Axisymmetric stagnation flow obliquely impinging on a circular cylinder

• Published in: European journal of mechanics, B, Fluids Vol. 22; no. 2; pp. 123 - 131
• Main Authors: Weidman, Patrick D., Putkaradze, Vakhtang
• Format: Journal Article
• Language: English
• Published: Paris Elsevier Masson SAS 01.03.2003; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Laminar flows; Low-reynolds-number (creeping) flows; Physics; Streamlines; Oblique incidence; Circular cylinder; Stagnation point flow; Interactions; Viscous fluids; Axial symmetry; Navier-Stokes equations; Exact solution
• ISSN: 0997-7546; 1873-7390
• DOI: 10.1016/S0997-7546(03)00019-0

Laminar stagnation flow, axisymmetrically yet obliquely impinging on the generators of a circular cylinder, is formulated as an exact solution of the Navier–Stokes equations. The outer stream is composed of a rotational axial flow superposed onto irrotational radial stagnation flow normal to the cylinder. The relative importance of these two flows is measured by a parameter  γ. The viscous problem is reduced to a coupled pair of ordinary differential equations governed by a Reynolds number R introduced by Wang (1974). Two-term asymptotic formulae valid for large  R are derived for the wall shear stress and for the position and slope of streamline attachment. These results agree well with exact numerical calculations for R>30. In checking the consistency of our solution in the planar limit R→∞ we uncover and correct an error in the work of Dorrepaal (2000) for the position of viscous streamline attachment.