PS20
静電浮遊中の Fe-Cu 液滴の相形成における液相分離と熱流動のシミュレーション
Modeling of liquid phase separation and thermofluidics
in levitated Fe-Cu droplets橘髙 里沙1, 小畠 秀和2, 清宮 優作3, 小澤 俊平3, 杉岡 健一4, 石川 毅彦5, 白鳥 英1
Risa KITTAKA1, Hidekazu KOBATAKE2, Yuusaku SEIMIYA3, Shunpei OZAWA3,Kenichi SUGIOKA4, Takehiko ISHIKAWA5 and Suguru SHIRATORI1
東京都市大学, Tokyo City University
同志社大学, Doshisha University
3 千葉工業大学, Chiba Institute of Technology
4 富山県立大学, Toyama Prefectural University
5 宇宙航空研究開発機構，Japan Aerospace Exploration Agency
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1. Introduction
For reliable and stable supply of renewable energy, various energy storage systems are being developed.
One method is using phase change materials (PCMs) for the Thermal Energy Storage (TES); the use ofimmiscible alloys as PCMs can increase energy efficiency and sustainability. The purpose of the Thermal Storage
Project is to obtain accurate thermophysical properties of alloys, necessary for the comprehensive engineering
design of TES. In the TS project, experiments were conducted to measure the thermophysical properties ofimmiscible Fe-Cu alloys melted in the Electrostatic Levitation Furnace (ELF) on the International Space Station.
The supercooled immiscible Fe-Cu alloy separates into two liquid phases, an Fe-rich phase and a Cu-rich phase.
Supercooling has been confirmed in ELF experiments from recorded camera images and temperature history.
The thermophysical properties obtained strongly dependent on which phase is exposed on the surface of thedroplet. As it is not feasible to identify the phase during the experiment due to opaqueness, it is imperative topredict the phase separation state through simulation.

1.

Levitated
Fe-Cu alloy

2.

Heating bylaser

3.

Measurement
Dropletoscillation

・ Frequency
・ Attenuation
constant

Fig 1. ELF Experiment Overview

1 of 3Modeling based on[Shi et al.]Previous studies

Liquid phaseseparation

Temperature
distribution bylaser heating

Marangoni effectat the liquidliquid interface

Marangoni effectat the gas-liquidinterface

Fig 2. Four elemental models

2. Model formulation
For simulations of ELF experiments, the physical model must involve heat transfer based on laser heating,the Marangoni effect at the gas-liquid interface, the Marangoni effect at the liquid-liquid interface, and liquid
phase separation by spinodal decomposition. Regarding the heat transfer with laser heating and theMarangoni effect on the gas-liquid interface, physical models have been developed in previous studies byauthor’s research group 1). In contrast, the models for liquid-liquid phase separation and the Marangoni effectat the liquid-liquid interface are newly developed in the present study, according to the work done by Shi etal. 2). The following governing equations are considered in this study.
(1)𝛻𝛻 ⋅ 𝒖𝒖 = 0,𝜌𝜌𝜕𝜕𝒖𝒖+ 𝛻𝛻𝛻𝛻 ⋅ (𝒖𝒖𝒖𝒖) = 𝜌𝜌𝒈𝒈 + 𝛻𝛻 2(𝜇𝜇𝒖𝒖) + 𝛻𝛻 ⋅ 𝝉𝝉,𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕+ 𝛻𝛻 ⋅ (𝒖𝒖𝑇𝑇) = ∇ ∙ (𝛼𝛼∇𝑇𝑇),
𝜕𝜕𝜕𝜕𝑙𝑙𝑙𝑙𝑙𝑙𝜕𝜕𝜕𝜕𝜕𝜕𝐺𝐺𝑚𝑚+ 𝛻𝛻 ⋅ (𝒖𝒖𝑐𝑐) = 𝑀𝑀𝑐𝑐 ∇2 �− 2𝜅𝜅∇2 𝑐𝑐� + 𝜁𝜁𝑐𝑐 ,𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕

(2)
(3)
(4)

where 𝒖𝒖 is velocity, 𝜌𝜌 is density, 𝝉𝝉 is stress tensor acting at the liquid-liquid interface, 𝑇𝑇 is the temperature,𝛼𝛼 is the thermal diffusivity, 𝑐𝑐 is the concentration of Cu, 𝑀𝑀𝑐𝑐 is the mobility of atomic diffusion, 𝜅𝜅 is theconcentration gradient energy coefficient, and 𝜁𝜁𝑐𝑐 is the thermal fluctuation. The aforementioned physicalmodel was implemented in OpenFOAM, an open-source computational fluid dynamics framework.
3. Simulation results
Figure 3 shows three snapshots extracted from the calculation results. The simulation conditions for theELF experiment were set to an initial concentration of 𝑐𝑐0 = 0.5 and a droplet diameter of 2 mm, and theboundary conditions of laser heating and the Marangoni effect at the gas-liquid interface were considered in
the simulation. From the simulation results, it is predicted that the Cu-rich and Fe-rich phases may exhibit
complex time evolution of separation and merging.

Fig 3. Simulation for ELF experiment
2 of 3References1)
2)

R.P. Shi et al., Acta Mat. 61(4), p.1229 (2013). DOI: 10.1016/j.actamat.2012.10.033
T. Usui et al., Int. J. Microgravity Sci. Appl. 40(3), p.400302 (2023). DOI: 10.15011/jasma.40.400302© 2024 by the authors. Submitted for possible open access publication under theterms and conditions of the Creative Commons Attribution (CC BY) license(http://creativecommons.org/li censes/by/4.0/).

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