Shock jump relations for a dusty gas atmosphere

TL;DR

This paper derives generalized shock jump relations for a dusty gas mixture, accounting for solid particles, and provides numerical results for various concentrations and conditions, extending classical shock relations.

Contribution

It introduces generalized shock jump relations for dusty gases, reducing to classical relations when solid particles are absent, and includes detailed numerical analysis.

Findings

Derived shock relations for dusty gases with solid particles.

Numerical results for different particle concentrations and Mach numbers.

Presented tables and graphs illustrating shock behavior in dusty gases.

Abstract

This paper presents generalized forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particle are continuously distributed. The generalized jump relations reduce to the Rankine-Hugoniot conditions for shocks in an idea gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. The jump relations for pressure, density, temperature, particle velocity, and change-in-entropy across the shock front are derived in terms of upstream Mach number. Finally, the useful forms of the shock jump relations for weak and strong shocks, respectively, are obtained in terms of the initial volume fraction of the solid particles. The computations have been performed for various values of mass concentration of the solid particles and for the ratio of density of solid particles to the constant initial density of gas. Tables and graphs of numerical results are presented and discussed.