A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and 3D direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterized by the Reynolds, Froude, Weber, and Ekman numbers. The variation of the Ekman number (Ek), defined to be proportional to the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of Ek values ($0\le \text{Ek}\le 484$) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing Ek, which leads to a rise in the magnitude of centrifugal forces, produces a stabilizing effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilization and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally and centrifugally driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

中文翻译：

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旋转圆柱体内表面降膜的数值模拟

研究了由于重力在垂直旋转的圆柱体的内表面上薄膜掉落的流动。这是使用二维（2D）和3D直接数值模拟执行的，并采用体积方法处理界面。该问题由雷诺数，弗洛德数，韦伯数和埃克曼数确定。依克曼数（Ek）的变化定义为与气缸的旋转速度成比例，对流量特性有很大的影响。模拟在广泛的Ek值范围内进行（$0\le \text{k}\le 484$），以便深入了解此参数如何影响流量。我们的结果表明，增加Ek会导致离心力的大小增加，从而产生稳定作用，从而抑制了波的形成。关键流动特征（例如从2D过渡到更复杂的3D波浪状态）会受到这种稳定性的显着影响，并进行了详细研究。此外，强加的旋转导致独特的流动特性，例如斜波的形成，这是由于分别在轴向和方位角上的重力和离心驱动运动的结合而产生的。