Boltzmann-Curtiss Description for Flows under Translational Nonequilibrium

TL;DR

This paper introduces a Boltzmann-Curtiss based continuum theory that incorporates rotational degrees of freedom, improving the modeling of nonequilibrium gas flows such as shock structures over traditional Navier-Stokes equations.

Contribution

It develops a new bulk viscosity model from the Boltzmann-Curtiss distribution and demonstrates its effectiveness in simulating shock profiles under nonequilibrium conditions.

Findings

Enhanced accuracy in density and stress predictions

Better shock thickness modeling than Navier-Stokes

Valid for a wider range of nonequilibrium flows

Abstract

Continuum-based theories, such as Navier-Stokes equations, have been considered inappropriate for flows under nonequilibrium conditions. In part, it is due to the lack of rotational degrees of freedom in the Maxwell-Boltzmann distribution. The Boltzmann-Curtiss formulation describes gases allowing both rotational and translational degrees of freedom and forms morphing continuum theory (MCT). The first order solution to Boltzmann-Curtiss equation yield a stress tensor that contains a coupling coefficient that is dependent on the particles number density, the temperature and the total relaxation time. A new bulk viscosity model derived from the Boltzmann-Curtiss distribution is employed for shock structure and temperature profile under translational and rotational nonequilibrium. Numerical simulations of argon and nitrogen shock profiles are performed in the Mach number range of 1.2 to 9. The current study, when comparing with experimental measurements and Direct Simulation Monte Carlo (DSMC) simulation, show a significant improvement in the density profile, normal stresses and shock thickness at nonequilibrium conditions than Navier-Stokes equations. The results indicate that equations derived from the Boltzmann-Curtiss distribution are valid for a wide range of nonequilibrium conditions than those from the Maxwell-Boltzmann distribution.