Global Instability Analysis of Unswept- and Swept-Wing Transonic Buffet Onset

摘要

Global stability analysis is used to analyze the onset of transonic buffet on infinite swept and unswept wings. This high-Reynolds-number flow is governed by the Unsteady Reynolds Averaged Navier-Stokes equations. The analysis generalizes earlier studies focused on two-dimensional airfoils. For the unswept wing, results show spatial-instability modes in addition to the earlier-observed unsteady mode. The spatial modes of instability exist over two bands of spanwise wavelengths centered around a wavelength of one wing chord, and around a wavelength of one-tenth a wing chord. The longer-wavelength modes have a flow structure characteristic of buffeting modes, concentrated at the shock and in the shear layer downstream of the shock. The shorter-wavelength modes are only concentrated in the shear layer downstream of the shock. These spatial modes can lead to spanwise-periodic flow structures for the unswept wing. For the swept wing, these spatial modes become unsteady propagating modes and contribute to the more complex buffeting-flow structures observed on swept wings as compared to unswept wings. The spanwise-wavelength bands of the spatial modes translate to different frequencies, resulting in a broad-banded unsteady response for the swept wing. For a 30-degree swept wing, the frequencies associated with the spatial modes are roughly 10 times higher than the swept-wing generalization of the two-dimensional unsteady mode, and roughly 6 times higher than the unsteady mode for the unswept wing. These instability characteristics are in good agreement with experimental observations.