Estimating curvature from volume fractions

Cummins, Sharen J.; François, Marianne M.; Kothe, Douglas B.

doi:10.1016/j.compstruc.2004.08.017

Cited by 356 publications

(346 citation statements)

References 10 publications

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“…The estimated curvature from the HF curvature calculation resembles more practicality. The accuracy of the estimated curvature is comparable to results reported by Cummins, Francois, and Kothe (2005).…”

Section: Computational Proceduressupporting

confidence: 78%

Numerical analysis of post-impact droplet deformation for direct-print

Hasan

Chandy

Choi

2015

Engineering Applications of Computational Fluid Mechanics

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Two-dimensional (2D) numerical investigations of droplet impacts on a solid surface and the consequent deformation have been performed. The application lies in the direct-print technology where droplets are used to create lines and instantly cured to maintain line dimension. The investigation focuses on the evolution of droplet shape at the initial stage after the impact for Newtonian fluids. More specifically, the investigation emphasized the time for an impacted droplet to start increasing its diameter after the initial compression due to impact. A computational model has been developed by utilizing an adaptive quadtree spatial discretization with piecewise-linear geometrical volume-of-fluid (VOF) for this multiphase problem. The continuum-surface-force method and the height-function (HF) were employed for estimating the surface tension and the interface curvature, respectively. The Gerris Flow Solver, an open-source finite-volume package, was used for developing the computational model. The investigation was performed for the governing parameters of the Froude number (Fr), Reynolds number (Re), and Weber number (We). The results are presented as the interface contour, spreading factor (ξ ), and deformation ratio (R δ ). The investigation shows that the results from the developed model have excellent agreement with the experimental results.

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Section: Computational Proceduressupporting

confidence: 78%

Numerical analysis of post-impact droplet deformation for direct-print

Hasan

Chandy

Choi

2015

Engineering Applications of Computational Fluid Mechanics

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“…(22) is discretized on the same computational stencil as the pressure gradient [47]. In order to diminish aliasing errors in the evaluation of the interface normal vectorm = ∇γ/|∇γ| and the interface curvature κ = − ∇ ·m, the volume fraction γ is convoluted by means of a cosine convolution kernel with a support of ε = 3∆x, where ∆x is the mesh spacing [37,47,70]. Convolution to smooth the surface force is not needed [71,72] and numerical artifacts that manifest in parasitic or spurious flow features near or at the interface are addressed by an interfacial shear stress correction [37].…”

Section: Numerical Methodologymentioning

confidence: 99%

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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“…This enables an accurate computation of interface curvature, which converges with mesh refinement. 18,27,28 Thus, the VOF-HF method is one of the recent developments that has extended the applicability of the VOF method to surface tension dominant phenomena. Below, we briefly describe the implemented VOF-HF methodology in our numerical model.…”

Section: Numerical Algorithmmentioning

confidence: 99%

Numerical investigation of elongated drops in a microfluidic T-junction

2011

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We present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is assumed to be small. The numerical results successfully capture existing asymptotic solutions for the motion of drops in unconfined and confined flows; examples include the analytic Stokes flow solution for a two-dimensional inviscid bubble placed in an unbounded parabolic flow field and asymptotic formulas for slender bubbles and drops in confined flows. An extensive investigation of the accuracy of the computations is presented to probe the efficacy of the methodology and algorithms. Thereafter, numerical simulations are presented for droplet breakup in a symmetric microfluidic T-junction. The results are shown to support a proposed mechanism for breakup, driven by a pressure drop in a narrow gap between the droplet and the outer channel wall, which was formally derived in the limit Ca 1/5 Ӷ 1 ͓A. M. Leshansky and L. M. Pismen, "Breakup of drops in a microfluidic T junction," Phys. Fluids 21, 023303 ͑2009͔͒.

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Estimating curvature from volume fractions

Cited by 356 publications

References 10 publications

Numerical analysis of post-impact droplet deformation for direct-print

Numerical analysis of post-impact droplet deformation for direct-print

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

Numerical investigation of elongated drops in a microfluidic T-junction

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