自由基反应挤出过程的数值模拟与优化设计
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摘要
反应挤出技术是化学反应与挤出成型相集成的高新技术。以螺杆挤出机作为反应器,反应物和完成反应所必需的引发剂、催化剂等在连续挤出过程中完成预定的化学反应,合成为期望的聚合物,然后通过在挤出机机头安装的口模成型得到相应制品。因周期短、生产连续、能耗低、环境污染小等诸多优点受到国内外的广泛关注,具有良好的发展前景。
反应挤出过程是物理流动、化学反应、传热与传质并存且相互影响的复杂过程,体系通常处于非等温、非等压和高剪切速率的复杂外场条件下,此外,反应挤出本身还存在一些特殊的工艺要求,如较高的反应速率、满足热传导条件、较高的转化率等,很难用经典反应器理论方法对现场工艺进行定量、实时研究与控制。解决上述问题的有效方法之一是开展反应挤出过程的数值模拟与优化设计,定量揭示化学反应对于高分子材料结构和物理化学性能的影响规律,进而优化设计反应器结构、材料组分和反应加工条件,扩大反应挤出技术的应用范围。可见,本课题具有重要的科学意义,并且具有广阔的工程应用前景。
通常的数值模拟采用一维的沿螺槽轴向展开的反应器模型,在模拟过程中一般简化处理各种因素之间的耦合作用,基本不涉及高分子材料物理化学性能的动态演变规律的分析、材料组分和反应加工条件的优化设计等内容。本文以自由基聚合及接枝改性体系作为研究对象,综合应用机械科学、高分子化学与物理、高分子反应统计理论、计算流体力学、工程优化与软件工程等学科知识,从宏观尺度模拟反应挤出过程的化学流变行为,建立材料配方、反应加工条件、材料微观结构与宏观性质之间的函数关系;采用半隐式、解耦合的数值逼近方法,解决在复杂的化学与物理条件下:众多场变量之间的相互耦合问题;自主开发数值模拟与优化设计系统的核心程序,定量预测反应挤出场量的演变,并辅助选择反应器结构和工艺操作参数,使反应挤出过程实现可控化、最优化。
主要工作与结论如下:
双螺杆挤出机结构复杂,流体在流道内发生复杂的物理和化学变化,导致难以按照真实的挤出机结构与工况模拟其内部的复杂流变。本文根据紧密啮合同向旋转双螺杆挤出机的几何结构和运动特点,将每一个顺螺槽料流的流道沿螺槽轴向展开,分析得到展开长度、横截面宽度、深度与横截面面积等特征参数的计算式,在此基础上,忽略物料在两螺杆间传递的非主流运动,同时对模型截面形状进行简化处理,建立了等效的轴对称反应器模型。将实际生产过程中的边界工况,即螺杆转动对流体的拖曳,以及机筒静止对流体的阻碍,等效处理为流道模型全部周壁通过作轴向移动对流道内的流体进行拖曳,同时假定流道模型处于全充满状态,为整个反应挤出过程的数值模拟提供了空间模型。
结合上述空间模型,给出了反应挤出过程的化学反应场、材料结构场与化学流变场的基本控制方程:根据自由基反应动力学理论,构建了自由基均聚及接枝反应的动力学模型,得到了反应速率、单体浓度、单体转化率、引发剂浓度的计算式;根据高分子反应统计理论,考虑相对分子质量三层意义上的统计平均——瞬时生成的聚合物平均相对分子质量、考虑了历史累积效应的聚合物平均相对分子质量与同时考虑反应物和产物的整个材料体系的平均相对分子质量——构建了每个层次数均、重均相对分子质量的计算式;给出了黏性不可压缩流体流动过程的连续性方程、运动方程和边界条件;根据高分子物理学,建立了反应体系的零剪切黏度、表观黏度与工艺条件、材料结构的关系式。
应用控制容积积分法(Control Volume Integration)导出了对流—扩散方程的离散表达式,引入交错网格技术与SIMPLE算法,实现了耦合的压力场与速度场的分离式求解,推导得到了流体的流动速度、压力等物理量的数值计算式;采用向后差分方法和增量方法,实现了化学反应场、材料结构场、化学流变场控制方程的离散,获得了反应转化率、聚合物平均相对分子质量、流体黏度等物理量的数值计算式。
采用半隐式、解耦合的数值逼近方法,解决了在复杂的化学与物理条件下众多场变量之间的相互耦合问题,开发了自由基聚合反应挤出过程数值模拟的核心程序和自由基接枝反应挤出过程数值模拟的核心程序。在给定的初始条件和边界条件下,实现了连续性方程、动量方程、化学反应动力学方程、平均相对分子质量计算式与化学流变本构方程的数值求解。
运行自由基聚合反应挤出过程的数值模拟程序,模拟了甲基丙烯酸正丁酯的反应挤出过程,获得了单体转化率、聚合物平均相对分子质量、流体表观黏度等场变量的演变情况,单体转化率的模拟结果与实验结果吻合一致。讨论了凝胶效应及流率对反应挤出场量的影响,分析了在聚合反应挤出过程中调控高分子材料结构与流变性质的规律,为设备参数与工艺操作参数的选择提供了理论依据。
运行自由基接枝反应挤出过程的数值模拟程序,模拟了乙烯基硅烷、丙烯酸及甲基丙烯酸甲酯接枝聚乙烯的反应挤出过程。获得了接枝度、均聚物质量分数、平均相对分子质量与材料黏度等场变量的动态演变情况,模拟结果与实验结果基本吻合。讨论了材料组成与工艺参数对接枝行为的影响规律,分析了提高接枝度与接枝效率的有效方法。
在数值模拟基础上,开展了反应挤出过程的优化设计研究。以反应挤出过程的有限容积模拟作为目标函数求解方法,以遗传算法作为搜索寻优方法,开发了反应挤出过程的优化设计系统。针对自由基聚合反应挤出过程,建立了面向单体转化率限制和/或反应效率的单目标和多目标优化模型,实现了螺杆几何参数和工艺操作参数的按需设计。
The reactive extrusion (REX) process is a new kind of polymer processing technology that integrates the chemical reaction and extrusion processing. Using twin-screw extruders as reactors, the reactants and other essential additives such as initiators and catalysts react to synthesize the expected polymers during the continuous extrusion process, and then products can be directly formed via the extrusion die. It has great prospects and has drawn wide attentions at home and abroad in its advantages such as the short periods, continuous production, low energy consumption and little environmental pollution.
In REX processes, the fluid flow, chemical reaction, heat transfer and mass transfer coexist and interact with each other. The physical and chemical changes are usually performed under nonisothermal, non-constant pressure and high shear rate conditions. In addition, there exist some special technological requirements such as the high reaction rate, good heat transfer ability and high conversion ratio. So it is difficult to carry out quantitative and in-situ investigations by means of the classical reactor theory. Researches involving the numerical simulation and optimization design can be used as one of the effective methods to solve the aforementioned problems, on the basis of which the effects of the chemical reaction on the material structures and physicochemical properties can be quantitatively studied, the reactor structure, material compositions and reactive processing conditions can be optimized, and then the application range of REX can be enlarged. To sum up, this project has an important scientific meaning and a good prospect of engineering application.
The existing theoretical investigations have been mainly confined to one-dimensional (1D) models and have generally simplified the intercoupling relations among variables involved in fluid flow, chemical reaction, material structures, physicochemical properties. And the optimization design of material composition and processing conditions are seldom studied. In this paper, using such disciplines as mechanical science, polymer chemistry, polymer physics, statistical theory of polymeric reactions, computational fluid dynamics, engineering optimization and software engineering, the chemorheological behaviors of REX processes for the free radical polymerization and free radical grafting modification were simulated in a macroscale. The functional relationships among the material compositions, reactive processing conditions, material microstructure and macroscopic properties were constructed. The intercoupling relations among the considerable field variables were solved by an uncoupled semi-implicit iterative algorithm. At the aim of making REX process controllable and optimal, the core programs for systems of numerical simulation and optimization design were developed to predict the evolution of field variables and select the optimum reactor structure and processing conditions.
The main contents and conclusions were as follows:
The configuration of the twin screw extruder is complex and the fluid undergoes complicated physical and chemical changes, which make it very difficult to perform the rheological simulation based on real reactor configurations and working conditions. According to the geometrical structure and movement characteristics of closely intermeshing co-rotating twin screw extruders, the flow space of each fluid were unfolded along the axial direction of the screw channel, and then the expressions involving characteristic parameters such as the unfold length, the width, depth and area of the cross section were derived. Neglecting the non-mainstream flow from one screw to the other and simplifying the shape of the cross section, an equivalent axisymmetric reactor model was established. The reactor model is assumed to be fully filled and its wall moves along the axial direction at a velocity equivalent to the comprehensive effect of the rotary screws and the static barrel on the fluid flow. Thus, the space model for the numerical simulation was constructed.
Combining with the aforementioned space model, the basic governing equations describing fields of chemical reaction, material structure and chemorheology were constructed. Based on the free radical reaction kinetics, kinetic models of the free radical polymerization and grafting were constructed, and expressions of reaction rate, monomer concentration, monomer conversion and initiator concentration were deduced. According to the statistical theory of polymeric reactions, the average molecular weight can be divided in three hierarchies: the first is that of polymer chains instantaneously produced, the second is that of polymer chains considering the cumulative effect and the third is that of the fluid with both the reactant and the production taken into account. Expressions of the number-average molecular weight and weight-average molecular weight for each hierarchy were constructed. The continuity equation, the momentum equation as well as the initial and bondary conditions were derived to describe the viscous incompressible fluid flow process. On the basis of polymer physics, expressions of zero shear viscosity and apparent viscosity related to processing conditions and material structures were built.
The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.
An uncoupled semi-implicit iterative algorithm was proposed to deal with the complicated relationships among the considerable field variables. Core programs for the numerical simulations of REX processes for the free radical polymerization and free radical grafting were developed. The continuity equation, the momentum equation, the chemical reaction kinetic equation, the average molecular weight and the constitutive equation can be solved numerically under the given initial and boundary conditions.
Runing the program for the numerical simulation of REX processes for the free radical polymerization, the evolutions of field variables such as monomer conversion, average molecular weight and apparent viscosity were predicted for the example of butyl methacrylate. The simulated result of the monomer conversion is in agreement with the experimental result. The influences of the gel effect and throughput on field variables were discussed. The analyses give laws controlling the materical structure and rheological properties and offer reliance to choose screw configuration and processing conditions.
Runing the program for the numerical simulation of REX processes for the free radical grafting, the evolutions of field variables such as grafting degree, mass fraction of homopolymer, average molecular weight and apparent viscosity were predicted for examples of polyethylene grafting with vinylsilicane, acrylic acid and methyl methacrylate. The simulated results are in agreement with the experimental results. The influences of the material compostion and processing conditions on grafting behaviors were discussed to search effective methods to increase the grafting degree and grafting efficiency.
The optimization design was carried out on the basis of the numerical simulation. The finite volume simulation of REX processes was used to solve objective functions, and the genetic algorithm was introduced to search optimum parameters, on the basis of which a new optimization system of REX processes was established. The single object and multi-object optimization models faced to the restriction of monomer conversion and the reaction efficiency for REX processes of the free radical polymerization were constructed respectivelly. The optimum screw geometric parameters and operating parameters can be obtained according to the pre-specified objectives.
反应挤出过程是物理流动、化学反应、传热与传质并存且相互影响的复杂过程,体系通常处于非等温、非等压和高剪切速率的复杂外场条件下,此外,反应挤出本身还存在一些特殊的工艺要求,如较高的反应速率、满足热传导条件、较高的转化率等,很难用经典反应器理论方法对现场工艺进行定量、实时研究与控制。解决上述问题的有效方法之一是开展反应挤出过程的数值模拟与优化设计,定量揭示化学反应对于高分子材料结构和物理化学性能的影响规律,进而优化设计反应器结构、材料组分和反应加工条件,扩大反应挤出技术的应用范围。可见,本课题具有重要的科学意义,并且具有广阔的工程应用前景。
通常的数值模拟采用一维的沿螺槽轴向展开的反应器模型,在模拟过程中一般简化处理各种因素之间的耦合作用,基本不涉及高分子材料物理化学性能的动态演变规律的分析、材料组分和反应加工条件的优化设计等内容。本文以自由基聚合及接枝改性体系作为研究对象,综合应用机械科学、高分子化学与物理、高分子反应统计理论、计算流体力学、工程优化与软件工程等学科知识,从宏观尺度模拟反应挤出过程的化学流变行为,建立材料配方、反应加工条件、材料微观结构与宏观性质之间的函数关系;采用半隐式、解耦合的数值逼近方法,解决在复杂的化学与物理条件下:众多场变量之间的相互耦合问题;自主开发数值模拟与优化设计系统的核心程序,定量预测反应挤出场量的演变,并辅助选择反应器结构和工艺操作参数,使反应挤出过程实现可控化、最优化。
主要工作与结论如下:
双螺杆挤出机结构复杂,流体在流道内发生复杂的物理和化学变化,导致难以按照真实的挤出机结构与工况模拟其内部的复杂流变。本文根据紧密啮合同向旋转双螺杆挤出机的几何结构和运动特点,将每一个顺螺槽料流的流道沿螺槽轴向展开,分析得到展开长度、横截面宽度、深度与横截面面积等特征参数的计算式,在此基础上,忽略物料在两螺杆间传递的非主流运动,同时对模型截面形状进行简化处理,建立了等效的轴对称反应器模型。将实际生产过程中的边界工况,即螺杆转动对流体的拖曳,以及机筒静止对流体的阻碍,等效处理为流道模型全部周壁通过作轴向移动对流道内的流体进行拖曳,同时假定流道模型处于全充满状态,为整个反应挤出过程的数值模拟提供了空间模型。
结合上述空间模型,给出了反应挤出过程的化学反应场、材料结构场与化学流变场的基本控制方程:根据自由基反应动力学理论,构建了自由基均聚及接枝反应的动力学模型,得到了反应速率、单体浓度、单体转化率、引发剂浓度的计算式;根据高分子反应统计理论,考虑相对分子质量三层意义上的统计平均——瞬时生成的聚合物平均相对分子质量、考虑了历史累积效应的聚合物平均相对分子质量与同时考虑反应物和产物的整个材料体系的平均相对分子质量——构建了每个层次数均、重均相对分子质量的计算式;给出了黏性不可压缩流体流动过程的连续性方程、运动方程和边界条件;根据高分子物理学,建立了反应体系的零剪切黏度、表观黏度与工艺条件、材料结构的关系式。
应用控制容积积分法(Control Volume Integration)导出了对流—扩散方程的离散表达式,引入交错网格技术与SIMPLE算法,实现了耦合的压力场与速度场的分离式求解,推导得到了流体的流动速度、压力等物理量的数值计算式;采用向后差分方法和增量方法,实现了化学反应场、材料结构场、化学流变场控制方程的离散,获得了反应转化率、聚合物平均相对分子质量、流体黏度等物理量的数值计算式。
采用半隐式、解耦合的数值逼近方法,解决了在复杂的化学与物理条件下众多场变量之间的相互耦合问题,开发了自由基聚合反应挤出过程数值模拟的核心程序和自由基接枝反应挤出过程数值模拟的核心程序。在给定的初始条件和边界条件下,实现了连续性方程、动量方程、化学反应动力学方程、平均相对分子质量计算式与化学流变本构方程的数值求解。
运行自由基聚合反应挤出过程的数值模拟程序,模拟了甲基丙烯酸正丁酯的反应挤出过程,获得了单体转化率、聚合物平均相对分子质量、流体表观黏度等场变量的演变情况,单体转化率的模拟结果与实验结果吻合一致。讨论了凝胶效应及流率对反应挤出场量的影响,分析了在聚合反应挤出过程中调控高分子材料结构与流变性质的规律,为设备参数与工艺操作参数的选择提供了理论依据。
运行自由基接枝反应挤出过程的数值模拟程序,模拟了乙烯基硅烷、丙烯酸及甲基丙烯酸甲酯接枝聚乙烯的反应挤出过程。获得了接枝度、均聚物质量分数、平均相对分子质量与材料黏度等场变量的动态演变情况,模拟结果与实验结果基本吻合。讨论了材料组成与工艺参数对接枝行为的影响规律,分析了提高接枝度与接枝效率的有效方法。
在数值模拟基础上,开展了反应挤出过程的优化设计研究。以反应挤出过程的有限容积模拟作为目标函数求解方法,以遗传算法作为搜索寻优方法,开发了反应挤出过程的优化设计系统。针对自由基聚合反应挤出过程,建立了面向单体转化率限制和/或反应效率的单目标和多目标优化模型,实现了螺杆几何参数和工艺操作参数的按需设计。
The reactive extrusion (REX) process is a new kind of polymer processing technology that integrates the chemical reaction and extrusion processing. Using twin-screw extruders as reactors, the reactants and other essential additives such as initiators and catalysts react to synthesize the expected polymers during the continuous extrusion process, and then products can be directly formed via the extrusion die. It has great prospects and has drawn wide attentions at home and abroad in its advantages such as the short periods, continuous production, low energy consumption and little environmental pollution.
In REX processes, the fluid flow, chemical reaction, heat transfer and mass transfer coexist and interact with each other. The physical and chemical changes are usually performed under nonisothermal, non-constant pressure and high shear rate conditions. In addition, there exist some special technological requirements such as the high reaction rate, good heat transfer ability and high conversion ratio. So it is difficult to carry out quantitative and in-situ investigations by means of the classical reactor theory. Researches involving the numerical simulation and optimization design can be used as one of the effective methods to solve the aforementioned problems, on the basis of which the effects of the chemical reaction on the material structures and physicochemical properties can be quantitatively studied, the reactor structure, material compositions and reactive processing conditions can be optimized, and then the application range of REX can be enlarged. To sum up, this project has an important scientific meaning and a good prospect of engineering application.
The existing theoretical investigations have been mainly confined to one-dimensional (1D) models and have generally simplified the intercoupling relations among variables involved in fluid flow, chemical reaction, material structures, physicochemical properties. And the optimization design of material composition and processing conditions are seldom studied. In this paper, using such disciplines as mechanical science, polymer chemistry, polymer physics, statistical theory of polymeric reactions, computational fluid dynamics, engineering optimization and software engineering, the chemorheological behaviors of REX processes for the free radical polymerization and free radical grafting modification were simulated in a macroscale. The functional relationships among the material compositions, reactive processing conditions, material microstructure and macroscopic properties were constructed. The intercoupling relations among the considerable field variables were solved by an uncoupled semi-implicit iterative algorithm. At the aim of making REX process controllable and optimal, the core programs for systems of numerical simulation and optimization design were developed to predict the evolution of field variables and select the optimum reactor structure and processing conditions.
The main contents and conclusions were as follows:
The configuration of the twin screw extruder is complex and the fluid undergoes complicated physical and chemical changes, which make it very difficult to perform the rheological simulation based on real reactor configurations and working conditions. According to the geometrical structure and movement characteristics of closely intermeshing co-rotating twin screw extruders, the flow space of each fluid were unfolded along the axial direction of the screw channel, and then the expressions involving characteristic parameters such as the unfold length, the width, depth and area of the cross section were derived. Neglecting the non-mainstream flow from one screw to the other and simplifying the shape of the cross section, an equivalent axisymmetric reactor model was established. The reactor model is assumed to be fully filled and its wall moves along the axial direction at a velocity equivalent to the comprehensive effect of the rotary screws and the static barrel on the fluid flow. Thus, the space model for the numerical simulation was constructed.
Combining with the aforementioned space model, the basic governing equations describing fields of chemical reaction, material structure and chemorheology were constructed. Based on the free radical reaction kinetics, kinetic models of the free radical polymerization and grafting were constructed, and expressions of reaction rate, monomer concentration, monomer conversion and initiator concentration were deduced. According to the statistical theory of polymeric reactions, the average molecular weight can be divided in three hierarchies: the first is that of polymer chains instantaneously produced, the second is that of polymer chains considering the cumulative effect and the third is that of the fluid with both the reactant and the production taken into account. Expressions of the number-average molecular weight and weight-average molecular weight for each hierarchy were constructed. The continuity equation, the momentum equation as well as the initial and bondary conditions were derived to describe the viscous incompressible fluid flow process. On the basis of polymer physics, expressions of zero shear viscosity and apparent viscosity related to processing conditions and material structures were built.
The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.
An uncoupled semi-implicit iterative algorithm was proposed to deal with the complicated relationships among the considerable field variables. Core programs for the numerical simulations of REX processes for the free radical polymerization and free radical grafting were developed. The continuity equation, the momentum equation, the chemical reaction kinetic equation, the average molecular weight and the constitutive equation can be solved numerically under the given initial and boundary conditions.
Runing the program for the numerical simulation of REX processes for the free radical polymerization, the evolutions of field variables such as monomer conversion, average molecular weight and apparent viscosity were predicted for the example of butyl methacrylate. The simulated result of the monomer conversion is in agreement with the experimental result. The influences of the gel effect and throughput on field variables were discussed. The analyses give laws controlling the materical structure and rheological properties and offer reliance to choose screw configuration and processing conditions.
Runing the program for the numerical simulation of REX processes for the free radical grafting, the evolutions of field variables such as grafting degree, mass fraction of homopolymer, average molecular weight and apparent viscosity were predicted for examples of polyethylene grafting with vinylsilicane, acrylic acid and methyl methacrylate. The simulated results are in agreement with the experimental results. The influences of the material compostion and processing conditions on grafting behaviors were discussed to search effective methods to increase the grafting degree and grafting efficiency.
The optimization design was carried out on the basis of the numerical simulation. The finite volume simulation of REX processes was used to solve objective functions, and the genetic algorithm was introduced to search optimum parameters, on the basis of which a new optimization system of REX processes was established. The single object and multi-object optimization models faced to the restriction of monomer conversion and the reaction efficiency for REX processes of the free radical polymerization were constructed respectivelly. The optimum screw geometric parameters and operating parameters can be obtained according to the pre-specified objectives.
引文
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