Theory of Inviscid Shear Flow over Bluff Bodies Attached to a Plane Wall : Part 1, Theoretical Formulation and Applications to Normal Plate and Semicircular Projection

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A theoretical investigation is attempted on a separated flow past two-dimensional bluff bodies attached to a plane wall on which a turbulent boundary layer develops. The velocity profile in the turbulent boundary layer which would have been measured if the bluff body had been absent was replaced by a hypothetical inviscid shear flow of constant vorticity. This model admits analytical solutions and generates closed streamlines in front of the bluff bodies which are geometrically akin to the observed separation bubbles. Because of the lack of knowledge about the turbulent mixing along the edge of the separation bubbles, the present theory includes three or four constants which should be determined on the basis of the experimental information, the number of constants depending upon the shape of the body. For bluff bodies for which these constants can properly be estimated, theoretical pressure distributions agree well with experimental results. Flows around two typical shapes of bluff bodies, i.e. the normal plate and the semicircular projection are worked out in detail.
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