Theoretical And Numerical Investigations Of Nonlinear Coupled Constitutive Relation Model In Rarefied Gas Flows

This dissertation mainly focuses on the flow mechanism and phenomena behind the hypersonic flight in the near space,and meanwhile considers the study of micro flow which is similar to rarefied gas flow.Aiming at these typical flows related to continuum flow,slip flow and transitional flow as well as the existing local non-equilibrium effect,this paper brings out a first systematical investigation on Eu 's generalized hydrodynamic theory with its related problems,hoping to obtain some better outcome of being more stable than Burnett-type equations and Grad moment equations and more accurate than NSF equations,and thus explores a brand new way for modeling and computation in the field of gas kinetic theory.Surrounding the key issues of rarefied gas dynamics,four significant aspects are included in this paper:1.Mathematical property and behavior of Eu's generalized hydrodynamic equations and nonlinear coupled constitutive relations(NCCR).The first aspect is divided into three parts below.First of all,the "sub-shock" problem with a moderate Mach number is preliminarily discussed using moment equations.Based on generalized hydrodynamic equations,closure theory and adiabatic approximation are adopted to qualitatively analyze the coupling effect on the mathematical property of macroscopic equations.And then,a direction instruction is given to overcome the shock singularity issue.Secondly,linearization and stability analysis are carried out on generalized hydrodynamic equations and nonlinear coupled constitutive relations.Results show that linearized generalized hydrodynamic equations and linearized NCCR model recover the conventional hydrodynamic equations,namely NSF equations.They are both unconditionally stable under small wavelength perturbations and reflect asymptotic preserving property.Thirdly,Myong's simplification on the two terms of generalized hydrodynamic equation is validated in the one-dimensional shock wave structure.The tiny effect on the evolution equations of non-conserved variables and NCCR model implies the reasonability of the simplification treatment.2.Three-dimensional undecomposed algorithm for nonlinear coupled constitutive relations(NCCR).In order to extend NCCR model into three-dimensional computation of monatomic and diatomic rarefied gas flows,and meanwhile validate its capability in prediction the hypersonic non-equilibrium flow,the computation algorithm of NCCR model is investigated in detail firstly.Based on the fully understanding of the limitations of Myong's decomposition algorithm in 3D flow simulation,an undecomposed idea is proposed to solve NCCR model With some different convergence properties of monatomic/diatomic constitutive models discovered,the undecomposed idea adopts the steepest descent techniques for the calculation of monatomic NCCR model,and develops a hybrid algorithm by combining the fixed-point iterative formulations and Newton iterative formulations for solving the diatomic NCCR model.Then the qualitative and quantitative analysis on the stability,convergence,accuracy and difference is carried out for these algorithms.3.Numerical investigation of rarefied non-equilibrium flows using a nonlinear constitutive model.This investigation mainly includes three significant parts.Firstly,a 3D parallel numerical computational system of NCCR equations for calorically perfect gas is built up based on finite-volume framework as well as message passing interface technique,in which modern CFD techniques are adopted,including LU-SGS implicit time-marching scheme,MUSCL reconstruction and AUSMPW+flux splitting scheme.Secondly,some non-equilibrium flows,such as 1D shock wave structure,hypersonic flows over a 2D cylinder,3D blunted cone tip,hollow cylinder-flare,Apollo command module and HTV-type vehicle,are investigated carefully.Computational results by NSF,DSMC,UGKS and experimental data are used for comparison with NCCR prediction,such that the computational stability and accuracy of NCCR's numerical computational system is validated for continuum flow,slip flow and some transitional flow.Furthermore,some typical continuum-breakdown regions,such as shock inside region,wake expansion-separation region,sharp-leading edge and Knudson layer near to wall,are chosen for analysis of the physical mechanism behind the discrepancy between NSF and NCCR computational data.4.An enhanced wall-boundary condition for nonlinear coupled constitutive relations.The final aspect also includes three research contents.First of all,through the detailed comparison of Maxwell's scattering and Langmuir's surface adsorption models as well as various macroscopic slip boundary conditions induced from them,a nonlinear modified slip boundary condition is proposed to keep the same accuracy with NCCR model and to manifest nonlinear characteristics with Knudsen layer near the wall.And then,the numerical experiment is carried out to solve the boundary-driven micro-channel Couette flow by using NCCR model and the enhanced boundary condition,and thus validate the new-developed boundary condition's capability in predicting the Knudsen layer flow.Lastly,two more typical hypersonic flows around cylinder and flat plate are simulated with NCCR model and the enhanced boundary condition.In-depth analysis is carried out on the key issue of accurate prediction of aircraft surface aerodynamic and aerothermal properties under rarefaction non-equilibrium effect.The feasibility of this enhanced NCCR-based boundary condition is also validated through the comparison with DSMC data.