Characteristics Of The Jet Impact Pressure Generated By An Underwater Explosion Bubble

Bubble dynamics have wide applications in traditional industrial systems and emerging technologies,such as underwater explosion,seismic air gun-generated bubbles for seabed geophysical exploration,cavitation on ship propellers and hydro-turbines,micro-bubbles in drag reduction technology,ultrasonic cleaning,contrast-enhanced ultrasound and targeted therapy.The bubble's dynamic behavior and the pressure caused by the violent collapsing bubble in the above applications are the core problems.The underwater explosion bubble and cavitation bubble have violent oscillation characteristics and often jet toward a nearby structure,which are the main subjects in this work.Both numerical and experimental methods are used to study the pressure caused by a collapsing bubble and the nonlinear interaction between a bubble and a nearby structure.First of all,the basic physical phenomena and the mechanical mechanisms associated with bubbles are introduced.Then some classical results and the latest developments of bubble dynamics in theory,experiment and numerical computation are briefly reviewed.However,there still exist some problems in bubble dynamics that are not well understood.For example,only a few works on toroidal bubble dynamics have been reported,and the numerical simulation is restricted to the stage before the splitting of toroidal bubble.Besides,the algorithm of the pressure caused by jet impact hasn't been well established.Furthermore,the impact of the free surface on bubble-induced pressure is not clear.At last,the nonlinear interaction between a bubble and a movable or deformable structure has been seldom studied.We noticed that only‘loose'coupling approach between bubble and structure is used in published literatures.Therefore,this study aims at putting forward some improved models and methods to deal with the above problems.Based on the potential flow theory,the boundary integral method?BIM?is adopted to simulate the dynamic behavior of a bubble before jet penetrates the opposite side.Bubble transforms from a singly-connected into a doubly-connected form after the jet impact,and there exists a velocity potential jump at the impact point.In the present study,an improved vortex ring model is used to handle this problem and the subsequent toroidal bubble phase is simulated.The toroidal bubble would split into several parts because of the microjets and instabilities.However,the traditional vortex ring model does not apply to multiple toroidal bubbles.Therefore,the computations of toroidal bubbles were always restricted to the pre-splitting phase.If the toroidal bubble is not rebounding at the splitting moment,we can't obtain the pressure peak caused by the bubble.In this study,we have proposed a‘toroidal bubble splitting model'to simulate the subsequent phase.To fully validate our numerical model,several experiments with different boundary conditions and system parameters are designed and performed.By comparing the bubble shape and pressure fields,we show that the numerical results agree well with experimental results.The pressure caused by a bubble is calculated using the Bernoulli equation,where the partial derivative of the potential in time is calculated using the auxiliary function method.Since there are two sources of bubble-induced pressure,the dynamic pressure can be decomposed into two parts correspondingly.The first part p_g,which is associated with the imbalanced pressure between the interior bubble gas and the ambient flow,measures the contribution of the high pressure gas to the dynamic pressure.p_g shows an approximately spherical distribution around the bubble surface,and the magnitude of p_g decays proportionally to 1/r with r being the distance from the bubble center.The variation of p_g with time has the same pattern as the gas pressure.The second part p_m is caused by the bubble motion.Before jet impact,p_m is the pressure caused by the lagging flow,the magnitude of which is much smaller than that of p_g.After jet impact,p_m is the jet impact pressure.The p_m contour displays some high pressure?several times of p_g?regions,which locate around the jet tip after jet impact.The effects of some important dimensionless parameters on the pressure field induced by a gas bubble are also investigated.It is found that if the bubble is initiated closer to a free surface the bubble-induced pressure becomes lower.The free surface effect can be neglected if the depth of the bubble is larger than 6R_m(R_m is the maximum bubble radius).The free surface Green function can be used if the depth is larger than 2R_m.The nonlinear effect of free surface should be taken into account when the depth is less than 2R_m.The Green function is modified to deal with a bubble near an infinite rigid wall.p_g on the wall reaches its peak at the minimum bubble volume.After the high-speed liquid jet impacts on the rigid wall,a stagnation point together with a high pressure region at the wall center is formed.The water layer between the bubble and the wall would dramatically decelerate the jet impact velocity on the wall and therefore the jet impact pressure on the wall will be greatly reduced.The maximum p_m decreases rapidly as the stand-off parameter??defined as?=d/R_m,where d is the distance between initial bubble center and the wall?is increased from 1 to1.4.Besides,it is easier for a toroidal bubble to split when?is small.The two sub-bubbles vary differently in volume after splitting,resulting in the inner gas pressures of the sub-bubbles will differ from each other gradually,resulting in the difference between pressures around the two sub-bubbles afterwards.If the smaller toroidal bubble after splitting is relatively far from the wall,the splitting has little effect on the variation of p_g.Otherwise,the splitting would result in the reduction of p_g.There exists a critical stand-off parameter?_c.If?<?_c,the pressure on the wall is dominated by the jet impact;otherwise,the bubble gas plays the dominant role.We have also investigated the effects of some important dimensionless parameters on bubble-induced pressure.It is found that the free surface effect would reduce the pressure caused by a collapsing bubble in shallow water.When ignoring the free surface effect,the error in terms of pressure peak is less than 5%if?_f?3.The violently expanding and collapsing bubble would drive the motion of a suspended object.On the contrary,the object's response may also strongly affect the bubble dynamics.Tranditionally,the so-named‘loose coupling'models,which means the output of one code is used either as a boundary condition or a loading condition for the other,are widely used.In this study,we have developed a fully coupled model by using an auxiliary function method to decouple the mutual interaction between the bubble load exerting on the object and the object's motion.Both axisymmetric and full 3D cases have been considered.When the radius of a suspended sphere is larger than the maximum radius of the bubble R_m,the relative error between the results obtained with the‘loose coupling'and our‘full coupling'models is about4%.However,the relative error increases rapidly when the sphere radius is smaller than R_m.When the bubble is initiated at a location very close to the sphere,the bubble surface would contact the object during the expansion phase,which would cause a stronger coupling effect and numerical instabilities.The‘coalescence technique'is proposed to handle this problem.Two experiments have been carried out for a spark-generated bubble interacting with a suspended sphere.For both cases,our numerical results of the bubble's shape and the sphere's displacement agree well with the experimental data.The effects of some dimensionless parameters on bubble dynamics and the pressure features on the suspended object surface have been investigated.At last,we have investigated the interaction between a bubble and a suspended cylinder with initial velocity.The influences of the relative position between bubble and object and the free surface on the physical process are also discussed.As for the interaction between a bubble and a deformable structure,we have developed a‘full coupling'algorithm to decouple the mutual dependence between bubble load and the structure's response,which improves the computational accuracy and stability.All the unknowns on bubble surface and structure response are solved simultaneously without the calculation of the pressure caused by bubble.Due to the change of the mass matrix in every time step,the commercial software is not suitable in this improved model.Thus a structural solver based on a finite element method is developed in present study.Finally,the interaction between a bubble and an elastic structure has been successfully simulated and the results have been carefully discussed.