Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Abstract:
The self-similar converging-diverging shock wave problem of Guderley in 1942 has been the major source of considerable mathematical and physical interest. We investigate an application of the Guderley's solution with reference to phase-plane analysis and a code has been developed for the verification test problem for compressible flow. In this an effort has been made in understanding the problem's mathematical and computational approach. The simplifications and group invariance properties reduce the compressible flow equations (for a medium whose equation of state (EOS) is of Mie-Gruneisen type), to two coupled s nonlinear equation whose solution is an eigenvalue problem. The information we provide, together with previously published material, gives a complete description to construct a semi-analytic Guderley solution. The assumption (1-?(G)= k) made led to developing an EOS and thus the pahse-plane analysis method employed provides a global numerical solution. Such assumption alone helped in obtaining the numerical solution. Taking k = ?, we developed the Guderley's polytropic gas results as a special case from our investigation and the results are matching well with the results of other authors and taking k= physically meaningful values led to condensed matter EOS and results. Thus k is a very general quantity which leads in obtaining different EOS.

Keywords: compressible flow; shock waves; exact fluid flow solution; convergent flow, Mie-Gruneisen

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