Wind-Up of a Spanwise Vortex in Deepening Transition and Stall |
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Authors: | FT Smith RI Bowles JDA Walker |
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Institution: | (1) Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England, GB;(2) Mechanical Engineering Department, Packard Laboratory No. 19, Lehigh University, Bethlehem, PA 18015, U.S.A., US |
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Abstract: | A fundamental flow problem of unsteady wind-up of a spanwise vortex is studied in this theoretical work on deepening dynamic
stall and transition in a boundary layer, internal layer or related unsteady motion. It examines the nonlinear evolution of
the spanwise vortex produced when the local wall pressure develops a maximum or minimum, subsequent to the finite-time break-up
of an interacting layer and the impact of normal pressure gradients. The evolution is controlled by an inner–outer interaction
between the effects of the normal pressure gradient and the momentum jumps across and outside the vortex, which is situated
near the strong inflexion point induced in the mean flow. Although the work concentrates on a particular internal-flow context,
many of the flow properties found are generic and in particular apply for a more general case including external flows. Analysis
and associated computations point to two main distinct trends in the vortex response, depending to a large extent on a parameter
gauging the relative strengths of the above effects. The response is either an explosive one, provoking enhanced wind-up, growth and pressure in the vortex, or it is implosive, causing the vortex to shrink and virtually empty itself through unwinding, leaving little local pressure variation. A further
discussion includes the after-effects of this vortex response and some of the connections with experiments and direct computations
on deepening stall and transition.
Received 22 February 1999 and accepted 28 March 2000 |
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