倾斜水层对流的动力学特性  

Dynamics of convection in an inclined water layer

作　　者：宁利中[1] 宁碧波[2] 吴昊[1] 田伟利[3] Ning Lizhong;Ning Bibo;Wu Hao;Tian Weili(Faculty of Water Resources and Hydro-electric Engineering,Xi’an University of Technology,710048,Xi’an,China;College of Civil Engineering and Architecture,Jiaxing University,314001,Jiaxing,China;Department of Architecture,Shanghai University,200444,Shanghai,China)

机构地区：[1]西安理工大学水利水电学院,西安710048 [2]嘉兴学院建筑工程学院,嘉兴314001 [3]上海大学建筑系,上海200444

出　　处：《应用力学学报》2021年第4期1650-1656,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10872164);西北旱区生态水利国家重点实验室基金(2017ZZKT-2)。

摘　　要：为了研究普朗特数Pr=6.99的倾斜水层对流的动力学特性,本文对流体力学方程组进行了数值模拟。对流特性参数随着时间的变化规律表明,倾角θ=24°情况和θ=60°情况变化规律基本相同,θ=10°时对流到达稳定值的过渡过程既存在振动又过渡时间较长。根据对流斑图随着倾角和相对瑞利数r的变化,对流可以分为三个区域,即多圈型对流、过渡状态和单圈型对流。给出了多圈型对流向过渡状态转变的倾角随着相对瑞利数r变化的关系式;建议了过渡状态向单圈型对流转变的倾角随着相对瑞利数r变化的关系式。得出当r=6时,对于对流的过渡状态和单圈型对流,对流特性参数有统一的变化规律。由于对流的过渡状态具有单圈型对流的特性,也可统称为单圈型对流。本文还给出了不同对流斑图情况下对流特性参数的变化关系式。In order to study the dynamics of convection in an inclined water layerat the Prandtl number Pr=6.99,the equations of hydrodynamics are numerically simulated in this paper.According to the study of the variation of the convective characteristic parameters with time,it is found that the variation at the inclination angleθ=24°andθ=60°are basically the same,and the transition process of the convection to the stable value atθ=10°has a vibration and a longer transition time.Based on the variation of the convection pattern with the inclination angle and the reduced Rayleigh number r,convection can be divided into three regions,namely,convection with multi roll,transition state and convection with single roll.The relationship of the inclination angleθc1 varing with r in the transition from convection with multi rolls to convective transition state is given,and the empirical formula of the inclination angleθc2 varing with r in the transition from convective transition state to convection with single roll is suggested.For the convective transition state and the convection with single roll at r=6,the convective characteristic parameters have a unified law.Because the convective transition state has the characteristic of convection with single roll,it can also be called the convection with single roll.In this paper,the formula of convective characteristic parameters under different convection patterns is given.

关 键 词：倾斜水层 对流 动力学 临界倾角 

分 类 号：O357[理学—流体力学]