An analysis of shock wave propagation in a dusty gas

Abstract

The present work uses a power series method to investigate the propagation of shock waves with generalized geometries generated by an intense explosion in a dusty gas. A mathematical model using a system of partial differential equations (PDEs) is presented for the considered problem. The density of the undisturbed medium is assumed to be constant. Approximate analytic solutions to the considered problem are obtained using the power series method by extending the power series of the flow variables. This work discusses the first‐order and second‐order approximate solutions and provides closed‐form solutions for the first‐order approximation. The behavior of the flow variables is depicted via figures behind the shock front for the first‐order approximation. Furthermore, the effects of geometry factor α, adiabatic exponent γ, and various dusty gas parameters such as Kp (the mass fraction of the dust particles), G0 (the ratio of the density of the dust particles to the initial density of the gas), and σ (the relative specific heat) are analyzed on the flow variables and total energy of disturbance J0 for the first‐order approximation. It is observed that an increase in any of the parameters Kp or σ causes the fluid velocity to increase and density and pressure to decrease. Increase in the parameter G0 causes the density and pressure to increase, whereas the fluid velocity does not get affected. An increase in the value of α results in a decrease in the density and pressure, while the fluid velocity remains the same. An increase in the value of γ results in a decrease in the fluid velocity; however, it has opposite effect on the pressure. The density decreases near the shock front and increases as we move towards the axis/center of symmetry with an increase in γ. Also, it is observed that J0 increases on increasing the value of G0 or σ, while it decreases on increasing the value of Kp, γ or α.