Laminar Boundary Layers behind Blast and Detonation Waves

摘要

The transformed coordinates devised by Mirels and Hamman have been modified in such a way that the transformed nonstationary-boundary-layer equations become applicable to boundary-layer flows induced by both blast and detonation waves moving with a power-law trajectory in planar, cylindrical and spherical geometries. Investigations were made of boundary-layer flows in air behind nonuniform strong blast waves and in the burned gas of a stoichiometric mixture of hydrogen and oxygen behind uniform Chapman-Jouguet detonation waves. The results show that the Prandtl number has a profound influence on boundary-layer flow. For a blast wave and Pr less than unity it controls a boundary-layer velocity-overshoot as one moves away from the wave. The overshoot decreases with increasing Prandtl number. For a Chapman-Jouguet detonation wave similar results are obtained for a Pr = 0.72. However, for an actual Pr = 2.26, a flow reversal occurs away from the wave where the inviscid flow velocity approaches a small value. In order to show some of the physical features of the various boundary layers, actual velocity profiles were computed for spherical and planar detonation waves in stoichiometric hydrogen-oxygen and for blast waves in air. In order to test the validity of the analysis, the heat transfer to the wall behind a planar detonation wave was calculated. The profile of the variation of the heat transfer with time at any given position behind a C-J detonation wave is in good agreement with the experimental data, and adds confidence to teh present analyses for cylindrical and spherical flows as well.