The effect of dust particles on the evolution of planar and non-planar shock wave in two-dimensional supersonic flow of van der Waals gas

Abstract

The motive of this study is to investigate the impact of the dust particles on the shock formation in two-dimensional steady supersonic flow of the composition of van der Waals gas and small solid dust particles for the planar, cylindrically symmetric and spherically symmetric cases. It is shown that the governing equations describing the van der Waals gas with dust particles is hyperbolic in nature. Further, by employing the method of wavefront analysis, we derived the transport equations for shock wave which lead to derivation of shock formation distance and also, provide the relations of shock formation. Also, it is determined as how the shock formation distance is affected by the presence of dust particles, parameter of van der Waals gas and upstream flow Mach number (M> 1) by using MATHEMATICA 11 software. © 2022, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.