Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynolds-averaged Navier–Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch – the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at near-critical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.
The boundary-layer receptivity resulting from acoustic forcing over a flat plate with a localized surface irregularity is analyzed using perturbation methods. The length-scale reduction, essential to acoustic receptivity, is captured within the framework of the classical stability theory. At first order, two disturbances are calculated: an unsteady disturbance resulting from the acoustic forcing and a steady disturbance resulting from the surface irregularity. These disturbance fields interact at second order to produce a traveling-wave field bearing the frequency of the acoustic wave and wave numbers associated with Fourier components of the surface irregularity. Components of the traveling-wave field scale linearly with both the acoustic forcing and the height of the surface irregularity. Receptivity occurs when the frequency and wave number of a traveling-wave component perfectly match the local eigenmode. Results are in general agreement with asymptotic analyses for irregularities in the neighborhood of branch I. Downstream of branch I, the current results show significant deviations from the asymptotic theory. Comparisons to experiments show good agreement for receptivity amplitudes when the height of the surface irregularity is small.
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