Numerical Investigation Of Compressible Multi-phase Flows And Application

In the field of numerical simulating compressible multiphase flow,Cut-Cell method with free interface had been developed by Chang et al.(2013)[1],We base on this method and use the code called MuSiC~+,have researched Richtmyer-Meshkov insta-bility including gas-gas,gas-liquid and gas-solid cases,verified firstly that the growth rate of gas-liquid interface under a small distribution condition agree with the linear model presented by Yang et al.(1994)[2]in earlier stage,and is consistent with the nonlinear model presented by Zhang et al.(1996,1997)[3,4]in the later.Besides we simulated the microjet phenomenon which will have a widely application prospect to the no-needle injection technology,and by modifying Peters's model(2013)[5]a semiempirical formula about the relationship among the maximum velocity of microjet induced by shock wave,the initial contact angle,the intensity of shock wave and the radius of arc interface is obtained;by fitting numerical data,a formula which is suitable for high Mach cases is also obtained.During the implementation of the code MuSiC~+,the material interface is evolved by Level Set function,and the interface is described by cutting and merging about small cells.When the interfacial topological structure changes,this code is invalid.We inherit the idea of cut-cell in this code MuSiC~+,and refer to the method of interface processing which is presented by Hu et al.(2006)[6].By introducing the ghost fluid(Fedkiw et al.1999,2000,2001[7-9];Liu et al.2003,2005[10,11]),we present a real-ghost mixing method on the cut cell,this method can well simulated some multi-phase flows includ-ing the topological changes.The one dimension shock tube problem(Air-SF6 case,Air-Helium case,Water-Air case)is tested,by comparing with the analytical results we find the present numerical results are accurate;by simulating and studying various two dimensional cases(the Richtmyer-Meshkov interfacial instability about Air-SF6 and Air-Helium,Shock and bubble interaction problem about Air-Helium and Air-R22,two-dimensional cylindrical cavity collapse underwater,underwater explosion prob-lem.shock and water-column interaction problem),and comparing these results to ex-periment results and previous numerical results,it can be seen that the present numerical method is receivable.Using the MuSiC~+ code and CCGF code,RM instability of Air-Air medium is considered in detail.The figure of the interface evolution is shown,and the curve fig-ure of interfacial growth rate is provided.Besides,we analysis the reason to cause the oscillation of interfacial growth rate,and compare the present numerical result-s to the theoretical models(Linear model of Yang et al.,Nonlinear models(Zhang&Sohn(ZS)[12],Sadot et al.(SEA),Dimonte&Ramaprabhu(DR)[13])),and previous nu-merical ones(Holmes et al.[14,15],Ullah et al.[16]).By considering the growth rate with different initial amplitudes,we verify that these nonlinear models is consistent with present numerical results under the small disturbance;for initial big amplitude cases,DR model agrees with numerical result,but ZS model show a lower growth rate and SEA model have a higher calculation than DR model.In order to research the more complicated flow problem(the collision and pene-tration with different media droplets),We try to simulate this kind of problem by using a new way that included the MuSiC~+ code and the present numerical method.So far we have finished the conversion between the two kind numerical methods,and simu-late the bubble collapse induced by shock wave underwater by such way.It is seen this idea is feasible.Multi-interface problem which simulated with this two kind numerical methods simultaneously is the future work.