A vorticity dynamics theory of fully three-dimensional flow separation near a generic separation line

Abstract

A predictive theory of three-dimensional steady flow separation is presented in terms of the on-wall signatures of vorticity dynamics during separation. A general framework is developed first as a combination of the boundary vorticity dynamics and local Taylor expansion, which applies to separation from a generic smooth curved wall at any Reynolds numbers. Necessary on-wall conditions are given for the separation to occur, either in small scales inside an attached boundary layer or the whole boundary layer breaks away. A criterion for uniquely identifying a separation line is postulated, no matter the line is closed or open. At large Reynolds numbers, a scale analysis under certain assumptions leads to a threedimensional triple-deck structure near a generic separation line. Two sets of criteria are obtained, of which the first serves as a “separation watch” which *Research Professor, Senior Member of AIAA. t Memb’er of AIAA. *Research Assistant, Student Member of AIAA. qProfessor. Copyright 01999 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. tells that separation may happen soon, and the second serves as a %eparation warning” which identifies the vorticity characteristics in an already formed separation zone. The Formation and orientation of the separated shear layer are explained, and the effect of the approaching boundary layers on the separating flow and the strength of the separated shear layer is clarified. A numerical example is given which confirms the predictions of the theory.