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Thermophysics and Aeromechanics

2025 year, number 4

Nonlinear evolution of unsteady disturbances in the boundary layer on a swept wing in the presence of intense crossflow vortices

V.I. Borodulin, A.V. Ivanov, Y.S. Kachanov, D.A. Mishchenko
Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia
Keywords: boundary layer on a swept wing, intense crossflow vortices, running instability waves, weakly nonlinear interactions, mechanism of oscillations of a strong shear layer

Abstract

The main goal of the study is an experimental investigation of the mechanism of weakly nonlinear interaction of low-amplitude unsteady modes of crossflow instability in the boundary layer on a 35-degree swept wing with steady vortices of crossflow instability. The dominating factor in the flow under study is crossflow instability, while the Tollmien-Schlichting instability is suppressed by the favorable pressure gradient. High-amplitude steady distur-bances (up to 20% at the end of the measurement region) are excited by a surface roughness element. Controlled low-amplitude unsteady disturbances are generated in the boundary layer by a source of disturbances located upstream from the roughness element. Their amplitude in the main interaction region does not exceed 1%. The source excites quasi-two-dimensional (spanwise-uniform) waves at low frequencies corresponding to the primary crossflow instability region. The results of hot-wire measurements show that the characteristics of the mean flow, as well as of steady and unsteady disturbances are independent of the disturbance amplitude. However, the evolution of unsteady disturbances is strongly affected by the presence of vortices. The excited quasi-two-dimensional instability waves rapidly decay in the downstream direction, while the forming and growing (in a certain range of transverse wave numbers) steady vortices transform two-dimensional waves to essentially three-dimensional waves with the transverse wave spectrum corresponding to the most rapidly growing crossflow instability modes. This transformation does not occur locally, in the near field of the surface roughness, but is distributed in the streamwise direction. The amplitudes of steady disturbances grow almost exponentially, with the growth rate depending on the transverse wave number in a manner typical for crossflow instability modes. The growth of the amplitudes of unsteady modes exhibits a more complicated, sometimes nonmonotonic character owing to their nonlinear interaction. It is found that the amplitudes of unsteady disturbances of all frequencies in the plane normal to the flow and the wall are strongly localized in regions of high values of the mean flow velocity gradient over the model span. An essentially three-dimensional physical mechanism of weakly nonlinear transformation of quasi-two-dimensional wave disturbances to three-dimensional waves by high-amplitude steady instability vortices is proposed, which is similar to the lift-up effect used previously to explain the growth of streaky structures in two-dimensional boundary layers.