Jump relations across a shock in non-ideal gas flow

TL;DR

This paper derives generalized shock jump relations for non-ideal gases, extending classical Rankine-Hugoniot conditions, and explores their implications for real fluid flows with upstream Mach numbers less than one.

Contribution

It presents new generalized jump relations for non-ideal gases, incorporating the non-idealness parameter, applicable to weak and strong shocks, extending classical shock wave theory.

Findings

Shock relations reduce to classical forms for ideal gases when non-idealness is zero.

Shock waves can occur in flows with upstream Mach number less than one.

Derived relations are expressed in terms of upstream Mach number and non-idealness parameter.

Abstract

Generalized forms of jump relations are obtained for one dimensional shock waves propagating in a non-ideal gas which reduce to Rankine-Hugoniot conditions for shocks in idea gas when non-idealness parameter becomes zero. The equation of state for non-ideal gas is considered as given by Landau and Lifshitz. The jump relations for pressure, density, temperature, particle velocity, and change in entropy across the shock 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 non-idealness parameter. It is observed that the shock waves may arise in flow of real fluids where upstream Mach number is less than unity.