On transonic viscous–inviscid interaction
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Published:2002-10-31
Issue:
Volume:470
Page:291-317
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ISSN:0022-1120
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Container-title:Journal of Fluid Mechanics
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language:en
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Short-container-title:J. Fluid Mech.
Author:
BULDAKOV E. V.,RUBAN A. I.
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 ∼ (−x)−1/3 of the distance (−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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
2 articles.
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