二维湍流热对流最大速度Re数特性及流态突变特征Re数  

Scaling of Reynolds number based on maximum velocity and characteristic Reynolds number in two-dimensional thermal turbulence convection

作　　者：何建超 方明卫 包芸 He Jian-Chao;Fang Ming-Wei;Bao Yun(School of Aeronautics Science and Engineering,Beijing University of Aeronautics and Astronautics,Beijing 100191,China;School of Aeronautics and Astronautics,Sun Yat-Sen University,Shenzhen 518107,China)

机构地区：[1]北京航空航天大学,航空科学与工程学院,北京100191 [2]中山大学,航空航天学院,深圳518107

出　　处：《物理学报》2022年第19期213-219,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11772362)资助的课题。

摘　　要：本文计算系列二维湍流热对流,Prandtl(Pr)数和Rayleigh(Ra)数范围分别为0.25-100和1×10^(7)-1×10^(12),研究Reynolds(Re)数的变化规律.以最大速度计算的Re数与Ra数存在标度律关系,但中间出现间断.研究表明,大尺度环流形态由椭圆形到圆形的突变引起流动失稳,导致最大速度值间断下降,影响Re数变化趋势的连续性.所有Pr数对应的流态突变特征Re数为常值,Re_(c)约为1.4×10^(4),即当Re数达到特征Re_(c)时,大尺度环流形态会发生从椭圆形到圆形的突变.间断点对应的Ra_(c)与Pr数之间存在标度关系Ra_(c)-Pr^(1.5).对Ra数进行补偿平移,所有Pr数的Re与RaPr^(-1.5)的变化曲线重合,不同Pr数有相同的间断临界点位置,Ra_(c)Pr^(-1.5)=10^(9).Rayleigh number(Ra)dependence in Rayleigh-Bénard(RB)convection has been studied by many investigators,but the reported power-law scaling expressions are different in these researches.Previous studies have found that when Ra reaches a critical value,the flow patterns change and a transition appears in the scaling of Nu(Ra)(where Nu represents Nusselt number)and Re(Ra)(where Re denotes Reynold number).The Grossmann-Lohse(GL)model divides the Ra-Pr(where Pr refers to Prandtl number)phase into several regions to predict the scaling expressions of Nu(Ra,Pr)and Re(Ra,Pr),indicating that the thermal dissipation behavior and kinetic dissipation behaviors are diverse in the different regions.Moreover,some physical quantities also show a transition and some structures in the flow fields,such as large scale circulation and boundary layer,change when Ra increases.In this work,we conduct a series of numerical simulations in two-dimensional RB convection with Ra ranging from 10^(7) to 10^(12) and Pr ranging from 0.25 to 100,which is unprecedentedly wide.The relationship between the maximum velocity and Ra is investigated,and an unexpected drop happens when Ra reaches a critical value Ra_(c),and Ra_(c) increases with Pr increasing.The Re number,which is defined as a maximum velocity,also shows a plateau at Ra_(c).Before and after Rac,the Ra scaling exponent of Re remains 0.55,which gets smaller at very high Ra.Specially,under different Pr values,the plateau appears at Re_(c)≈1.4×10^(4).In addition,a scaling Ra_(c)~Pr^(1.5) is found and the Ra is compensated for by Pr^(-1.5) to disscuss the relationship between Re and RaPr^(-1.5).It is interesting that the Re(RaPr^(-1.5))expressons at different Pr values well coincide,indicating a self-similarity of Re(RaPr^(-1.5)).The plateau appears at RaPr^(-1.5)=1×10^(9),meaning that Re_(c) would reach 1.4×10^(4) at any Pr value when RaPr^(-1.5)=1×10^(9).To further investigate the plateau of Re,the flow patterns are compared with time-averaged velocity fields and we find that the larg

关 键 词：热对流 REYNOLDS数 流态 Prandtl数 

分 类 号：O357.5[理学—流体力学]