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
钱庆余 1方爱平 1范富豪 1段玉文 1吴一粟 1蒋臣威 1冯俊 1张修兴 2王小力1
作者信息
- 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
- 折叠
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Rc1=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Rc2=46177.据此得到贝纳德对流的产生条件为Rc1<Ra<Rc2.
Abstract
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 sys-tem.In order to study the conditions and physical properties of its generation,this paper es-tablishes a fluid model,derives the characteristic equations satisfied by physical quantities un-der fixed boundary conditions from the basic set of control equations,uses an important di-mensionless 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 Rc1=1708.The theoretical value is obtained and simulated using COMSOL Multiphysics® to 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 Rc2 can be solved by substituting the parameter,and under the assumption of the present paper,Rc2=46177.Accordingly,the conditions for the generation of Benard convection are Rc1<Ra<Rc2.
关键词
瑞利-贝纳德对流/耗散结构/流体力学Key words
Rayleigh-Bénard convection/dissipative structure/hydrodynamics引用本文复制引用
基金项目
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)
出版年
2024
国家科技期刊平台
NSTL
万方数据