Conservative Sharp Interface Method And Shock-induced Dynamics Of Droplet Containing A Bubble

Compressible multi-phase flow phenomenon not only involves a large number of natural phenomena and engineering applications,but also is a key basic scientific prob-lem of fluid mechanics.In this thesis,a conservative sharp interface method for sim-ulation of compressible multi-phase flow is developed,and based on this method,two typical compressible multi-phase flow problems were studied.The main work content and research conclusions are as follows:(1)Combining the cut cell method and the finite volume method under the frame-work of Arbitrary Lagrangian-Eulerian(ALE),a numerical method for conserva-tive sharp interface suitable for simulating 2D and 3D compressible multi-phase flow is proposed.Based on the Cartesian cell,first use the cut cell reconstruction-assembly technique to generate unstructured cells near the interface in which the cell boundary coincides with the interface all the time,and keep the structural Cartesian cell away from the interface;conservative Euler equations characterizing fluid motion are discretized into finite volume equations under the ALE framework and numerically solved.Using the symmetry and rotational symmetry of the fluid position in the cut cell,the complexity of unstructured cell generation is signif-icantly reduced;at the same time,compared with the previous two-dimensional method(Lin et al.,2017),the new cell assembly technique is effective avoid the appearance of large size unstructured cells,thereby improving the resolution of the interface.The accuracy and robustness of this method are verified by simulating several typical compressible two-phase flow problems.(2)We numerically studied the problem of shock impact bubble-containing droplets near rigid wall.Three configurations,i.e.concentricity,left eccentricity and right eccentricity are mainly investigated.Specifically,we divided the dynamic process into three stages.In the early stage,the droplet has not deformed significantly.The generation and propagation of the zigzag waves in the droplet and the in-duced waves are the main flow characteristics at this stage.We found that the zigzag waves consisted of alternating periodic compression waves and expansion waves in the droplet,and induced ripple-like compression waves with the same period in the bubble.In the intermediate stage,Under the continuous pressure difference between the high pressure of the air flow and the low pressure in the bubble,the upstream and downstream liquid layers accelerate each other and the droplets squeeze and deform rapidly.Because the acceleration of the liquid layer is inversely proportional to the thickness of the liquid layer,the upstream liq?uid layer movement in the three configurations of left eccentricity,concentricity and right eccentricity becomes faster and the deformation becomes larger in turn,while the downstream liquid layer is the opposite.In the late stage of evolution,the upstream and downstream liquid layers collided towards each other,produc-ing water hammer shock waves and rebound jets.The difference in the thickness and velocity of the liquid layer during the impact caused the diversification of the rebound jet directions.(3)We numerically studied the problem of shock impact bubble-containing droplets near attached to rigid wall.Three configurations,i.e.pure droplets,concentric bubble-containing droplets and eccentric bubble-containing droplets,are consid-ered.In the pure droplet configuration,pressure wave propagation within droplet,variation of droplet energy with time and the dynamic process of droplet interface evolution are mainly studied.We found that the pressure wave in the droplet re-peatedly hits and reflects between the droplet interface and the wall surface,and alternately generates compression waves and expansion waves,which periodically propagate back and forth in the droplet and induce the periodicity of the energy-in the droplet.The fluid near the stagnation point of the droplet on the windward side and the stagnation point of the wall surface is gradually depressed toward the center of the droplet due to the squeezing effect of the continuous high-pressure air flow.In the concentric configuration,a comparative study was carried out by changing the initial radius of the bubble.The propagation of the collapse pressure wave in the droplet,the propagation of the pulse compression wave in the gas flow,the vibration of the bubble volume,and the energy fluctuation of the droplet were revealed.We find that the kinetic energy of the droplet when the bubble collapses to the minimum for the first time has a linear relationship with the initial volume of the bubble.The larger the kinetic energy of the droplet,the more intense the bubble collapse.The extremely high pressure caused by the collapse of the bubble induces a high-strength collapse pressure wave in the droplet.Its periodic propagation in the droplet is similar to the pure droplet configuration.Not only that,the collapse pressure wave also induces the sub-frequency vibration of the bubble volume and the pulse compression wave.In the eccentric configuration,keeping the volume of the bubble unchanged and changing the eccentric distance for comparative study,we found that the smaller the eccentric distance,the larg-er the kinetic energy of the droplet when the bubble collapses to the minimum for the first time,so the more intense the bubble collapse,the higher maximum wall pressure;we also found that when the bubble eccentric distance is large and the upstream liquid layer is thin,a reverse jet will be generated upstream of the droplet.