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Optimal perturbations in swept leading edge boundary layers.

Abstract : The flow at the leading edge of a swept wing is accurately modelled by swept Hiemenz flow. At large enough sweep angles swept Hiemenz flow is linearly unstable to G¨ortler Hammerlin (GH) disturbances, which are essentially two dimensional. Obrist and Schmid (2003) have shown that even at moderate sweep angles at which the flow is linearly stable, GH disturbances may be considerably amplified on short time scales. The goal of the present thesis is to quantify transient growth phenomena in swept Hiemenz flow and study the underlying physical mechanisms. GH perturbations are used as a model problem to set up and validate a very general gradient-based optimization algorithm. Temporal amplification of up to three orders of magnitude has been observed in GH disturbances, which is due to an analogue of the well-known two-dimensional Orr mechanism in two-dimensional shear flows. The optimal amplification of temporal disturbances has been observed for counter rotating spanwise vortices that do not satisfy the GH assumption; the amplification mechanism could be linked with the classical lift-up mechanism. Transient spatial energy growth in the spanwise direction has also been investigated. The results in terms of optimal spatial disturbances, spatial energy amplification and the underly- ing mechanism have been successfully linked with lift-up induced spatial growth in two-dimensional Blasius boundary layers.
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Submitted on : Friday, July 23, 2010 - 2:40:09 PM
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  • HAL Id : pastel-00003047, version 1



Alan Guegan. Optimal perturbations in swept leading edge boundary layers.. Engineering Sciences [physics]. Ecole Polytechnique X, 2007. English. ⟨pastel-00003047⟩



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