聚合物发泡与挤出胀大过程数值模拟及实验研究
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摘要
当今世界经济发展的三大工业支柱是材料、能源和信息,没有材料工业的发展就没有现代技术的发展。随着社会经济技术的发展,塑料已发展成为在国民经济中与钢铁、木材、水泥三大传统材料并驾齐驱的重要材料,并在科学技术领域里发挥着越来越重要的作用,成为仪器仪表、交通运输、无线电、电讯器材及日用品生产不可缺少的新型材料。塑料制品的成型加工方法很多,例如注塑、挤出、吹塑、压延等等。其中挤出成型具有效率高、投资少、制造简便、可以实现连续化生产、占地面积小和环境清洁等优点而成为塑料制品的主要成型方法之一。挤出成型工艺和模具设计开发过程中,传统的经验设计和常规的实验方法已经不能很好地满足生产指导的需要,而随着计算机软硬件技术的发展以及计算流体力学理论的发展,数值模拟技术显示出了巨大优势,为工艺设计和模具优化提供了理论基础。
本文建立了挤出微孔发泡工艺中气泡在粘性不可压缩流体中非稳态等温长大的有限元模型,针对气泡长大过程进行数值模拟计算,获得了发泡过程中气泡压力和气泡尺寸的变化规律,并得到了聚合物熔体内发泡剂浓度场的分布规律。讨论了气泡长大的驱动力以及影响气泡长大的材料因素和工艺因素,预测了挤出微孔发泡过程中气泡长大规律,对挤出微孔发泡工艺具有一定的指导意义。在挤出微孔发泡工艺中,聚合物熔体离开口模后,气泡长大引起聚合物熔体膨胀,与此同时,聚合物熔体本身也存在挤出胀大现象,且聚合物熔体自身的挤出胀大对产品尺寸的影响不容忽视。针对聚合物挤出胀大过程,建立了不可压缩流体三维稳态等温流动的有限元模型,考虑了不同聚合物流变模型,对非牛顿流体挤出胀大过程进行了数值模拟,得到了聚合物熔体的速度分布规律,并获得了口模几何形状、材料参数以及工艺参数对挤出胀大率的影响规律。
以聚合物流变学和流体动力学理论为基础,建立了挤出微孔发泡工艺中气泡在非牛顿聚合物熔体内等温长大过程的几何模型和数学模型。利用伽辽金加权余量法离散控制方程,并通过高斯积分变换获得数值计算的有限元方程。由于气泡长大过程时间短,长大速度快,发泡剂浓度梯度急剧增加,增加了数学求解的困难,数值结果振荡严重。针对以上情况,对控制方程进行无量纲化处理,有效提高了数值计算稳定性。
基于有限元模拟技术,对挤出微孔发泡工艺中气泡长大过程进行数值模拟,研究了气泡在非牛顿聚合物熔体内的等温长大过程。分析了挤出微孔发泡工艺中气泡长大的动力来源,获得了气泡压力和气泡半径随时间的变化规律,研究了气液界面处发泡剂浓度梯度以及“细胞”内外壁处发泡剂浓度的变化规律。讨论了几何模型(气泡初始半径以及“细胞”外径尺寸)、材料参数(零剪切粘度、扩散系数、亨利常数以及表面张力系数)以及工艺参数(发泡温度和气泡压力)对气泡长大过程的影响。
以流体力学有限元理论为基础,建立了粘性不可压缩流体挤出胀大的有限元模型。采用罚函数法将连续性方程代入动量方程,从而避免了对压力项直接求解,减少了同时计算的变量数,有效提高了计算效率。挤出胀大问题的求解困难在于聚合物胀大部分的自由表面位置是事先未知的,给数值求解额外增加了非线性。本文采用解耦合方法求解自由胀大表面位置,先假设一个自由表面的位置,利用流线方程更新自由表面节点坐标从而得到真实表面位置。考虑聚合物熔体的非牛顿特性,采用幂律本构流变模型,针对常见的正方形口模进行挤出胀大过程的数值模拟。引入的罚数是一个不确定量,通过系统地数值计算获得罚数的最佳取值。分析了聚合物熔体离开口模后的速度分布规律,探讨了非牛顿流体挤出胀大现象的产生机理。同时研究了体积流量对挤出胀大率的影响。讨论了相同体积流量和相同口模截面面积的情况下口模截面形状对挤出胀大率的影响。
粘弹性是聚合物熔体的一种重要特性,在实际加工生产中,对塑料产品的形状及尺寸具有较大影响。本文采用PTT本构方程,充分考虑聚合物熔体的粘弹特性,建立了粘弹流体的挤出胀大有限元数学模型。通过引入参考粘度对动量方程进行了椭圆化处理,提高了方程求解的稳定性。采用Streamline Upwind/Petrov-Galerkin formulation(SUPG)方法构造非对称权函数,克服了本构方程对流项占优时导致的数值解的振荡。针对圆环截面及椭环截面口模的挤出胀大过程进行数值模拟。针对圆环口模,分析了聚合物熔体内外边界处第一法向应力差的分布规律。在口模外径尺寸相同的情况下,选取了不同的口模内外径比例,分析了相同体积流量下,口模尺寸对挤出胀大率的影响。讨论了体积流量对挤出胀大率的影响规律。针对椭环形口模,研究了与材料本身性质有关的零剪切粘度、松弛时间以及拉伸参数对挤出胀大率的影响,同时也考虑了体积流量对挤出胀大率的影响。
采用能够精确控制工艺参数的间歇法发泡工艺中的快速降压法,以实验中常用的聚苯乙烯为基体,超临界CO_2为发泡剂进行了微孔发泡实验研究。通过饱和吸收/解吸实验获得了发泡剂扩散系数和亨利常数;采用毛细管流变仪测定了150℃下纯聚苯乙烯的粘度;利用WLF方程计算得到实验条件下PS/CO_2均相体系的粘度;采用专业图像分析软件Image-Pro Plus对发泡样品的SEM照片进行统计计算,获得泡孔密度和泡孔平均直径。根据间歇法发泡实验获得的结果,得到了相同温度下压力对发泡工艺过程的影响规律。通过饱和吸收/解吸实验结果,获得了压力对气体在聚合物里的溶解度的影响。同时采用实验获得的材料参数与工艺参数进行了相应的有限元数值模拟,对比了模拟结果与实验结果。
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 CO_2 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/CO_2 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.
本文建立了挤出微孔发泡工艺中气泡在粘性不可压缩流体中非稳态等温长大的有限元模型,针对气泡长大过程进行数值模拟计算,获得了发泡过程中气泡压力和气泡尺寸的变化规律,并得到了聚合物熔体内发泡剂浓度场的分布规律。讨论了气泡长大的驱动力以及影响气泡长大的材料因素和工艺因素,预测了挤出微孔发泡过程中气泡长大规律,对挤出微孔发泡工艺具有一定的指导意义。在挤出微孔发泡工艺中,聚合物熔体离开口模后,气泡长大引起聚合物熔体膨胀,与此同时,聚合物熔体本身也存在挤出胀大现象,且聚合物熔体自身的挤出胀大对产品尺寸的影响不容忽视。针对聚合物挤出胀大过程,建立了不可压缩流体三维稳态等温流动的有限元模型,考虑了不同聚合物流变模型,对非牛顿流体挤出胀大过程进行了数值模拟,得到了聚合物熔体的速度分布规律,并获得了口模几何形状、材料参数以及工艺参数对挤出胀大率的影响规律。
以聚合物流变学和流体动力学理论为基础,建立了挤出微孔发泡工艺中气泡在非牛顿聚合物熔体内等温长大过程的几何模型和数学模型。利用伽辽金加权余量法离散控制方程,并通过高斯积分变换获得数值计算的有限元方程。由于气泡长大过程时间短,长大速度快,发泡剂浓度梯度急剧增加,增加了数学求解的困难,数值结果振荡严重。针对以上情况,对控制方程进行无量纲化处理,有效提高了数值计算稳定性。
基于有限元模拟技术,对挤出微孔发泡工艺中气泡长大过程进行数值模拟,研究了气泡在非牛顿聚合物熔体内的等温长大过程。分析了挤出微孔发泡工艺中气泡长大的动力来源,获得了气泡压力和气泡半径随时间的变化规律,研究了气液界面处发泡剂浓度梯度以及“细胞”内外壁处发泡剂浓度的变化规律。讨论了几何模型(气泡初始半径以及“细胞”外径尺寸)、材料参数(零剪切粘度、扩散系数、亨利常数以及表面张力系数)以及工艺参数(发泡温度和气泡压力)对气泡长大过程的影响。
以流体力学有限元理论为基础,建立了粘性不可压缩流体挤出胀大的有限元模型。采用罚函数法将连续性方程代入动量方程,从而避免了对压力项直接求解,减少了同时计算的变量数,有效提高了计算效率。挤出胀大问题的求解困难在于聚合物胀大部分的自由表面位置是事先未知的,给数值求解额外增加了非线性。本文采用解耦合方法求解自由胀大表面位置,先假设一个自由表面的位置,利用流线方程更新自由表面节点坐标从而得到真实表面位置。考虑聚合物熔体的非牛顿特性,采用幂律本构流变模型,针对常见的正方形口模进行挤出胀大过程的数值模拟。引入的罚数是一个不确定量,通过系统地数值计算获得罚数的最佳取值。分析了聚合物熔体离开口模后的速度分布规律,探讨了非牛顿流体挤出胀大现象的产生机理。同时研究了体积流量对挤出胀大率的影响。讨论了相同体积流量和相同口模截面面积的情况下口模截面形状对挤出胀大率的影响。
粘弹性是聚合物熔体的一种重要特性,在实际加工生产中,对塑料产品的形状及尺寸具有较大影响。本文采用PTT本构方程,充分考虑聚合物熔体的粘弹特性,建立了粘弹流体的挤出胀大有限元数学模型。通过引入参考粘度对动量方程进行了椭圆化处理,提高了方程求解的稳定性。采用Streamline Upwind/Petrov-Galerkin formulation(SUPG)方法构造非对称权函数,克服了本构方程对流项占优时导致的数值解的振荡。针对圆环截面及椭环截面口模的挤出胀大过程进行数值模拟。针对圆环口模,分析了聚合物熔体内外边界处第一法向应力差的分布规律。在口模外径尺寸相同的情况下,选取了不同的口模内外径比例,分析了相同体积流量下,口模尺寸对挤出胀大率的影响。讨论了体积流量对挤出胀大率的影响规律。针对椭环形口模,研究了与材料本身性质有关的零剪切粘度、松弛时间以及拉伸参数对挤出胀大率的影响,同时也考虑了体积流量对挤出胀大率的影响。
采用能够精确控制工艺参数的间歇法发泡工艺中的快速降压法,以实验中常用的聚苯乙烯为基体,超临界CO_2为发泡剂进行了微孔发泡实验研究。通过饱和吸收/解吸实验获得了发泡剂扩散系数和亨利常数;采用毛细管流变仪测定了150℃下纯聚苯乙烯的粘度;利用WLF方程计算得到实验条件下PS/CO_2均相体系的粘度;采用专业图像分析软件Image-Pro Plus对发泡样品的SEM照片进行统计计算,获得泡孔密度和泡孔平均直径。根据间歇法发泡实验获得的结果,得到了相同温度下压力对发泡工艺过程的影响规律。通过饱和吸收/解吸实验结果,获得了压力对气体在聚合物里的溶解度的影响。同时采用实验获得的材料参数与工艺参数进行了相应的有限元数值模拟,对比了模拟结果与实验结果。
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 CO_2 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/CO_2 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.
引文
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