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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。
Based on the research on relaxation characteristics of rotational freedom, the rotational inertia of gas molecules is used to describe the spin motion of gas molecules, and the Boltzmann model equation of each basin with rotational unbalance effect is established by using the conservation of total angular momentum as a new collision invariant. Based on the conservation of rotational energy space, the governing equations of molecular velocity distribution function are derived. The governing equations of molecular velocity distribution function are obtained by considering the rotational unbalance effect. The velocity and spatial dependence of velocity distribution function equation is discretely reduced and reduced by using the gas molecular motion discrete velocity coordinate method. A uniform format of gas kinetic theory for directly solving molecular velocity distribution function is constructed. Based on the relationship between the flux conservation and the energy balance of object-surface mass flux, a mathematic model and numerical method for the boundary conditions of gas molecular kinematics that affect the non-equilibrium of rotation are developed. Therefore, a unified Boltzmann model equation algorithm is proposed to simulate the non-equilibrium effect of high-molecular-weight molecules flowed into the continuous stream. The nitrogen shock wave structure with different Knudsen numbers of 9 × 10-4≤Kn! ≤10 re-entry vertical plate, Ramp brake, sharp biconvex shape The simulation study of the hypersonic flow around the river basin is carried out. Comparing the calculated results with the related experimental data, the generalized degenerated Boltzmann and ES ellipsoid statistical models, the unified algorithm of Boltzmann model with rotational unbalance effect is verified to solve the problem of free molecular flow to continuous Flow around the river basin flow problem reliability.