利用瑞利数理论研究贝纳德对流的产生条件  

USING RAYLEIGH NUMBER THEORY TO STUDY THE CONDITIONS OF BÉNARD CONVECTION

作　　者：钱庆余 方爱平 范富豪 段玉文 吴一粟 蒋臣威 冯俊 张修兴[2] 王小力[1] QIAN Qingyu;FANG Aiping;FAN Fuhao;DUAN Yuwen;WU Yisu;JIANG Chenwei;FENG Jun;ZHANG Xiuxing;WANG Xiaoli(School of Physics,Xi'an Jiaotong University,Xi'an,Shaanxi 710049;School of Physics and Electrical Engineering,Weinan Normal University,Weinan,Shaanxi 714099)

机构地区：[1]西安交通大学物理学院,陕西西安710049 [2]渭南师范学院物理与电气工程学院,陕西渭南714099

出　　处：《物理与工程》2024年第4期156-168,共13页Physics and Engineering

基　　金：西安交通大学2023年基层教师教学发展组织建设项目(2302JF-01);2023年基层教学组织教学改革研究专项(基础课程);渭南师范学院教育科学研究项目(2020JYKX021)。

摘　　要：贝纳德对流是在从下方加热的流体的平面水平层中发生的一种自然对流现象。研究此现象对于深刻认识耗散结构的物理图像以及流体在混沌系统中的运动具有重要意义。为研究其产生的条件以及物理特性,本文建立流体模型,从基本控制方程组出发,导出在固定边界条件下物理量满足的特征方程,利用重要的无量纲数——瑞利数Ra来表征是否发生对流,并推导出从静态突变至稳定对流的临界值R_(c1)=1708。在理论结果的基础上,使用COMSOL Multiphysics进行了仿真模拟,所得结果符合理论预言,且通过导出运动动画进一步分析了液体的运动特性。为考察温度梯度较大时对流的第二次失稳,引入洛伦兹方程组理论求解,获得了第二个临界值R_(c2)=46177。据此得到贝纳德对流的产生条件为R_(c1)<R_(a)<R_(c2)。Bénard Convection is a natural convection phenomenon in the plane horizontal layer of fluid heated from below.The study of this phenomenon is of great significance to deeply understand the physical image of dissipative structure and the motion of fluid in chaotic system.In order to study the conditions and physical properties of its generation,this paper establishes a fluid model,derives the characteristic equations satisfied by physical quantities under fixed boundary conditions from the basic set of control equations,uses an important dimensionless number,the Rayleigh number Ra,to characterize whether convection occurs or not,and deduces a critical value of convection from the static mutation to the stable convection R_(c1)=1708.The theoretical value is obtained and simulated using COMSOL Multiphysicsto verify that it meets the theoretical prediction and the motion characteristics of the liquid are further analyzed by deriving motion animations.In order to investigate the second instability of convection when the temperature gradient is large,Lorentz equations theory is introduced,and the second critical value R_(c2) can be solved by substituting the parameter,and under the assumption of the present paper,R_(c2)=46177.Accordingly,the conditions for the generation of Benard convection are R_(c1)<R_(a)<R_(c2).

关 键 词：瑞利贝纳德对流 耗散结构 流体力学 

分 类 号：O35[理学—流体力学]