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Shock Wave and High-Pressure Phenomena

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Dimensional Analysis Beyond the Pi Theorem

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Abstract

The propagation of self-sustained gaseous detonations either implosion or explosion is a complex, multidimensional process involving interactions between incident shocks, Mach stems, transverse waves, and boundaries of the regions through which the detonation is moving. In this chapter, we are interested in problems that fall into one-dimensional process categories in particular when they are involved with an implosion or explosion of homogeneous and symmetric types. Self-similarity offers an excellent simplified solution, by reducing complex sets of equation to some simple ordinary sets of differential equations, where a simple exact solution can be found. Here we study well-known problems of implosion and explosion of symmetry nature, where a three-dimensional problem has reduced to one-dimensional status and obeying either Lagrangian or Eulerian schema or in some cases the problem has followed an Arbitrary Lagrangian–Eulerian (ALE) roles.

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  1. Galaxy Advanced Engineering, Inc., San Mateo, California, USA

    Bahman Zohuri

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  1. Bahman Zohuri
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Zohuri, B. (2017). Shock Wave and High-Pressure Phenomena. In: Dimensional Analysis Beyond the Pi Theorem. Springer, Cham. https://doi.org/10.1007/978-3-319-45726-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-45726-0_3

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