The Investigation Of Effect Of Aeration Bubbles With Different Radii On Cavitation Bubble Dynamics

With the development of hydropower and hydraulic structures, theincrease of discharge structure from high dams, the issues ofhigh-velocity flow has been concerned, such as aeration, cavitation,fluctuation, vibration, energy dissipation and erosion control etc.Especially in spillway dams, spillway tunnels and chute spillways ofhigh-head discharge structures, cavitation phenomena will occur whileflow velocity reaches a certain value and flow pressure is lower than therelevant saturated vapor pressure. Cavitation erosion arises from thecavity flow from low-pressure to higher pressure. In order to prevent theproblem of cavitation damage because of high-velocity flow, an economicand effective measure is to set up aerators for generating forced aerationin the low-pressure cavitation regions or upper locations liable tocavitation erosion. So far, the research only on the interaction betweencavitation bubble and cavitation bubble, but there is little study of interactions between aeration bubble and cavitation bubble in thecavitation region on the condition of aeration in the flow. So it isnecessary to develop the relation study on aeration bubble and cavitationbubble.In this paper, cavitation characteristics in cavitation region on thecondition of aeration and basic equations for interaction of cavitationbubble with aeration bubble in a viscous compressible liquid aresystemically investigated by theoretic, numerical and experimentalanalyses. Meanwhile, the effects of initial cavitation bubbles and initialaeration bubbles with different radii on fluctuation characteristics ofcavitation bubble wall are also performed.Firstly, based on the study of motion equations of cavitation bubblewith cavitation bubble and conservation of energy equation in cavitationregion of flow is set up. Numerical simulations are presented to describethe effects of cavitation characteristics at different flow velocities incylindrical irregularity cavitation region. The results indicate that bubbleradius will gradually decrease with increase of gas concentration at thesame flow velocity. Gas concentration is higher and bubble radius islower for high-velocity flow. The cavitation number will increase with thegas concentrate at the same flow velocity. The maximum of cavitationnumber for low flow velocity is larger than that of high flow velocity.And based on the study of bubble motion of aeration in the flow, the collapse impulse pressure equation of the bubble wall was founded andthe characteristics of bubble collapse were investigated. The effects of thebubble collapse at different flow velocities and different gasconcentrations and cavitation number curves were simulated. It is shownthat the cavitation number will increase with the gas concentrate at thesame flow velocity, and cavitating erosion ability is weakened. Thecavitation number increases is larger with the gas concentrate at low flowvelocity, while is smaller at high flow velocity. The flow velocity ishigher，the cavitation number is less.Secondly, the spherical and non-spherical dynamical models forinteraction of cavitation bubble with aeration bubble are theoreticallydeveloped in consideration of the effects of the vapor andnoncondensable gas in the cavitation bubble and air in the aeration bubble.With the help of the PLK coordinate perturbation technique theinteraction between cavitation bubble and aeration bubble in a viscouscompressible liquid are theoretically investigated. The first-order andsecond-order asymptotic solutions of velocity potential for sphericalcavitation bubble and aeration bubble are presented, and the equations forinteraction of cavitation bubble with aeration bubble are developed. Thecouple equations are used to describe the effects of aeration bubble oncavitation bubble. The equations depend on not only the initial radius,wall velocities of bubbles and distance between cavitation bubble and aeration bubble, but also the air content.Lastly, the behavior of cavitation bubble collapse radius and wallpressure for different aeration bubble radii is investigated, and based onthe dynamical models for interaction of cavitation bubble with aerationbubble are studied in a viscous compressible liquid. The numericalcalculation results indicate that the minimum radius of cavitation bubblecollapse decreases and the collapse time increases with the interaction ofcavitation bubble and aeration bubble, which shows that the interactionreduce the collapse speed. The maximum pressure climbs up and thendeclines with the increase of initial aeration bubble radius, and extremevalue of the maximum pressure is derived. This means cavitation bubblewill be prevented from excessive compression when it collapses in higherpressure region, and cavitation erosion capacity be weakened, whichshows that the aeration bubble radius has an optimum value in theinteraction between cavitation bubble and aeration bubble on cavitationcontrol by aeration, and the optimum distance of cavitation bubble andaeration bubble is obtained by means of the optimum aeration bubbleradius.