Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

This paper applies the finite‐volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three‐dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau–Yasuda as also Upper‐Convected Maxwell and Phan‐Thien/Tanner differential models, with a Williams–Landel–Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects. Copyright © 2009 John Wiley & Sons, Ltd.     

Extended finite element method for viscous flow inside complex three‐dimensional geometries with moving internal boundaries

A three‐dimensional extended finite element method is presented to simulate Stokes flow in complex geometries with internal moving parts. Instead of re‐meshing the flow domain, the kinematics of the internal objects are imposed on the conservation equations using a constraint, implemented with a Lagrangian multiplier. To capture discontinuities of field variables, such as pressure and velocity, on the intersected elements, XFEM is used. To validate our method, it is first applied to a relatively simple problem, that is, the flow around a cylinder in a channel. The results are verified by comparing with a boundary‐fitted solution. After validation of the model and its implementation, the three‐dimensional flow in a twin‐screw extruder is simulated and the results are compared with experimental data from literature. XFEM shows very good accuracy for complex geometries with internal moving parts and narrow gap regions where the shear rate is orders of magnitude higher than in other regions. Copyright © 2011 John Wiley & Sons, Ltd.     

同向啮合双螺杆挤出机挤出过程的计算机模拟

计算机模拟研究了聚苯乙烯在TSE-35A型同向啮合双螺杆挤出机的挤出过程.计算得到不同喂料速率与不同转速下的停留时间分布,并与在线荧光法测量值对比,二者基本相符.确定了停留时间与螺杆转速及喂料速率之间的函数关系式.模拟结果还预测了喂料速率、螺杆转速等工艺参数对双螺杆内流场变量,如温度、填充率、压力及粘度等的影响.模拟计算有助于了解双螺杆挤出机内部聚合物材料流动状态及停留时间长短,从而指导实际聚合物生产.     

Poly(lactic acid)/poly(butylene succinate)/calcium sulfate whiskers biodegradable blends prepared by vane extruder: Analysis of mechanical properties,morphology, and crystallization behavior

Ternary blends of PLA/PBS/CSW with different weight fractions were prepared using a vane extruder. The mechanical properties, morphology, crystallization behavior and thermal stability of the blends were investigated. For the PLA/CSW blend, the tensile strength decreased, the flexural strength and modulus increased compared with pure PLA. For PBS, the addition of CSW had little influence on the mechanical properties. For the ternary blends PLA/PBS/CSW, the tensile strength, flexural strength and modulus decreased compared with pure PLA, while the elongation at break and the impact strength increased significantly. The brittle-ductile transition of the blends took place when the PBS weight fraction reaching 30 wt%. As a soft component in the blends, PBS was beneficial to improve the tensile ductility and the toughness of PLA. SEM measurements reveal that PLA/PBS/CSW blends were immiscible. When the weight fraction of PBS was 50 wt%, significant phase separation was observed, and CSW had preferential location in the PBS phase of the blend. DSC measurement and POM observation reveal that CSW had a heterogeneous nucleation effect on PLA and PBS matrix. The addition of PBS improved the crystallization of PLA and the thermal resistance of the PLA/PBS/CSW blends significantly.     

Study of high Deborah number flow of polyisobutylene in square die

A large capacity RAM extruder was designed which provides the opportunity to study high Deborah number (D) flows, with D < 1,000. A modified version of particle image velocimetry was developed to enable the measurement of the velocity field in dies of arbitrary cross section. During the measurement process, tracer particles were simultaneously illuminated by both a focused laser beam locally and a lamp globally. Only those particles that passed through the laser beam were taken into account. The beam was scanned to achieve full field measurements. This method of measurement allowed us to find the location of a particle in the direction of the optical axis of the lens, i.e. that which makes the particle image on the CCD detector of the video camera. A device employing this method was designed and used to measure velocity profiles. The results of these measurements in two cross sections of the square die, at three values of pressure, are presented. The velocity was defined as the ratio of displacement to the elapsed time during which this displacement occurred. Errors in measurements of the coordinates and the observation time of particles were estimated as ±20 μm and less than 0.1%, respectively. A large plateau in the axial velocity profile was found at relatively small Deborah numbers, e.g. D ≈ 28. In flows with higher Deborah numbers, e.g. D ≈ 766, an almost flat velocity profile was detected. Two components of velocity, one longitudinal and one transversal, were measured simultaneously. However, the transversal component appeared to be less than the error of measurements and less than 1% of the axial velocity. Received: 4 August 1998 Accepted: 5 April 1999     

Thermal degradation of high density polyethylene in a reactive extruder

The thermal degradation of high density polyethylene was conducted in a reactive extruder at various screw speeds with reaction temperatures of 400 °C and 425 °C. The residence time of the extruder was estimated and the molecular weight distribution of the fed plastic and reaction products was analysed using gel permeation chromatography. A continuous kinetic model was used to describe the degradation of the high density polyethylene in the reactive extruder. The breakage kernel and the scission rate model parameters were estimated from the experimental data for a variety of cases. It was found that purely random breakage and a scission rate which had a power law dependence on molecular size of 0.474 best described the experimental data.     

用反应挤出法制备尼龙6塑料

利用双螺杆挤出机进行了尼龙６阴离子开环聚合反应的研究，通过改变引发剂及活化剂的浓度、螺杆转速、机筒的温度分布以及螺杆元件构型的排布等，研究这些工艺参数对尼龙６反应挤出产物性能的影响。结果表明，反应挤出的尼龙６综合机械性能比水解缩聚法生产，且具有较高的性能价格比。     

Extrudate swell and flow analysis of polystyrene melt flowing in an electro‐magnetized die in a single screw extruder

An electro‐magnetized capillary die via a parallel co‐extrusion technique was used to study the changes in the overall and radial extrudate swell ratio of polystyrene (PS) melt flowing in a single screw extruder. The effects of magnetic flux density, wall shear rate (screw rotating speed) and die temperature were studied. The results suggested that, in the case of non‐magnetic die the average overall swell ratio of the melt ranged from 1.25 to 1.55. The swelling ratio increased with increasing wall shear rate up to 8.5 sec^?1 and then decreased at 17.1 sec^?1. Increasing die temperature caused a reduction of extrudate swell ratio. The changes in extrudate swell ratio can be explained using the simultaneously measured velocity profiles during the flow in the die, and the swell ratio decreased with increasing radial position. Melt contraction of the melt layer near the die wall was observed. The die temperature was found to have no effect on the change of the radial extrudate swell profiles. When an electro‐magnetized die was used, the average overall swell ratio was found to increase with increasing magnetic flux density to a maximum value and then decreased at higher flux densities. The magnetic flux density of the maximum swell was changed by the wall shear rate. It was associated with a balance of elastic and magnetic energies during the flow. The magnetic energy was thought to have a pronounced effect on the swell ratio at low shear rate and low die temperature. Considering the radial position, the highest swell ratio occurred at the duct center, in the range 2.4–3.3. There was no extrudate contraction of the melt layer near the die wall. Copyright © 2005 John Wiley & Sons, Ltd.     

四螺杆扰动下粘性流体混沌动力学特性研究

在螺杆的周期性扰动下,聚合粘性物流体在螺杆挤出机内的运动具有混沌特性。区别于传统欧拉方法,从Lagrangian新视角分析了四螺杆扰动下粘性流体的混沌动力学特性。基于有限时间不变流形理论,计算了四螺杆挤出机不同初始时刻位的有限时间Lyapunov指数FTLE和拉格朗日拟序结构LCS;利用LCS准边界特性分析了四螺杆挤出系统不同区域的流体运动的动力学特性,指出了抑制和促进四螺杆流体输运的局部区域;结合Poincaré截面验证了分析结果的正确性。结果表明,在同向旋转四螺杆的周期性扰动作用下,四螺杆挤出机中心区由LCS包围,成为流体输运的死区。通过改变螺杆的扰动方向,可以消除中心区LCS的封闭结构,强化异向旋转四螺杆挤出机的物质交换,有效提高了设备的混合效率。     

Velocity Distribution of Extensional Flow Fields in an Eccentric Cylinder of an Extensional Extruder

The extensional extruder is a novel method of polymer processing which generates high elongation stress within a polymer. A mathematical model is proposed which describes the velocity distribution during polymer processing in such an extruder. The modeling results indicate that the dimensionless velocity profiles for power-law fluids decrease as the power-law index increases. Overall, the extensional extruder has an advantage for dispersion effects over traditional screw extruders based on the extensional rheology.