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Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

Published online by Cambridge University Press:  26 April 2006

M. Tadjfar  and
R. J. Bodonyi
M. Tadjfar
Affiliation:
MCAT Institute, Fluid Mechanics Laboratory, NASA Ames Research Center, Mail Stop 260-1, Moffett Field, CA 94035, USA
R. J. Bodonyi
Affiliation:
Department of Aeronautical and Astronautical Engineering. The Ohio State University, 2036 Neil Ave. Mall, Columbus, OH 43210, USA
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Abstract

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 242 , September 1992 , pp. 701 - 720
Copyright
© 1992 Cambridge University Press

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