Laminar Boundary-Layer Flow Near the Entry of a Curved Circular Pipe

The fluid mechanics of a viscous, incompressible fluid entering a circular curved pipe at large Reynolds number is investigated numerically. The flow field is divided into two regions, the boundary-layer region and the inviscid core region. The boundary layer is assumed to be laminar and the method of integral relations is used to solve the governing equations. The core region, on the other hand, is assumed irrotational and is solved by a modified version of Telenin’s method. The coupling of the two regions is accounted for through the imposition of the outer edge normal velocity as a boundary condition for the core region. Results are presented for a Reynolds number of 10⁴ and a curvature ratio of 0.1. It has been shown that the cross flow in the core region is initially directed from the outer to the inner bend and reverses its direction downstream for the entry condition of uniform axial motion. The core velocity profiles are consistent with a recent experimental investigation, while the boundary-layer results are qualitatively similar to those of Yao and Berger, although a direct quantitative comparison is not applicable, due to the different range of Reynolds number considered.