环形腔内密度极值流体Rayleigh-Bénard对流三维数值模拟

Three-dimensional numerical simulations of Rayleigh-Bénard convection of liquid with density maximum in annular containers

为了了解环形腔内流体密度倒置参数对导热态一次分岔临界条件及流动结构的影响,采用有限容积法对侧壁为导热边界条件时具有密度极值流体Rayleigh-Bénard对流进行了三维数值模拟。选用工质为冷水,其普朗特数为11.67。结果表明,随着半径比的增加,系统更加稳定,Rayleigh-Bénard对流发生的临界Ra逐渐增大,流动发生时周向对流涡卷数增加;随着密度倒置参数的增加,导热态一次失稳时的临界Ra显著增加,且大于常规流体中流动发生的临界Ra;在较大的密度倒置参数下,发现了Rayleigh-Bénard对流中的分层现象。

To understand the influence of the density inversion parameter of cold water in the annular containers on the onset of convection,a series of three-dimensional numerical simulations on the Rayleigh-Bénard convection is presented.Finite volume method is adopted and the thermal boundary condition is perfectly conducting in the present paper.The Prandtl number of cold water is Pr =11.57.The results show that the increase of the radius ratio enhances the stability of the system.Thus,thecritical Rayleigh number at the onset of convection is increased gradually.The convective rolls along the azimuthal direction are increased as well.With the increase of the density inversion parameter,the critical Rayleigh number at the onset of convection is dramatically increased.The critical Rayleigh number of cold water is larger than that of Boussinesq fluid due to the density inversion phenomenon.The stratified flow phenomenon is observed in cold water with a relatively larger density inversion parameter.