A Study on the Hydrodynamic Load in a Water Pool When Discharged Air Forms a Bubble Cloud (PVP2006-ICPVT11-93281)

This paper presents a numerical and qualitative study on the expected hydrodynamic load-reducing effect of bubbly medium 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 cubic interpolated pseudoparticle combined unified procedure method, which is a unified analysis method for both compressible and incompressible fluids proposed by Yabe and Wang (1991, “Unidied Numerical Procedure for Compressible and Incompressible Fluid,” J. Phys. Soc. Jpn., 60, pp. 2105–2108) in order to treat interaction among gas, liquid, and two-phase medium 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 is 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 medium 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 medium layer covers the bubble. The measured results from a blowdown test we previously reported also show a similar higher mode of oscillation. The amplitude of pressure oscillation in the water region was apparently reduced when a thick bubbly medium layer covers the bubble. Thus, if the bubbly medium are ejected from sparger holes prior to the ejection of a high-pressure bubble, the bubbly medium might reduce the hydrodynamic load induced in a water pool made by volumetric oscillation of the bubble.