Modified level set equation and its numerical assessment

Sabelnikov, Vladimir; Ovsyannikov, Andrey; Gorokhovski, Mikhael

doi:10.1016/j.jcp.2014.08.018

Cited by 13 publications

(6 citation statements)

References 32 publications

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“…In short, the incompressible Navier-Stokes equations for the two fluids are combined into a one-fluid formulation that accounts for the interface conditions and are solved by a projection method [27], the deformable gas-liquid interface is captured by a modified level-set method [28,29], and surface tension is accounted for using the continuum surface force model [30]. These are described in the following.…”

Section: B Numerical Methodsmentioning

confidence: 99%

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Interaction between a large buoyant bubble and turbulence

Loisy

Naso

2017

Phys. Rev. Fluids

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International audienceThe free rise of isolated, deformable, finite-size bubbles in otherwise homogeneous isotropic turbulence is investigated by direct numerical simulation. The Navier-Stokes equations are solved in both phases subject to the pertinent velocity and stress conditions at the deformable gas-liquid interface. The bubble rise velocity is found to be drastically reduced by turbulence, as is widely known for microbubbles. The probability distribution functions of the horizontal bubble acceleration component are well fitted by a log-normal distribution. The distributions of the vertical components are negatively skewed, a property related to the fact that bubbles experience on average stronger decelerations than accelerations. An assessment of the correlations of bubble acceleration with properties of the surrounding flow is used to define estimates of the liquid velocity and vorticity entering in liquid acceleration and lift forces. Finally, fast rising bubbles are found to preferentially sample downflow regions of the flow, whereas those subjected to a higher turbulence level have an increased residence time in swirling regions, some features similar to those of small bubbles

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Section: B Numerical Methodsmentioning

confidence: 99%

“…Specific methods must therefore be used to solve this issue. To this aim, a source term is embedded in our code in the advection equation of the level-set function, as proposed by [29]…”

Section: B Numerical Methodsmentioning

confidence: 99%

Interaction between a large buoyant bubble and turbulence

Loisy

Naso

2017

Phys. Rev. Fluids

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“…ψ denotes the level-set function, positive in the continuous phase and negative in the disperse one. It is the solution of the following advection equation, in which the zeroth-order approximation of the additional source term proposed by Sabelnikov et al (2014) is embedded:…”

Section: Methodsmentioning

confidence: 99%

Buoyancy-driven bubbly flows: ordered and free rise at small and intermediate volume fraction

2017

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Various expressions have been proposed previously for the rise velocity of gas bubbles in homogeneous steady bubbly flows, generally a monotonically decreasing function of the bubble volume fraction. For suspensions of freely moving bubbles, some of these are of the form expected for ordered arrays of bubbles, and vice versa, as they do not reduce to the behaviour expected theoretically in the dilute limit. The microstructure of weakly inhomogeneous bubbly flows not being known generally, the effect of microstructure is an important consideration. We revisit this problem here for bubbly flows at small to moderate Reynolds number values for deformable bubbles, using direct numerical simulation and analysis. For ordered suspensions, the rise velocity is demonstrated not to be monotonically decreasing with volume fraction due to cooperative wake interactions. The fore-and-aft asymmetry of an isolated ellipsoidal bubble is reversed upon increasing the volume fraction, and the bubble aspect ratio approaches unity. Recent work on rising bubble pairs is used to explain most of these results; the present work therefore forms a platform of extending the former to suspensions of many bubbles. We adopt this new strategy also to support the existence of the oblique rise of ordered suspensions, the possibility of which is also demonstrated analytically. Finally, we demonstrate that most of the trends observed in ordered systems also appear in freely evolving suspensions. These similarities are supported by prior experimental measurements and attributed to the fact that free bubbles keep the same neighbours for extended periods of time.

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“…τ → ∞. In a recent paper, Sabelnikov et al [93] presented an alternative approach which appears promising, since it has a lower computational cost.…”

Section: The Level-set Methodsmentioning

confidence: 99%

A multiscale method for simulating fluid interfaces covered with large molecules such as asphaltenes

Ervik

Lysgaard

Herdes

et al. 2016

Journal of Computational Physics

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The interface between two liquids is fully described by the interfacial tension only for very pure liquids. In most cases the system also contains surfactant molecules which modify the interfacial tension according to their concentration at the interface. This has been widely studied over the years, and interesting phenomena arise, e.g. the Marangoni effect. An even more complicated situation arises for complex fluids like crude oil, where large molecules such as asphaltenes migrate to the interface and give rise to further phenomena not seen in surfactant-contaminated systems. An example of this is the "crumpling drop" experiments, where the interface of a drop being deflated becomes non-smooth at some point. In this paper we report on the development of a multiscale method for simulating such complex liquid-liquid systems. We consider simulations where water drops covered with asphaltenes are deflated, and reproduce the crumpling observed in experiments. The method on the nanoscale is based on using coarse-grained molecular dynamics simulations of the interface, with an accurate model for the asphaltene molecules. This enables the calculation of interfacial properties. These properties are then used in the macroscale simulation, which is performed with a two-phase incompressible flow solver using a novel hybrid level-set/ghost-fluid/immersed-boundary method for taking the complex interface behaviour into account. We validate both the nano-and macroscale methods. Results are presented from nano-and macroscale simulations which showcase some of the interesting behaviour caused by asphaltenes affecting the interface. The molecular simulations presented here are the first in the literature to obtain the correct interfacial orientation of asphaltenes. Results from the macroscale simulations present a new physical explanation of the crumpled drop phenomenon, while highlighting shortcomings in previous hypotheses.

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Modified level set equation and its numerical assessment

Cited by 13 publications

References 32 publications

Interaction between a large buoyant bubble and turbulence

Interaction between a large buoyant bubble and turbulence

Buoyancy-driven bubbly flows: ordered and free rise at small and intermediate volume fraction

A multiscale method for simulating fluid interfaces covered with large molecules such as asphaltenes

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