层叠流道中天然高分子挤压流动过程的数值模拟

为探究层叠流道中天然高分子材料挤压流动过程与混合特性，建立层叠流道的三维物理模型和有限元网格模型，利用POLYFLOW软件计算了食品熔体在不同的入口流量，挤压过程中的压力、速度、剪切速率分布。结果表明，压力沿着挤出方向呈梯度递减，随着入口流量增大中间位置压力差增大；剪切速率在流道中变化明显，剪切速率从流道中间位置向四周递减，从壁面到流道内部递减；速度在流道内沿着挤出方向先增大后减小，靠近壁面速度小；层叠扭转流道的结构和尺寸设计，有助于提高天然高分子物料的混合效果，并且第1、4层流道混合效果优于第2、3层流道，提高入口流量也有利于提高物料的混合效果。     

Numerical simulation of profile extrusion dies without flow separation

Lubrication theory has been applied to solve flow problems in profile extrusion dies without flow separations, for Newtonian and power law type fluids. The method is based on velocity calculation within cross sections perpendicular to the flow. Pressure drop can also be obtained from a macroscopic balance, if the flow rate is known. Comparison of pressure drops in 2-D and 3-D geometries has been made with numerical simulation obtained by a finite element method. Results show a good accuracy of the proposed method.     

Numerical study of nonisothermal polymer extrusion flow with a differential viscoelastic model

A numerical study of nonisothermal viscoelastic flow is conducted to investigate the complex flow characteristics of polymer melts in the extrusion process. A general thermodynamic model for the energy conversion related to viscoelastic fluid flow is introduced. The mathematical model for three‐dimensional nonisothermal viscoelastic flow of the polymer melts obeying a differential constitutive equation (Phan‐Thien and Tanner model) is established. A decoupled algorithm based on the penalty finite element method is performed on the calculation. The discrete elastic‐viscous split stress (DEVSS) algorithm, incorporating the streamline‐upwind Petrov‐Galerkin (SUPG) scheme is employed to improve the computation stability. Essential flow characteristics of polymer melts in the extrusion die for hollow square plastic profile is investigated based on the proposed numerical scheme with ignoring the outer thermal resource. The energy partitioning, which quantified the conversion of mechanical energy into thermal energy, is discussed. The effects of volume flow rate and die contraction angle upon the flow patterns are further investigated. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Numerical simulation of contraction flow of a dilute polymer solution

Numerical results are presented for a contraction flow of a non-Newtonian fluid. In this work a new finite-volume algorithm was used and various non-Newtonian fluid models (with and without elasticity) were studied. The results are discussed and compared to experimental results obtained with a dilute polymer solution.     

Prediction of flow patterns in the polyurethane foaming process by numerical simulation considering foam expansion

We present a foam flow model for flow pattern prediction in the polyurethane foaming process that considers the flow caused by foam expansion due to bubble generation. The flow pattern in the cavity is calculated by taking into account the initial volume shape and the rate of foam expansion of a poured reaction mixture. The validity of the model is investigated by applying it to the Hele‐Shaw formulation, which assumes that the cavity is very thin compared to its width. The predicted flow patterns generally agree closely with experimental results measured in panel‐type molds. A three‐dimensional simulation is further developed based on the Stokes flow. The numerical formulation is performed by the control volume based‐finite element method with an equal‐order velocity‐pressure formulation that does not exhibit spurious pressure modes. The flow patterns predicted by the three‐dimensional simulation agree very closely with the experimental results. In particular, it clearly expresses the edge effect, in which the flow slows down at the edge, which is ignored in the Hele‐Shaw formulation. This numerical simulation is suitable for rapid determination of the pouring position, volume of the mixture, and the air vent position.     

Supercritical CO2-assisted extrusion foaming: A suitable process to produce very lightweight acrylic polymer micro foams

A strategy of CO₂-assisted extrusion foaming of PMMA-based materials was established to minimize both foam density and porosities dimension. First a highly CO₂-philic block copolymer (MAM: PMMA-PBA-PMMA) was added in PMMA in order to improve CO₂ saturation before foaming. Then the extruding conditions were optimized to maximize CO₂ uptake and prevent coalescence. The extruding temperature reduction led to an increase of pressure in the barrel, favorable to cell size reduction. With the combination of material formulation and extruding strategy, very lightweight homogeneous foams with small porosities have been produced. Lightest PMMA micro foams (ρ = 0.06 g cm⁻³) are demonstrated with 7 wt% CO₂ at 130°C and lightest blend micro foams (ρ = 0.04 g cm⁻³) are obtained at lower temperature (110°C, 7.7 wt% CO₂). If MAM allows a reduction of T^foaming, it also allows a much better cell homogeneity, an increase in cell density (e.g., from 3.6 10⁷ cells cm⁻³ to 2 to 6 10⁸ cells cm⁻³) and an overall decrease in cell size (from 100 to 40 μm). These acrylic foams produced through scCO₂-assisted extrusion has a much lower density than those ever produced in batch (ρ ≥ 0.2 g cm⁻³).     

Converging flow of polymer melts in extrusion dies

Practical extrusion processes often involve geometrically complex dies. Such dies are usually tapered, or streamlined, to achieve maximum output rate under conditions of laminar flow. These converging flows may be analysed in terms of their extensional and simple shear components to calculate the relationships between volume flow rate, pressure drop, and post extrusion swelling. The analysis can also be extended to cover the free convergence as fluid flows from a reservior into a die. Comparisons between predicted and observed data for a series of coni-cylindrical dies suggest that using this approach the pressure drop/flow rate relationship can be predicted within ±20% and the swell ratio/flow rate relationship within ±10%. Similar treatments have been in use for the last three years in solving such complex flow problems as radial flow in injection moulding and two-dimensional annular convergence in blow moulding dies.     

聚丙烯片材挤出发泡工艺及发泡体系研究

采用自行研制的高熔体强度聚丙烯(PP),通过挤出片材发泡实验,研究了口模温度、挤出温度、螺杆转速等工艺条件以及PP熔体强度和发泡成核剂对片材发泡效果的影响。PP发泡片材最佳挤出工艺条件为:挤出温度210℃,口模温度160℃,螺杆转速40 r/min。PP熔体强度为13 cN,发泡成核剂用量为6 phr时,发泡片材密度最低(0.450g/cm~3),片材表面光滑平整,挤出发泡效果最好。     

聚合物溶解槽内双搅拌器流场特性的数值模拟

搅拌设备是目前海上油田实施聚合物驱油的配注系统的关键设备之一。利用计算流体力学方法对聚合物溶解过程采用翼型上推式搅拌器KCXU和锚式搅拌器MS的内外3种组合槽内流场进行了数值模拟,获得了搅拌器槽内的流场特性、循环流量及搅拌器的功率消耗。结果表明:在第1种混合状态时,KCXU搅拌器与转动的MS搅拌器组合时的流场变得更为复杂、无序。在第2,3种混合状态时,KCXU搅拌器与正转的MS搅拌器的组合形成的流场速度较大,加强了KCXU搅拌器的流动范围,并,且形成了最大的循环流量,其功率居中。     

淬火过程流动与传递现象数值模拟

根据淬火过程中多相流动与传热的特点,提出了简化模型。基于两相流体动力学及流固耦合传热建立了流动与传热方程。推导出了计算模型并结合大型软件Fluent进行了用户子程序（UDF）设计,利用此方法对影响流动与沸腾传热的几个因素进行了数值研究,数值计算结果与理论分析吻合。最后对金属铝块的淬火过程进行了计算,计算得到的金属表面测点温度随时间变化历程与文献中实验数据误差在15%以下,表明计算方法可行并且把握了物理过程的本质。     

Numerical simulation of polypropylene foaming process assisted by carbon dioxide: Bubble growth dynamics and stability

A mathematical model was established to simulate the bubble growth process during foaming of polypropylene (PP) by carbon dioxide, taking into account of a wide range of physical and rheological properties (solubility, diffusivity, surface tension, long-chain branching, zero shear viscosity, relaxation time, strain hardening), as well as processing conditions. By employing the Considère construction the possibility of growth instability and bubble rupture at later stage of bubble growth was predicted. The simulation revealed that the improvement of foamability of polypropylene by introducing long-chain branching was due to the well-defined viscoelastic characteristics of the melt. Rheological factors that impede bubble growth are beneficial in stabilizing the bubble growth. Stability during bubble growth is further facilitated by moderate strain hardening characteristics and elastics properties of the polymers. The diffusivity and solubility characteristics also have profound impact on the bubble growth stability, while the influence of the surface tension is negligible.     

Conjugate transport in polymer melt flow through extrusion dies

A numerical study is carried out on the conjugate thermal transport in polymer and food melts flowing through extrusion dies. The simulation is performed to determine the influence of conduction through the die wall and of the thermal boundary conditions on the transport in the fluid and on the conditions at the outlet. An extrusion die with a uniform temperature or heat transfer coefficient specified at the outer surface is considered. It is found that, because of conduction in the solid wall, important physical variables such as centerline velocity, pressure drop, bulk temperature of the fluid and shear experienced by the fluid are strongly affected by the boundary conditions, as well as by the wall thermal conductivity and thickness. Channels of different geometries are used for the study. The flow in a circular straight tube with constant wall thickness is studied first. Flow and thermal transport in different, constricted, channels are studied next. Different wall materials are also considered. Comparisons with some experimental results are presented, indicating good agreement. The fluids considered in this study are highly viscous, polymer melts. Due to high viscous dissipation and temperature-dependent viscosity, the flow and heat transfer are coupled and the problem is quite complicated. The results show that, for some operating conditions, the bulk temperature can be high enough to cause significant heat transfer from the fluid to the wall. The downstream variation in the pressure and temperature are calculated. The thermal boundary conditions are found to have a strong influence on the temperature field and thus on the flow. The general dependence of pressure drop on temperature, flow rate, and geometry is investigated. Several other basic aspects of this problem are also discussed.     

双室蒸发分离室内流动及蒸发过程的数值模拟

掌握双室双管程蒸发器分离室内汽液二相流动及蒸发过程特性是其进一步结构优化的基础,应用STARCCM+软件对分离室内隔离板上平衡孔的形状和位置对汽液二相流动及蒸发过程的影响进行了数值模拟。模拟结果表明:分离室内隔离板上平衡孔较佳的形状为圆形孔,其适宜的设置位置为距分离室底部与距汽液入口处距离之比在2∶3—2∶1之间。设置在该区域时,分离室内流场均匀,流动阻力损失较小,推动力较大;在平衡孔形状及位置较佳的情况下,分离室一内液位高于分离室二,隔离板两侧温度分布相对比较均匀,并能够建立起稳定的温度差和浓度差,在分离室上方汽液能够实现较好的分离;模拟结果进一步证实了双室双管程蒸发器实际操作的可行性。     

Numerical simulation for bubble growth during supercritical CO2 foaming epoxy resin process based on chemorheology

The bubble growth process of epoxy resin foams has been evaluated through a combination of numerical simulation and chemorheology. It was discovered that rheological properties play an essential role in forecasting bubble growth during supercritical CO₂ epoxy resin foaming. Time–cure superposition was conducted revealing that shear storage modulus increased from 10⁻³ to 10⁶ Pa during the curing reaction process. The complex viscosity increased up to 10⁵ Pa s and the characteristic relaxation time increased up to 53.1 s with the curing degree. The epoxy resin with high rigid modulus could effectively inhibit bubble growth. Furthermore, the simulation results indicated that the bubble growth process for epoxy resin foams was influenced by both the CO₂ content and CO₂ plasticization on rheology properties.     

New challenges in polymer foaming: A review of extrusion processes assisted by supercritical carbon dioxide

It is well known that supercritical carbon dioxide (sc-CO₂) is soluble in molten polymers and acts as a plasticizer. The dissolution of sc-CO₂ leads to a decrease in the viscosity of the liquid polymer, the melting point and the glass transition temperature. These properties have been used in several particle generation processes such as PGSS (particles from gas saturated solutions).It is therefore highly likely that extrusion processes would benefit from the use of sc-CO₂ since the rationale of the extrusion processes is to formulate, texture and shape molten polymers by forcing them through a die. Combining these two technologies, extrusion and supercritical fluids, could open up new applications in extrusion.The main advantage of introducing sc-CO₂ in the barrel of an extruder is its function as a plasticizer, which allows the processing of molecules which would otherwise be too fragile to withstand the mechanical stresses and the operating temperatures of a standard extrusion process. In addition, the dissolved CO₂ acts as a foaming agent during expansion through the die. It is therefore possible to control pore generation and growth by controlling the operating conditions.This review focuses on experimental work carried out using continuous extrusion. A continuous process is more economically favourable than batch foaming processes because it is easier to control, has a higher throughput and is very versatile in the properties and shapes of the products obtained.The coupling of extrusion and supercritical CO₂ technologies has already broadened the range of application of extrusion processes. The first applications were developed for the agro-food industry 20 years ago. However, most thermoplastics could potentially be submitted to sc-CO₂-assisted extrusion, opening new challenging opportunities, particularly in the field of pharmaceutical applications.This coupled technology is however still very new and further developments of both experimental and modelling studies will be necessary to gain better theoretical understanding and technical expertise prior to industrial use, especially in the pharmaceutical field.     

Effect of viscoelastic properties of the base polymer on extrusion foaming with thermally expandable microcapsules

Thermally expandable microcapsules (MCs) are applicable to the foam processing of polypropylene (PP). The purpose of this study is to clarify the influence of processing conditions, such as temperature, shear rate and resin selection, on the behavior of thermally expandable MCs in PP. In this study, MC was added to several types of PP and extrusion foaming was performed. The average diameter of the MCs after processing was calculated to characterize the expansion of PP including MCs. Two types of molecular architecture, homo- and impact-PP, were examined in this study. The expansion behavior could be summarized by the shear viscosity at the extrusion die. Irrespective of the molecular architecture, data were summarized on one curve on a plane that expressed the relation between the shear viscosity and average MC diameter. Shear viscosity is thus an effective parameter to examine base resin selection for MC foaming. POLYM. ENG. SCI., 60:558–562, 2020. © 2020 Society of Plastics Engineers     

Overall numerical simulation of extrusion blow molding process

This paper focuses on the overall numerical simulation of the parison formation and inflation process of extrusion blow molding. The competing effects due to swell and drawdown in the parison formation process were analyzed by a Lagrangian Eulerian (LE) finite element method (FEM) using an automatic remeshing technique. The parison extruded through an annular die was modeled as an axisymmetric unsteady nonisothermal flow with free surfaces and its viscoelastic properties were described by a K‐BKZ integral constitutive equation. An unsteady die‐swell simulation was performed to predict the time course of the extrudate parison shape under the influence of gravity and the parison controller. In addition, an unsteady large deformation analysis of the parison inflation process was also carried out using a three‐dimensional membrane FEM for viscoelastic material. The inflation sequence for the parison molded into a complex‐shaped mold cavity was analyzed. The numerical results were verified using experimental data from each of the sub‐processes. The greatest advantage of the overall simulation is that the variation in the parison dimension caused by the swell and drawdown effect can be incorporated into the inflation analysis, and consequently, the accuracy of the numerical prediction can be enhanced. The overall simulation technique provides a rational means to assist the mold design and the determination of the optimal process conditions.     

On‐line NIR sensing of CO2 concentration for polymer extrusion foaming processes

An on‐line sensor using near infrared (NIR) spectroscopy is developed for monitoring CO₂ concentration in polymeric extrusion foaming processes. NIR absorption spectra are acquired by a probe installed at the foaming extruder die. The calibration curve relating the absorbance spectrum at 2019 nm to the dissolved gas concentration is derived so as to infer dissolved CO₂ gas concentration on‐line from measured NIR spectra. Experimental results show the developed on‐line NIR sensor can successfully estimate dissolved CO₂ concentration in the molten polymer and illustrate that the developed NIR sensing technique is among the more promising methods for quality control of polymeric extrusion foaming processes.     

Numerical simulation of reactive extrusion processes of PA6

To analyze the complicated relationships among the variables during the reactive extrusion process of polyamide 6 (PA6), and then control the chemical reaction and the material structures, the process of continuous polymerization of caprolactam into PA6 in a closely intermeshing co‐rotating twin screw extruder was simulated by means of the finite volume method, and the influences of three key processing parameters on the reactive extrusion process were discussed. The simulated results of an example were in good agreement with the experimental results. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2331–2336, 2007