Studies of shock wave focusing using geometrical shock dynamics

Citation

Cates, Joseph Eugene (1996) Studies of shock wave focusing using geometrical shock dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/bfhf-3w47. https://resolver.caltech.edu/CaltechETD:etd-10042006-142406

Abstract

A finite-difference numerical method for geometrical shock dynamics has been developed, based on the analogy between the equations and the supersonic potential equation. The method has proven to be a valuable tool for analyzing the complex nonlinear processes that occur in shock focusing. The approximate shock dynamics theory is able to capture the effects of initial Mach number and aperture angle on the focal region. The numerical results duplicate the strong, moderate, and weak shock behaviors observed in experiments, with good agreement for focal pressure and triple-point path. The primary error arises due to the inability of shock dynamics to allow regular reflection along the centerline. Adequate resolution of the focal region proves to be particularly important to properly judge the accuracy of the shock dynamics solution. The appropriate shock dynamics equations are developed for the case of shock propagation into a nonuniform media for a general equation of state with nonuniform freestream velocity. The modification of the numerical method to this more general problem is straightforward. The complete shock dynamics equations are derived for both perfect gas and water using the modified Tait equation. The results for propagation of a planar shock over cylindrical gas inhomogeneities shows excellent agreement with experimental results.

The propagation of sonic booms through the atmosphere provides examples of all major types of weak shock behavior. The extensive seismic network in Southern California, consisting of over two hundred sites covering over 50,000 square kilometers, is used to map primary and secondary sonic boom carpets. The results show sonic boom ground exposure under the real atmosphere is much larger than previously expected.

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