Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity $\unicode[STIX]{x1D6FA}_{i}$ and the outer cylinder stationary. With $R_{i},R_{o}$ the inner and outer radii respectively, the radius ratio is $\unicode[STIX]{x1D702}=0.909$ . The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range $Re_{i}=10^{5}{-}10^{6}$ where $Re_{i}=\unicode[STIX]{x1D6FA}_{i}R_{i}d/\unicode[STIX]{x1D708}$ and $d=R_{o}-R_{i}$ is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number $Nu$ (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number $Ta$ and $\unicode[STIX]{x1D702}$ . These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of $Re_{i}/Ta$ , and where $Nu\sim Ta^{1/2}$ .

中文翻译：

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Taylor-Couette 流的大涡模拟和建模

介绍了不可压缩 Navier-Stokes 方程的壁分辨大涡模拟 (LES) 以及湍流 Taylor-Couette (TC) 流的经验建模。LES 在内圆柱以角速度 $\unicode[STIX]{x1D6FA}_{i}$ 旋转且外圆柱静止的情况下进行。$R_{i},R_{o}$ 分别为内半径和外半径，半径比为 $\unicode[STIX]{x1D702}=0.909$ 。亚网格尺度应力使用拉伸涡流亚网格尺度模型表示，而流动在靠近壁处解析。LES 在 $Re_{i}=10^{5}{-}10^{6}$ 范围内实现，其中 $Re_{i}=\unicode[STIX]{x1D6FA}_{i}R_{i}d /\unicode[STIX]{x1D708}$ 和 $d=R_{o}-R_{i}$ 是圆柱间隙。结果表明，LES 可以捕获流的显着特征，包括展向泰勒滚的定量行为、内圆柱平均速度剖面的对数变化以及由于泰勒滚的存在而导致的角动量重新分布。开发了一个简单的经验模型，用于固定外圆柱体和同向旋转圆柱体的湍流 TC 流。这包括由恒定角动量环隔开的近壁、日志状湍流壁层。模型结果包括努塞尔数 $Nu$（维持流动所需的扭矩）和作为泰勒数 $Ta$ 和 $\unicode[STIX]{x1D702}$ 函数的壁层厚度的测量值。将这些结果与测量、直接数值模拟和 LES 的结果进行比较。描述了粗糙壁湍流的模型扩展。这表明渐近，