Analysis of the fluid–structure interaction in the optimization‐based design of polymer sheeting dies

A polymer‐sheeting‐die‐design methodology is presented that integrates a simulation of the polymer melt flow and die‐cavity deformation with numerical optimization to compute a die‐cavity geometry capable of giving a nearly uniform exit flow rate. Both the polymer melt flow and sheeting‐die deformation are analyzed with a general‐purpose finite‐element program. The approach includes a user‐defined element that is used to evaluate the purely viscous non‐Newtonian flow in a flat die. The flow analysis, which is simplified with the Hele–Shaw approximation, is coupled to a three‐dimensional finite‐element simulation for die deformation. In addition, shape optimization of a polymer sheeting die is performed by the incorporation of the coupled analyses in our constrained optimization algorithm. A sample problem is discussed to illustrate the die‐design methodology. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3994–4004, 2007     

Optimal design of the coat‐hanger die used for producing melt‐blown fabrics by finite element method and evolution strategies

In this article, an optimal design procedure that improves the uniformity of flow rate distribution at the outlet of the coat‐hanger die is proposed. The two‐membered evolution strategy was combined with the finite element method to optimize the design parameters of an initial coat‐hanger die geometry designed by analytical method based on one‐dimensional lubrication method. The slot gap and the manifold angle were chosen to be the optimized design parameters, and the coefficient of variation (CV) value of the flow velocity at the die outlet is regarded as the objective function. The optimal results were achieved in the 22nd generation after 100 generations' evolution, which show that the CV% value of the flow velocity at the die outlet is only 1.3631% and decreases by 68% of the initial value caused by unoptimizable die geometry. POLYM. ENG. SCI., 2009. © 2008 Society of Plastics Engineers     

The flow distribution of molten polymers in slit dies and coathanger dies through three-dimensional finite element analysis

The isothermal flow of power-law fluids in slit dies and coathanger dies is studied. A general three-dimensional finite element code is developed for the purpose of flow analysis. The pressure distribution, the velocity distribution, and the transverse flow rate distribution are obtained. The effect of the die geometry on the flow distribution is critically discussed. It is found that a die channel with cross section of dog bone profile produces a flatter transverse flow rate distribution.     

Model for the outer cavity of a dual‐cavity die with parameters determined by two‐dimensional finite‐element analysis

A coating die forms liquid layers of uniform thickness for application to a substrate. In a dual‐cavity coating die an outer cavity and slot improves flow distribution from an inner cavity and slot. A model for axial flow in the outer cavity must consider the ever‐present cross flow. A 1‐D equation for the pressure gradient for a power‐law liquid is obtained as a small departure from a uniform flow distribution and no axial flow. The equation contains a shape factor dependent on cavity shape, Reynolds number, and power‐law index. The shape factor for five triangular cavity shapes is obtained by finite‐element analysis and correlated for application to die design up to the onset of flow recirculation which arises at the junction of the cavity and outer slot. The performance of the combined cavity and slot is considered and the most effective design determined. © 2017 American Institute of Chemical Engineers AIChE J, 64: 708–716, 2018     

A local power‐law approximation to a smooth viscosity curve with application to flow in conduits and coating dies

Coating dies distribute liquid into a uniform layer for coating onto a moving substrate. A die comprises one or two cavities spanning the coating width and adjoining narrow slots of much higher resistance to flow. In modeling coating dies, the flows in the slots and cavities are often approximated as one‐dimensional to achieve a fully geometrically parameterized model of low computational load suitable for optimizing design for multiple liquids and flow rates. The power‐law model is mathematically efficient for one‐dimensional flows of shear‐thinning liquids but does not include limiting viscosities at low and high shear rates that are frequently present. In previous work, the truncated power‐law model, which is terminated at the limiting Newtonian viscosities, was used to alleviate this shortcoming without sacrificing the mathematical advantages. In this work, the Carreau–Yasuda model replaces the truncated power‐law model as an improvement. For flows in slots and cavities, the Carreau–Yasuda model can be approximated accurately by a local power‐law model with little increase in computational load over the truncated power‐law model. In the transition regions of the Carreau–Yasuda model between Newtonian and power‐law behavior, the local power‐law model gives more accurate results than the truncated power‐law model. POLYM. ENG. SCI., 54:2301–2309, 2014. © 2013 Society of Plastics Engineers     

A flow model for non-newtonian liquids inside a slot die

A one-dimensional flow model for non-Newtonian liquids inside a dual-cavity slot die is presented. The model is capable of analyzing slot dies of any cavity shape, cavity taper, slot-length variations, and slot-gap variations. The proposed model incorporates a truncated-power-law model for the viscosity of non-Newtonian liquids. According to flow models with power-law approximation for liquid viscosity, the distribution of non-Newtonian liquid through a slot die depends on the slot Reynolds number only. With our model, we find that the zero shear viscosity and the relaxation time of a non-Newtonian liquid have large effects on its distribution. For non-Newtonian liquids which are expected to experience shear-thinning over portion of a slot die, it is concluded that a flow model with a truncated-power-law approximation for liquid viscosity be used to predict the liquid distribution from the die.     

Three-dimensional path line tracking and residence time distribution in fishtail dies

The flow kinematics of power-law fluids in fishtail dies is studied. A general isothermal three-dimensional finite element code developed by the authors is used for the flow analysis purpose. The basic geometry of the fishtail die is defined by simple super-elliptical curves, which allows a smooth transition from a circle to a slit. The three-dimensional path line and the residence time distribution (RTD) are calculated from the velocity field obtained from the finite element solution of the conservation equations. The effects of the rheological properties and the die geometry on the path line pattern and the residence time distribution are investigated. The results indicate that as both the length of the transition zone and the fishtail angle increases, the residence time distribution becomes more uniform. However, the power-law index does not affect the residence time distribution significantly.     

Numerical analysis of the stagnation phenomenon in the coat‐hanger die of melt blowing process

In this paper the stagnation phenomenon occurred in the coat‐hanger die is investigated using a three‐dimensional finite element method to simulate the polymer fluid flow in the die. The stagnation zone is defined to evaluate the degree of the stagnation. The effects of the inlet flow rate, the slot gap, the manifold angle, and the power‐law index on the stagnation are then analyzed numerically. It is found that the manifold angle and the geometric abrupt change between the manifold and the slot have significant influence on the stagnation, and a coat‐hanger die with tear‐dropped manifolds to be capable of diminishing the stagnation. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Inertia and gravitational effects in extrusion dies for non-Newtonian fluids

An analysis is presented which allows the sheet or film die designer to estimate when inertial and gravitational effects are important. General theoretical equations are developed for end fed dies with arbitrary variation of the cavity cross sectional shape, cavity taper, slot length, and gap over the width. The method assumes viscous flow and a two dimensional approximation for the cavity flow. For fluid flow properties, it is assumed only that the apparent viscosity is a single valued function of the shear rate. In the important special case of constant die geometry and power law fluids, three dimensionless numbers plus the power law index are the parameters controlling the uniformity of flow from the die. Results are presented that illustrate when die orientations with respect to gravity and when fluid inertia are important. When they are not, simple expressions for die inlet pressure and uniformity index are given.     

塑料异型材挤出口模的三维罚有限元设计

讨论了现有塑料异型材挤出口模研究中的流变学分析方法,指出了前人运用流变学方法设计挤出口模的不足。本文采用三维罚有限元方法,对幂律流体在塑料异型材口模中的流动进行了计算机模拟研究,阐述了采用三维罚有限元方法进行塑料异型材挤出口模设计的重要意义     

Modeling and simulation of the hole pressure problem

Whenever a polymeric or viscoelastic liquid flows over a depression in a channel, the phenomenon of hole pressure occurs. Modeling and simulation for the flow of an Oldroyd‐B type fluid passing over a transverse slot is considered here. This type of fluid is a good model for some polymeric liquids. In the model, it is assumed that the extra stress of the solution is the sum of the contribution from the solvent and the contribution from the polymer molecules. The results obtained in the study are computed by using the elastic‐viscous split‐stress finite element method incorporating the non‐consistent streamline‐upwind scheme (EVSS/SU finite element method). As a verification of the numerical scheme, the algorithm is first applied to compute the corresponding flow of the upper‐convected Maxwell fluid model, a special case of the Oldroyd‐B model. Hole‐pressure is evaluated for various Deborah numbers (De), and compared with that derived from the Higashitani‐Pritchard (HP) theory. The agreement between the two is found to be satisfactory for creeping flow in the De range for which the Higashitani‐Pritchard theory is valid. Subsequently, hole‐pressure and characteristics of this flow problem are predicted. Futhermore, the effects of fluid elasticity, inertia, and slot geometry on hole‐pressure are investigated.     

Response of slot coating flows to periodic disturbances

Slot coating is a common method in the manufacture of a wide variety of products. It belongs to a class of coating method known as premetered coating: in a steady-state operation, the thickness of the coated liquid layer is set by the flow rate fed to the die and the speed of the substrate moving past, and is independent of other process variables. Thus premetered methods are ideal for high precision coating. However, even the best designed slot coating operations are subjected to small oscillations on the process conditions, such as flow rate, vacuum pressure and gap fluctuations. These oscillation may lead to unacceptable variation on the thickness of the deposited liquid layer. The effect of process condition disturbances on the coated layer has to be minimized to assure a wet thickness as uniform as possible.The effect of an imposed periodic perturbation on the liquid flow rate or on the gap clearance in the coated layer thickness is explored in this work by computer-aided analysis. The amplitude of the thickness variation is determined at different process conditions and die configurations by solving the transient, two-dimensional, viscous free surface liquid flow in the coating bead. The system of equations, with appropriate boundary conditions, was solved by the Galerkin/finite element method, and an implicit time integration. The results show the response as a function of the imposed perturbation frequency and of the die geometry. They indicate that the die geometry may be optimized in order to minimize the film thickness oscillation of a slot coating operation.     

一种新型多流道分配机头的设计及其流场分析

本文涉及一种新型的多流道熔体分配机头,其分配流道的设计能够尽可能保证熔体流动路径的一致性。运用基于有限元的CFD分析软件Polyflow对熔体进行了模拟计算,并运用后处理软件Fieldview,对三种不同流道的分配机头模型的压力场、速度场及黏度场进行了分析比较,得出了一些有关该新型分配机头的设计要点。     

A finite piece method for simulating polymer melt flows in extrusion sheet dies

A finite piece method is proposed to simulate three‐dimensional slit flows in extrusion sheet dies in this paper. The simulations concern incompressible fluids obeying different constitutive equations: generalized Newtonian (Carreau‐Yasuda law), and viscoelastic Phan‐Thien Tanner (PTT) models. Numerical simulations are carried out for the isothermal and nonisothermal flows of polymer melt through sheet dies. The Picard iteration method is utilized to solve nonlinear equations. The results of the finite piece method are compared with the three‐dimensional (3D) finite element method (FEM) simulation and experiments. At the die exit, the relative error of the volumetric flow between the finite piece method and the 3D FEM is below 1.2%. The discrepancy of the pressure distributions does not exceed 6%. The Maximum error of the uniformity index between the simulations and experiments is about 2.3%. It shows that the solution accuracy of the finite piece method is excellent, and a substantial amount of computing time and memory requirement can be saved. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Optimal geometry design of the coat‐hanger die with uniform outlet velocity and minimal residence time

In this article a method combining the orthogonal array design and the numerical simulation is used to optimize the geometry parameters of the coat‐hanger die with uniform outlet velocity and minimal residence time. The outlet velocity and the residence time are obtained by simulating the three‐dimensional nonisothermal polymer flow in the coat‐hanger die, while the optimal geometry design is accomplished via the orthogonal array method. The effects of the manifold angle, the land height and the slot gap on the outlet velocity and the residence time are investigated. The results show that the effects of all the three parameters are significant for the outlet velocity. For the residence time, the manifold angle and the slot gap are the significant factors, while the effect of the land height is insignificant. The optimal geometry parameters of the coat‐hanger die achieved in this study are that the manifold angle is 5°, the height land is 70 mm, and the slot gap is 3 mm. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

挤塑口模中三维路线示踪与停留时间分布

用PTT模型研究了聚合物在挤塑口模中的三维流动,提出一种通用的三维路线示踪方法用于流动分析。用有限元法分析控制方程得到的速度场,可以计算熔体的三维流动路线和停留时间分布,算例表明这是一种简单、实用的求解停留时间分布的方法。     

Two-layer tensioned-web-over-slot die coating: Effect of operating conditions on coating window

Tensioned-web-over-slot die (TWOSD) coating deploys elastohydrodynamic interaction to control the distance between the moving substrate and the coating die lip surface in order to be able to coat an ultra-thin liquid layer. Dual slot TWOSD coating is designed to deposit two thin uniform liquid layers onto a moving web simultaneously. Like in the fixed-gap dual slot coating, the interlayer separation point needs to be at the downstream corner of the mid lip in order to prevent coating defects. Different flow features, like weeping, bead breakup and feed slot vortices, limit the range of operating parameters that ensures uniform coating, and define the operating window of the process. In this study, we analyze dual slot TWOSD coating flow by solving the Navier–Stokes equation coupled with thin cylindrical shell equation using the finite element method. The boundaries in the parameter space that define the operating window or vortex-free window are automatically computed by a direct tracking method of flow features. The effect of operating conditions, such as liquid viscosity, web tension and web speed, on the critical layer thickness at which the coating becomes non-uniform is determined by this study.     

工作参数对2.4m幅宽中央进料式螺杆分配机头内部流场的影响

运用ANSYS的二次开发语言APDL建立了参数化的2.4 m幅宽螺杆分配机头的几何、有限元模型,并生成了宏文件。对分配螺杆的歧管部分采用自由划分网格,狭缝型流道则采用规则的六面体映射网格。借助于ANSYS有限元软件对2.4 m幅宽中央进料式螺杆分配机头内的流场进行了三维模拟分析,比较了入口压力的变化、分配螺杆的转速对机头内部压力场、速度场的影响。分析得出,入口压力值降低有助于机头内的压力均匀分布,增加螺杆转速有助于提高机头内的压力分布的均匀性。     

注塑机拉杆应力分布的影响因素研究

针对注塑机拉杆的早期断裂问题，为使拉杆应力分布合理化，以拉杆与定模板、动模板和调模板等组成的整体有限元分析模型为基础，用优化方法研究拉杆卸载槽的合理位置以及各模板基本厚度的确定，以及拉杆卸载槽的位置和各模板基本厚度对拉杆应力分布的影响。用有限元分析方法对优化结果进行分析，可直观分析与判断拉杆、模板的应力分布状况，用以保证模板结构拓扑优化对其基本参数的要求。有限元分析方法和优化方法的综合运用，可在保证拉杆应力分布合理的前提下，保证模板变形的协调性，以减少其弯曲变形而产生的附加弯矩对拉杆的不利影响。本文的研究方法，可为注塑机拉杆与各模板的设计与改进提供理论依据。