Numerical time-step restrictions as a result of capillary waves

Denner, Fabian; Wachem, Berend G. M. van

doi:10.1016/j.jcp.2015.01.021

Cited by 91 publications

(78 citation statements)

References 48 publications

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“…In a previous study on the dynamics of solitary waves on inertia-dominated falling liquid film of Denner et al [37], the results obtained with the DNS framework [47][48][49] used in this study showed excellent agreement with experimental measurements [6]. We propose a novel scaling for solitary waves, which we derive from the Nusselt flat film solution based on the physical mechanisms that underpin the growth and dispersion of solitary waves.…”

Section: Introductionsupporting

confidence: 75%

“…We note that the transverse dimension is resolved with only one mesh cell, so that the simulation can be regarded as being effectively two-dimensional. The numerical time-step applied in the simulations satisfies a Courant number of Co = ∆t u |u|/∆x ≤ 0.25, as well as the capillary time-step constraint proposed by Denner and van Wachem [49].…”

Section: Setup Of the Numerical Experimentsmentioning

confidence: 99%

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Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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We propose the first consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re = 20 − 120 and surface tension coefficients σ = 0.0512 − 0.072 N m −1 on substrates with inclination angles β = 19 • − 90 • . Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e. height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by non-linear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

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Section: Introductionsupporting

confidence: 75%

Section: Setup Of the Numerical Experimentsmentioning

confidence: 99%

Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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“…The computational domain is represented by an equidistant Cartesian mesh with a resolution of 10 cells per film height h N . The time step t satisfies a Courant number of Co = |u| t/ x 0.25 as well as the capillary time-step constraint derived by Denner & van Wachem (2015). The properties of the liquid film are directly taken from the experimental measurements (see § 3.4) and the gas phase is assumed to be air with density ρ g = 1.205 kg m −3 and viscosity µ g = 1.82 × 10 −5 Pa s. At the bottom (liquid-side) wall a no-slip condition is enforced and at the top (gasside) boundary a free-slip wall is applied.…”

Section: Simulation Set-upmentioning

confidence: 99%

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

et al. 2018

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We offer new insights and results on the hydrodynamics of solitary waves on inertiadominated 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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“…Here the full Navier-Stokes equations are solved with appropriate 95 boundary conditions applied at the deforming interface between layers and at the free surface. Alternatively the Volume of Fluid (VOF) method, popular in multiphase CFD, may be used to obtain the film surface by solving a convection equation for an indicator function as recently examined in numerical experiments of vertically-falling films [31].…”

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confidence: 99%

“…The single nonlinear function C, representing the the integrated continuity equation with parabolic forms for the velocity and temperature, depends on h and all other the coeffi-240 cients in (30) and (31).…”

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A multi-layer integral model for locally-heated thin film flow

Kay¹,

Hibberd

Power

2017

Journal of Computational Physics

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Based on an approach used to model environmental flows such as rivers and estuaries, we develop a new multi-layered model for thin liquid film flow on a locally-heated inclined plane. The film is segmented into layers of equal thickness with the velocity and temperature of each governed by a momentum and energy equation integrated across each layer individually. Matching conditions applied between the layers ensure the continuity of down-plane velocity, temperature, stress and heat flux. Variation in surface tension of the liquid with temperature is considered so that local heating induces a surface shear stress which leads to variation in the film height profile (the Marangoni effect). Moderate inertia and heat convection effects are also included.In the absence of Marangoni effects, when the film height is uniform, we test the accuracy of the model by comparing it against a solution of the full heat equation using finite differences. The multi-layer model offers significant improvements over that of a single layer. Notably, with a sufficient number of layers, the solution does not exhibit local regions of negative temperature often predicted using a single-layer model.With Marangoni effects included the film height varies however we find heat convection can mitigate this variation by reducing the surface temperature gradient and hence the surface shear stress. Numerical results corresponding to the flow of water on a vertical plane show that very thin films are dominated by the Marangoni shear stress which can be sufficiently strong to overcome gravity leading to a recirculation in the velocity field. This effect reduces with increasing film thickness and the recirculation eventually disappears. In this case heating is confined entirely to the interior of the film leading to a uniform height profile.

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Numerical time-step restrictions as a result of capillary waves

Abstract: 22.04.15 Kb. Ok to add published version to spiral, OA pape

Cited by 91 publications

References 48 publications

Self-similarity of solitary waves on inertia-dominated falling liquid films

Self-similarity of solitary waves on inertia-dominated falling liquid films

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

A multi-layer integral model for locally-heated thin film flow

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