CALCULATIONS OF EXPANDING SHOCK WAVES AND LATE-STAGE EQUIVALENCE
Final rept. Aug 1965-Nov 1967
DREXEL INST OF TECH PHILADELPHIA PA
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A numerical scheme based on the method of characteristics is developed and applied to the flow field of the expansion of a high pressure sphere into atmosphere. It is shown that this method is very accurate, involving errors of less than 1. In calculating the expanding sphere, two rather challenging problems, namely, the initial singularity and the formation of a second shock, are successfully solved through special techniques. The formation of an inward traveling shock, in addition to the main shock, is found to exist at the tail of the left traveling rarefaction wave. The strength of the second shock remains rather weak at the early stage of its development, it becomes very strong just before reaching the center of the sphere. It is shown that late-stage equivalence exists in the expansion of high pressure spheres into atmosphere, provided the initial total energy in each of the spheres is held constant. Late-stage equivalence is assumed to exist if the peak pressure distribution for different expanding spheres are the same for long times.
- Fluid Mechanics