Abstract
A reduced two-phase model suitable for industrial uptake is introduced to predict the onset of flow reversal in falling films under countercurrent flow. Analysis of spatiotemporal stability and wave topology shows that vortex distribution plays a crucial role in the incipience of flow reversal.
Highlights
Thin films sheared by a countercurrent flow have wide industrial applications, such as in absorption and distillation processes
In the above-mentioned applications, the liquid film is often very thin compared to the wavelength of interfacial waves; this has encouraged the development of integral models in which the film dynamics is enslaved to thickness and flow rate only, with the main advantage of providing faster numerical simulations with respect to direct numerical simulation (DNS)
In presence of low density contrast and low surface tension, the temporal growth of linear and weakly nonlinear waves matches with the results of the Orr-Sommerfeld and the weakly nonlinear theory
Summary
Thin films sheared by a countercurrent flow have wide industrial applications, such as in absorption and distillation processes. LAVALLE, VILA, LUCQUIAUD, AND VALLURI the multiphase systems, the integral models have been first employed by Jurman and McCready [15] for liquid films sheared by a turbulent gas flow; later studies have extended the integral formulation to the second phase, providing an evolution equation for the interface between two superposed layers [16,17] These works follow those of Benney and Shkadov and experience the aforementioned shortcomings. Our methodology originates from the work of Lavalle et al [23], whose shallow water Arbitrary Lagrangian-Eulerian Navier-Stokes model (SWANS) consists of first-order depth-integrated equations applied to the lower layer and compressible Navier-Stokes equations for the upper layer As it is, the SWANS model is unsuitable for countercurrent flows, because the shear stress exerted by the upper phase is negative and might cause a blowup of the Rusanov numerical flux when the characteristic velocity is negative.
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