Acoustic-roughness receptivity in subsonic boundary-layer flows over aerofoils

Abstract

The generation of a viscous–inviscid instability through scattering of an acoustic wave by localised and distributed roughness on the upper surface of a NACA 0012 aerofoil is studied with a time-harmonic compressible adjoint linearised Navier–Stokes approach. This extends previous work by the authors dedicated to flat plate geometries. The key advancement lies in the modelling of the inviscid acoustic field external to the aerofoil boundary layer, requiring a numerical solution of the convected Helmholtz equation in a non-uniform inviscid field to determine the unsteady pressure field on the curved aerofoil surface. This externally imposed acoustic pressure field subsequently drives the acoustic boundary layer, which fundamentally determines the amplitudes of acoustic-roughness receptivity. A study of receptivity in the presence of Gaussian-shaped roughness and sinusoidally distributed roughness at Mach number $M_\infty =0.4$ and Strouhal numbers $\mathcal {S} \approx \{46,69,115\}$ shows the effects of various parameters, most notably angle of attack, angle of incidence of the externally imposed plane acoustic wave and geometry of surface roughness; the latter is varied from viewpoint of its placement on the aerofoil surface and its wavelength. The parametric study suggests that non-parallel effects are quite substantial and that considerable differences arise when using parallel flow theory to estimate the optimal width of Gaussian-shaped roughness elements to provoke the greatest response. Furthermore, receptivity amplitudes for distributed roughness are observed to be generally higher for lower angles of attack, i.e. for less adverse pressure gradients. It is also shown that the boundary layer is more receptive to upstream-travelling acoustic waves.

On subsonic boundary-layer receptivity to acoustic waves over an aircraft wing coated by a thin liquid film

“…While this is the first paper on the receptivity of a multi-fluid flow to acoustic–roughness interaction, one could compare our results with the similar work, such as Raposo et al. (2021). Their numerical studies of acoustic–roughness receptivity in subsonic boundary-layer flow over aerofoils show that the receptivity amplitude varies with the position of a Gaussian-shaped roughness in the absence of a thin film.…”

Asymptotic theory of Mack-mode receptivity in hypersonic boundary layers due to interaction of a heating/cooling source and a freestream sound wave

“…The latter was later applied to the roughness–acoustic receptivity in boundary layers over subsonic aerofoils (Raposo et al. 2021). Remarkably, a strong receptivity regime in supersonic boundary layers was reported by Liu, Dong & Wu (2020); namely, if the incident angle of the freestream acoustic wave is around a particular value such that its streamwise phase speed is quasi-zero, then the perturbation velocity of the acoustic signature in the near-wall viscous layer could be amplified by a factor of compared to its freestream value, leading to an extra amplification of the receptivity efficiency in comparison with the Ruban–Goldstein regime, where is the Reynolds number, with the length scale being the distance to the leading edge.…”

Instability evolution in the hypersonic boundary layer over a wavy wall

“…The leading-order contribution to the receptivity of inviscid modes depends on the deformation of the sound-generated Stokes layer by the curved wall. The acoustic receptivity has also been studied in detail using the harmonic linear Navier-Stokes (HLNS) equations in the context of incompressible flow (Raposo, Mughal & Ashworth 2018) and subsonic flow conditions (Raposo, Mughal & Ashworth 2019;Raposo et al 2021), and an acoustic receptivity model is proposed to account for the effects of variances in the freestream acoustic field on the instabilities when localized surface roughness is present.…”