This paper presents general methods for calculating three dimensional laminar boundary layers over inclined blunt bodies (not necessarily bodies of revolution). Complete incompressible results for a prolate spheroid at 30° incidence are presented, and the computational procedures are described. The rule of the zone of dependence was observed. The results display for the first time the boundary layer structure over a non-spherical and non-conical blunt body in all details, and confirm the open-type of separation proposed earlier.

This paper investigates the three-dimensional laminar boundary layer over a blunt body (a prolate spheroid) at low incidence and with reversed flow. Results reflecting the general characteristics of such a problem are presented. More significant are the features relating to the circumferential flow reversal. Some of these features confirm our early hypotheses concerning the existence of a reversed region ahead of separation and the role of the zero-cfθ line in the general context of separation in three dimensions. Other features are unexpected, including the distribution of cfμ and the shape of the separation line. Here cfθ and cfμ denote, respectively, the circumferential and meridional components of the skin friction.

An incompressible laminar flow over a spinning blunt-body at incidence is investigated. The approach follows strictly the three-dimensional boundary layer theory, and the lack of initial profiles is readily resolved. The rule of the dependence zone is satisfied with the Krause scheme, and complete numerical solutions are obtained for an ellipsoid of revolution at 6° incidence and two spin rates. Spinning causes asymmetry which, in turn, introduces the Magnus force. The asymmetry is most pronounced in crossflow, but is also noticeable in the skin friction and displacement thickness of the meridional flow. A variety of crossflow profiles are determined as are the streamline patterns in the cross- and meridional-plane which are especially useful in visualizing the flow structure. Detailed distribution of skin friction, displacement thickness, and centrifugal pressure are presented. A negative crossflow displacement thickness is found to be physically meaningful. The Magnus forces due to the crossflow skin friction and the centrifugal pressure are determined; these two forces partly compensate for each other. At lower spin rate, the frictional force is larger, resulting in a positive Magnus force. At high spin rate, the opposite is obtained. At high incidence (30°) the present boundary layer calculations could be carried out in the longitudinal direction, only up to the beginning of an open separation.

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 |