Laminar flow along corners having arbitrarily large transverse curvature

• Main Author: Ridha, A. H.
• Published: University College London (University of London) 1978
• Subjects: 620.106
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.470484

Theoretical and experimental studies of the behaviour of flows in streamwise corners have hitherto been confined to corners formed by intersecting planes (sharp corners). The new work presented here concerns situations where the region of intersection is replaced by a symmetrical surface of finite curvature which smoothly joins the planes (radiused corner). The curved surface is chosen to be invariant with respect to the streamwise coordinate and asymptotes to a flat plate within a distance from the symmetry plane of the same order as the boundary layer thickness. A new analytical formulation of the equations of motion is developed to handle the problem along such corners and is of considerable generality. It contains the sharp corner geometry as a special case and is applicable to corners of angles greater or less than 180 Numerical solutions are obtained for corners of included angle from 45° to 315° and include results for sharp and radiused corners. The agreement between an existing exact solution for the 90° sharp corner and the corresponding results given here is excellent. The only other solutions available for sharp corners of angles different from 90° are inexact as is shown. Results obtained from measurements of the flow along a rectangular radiused corner are given and when compared with the theoretical results show fair qualitative agreement although at any point within the boundary layer the experimental flow velocity is somewhat higher than predicted.