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Influence of camber on sound generation by airfoils interacting with high-frequency gusts. (English) Zbl 0916.76080

This paper considers the sound generation through the interaction of gusts with airfoils. Solution for a flat plate airfoil is extended to the case of a zero-thickness cambered airfoil, where the solution is developed as an asymptotic series based on the small-loading and high-frequency parameters. The singular perturbation analysis retains asymptotic regions present in a flat-plate airfoil; additionally, the airfoil curvature effects require the introduction of an additional region in the form of an acoustic boundary layer adjacent to the airfoil surface.
The authors show that for short-wave-length gusts, the primary sound generation is concentrated in the local leading-edge region. In this region, the lengthscale of the mean-flow gradients is the same as the wavelength, so that the gust is distorted ‘rapidly’. Sound is generated by interaction of the gust with the airfoil surface, by interaction of the gust with mean-flow gradients, and by scattering effects due to the sound propagation through the locally non-uniform mean flow. As the sound which was generated in the local leading-edge region propagates through the outer region as a ray field, it undergoes \(O(1)\) phase shifts due to the mean-flow variations. Two rays which propagate along the upper and lower surfaces of the airfoil, with some modifications due to the surface curvature, are then scattered by the trailing edge. The far-field sound is a combination of the direct rays from the leading edge and the scattered rays from the trailing edge. At shallow angles, the far field exhibits diffraction characteristics related to the propagation along curved surfaces of the airfoil and to the shadow boundaries of the trailing edge. There are two important parameters, the effective leading-edge incidence angle, \(\alpha_{\text{eff}}\), and the total loading parameter, \(\alpha_g\). They contain both the airfoil incidence angle and its camber distribution. However, the total sound power radiated to the far field is correlated very well by a single aerodynamic loading parameter. Finally, the authors perform numerical calculations to assess the influence of various parameters characterizing the mean flow and convected disturbances.

MSC:

76Q05 Hydro- and aero-acoustics
76G25 General aerodynamics and subsonic flows
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