Supersonic flow kinetics: Mesoscale structures, thermodynamic nonequilibrium effects and entropy production mechanisms

TL;DR

This paper develops a Burnett-level discrete Boltzmann model to simulate supersonic flows, revealing detailed nonequilibrium effects, entropy production mechanisms, and the influence of Mach number, advancing the understanding of complex flow phenomena.

Contribution

It introduces a higher-order DBM for supersonic flow based on the Shakhov-BGK model, providing analytical expressions for nonequilibrium effects and criteria for model validity.

Findings

Burnett-level DBM improves accuracy over NS-level models.

Strong nonequilibrium effects occur near shock interfaces.

Mach number influences nonequilibrium intensities in a power-law manner.

Abstract

Supersonic flow is a typical nonlinear, nonequilibrium, multiscale, and complex phenomenon. This paper applies discrete Boltzmann method/model (DBM) to simulate and analyze these characteristics. A Burnett-level DBM for supersonic flow is constructed based on the Shakhov-BGK model. Higher-order analytical expressions for thermodynamic nonequilibrium effects are derived, providing a constitutive basis for improving traditional macroscopic hydrodynamics modeling. Criteria for evaluating the validity of DBM are established by comparing numerical and analytical solutions of nonequilibrium measures. The multiscale DBM is used to investigate discrete/nonequilibrium characteristics and entropy production mechanisms in shock regular reflection. The findings include: (a) Compared to NS-level DBM, the Burnett-level DBM offers more accurate representations of viscous stress and heat flux, ensures non-negativity of entropy production in accordance with the second law of thermodynamics, and exhibits better numerical stability. (b) Near the interfaces of incident and reflected shock waves, strong nonequilibrium driving forces lead to prominent nonequilibrium effects. By monitoring the timing and location of peak nonequilibrium quantities, the evolution characteristics of incident and reflected shock waves can be accurately and dynamically tracked. (c) In the intermediate state, the bent reflected shock and incident shock interface are wider and exhibit lower nonequilibrium intensities compared to their final state. (d) The Mach number enhances various kinds of nonequilibrium intensities in a power-law manner $D_{mn} \sim \mathtt{Ma}^\alpha $. The power exponent $\alpha$ and kinetic modes of nonequilibrium effects $m$ follows a logarithmic relation $\alpha \sim \ln (m - m_0)$. This research provides new perspectives and kinetic insights into supersonic flow studies.