Flow structure and heat transport in low Prandtl-number vertical convection

在Dresden小组（T. Vogt，实验研究）和Göttingen小组（O. Shishkina，理论研究）的共同努力下，我们的目标是在理解极低普朗特数大瑞利数下的垂直热对流方面取得重大进展。这种对流对于晶体生长过程、金属锭的凝固以及液态金属在聚光太阳能电站高温换热器或接收器中的应用具有重要意义，并且与行星核心和恒星内部的对流过程有关。在互补的实验和理论研究中，我们将相互验证液体镓铟锡（GaInSn， Pr约0.03）的德累斯顿测量和Göttingen直接数值模拟（DNS）中普朗特数Pr = 0.03的中间瑞利数Ra。对于较高的瑞利数（Ra至少为2乘以10^9），德累斯顿实验将以一定数量的测量线速度剖面的形式提供有关流场的信息，以及系统中全局热输运和动量输运与瑞利数Ra的标度关系的统计信息，分别表示为：由于需要在非常精细的计算网格上解析Kolmogorov微尺度，因此很难在DNS中获得非常大的Ra和极小的Pr的统计信息。另一方面，在与实验相似的参数范围内，Göttingen DNS将提供完整的速度和温度空间分布及相关流场特征信息。最后，在Göttingen中，将先前建立的层流垂直对流中平均热量和动量输运的边界层模型和标度模型推广到湍流情况。

With joint efforts of the Dresden group (T. Vogt, experimental studies) and the Göttingen group (O. Shishkina, theoretical studies) we are aimed to make a significant progressin understanding of vertical thermal convection in very-low-Prandtl number fluids at large Rayleigh numbers. This type of convection has a great significance for crystal growth processes, the solidification of metal ingots and the application of liquid metals in high-temperature heat exchangers or receivers of concentrated solar power stations and is relevant in convective processes in planetary cores and stellar interiors.Within the complementary experimental and theoretical study, we will mutually verify the Dresden measurements in liquid gallium-indium-tin (GaInSn, Pr ca. 0.03) and the Göttingen Direct Numerical Simulations (DNS) for Prandtl number Pr = 0.03 for intermediate Rayleigh numbers Ra. For higher Rayleigh numbers (Ra at least 2 times 10^9), the Dresden experiments will provide information about the flow fields in form of a certain number of measured linear velocity profiles and the statistical information about the scaling relations with the Rayleigh number Ra of the global heat transport and momentum transport in the system, which are represented, respectively, by the Nusselt number Nu and Reynolds number Re. To attain statistical information in the DNS for very large Ra at such extremely small Pr is difficult due to the necessity to resolve the Kolmogorov microscales on very fine computational meshes. On the other hand, the Göttingen DNS will provide complete information on the velocity and temperature spatial distributions and related flow field characteristics, for similar parameter range as in the experiment. Finally, in Göttingen, the earlier developed boundary-layer model and scaling model for the mean heat and momentum transport in laminar vertical convection will be extended to the turbulent case.