A hybrid VOF-IBM method for the simulation of freezing liquid films and freezing drops

Lyu, Sijia; Wang, Ke; Zhang, Zhentong; Pedrono, Annaig; Sun, Chao; Legendre, Dominique

doi:10.1016/j.jcp.2021.110160

Cited by 26 publications

(27 citation statements)

References 47 publications

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“…An extension of this method called CLSMOF was introduced in [44] with application to the freezing of supercooled droplets in [45]. Recently, a hybrid VOF-IBM (Immersed Boundary Method) method has been developed for the simulation of freezing films and drops [46].…”

Section: A Brief Review Of Existing Schemesmentioning

confidence: 99%

“…Its definition might depend on the specificity of the problem (geometry, boundary conditions). For the sake of simplicity, we will consider later on that the density of the liquid and the solid are the same (ρ L = ρ S = ρ): although it is not true in general (for the ice/water phase change, we have ρ S /ρ L ∼ 0.9 for instance), it is not a crucial ingredient for the numerics [46]. Considering a domain of size L 0 and defining thus a time scale τ = L 2 0 /D S ) using the thermal diffusion coefficient in the solid (D S = λ S /(ρ S C S )), we obtain the following set of dimensionless equation (defining also…”

Section: Physical Modelmentioning

confidence: 99%

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A hybrid level-set / embedded boundary method applied to solidification-melt problems

Limare¹,

Popinet²,

Josserand³

et al. 2022

Preprint

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In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible change of topology while retaining a high-order representation of the gradients on the interface and the capability of properly applying boundary conditions on the interface. This leads to a two-fluid conservative second-order numerical method. The ability of the method to correctly solve Stefan problems, onset dendrite growth with and without anisotropy is demonstrated through a variety of test cases. Finally, we take advantage of the two-fluid representation to model a Rayleigh-Bénard instability with a melting boundary.

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Section: A Brief Review Of Existing Schemesmentioning

confidence: 99%

Section: Physical Modelmentioning

confidence: 99%

A hybrid level-set / embedded boundary method applied to solidification-melt problems

Limare¹,

Popinet²,

Josserand³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…dx, is applied over Eq. (12), and Leibniz rule for differentiation of integrals is recalled in the form…”

Section: Model Reduction: Coupled Integral Equations Approachmentioning

confidence: 99%

“…In this sense, the mathematical modeling of the freezing mechanism is particularly useful for proper design and satisfactory performance of "icephobic" surface modifications for aeronautical sensors and components [1][2][3]. Freezing of supercooled droplets, either suspended (or flowing) in a gaseous environment or brought in contact with a cold substrate, has been studied before, and some of these previous works are here reviewed [4][5][6][7][8][9][10][11][12][13]. The freezing process of a supercooled droplet can be described in four distinct stages.…”

Section: Introductionmentioning

confidence: 99%

“…They also analyzed the nucleation temperature for droplets of different sizes, concluding that large-sized droplets had higher nucleation temperature than the smaller one and the temperatures for the salty water droplet were always lower than the fresh water ones. In [12], the integral balance method (IBM) was employed in combination with a VOF multiphase model for tracking the interface position, and employed in the simulation of both freezing liquid films and droplets. The employment of purely numerical approaches has allowed for the more computationally involved simulation of such moving boundary problems governed by an increased number of parameters, but has also confirmed the higher computational costs required for an error-controlled solution.…”

Section: Introductionmentioning

confidence: 99%

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An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream

et al. 2021

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This work deals with the mathematical modeling of the transient freezing process of a supercooled water droplet in a cold air stream. The aim is to develop a simple yet accurate lumped-differential model for the energy balance for a freely suspended water droplet undergoing solidification, that allows for cost effective computations of the temperatures and freezing front evolution along the whole process. The complete freezing process was described by four distinct stages, namely, supercooling, recalescence, solidification, and cooling. At each stage, the Coupled Integral Equations Approach (CIEA) is employed, which reduces the partial differential equation for the temperature distribution within the spherical droplet into coupled ordinary differential equations for dimensionless boundary temperatures and the moving interface position. The resulting lumped-differential model is expected to offer improved accuracy with respect to the classical lumped system analysis, since boundary conditions are accounted for in the averaging process through Hermite approximations for integrals. The results of the CIEA were verified using a recently advanced accurate hybrid numerical-analytical solution through the Generalized Integral Transform Technique (GITT), for the full partial differential formulation, and comparisons with numerical and experimental results from the literature. After verification and validation of the proposed model, a parametric analysis is implemented, for different conditions of airflow velocity and droplet radius, which lead to variations in the Biot numbers that allow to inspect for their influence on the accuracy of the improved lumped-differential formulation.

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Liquid encapsulation in a freezing sessile drop

Lyu,

Zhu,

Legendre

et al. 2023

Droplet

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During the solidification of a sessile drop, the effect of heat exchange from the gaseous environmental medium is generally ignored. However, by combining experimental observations, direct numerical simulations, and a theoretical model, we have demonstrated that the environmental medium, particularly one with high thermal conductivity such as a liquid, has nonnegligible heat exchange with both the drop and the substrate, leading to accelerated cooling of the outer surface of the sessile drop. Consequently, it causes alterations in the geometry of the freezing front and ultimately results in the formation of a solidified shell that encloses the drop. Furthermore, the encapsulated liquid continues to solidify, which induces volume change and consequently changes the final outcome of the freezing process. This study highlights the importance of considering the properties of the environmental medium and provides novel strategies to manipulate the freezing rate and reshape the morphology of the solidified drop.

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A hybrid VOF-IBM method for the simulation of freezing liquid films and freezing drops

Cited by 26 publications

References 47 publications

A hybrid level-set / embedded boundary method applied to solidification-melt problems

A hybrid level-set / embedded boundary method applied to solidification-melt problems

An improved lumped model for freezing of a freely suspended supercooled water droplet in air stream

Liquid encapsulation in a freezing sessile drop

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