Three-dimensional modelling of Non-Newtonian fluid flow in a coat-hanger die

The three-dimensional model of isothermal flow of power-law fluid in a coat-hanger die has been developed using finite element method. The shape of coat-hanger die used in the present model was determined according to the previous analytical design equation which is based on one-dimensional flow model in the manifold and the slot. Because uniform flow rate across the die outlet is most important to achieve uniform thickness of extruded polymer sheet or film, flow rate distribution is mainly examined to determine the valid process condition for the design equation as the design parameters are changed. The effects of fluid property in terms of power-law index and process parameters not considered in one-dimensional design equation such as die inlet size and the presence of land were analyzed. Results show that the manifold angle is the most influencing design parameter on flow rate distribution. When the material of different power-law index from design value is processed, the change of power-law index affects the uniformity of flow rate appreciably.     

Non-isothermal flow of a molten polymer in a coat-hanger die

The non-isothermal flow of a power-law fluid in a coal-hanger flat die is studied. Equilibrium and thermal equations are solved by using an iterative finite difference method. The pressure distribution, the flow lines, the residence time distribution, the temperature distribution, and the flow uniformity at the end of the die are obtained, with a stress on the effect of thermal regulation and of temperature dependence of the viscosity.     

Geometry design of a coat-hanger die with uniform flow rate and residence time across the die width

This article provides an approximate but sufficiently practical method of geometry design of a coat-hanger die having both uniform flow rate and residence time across the full width of the die. Such a die is often needed when a heat-sensitive resin such as poly(vinyl chloride) is sheeted, because different residence times across the die width are apt to cause a sheet defect in the transverse direction of the sheet. Although some assumptions were made facilitating mathematical analysis, an application of this method to a sheeting die 1 m wide gave good uniformity of flow rate and residence time.     

Design and analysis of a dual-cavity coat-hanger die

A method for the design and analysis of a dual-cavity coat-hanger die is presented in this paper. A macroscopic material balance and a microscopic flow analysis using the finite element method are combined to simulate polymeric fluid flow inside the die. Leonard's macroscopic procedure was adopted to include inertial, gravitational, and viscous effects, and the finite element method was then applied to estimate the contributions of inertial and viscous terms. In addition, the flow patterns in the outer cavity were computed by the finite element method so that the appearance of an undesirable vortex could be predicted. The residence time distributions for flow in the die were approximated by a simple, statistical approach. It was found through a case study that a dual-cavity coathanger die can effectively reduce the flow non-uniformities caused by fluid inertia and viscosity variations.     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part I: Modeling

The multilayer stratified flow of several polymers in a flat coat-hanger die was modeled using a finite element method. The problem was formulated using the lubrication approximation theory. A solution procedure in decoupling pressure and streamlines was developed. This new method is very powerful in comparison with more classical approaches, permitting the solution of flow problems involving a great number of layers in a complex industrial geometry. It allows us to obtain, among other things, pressure field, streamlines, residence times, and the values of the interface positions in the whole die.     

Simulation of polymer flow through a coat-hanger die: A comparison of two numerical approaches

Coat-hanger dies are commonly used for the extrusion of plastic sheets and films. To describe the flow of a molten polymer through a coat-hanger die, a two-dimensional approach is necessary. Moreover, the thermal effects, which play an important role in the flow distribution, have to be taken into account. In this paper, two numerical models for the simulation of coat-hanger dies are described and compared. These models differ mainly in the simplifying assumptions used and in the treatment of the thermal problem. The simulations obtained with the two models were compared with each other and with experimental data. The discrepancies between the two models can be explained by the different theoretical treatments.     

Computer-aided analysis of a linearly tapered coat-hanger die

We describe the computer-aided engineering analysis of a linearly tapered coat-hanger die in this paper. The general governing equation for flow distribution inside the die was derived first. On the basis of this equation, we have developed the design formula for a die to deliver uniform flow. In addition, we have also examined the variations of lateral flow uniformities and residence time distributions of polymeric liquids under several different design and operating conditions: (1) using manifolds with non-circular cross-sections, (2) adjusting production widths, (3) delivering fluids with different viscosities, and (4) enlarging manifolds for practical production considerations.     

Two-dimensional multilayer coextrusion flow in a flat coat-hanger die. Part 2: Experiments and theoretical validation

In a previous paper (1), a two-dimensional computation model for multilayer flows in coat-hanger dies was proposed. It was based on lubrication approximation theory and enabled us to obtain the pressure field, the streamlines, and the interface positions in the whole die. The present paper is aimed to present experimental results obtained on an industrial line for a three-layer configuration and to compare the results to the theoretical computation. The order of magnitude of pressure drops, flow rates, and interface positions were correctly predicted by the model. Some remaining discrepancies may be explained by the isothermal assumption and the lack of encapsulation mechanism in the computation.     

A unified lubrication approach for the design of a coat-hanger die

A simple unified lubrication approach has been proposed to design a coat-hanger die that can deliver wide and uniform liquid sheets. This approach requires that the wall stress in the manifold be constant. With this constraint, any inelastic non-Newtonian fluid model can be used to describe the liquid motion inside the die. Fluid models that can represent the pseudoplastic or viscoplastic behavior of polymeric liquids have been selected for illustration. A general equation that can be solved to determine the effect of production variations on flow uniformity inside the die has also been derived.     

非牛顿流体搅拌流场的数值模拟研究进展

对非牛顿流体搅拌流场数值模拟过程中的控制方程、旋转桨叶的处理以及数值计算方法三个方面进行了综合论述。阐述了广义牛顿流体模型形式简单、计算量低,在非牛顿流体搅拌流场数值模拟过程中应用广泛;黏弹性流体本构方程具有高度的非线性,采用计算流体力学(CFD)方法对其搅拌流场进行数值模拟难度较高,目前仍处于起步阶段;通过合理简化黏弹性流体本构方程以及采用恰当的数值离散方法,有助于在黏弹性流体的搅拌流场数值模拟中取得进展。     

水力旋流器内非牛顿流体多相流场的数值模拟

利用一种非牛顿流体黏度修正模型描述水力旋流器内高浓度矿浆的非牛顿流动特性,并结合雷诺应力模型(RSM)、混合多相流模型(Mixture)以及拉格朗日颗粒追踪模型(LPT)建立了一种适用于模拟水力旋流器内非牛顿流体多相流场的数学模型。模拟结果与报道的实验值的相对误差均在10%以内,表明了该模型的可靠性。结果表明,非牛顿流体黏度的空间分布与矿浆密度的空间分布类似。沿零轴速包络面(LZVV)的轮廓存在一个高密度环,其原因为某粒径范围内的颗粒受到的径向合力为零,颗粒群沿LZVV做高速旋转运动。分散相的空间分布取决于不同粒径的颗粒受力。对于不同粒径的单位质量颗粒,向外离心力的数值大约为向内压力梯度力的两倍左右,使得大颗粒进入下行流并在底流口收集。随着颗粒粒径的减小,总体向内且具有波动性的流体曳力呈指数增长。向内的流体曳力将部分颗粒推向轴心,经上行流逃逸,同时也增强了颗粒运动的随机性。当颗粒粒径小于一定值后,流体曳力远远大于离心力和压力梯度力,颗粒运动的随机性非常强,宏观表现为均匀分布。     

Three-dimensional flow simulation of a film-casting process

Three-dimensional flow simulation of a film-casting process was performed using a finite element method assuming an isothermal and steady Newtonian flow. The simulation was carried out under industrial operation conditions. The neck-in and the edge bead phenomena could be simulated. The effects of draw ratio, air gap length, and die width on these phenomena are discussed. The neck-in and the edge bead phenomena were affected by the draw ratio and air gap length and not by the die width. The neck-in value, which was defined as the difference between the die width and film width at the chill roll, increased with the draw ratio and air gap length.     

Residence time distribution of polymer melts in the linearly tapered coat-hanger die

This article analyzes the average residence time distribution of polymer melt across the die width in a common linearly tapered coat-hanger die, which excells the T die but is a little inferior to the curvilinearly tapered coat-hanger die in residence time uniformity according to the approximated calculation of ten used. From another point of view, a linearly tapered coat-hanger die may be designed so that a desired ratio of the residence time through the die far end to that along the die center line may be imposed as one of the design constraints.     

Application of neural networks to meltblown process control

Process modeling is essential for the control of optimization and an on-line prediction is very useful for process monitoring and quality control. Up to now, no satisfactory methods have been found to model an industrial meltblown process since it is of highly dimensional and nonlinear complexity. In this article, back-propagation neural networks (BPNNs) were investigated for modeling the meltblown process and on-line predicting the product specifications such as fiber diameter and web thickness. The feasibility of this application was successfully demonstrated by agreement of the prediction results from the BPNN to the actual measurements of a practical case. The network inputs included extruder temperature, die temperature, melt flow rate, air temperature at die, air pressure at die, and die-to-collector distance (DCD). The output of the fiber diameter was obtained by neural computing. The network training was based on 160 sets of the training samples and the trained network was tested with 70 sets of test samples which were different from the training data. This research is preliminary and of industrial significance and especially valuable for the optimal control of advanced meltblown processes. © 1996 John Wiley & Sons, Inc.     

On non-Newtonian flow past a sphere

The approximate solutions for flow of and Ostwald-de Waele fluid past a sphere at R_e·0 = 60 and 1 ? n ? 0·8 are obtained by the use of an extended method of moments. As n decreases, (1) friction drag decreases, (2) pressure drag increases for flow past a blunt body, (3) total drag increases for flow past a sphere, (4) wake length increases for flow past a sphere, (5) separation point moves forward for flow past a sphere.     

Numerical simulation of fluid flow and heat transfer in twin-screw extruders for non-Newtonian materials

A new simplified approach has been proposed for the numerical simulation of the thermal transport in corotating, tangential, and self-wiping twin-screw extruders. It is assumed that the flow domain in a twin-screw extruder can be divided into (i) the translation region (T-region), which represents a flow similar to that in a single-screw channel and (ii) the intermeshing region (I-region), which is located between the two screws. The two regions are simulated separately and then coupled for each screw section to model the overall transport in tangential and self-wiping twin-screw extruders. A finite difference method is employed for the developing flow and temperature fields in the T-region, in order to minimize the computing effort, while a finite element method is employed for determining the interchannel flow mixing and the thermal transport in the I-region. Results are obtained in terms of temperature, velocity, and pressure variations along the screw channels and mixing between the two screws.     

三维非等温非牛顿流体充模过程的建模与模拟

为了避免使用速度延拓法处理自由表面边界条件,更真实地反映非牛顿熔体的充模过程,耦合Navier-Stokes方程组,建立了三维实体气液两相流模型。采用基于SIMPLE算法的同位网格有限体积法求解流场物理量,并结合Level Set界面追踪技术实现了非等温熔体充模阶段的动态模拟。为防止出现三维情形下棋盘型压力场,利用同位网格动量插值技术,解决压力与速度失耦的问题。分析了充模过程中,流场物理量的变化情况,研究了注射速率、入口温度等对充模过程及熔体凝固层厚度的影响,得出了与实验相吻合的模拟结果。数值结果表明,三维实体气液两相流模型能更准确地描述聚合物熔体的充模过程;当注射速率较大、入口温度较高时,充模时间较短,熔体凝固层的厚度较小。     

A simulation model to approximate penetration of a non-Newtonian fluid into a porous media during slot die coating

A computational fluid dynamics (CFD) model has been developed to predict the penetration depth of a non-Newtonian fluid as it is directly coated onto porous media by a slot die coating process. The model couples 1-D modified Blake–Kozeny equations and Navier–Stokes equations. Experiments of coating a non-Newtonian solution (black strap molasses) onto carbon paper (Toray 090) are conducted and the penetration depths are measured to validate the model. Preliminary results show that predicted and measured penetration depths follow the same trend; that is, as the coating speed increases the penetration depth decreases. However, the simulated penetration depths are found to be one to two times higher than measured values at low coating speeds. Even so, the results are considered reasonable, due to imposed simplifications and approximations of the CFD model and errors associated with the experiments and measurements.     

Experimental study and numerical simulation the air jet flow field of a dual slot sharp blunt die in the melt blowing nonwoven process

In this work, the physical model of a polymer in a melt blowing process is established and solved by introducing the numerical computation results of the air jet flow field of the dual slot sharp inset die. The influence of the melt blowing processing parameters and the die design parameters on the fiber diameter is also studied. A lower polymer throughput rate, higher polymer melt initial temperature, higher air initial temperature, higher air initial velocity, smaller angle between slot and axis of the spinneret, smaller width of the die head, and larger width of the slot can all produce finer fibers. At the same time, the air jet flow field model of the dual slot sharp inset die of polypropylene polymer nonwovens fabrics in melt blowing process was also established. The air jet flow field model was solved by using the finite difference method. The computational simulation results of the distributions of the z‐components of air temperature and air velocity along the spinline during melt blowing process are in accordance with the experimental data. The air drawing model of melt blowing process was simulated by means of the numerical simulation results of the air jet flow field. The predicted fiber diameter agree with the experimental data. The effects of the air initial velocity and air initial temperature on the fiber diameter were studied and discussed. The results demonstrate that a higher air initial velocity and a higher air initial temperature are beneficial to the air drawing of the polymer melt and thus to reduced fiber diameter. The results show the great potential of this research for computer assisted design in melt blowing nonwoven process and technology. POLYM. ENG. SCI., 57:417–423, 2017. © 2016 Society of Plastics Engineers