On transonic viscous-inviscid interaction

Buldakov, E. V. and Ruban, A. I. (2002) On transonic viscous-inviscid interaction. Journal of Fluid Mechanics, 470. pp. 291-317. ISSN 0022-1120

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Abstract

The paper is concerned with the interaction between the boundary layer on a smooth body surface and the outer inviscid compressible flow in the vicinity of a sonic point. First, a family of local self-similar solutions of the Kármán–Guderley equation describing the inviscid flow behaviour immediately outside the interaction region is analysed; one of them was found to be suitable for describing the boundary-layer separation. In this solution the pressure has a singularity at the sonic point with the pressure gradient on the body surface being inversely proportional to the cubic root dpw/dx [similar] ([minus sign]x)[minus sign]1/3 of the distance ([minus sign]x) from the sonic point. This pressure gradient causes the boundary layer to interact with the inviscid part of the flow. It is interesting that the skin friction in the boundary layer upstream of the interaction region shows a characteristic logarithmic decay which determines an unusual behaviour of the flow inside the interaction region. This region has a conventional triple-deck structure. To study the interactive flow one has to solve simultaneously the Prandtl boundary-layer equations in the lower deck which occupies a thin viscous sublayer near the body surface and the Kármán–Guderley equations for the upper deck situated in the inviscid flow outside the boundary layer. In this paper a numerical solution of the interaction problem is constructed for the case when the separation region is entirely contained within the viscous sublayer and the inviscid part of the flow remains marginally supersonic. The solution proves to be non-unique, revealing a hysteresis character of the flow in the interaction region.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	Ms Lucy van Russelt
Date Deposited:	14 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/484

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