Roschektayev VORTEX RECEPTIVITY OF A SWEPT-WING BOUNDARY LAYER IN PRESENCE OF SURFACE VIBRATIONS

The paper is devoted to an experimental investigation of the free-stream vortex receptivity of a laminar swept-wing boundary layer due to scattering of vortices on localized (in the streamwise direction) surface vibrations. The experiments were conducted under completely controlled disturbance conditions on a model of a swept wing with sweep angle of 25 degree. Both the free-stream vortices and the surface vibrations were generated by disturbance sources. The freestream vorticity vectors were directed perpendicular to the incident flow velocity vector and parallel to the swept-wing-model surface. The vibration-vortex receptivity coefficients are defined and determined as functions of the disturbance frequency, spanwise wavenumber, and vortex offset parameter. The results are independent of the specific surface-vibration shape and vortex offset. Introduction. Previous experimental studies have shown that the problem of mechanisms of transformation of the free-stream turbulence into the cross-flow instability modes is very important for understanding the physics of the transition process and for designing advanced methods of transition prediction such as the amplitude method, variable N-factor method [1], and their modifications. The amount of studies of boundary-layer receptivity to unsteady free-stream vortices was rather restricted initially (see e.g. [2, 4]). The main attention concentrated on generation of steady streaky structures rather than unsteady instability modes (see e.g. [5-7]). Most of these studies were devoted either to 2D-receptivity problems. For steady streamwise vortices first quantitative experimental data were obtained by Kendall [5]. Later these results were compared with calculations by Bertolotti in joint work [6]. A very good agreement was found for the mechanism of excitation of streamwise streaks by free-stream vortices. A mechanism of transformation of wall-normal steady free-stream vortices to streaks on the model leading edge was investigated in detail experimentally and theoretically in [7]. First quantitative experimental study of the receptivity problem for unsteady free-stream vortices has been performed in [2] (see also [8]) for the case of a 2D problem with the vorticity vector orientation being perpendicular to the flow and parallel to the flat-plate surface. It was found, in particular, that such vortical disturbances do not excite measurable Tollmien-Schlichting (TS) waves far from the leading edge if the model surface is smooth. Almost all subsequent investigations of the problem of unsteady vortex receptivity of boundary layers were either theoretical or were performed for purely 2D base flows and disturbances. A quantitative experimental study of the 2D problem of vortex receptivity in presence of controlled surface roughness was carried out in [9]. In contrast to [2] (performed on a smooth surface) the excitation of the TS-waves was detected and examined successfully. The first experimental study of a localized receptivity mechanism for scattering of (quasi-2D) free-stream vortices on surface vibrations was performed in [10]. The corresponding receptivity coefficients were obtained as functions of the spanwise wavenumber of surface vibrations. First quantitative experimental investigation of the distributed problem of an airfoilboundary-layer receptivity to unsteady free-stream vortices was reported in [11] for the case of scattering of 3D vortices (which were normal to the incident flow and leading edge) on “natural” baseflow and surface non-uniformities. Excitation of 3D TS-waves was detected and studied. Later some more detailed results were obtained in [12-14] for cases of both wall-normal and surfaceparallel orientations of the free-stream vorticity vectors. Thus, the vortex-receptivity problem is not studied experimentally for 3D boundary layers, including the swept-wing boundary layers. The goal of the present experiments is to meet this lack.