The effect of melt compressibility on a high-speed wire-coating process

The effects of melt compressibility on a wire-coating process have been investigated, assuming that the compressible behavior of a polymeric melt obeys the Spencer-Gilmore equation of state. The compressible model is distinctly different from the incompressible model in two ways: (1) it has substantially lower pressure build-up within the die, and (2) the location of the maximum velocity is closer to the traveling wire position. As a result, the velocity profile within the die may change from a parabolic shape to a shape somewhat similar to that observed in a drag-flow case; and the shear stress generated by the fluid on the moving wire is no longer constant. Calculations indicate that the effect of melt compressibility during wire coming may not be neglected if the wire speed Ls greater than 50 cm/s (100 ft/min). In addition, the relationships between processing parameters and product coating thickness for both compressible and incompressible fluids are quite different.     

Rheological analysis of stabilizing forces in wire-coating dies

A rheological analysis of a wire-coating die is presented. The rheological forces which might play a role in the stability of the wire are estimated. In particular, consideration is given to lateral forces related to the secondary normal stress function acting on the wire which is in an eccentric position, and the hydrodynamic force related to the viscosity function acting on the wire which moves at an angle to the die axis. For the former a simple, yet general, expression was derived by solving the flow problem (without axial pressure gradient) with the Ericksen equation in bipolar coordinates. Results indicate that normal stresses stabilize the wire, i.e., tend to restore it to the central location, provided the secondary normal stress function is negative. The hydrodynamic effect tends to reduce the angle between wire and die axes, thus drawing attention to the need of perfect mechanical centering of the guider tip, since in this case this effect also reduces eccentricity. The need is stressed for further work, in particular, experimental measurement of the secondary normal stress function.     

An analytical method for selecting the optimal nozzle external geometry for fluid dynamic gauging

Fluid dynamic gauging (FDG) was developed to measure, in situ and in real time, the thickness of a soft deposit layer immersed in a liquid without contacting the surface of the layer. An analysis based on the lubrication assumption for the flow patterns in the space between the nozzle and the surface being gauged yielded analytical expressions for the relationships between the main flow variables and system parameters. Nozzle shapes for particular pressure, pressure gradient and shear stress profiles could then be identified. The effect of flow rate, nozzle geometry and nozzle position on the pressure beneath the nozzle and shear stress on the gauged surface showed very good agreement with computational fluid dynamics (CFD) simulations. Case studies presented include nozzle shapes for uniform pressure and shear stress profiles, which are useful for measuring the strength of soft deposit layers.     

Analysis of Polymer Flow in a Stepped Parallel Bore Coating Unit by Power Law

Polymer flow for a continuum coating in a stepped parallel bore pressure unit was simulated where the flow is dependent on the wire velocity, geometry of the unit, and the properties of the polymer melt. In a hydrodynamic wire coating process the pulling action of the solid continuum through a circular cross-section stepped parallel or conical orifice filled with polymer melt generates hydrodynamic pressure as well as polymer coating on the continuum. In this paper a mathematical model was developed for the pressure distribution within a stepped parallel bore pressure unit. Results were also obtained for different wire speeds in terms of the changes in viscosity, shear rate, shear stress, and drawing force within the unit. Theoretical hydrodynamic pressure and drawing force results have been compared with the experimental results from literature.     

Studies on wire coating extrusion. II. The rheology of wire coating coextrusion

An experimental and theoretical study of wire coating coextrusion through a pressure-type die was carried out. For the experimental study, the wire coating apparatus employed was the same as that described in Part I of this series (14), except for the newly constructed coextrusion die. The die was provided with three melt pressure transducers along the axial direction, which permitted us to determine the pressure gradient in the die. It was found that a reduction in pressure gradient was realized when a lower viscosity polymer was coextruded with a high viscosity polymer. The materials used for the coextrusion were combinations of low-density polyethylene, high-density polyethylene, polystyrene, and two different commercially available thermoplastic rubbers (UniRoyal TPR-1900 and Shell Kraton G 2701). The use of a high shrinking (crystalline) polymer inside a low shrinking (amorphous) polymer was found to give rise to distorted coatings (non-circular cross section of the coated wire). The interface between the coextruded layers was examined under a magnifying lens, and it was found that under certain processing conditions, the interface was highly irregular. Experimental correlations were obtained to explain the onset of an unstable interface in terms of the rheological properties of the individual components being coextruded, and of the processing variables. It was found that interfacial instability occurs when the shear stress and the viscosity ratio (also elasticity ratio) of the two components at the interface exceed certain critical values. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymers being coextruded. Solution of the system of equations permitted us to predict the velocity profile and shear stress distributions of two molten polymers inside a pressure-type wire coating coextrusion die. Comparisons were made between the experimental and theoretically predicted volumetric flow rates. The comparison was found to be reasonably good with certain systems. The discrepancy between the experimentally obtained and the theoretically predicted volumetric flow rates was attributed to interface migration and interfacial instability.     

细粉下料过程的气固流体动力学作用分析

细颗粒粉体下料时受气固流体力学作用在料仓出口附近形成逆压力梯度,使得粉体下料流率实验值远低于理论预测值。而且该压力梯度力直接测量较困难,对模型修正和发展提出了挑战。以玻璃微珠、流化催化裂化（FCC）催化剂颗粒、褐煤和聚氯乙烯（PVC）颗粒为实验材料,首先开展粉体静力学与动力学测试,借助休止角（AOR）、豪斯纳比（HR）和卡尔流动指数（CFI）多个粉体流动性判据综合分析不同粉体的流动特性;在分析粉体料仓出口附近气固流动特征的基础上,结合Jenike流动与不流动判据,将作用在细颗粒粉体上的逆压力梯度力引入到拱应力平衡方程;进一步,提出了利用迭代算法获得逆压力梯度力的方法,实现了对逆压力梯度力与粉体料仓下料流率的预测。建立的粉体下料流率模型考虑了气固流体动力学作用对粉体下料流动的影响,有效改善了传统模型对细粉体流率预测偏高的问题,模型预测偏差从60%以上降低至±20%。     

表面活性剂虫状胶束流体中颗粒沉降负尾迹模拟

颗粒在剪切稀释黏弹性表面活性剂形成的蠕虫状胶束流体中沉降时会产生负尾迹，负尾迹的形成对该种复杂流体与固体颗粒之间的相互作用具有重要影响。基于Giesekus本构方程，采用POLYFLOW软件模拟了黏弹性表面活性剂(Viscoelastic Surfactant, VES)蠕虫状胶束流体中单颗粒的沉降过程，分析了流体松弛时间和迁移因子对颗粒周围速度场及应力场的影响，重点研究了颗粒尾部速度负尾迹的产生原因及其对颗粒曳力的影响。结果表明，Giesekus本构方程能够描述VES流体的非线性剪切变稀行为和弹性导致的拉伸变形。流体弹性导致颗粒尾部产生较大的拉伸变形，剪切稀化和流体弹性的共同作用使颗粒尾部产生拉伸变形，导致负尾迹出现。表征流体弹性的De(黛博拉数)越大，流体拉伸黏度的Tr(特劳顿数)越小，负尾迹越长。负尾迹的出现使VES流体中颗粒所受曳力减小，沉降速度开始增加。模拟结果为此种流体的进一步应用提供了一定的研究基础。     

基于湍流模型的S-CO2干气密封流场与稳态性能分析

为探究湍流效应对S-CO₂干气密封性能的影响规律,以螺旋槽干气密封为研究对象,引用考虑离心惯性力效应的湍流Reynolds方程,选择Ng-Pan湍流系数表达式,采用物性软件REFPROP对CO₂真实物性进行计算。之后,根据普适能量方程,通过引入包含湍流效应、离心惯性力效应的平均速度,建立了可压缩流体简化能量方程。通过对湍流Reynolds方程与简化能量方程进行耦合求解,分析讨论了不同工况参数与平均膜厚下湍流效应对密封性能的影响。研究表明：湍流效应使得气膜流场内压力与温度分布发生显著变化,流场计算时不可忽略;在不同进口压力、进口温度下,湍流下的开启力和泄漏率显示出与层流一致的变化趋势;在不同平均膜厚下,考虑湍流效应后的开启力呈现出与层流不同的变化规律,而泄漏率表现出与层流相同的变化趋势;在不同进口压力、进口温度、平均膜厚下,湍流下的开启力和泄漏率均比层流下的低,且在两种流态下的这种差异随着进口压力、进口温度、平均膜厚的增大而逐渐增大;在不同转速下,开启力和泄漏率在湍流下分别表现出与层流不同的变化趋势。这些结果为进一步研究湍流效应对S-CO₂干气密封的影响提供了支撑。     

神府煤水煤浆管道输送试验研究

为获得神府煤水煤浆最佳管道输送参数,进行了水煤浆流变性试验,确定了水煤浆临界剪切速率。通过水煤浆剪切速率和剪切应力的关系确定神府煤水煤浆流变性模型,拟合出适于神府煤水煤浆流变性的数学方程。在不同管道直径和水煤浆浓度下,研究了水煤浆平均速率对管道压力损失的影响,得到了最佳水煤浆管道输送参数。结果表明:神府煤水煤浆临界剪切速率为40.74 s-1,水煤浆拟合后的流变方程符合宾汉塑性体模型,适宜泵送和管道输送。低浓度、低黏度的水煤浆更适合管道输送。在水煤浆平均流速相同的条件下,管道直径越小,管道压力损失越大。管道直径为200~300 mm时,神府煤水煤浆在管道输送中的压力损失在工业应用合理范围内,适宜管道输送。     

Studies on wire coating extrusion. I. The rheology of wire coating extrusion

Wire coating extrusion was studied, both experimentally and theoretically, using a pressure-type die. For the experimental study, a wire coating apparatus of laboratory scale was constructed, consisting of a pay-off device, extruder, cross-head and pressure-type die, cooling trough, and take-up device. The materials used were low- and high-density polyethylenes and thermoplastic rubber. The following measurements were taken during the experiments: (1) the axial pressure profiles in the die, (2) melt flow rate, and (3) take-up speed. The measurements were then used to determine the effect of the rheological properties of the polymers on the performance of the wire coating operation. It was found that a reduction in axial pressure gradient and a reduction in the recoverable elastic strain of a molten polymer at the die exit can be realized as the speed of the wire is increased. For the theoretical study, using a power-law model, the equations of motion were solved numerically to predict the volumetric flow rate as functions of the pressure gradient in the die and the rheological properties of the polymer being extruded. Solution of the system equations permitted us to predict the velocity profile and shear stress distributions of a molten polymer inside a pressure-type wire coating die.     

Studies on multilayer film coextrusion III. The rheology of blown film coextrusion

Multilayer blown film coextrusion was studied, both experimentally and theoretically. For the experimental study, an annular die with a feed-port system was designed and multilayer blown films were produced by rotating the inner mandrel with a one horsepower variable-speed drive at speeds from nearly 2 to 6 rpm, and by inflating the tubular molten film with air. The die has 16 feed slots and melt pressure transducers are mounted along the axial direction of the outer wall of the annular flow channel. The transducers were used to determine the pressure gradient in the annular flow channel, which then permitted determination of the reduction in pressure drop when different combinations of two polymer systems were coextruded. Polymers used for b own film coextrusion were: (1) low-density polyethylene with ethylene-vinyl acetate; (2) low-density polyethylene with high-density polyethylene; (3) low-density polyethylene with polypropylene; (4) high-density polyethylene with ethylene-vinyl acetate. For the theoretical study, stratified helical flow was analyzed using a power-law non-Newtonian model. A computational procedure was developed to predict the number of layers, layer thickness, and the volumetric flow rate as functions of certain processing variables (namely, the pressure drop in the die, and the angular speed of rotation of the inner mandrel of the die) and the rheological parameters of the individual polymers concerned. Comparison was made of the theoretical prediction of volumetric flow rate with experimental ones. Some representative results are presented of the theoretically predicted axial and angular velocity distributions, shear stress profiles, and shear rate profiles.     

PREDICTION OF VELOCITY PROFILES OF SHEAR THINNING FLUIDS FLOWING IN ELASTIC TUBES

Non-Newtonian fluid flow characteristics in inflatable and collapsible elastic tubes are relevant to bio-fluid mechanics and other applications. The radial velocity profiles in an elastic tube during steady laminar flow of a shear thinning aqueous solution of 1.5% carboxy methyl cellulose (CMC) were investigated using ultrasound Doppler velocimetry. The shear rate–dependent viscosities obtained using a rheometer were well represented by the Carreau model. Measured storage and loss moduli indicated the CMC solution to be inelastic up to 2% concentration. The velocity profiles were predicted by integrating the theoretical equation derived by equating the shear stress along the tube radius involving pressure drop to that of the Carreau model using its parameters. The agreement between predicted and measured velocity profiles was good. The predicted pressure drop is about the same as the experimental value at lower flow rates. In contrast, the measured pressure drop is lower than that predicted at higher flow rates due to inflation of the tube. Good agreement between estimation (Hagen-Poiseuille's law) and measurement (tube shape image analysis) for the detection of elastic tube expansion while increasing flow rates is found.     

Finite element analysis of wire coating

A general-purpose finite element program has been used to simulate the flow of polymers through wire-coating dies. The analysis includes Newtonian and power-law fluids. The effect of normal stresses was examined through a simple viscoelastic constitutive equation, Nonisothermal wire coating was studied to obtain the temperature field within the melt. The effect of a slip condition at the solid boundaries was also examined. The determination of the coating melt free surface was carried out through an iterative procedure. The finite element solution provides details about the existence and extent of recirculation regions, about hot spots due to viscous dissipation, and also captures the stress singularities present at the impact of the melt with the wire and at the exit from the die. Pressure distribution, maximum temperature rise, haul-off wire tension, maximum wire tension, and stresses at the wire surface and die wall are also presented.     

Numerical simulation of wire-coating low-density polyethylene: Theory and experiments

The wire-coating process was analyzed numerically making use of a particular die design employed in highspeed industrial operations. Both the lubrication approximation theory and a fully two-dimensional finite element analysis were applied under isothermal and nonisothermal conditions, respectively. Particular emphasis has been given to the heat transfer effects between the melt arid the solid and free boundaries. A variety of thermal boundary conditions was studied, ranging from adiabatic to constant temperature walls. The influence of dimension less groups such as Peclet, Nahme, and Biot numbers is examined. Oscillation-free solutions are obtained for the temperature field by using a standard finite element Streamline-Upwind/Petrov-Galerkin technique. Rheological data for a wire-coating low-density polyethylene (LDPE) resin (Alathon-3535) were used in the analysis. The predictions include pressure and temperature distributions, shear stresses and shear rates both at the die wall and the wire, and wire tension for different wire speeds. The numerical results are compared with a set of experimental data for LDPE in a typical die used by Du Pont Co. It is found that the isothermal lubrication approximation for power-law fluids overestimates pressure distributions when applied at die operating temperature. The nonisothermal finite element analysis gives better predictions, especially when realistic thermal boundary conditions are imposed, with the experimental results lying between those found from simulations assuming isothermal walls (upper limit) and adiabatic walls (lower limit).     

管壁厚度对微挤出成型的影响分析

基于Bird-Carreau黏度模型,运用有限元方法对三维等温微管挤出成型流动模型进行了数值分析,主要研究了管壁厚度对微管挤出成型过程中挤出胀大、速度分布、剪切速率和口模压降等重要指标的影响。结果表明,当熔体入口体积流率相等时,随着管壁厚度的增大,挤出物挤出胀大率和横截面尺寸变化量增大;口模出口端面上熔体的二次流动增强,但挤出速度和剪切速率减小;熔体在口模内的压力降明显下降;适当增加管壁厚度,有利于提高微管挤出质量。     

水包油型乳化液油滴的管内节流破碎行为与机理

实验研究了水包油型乳化液油滴在管内节流元件处的破碎行为,分析了破碎机理. 结果表明,液滴破碎主要发生在节流元件内壁及下游附近,其概率是施于液滴上湍流应力与液滴表面能之比的递增函数,是流体韦伯数及节流元件两侧最大压差的递增函数;在湍流状态(Re>4000)下,液滴充分振荡且受到较大的水流惯性力和速度梯度剪切力,更易破碎;由苏丹红IV染色的正庚烷体系界面张力由非染色时的47 mN/m降到23.6 mN/m,黏性力对液滴破碎的影响程度下降,受流速、压差等影响的惯性力起决定性作用,液滴破碎程度更大;流速决定流体对分散相油滴的湍流剪切破碎力,流速增大则油滴粒径破裂程度加大,而流速取决于流量和节流比;注入染色正庚烷油相体积增大(0.5~5 mL),削弱了节流元件的液滴破碎作用,两相流体系倾向于形成更大直径的液滴,中位径一般为20~35 mm.     

新型锥形双螺杆混合元件三维流场分析

利用ANSYS有限元分析软件对带有混合块的新型锥形双螺杆的混合段流场进行了三维模拟分析，通过速度场求出流量，并求出剪切速率，剪切应力及回流量来衡量混合效果，找出了混合块几何条件（间隙，错列角）及操作条件（转速，压差等）对挤出机混合效果的影响。     

Effect of die gap width on annular extrudates by the annular extrudate swell simulation in steady-states

We calculated the steady-state annular extrudate swell of polymer melts through flow geometries encountered in processes used to control parison thickness. A streamline-upwinding finite element method with an under-relaxation for the rate of deformation tensor was used. The Giesekus model was employed as the constitutive equation. An operation that widens the die gap is appropriate for the control of parison thickness corresponding to the change of die gap width. However, a control process that decreases the die gap width is not useful, because the parison thickness does not correspond to the die gap width. Furthermore, thickness swells change strikingly with the Weissenberg number. It is difficult to control the parison outer diameter in the case of a converging die, because the change of the outer diameter swell becomes large with increasing Weissenberg number. In the case of a diverging die, the changing value of the outer diameter swell is smaller than that in the case of a converging die.     

含杂质二氧化碳实际气体干气密封性能研究

基于EOS-CG模型和GERG-2008模型计算含杂质二氧化碳混合气体的密度，基于CO₂-Pedersen模型计算混合气体的黏度。利用模型计算数据拟合获得含杂质二氧化碳混合气体密度、黏度与压力的关系式，用以描述混合气体的实际行为以及黏度随压力变化的规律。采用有限差分法求解稳态雷诺方程，得到了纯二氧化碳和含杂质二氧化碳干气密封开启力、泄漏率以及气膜刚度，并分析了杂质对二氧化碳干气密封性能(开启力、泄漏率、气膜刚度)的影响。考虑的变量有端面平均线速度、气膜厚度、进口温度以及进口压力等。结果表明：当进口压力为15.26 MPa，进口温度为363.15 K，线速度为74.030 m/s，气膜厚度为3.05 μm时，含杂质二氧化碳干气密封开启力和泄漏率都小于纯二氧化碳干气密封开启力和泄漏率，且杂质含量越多，差别越明显；杂质对二氧化碳干气密封开启力、泄漏率、气膜刚度的影响随端面平均线速度的增大而增大；对泄漏率、气膜刚度的影响随气膜厚度的增加而减小；对开启力、泄漏率、气膜刚度的影响随进口温度的增大而减小；对开启力的影响随进口压力的增大先减小，再增大，最后减小，对泄漏率的影响随进口压力的增大先增大后减小，对气膜刚度的影响随进口压力的增大先减小后增大。