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 (199], "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 tne bubble.