Drag reduction by injecting bubbles into a turbulent boundary layer is a complex physical phenomenon, which has been studied for many years by researchers in various fields worldwide. The benefits of a success in drag reduction control are enormous. Reduction in drag can increase the range of speed in transportation system, reduce the energy consumption in pumping system such as pipeline, improve systems efficiency, and decrease fuel consumption, which directly leads to cost savings and decrease in pollutants emission. Since the first experimental study was carried out by McCormick & Bhattacharrya (1973), A series of experimental and numerical studies were conducted mainly in USA, Russia and Japan. These studies revealed fundamental characteristics of the phenomenon, and confirmed that as much as 80% of the skin friction drag can be reduced with bubbles (Bogdevich et al. 1976, Madavan et al. 1984, Pal et al. 1988, Deutsch et al. 1990, Clark III et al. 1991, Kate et al. 1998). Recently, practical researches on the application to ships have made great progress in Japan. The first successful full-scale experiment was carried out using a cement carrier, and it was reported that approximately 5.3% net fuel consumption was saved by the air injection (Kodama et al. 2008). It is considered that drag reduction by bubbles is a promising engineering method for ships. However, the mechanism of this physical phenomenon has been not fully understood until now. Consequently, it is confronted with many difficulties in making actual design and application to ships and improving the effect of bubbles.

An important step towards the understanding of the mechanism is to find parameters which have significant influences on the drag reduction. In the present research, we put the focus upon the relation between bubble size and drag reduction. The knowledge on the effect of the bubble size especially in the very small bubble size range has been very limited because generating such small bubbles is very difficult.Therefore, a method for generating very small microbubbles by electrolysis was developed first. Using this technique, a series of experiments were carried out for a fully developed turbulent channel flow in a circulating water tunnel for gaining a new insight into the effect of the bubble size on the interaction between bubbles and turbulence and its contribution to the drag reduction.

In the first set of experiments, the drag reduction effect of small microbubbles generated by electrolysis was measured by shear stress transducers and by a differential pressure gauge. By comparing with the results for large bubbles generated by air injection, it was clearly shown that small bubbles are 10~1000 times more effective in terms of the drag reduction per unit gas volume than large air bubbles. This experiment is described in Chapter 2

In Chapter 3, the bubble size distribution and the void fraction profile were investigated by means of microscope photography. Through the image processing of the microscope photographs taken by a backlight method, the size and position of individual bubbles were receded. It was confirmed that the diameter distribution of small bubbles peaks around 30 fEm, and that small microbubbles are more concentrated near the wall compared with large air bubbles. The ratio of the peak void fraction fp to the mean value fm was approximately 7 with small microbubbles, while the value with large air bubbles was about 1.5. The peak of the void fraction was located within 0.25H from the wall with H being the half channel width, while that of large air bubbles was between 0.25H and 0.5H. It is suggested that this difference in the void fraction profiles is one of the reason for the high drag reducing efficiency of small microbubbles.

The relation between bubble size and turbulence statistics was investigated by means of a particle tracking velocimetry (PTV) for smaller bubble size. The mean velocity profiles of the liquid phase without or with microbubbles were almost the same.. Interesting findings were that the mean velocity of microbubbles was smaller than that of the liquid phase, and that the mean relative velocity between water and microbubbles increases with the increasing bubble diameter. It was also found that the velocity fluctuation of liquid phase with microbubbles is smaller than that without microbubbles. The velocity fluctuation of microbubbles was smaller than that of water, and that this tendency has positive correlation with bubble diameters. The Reynolds shear stress of microbubble-laden flow was smaller than that of single-phase flow, and the difference was consistent with the measured drag reduction by direct methods. The correlation of the streamwise and wall-normal velocity fluctuation of microbubbles was smaller than that of the liquid phase, and the difference increases with the increasing microbubble diameter. These results are summarized in Chapter 4.

In Chapter 5, the preferential concentration of microbubbles in the region near the wall was investigated by photography. It was found that the tendency of the preferential concentration is strongly dependent on the bubble size. The preferential concentration was observed by the visualization for microbubbles between 10 and 80m in diameter. While such behavior was not observed for large air bubbles. The bubble relaxation time normalized by viscous unitsτ+p ranges between 0.011 and 0.702 when the mean velocity is 1.0m/s, and between 0.020 and 1.288 when the mean velocity is 1.5m/s, respectively.

Based on the experimental evidences obtained in the previous chapters, the mechanism of the drag reduction by very small microbubbles is discussed in Chapter 6. Fugakata et al. (2002) derived theoretically that the reduction of Reynolds shear stress near the wall can induce the drag reduction more effectively. Kim et al. (1971) has shown that this bursting of low-speed streaks contributes the majority of the turbulent kinetic energy produced in a turbulent boundary layer. The near-wall vortices extract a large amount of turbulent kinetic energy from the mean flow (Iwamoto et al. 2002). On the other hand, the large-scale structures also gain substantial energy from the mean flow. The energy is not dissipated by themselves, but transferred to the smaller vortices through the energy cascade. By combining those knowledge on the mechanism of the production of the turbulent energy and the findings of the present study, it is reasonable to conclude that the sharp peak of the void fraction profile and the tendency towards the preferential concentration near the wall are two important reasons for the highly efficient drag reduction caused by small scale microbubbles. The behavior of a bubble in a vortex is strongly dependent on the ratio of the time scale between the bubble and the vortex. It is known that the interaction becomes strong when the time scale ratio is on the order of unity. The large air bubbles, of which diameter is larger than 200 fEm, have longer time scale, or relaxation time. Thus they interact with the large scale vortex structure which spans the entire channel width. As shown in Chapter 5, small microbubbles, of which the diameter is smaller than 80 fEm, have time scale on the order of unity when scaled in the viscous units. Therefore they interact with the near wall vortical structure which has large contribution to the skin friction. Consequently, as shown in Chapter 2, small microbubbles are two orders of magnitude more efficiently reduce the skin friction than large air bubbles. Although further investigation is desired, the proposed mechanism of the drag reduction by small microbubbles is consistent with the experiments in the past and in the present study.

Finally, Chapter 7 summarizes this study. The findings in the present work are expected to contribute to the development of rational models for predicting the drag reduction, and optimizing its use in practical applications.

地球温暖化ガスの排出規制の強化や燃料価格の高騰のため、船舶の抵抗低減技術に対し、近年強い関心が持たれている。中でも、気泡を用いた摩擦抵抗低減法は実用化が近いと期待されている。

これまで、気泡を用いた摩擦抵抗低減技術の研究においては、多孔質板などからの、空気吹き出しにより生成された1ミリメートルから2ミリメートル程度の直径の気泡が用いられてきた。しかし、最近の研究により、電気分解により生成された直径50マイクロメートル程度の微細気泡では、気泡単位体積当たりの摩擦抵抗低減効果が飛躍的に大きくなる可能性が指摘されてきた。本研究はで、この微細気泡による摩擦抵抗低減のメカニズムを解明することを目的として、実験により様々な面から検討を行っている。

本論文は7つの章で構成されている。第1章では、気泡による摩擦抵抗低減技術に関する過去の研究について調査した結果と、明らかにするべき課題を整理している。実験結果は第2章から第6章までにまとめられている。まず、第2章では、電気分解により生成された微細気泡を用いた場合と、空気吹き出しにより生成された気泡を用いた場合についてそれぞれ摩擦抵抗の計測を行い、気泡直径と摩擦抵抗低減効果の関係を明らかにしている。実験結果によれば、気泡体積率が同じ場合、微細気泡は、大きい直径の気泡より摩擦抵抗低減効果が100倍以上大きいことを確認した。これは他の研究者によって発表されている結果と整合性があるものであるとともに、本研究においては、剪断力計と差圧計という2つの異なる方法で摩擦抵抗を計測して、効果を確認したことが重要な成果である。続いて第3章では、画像解析による気泡径分布の計測と、気泡体積率の空間分布の計測を行っている。この実験結果から、微細気泡の分布は壁面近くに鋭いピークを持つことが明らかになった。

第4章では高速度ビデオ映像を用いたPTV(Particle Tracking Velocimetry)解析により、微細気泡を含むチャネル乱流の各種統計量を計測している。液相の運動と、気泡の運動を分離して計測し、さらに気泡の運動については気泡の直径別に整理することで、様々な新しい知見を得ている。まず、微細気泡の存在下では液相のレイノルズ応力は低下していることを初めて明らかにした。また、気泡の乱流統計量と直径の間には強い相関関係があることも初めて明らかになった。

第5章では、壁面近傍における気泡分布の空間構造に関する実験結果を示している。高速度ビデオ映像の解析から、気泡の分布は縦筋状になっており、その間隔は壁面近傍の低速ストリークの間隔と同じ約100粘性長であることを示した。

第6章では、本研究における実験結果をまとめて、微細気泡による摩擦抵抗低減のメカニズムに対する検討を行っている。ここで、微細気泡では分布のピークが鋭く、最大値の平均値に対する倍率が約7倍であること、また、レイノルズ応力の生産に対する寄与が大きいバッファー層に体積率分布のピークを持つこと、乱流構造に対して選択的に集積することにより、実効的な体積率が高まることの3つの要因が重要であるとのメカニズムに関する仮説を示している。

最後の第7章においては、本研究における成果をまとめるとともに、応用の可能性について述べている。

以上に示したように、本論文では、工学的に応用価値が高い、微細気泡による摩擦抵抗低減技術に関し、実験的に多くの新事実を明らかにした。また、これまで不明であった抵抗低減のメカニズムに対して合理的な解釈を与えた。これらの成果は当該分野において画期的なものである。

よって本論文は博士(工学)の学位請求論文として合格と認められる。