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TsAGI Science Journal

ISSN Печать: 1948-2590
ISSN Онлайн: 1948-2604

TsAGI Science Journal

DOI: 10.1615/TsAGISciJ.2015014084
pages 193-207

SELF-SIMILAR AND LIMITING SOLUTIONS OF TURBULENT BOUNDARY LAYER EQUATIONS: CONDITIONS OF D'ALEMBERT'S PARADOX

Vladimir Victorovich Mikhailov
Central Aerohydrodynamic Institute (TsAGI), Zhukovsky str. 1, Zhukovsky, 140180, Russia
Nina Veniaminovna Samoilova
Central Aerohydrodynamic Institute (TsAGI), Zhukovsky str. 1, Zhukovsky, 140180, Russia

Краткое описание

The mean flow equations in a plane turbulent boundary layer of an incompressible fluid are considered. A self-similar solution to these equations is obtained, and the criterion of relaminarization of the boundary layer (reverse transition) is refined. For the limit of high Reynolds numbers in the flow around a hydraulically smooth body, the distribution of the Clauser parameter and the skin friction coefficient over the body surface are obtained in quadratures. If there is no relaminarization of the boundary layer and no effect of surface roughness, it is shown that flow separation is localized at the rear stagnation point of the body, i.e., d'Alembert's paradox occurs in this case. The result obtained is illustrated by the example of a limiting analytical solution for a symmetric flow around elliptical cylinders. In this case, a sufficient condition of a non-separated flow is the inequality k < 4.78, where k is the ratio of the vertical to the horizontal axis of the ellipse aligned in the streamwise direction.


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