Unsteady laminar boundary layer along the symmetry plane of an impulsively started prolate spheroid

The symmetry-plane laminar boundary layer over an impulsively-started prolate spheroid of axes ratio 1/4 at various incidence is calculated in detail. Results agree with the steady solutions at large times. The most important one is concerned with the similarity between the distribution of the leeside skin friction at a fixed incidence, but varying in time, and that of the leeside skin friction for steady flows varying in incidence. The latter patterns led previously to the concept of an open and closed separation sequence for steady flows, likewise the newly found similarity suggests an unsteady open and closed sequence; i.e. at low incidence, separation starts around the rear stagnation point and gradually expands upstream in time, but it is always of the closed type. At moderate to high incidence, closed separation prevails at small times, open separation develops at large times, but separation may either remain open at moderate incidence or return to closed at high incidence as the steady-state condition is approached. The rate of approach toward the steady-state condition increases with incidence. For a less slender spheroid there is no open separation involved; unsteady separation lines are all of the closed type. For bodies other than spheroids, similar ideas may be applied.