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On the nature of unsteady three-dimensional laminar boundary-layer separation

Published online by Cambridge University Press:  19 April 2006

James C. Williams
James C. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh
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Abstract

Solutions have been obtained for a family of unsteady three-dimensional boundary-layer flows which approach separation as a result of the imposed pressure gradient. These solutions have been obtained in a co-ordinate system which is moving with a constant velocity relative to the body-fixed co-ordinate system. The flows studied are those which are steady in the moving co-ordinate system. The boundary-layer solutions have been obtained in the moving co-ordinate system using the technique of semi-similar solutions. The behaviour of the solutions as separation is approached has been used to infer the physical characteristics of unsteady three-dimensional separation.

In the numerical solutions of the three-dimensional unsteady laminar boundary-layer equations, subject to an imposed pressure distribution, the approach to separation is characterized by a rapid increase in the number of iterations required to obtain converged solutions at each station and a corresponding rapid increase in the component of velocity normal to the body surface. The solutions obtained indicate that separation is best observed in a co-ordinate system moving with separation where streamlines turn to form an envelope which is the separation line, as in steady three-dimensional flow, and that this process occurs within the boundary layer (away from the wall) as in the unsteady two-dimensional case. This description of three-dimensional unsteady separation is a generalization of the two-dimensional (Moore-Rott-Sears) model for unsteady separation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 2 , 27 September 1978 , pp. 241 - 258
Copyright
© 1978 Cambridge University Press

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