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arXiv · 1201.2005

Beyond the Knudsen number: assessing thermodynamic non-equilibrium in gas flows

Jianping Meng·Nishanth Dongari·Jason M. Reese·Yonghao Zhang
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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.

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Jianping Meng, Nishanth Dongari, Jason M. Reese, Yonghao Zhang. 2012-01-10. Beyond the Knudsen number: assessing thermodynamic non-equilibrium in gas flows. https://arxiv.org/abs/1201.2005

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