On the evolution of shock waves in Van der Waals reacting gas with small solid dust particles

Abstract

This study delves into the evolutionary dynamics of shock wave within the context of van der Waals reacting gas, particularly when small dust particles are present. The investigation involves an analysis of the governing equations in various coordinate systems, followed by a reformulation of these equations into Bernoulli’s differential equation. Through our analysis, we uncover nonlinear phenomena in the physical domain, elucidating the influence of reacting gas parameters on the propagation of expansive waves. Additionally, we investigate the impact of dust particles on wave behavior, exploring both their role in wave growth and decay. Moreover, we examine the significance of the transport equation in dictating the progression of shock wave, deriving relationships that elucidate the formation of shocks. To provide comprehensive insights, we conduct a comparative analysis across different flow geometries, including planar, circular, and spherical symmetric flows, to evaluate the effects of reacting gas parameters and small dust particles on flow patterns and the distortion of shock wave.