P21
ガスジェット浮遊法による溶融金属酸化物の熱物性値測定法の確立：静的形状からの表面張力同定
Measurement framework for thermophysical propertiesof molten metal oxides by aerodynamic levitation:
Identification procedure of surface tension from static
droplet shape
吉野 裕斗 1, 白鳥 英 2, 清宮 優作 3, 小澤 俊平 4, 小畠 秀和 5, 杉岡 健一 6, 石川 毅彦 7
Yuto YOSHINO1, Suguru SHIRATORI2, Yusaku SEIMIYA3, Shumpei OZAWA4 ,Hidekazu KOBATAKE5, Ken-ichi SUGIOKA6 and Takehiko ISHIKAWA7
東京都市大学大学院， Graduate School, Tokyo City University
東京都市大学， Tokyo City University
3 千葉工業大学大学院， Graduate School, Chiba Institute of Technology4 千葉工業大学， Chiba Institute of Technology
5 同志社大学， Doshisha University
6 富山県立大学，Toyama Prefectural University
7 宇宙航空研究開発機構， Japan Aerospace Exploration Agency
121.

Introduction
For sustainable manned activities on the moon, manufacturing with lunar regolith is essential 1,2). Especially,

the melting and solidification process is necessary for the exterior walls so that they can survive in the severe
lunar environment. For this purpose, preliminary numerical simulations play significant roles in the design ofefficient manufacturing processes. Although the main components of the lunar regolith are metal oxides,
however, the thermophysical properties of molten metal oxides have been measured for only a few materials.
Therefore, the measurements of the thermophysical properties of molten metal oxides are an important task.
For such measurements, aerodynamic levitation (ADL) is regarded as a suitable method, but there is anuncertainty problem because a part of the droplet ishidden by the nozzle. In this study, we propose amethod to identify the thermophysical properties ofdroplets by minimizing the effect of droplet hiding
with a physical model constructed to add gas-jetpressure to the Young-Laplace equation and a data
assimilation method with a Physics-Informed Neural
Networks (PINN) 3).

Fig.1 . Things of ADL that need to be improved.
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2.1.

Identification of surface tension
Method of identifying physical properties by data assimilation

Even if a part of the droplet is hidden by the nozzle, the droplet shape of the observable parts is affected by
the surface tension. In this study, the surface tension is identified from a part of droplet shapes by the method
shown in Fig.2. A mathematical model is constructed assuming that the levitated droplet is under equilibrium
where gravity, Laplace pressure, and gas-jet pressure are balanced. Using this model, the equilibrium droplet
shape can be predicted from a given surface tension. The predicted surface shape is compared with themeasured droplet shape, then the error between them is evaluated. The surface tension of a droplet isdetermined so that the error is minimized.

Fig.2 . Proposed method for physical property identification method by data assimilation.

2.2.

Mathematical model of droplet shapeThe droplet is assumed to be axisymmetric with respect to the direction of gravity. The following differential
equations are obtained for the static shape of a droplet using the axisymmetric coordinate system 𝑅, 𝜑, 𝑍 as2
𝐾 − − 𝐵𝑜(1 − 𝑍) + 𝐵𝑜𝑃𝑠 𝐶𝑝 (𝜑) = 0,Γ𝐾=

𝑅2 + 2𝑅′2 − 𝑅𝑅′′3(𝑅2 + 𝑅′2 )2+(1a)𝑅 + 𝑅′ tan⁡(𝜑)

1,

𝑅(𝑅2 + 𝑅′2 )2(1b)where equation (1a) is the modified Young-Laplace equation which involves the gas-jet pressure, Laplacepressure, and gravity. Equation (1b) is a curvature in a spherical coordinate system. 𝐶𝑝 (𝜑) gas-jet pressure
distribution normalized by the stagnation pressure, 𝜌 is density, and 𝑔 is the acceleration of gravity. Theequations are nondimensionalized with the length scale as the radius of the sphere 𝑅0 and the pressure scaleas 𝜌𝑔𝑅0 . The dimensionless numbers used in the model are as below:
𝑅=𝑟𝑧
𝜌𝑔𝑅02
𝑝𝑠𝑅𝑠,𝑍 =, 𝐵𝑜 =, 𝑃𝑠 =,Γ = ,𝑅0
𝑅0𝜎
𝜌𝑔𝑅0𝑅0(2)where 𝜎 is surface tension, 𝑝𝑠 is stagnation pressure of gas-jet pressure distribution, and 𝑅𝑠 is the radius ofcurvature at the droplet top surface, respectively.

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3.

Results
Fig.3(a) shows the droplet shape calculated by the PINN for three different values of Bo=0.1,0.5,1.0. The

larger the Bond number, the smaller the relative contribution of surface tension, and the larger droplet
deformation are recognized.

In this study, the validity of the proposed data assimilation method wasconfirmed by the twin experiments whose results are shown in Fig.3(b). When the noise is sufficiently small,the Bond number can be identified even if the only small top region of the droplet is observed. However, as
the noise increases, the identification accuracy decreases if the droplet's bottom cannot be observed.

(a)Fig.3.

(b)(a) Calculated droplet shapes,(b) Results on whether the surface tension is reconstructed from the observed data.

Acknowledgments
This study was partly supported by the Grant-in-Aid for Front Loading Research from the Advisory
Committee for Space Utilization Research in ISAS/JAXA.
References1)

Space Exploration Systems Engineering Unit, International Space Exploration Center, JAXA: Japan’s Scenario forInternational Space Exploration, JAXA proposal 2021 (Public Version) (2022) (in Japanese).
2)
3)NASA (2022): “Artemis,” https://www.nasa.gov/specials/artemis/, Accessed on 30/08/2023.
M. Raissi et al.; J. Comp. Phys. 378, pp.686-707 (2019).
© 2023 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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