中文摘要：

通过对转动自由度松弛变化特性的研究,采用转动惯量描述气体分子自旋运动,利用分子总角动量守恒作为一个新的碰撞不变量,确立含转动非平衡效应各流域统一的Boltzmann模型方程。基于转动能量空间对分布函数进行守恒积分,得到计及转动非平衡效应的分子速度分布函数控制方程组,应用气体分子运动论离散速度坐标法对速度分布函数方程所依赖的速度空间离散降维,构造直接求解分子速度分布函数的气体动理论统一格式。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影响的气体分子运动论边界条件数学模型及数值处理方法。由此提出模拟高稀薄自由分子流到连续流各流域转动非平衡效应的Boltzmann模型方程统一算法。通过对高、低不同马赫数1.5≤Ms≤25考虑转动非平衡效应的氮气激波结构与不同Knudsen数9×10-4≤Kn!≤10再入竖直平板、Ramp制动器、尖双锥外形跨流域高超声速绕流问题模拟研究,将计算结果与有关实验数据、广义退化Boltzmann与ES椭球统计模型等研究结果对比分析,验证含转动非平衡效应Boltzmann模型方程统一算法求解自由分子流到连续流跨流域绕流问题可靠性。

英文摘要：

Based on the Gas-Kinetic Unified Algorithm（GKUA）for flows from rarefied transition to continuum,the effect of rotational non-equilibrium is investigated on the gas flow involving 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 treated 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,then the numerical algorithm of the Boltzmann kinetic model equation involving rotational nonequilibrium effect is developed.As the applications of the GKUA,the supersonic and 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 1.2≤Ms≤25,the two-dimensional erect plate and planar ramp flows with the whole of Knudsen numbers of 9×10-4≤Kn∞ ≤10and the threedimensional re-entering rarefied flow around a tine double-cone body.The computed results match the relevant experimental data,the results of the Generalized Boltzmann Equation（GBE）and Ellipsoidal Statistical（ES） model equation well.It has been validated that the unified algorithm in solving the Boltzmann model equation involving rotational non-equilibrium effect can simulate the one-,two-and three-dimensional gas flows covering various flow regimes well and truly.The non-equilibrium flow phenomena and mechanisms from high rarefied free-molecule to continuum covering the medium transition regimes are revealed and analyzed.