多模态瑞利-泰勒不稳定性的离散玻尔兹曼数值研究  

Numerical study of multimode Rayleigh-Taylor instability by using the discrete Boltzmann method

作　　者：陈璐[1,2,3] 赖惠林[1,2,3] 林传栋 李德梅[1,2,3] CHEN Lu;LAI Huilin;LIN Chuandong;LI Demei(College of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Fujian Key Laboratory of Analytical Mathematics and Application,Fujian Normal University,Fuzhou 350117,China;Center for Applied Mathematics of Fujian Province,Fujian Normal University,Fuzhou 350117,China;Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-sen University,Zhuhai 519082,China)

机构地区：[1]福建师范大学数学与统计学院,福州350117 [2]福建师范大学福建省分析数学及应用重点实验室,福州350117 [3]福建师范大学福建省应用数学研究中心,福州350117 [4]中山大学中法核工程与技术学院,珠海519082

出　　处：《空气动力学学报》2022年第3期140-150,I0003,共12页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(51806116,11875001);福建省自然科学基金(2021J01652,2021J01655)。

摘　　要：瑞利-泰勒(Rayleigh-Taylor,RT)不稳定性广泛存在于自然界和工程领域,认清RT不稳定性演化过程中的物理机理具有重要的理论意义和实用价值。本文利用离散玻尔兹曼方法模拟了可压缩流体的RT不稳定性现象,并利用该方法对界面连续的随机多模初始扰动的可压缩RT不稳定性进行了数值研究。研究结果表明,在温度梯度的影响下,与热通量相关的热力学非平衡强度呈现先增大后减小的趋势;在热扩散作用下,界面上的热力学非平衡强度先减小后增大,继而影响热力学非平衡区域的占比,使之呈现相同的变化趋势。最后,分析了全局平均热力学非平衡强度随时间的演化规律,发现在宏观物理量梯度和热力学非平衡面积的共同作用下,全局平均热力学非平衡强度先增后减,最后趋于稳定。不仅如此,热力学非平衡区域面积的增大(减小)会增强(减弱)热力学非平衡的强度;同时,物质界面物理量梯度的增大(减小)对全局平均热力学非平衡强度也有相同的影响,二者相互作用、相互竞争。Rayleigh-Taylor(RT) instability phenomenon exists widely in nature and engineering fields.It is of great theoretical significance and practical value to clearly understand the physical mechanism of the RT instability.In this paper,the compressible RT instability is simulated by the discrete Boltzmann method(DBM),and the compressible RT instability with random multimode initial perturbations at continuous interfaces is numerically investigated by means of the DBM.The results show that with the influence of temperature gradient,the thermodynamic non-equilibrium strength related to heat flux firstly increases and then decreases.Under the action of thermal diffusion,the thermodynamic non-equilibrium strength at the interface firstly decreases and then increases,which affects the time evolution of proportion of the thermodynamic non-equilibrium region.In this respect,effects of temperature gradient and thermal diffusion on the time evolution trend of non-equilibrium strength at the interface are the same.Finally,we analyze the time evolution of the global average thermodynamic non-equilibrium strength,and find that under the joint action of macroscopic physical gradients and thermodynamic non-equilibrium area,the global average thermodynamic non-equilibrium strength firstly increases,then decreases,and finally tends to be stable.On the one hand,the increase(decrease) of the area of thermodynamic non-equilibrium region will increase(decrease) the strength of thermodynamic non-equilibrium.On the other hand,the increase(decrease) of physical gradients at the material interface also has the same effect on the global average thermodynamic non-equilibrium strength.The two physical mechanisms interact and compete with each other.

关 键 词：瑞利-泰勒不稳定性 离散玻尔兹曼方法 统计物理 粗粒化建模 非平衡效应 动理学建模 

分 类 号：O359[理学—流体力学]