Oscillatory Thermal Convection of Liquid Metal and its Three-Dimensional Structure.

本文对低普朗特数（Pr）流体（如液态金属）的自然对流进行了三维时变数值模拟。对长径比（Ar）为2和4，宽比（Wr）为0.5至4.2的具有不同加热侧壁和绝热壁的矩形外壳进行了计算。结果如下：1。在(Ar, Wr)=(2,1),（2,2）和（4,1）的情况下，发生振荡的临界Grashof数（Gr^c）在很大程度上取决于Pr.2。流动结构以胞状和纵向涡（卷）为特征。随着Wr的增大，Gr_c除在Wr的短范围内外均呈减小趋势。Gr_c在这里发生了突然的变化。这是由于细胞模式的转变，或由于卷排列的变化。当Pr=0和0.015时，Gr_c处的对流结构一般为单细胞结构。然而，在Pr=0.025的情况下，当Ar=2时，在Wr【小于或等于】1的范围内，或者当Ar=4时，在Wr【小于或等于】1.4的范围内，可以观察到振荡的双胞模式。在Wr.5的其他范围内，流动结构为单细胞。振荡对流对换热速率有显著影响。当Ar=4时，振荡对平均努塞尔数的影响约为10%。在Arz2、4和Wr=0.5-4的条件下，用镓进行了实验，结果如下：出现可重复的振荡。由温度振荡确定的临界格拉什夫数与数值值具有质的一致性。在两种纵横比下，Gr_c都随着Wr的增大而减小。Gr_c.3中存在一些滞回。振荡的周期从大约10秒到1分钟不等。周期在一个特定的Wr附近有一个跳跃。当Ar=4时，实验数据与仿真结果吻合较好。

Three-dimensional, time-dependent numerical simulation has been performed on natural convection of low Prandtl number (Pr) fluids such as liquid metals. Calculations are carried out for rectangular enclosures with differentially heated sidewalls and adiabatic walls of aspect ratios (Ar) 2 and 4, and width ratios (Wr) ranging 0.5 to 4.2. The results are as follows.1. In cases (Ar, Wr)=(2, 1), (2, 2) and (4, 1), the critical Grashof number (Gr^c) at which the onset of oscillation occurs largely depends on Pr.2. The flow structure is characterized by cellular pattern and longitudinal vortices (rolls). As Wr is increased, Gr_c decreases except in a short range of Wr. An abrupt change in Gr_c occurs there. This is attributed to transition in the cellular pattern, or to variation in the arrangement of rolls.3. In cases Pr=0 and 0.015, the convective structures at Gr_c are unicellular in general.4. In the case Pr=0.025, however, oscillatory two-cell patterns are observed in the range Wr【less than or equal】1 for Ar=2, or Wr【less than or equal】1.4 for Ar=4. The flow structures are unicellular for other range of Wr.5. The oscillatory convection has significant effect on heat transfer rate. For Ar=4, oscillations make an about 10 percent difference among the average Nusselt numbers.The experiments conducted using Gallium for Arz2, 4, and Wr=0.5-4 show following results.1. Reproducible oscillations occur. The critical Grashof numbers determined from temperature oscillations show qualitative agreement with numerical ones.2. In both aspect ratios, Gr_c decrease as Wr is increased. Some hystereses exist among Gr_c.3. The period of oscillation varies from about 10 seconds to one minute. The period shows a jump around a particular Wr. For Ar=4, experimental data are in good agreement with simulation results.