论文标题
使用半密度移动浸入边界方法对旋转的von karman流的直接数值模拟
Direct Numerical Simulations of the Swirling von Karman Flow Using a Semi-implicit Moving Immersed Boundary Method
论文作者
论文摘要
我们提出了一种新颖的移动浸入边界方法（IBM），并将其用于层状和湍流方案中的闭合式旋转von karman流的直接数值模拟（DNS）。 IBM通过利用时间集成方案来扩展直接构造方法，该方案将浸入的边界强迫嵌入半径迭代的迭代曲柄 - 尼科尔森方案中。总体方法是稳健，稳定的，并且在具有静态和移动边界的规范案例中产生了出色的结果。移动的IBM允许我们在（F. Ravelet，A。Chiffaudel和F. Daviaud，JFM 601，339（2008））上重现漩涡von Karman流量实验的几何和参数。在这些DNS中，流动是由装有弯曲惯性搅拌的两表旋转叶轮驱动的。我们通过提高反向旋转的裂缝的旋转速率来分析从层流到湍流的过渡，以达到四个雷诺数字90、360、2000和4000。在雷诺数字90和360的层状状态下，我们观察到与相似的360型静止的特征，尤其是在相似的情况下，我们的静止序列是众所周知的。观察雷诺数2000的过渡性湍流。在雷诺数字4000中实现了完全开发的湍流。从模拟计算出的非二维扭矩与实验数据相关的相关性。低雷诺数的对称性，随着雷诺数的增加而丢失，在完全发达的湍流状态下的平均流中恢复了，我们观察到两个关于中期平面的托里对称。我们注意到，即使在最高的雷诺（Reynolds）4000号，该设备中央区域的湍流波动仍然保持各向异性，这表明各向同性化需要更高的雷诺数数字。
We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank-Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Karman flow experiments in (F. Ravelet, A. Chiffaudel, and F. Daviaud, JFM 601, 339 (2008)) on a Cartesian grid. In these DNS, the flow is driven by two-counter rotating impellers fitted with curved inertial stirrers. We analyze the transition from laminar to turbulent flow by increasing the rotation rate of the counter-rotating impellers to attain the four Reynolds numbers 90, 360, 2000, and 4000. In the laminar regime at Reynolds number 90 and 360, we observe flow features similar to those reported in the experiments and in particular, the appearance of a symmetry-breaking instability at Reynolds number 360. We observe transitional turbulence at Reynolds number 2000. Fully developed turbulence is achieved at Reynolds number 4000. Non-dimensional torque computed from simulations matches correlations from experimental data. The low Reynolds number symmetries, lost with increasing Reynolds number, are recovered in the mean flow in the fully developed turbulent regime, where we observe two tori symmetrical about the mid-height plane. We note that turbulent fluctuations in the central region of the device remain anisotropic even at the highest Reynolds number 4000, suggesting that isotropization requires significantly higher Reynolds numbers.
