Laminar Boundary Layer near the Symmetry Plane of a Prolate Spheroid

Abstract

The previous investigation of a three-dimensional boundary layer near the plane of symmetry of an inclined spheroid has been extended to provide 1) wider range of solutions, 2) explanations to questions left unanswered before, and 3) comparisons with experiments. Extended solutions provide more complete trends of the boundary-layer behavior for incidences from 0°-90° and for thickness ratios ranging from unity for a sphere to nearly zero for a long inclined cylinder. Among these trends is how the separation changes from one type to another and then back again with increasing incidence. Explanations are given for a number of unconventional features, including the reversal of the lateral derivative of the cross velocity profile and the flattening of the longitudinal velocity profile. The latter has long been known as a two-dimensional turbulent boundary-layer phenomenon, and it is seen here also to be a three-dimensional phenomenon. Agreement with Wilson's recent experiments (designed specifically for partial check of the results obtained earlier) enhances the significance of the results. a A b B C c f Nomenclature = semimajor axis : regular boundary-layer region = semiminor axis = partially reversed region = separated region = skin friction . p = pressure h^ -metric coefficient h e = metric coefficient R -vortex starting point Re = Reynolds number S -separation point u = meridional velocity U = freestream meridional velocity v = circumferential velocity dv/dO = circumferential derivative of v 8V/36 = freestream dv/dO z = normal coordinate a = incidence angle H = meridional coordinate 9 -circumferential coordinate Downloaded by UNIVERSITY OF ILLINOIS on March 11, 2015 | http://arc.aiaa.org |