Numerical investigation of the tone noise mechanism over laminar airfoils

Abstract

This paper presents the first numerical investigation via direct numerical simulation of the tone noise phenomenon occurring in the flow past laminar airfoils. This phenomenon corresponds to the radiation of discrete acoustic tones in some specific flow conditions, and has received much attention since the 1970s, and several experimental studies have been carried out to identify and understand the underlying physical mechanisms. However, several points remain to be clarified in order to provide a complete explanation of its origin. The flow around a two-dimensional NACA0012 airfoil is considered in order to have a deeper understanding of the tone noise phenomenon. Consistently with previous experimental studies, it is shown that depending on the Reynolds number and angle of attack, two different types of acoustic spectrum are observed: one which exhibits a broadband contribution with a dominant frequency together with a sequence of regularly spaced discrete frequencies, while the other one is only characterized by a simple broadband contribution. The first configuration is typical of the tone noise phenomenon. The present work shows that in this case, the mean flow on the pressure side of the airfoil exhibits a separation bubble near the trailing edge and the main tone frequency is close to the most amplified frequency of the boundary layer. The mechanism proposed in previous works for the main tone generation – which implies the existence of a separation bubble at the pressure side – is therefore validated by numerical simulation. On the other hand, the analysis of the suction side boundary layer reveals that there is no separation and that the most amplified frequency is different from the main tonal one. However, the suction side boundary layer is highly receptive to the tone frequency. Finally, an original explanation for the existence of the secondary discrete frequencies observed in the radiated pressure spectrum is given. They are associated to a bifurcation of the airfoil wake from a symmetric to a non-symmetric vortex pattern. A possible explanation for the existence of this bifurcation is the interaction between the disturbances which are the most amplified by the suction side boundary layer and those originating in the forcing of the suction side flow by the main tone noise mechanism.

On the receptivity of aerofoil tonal noise: an adjoint analysis

“…This finding corroborates previous observations, including the early investigations of Paterson et al (1973) as well as the numerical simulations of Desquesnes et al (2007) and Fosas de Pando et al (2014). It identifies the most sensitive part of the hydrodynamic-acoustic feedback loop and suggests the placement of actuators or surface elements on the aerofoil's upstream pressure side for an active or passive strategy to weaken or suppress acoustic tones.…”

“…This receptivity mechanism prevails over the direct growth of instabilities on the suction surface as the total spatial growth along the pressure-surface is larger than the analogous growth on the suction-surface. This observation is supported by previous experiments (Nash et al, 1999) and numerical calculations (Desquesnes et al, 2007): the frequency of the dominant tone in the spectrum coincides with the most amplified frequency along the pressure surface based on local stability theory.…”

“…Arbey & Bataille, 1983) and a resulting ladder structure as the free-stream velocity is varied. The multi-peak structure has been confirmed in further experiments as well as in numerical simulations by, e.g., Desquesnes et al (2007); Jones & Sandberg (2011);Fosas de Pando et al (2014) and has been linked to feedback loops consisting of boundary layer instabilities and acoustic radiation. Simplified theoretical models -relying on a phase condition between local spatial growth, acoustic scattering on the trailing edge and a receptivity process at a prescribed location -have been proposed by Kingan & Pearse (2009), which reproduced well the observed frequencies for the tonal noise problem.…”

“…A first indication of the wavemaker location on the pressure surface has been reported in the previous numerical study of Desquesnes et al (2007), where they state: "The computation of the amplification ratio for different chordwise stations and the same x 0 [distance from the leading edge] shows that the most amplified frequency is constant and equal to 845Hz from x/c = 0.7 to x/c = 0.96. The tone noise frequency is therefore selected before the boundary-layer separation."…”

“…This flow configuration was chosen to match typical mean flow characteristics described in the experimental work of Paterson et al (1973); Nash et al (1999) and the numerical simulations of Desquesnes et al (2007). The modal structures span a rather wide frequency range, but only a few modes (in the leading M-category) contain a significant acoustic component to account for the observed sound pressure levels as well as the observed frequencies.…”