摘要
为模拟研究高温高马赫数下多原子气体内能激发对跨流域非平衡流动的影响,将转动能、振动能分别作为气体分子速度分布函数的自变量,把转动能和振动能处理为连续分布的能量模式,将Boltzmann方程的碰撞项分解成弹性碰撞项和非弹性碰撞项,同时将非弹性碰撞按一定松弛速率分解为平动-转动能松弛过程和平动-转动-振动能松弛过程,构造了一类考虑振动能激发的Boltzmann模型方程,并证明了其守恒性和H定理.基于内部能量变量对分布函数无穷积分,引入三个约化速度分布函数,得到一组考虑振动能激发的约化速度分布函数控制方程组,使用离散速度坐标法,基于LU-SGS隐式格式和有限体积法求解离散速度分布函数,建立含振动能激发的气体动理论统一算法.通过开展高稀薄流到连续流圆柱绕流问题统一算法与直接模拟蒙特卡罗法模拟结果对比分析,特别是过渡流区平动、转动、振动非平衡效应对绕流流场与物面力热特性的影响机制,证实了所建立的含振动能激发的Boltzmann模型方程及气体动理论统一算法的准确可靠性.
With the increase of temperature in flow field, gas molecules possess not only rotational degree of freedom, but also vibrational energy excitation. In order to simulate and study the influence of internal energy excitation on polyatomic gas flow with high temperature and high Mach number, according to the general Boltzmann equation, we consider the rotational and vibrational energy modes as the independent variables of gas molecular velocity distribution function. It is assumed that the rotational and vibrational energy modes are described by continuous distribution with degree of freedom and temperature. Based on the Borgnakke-Larsen collision model used in direct simulation Monte Carlo（DSMC） method,the collision term of Boltzmann equation with internal energy excitation is divided into elastic and inelastic collision terms. The inelastic collision is decomposed into translational-rotational energy relaxation and translational-rotationalvibrational energy relaxation according to a certain relaxation rate obtained from the reciprocalities of rotational and vibrational collisions numbers per one elastic collision. Then a kind of Boltzmann model equation considering the excitation of vibrational energy is constructed. For showing the consistency between the present model equation and Boltzmann equation, the conservation of summational invariants and the H-theorem of this model are proved. When solving the present model equation with numerical methods, because of the continuous energy modes, it is difficult to simulate this model equation directly. In this paper, three control equations are derived and solved by the LU-SGS（lower-upper symmetric Gauss-Seidel） method, and the cell-centered finite volume method with multi-block patched grid technique in physical space. As a result, these gas-kinetic unified algorithm（GKUA） with vibrational energy excitation has been developed. Results are presented for N_2 with different Knudsen numbers around cylinder from continuum to rarefied gas flow by using the prese
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2017年第20期176-192,共17页
Acta Physica Sinica
基金
国家重点基础研究发展计划(批准号:2014CB744100)
国家自然科学基金(批准号:11325212
91016027)资助的课题~~
