具有水平流动的混合流体对流的扰动方程组  

Perturbation equations for binary fluid convection with horizontal flow

作　　者：宁利中[1] 张迪 宁碧波[2] 田伟利[3] NING Li-Zhong;ZHANG Di;NING Bi-Bo;TIAN Wei-Li(College of Water Resources and Hydro-electric Engineering,Xi'an University of Technology, Xi'an 710048, China;College of Civil Engineering and Architecture, Jiaxing University, Jiaxing 314001,Zhejiang, China;Department of Architecture, Shanghai University, Shanghai 200444, 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,浙江嘉兴314001 [3]上海大学建筑系,上海200444

出　　处：《黑龙江大学工程学报》2020年第1期7-14,共8页Journal of Engineering of Heilongjiang University

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

摘　　要：讨论了混合流体对流的流体力学方程组和扰动方程组。基于布辛涅斯克近似,给出了考虑Soret效应和Dufour效应的混合流体对流的基本方程组,对其进行了无因次化处理。给出了基本方程组的无对流运动的传导解。对于混合液体在忽略Dufour效应的情况下,引入扰动物理量,推导了具有水平流动的混合流体对流的扰动方程组。应用扰动方程组可以计算具有水平流动的混合流体对流的稳定性和对流特性。根据不同的简化条件,具有水平流动的混合流体对流的扰动方程组可以变成具有水平流动的单流体对流情况,混合流体对流情况,单流体对流情况,或者单流体水平流动情况的扰动方程组等。如果忽略扰动方程组中二阶以上的高阶项,方程组可简化成线性稳定分析的扰动方程组。Hydrodynamic equations and perturbation equations for binary fluid convection are discussed.Firstly,based on the Boussinessq approximation,the basic equations of binary fluid convection considering Soret effect and Dufour effect are given,and the basic equations are dimensionless treated.The conduction solutions of the basic equations without convection are given.Then,when the Dufour effect is neglected,the perturbation physical quantities are introduced to derive the perturbation equations for the binary fluid convection with horizontal flow.The perturbation equations can be used to calculate the convection stability and convection characteristics of binary fluid mixture with horizontal flow.According to different simplified conditions,the perturbation equations for the binary fluid convection with horizontal flow can be transformed into the perturbation equations for the single fluid convection with horizontal flow,the binary fluid convection,the single fluid convection,or the horizontal flow of single fluid.If the higher order terms above the second order in the perturbation equations are neglected,the equations can be simplified to perturbation equations for linear stability analysis.

关 键 词：流体力学方程组 扰动方程组 对流 水平流动 混合流体 单流体 

分 类 号：O357[理学—流体力学]