Prandtl数对Rayleigh-Bénard对流中羽流结构及大尺度环流影响的实验研究

Experimental studies of Prandtl-dependence of plume and large scale circulation in Rayleigh-Bénard convection

郝鹏

11749081

硕士

力学

黄仕迪

2019-05-28

2019-07-20

哈尔滨工业大学

深圳

热对流不仅广泛存在于自然界中，而且由于其优良的换热效果，在工业中也常常被应用于换热器和电子元件的冷却、晶体生长以及核反应堆设计等领域。Rayleigh-Bénard(RB) 对流系统是从众多自然现象和工业实际中抽象出来的热对流物理模型。其中，Prandtl(Pr) 数作为表征流体特性的系统控制参数，对RB 对流有着非常重要的影响。然而，在以往的工作中，这方面的实验研究还比较缺乏。 本文对Pr 数如何影响RB 对流中的羽流、大尺度环流以及它们的相关性质开展了实验研究。我们采用5 种不同粘度的二甲基硅油(Pr = 11.7、20.5、49.3、81.6、145.7) 作为工作流体，并在4 个尺寸不同、但几何比例一样（长高比Γx=1.0，宽高比Γy=0.3）的长方体对流槽中开展实验，从而保证在改变Pr 数的同时，Rayleigh(Ra)数的变化范围保持不变。本论文的内容主要包括以下两个部分。 在第一部分，我们使用标准的阴影流动显示技术，观测不同Pr 数下RB 对流中的羽流和大尺度环流结构，并利用光学流测速法对流场阴影图进行半定量分析。第一部分实验中的Ra 数变化范围为2.4 × 109 ≤ Ra ≤ 2.1 × 1010。我们发现，随着Pr 数增大，羽流变得更加细长，且更倾向于聚集在靠近系统侧壁的区域；相应的，进入对流中央区的羽流变少。这使得流场内的羽流富集区变得更加集中，而湍流体区间的区域则变宽。另一方面，大尺度环流在变得更相干的同时，流动却变得更慢。这些变化，可以归结为随着Pr 数增加，流体的粘性变大、热扩散变慢所致。 由于羽流和大尺度环流是RB 对流中的主要湍流结构，很大程度上决定了系统的动力学和输运特性。为此，我们在本论文的第二部分，对Pr 数如何影响RB 对流的湍流强度和热输运能力进行了研究。由于第二部分实验中需要更多数据点拟合曲线，故Ra 数范围为4.1×108 ≤ Ra ≤ 7.1×1010。我们主要测量了Reynolds(Re) 数、传热效率Nusselt(Nu) 数以及对流中央区和侧壁区的温度涨落(σ/ΔT) 随Pr 数和Ra 数的标度律关系，相应的结果分别为：Re ∼ Pr−0.81±0.07Ra0.57±0.01；中央区温度涨落(σ/ΔT) ∼ Pr−0.19±0.02Ra−0.280±0.003；侧壁区温度涨落(σ/ΔT) ∼ Pr0.10±0.03Ra−0.200±0.007；Nu ∼ Pr−0.026±0.004Ra0.295±0.001。这些结果定量证明了随着Pr 数增大，羽流更倾向于沿着系统侧壁运动而不是经过对流中央区，且大尺度环流的流动变慢。另一方面，尽管Re 数、Nu 数和前人在其他构型的对流系统获得的结果基本一致，但温度涨落却与现有文献报道和主流理论预测非常不同，表明对流槽的几何形状对系统的整体输运影响很小，却对局部特性影响很大，这需要在今后的理论模型中给予充分考虑。

Thermal convection is not only widely found in nature, but also often used in the fields of heat exchanger and electronic component cooling, crystal growth and nuclear reactor design because of its excellent heat transfer effeciency. The Rayleigh-Bénard (RB) convection system is a physical model abstracted from those natural phenomena and industrial applications. The Prandtl (Pr) number, a system control parameter that describes the characteristics of the working fluid, plays an important role in the RB convection. However, in the past work, experimental studies of the Pr number effects in this area remain rare.In this thesis, we conducted experimental studies on how the Pr number affects the plume, large-scale circulation, and their related properties in RB convection. We used fivedifferent kinds of dimethicone (Pr = 11.7, 20.5, 49.3, 81.6, 145.7) as the working fluid, and four kinds of convection cells whose dimensions are different, but the geometric ratios are the same (length to height ratio Γx=1.0，aspect ratio Γy=0.3) to ensure that the range of Rayleigh(Ra) number remains unchanged while the Pr number varies. The content of this thesis mainly consists of two parts. In the first part, we used standard shadowgraph technology to visualize the plume and large-scale circulation structure in RB convection under different Pr numbers, and then applied the optical flow method to analyze the flow field semi-quantitatively. The range of the Ra number in the first part of the experiment is 2.4 × 109 ≤ Ra ≤ 2.1 × 1010. We found that as Pr number increases, the plume becomes more slender and tends to gather along the sidewall. This makes the plume-dominant zone in the flow field becomes more concentrated, and the area of turbulent bulk flow region becomes wider. We further found that while the large-scale circulation becomes more coherent, its motions slow down as Pr number increases. These changes could be attributed to increase in both the viscosity of fluid and the thermal diffusion time.Since plume and large-scale circulation are the main turbulent structures that largely determine the dynamics and transport properties of the system, so in the second part of this thesis, we investigated how the Pr number influences the turbulence intensity and heat transport of RB convection. Because more data is needed to fit curves in the second part of the experiment, the range of the Ra number is 4.1 × 108 ≤ Ra ≤7.1 × 1010. We mainly measured the Reynolds(Re) number, heat transfer efficiency, i.e. the Nusselt (Nu) number, and temperature fluctuations (σ/ΔT) in the cell center and near the sidewall region with the scaling law of Pr number and Ra number, and the corresponding results are: Re ∼ Pr−0.81±0.07Ra0.57±0.01; the temperature fluctuations in the bulk (σ/ΔT) ∼ Pr−0.19±0.02Ra−0.280±0.003; the temperature fluctuations near the sidewall region (σ/ΔT) ∼ Pr0.10±0.03Ra−0.200±0.007; Nu ∼ Pr−0.026±0.004Ra0.295±0.001. These results quantitatively demonstrate that as the value of Pr increases, the plume tends to move along the sidewall of the system rather than through the central region of the cell, and the motion of the large-scale circulation becomes slower. On the other hand, although the scaling law of the Re number and the Nu number are basically the same with the previous results obtained by the convection system of other configurations, the temperature fluctuation is quite different from the existing literature and the mainstream theoretical prediction, indicating that the configurations of the convection cell have little influence on the global transport of the system, but have a great impact on local characteristics, which needs to be fully considered in future theoretical models.

Rayleigh-Bénard 对流 Prandtl 数 羽流 大尺度环流

Rayleigh-Bénard convection Prandtl number plume large-scale circulation

中文

联合培养

南方科技大学

郝鹏. Prandtl数对Rayleigh-Bénard对流中羽流结构及大尺度环流影响的实验研究[D]. 深圳. 哈尔滨工业大学,2019.