Numerical simulations of a falling film on the inner surface of a rotating cylinder

Abstract

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 ≤ Ek ≤ 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.