转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架，采用转动惯量描述气体分子自旋运动，确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分，得到计及转动非平衡效应气体分子速度分布函数方程组，使用离散速度坐标法对分布函数方程所依赖速度空间离散降维；应用拓展计算流体力学有限差分方法，构造直接求解分子速度分布函数的气体动理论数值格式；基于物面质量流量通量守恒与能量平衡关系，发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法，提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1:5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究，将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析，验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度. 

GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

Based on the gas-kinetic unified algorithm (GKUA) for flows from rarefied transition to continuum, the effect of rotational non-equilibrium is investigated involving the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant, then the unified Boltzmann model equation involving rotational non-equilibrium effect is presented for various flow regimes. The molecular velocity distribution function is integrated by the weight factor on the energy of rotational motion, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The discrete velocity ordinate technique and numerical quadrature methods are applied to discretize the velocity space, and the gas-kinetic finite-difference numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in rotational non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of the Boltzmann kinetic model equation involving rotational non-equilibrium effect is presented for the whole range of flow regimes. As the applications of the GKUA, the hypersonic flows of diatomic gas involving rotational non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-25, the two-dimensional planar Ramp flow with the whole range of Knudsen numbers of 9×10-4-10 and the three-dimensional re-entering hypersonic flows around sphere, tine double-cone and spacecraft body. The computed results match the relevant experimental data, DSMC results, and the solutions of the generalized Boltzmann equation (GBE) and ellipsoidal statistical (ES) model equation well. It is tested and validated from this study that the GKUA solving the Boltzmann model equation in rotational nonequilibrium can simulate the complex hypersonic flow problems and flow mechanisms from high rarefied free-molecule flow to continuum flow regimes with good reliability and precision.