Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms

AbstractThe linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height $h$ and diameter $d$ immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar–turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio ${\it\eta}=1$ (with ${\it\eta}=d/h$) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement.

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A global analysis of tonal noise in flows around aerofoils

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.356 ◽

2014 ◽

Vol 754 ◽

pp. 5-38 ◽

Cited By ~ 35

Author(s):

Miguel Fosas de Pando ◽

Peter J. Schmid ◽

Denis Sipp

Keyword(s):

Global Stability ◽

Acoustic Radiation ◽

Global Analysis ◽

Feedback Loops ◽

Surface Boundary ◽

Mean Flow ◽

Suction Surface ◽

Stability Analyses ◽

Pressure Surface ◽

Linearized Operator

AbstractThe generation of discrete acoustic tones in the compressible flow around an aerofoil is addressed in this work by means of nonlinear numerical simulations and global stability analyses. The nonlinear simulations confirm the appearance of discrete tones in the acoustic spectrum and, for the chosen flow case, the global stability analyses of the mean-flow dynamics reveal that the linearized operator is stable. However, the flow response to incoming disturbances exhibits important transient growth effects that culminate in the onset of aeroacoustic feedback loops, involving instability processes on the suction- and pressure-surface boundary layers together with their cross-interaction by acoustic radiation at the trailing edge. The features of the aeroacoustic feedback loops and the appearance of discrete tones are then related to the features of the least-stable modes in the global spectrum: the spatial structure of the direct modes displays the coupled dynamics of hydrodynamic instabilities on the suction surface and in the near wake. Finally, different families of global modes will be identified and the dynamics that they represent will be discussed.

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