By loading Cross model and Oldroyd-B model with User-defined Function (UDF) program, a method to simulate the extrusion flow of viscoelastic non-Newtonian fluid in Fluent software was proposed. In the homogeneous solution of Polyethylene terephthalate (PET) and supercritical CO2, the microscopic bubble growth kinetics model was coupled with the Population Balance Module (PBM), analysis effect of shear rate on bubble nucleation and growth, numerically simulated of the nucleation and growth of bubbles in the extrusion die of PET microcellular foam sheet. Through analysis, the bubble size distribution is more uniform under the condition of 60° template convergence angle. The larger the extrusion speed, the wider the uniform distribution range of bubble density at the outlet position. The initial concentration of CO2 has the greatest impact on the bubble density. Increasing the initial concentration of CO2 can improve the bubble density, but appropriately reducing the initial concentration of CO2 can improve the effective distribution range of bubble density of foam sheet.

The numerical simulation length of the cassette model is determined by studying the effects of the cassette frame rotated alone and the rotated together with the agitator on mixing under different cassette lengths. The effects of different rotating speed, filling ratio of silicon particles, shape and number of agitators on the mixing characteristics of silicon particles in the cassette are studied when the outer frame of the cassette rotated alone and the cassette rotated together with the agitator. The mixing degree is quantitatively analyzed by particle trajectory, mixing index and rate, and the optimum working conditions of each influencing parameter are obtained. The results show that considering the computation time and the influence of the two motion modes on the mixing index and rate, the numerical simulation length of the cassette model is 115 mm. In order to obtain the best mixing effect and mixing speed, it is recommended that the rotating speed of the cassette is 8.91 rad/s, the filling rate is 23.60 %, and the shape of the agitator is rectangular and the number is 6. When the cassette and agitator rotate together, the filling rate has little effect on particle mixing. Considering the production efficiency, mixing effect and rate, as well as the stability of mixing, the recommended speed is 4.08 rad/s, the filling rate is 41.40 %, and the rectangular shape and number of six agitators are ideal choices.