基于气液相界面捕捉的统一气体动理学格式  

UNIFIED GAS-KINETIC SCHEME FOR TWO PHASE INTERFACE CAPTURING

作　　者：王昭 严红[1,2,3] Wang Zhao;Yan Hong(School of Power and Energy,Northwestern P olytechnical University,Xi＇ an 710072,China;Shaanxi Key Laboratory of Internal Aerodynamics in Aero-Engine,Northwestern Polytechnical University,Xi＇ an 710072,China;Collaborative Innovation Center for Advaneed Aero-Engine,Beijing 100191,Chin)

机构地区：[1]西北工业大学动力与能源学院,西安710072 [2]西北工业大学陕西省航空发动机内流动力学重点实验室,西安710072 [3]先进航空发动机协同创新中心,北京100191

出　　处：《力学学报》2018年第4期711-721,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国防基础科研科学挑战计划资助项目(TZ2016001)

摘　　要：气液相界面运动的研究无论是在科学还是工程领域都是非常重要的.其中,非平衡流动的计算尤其受到关注.基于此,我们构造了捕捉气液相界面的统一气体动理学格式.由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数,故而可以求解非平衡流动.具体思路是,通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面,两相的分离与共存通过范德瓦尔斯状态方程描述.由于流体在椭圆区域是不稳定的,因此气液相界面可以通过蒸发和凝结过程自动捕捉.如此,一个锋锐的相界面便可以通过数值耗散和相变而得到.利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解,并与其相应的理论解相比较,二者符合良好.而后,通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算,验证了Laplace定理.此外,通过模拟两个液滴的碰撞融合过程,进一步证明了该格式的有效性.但是,由于范德瓦尔斯状态方程的特性,其所构造的格式仅适用于液/气两相密度比小于5的情况.The study of interfacial motion of gas-liquid phase is very important in science and engineering. Considering the non-equilibrium flow calculation, a unified gas-kinetic scheme for gas-liquid two phase interface capturing is presented in this paper. Since the free transport and particle collision are coupled to update the macroscopic variables and microscopic distribution functions, the unified gas-kinetic scheme can solve the non-equilibrium flow. The van der Waals（vd W） equation of state（EOS） is included to describe the coexistence of gas and liquid and the phase transition between them. Because of the characteristics of vd W EOS, the interface between gas and liquid can be captured naturally through condensation and evaporation processes. As a result, the new scheme can solve the gas-liquid two phase problems. Finally, the proposed method is used to obtain the numerical solution of Maxwell construction, which agrees well with the corresponding theoretical solution. Then, the Laplace＇s theorem is verified by numerical calculation of the surface tension of the droplet corresponding to the van der Waals state equation. In addition, the collision of the two droplets is simulated,which proves the validity of the scheme further. However, due to the characteristics of the van der Waals equation of state, the constructed scheme is only applicable to the case where the liquid/gas two-phase density ratio is less than 5.

关 键 词：统一气体动理学格式 范德瓦尔斯状态方程 相界面捕捉 麦克斯韦等面积律 液滴表面张力 

分 类 号：O359[理学—流体力学]