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Global instability in the onset of transonic-wing buffet. (English) Zbl 1430.76343
J. Fluid Mech. 881, 3-22 (2019); corrigendum ibid. 901, Article ID E1, 6 p. (2020).
Summary: Global stability analysis is used to analyse 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 spanwise-periodic stationary modes in addition to the earlier-observed oscillatory mode. The oscillatory mode is nominally two-dimensional with a spanwise wavelength greater than ten wing chords. The stationary modes of instability exist over two bands of spanwise wavelengths centred around an intermediate wavelength of one wing chord, and around a short wavelength of one tenth of a wing chord. The intermediate-wavelength modes have a flow structure characteristic of airfoil buffeting modes, concentrated at the shock and in the shear layer downstream of the shock. The short-wavelength modes are only concentrated in the shear layer downstream of the shock. These stationary modes can lead to spanwise-periodic flow structures for the unswept wing. For the swept wing, these stationary modes become unsteady travelling modes and contribute to the more complex buffeting-flow structures observed on swept wings as compared with unswept wings. The spanwise-wavelength bands of the travelling modes translate to different frequencies, resulting in a broad-banded unsteady response for the swept wing. For a \(30^°\) swept wing, the frequencies associated with the intermediate-wavelength modes are approximately 10 times higher than the swept-wing generalization of the long-wavelength oscillatory mode, and approximately 6 times higher than the long-wavelength mode for the unswept wing. These instability characteristics are in good agreement with experimental observations.

76H05 Transonic flows
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76D25 Wakes and jets
high-speed flow
Full Text: DOI
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