Abstract
The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this study, we first report the important and detailed issues in the use of the H theorem and positive entropy generation in the NCCM. Importantly, the unified nonlinear dissipation model and its relationships to the Rayleigh–Onsager function were demonstrated in the treatment of the collision term of the Boltzmann equation. In addition, we compare the Grad moment method, the Burnett equation, and the NCCM. Next, differences between the NCCM equations and the Navier–Stokes equations are explained in detail. For validation, numerical studies of rarefied and continuum gas flows were conducted. These studies include rarefied and/or continuum gas flows around a two-dimensional (2D) cavity, a 2D airfoil, a 2D cylinder, and a three-dimensional space shuttle. It was observed that the present results of the NCCM are in good agreement with those of the Direct Simulation Monte Carlo (DSMC) method in rarefied cases and are in good agreement with those of the Navier–Stokes equations in continuum cases. Finally, this study can be regarded as a theoretical basis of the NCCM for the development of a unified framework for solving continuum-rarefied gas flows.
Highlights
The numerical study of continuum-rarefied gas flows is of great interest because it can provide fundamental knowledge regarding flow physics and provide a theoretical tool to precisely predict the aerodynamic or aerothermodynamic performance of hypersonic vehicles and/orMicro-Electro-Mechanical Systems [1,2,3,4]
This study can be regarded as an extension of the previous study of the nonlinear coupled constitutive method (NCCM) and Eu method, in which we focus on the numerical scheme for solving NCCM equations and its validation in typical continuum-rarefied gas flows
The processes for the derivation of the NCCM equations from the Boltzmann equation were given in detail in the present study
Summary
Micro-Electro-Mechanical Systems [1,2,3,4]. For more than 150 years, the Navier–Stokes–Fourier (NSF). For the investigation of rarefied and/or micro-gas flows, much effort has been put into the development of computational models beyond the NSF framework. We reported and validated the nonlinear coupled constitutive method (NCCM) for the development of a unified scheme for modelling continuum-rarefied gas flows [4]. It can be regarded as another option to treat EU equations. Nonconserved variables associated with thermal nonequilibrium, such as the shear stress tensor and the heat flux vector, are described by the evolution equations These variables are quite different from those in the NSF equations in conjunction only with the linear constitutive relations of the gradients of velocity and temperature. This study can be regarded as an extension of the previous study of the NCCM and Eu method, in which we focus on the numerical scheme for solving NCCM equations and its validation in typical continuum-rarefied gas flows
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