Numerical Simulation Of Batch Microfoaming Process Of Polymer

Microcellular foaming materials are widely used in aerospace,biomedicine,sanitary environment etc because of their features of light weight,heat insulation,sound insulation,impact resistance and so on.With the continuous extend of its application field,the research of micro-foaming technology is increasingly focused.the nucleation and growth of cell are two key problems in micro-foaming process,it is of great significance to investigate the factors that affect the cell density and size of microfoams to improve the structure and properties of microfoamed products.In this paper,a mathematical model for the nucleation and bubble growth of batch microfoaming was established based on the classical nucleation theory and cell model of cell growth,and the numerical simulation of the batch microfoaming process was implemented using the four order Runge-Kutta method on the matlab platform.The graphical user interface was designed and developed,,and the program was encapsulated based on the hybrid programming technology of matlab and C language.An executable program was compiled and can be executed independently.Meanwhile,a dynamic link library was encapsulated for cal of the simulation program of the subsequent extrusion micro foaming process developed using C.language.The main works and conclusions are as following:(1)Mathematical model establishment of batch micro foaming process.The goverment equations for the nucleation and bubble growth of batch microfoaming was established based on the classical nucleation theory and the cell model hypothesis of bubble growth,and the equations include: equation of Blander-Katz bubble nucleation rate,the mass equilibrium equation of gas passing through the boundary of bubble pore,and the convection diffusion equation of gas,the governing equations of conservation of momentum of polymer melts and gas mixtures around bubbles.Combined with the constitutive equation of the power law model of viscous fluid,the mathematical model of bubble nucleation and growth was established.Further,the coupling relationship between nucleation and growth process was established based on the analysis of bubble nucleation and growth process.The functional relation of the variations.(2)Numerical simulation implement of the batch microfoaming process.The coupling calculation of bubble nucleation and growth process of the batch microfoaming process was implemented using the four order Runge-Kutta method on the matlab platform based on the coupling relationship of bubble nucleation and growth process,and the nucleation number,cell radius,bubble pressure at different times and evolution of microbubble morphology were obtained.The influence of different pressure relief functions on nucleation and growth process is analyzed using numerical example.The results indicated that,the instant of nucleation beginning is late under the linear pressure relief process,and the pressure rate is faster after the nucleation point,and the later pressure relif rate is faster,which makes the high cell density that inhibiting the growth of the bubble hole,thus the microporous foam material with larger cell density and smaller size of the cell was obtained,and on the basis of linear pressure relief.The cell size decrease and the cell density increase with the pressure relief rate increasing.(3)Development of graphic interface.For the convenience of users,a simple and convenient graphical user interface system has been established using the user graphical interface(GUI)technology of matlab.The design of the system is based on the core calculation program of micro foaming,and the functions of construction of engineering documents,data input and storage,the numerical calculation of micro foaming,and the graphical input of the results were established.The function of graphic output and so on.Convenient operation mode can be provided through visual graphical user interface system.(4)The encapsulation of the simulation program.For the sake of secrecy of the program and facilitate in the development of the subsequent extrusion micro foaming numerical simulation software,the main program of numerical computation written by matlab was complimed into an independent executable execution file using the compiler(MCR)based on the hybrid programming technology of matlab and C language,and the dynamics link library file for the call of C language on the VC++ platform was also estabished.The encapsulation of matlab program was implement,and provide the functions which can be called by subsequent programs developed by C language.