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.