Calculation Method And Verification Of Nonlinear Coupled Constitutive Equations

The near space includes watersheds such as near continuous flow,slip flow,and partial transitional flow.It is a necessary area for hypersonic vehicles to enter orbit and return.The particularity of the space environment determines that the impact of the thin atmosphere on the aerodynamics / heat of the aircraft must be considered when the hypersonic aircraft passes through.At the same time,considering that numerical simulation has been widely used in aerodynamic / thermal prediction,and the mesh quality is one of the keys to determine the success or failure of numerical calculations,so in order to accurately predict the aerodynamic / heat on the surface of hypersonic aircraft under the thinning effect,this paper is A series of studies have been performed on the nonlinear coupled constitutive equations?NCCR?.First,based on the local gradient Knudsen number,this paper proposes a set of grid scale parameter criteria applicable to the two macro equations of NS and NCCR,and analyzes the influence of different factors on the applicability and consistency of the grid criteria,and validates the grid.The engineering applicability of the criterion is based on the grid convergence judgment criteria for determining the upper limit of the normal grid scale of the wall based on the Kn_GLL.Under different incoming temperature conditions,the Kn_GLL is compared with the traditional grid Reynolds number criterion based on the incoming parameters,and the superiority of the Kn_GLL over the grid Reynolds number is analyzed.In the windward area of the calculated shape,the applicability of the NCCR equation to the grid criterion and the grid convergence criterion return to the NS equation,which is closely related to the degradation of the NCCR equation to the NS equation in near continuous flow.In calculating the leeward area of the shape,the dispersion of different sparse grids in predicting the leeward area flow is studied,and it is pointed out that the main reason for the difference between the dispersion of the ns and NCCR in the leeward area is that the two sets of models deal with unbalanced multiscale problems Different applicable theoretical scales lead to different requirements for the normal first-level grid scale of the leeward thin area,and it is concluded that there is a lower limit for the wall normal grid scale.In addition,by comparing the dispersion of the results from the leeward region of the NCCR equation with the NS equation,it is concluded that the lower theoretical limit of the applicable NCCR equation is smaller than the NS equation and has better grid adaptability than the NS equation.Finally,based on the grid convergence criterion,this paper compares the calculation examples of flat plates,return capsules,and Type IV and V shock waves and shock waves with the literature or DSMC calculation results,and verifies that the NCCR equation is very good for different calculation shapes and the universality of the grid convergence criterion.