Numerical Study On Collapse Characteristics Of Double Bubbles In A Free Flow Field And Near A Rigid Solid Wall

Microjet and shock wave are induced by collapse of bubbles,which are highly concentrated in terms of time and space.Both of them possessing physical properties such as high temperature and high pressure,often are regarded as the sources of disturbance of fluid power,erosion of materials,radiation of noise and excitation of vibration,which seriously affect the working stability and service life of hydraulic machinery.Cavitation in nature and the engineering field often exists in the form of multiple bubbles,not a single isolated bubble.Due to the interaction,interference and coupling between bubbles,bubbles and adjacent boundaries under different conditions,the dynamic characteristics of bubbles possess complex and various characteristics.Firstly,considering the effect of radiation pressure wave between bubbles in a free flow field,the dynamic equation of multiple bubbles is deduced.The influence of the secondary Bjerknes force on the collapse characteristics of bubbles is analyzed.Subsequently,the collapse characteristics of double bubbles in the free flow field and near the rigid solid wall are numerically simulated based on the computational fluid dynamics method.The physical quantities including vapor volume fraction(VVF),flow field pressure and velocity are obtained,and the shape evolution at the process of bubble collapse is captured.The dynamic collapse characteristics of double bubbles are analyzed,and the influence of the adjacent bubble and the rigid wall on collapse characteristics of bubbles is revealed.Based on the Rayleigh-Plesset-Keller-Miksis model,the dynamic equation of multiple bubbles under the effect of secondary Bjerknes force is deduced.The effects of secondary Bjerknes force and instantaneous force between bubbles on the collapse characteristics of bubbles are analyzed.For in-phase double bubbles with the equal initial size,the secondary Bjerknes force between the two bubbles is negative during a collapse period,which shows attraction,contributing to push the bubbles closer to each other.The secondary Bjerknes force is positively correlated with the square of the initial bubble diameter Rij,0,and negatively correlated with the bubble-bubble distance parameter D*.For D*>20.0,the secondary Bjerknes force between bubbles can be ignored.For the unequal-size double bubbles,the attraction and repulsion of the small bubble to the large one alternately occur in a collapse period of the large bubble.As the small bubble oscillates,the large bubble is subjected to a great repulsion force by the small bubble at the end of its collapse and early rebound.The instantaneous force on the large bubble exerted by the small bubble is sensitive to the initial size of the large bubble.Considering the liquid viscosity,the bubble surface tension and the gas compressibility,the collapse process of equal-size double bubbles in a free flow field for different D* is numerically simulated by applying the multiphase model of volume of fluid.It is found that the collapse behavior of double bubbles is mirror symmetric with respect to the center of symmetry.For 1.0<D*<10.0,the bubbles tend to be close to each other during the collapse process.At the end of collapse,two opposite jets are generated,which point to the symmetry center.Finally,the two bubbles evolve into annular bubbles and then collapse.For D*=1.0,the two bubbles constantly merges to form a single bubble,and the bubble is penetrated twice by the jet during the collapse.For D*>3.0,the impact effect of the opposite jets becomes very weak.For D*>10.0,there is no jet between bubbles.Under the condition of D*=γ(distance parameter between bubble and wall),the collapse dynamic characteristics of double bubbles in a free flow field is very similar to that of the single bubble near a solid wall.The collapse process of double bubbles near a solid wall is numerically simulated.The influence of D* and γ on the collapse characteristics of double bubbles is discussed.As D*=γ,the jet direction is at an angle of 45° with the wall normal and the evolution of bubble shape is symmetrical about the jet.For D*≠γ,the bubbles undergo asymmetric shape evolution.For the two conditions in which the values of D* and γ are exchanged,the collapse behavior of bubbles shows mirror symmetry.The mirror symmetry axis has an angle of 45° with the wall normal.The distributions of pressure and velocity in the flow field under the two conditions are mirror symmetry to each other.Moreover,the collapse time and the jet velocity are basically the same.It is also discovered that the wall is a dominant factor affecting the collapse characteristics of bubble for D*/γ>1.73 while the adjacent bubble becomes a determining factor affecting that for D*/γ<0.56.As 0.56<D*/γ<1.73,the dynamic characteristics of bubble collapse are combinedly affected by the adjacent bubble and the wall.