Role of Azimuthal Attractive Fields in Shock Wave Formation in Non-Conducting Gase

Abstract: This paper examines the development of shock waves in a nonconductive gas with a circumferentially directed attractive force using both analytical and mathematical methods. Shock waves develop in accordance with the principles of classical shock theory when there exists a high degree of one dimensional planarity (such as in a nozzle) governed by the law of conservation of mass, momentum and energy. Nonlinear steepening of compressional waves leads to shock waves. The introduction of a circumferential attractive force modifies the flow significantly as it causes rotationally convergent flow resulting in the redistribution of circumferential momentum. The governing equations for the modified problem which includes the effect of the circumferential attractive force are derived. The impact of the attractive force upon the characteristics of shock waves such as shock structure, shock propagation velocity, and shock stability is evaluated. It is demonstrated that the attractive force accelerates nonlinear steepening thereby increasing shock wave speed, decreasing shock wave thickness and increasing the compression ratio at the shock front. In addition, the presence of the attractive force changes the planar nature of shock fronts to curved or spiral shocks depending upon whether the flow exhibits multidimensional characteristics. Parametric studies were conducted utilizing nondimensional parameters to evaluate the effect of field strength upon various properties associated with shock waves. Numerical simulations were also utilized to illustrate these concepts. The results demonstrate that a circumferentially attractive force can act as a second source of concentrated energy. Thus, the attractive force has significant effects upon the shock dynamics associated with compressible flows. This study establishes a basis for studying field influenced shock phenomena in compressible flows and suggests several avenues for future experimental and numerical research.

Keywords: Shock wave, non-conducting gas, azimuthal attractive field, compressible flow, shock curvature, Mach number, dimensionless analysis