Xiao Hong, Tang Ke
School of Power and Energy, Northwestern Polytechnical University, Xi'an, 710072, China.
Department of Engineering, University of Cambridge, Cambridge, CB2 1PZ, UK.
Sci Rep. 2017 Oct 12;7(1):13108. doi: 10.1038/s41598-017-13274-7.
The momentum and heat transport in rarefied gas flows is known to deviate from the classical laws of Navier and Fourier in Navier-Stokes-Fourier (NSF) equations. A more sophisticated Nonlinear Coupled Constitutive Model (NCCM) has been derived from the Boltzmann equation to describe gaseous and thermal transport both in continuum and rarefied gas flows. We first develop a unified numerical framework for modeling continuum and rarefied flows based on the NCCM model both in two and three dimensions. Special treatment is given to the complex highly nonlinear transport equations for non-conserved variables that arise from the high degree of thermal nonequilibrium. For verification and validation, we apply the present scheme to a stiff problem of hypersonic gas flows around a 2D cylinder, a 3D sphere, and the Apollo configuration both in continuum and rarefied situations. The results show that the present unified framework yields solutions that are in better agreement with the benchmark and experimental data than are the NSF results in all studied cases of rarefied problems. Good agreement is observed between the present study and the NSF results for continuum cases. The results show that this study provides a unified framework for modeling continuum and rarefied gas flows.
稀薄气体流动中的动量和热传输已知会偏离纳维 - 斯托克斯 - 傅里叶（NSF）方程中的经典纳维和傅里叶定律。一种更复杂的非线性耦合本构模型（NCCM）已从玻尔兹曼方程推导得出，用于描述连续介质和稀薄气体流动中的气体和热传输。我们首先基于NCCM模型开发了一个统一的数值框架，用于对二维和三维的连续介质和稀薄流动进行建模。对于因高度热非平衡而产生的非守恒变量的复杂高度非线性传输方程，我们进行了特殊处理。为了进行验证和确认，我们将当前方案应用于二维圆柱、三维球体以及阿波罗构型周围的高超音速气体流动的刚性问题，涵盖连续介质和稀薄情况。结果表明，在所有研究的稀薄问题案例中，当前的统一框架所产生的解比NSF结果与基准和实验数据的吻合度更高。对于连续介质情况，本研究与NSF结果之间观察到良好的一致性。结果表明，本研究为连续介质和稀薄气体流动建模提供了一个统一的框架。
