湍流Rayleigh-Bénard热对流温度剖面中对数律研究  

Logarithmic mean temperature profiles in turbulent Rayleigh-Bénard convection

作　　者：黄茂静 包芸[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275

出　　处：《中国科学：物理学、力学、天文学》2017年第6期68-73,共6页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:11372362,11452002);中央高校基本科研业务费专项资金(编号:14lgjc02);国家自然科学基金委员会-广东省人民政府联合基金(第二期)超级计算科学应用研究专项(编号:nsfc2015_570)资助

摘　　要：本文采用湍流热对流的并行直接数值模拟(Parallel Direct Method of Direct Numerical Simulation,PDM-DNS),计算了系列Ra数的二维方腔Rayleigh-Bénard热对流.选取典型Ra=10^(10),Pr=4.3,讨论了流动平均场的近底板区域温度分布.温度边界层沿横向可分为三个区域:羽流发射区、冲击区和大尺度环流剪切区.在羽流发射区温度剖面存在对数律,冲击区和大尺度环流剪切区没有明显的对数律特征.横向平均得到的温度剖面也存在对数律.研究系列Ra数的横向平均温度剖面,得到温度变化满足A×log(y)+B的关系,温度剖面对数律振幅–A和Ra数呈现标度关系–A^Ra^(–0.145),与实验中发现的关系基本一致.Results of two-dimensional turbulent Rayleigh-Bénard （RB） convection based on the parallel direct method of direct numerical simulation （PDM-DNS） in sample of aspect ratio Г=1 up to Rayleigh number Ra=10^12 are presented. Mean temperature field near the bottom of the sample for Ra=10^10 and Pr=4.3 is studied. The boundary layer of Rayleigh-Bénard convection can be divided horizontally into three regions, namely, ejecting region where thermal plumes are emitted, impacting region and large-scale circulation shearing region. The temperature profile is logarithmic in the ejecting region while the logarithmic behavior is not visible in the impacting region and the large-scale circulation sheafing region. In addition, the horizontally averaged profile also reveals a logarithm. The horizontally averaged temperature varies as A×log（y）＋B with the distance y from the bottom plate of the sample. The log amplitude -A scales as Ra-0.145, in good agreement with the experiment.

关 键 词：Rayleigh—Bμnard热对流 湍流 温度剖面对数律 PDM.DNS 

分 类 号：O357.5[理学—流体力学]