3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

Anjos, Gustavo Rabello dos; Mangiavacchi, Norberto; Borhani, Navid; Thome, John R.

doi:10.1080/01457632.2013.833407

Cited by 29 publications

(19 citation statements)

References 75 publications

(94 reference statements)

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“…Due to the shortcomings of purely Eulerian and purely Lagrangian formulations, the Arbitrary Lagrangian-Eulerian description allows these two frameworks to be combined in one single formulation so that the best aspect of each separately approach can be used in conjunction, that is, the computational mesh nodes may move with the continuum in normal Lagrangian fashion or to be held fixed in Eulerian manner. The ALE description has shown to be suitable to describe fluid flow problems (see, for instance [4]) and this work extends its capability to two-phase flows with phase change.…”

Section: Introductionmentioning

confidence: 79%

ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

Anjos

Mangiavacchi

Pontes

et al. 2015

Volume 3: Advanced Fabrication and Manufacturing; Emerging Technology Frontiers; Energy, Health and Water- Applications of Nano

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A numerical method is described to study two-phase flows for single and multiple bubbles with phase change. The fluid flow equations are based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a new two-phase method with an improved model for the liquid-gas interface in microchannels. A successful adaptive mesh update procedure is also described for effective management of the mesh at the two-phase interface to remove, add and repair surface elements, since the computational mesh nodes move according to the flow. The Lagrangian description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The methodology proposed for computing the curvature leads to accurate results with moderate programming effort and computational cost and it can also be applied to different configurations with an explicit description of the interface. Such a methodology can be employed to study accurately many problems such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modelling of biological systems and efficient cooling of electronics for computational purposes, being the latter the aim of this research. The obtained numerical results will be described, therefore proving the capability of the proposed new methodology.

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Section: Introductionmentioning

confidence: 79%

ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

Anjos

Mangiavacchi

Pontes

et al. 2015

Volume 3: Advanced Fabrication and Manufacturing; Emerging Technology Frontiers; Energy, Health and Water- Applications of Nano

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“…The new position

{\overset{x}{true}}_{i}

of a point i is calculated as follows

{\tilde{bold-italicx}}_{i} = \frac{1}{N} \sum_{j}^{N} {bold-italicx}_{j},

where the sum is conducted over the N neighbour points of i . This is a modification of the procedure first proposed in Anjos and was found to lead to an improved mesh quality.…”

Section: Handling Of the Computational Meshmentioning

confidence: 99%

“…The auxiliary density function

\overset{h}{true}

, which needs not be smooth, is specified directly by expressing the desired edge length in each region based on threshold functions. For low values of k , h is close to

\overset{h}{true}

, while for high values of k , Equation tends towards the Laplace equation, which tends to smooth out peaks . Equation is solved using linear finite elements on the same mesh used to solve the flow equations.…”

Section: Handling Of the Computational Meshmentioning

confidence: 99%

“…where the sum is conducted over the N neighbour points of i. This is a modification of the procedure first proposed in Anjos 28 and was found to lead to an improved mesh quality. After mesh motion and smoothing, mesh points are added and removed to keep the desired resolution in any region of the flow.…”

Section: Handling Of the Computational Meshmentioning

confidence: 99%

“…For low values of k, h is close toh, while for high values of k, Equation 15 tends towards the Laplace equation, which tends to smooth out peaks. 16,28 Equation 15 is solved using linear finite elements on the same mesh used to solve the flow equations. The prescription of an adequateh is case dependent.…”

Section: Adaptive Refinementmentioning

confidence: 99%

See 2 more Smart Citations

Interface‐fitted moving mesh method for axisymmetric two‐phase flow in microchannels

Gros

Anjos

Thome

2017

Numerical Methods in Fluids

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Summary A boundary‐fitted moving mesh scheme is presented for the simulation of two‐phase flow in two‐dimensional and axisymmetric geometries. The incompressible Navier‐Stokes equations are solved using the finite element method, and the mini element is used to satisfy the inf‐sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data.

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Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models

Balestra

Zhu

Gallaire

2018

Microfluid Nanofluid

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The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from 10 −4 to 1 and inner-to-outer viscosity ratios, λ , from 0, i.e. a bubble, to high viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers (Ca < 10 −3 ) agrees well with Bretherton's scaling for bubbles as long as λ < 1. For larger viscosity ratios, the film thickness increases monotonically, before saturating for λ > 10 3 to a value 2 2/3 times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous & Quéré [5] for bubbles, with a fitting coefficient which

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3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

Cited by 29 publications

References 75 publications

ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

ALE-FEM for Two-Phase Flows With Heat and Mass Transfer in Microchannels

Interface‐fitted moving mesh method for axisymmetric two‐phase flow in microchannels

Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models

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