We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh-Benard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number ($Ra$) of $10^{8}$ and the Prandtl number ($Pr$) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number ($St$) less than $10^{-3}$, and they tend to cluster into bands for $10^{-3} \lesssim St \lesssim 10^{-2}$. At even larger $St$, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle's trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle's density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

中文翻译：

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湍流热对流中稀释微粒的传输和沉积

我们分析了湍流 Rayleigh-Benard 对流中稀释微粒的传输和沉积行为。对$10^{8}$的Rayleigh数($Ra$)和0.71的Prandtl数($Pr$)(对应于空气的工作流体)进行二维直接数值模拟。拉格朗日点粒子模型用于描述湍流中微粒的运动。我们的结果表明，当斯托克斯数 ($St$) 小于 $10^{-3}$ 时，悬浮颗粒均匀分布在湍流中，并且在 $10^{-3}\lesssim St\ 时，它们倾向于聚集成带少 10^{-2}$。在更大的 $St$ 下，微粒会在对流中迅速沉淀。我们还计算了粒子轨迹的均方位移 (MSD)。在很短的时间间隔内，MSD表现出弹道状态，在垂直和横向方向上是各向同性的；在较长的时间间隔内，MSD 反映了粒子的受限运动，并且在不同方向上是各向异性的。我们进一步获得了壁上颗粒沉积位置的相图，并根据颗粒的密度和直径确定了三种沉积状态。一个有趣的发现是分散的颗粒更喜欢沉积在热羽流出现的垂直壁上，这通过倾​​斜单元和改变大规模环流的旋转方向得到了证实。我们进一步获得了壁上颗粒沉积位置的相图，并根据颗粒的密度和直径确定了三种沉积状态。一个有趣的发现是分散的颗粒更喜欢沉积在热羽流产生的垂直壁上，这通过倾​​斜单元和改变大规模环流的旋转方向得到了证实。我们进一步获得了壁上颗粒沉积位置的相图，并根据颗粒的密度和直径确定了三种沉积状态。一个有趣的发现是分散的颗粒更喜欢沉积在热羽流出现的垂直壁上，这通过倾​​斜单元和改变大规模环流的旋转方向得到了证实。