UNSTEADY SEPARATION AND HEAT-TRANSFER UPSTREAM OF OBSTACLES

The development of a laminar boundary layer upstream of both two- and three-dimensional obstacles mounted on a plane wall is considered. The motion is impulsively started from rest, and it is shown that the bou ndary layer upstream of the obstacle initially develops independently from that on the obstacle itself. Numerical solutions for the unsteady boundary-layer flow on the plane wall are obtained in both Eulerian a nd Lagrangian coordinates. It is demonstrated that in both situations the flow focuses into a narrow-band eruption characteristic of separat ion phenomena at high Reynolds number. For the three-dimensional probl em, results are obtained on a symmetry plane upstream of the obstacle which indicate the evolution, and subsequent sharp compression, of a s piral vortex in the near-wall flow in a manner consistent with recent experimental studies. The eruptive response of the two-dimensional bou ndary layer is found to be considerably stronger than the correspondin g event in three dimensions. Calculated results for the temperature di stribution are obtained for the situation where the wall temperature i s constant but different from that of the mainstream. It is shown that a concentrated response develops in the surface heat transfer rate as the boundary layer starts to separate from the surface.