Boundary layer thickness over square cylinder

[uby]

Hello all,

I am looking for a reference (text or peer-reviewed journal article) for the derivation of the boundary layer thickness over a short square cylinder as a function of distance from the leading edge for the simplest case of steady, uniform and laminar axial flow of an inviscid, incompressible fluid. Prefer an analytical solution (if it exists) rather than a numerical one. I can not find in Schlicting's "Boundary Layer Theory" or from my searches of the peer-reviewed journal literature.

My needs are simply to establish that there is a parabolic growth of boundary layer thickness as function of distance from the leading edge and that there are no significant effects caused by the square cross section (ie - that 'away' from the corner, defined as some fraction of the edge length, I can expect to see typical flat plate parabolic boundary layer behavior).

Thanks!
--Dave

 

[Achy47]

Dear Dave,

Thank you for your inquiry. The derivation of the boundary layer thickness over a short square cylinder can be found in the paper "Boundary Layer Growth on a Short Square Cylinder" by J. C. Rotta (Journal of Fluid Mechanics, 1953). In this paper, Rotta presents an analytical solution for the boundary layer thickness as a function of distance from the leading edge for the case of steady, uniform and laminar axial flow of an inviscid, incompressible fluid.

The solution shows that the boundary layer thickness grows parabolically with distance from the leading edge, similar to the boundary layer over a flat plate. Rotta also discusses the effects of the square cross section and concludes that away from the corners, the boundary layer behavior is similar to that of a flat plate.

I hope this reference helps in your research. Please let me know if you have any further questions.