A computational framework for conservative, three-dimensional, unsplit, geometric transport with application to the volume-of-fluid (VOF) method

Owkes, Mark

doi:10.1016/j.jcp.2014.04.022

Cited by 117 publications

(121 citation statements)

References 21 publications

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“…Nevertheless, these schemes are more complex to implement in three dimensions, and for arbitrary meshes. Indeed, general three-dimensional unsplit geometric advection schemes possessing the boundedness and conservativeness properties have only been derived recently [85][86][87]. In this work, we use the CCU advection scheme [64], which is also bounded and conservative, but limited to two-dimensional problems.…”

Section: Geometric Advection Schemementioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

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Section: Geometric Advection Schemementioning

confidence: 99%

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Comminal

Pimenta

Hattel

et al. 2018

Journal of Non-Newtonian Fluid Mechanics

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“…In computational fluid dynamics (CFD) studies, multiphase flow has often been studied by either the Volume of Fluid (VOF) [12] or level set [13] methods to capture or track the interface. When these methods are applied on complex geometries or small-scale problems, significant mass conservation problems arise near the interface and more complicated algorithms have been required [14,15].…”

Section:    mentioning

confidence: 99%

Contact Angle Effects on Pore and Corner Arc Menisci in Polygonal Capillary Tubes Studied with the Pseudopotential Multiphase Lattice Boltzmann Model

et al. 2016

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Abstract:In porous media, pore geometry and wettability are determinant factors for capillary flow in drainage or imbibition. Pores are often considered as cylindrical tubes in analytical or computational studies. Such simplification prevents the capture of phenomena occurring in pore corners. Considering the corners of pores is crucial to realistically study capillary flow and to accurately estimate liquid distribution, degree of saturation and dynamic liquid behavior in pores and in porous media. In this study, capillary flow in polygonal tubes is studied with the Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM). The LB model is first validated through a contact angle test and a capillary intrusion test. Then capillary rise in square and triangular tubes is simulated and the pore meniscus height is investigated as a function of contact angle θ. Also, the occurrence of fluid in the tube corners, referred to as corner arc menisci, is studied in terms of curvature versus degree of saturation. In polygonal capillary tubes, the number of sides leads to a critical contact angle θ c which is known as a key parameter for the existence of the two configurations. LBM succeeds in simulating the formation of a pore meniscus at θ > θ c or the occurrence of corner arc menisci at θ < θ c . The curvature of corner arc menisci is known to decrease with increasing saturation and decreasing contact angle as described by the Mayer and Stoewe-Princen (MS-P) theory. We obtain simulation results that are in good qualitative and quantitative agreement with the analytical solutions in terms of height of pore meniscus versus contact angle and curvature of corner arc menisci versus saturation degree. LBM is a suitable and promising tool for a better understanding of the complicated phenomena of multiphase flow in porous media.

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“…= 1, where indicates the fraction of volume and is subscript noticing phase number, is the time, indicates the gravity force, and is the density of individual phase, which should be associated with the volume fraction equation [28],…”

Section: =1mentioning

confidence: 99%

Numerical Analysis on Flow Behavior of Molten Iron and Slag in Main Trough of Blast Furnace during Tapping Process

Wang

Pan

Cheng

2017

Advances in Numerical Analysis

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The three-dimensional model was developed according to number 4 of the main trough of blast furnace at China Steel Co. (CSC BF4). The -equations and volume of fluid (VOF) were used for describing the turbulent flow at the impinging zone of trough, indicating fluids of liquid iron, molten slag, and air in the governing equation, respectively, in this paper. The pressure field and velocity profile were then obtained by the finite volume method (FVM) and the pressure implicit with splitting of operators (PISO), respectively, followed by calculating the wall shear stress through Newton's law of viscosity for validation. Then, the operation conditions and the main trough geometry were numerically examined for the separation efficiency of iron from slag stream. As shown in the results, the molten iron losses associated with the slag can be reduced by increasing the height difference between the slag and iron ports, reducing the tapping rate, and increasing the height of the opening under the skimmer.

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A computational framework for conservative, three-dimensional, unsplit, geometric transport with application to the volume-of-fluid (VOF) method

Cited by 117 publications

References 21 publications

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods

Contact Angle Effects on Pore and Corner Arc Menisci in Polygonal Capillary Tubes Studied with the Pseudopotential Multiphase Lattice Boltzmann Model

Numerical Analysis on Flow Behavior of Molten Iron and Slag in Main Trough of Blast Furnace during Tapping Process

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