Instabilities in heated falling films: A full-scale direct numerical simulation

[摘要] A thin liquid layer draining on a heated inclined plane is susceptible to long surface waves, and can either form waves and stay continuous or go through a rupture process leading to the formation of rivulets. It is of great engineering significance to understand how various instability mechanisms decide the final state of the flow. In this regard, a numerical procedure has been developed to solve the governing equations for the conservation of mass, momentum, and energy. Temporal discretization is done using a Chorin-type projection scheme and the spatial discretization is done using the finite-element method in an Arbitrary Lagrangian Eulerian frame of reference.The liquid layer is subjected to the thermocapillary instability when it is heated from below. When the layer is tilted, it drains downstream and can become unstable, even in the absence of heat transfer, due to surface-wave instability. When the layer is tilted and heated, both thermocapillary and the surface-wave instabilities coexist and dictate the dynamics of the flow in a competitive manner. The purpose of this study was to gain further insight into the underlying instability mechanisms.Through extensive numerical simulations, it is shown that in a horizontal layer, when the interfacial mode of thermocapillarity is dominant, the film always ruptures via fingering mechanism associated with the lubrication pressure. When the Pearson mode of the thermocapillarity is dominant, the film stays continuous. In a vertical layer, the surface-wave instability is dominant and the film never ruptures and always stays continuous in the parametric range where long-wave theory is valid. For intermediate angles of inclination, rupture occurs for a disturbance with small enough wavenumber. A series of phase diagrams depicting the boundaries between wavy but continuous film and ruptured film are presented, and the interplay among instability mechanisms involved is examined. Lastly, formation of rivulets due to three-dimensional instabilities is studied in horizontal and vertical layers. A mechanism for rivulet formation, based on the instability phenomena, is discussed.

[发布机构] Rice University

[效力级别] engineering