Viscous eddies near a 90° and a 45° corner in flow through a curved tube of triangular cross-section

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Abstract
A numerical calculation is presented for the slow flow of a viscous fluid in a region bounded by a right-angled isosceles triangle. The particular flow considered is the secondary flow generated in the plane of a cross-section by the primary axial flow, under a constant pressure gradient, through a slightly curved tube of triangular cross-section. The flow is assumed to be at small Dean number so that the stream function of the secondary flow satisfies the biharmonic equation. The sequence of eddies of decreasing size and intensity first identified by Moffatt (1964a) is observed in each of the corners. Numerical details of a number of these eddies are given and their properties are found to be in excellent agreement with the theory.

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