Improved theory for shock waves using simplified van der Waals equation of state at high Mach numbers

Abstract

The primary goal of this research is to present an improved shock wave theory that takes into account the gaseous non-ideality for a monatomic gas system composed of hard-sphere molecules using simplified van der Waals equation of state at high Mach numbers. In non-ideal gas, dimensionless conservation equations and new Rankine–Hugoniot conditions are given. The SSTNM (similar simplified translational non-equilibrium model) and OBurnett constitutive equations with non-ideal parameters are extended. The differential equations of improved theory for shock waves are established and solved. The validity of constitutive relations in non-ideal gas situations is proved, and the results are verified by direct simulation Monte Carlo methods. By examining the orbital structure, internal structure of shock waves and structural parameters of density–temperature separation, it becomes apparent that the improved shock wave theory considering the gaseous non-ideality has a better predictive effect than treating it as an ideal gas. Further experimental verification using density results indicates that the higher the Mach number, the closer the results predicted by the two constitutive equations are to the experimental results in the prediction region they are good at. This article improves the prediction effect of the shock wave structure using the improved shock wave theory, and it also introduces novel perspectives and strategies for avoiding the use of high-order constitutive relations that are prone to numerical instability.