding approaches such as large eddy simulation (LES) or direct numerical simulation (DNS). This paper aims at presenting the results of numerical experiments for evaluating the capability of capturing the tonal airborne noise by using an advanced, yet low computationally demanding, unsteady Reynolds-averaged Navier-Stokes (URANS) turbulence model augmented with a transitional model to account for the laminar to turbulent transition. This approach, coupled with the Ffowcs Williams and Hawkings (FW-H) acoustic analogy, is adopted for predicting the far-field acoustic sound pressure of a NACA 0012 aerofoil with Reynolds number ranging from $0.39 · 10^6$ to $1.09 · 10^6$. The results show a main tone located approximately at 1.6–1.8 kHz for a Reynolds number equal to $0.62 · 10^6$, increasing to 2.4 kHz at Reynolds number equal to $0.85 · 10^6$ and 3.4 kHz at $1.09 · 10^6$, while no main tones are observed at $0.39 · 10^6$. The computed spectra confirm that the acoustic emission of the aerofoil is dominated by tonal structures and that the frequency of the main tone depends on the Reynolds number consistently with the ladder-like tonal structure suggested by Paterson et al. Moreover, in specific conditions, the acoustic spectra exhibit a multi-tonal structure visible in narrowband spectra, in line with the findings of Arbey and Bataille. The presented results demonstrate the capability of the numerical model of predicting the physics of the tonal airborne noise generation.