Development Of Cut-Cell Method And Dynamics Of Shock-Bubble Interactions

A new cut-cell method is proposed for compressible two-phase flow with large topology changes, and is applied to investigating the dynamics of shock induced bubble collapse in water. The results and conclusions are briefly given as follows:(1) A new cut-cell method for compressible two-phase flow is developed. A new strat-egy for formation of the unstructured cells is proposed to prevent the emergence of small cells when no merging strategy is used and this method can be easily used to simulate flows with large topology changes. A delayed reinitialization method is given to prevent the large error of pressure or density due to the non-physical interface moving caused by the traditional reinitiallization method when it is cou-pled with conservative cut-cell method. A variety of numerical examples have been used to validate the method, including the problem shock interaction with He bubble, shock interaction with SF6 bubble, shock induced bubble collapse and underwater explosion. These tests validate present method well.(2) The performance of three typical numerical methods for multiphase compressible flows, e.g. the cut-cell method, the modified ghost fluid method and the dif-fuse interface method are compared by numerical experiments. These numerical simulations include the Richtmyer-Meshkov instability of single mode, the shock interaction with a block of SF6 bubble, the Rayleigh collapse and shock-induced bubble collapse in water. The convergence order of the interface position, the conservation of mass, the capability to resolve the interfacial structures and the computational loads have been assessed.(3) We studied the collapse process of air bubble, which is initially attached to the rigid wall, under the impacting of initial strong plane shock. Three different modes are found. A phase diagram is given and shows the influences of the strength of the initial shock and the initial shape of the bubble. Typical wave structures and bubble evolution processes are analyzed. The effects of the incident shock and the initial bubble shape on the formation of different modes are discussed. Quantitative results are given to show the influences of the initial parameters on the maximum jet velocity, the pressure after the water-hammer shock, the max-imum wall pressure and the collapse time. We also compare the different results of the maximum wall pressure and the collapse time in axisymmetric collapse and two-dimensional collapse.(4) The cut-cell method is used to study the collapse process of two-dimensional elliptical bubble induced by the strong plane shock. Two typical modes are found. The influences of the incident shock Mach number and the elongation rate of the elliptical bubble on the formation of different modes are discussed. Different wave structures are found in the collapse of elliptical bubble compared with the spherical one, e.g. the lateral water hammer shock and the shocklets near the entrance and the exit of the jet. Explanations to the formation of the shocklets are given. The instability on the jet head, vorticity production and the circulation evolution are discussed too.