Extreme solitary waves on falling liquid films

AbstractDirect numerical simulation (DNS) of liquid film flow is used to compute fully developed solitary waves and to compare their characteristics with the predictions of low-dimensional models. Emphasis is placed on the regime of high inertia, where available models provide widely differing results. It is found that the parametric dependence of wave properties on inertia is highly non-trivial, and is satisfactorily approximated only by the four-equation model of Ruyer-Quil & Manneville (Eur. Phys. J. B, vol. 15, 2000, pp. 357–369). Detailed comparison of the asymptotic shapes of upstream and downstream tails is performed, and inherent limitations of all long-wave models are revealed. Local flow reversal in front of the main hump, which has been previously discussed in the literature, is shown to occur for an inertia range bounded from below and from above, and the boundaries are interpreted in terms of the capillary origin of the phenomenon. Computational results are reported for the entire range of Froude numbers, providing benchmark data for all wall inclinations.

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Robust low-dimensional modelling of falling liquid films subject to variable wall heating

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.580 ◽

2019 ◽

Vol 877 ◽

pp. 844-881 ◽

Cited By ~ 1

Author(s):

Alice B. Thompson ◽

Susana N. Gomes ◽

Fabian Denner ◽

Michael C. Dallaston ◽

Serafim Kalliadasis

Keyword(s):

Temperature Field ◽

Surface Temperature ◽

Surface Displacement ◽

Liquid Films ◽

Quantitative Agreement ◽

Navier Stokes ◽

Variable Wall ◽

Wave Models ◽

Low Dimensional ◽

Falling Liquid Films

Accurate low-dimensional models for the dynamics of falling liquid films subject to localized or time-varying heating are essential for applications that involve patterning or control. However, existing modelling methodologies either fail to respect fundamental thermodynamic properties or else do not accurately capture the effects of advection and diffusion on the temperature profile. We argue that the best-performing long-wave models are those that give the surface temperature implicitly as the solution of an evolution equation in which the wall temperature alone (and none of its derivatives) appears as a source term. We show that, for both flat and non-uniform films, such a model can be rationally derived by expanding the temperature field about its free-surface values. We test this model in linear and nonlinear regimes, and show that its predictions are in remarkable quantitative agreement with full Navier–Stokes calculations regarding the surface temperature, the internal temperature field and the surface displacement that would result from temperature-induced Marangoni stresses.

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Numerical Simulations of Hydrodynamics and Heat Transfer in Wavy Falling Liquid Films on Vertical and Inclined Walls

Journal of Heat Transfer ◽

10.1115/1.4024550 ◽

2013 ◽

Vol 135 (10) ◽

Cited By ~ 7

Author(s):

Hongyi Yu ◽

Tatiana Gambaryan-Roisman ◽

Peter Stephan

Keyword(s):

Heat Transfer ◽

Solitary Waves ◽

Flow Instability ◽

Liquid Films ◽

Capillary Waves ◽

Wave Dynamics ◽

Disturbance Frequency ◽

Wide Range ◽

Falling Liquid Films ◽

Low Amplitude

The flow of thin falling liquid films is unstable to long-wave disturbances. The flow instability leads to development of waves at the liquid–gas interface. The effect of the waves on heat and mass transfer in falling liquid films is a subject of ongoing scientific discussion. In this work, numerical investigation of the wave dynamics has been performed using a modified volume-of-fluid (VOF) method for tracking the free surface. The surface tension is described using the continuum surface force (CSF) model. With low disturbance frequency, solitary waves of large amplitude are developed, which are preceded by low-amplitude capillary waves. With high disturbance frequency, low amplitude sinusoidal waves are developed. The waveforms dependent on the Reynolds number and disturbance frequency are summarized in a form of a regime map. A correlation describing the separation curve between the sinusoidal waves regime and solitary waves regime is proposed. The wave parameters (peak height, length, and propagation speed) are computed from the simulation results and compared with available experimental correlations in a wide range of parameters. The effects of the disturbance frequency and the plane inclination angle on the wave dynamics have been studied. The interaction of waves initiated by simultaneous disturbances of two different frequencies has been investigated. The heat transfer in the wavy film has been simulated for the constant wall temperature boundary condition. The effects of Prandtl number and disturbance frequency on local and global heat transfer parameters have been investigated. It has been shown that the influence of waves on heat transfer is significant for large Prandtl numbers in a specific range of disturbance frequencies.

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Solitary waves on superconfined falling liquid films

Physical Review Fluids ◽

10.1103/physrevfluids.5.032001 ◽

2020 ◽

Vol 5 (3) ◽

Cited By ~ 2

Author(s):

Gianluca Lavalle ◽

Nicolas Grenier ◽

Sophie Mergui ◽

Georg F. Dietze

Keyword(s):

Solitary Waves ◽

Liquid Films ◽

Falling Liquid Films

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Solitary waves on falling liquid films in the inertia-dominated regime

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.867 ◽

2018 ◽

Vol 837 ◽

pp. 491-519 ◽

Cited By ~ 19

Author(s):

Fabian Denner ◽

Alexandros Charogiannis ◽

Marc Pradas ◽

Christos N. Markides ◽

Berend G. M. van Wachem ◽

...

Keyword(s):

Reynolds Number ◽

Solitary Waves ◽

Reynolds Numbers ◽

Liquid Films ◽

Flow Reversal ◽

Experimental Measurements ◽

Flow Recirculation ◽

High Reynolds Numbers ◽

High Reynolds ◽

Falling Liquid Films

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development.

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