A study on the hydrodynamic load in a water pool when discharged air forms a bubble cloud

This paper presents a numerical and qualitative study on the expected hydro-dynamic load-reducing effect of bubbly media near a volumetrically oscillating bubble. In this study, the bubble or bubble cloud is assumed to be spherically symmetric, and its motion is analyzed as a one-dimensional compressible two-phase flow in the radial direction in spherical coordinates. We adopted the CCUP (CIP-Combined Unified Procedure) method, which is a unified analysis method for both compressible and incompressible fluids proposed by Yabe et al. (1991) in order to treat interaction among gas, liquid, and two-phase media, and to avoid large numerical dissipation at density discontinuities. To verify the analysis program we developed, we analyzed free oscillations of a bubble with a unity void fraction and of a bubble cloud with an initial void fraction of 0.5, and found that the natural frequency from numerical results are well reproduced with an error of 0.9% for the bubble and 5% for the bubble cloud as compared to those obtained on a theoretical basis. Using this method, we analyzed the free oscillation of a bubble cloud in which a bubble with a unity void fraction is covered by a bubbly media layer with an initial void fraction of 0.5. Numerical results show that the amplitude of pressure oscillation inside the bubble is about halved, and that a higher mode of oscillation appears when a bubbly media layer covers the bubble. The measured results from a blowdown test we previously reported also shows a similar higher mode of oscillation. The amplitude of pressure oscillation in the water region was apparently reduced when a thick bubbly media layer covers the bubble. Thus, if the bubbly media is ejected from sparger holes prior to the ejection of a high-pressure bubble, the bubbly media might reduce the hydrodynamic load induced in a water pool made by volumetric oscillation of the bubble.