Rayleigh­Bénard 热对流中惯性小球的拉格朗日动力学及其影响

颗粒负载流广泛存在于自然界以及工程应用中，如沙尘暴、海洋浮标、催化剂 粒子的混合与输运等。其中，大尺寸惯性颗粒在湍流中的动力学及其对流动的影响，目前还有待研究。本文基于经典 Rayleigh­Bénard 对流系统，制备了一种能跟随流体运动的厘米尺度的惯性小球，通过 PIV 测量技术和光影显示技术，实验研究了大尺寸惯性小球在经典 Rayleigh­Béard 热对流系统中的拉格朗日动力学行为， 以及不同体积分数 𝜙 下惯性小球对流动和系统传热的影响。本文的主要结论如下。 在 𝑅𝑎 数 8.8 × 10⁸ ∼ 8.8 × 10⁹ 范围内，单个惯性小球的均方位移 (MSD) 在较长的时间里满足弹道扩散，并在到达由于空间受限所引起的平台区后表现出一定程度的振荡，相应的特征时间与系统中大尺度流动结构的周期一致。这种周期在其它物理量如自关联函数中亦有体现。拉格朗日速度、加速度的概率密度分布分别为高斯分布和拉伸的指数分布，与通过示踪粒子得到的结果一致。此外，我们还发现欧拉视角和拉格朗日视角刻画的速度场在空间分布和统计特性上基本一致， 但在强度大小上有一定差别。 改变惯性小球的体积分数，发现 𝜙 在 0 ∼ 10.4％范围内时，惯性小球的拉格朗日动力学基本不变。当 𝜙=17.2％、28％时，贯穿全场的 Rayleigh­-Bénard 系统大尺度结构消失，出现局部的流动结构，相应的 MSD 弹道扩散特征消失，速度的概 率密度函数也开始偏离高斯分布。让人意外的是，当惯性小球在跟随流体运动时， 系统传热效率几乎不受小球体积分数的影响；而当小球沉积在系统底部时，传热效率则与其堆积面积有关。 这些结果为颗粒负载流的相关研究，尤其是大尺寸惯性颗粒在湍流中的动力学及潜在应用 (如海洋浮标观测技术)，提供了一定的实验依据和启示。

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