Numerical Simulation And Experimental Study Of Polymer Foaming And Extrudate Swell Process

The material,energy and information are the mainstay industries in the world's economic development today.Modern technology can't develop well without the development of material industry.With the development of social economy and technology,the plastics has become as important as the three traditional materials i.e.the steel,wood and the cement in national economy, and plays a significant role in scientific and technological fields.The plastics prove to be indispensable new materials in the production of instruments and meters,transport and communication trade,wireless,communication telephone and articles of everyday use.There are many methods that can be used to form plastics,for instant,injection,extrusion,blow molding,rolling etc.,among which the extrusion is one of the most widely-used methods as it has several merits such as high efficiency,less investment,applicability in manufacturing and continuous production,less space occupation and environmental cleaning etc.Conventional empirical design and routine experiments can not direct production well any more,while computer aided engineering has great advantages in providing the theoretical foundation for technological design and die optimization,due to the development of computer hardware and software technology,as well as the theories of computational fluid dynamics theory.A finite element model was established to analyze the growth of bubble in viscous incompressible fluid.The growth process of bubble in extrusion foaming technology was simulated,presenting the regularity of bubble pressure and bubble radius as well as that of the foaming agent concentration distribution. The driving force of bubble growth and effects of materials and technological factors on bubble growth were discussed,predicting the regularity of bubble growth.The bubble growth leads to an expansion process after the polymer flows out of the die in extrusion foaming process.Meanwhile,extrudate swell is a common phenomenon for polymer itself and its effect on product size can't be ignored.Aiming at the extrudate swell phenomenon in extrusion foaming process,a finite element model of three-dimensional incompressible fluid isothermal steady flow was also created.Considering different rheological models,the extrudate swell of non-Newtonian fluid,as well as the influences of die geometry,material parameters and technological parameters on extrudate swell ratio were discussed.Based on the theories of polymer rheology and fluid dynamics,this thesis established the geometrical and mathematical models for bubble growth in isothermal non-Newtonian polymer melt,and obtained the finite elemental model by Gaussian integral transformation.Due to the rapidity of bubble growth, the concentration of foaming agent increases drastically which leads to solving difficulty and oscillation of results.As a reslut,controlling equations were nondimensionalized to improve their numerical stability currently.Based on the finite element method,the bubble growth in extrusion foaming process was simulated,investigating the bubble growth in isothermal non-Newtonian polymer melt.The driving force of bubble growth was studied and variation tendency of bubble pressure and bubble radius were analyzed. Concentration gradient of foaming agent on the gas-liquid interface and that on both inside and outside wall of the "cell" were obtained.The effects of geometry model(initial bubble radius and outer radius of the "cell"),material parameters (zero-shear viscosity,confusion coefficient,Henry's constant and surface tension coefficient) and technological parameters(foaming temperature and initial pressure) on bubble growth were discussed in details.Finite elemental model of extrudate swell in viscous incompressible fluid was obtained based on the theory of finite element theory in fluid mechanics. In order to avoid solving pressure directly,continuity equations were substituted into momentum equation by penalty finite element method,and this reduced the number of variables calculated simultaneously,leading to the improvement of the computational efficiency.The difficulty in the solving of extrudate swell lay in the fact that the free surface is unknown,which introduces non-linearity in the solving process.Presently,a contour of the free surface is assumed,and the streamline equations were adopted to update the free surface to obtain the real free surface.Taking non-Newtonian viscosity behavior into consideration,numerical simulation was conducted for square shaped die with power law constitutive model.Optimal penalty number was fixed by a serial of numerical calculations.The velocity field distribution of polymer melt out of the die was analyzed and the mechanism of extrudate swell of non-Newtonian polymer was discussed furthermore.The effect of volumetric flow rate on extrudate swell ratio was considered.In addition,the effect of die shape on extrudate swell ratio was discussed with the same volumetric flow rate and cross sectional area.Viscoelasticity is a key property for polymer melt and its effect on geometry and dimension of product in production and processing can't be neglected.Considering the characteristic of viscoelasticity for polymer melt, PTT constitutive equation was adopted in this dissertation.A finite element mathematical model was developed to simulate extrudate swell of viscoelastic fluid.Reference viscosity was introduced to improve the ellipticity of the momentum equation and the solving stability.Asymmetric weight function was constructed by Streamline Upwind/Petrov-Galerkin formulation method,in order to overcome unstability in solving caused by dominant convective term in constitutive equation.Extrudate swell in annular and elliptical ring dies were simulated respectively.For annular die,the distribution of first normal-stress difference on both inner and outer boundaries of polymer melt was obtained,and the effect of die dimension and volumetric flow rate on extrudate swell ratio was analyzed.For elliptical ring die,the effects of zero-shear viscosity,relax time, extensograph parameter and volumetric flow rate on extrudate swell ratio were studied. Microcellular foaming experiment with batch method was carried out using polystyrene as matrix and CO₂ as foaming agent.Confusion coefficient and Henry's constant were obtained by saturated absorption/desorption experiments.Viscosity of pure polystyrene was measured by capillary rheometer at the temperature of 150℃.The viscosity of PS/CO₂ homogeneous system was calculated with WLF equation.With the professional image analysis software Image-Pro Plus,cell density and cell diameter was calculated statistically according to SEM photograph of foaming plastic sample.The experimental results with batch method revealed the effect of pressure on foaming processing at the same temperature.While the infulence of pressure on the solubility of the gases in polymer was demonstrated by the results of saturated absorption/desorption experiments.Simulation was carried out with the parameters obtained by experiment,and the results of simulation and experiment were compared.