Unsteady separation and heat transfer upstream of obstacles

Abstract

The development of a laminar boundary layer upstream of both two- and threedimensional obstacles mounted on a plane wall is considered. The motion is impulsively started from rest, and it is shown that the boundary 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 and Lagrangian coordinates. It is demonstrated that in both situations the flow focuses into a narrow-band eruption characteristic of separation phenomena at high Reynolds number. For the three-dimensional problem, results are obtained on a symmetry plane upstream of the obstacle which indicate the evolution, and subsequent sharp compression, of a spiral vortex in the near-wall flow in a manner consistent with recent experimental studies. The eruptive response of the two-dimensional boundary layer is found to be considerably stronger than the corresponding event in three dimensions. Calculated results for the temperature distribution are obtained for the situation where the wall temperature is 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.