On the effect of the correction of modelled airfoil tonal noise for a spanwise extension

Abstract

Airfoil self-noise at high Reynolds numbers is caused by turbulent boundary layers. In modelling such a case with Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS), the acoustic source and thus surface pressure fluctuations are incoherent along the modelled spanwise length, assuming the simulated span is wide enough to capture turbulent flow structures. In literature, the spanwise coherence of surface pressure is normally inspected at 0.95% of the chord. A sound pressure level (SPL) correction for an increase in spanwise length can be applied, for example, for comparison of the modelled SPL spectra with experimental measurements. For a larger spanwise surface pressure coherence length, the SPL correction increases. In contrast, airfoils at low Reynolds numbers emit self-noise with a tonal signature. An acoustic feedback mechanism propagates instabilities upstream and is responsible for the tonal amplification. Consequently, the source of noise is not highly localized and may not be fully incoherent at all frequencies. Therefore, the chordwise position at which the surface pressure coherence length is to be calculated for a SPL correction for spanwise length, is not straightforward. In this paper, the sources of tonal acoustic noise and the effect of the position of spanwise coherence length calculation for SPL correction is investigated. A NACA 0012 airfoil is modelled using LES, at a chord-based Reynolds number of Rec = 1.1×105 and an angle of attack of α = 3°. The far field acoustic pressure is calculated with the Ffowcs-Williams Hawkings acoustic analogy Formulation 1C. The airfoil source regions are separated by their boundary layer flow characteristics and their relative contributions to the far field SPL are analysed to find a chordwise point on the airfoil surface which has a spanwise coherence length that is representative of the nature of the far field acoustic radiation. The spanwise coherence length at this position can be used to calculate the SPL correction for an increase in spanwise length. Two chordwise points are identified for which the resulting corrected SPL spectra agree well overall with experimental data.