Beyond the Knudsen number: assessing thermodynamic non-equilibrium in gas flows
Abstract
For more than 150 years the Navier-Stokes equations for thermodynamically quasi-equilibrium flows have been the cornerstone of modern computational fluid dynamics that underpins new fluid technologies. However, the applicable regime of the Navier-Stokes model in terms of the level of thermodynamic non-equilibrium in the local flowfield is not clear especially for hypersonic and low-speed micro/nano flows. Here, we re-visit the Navier-Stokes model in the framework of Boltzmann statistics, and propose a new and more appropriate way of assessing non-equilibrium in the local flowfield, and the corresponding appropriateness of the Navier-Stokes model. Our theoretical analysis and numerical simulations confirm our proposed method. Through molecular dynamics simulations we reveal that the commonly-used Knudsen number, or a parametric combination of Knudsen and Mach numbers, may not be sufficient to accurately assess the departure of flowfields from equilibrium, and the applicability of the Navier-Stokes model.
Keywords
Cite
@article{arxiv.1201.2005,
title = {Beyond the Knudsen number: assessing thermodynamic non-equilibrium in gas flows},
author = {Jianping Meng and Nishanth Dongari and Jason M. Reese and Yonghao Zhang},
journal= {arXiv preprint arXiv:1201.2005},
year = {2012}
}