Application And Research Of NCCR Model In Supersonic Rarefied Gas Flow

The model equation is the basis of numerical simulation,and the accuracy of the fluid model is directly related to the numerical simulation results.A rarefied effect occurs when the aircraft is flying in hypersonic speed or in rarefied gas at high altitude.Thus,the linear constitutive equation of the NS equation based on the continuity assumption is no longer applicable,which leads to the limitation.Therefore,under the rarefied effect,the model equations need to make corresponding improvements.In this paper,the velocity distribution function of the nonequilibrium state is proposed.By using the moment equation method,the generalized hydrodynamic equations with nonlinear coupled constitutive relations(NCCR)are established gradually from microscopic to macroscopic.Then,a more reasonable approximation and simplification of the equation is made to make it more applicable to computational fluid dynamics,and the model equations are applied to the numerical simulation in one and two dimensions.Since the NCCR model is also derived from the core Boltzmann equation of hydrodynamics,it is theoretically applicable to the numerical simulation in each regime.Taking the convection-diffusion equation as an example,the stress-strain relationship of the new nonlinear coupled constitutive equation is studied,and its unique characteristics are summarized.The finite volume method and the AUSMPW + scheme are used to compose the program.The single-atom gas in one dimension is numerically simulated by the Maxwell molecular model,and the detailed study is carried out.The variation law of shock wave structure under different Mach number is given,and the superiority of nonlinear constitutive relation to linear constitutive relation of NS equation is analyzed.The numerical simulation of the flow around a cylinder under two-dimensional single-atom argon conditions is carried out,and the characteristics of shear stress are analyzed.Owing to nonlinear terms in NCCR model,an iterative method is developed to solve two-dimensional problem.The flow contour under different Knudsen numbers is given,and the results are compared with the NS equations.The results of the comparison show that the results of the NCCR model are more consistent with the calculation data of the DSMC and physical process.