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Numerical studies of natural transition in a decelerating boundary layer

Published online by Cambridge University Press:  26 April 2006

Kyung-Soo Yang ,
Philippe R. Spalart  and
Joel H. Ferziger
Kyung-Soo Yang
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Present address: Boeing Commercial Airplane Group, P.O. Box 3707, MS 7H-96, Seattle, WA 98124-2207, USA.
Philippe R. Spalart
Affiliation:
NASA-Ames Research Center, Moffett Field, CA 94035, USA
Joel H. Ferziger
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

Laminar—turbulent transition in the decelerating boundary layer of Gad-el-Hak et al. (1984) is studied by solving the incompressible, time-dependent, three-dimensional Navier—Stokes equations numerically. The temporal and spatial evolution of the experimental flow structures is approximated with spatial periodicity and temporal evolution while maintaining mean-velocity profiles appropriate to the spatially-developing flow. Other than the mean flow, the initial flow fields include only small-amplitude white random noise. This and the large streamwise and spanwise dimensions of the numerical domain allow unstable waves to be selected by the dynamics, instead of being imposed arbitrarily as in previous numerical studies. In that sense, the transition is natural. In the early stages of transition, two-dimensional and slightly oblique waves grow rapidly owing to inflexional instability. Their subsequent nonlinear interactions trigger the breakdown and create a pattern of Λ vortices. The patterns of Λ vortices are more irregular than those found in ribbon-induced transition. The tips of the Λ vortices are rarely aligned with the flow direction, and they appear in local patches, consistent with the experimental visualizations of Gad-el-Hak et al. A simple model based on the interference of multiple modes of instability accounts for these features, but the specific pattern of Λ vortices depends on the random content of the initial flow field. A simulation of the later stages of transition is performed with higher numerical resolution, showing that the ‘naturally-born’ Λ vortices undergo breakdown processes similar to those of their ribbon-induced counterparts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 240 , July 1992 , pp. 433 - 468
Copyright
© 1992 Cambridge University Press

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