Boundary layer over spinning blunt body of revolution at incidence including Magnus forces

Abstract

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.