Unsteady symmetry-plane boundary layer and 3-D unsteady separation. Part 1: High incidence

The symmetry-plane laminar boundary layer of an impulsively-started ellipsoid of revolution at high incidence is solved to shed light on some basic characteristics of three dimensional, unsteady flows. The governing equations are formally similar to those for the 3-dimensional, steady case, so the same method of solution and computer programs previously developed were employed in the present work. The most important result obtained is concerned with the meridional skin friction c(fu). The zero-c(fu) point (at which c(fu) vanishes) does not, as expected, move forward as time increases, instead it remains over the rear body. As t approaches infinity, it jumps to the front nose. This implies that there is no flow separation over the symmetry-plane at finite times. In the meanwhile, it is argued that separation must occur on two sides of the body. This situation leads us to propose a new unsteady separation sequence, i.e. an open type separation prevails at earlier times, while a closed type of separation occurs only at the steady-state condition. This sequence presents a sharp contrast to the conventional notion of unsteady separation which consists of a series of closed separations only. Furthermore, this sequence with the time as the parameter is found to be similar to that for previously-studied steady flows with varying incidences.