NCCR方程在近平衡气体流动区域的验证

Validation of Nonlinear Coupled Constitutive Relations in Near-equilibrium Gas Flows

不同于Grad矩方法(R13方程)和Chapman-Enskog展开(Burnett方程),Eu方法考虑H定理和熵增,由Boltzmann方程导出了气体动力学守恒方程的高阶量本构方程,暨NCCR方程,其在二维高Kn数稀薄气体领域得到了验证。首先呈现了NCCR与Grad矩方法和Burnett方程的区别,而后展示了由Boltzmann方程到守恒方程和NCCR本构方程暨建立联系稀薄统一算法的过程。解决NCCR方程强非线性难题,扩展了间断伽辽金求解NCCR和守恒方程的数值方法,耦合了Langmuir边界条件,并在近平衡区域对典型圆柱绕流、三维高超构型流场进行了数值计算和验证。验证结果表明,在近平衡区域NCCR准确捕捉到了流场信息,包括滞止线参数分布等;同时,NCCR模型在高超构型的后体区域,相比于NS方程更吻合于实验结果。研究为NCCR方程在三维领域的完善和在高Kn数稀薄流动区域的进一步验证提供了基础。

Different from Grad moment method（R-13 equations） and Chapman-Enskog method（Burnett equation）,the Nonlinear Coupled Constitutive Relations（NCCR） of high order terms including viscous stress and heat flux were derived from Boltzmann equation in B.C.Eu method by considering the H theorem and entropy generation.And it was validated in the two dimensional rarefied gas flow.Firstly,the difference between Grad moment method,Burnett equation and NCCR were presented.Conservations laws and transport equations of non-conservation variables were derived from Boltzmann equation and then a unified scheme of continuum-rarefied gas flows,named by nonlinear coupled constitutive relations（NCCR）,was proposed.For solving the conservation laws with NCCR model,a modal mixed discontinuous Galerkin（DG） method with Langmuir slip condition,was developed based on unstructured grids.To validate the present DG-NCCR method,hypersonic rarefied gas flow over a cylinder and 3D hypersonic configuration,were considered by NCCR.It is observed that,compared with DSMC results,DG-NCCR could capture shockwave which is better than NSF.Investigations also showed that the DG-NCCR results were close with DSMC data than the NSF results in velocity at stagnation line.Furthermore,NCCR results were found to be in good agreement with experiment in pressure distribution of the gas flow in the afterbody of 3D hypersonic configuration.The present study provided a foundation for the improvement of NCCR and its validation in 3D high Kn number gas flows.