Axisymmetric stagnation flow obliquely impinging on a circular cylinder. (English) Zbl 1058.76022
Eur. J. Mech., B, Fluids 22, No. 2, 123-131 (2003); erratum ibid. 24, No. 6, 788-790 (2005).
Summary: Laminar stagnation flow, axisymmetrically yet obliquely impinging on generators of a circular cylinder, is formulated as an exact solution of 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 \(\gamma\). The viscous problem is reduced to a coupled pair of ordinary differential equations governed by a Reynolds number \(R\) introduced by C.-Y. Wang [Q. Appl. Math. 32, 207–213 (1974; Zbl 0283.76019)]. 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 \(R\to \infty\), we uncover and correct an error in the work of J. M. Dorrepaal [Can. Appl. Math. Q. 8, No. 1, 61–66 (2000; Zbl 1016.76017)] for the position of viscous streamline attachment.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |
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