Triple-deck analysis of formation of supersonic and local separation regions in transonic steady flow over a roughness element on the surface of a body of revolution

Transonic axisymmetric flow over a body of rotation with a small roughness element located on its surface is considered. The body is manly cylindrical. The roughness height is assumed to be much smaller than the radius of the cylinder and such that a triple-deck flow is induced in its neighborhood. The goal of the work is to study the effect of the cylinder radius and the roughness shape on the triple-deck flow when the cylinder radius is of the same order as the transverse size of the triple-deck interaction region. In this case, the effect of three-dimensionality of the flow is exhibited even in the first approximation. Special attention is given to the structure of supersonic regions and closing shock waves arising in the outer potential region, as well as to local separation regions if they develop in the lower viscous boundary sublayer. Specifically, it is shown that, as the radius of the cylinder increases at a fixed roughness height, the shock intensity grows considerably, whereas the position of the main shock varies little.