学术文献库

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 three-dimensional (3D) direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterised by the Reynolds, Froude, Weber and Ekman numbers. The variation of the Ekman number ($Ek$), defined to be proportional of the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of $Ek$ values ($0 \leq Ek \leq 484$) 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 stabilising 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 stabilisation, 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.