Uniformity of flow from sheeting dies

A numerical method for analyzing the uniformity of flow from sheeting dies is presented. The method assumes that the flow is isothermal and that the material is a power law fluid. A uniformity index is defined and methods are presented which enable die dimensions to be established which will result in a specified uniformity at particular flow rates and pressure drops. The analysis shows that the flow index “n” of the power law is the key parameter determining the uniformity of flow from a sheeting die.     

Optimization‐based design of polymer sheeting dies using generalized Newtonian fluid models

A polymer sheeting die design methodology is presented, which integrates finite element flow simulations, numerical optimization, and design sensitivity analyses to compute die cavity geometries capable of giving a near‐uniform exit velocity. This work extends earlier die design methods to include generalized Newtonian fluid (GNF) models that represent the shear‐thinning behavior of polymer melt. Melt flow computations and design sensitivity analyses are provided using the generalized Hele‐Shaw flow approximation with isothermal power‐law, Carreau‐Yasuda, Cross, Ellis, and Bingham fluid models. The nonlinear equations for die cavity pressure are solved using the Newton‐Raphson iteration method and design sensitivities are derived with the adjoint variable method. The die design method is applied to an industrial coat hanger die, in which a design parameterization is defined that allows for an arbitrary gap height distribution in the manifold of the die. In addition, die performance is assessed and compared for power‐law and Carreau‐Yasuda fluid flow over a range of die operating conditions. Pareto optimal die designs are also considered in this study. POLYM. ENG. SCI., 45:953–965, 2005. © 2005 Society of Plastics Engineers     

The influence of power‐law rheology on flow distribution in coathanger manifolds

Coathanger dies are effective in delivering uniform flow if a polymer melt; however, when the fluid flow index varies from the design values, the flow is not uniform. Although mechanisms such as die lip adjustments have been effective tools for adjusting flow profiles, the issue of a variable flow index has not been fully addressed at the design stage. An analytical solution, based on the assumptions present in the 1‐D design equation, has been developed for the flow distribution in a coathanger manifold. This solution determines the flow distribution for a power‐law fluid with a flow index n* in a manifold designed for a separate flow index n*. From this solution, a uniformity index and a critical design angle are defined. The critical design angle is the angle at which the local derivative of the uniformity index with respect to n* approaches a maximum (for n* < n) or a minimum (for n* > n) as a function of the design angle. The critical design angle is independent of n and is presented as a function of the manifold aspect ratio.     

Effect of wall slip on the uniformity of flow from sheeting extrusion dies

A theoretical study for analyzing the uniformity of flow from sheeting extrusion dies is presented. In this study it is assume that a slip condition exists at the wall of the die, the magnitude of slip velocity is proportional to the shear stress at the wall, the flow is isothermal and steady state, and a power law model is valid for viscosity. Two extrusion dies, T-dies and coat-hanger dies, are examined. The flow uniformity at the exit of the die is calculated and compared with that for a nonslip analysis. The discrepancies between the slip and nonslip models imply that the wall slip condition induces a significant nonuniform flow distribution. Traditional design criticism based on the nonslip model are invalid for flow with the wall slip condition, and it is necessary to increase the length of the die land to even the flow distribution at the exit of the die.     

Theoretical Analysis on Flow of Polymer Melts in Screw Die

Abstract

Flow of polymer melt in screw dies is theoretically analyzed by the broken section method with the uniformity of the extrudates. An isothermal, laminar and steady state power law fluid is assumed. The analysis is discussed in two parts, i.e., screw flow and die slit flow. A way of computer calculation by means of a method of iteration is presented by considering volume balance between screw flow and slit flow.

An ideal screw die is one in which pressure distribution is constant along the screw axis, i.e., the shape of the die slit is constant along the axis and the screw is such that the depth of screw channel decreases almost linearly.     

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     

Flow distribution in spiral mandrel dies

An analysis of flow of a power law fluid in a spiral mandrel die is presented. The analysis is applied to study the effect of various die design parameters on the flow distribution at the end of the spiral mandrel section. Three variables that have a very strong effect on the flow distribution are the number of grooves, the initial clearance, and the groove helix angle. The distribution is improved by increasing the number of grooves, by using a non-zero initial clearance, and a relatively small helix angle. Two more variables that have a significant effect on the flow distribution are the taper angle and the initial groove depth. The optimum taper angle was found to be between 1 and 3 degrees. The distribution uniformity improves with the initial groove depth, while the pressure drop reduces at the same time.     

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.     

Flow behavior of polypropylenes with different molecular structures in a coat‐hanger die

An experimental investigation of the flow behavior of three polypropylene melts with different molecular structures during extrusion through a coat‐hanger die is presented. Two linear and one long‐chain branched material, rheologically characterized in shear and elongation, were investigated. Using laser–Doppler velocimeter measurements of the velocity profiles across the gap height were performed at five various locations along the die. The uniformity of the velocity distribution along the die has been assessed using the maximum velocities v₀ of the corresponding velocity profiles across the gap. The velocity distribution along the die changes with throughput and temperature. Regarding the rheological properties, it was found that the power‐law index of the viscosity as a function of shear rate has a decisive influence on the uniformity of flow but that the pronounced strain hardening in elongation typical of the long‐chain branched polypropylene is not reflected by the velocity distribution along the die. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

A systematic approach for the design of a spiral mandrel die

An effective design strategy is presented for the determination of optimal flow channel geometry of a spiral mandrel die, which can produce annular, thin, and uniform products of polymer melt. This strategy includes two steps: First, a two-dimensional flow simulation associated with the Taguchi approach is applied to search several sets of die geometric parameters, from which process the flow uniformity is assessed. Second, the optimum one parameter set selected by further considering total pressure drop, mixing degree and residence time distribution (RTD). The strategy is illustrated through the design of a spiral mandrel die with four spirals traveling a full 360°, and the viscosity of polymer melt is assumed to be power law model. The results indicated that the design criteria such as high flow uniformity, low pressure drop, good mixing degree and narrow RTD are difficult to attain simultaneously. For a particular polymer melt, there exists a design window for the geometric parameters; within the window the geometric parameter set may satisfy most of the design criteria.     

入口流速对间断微通道内流型演变及流量分配特性影响

微通道内气液两相流动规律是影响微通道换热器换热系数和流场温度均匀性的主要因素。以N2和H2O为工质，对间断、并联矩形微通道换热器内气液两相流型的起始、发展、稳定过程的演化以及并联通道内流量分配不均匀特性进行了数值模拟研究。结果表明，不同的进口Re对微通道内流型的演变过程和流动周期有重要影响，当进口Re为450时，气相工质在均流腔内以离散的散团状形态脉动扩散至微通道中，并联通道内气相工质从弹状流型态逐渐转变为泡状流型态；当进口Re增至为1600时，气相工质在均流腔内以较连续的椭圆状型态扩散至微通道中，并联通道内气相工质从环状流型态逐渐转变为泡状流型态。通道结构还将影响并联通道间的流量分配的均匀性，间断微腔的存在使微通道内工质质量流量分布均匀性提升38.7%，通过研究通道内压力分布规律，发现通道内静压的分布不均匀是导致两相工质从均流腔进入微通道时发生不均匀分配的重要原因。     

The effect of mandrel rotation on power consumption in polypropylene extrusion

Improved properties of thermoplastic pipes may be achieved by rotating the core of the extrusion die, to produce orientation in the tangential direction. It has been suggested that a further advantage of mandrel rotation is an increased output rate for a given power input. The flow of a “power law” fluid through a rotating die is analyzed, and the power consumption and throughput are investigated. Experimental results for polypropylene melt are presented, which illustrate the effect of rotation on the die characteristics. It is found that the output is increased, but the savings are minimal in view of the power which must be introduced via the rotating mandrel.     

发射药药料离模膨胀和流动均匀性模拟及在模具设计中的应用

为了分析挤出成型过程中模具结构参数对七孔硝基胍发射药离模膨胀率及流动均匀性的影响规律,采用计算流体力学方法,对挤出成型过程进行模拟计算,讨论了模具各结构参数重要性的主次关系;对七孔发射药制备模具进行了结构优化,并进行了实验验证。结果表明,模具收缩角对膨胀率和药料出口速度均匀性的影响最大,压缩段高度次之,成型段长度的影响最小。模具优化后流道出口端速度分布均匀性提高36.53%,表明该模拟计算的可靠性与实用性。     

Modeling of mold filling process for powder injection molding

The mold filling process has been modeled for the injection molding of different polymer-based binders and powder-polymer mixtures. It is essentially a two dimensional non-Newtonian fluid flow analysis in a non-isothermal environment. A complete analysis is accomplished by combining a finite element method and control volume technique to describe an increment of flow front movement, whereas a finite difference method is used to solve the energy equation to characterize the temperature distribution. Numerical results are compared to exact solutions for a circular ring cavity using a power law fluid model under an isothermal condition. Comparison of computed results against published data for a simple circular disk shows good agreement between the two analysis methods. After making selected comparison studies, it is demonstrated that the filling process in Powder Injection Modeling with different combination of powder-polymer mixtures is markedly dependent on specific combinations of powder; and polymer based binders. Computed flow front results for a rectangular cavity also compared favorably against the data for a power law fluid model under non-isothermal conditions.     

Natural convection in a vertical porous cavity filled with a non‐newtonian binary fluid

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non‐Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power‐law model is used to characterize the non‐Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double‐diffusive convection (a = 0) and Soret‐induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat‐driven and solute‐driven natural convection. For convection in a thin vertical layer (A ? 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, φ, the power‐law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012     

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     

NEWTONIAN FLUID SPHERE WITH RIGID OR MOBILE INTERFACE IN A SHEAR-THINNING LIQUID: DRAG AND MASS TRANSFER

The drag force and the mass transfer rate of a Newtonian fluid sphere, having mobile or rigid interface, moving in a power law fluid, are obtained by an approximate solution of equations of motion in the creeping flow regime. It is shown that both the drag and mass transfer increase as the flow index of the external fluid decreases.

The increase of drag due to the pseudoplastic anomaly is more significant at large viscosity ratio parameter. The results obtained are in good agreement with available experimental data and with those analyses based on variational principle when the non-Newtonian flow behavior is not very pronounced.

Also, the predicted mass transfer rates are in good agreement with the trends presented in the literature. Unlike in the case of drag force, the effect of the pseudoplastic anomaly on mass transfer rate is more pronounced for low values of the viscosity ratio parameter. The analysis was extended to include the case when the surface of the sphere was immobilized by surface-active contaminants.     

NEWTONIAN FLUID SPHERE WITH RIGID OR MOBILE INTERFACE IN A SHEAR-THINNING LIQUID: DRAG AND MASS TRANSFER

The drag force and the mass transfer rate of a Newtonian fluid sphere, having mobile or rigid interface, moving in a power law fluid, are obtained by an approximate solution of equations of motion in the creeping flow regime. It is shown that both the drag and mass transfer increase as the flow index of the external fluid decreases.

The increase of drag due to the pseudoplastic anomaly is more significant at large viscosity ratio parameter. The results obtained are in good agreement with available experimental data and with those analyses based on variational principle when the non-Newtonian flow behavior is not very pronounced.

Also, the predicted mass transfer rates are in good agreement with the trends presented in the literature. Unlike in the case of drag force, the effect of the pseudoplastic anomaly on mass transfer rate is more pronounced for low values of the viscosity ratio parameter. The analysis was extended to include the case when the surface of the sphere was immobilized by surface-active contaminants.     

LLDPE／LDPE共混物熔体挤出胀大行为的研究

应用毛细管流变仪，考察了实验条件下线性低密度聚乙烯与低密度聚乙烯共混物（ＬＬＤＰＥ／ＬＤＰＥ）熔体挤出胀大行为及其影响因素。结果表明，挤出胀大比Ｂ与剪切应力近似呈幂律关系，而随口型长径比的增加呈指数衰减，当共混比为５０／５０时，Ｂ产生局部极涉值现象。     

Effect of elongational viscosity on axisymmetric entrance flow of polymers

A finite element simulation of the flow in a channel with an abrupt contraction is presented. The effects of the shear and elongational viscosities of a polymer on the entrance flow are analyzed employing a truncated power‐law model. The power‐law index and the strain rate characterizing the transition from Newtonian to power‐law behavior for the elongational viscosity are treated as being independent of the values of these two parameters for the shear viscosity. The effect of flow rate on entrance flow is also analyzed. It is confirmed that the Trouton ratio is important in determining the recirculating vortex and the extra pressure loss in entrance flow. Extra pressure loss and vortex length predicted by a finite element simulation of entrance loss are compared with the corresponding predictions from Binding's approximate analysis.