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Interaction of a potential vortex with a local roughness on a smooth surface

Published online by Cambridge University Press:  26 April 2006

Oleg S. Ryzhov  and
Sergey V. Timofeev
Oleg S. Ryzhov
Affiliation:
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, USA
Sergey V. Timofeev
Affiliation:
Computing Center, Russian Academy of Sciences, 40 Vavilov Street; 117333 Moscow, Russian Federation
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Abstract

Disturbances generated by a potential vortex moving past a small hump or dent on the otherwise smooth flat plate are considered. Features peculiar to this problem derive from the fact that the vortex is stuck with a fixed fluid particle; hence the nonlinear dependence of the pressure on the induced velocity field ensues even if the vortex intensity tends to zero. Formulation of the problem on a flow in the viscous wall sublayer given in canonical variables involves four similarity parameters for any particular shape of a roughness. The parallels between the process at hand and sound scattering from a boundary layer with a small obstacle at the bottom are indicated. Results from numerical integration of the boundary-value problem posed allow us to trace the evolution of the wave-packet structure depending on the potential vortex intensity. Overlapping of the peak wings and formation of an almost continuous spectrum in the Fourier decomposition of the signal serve as a guide for explaining the explosive development of the wave packet as distinct from the Tollmien–Schlichting wavetrain that has been registered experimentally.

The theory developed is applied to discussing the so-called bypass mode of transition provoked by external turbulence. Special emphasis is laid on flows in gas turbine engines where bypass transition plays a dominant role owing to extremely high free-stream turbulence levels.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 21 - 58
Copyright
© 1995 Cambridge University Press

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