The effect of wall shape on the degree of reinforcement of a shock wave moving into a converging channel

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Abstract
The one-dimensional theory for the interaction between a normal shock wave and a discontinuous reduction in a area is applied to the flow in a two-dimensional channel. It is shown that, for a given overall area ratio, a channel shape consisting of two equal discontinuous reductions in area produces a larger gain in shock strength than a channel having a single discontinuity. The gain in shock strength continues to increase with the number of steps, until the ideal limiting case of an infinite number of vanishingly small changes in area is reached.A drum camera was used to measure, in a shock tube, the increase in speed of normal shock waves passing through two-dimensional converging channels of different wall shape. It was found that a single discontinuous change produced a gain in shock strength which was less than half that given by the one-dimensional analysis. However, the gain increased as the area change was made more gradual and for long smooth nozzles the value for the ideal case was nearly attained.