A numerical study of the laminar incompressible flow over a 6:1 prolate spheroid at 10° incidence

The steady incompressible laminar flow field over a 6:1 prolate spheroid at 10° incidence and a Reynolds number of 1·6 × 10⁶ is investigated numerically by solving a reduced set of the Navier‐Stokes equations. The present study moves one step beyond the boundary layer approximation by relaxing the requirement of an imposed pressure field to permit the calculation of both attached and longitudinal vortical flow fields. The results shed light on the flow properties over slender bodies at intermediate incidence. The longitudinal vortex is found to be weak relative to vortex‐dominated flows. Nevertheless, it has pronounced effects on the flow near the surface and on global features of the flow field. A displacement velocity which describes the effect of the vortical flow on the outer inviscid flow is defined. The line on the spheroid where the displacement velocity vanishes closely follows the projection of the vortex centreline on the surface of the spheroid. It is demonstrated numerically that the convergence of the skin friction lines is not a unique criterion for identifying a vortex flow.