稀薄气体流动非线性耦合本构关系研究进展

临近空间高超声速飞行器流场蕴含着复杂的非线性流动机理与丰富的热化学非平衡流动现象, 基于Newton摩擦定律和Fourier热传导定律的Navier-Stokes(N-S)方程不足以描述高超声速飞行器从连续流到稀薄流的多尺度非平衡现象。非线性耦合本构关系(nonlinear coupled constitutive relations, NCCR)作为一种全新的本构方程体系, 在严格满足热力学熵条件的基础上, 巧妙地构建了应力与热流的非线性表达形式。然而, NCCR方程的强非线性耦合特性是求解过程的一大难题。为了克服这一技术瓶颈, 提出了混合迭代算法, 为实现NCCR方程的高效稳定求解提供了坚实的理论基础。在该理论研究的基础上, 考虑到原始NCCR方程对热通量演化方程的简化处理, 降低了方程的计算精度, 提出了改进的NCCR+方程。该方程在强激波压缩区域和膨胀区域表现出比传统NCCR方程更高的计算精度与更强的非平衡流动模拟能力。同时, 为了解决临近空间高超声速空气动力学的多尺度与多物理效应耦合难题, 提出了NCCR与转动非平衡的耦合计算模型, 拓展了NCCR方程在双原子气体中的模拟能力。为了揭示稀薄气体效应与真实气体效应的耦合作用机理, 进一步建立了NCCR与热化学反应的耦合计算方法。大量研究结果表明, 考虑多物理效应的NCCR方程在低Kn下能够恢复到与N-S方程一致的解。随着Kn的增加, 流场的非平衡程度逐渐增强, 其结果与N-S方程差异显著, 而与DSMC方法计算结果和实验数据具有更好的一致性。 

Advance in Nonlinear Coupled Constitutive Relations for Rarefied Gas Flows

The flow field of near space hypersonic vehicles contains complex nonlinear flow mechanism and abundant thermo-chemical non-equilibrium flow phenomena. The Navier-Stokes(N-S) equations based on Newton's law of friction and Fourier's law of heat conduction are insufficient to describe the multi-scale non-equilibrium phenomena for flows from continuum to rarefied regimes, especially for the hypersonic flows. Nonlinear coupled constitutive relations (NCCR) serve as a new system of constitutive equations. On the basis of the thermodynamic entropy condition, the nonlinear expressions of stress tensor and heat flux are ingeniously constructed. However, the strong nonlinear coupling characteristic of NCCR model is a tough problem in the solution process. In order to overcome this tough issue, the hybrid iterative algorithm was proposed, which provides a solid theoretical basis for the efficient and stable solutions of NCCR model. On the basis of the theoretical study, an improved NCCR+ model was proposed because the simplification of heat flux evolution equation in ori-ginal NCCR model may reduce the simulation accuracy. Compared with the conventional NCCR model, the improved one has higher accuracy for the simulation of strong shock compression and expansion regions. At the same time, in order to solve the hypersonic problems with multi-scale and multi-physics coupling effects, NCCR model was coupled with rotational non-equilibrium model. This new model enhances the simulation ability of NCCR model in diatomic gas. In order to reveal the coupling mechanism between rarefied gas effect and real gas effect, NCCR model was extended by coupling with thermo-chemical reaction model. A large number of results show that NCCR model can recover solutions of N-S equations at low Kn. With the increase of Kn, the non-equilibrium degree of the flow field increases gradually, and the results are significantly different from N-S equations, and in better agreement with DSMC method and experimental data.