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軸対称な流体-液体界面形状の極座標系による数値計算とU-Pu混合転換技術にかかわる界面の例

Numerical calculation of axisymmetric fluid-liquid interfaces by polar coordinate system and examples associated with U-Pu co-conversion technology

細馬 隆  

Hosoma, Takashi

泡や滴あるいは液架橋などの気液界面の美しい形は、界面の表面張力及び平均曲率による圧力と、界面内外の密度差による圧力が、垂直方向でそれぞれ連続的に変化しながらも釣り合うという関係から生み出される。しかしながら、その正確な形状や曲率及び体積等を論じた資料は意外に少ない。U-Pu混合転換技術に関する研究開発では、これらを正確に求めることにより理解を深めることのできた現象が幾つかあり、静的で軸対称という条件ではあるものの、極座標系を導入し、原点移動アルゴリズムにより適用範囲を拡大することにより、水平接面と垂直接面をともに複数有する形状に適用可能な数値計算方法を導いた。本方法では、実際に観察される界面形状は、数値計算によって得られる曲線の一部が、物理的条件に対応して選ばれると考える。実例として、密度及び液位の測定に用いられる浸漬管の先端に生じる気泡、マイクロ波加熱により円筒形状の液中に核生成する気泡、転換後の造粒物中に生じていると推定される液架橋をとりあげた。体系的な計算の例は、室温,大気圧下における水と空気の界面とした。曲線の一部が選ばれる際の物理的条件は、接触角,内外圧力差,体積,表面エネルギー及び周期的に変化する形状の波長等である。

An exquisite shape of gas-liquid interface, that is a bubble/drop/liquid bridge, is the result of continuous pressure balance along vertical axis between the pressure due to difference of density and the pressure due to surface tension and curvature of interface. However, there have been surprisingly a little papers arguing the accurate shape, curvatures and volume. Regarding the research and development of U-Pu co-conversion technology, some phenomena were well understood by obtaining the accurate shape and/or volume. A numerical solving method by polar coordinate system with a switched-origin algorithm applicable to the shape that includes multiple tangential planes both in horizontal and in vertical was derived through such experiences, although static physical conditions and axisymmetrical property are assumed. The real interface shape is actualized or selected as a part of the calculated curve, which depends on physical conditions. A bubble at the tip of dip-tube used for density/level measurement, a bubble nucleates in the cylindrical shape of liquid heated by microwave and an estimated liquid bridge in the granule after co-conversion were described as actual examples. Interfaces between water and air under normal temperature and atmospheric pressure were described as numerical examples for systematic investigation. Contact angle, internal/external pressure difference, volume, surface energy and wavelength of periodically deforming shape are physical conditions actualizing the calculation.

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