圆柱绕流的湍流统计

Statistics of Turbulence in Cylindrical Flow

摘要: 为了调查现有的湍流模型无法再现圆柱绕流湍流时的尾流处周期性摆动的问题，我们对三维不可压缩流体的圆柱绕流进行了直接数值仿真，并使用无惯性拉格朗日系粒子来观察湍流统计量的规律，此外我们还提取圆柱壁面的时序数据用以讨论扰动的扩散问题。数值实验的结果显示：1) 高雷诺数情况下湍流动能和湍流动能耗散率会随时间发生剧烈震荡，这个震荡可能是圆柱壁面附近的扰动引起的；2) 湍流粘性模型要求的雷诺应力方向和速度剪切方向一致或者完全无关，但这个条件无法在圆柱绕流问题中得到满足。这些发现对我们将来改进湍流模型以得到更贴近实际的仿真结果可能有所帮助。

Abstract: To investigate why the current turbulent models cannot represent shaking behaviors in the wake of turbulent cylindrical flow, the three-dimensional direct numerical simulations of incompressible cylindrical flow were performed. We used Lagrangian inertialess particles to collect the information of turbulent fields, and discussed the features of diffusion of disturbs near the cylindrical walls. It was found via the numerical experiments that: 1) Fluctuations of turbulent kinetic energy and dissipation rate of kinetic energy occurred in the cases of higher Reynolds numbers; this behavior may be caused by the disturbs from the walls. 2) It was expected that directions of Reynolds stress and macro-scale strain of fluid velocity are aligned or independent, but this precondition is not satisfied in cylindrical flow. These results may help us to improve the turbulent models in the future.