Coextrusion flow of two molten polymers between parallel plates: Non isothermal computation and experimental study

A theoretical study of the one-directional coextrusion flow of two molten polymers between parallel plates has been carried out using a non-isothermal power-law model. A numerical method has been used to solve simultaneously the momentum and energy balance equations, in order to obtain the evolutions of the interface position, the pressure gradient, and the temperature profiles all along the flow. The theoretical results are in good agreement with experimental values measured on an industrial coextrusion line.     

Stratified two-phase flow of molten polymers

A study has been made of stratified two-phase flow of molten polymers in a slit die. For the experimental study, measurements were taken of wall normal stresses along the longitudinal axis of a rectangular duct which had an aspect ratio of 10. Three pressure transducers were flush-mounted on each of the rectangle's long sides, directly opposite from each other. The measurements permitted one to determine the pressure gradients of each component (their viscous properties) and the exit pressures of each component (their elastic properties). For the theoretical study, the fully developed velocity distributions of two-phase flow were determined by solving the equations of motion by use of a power law model. The volumetric flow rates, calculated theoretically by use of a power law model, are compared with experimentally observed ones. Experimental evidence is presented which clearly shows that polystyrene and polypropylene form two incompatible phases in the molten state.     

Steady-state mass transfer between two opposite discs and a liquid in radial divergent flow

The paper deals with global and local mass transfer between a liquid and two opposite fixed discs. The liquid is introduced through a central hole in one of the discs and flows radially. The mass transfer coefficients, measured by the electrochemical method, are empirically correlated. The correlations are compared with corresponding empirical correlations from the literature. Local measurements using microelectrodes allowed to determine the evolution of the local mass transfer coefficients over each disc as a function of the geometrical parameters, particularly the gap between the discs.     

On the pressure dependency of the viscosity of molten polymers

A slit viscometer to measure the viscosity of polymer melts under processing conditions is described. Along the slit a pressure drop is generated by applying a pressure at both the entrance and the exit. In this way the pressure in the center can be controlled independently of the shear rate. The pressure gradient in the slit is measured by means of three pressure transducers which are mounted in the region of fully developed flow. Results of pressure-dependent viscosity measurements on polystyrene, polyacrylonitrile-butadiene-styrene, and polypropylene are presented in a shear rate range of five decades. The flow curves obtained at different pressures and temperatures can be shifted onto a master curve. The shear thinning behavior of the three materials is adequately described with the generalized Cross-Carreau equation, while the zero shear viscosity is modeled with a generalized Arrhenius-W.L.F. relationship, incorporating a pressure dependency. Alternatively, it is possible to describe the zero shear viscosity in terms of the free volume fraction and the temperature.     

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.     

Two directional coextrusion flow of two molten polymers in flat dies

A theoretical study has been carried out of the two directional isothermal flow of two molten polymers in a flat die. The viscous behavior of each fluid is described by a power-law. Using an iterative finite difference method, a numerical program predicts the influence of geometrical and Theological parameters on the variations of the interface position. Theoretical values are in good agreement with experimental results obtained on a fish-tail die. In the case of a coat hanger-die, the mean value of the interface position is correct, but the general shape may be quite different.     

A Re‐Examination of heat transfer in laminar divergent flow between two parallel fixed discs

Upon a critical review of pertinent literature, new theoretical expressions for dimensionless heat transfer rates between two parallel fixed circular discs and a fluid in radial divergent laminar flow are established and compared to previously published theory and experimental data. Based on the logarithmic mean temperature difference, the new analytical relationships are shown to adequately predict dimensionless heat transfer rates, and it is recommended that they be used in preference to certain earlier expressions which are either erroneous or of strongly limited applicability.     

Influence of elastic effects on capillary flow of molten polymers

Capillary viscometer measurements for a number of polyethylenes and polystyrenes reveal deviations from linearity in plots of applied pressure versus capillary length to diameter ratio, at constant rates of shear, resulting in apparently negative end corrections. This is contrary to previous physical considerations. Some polymers obey Hooke's law in shear permitting the separation of the end correction into two components. A Couette correction, dependent upon the capillary dimensions, is constant for any given polymer, shear rate, and temperature; an elastic shear strain correction, dependent upon the transit time through the capillary, may be determined by post-extrusion measurements. Determination of these two correction leads to linear plots of pressure versus capillary length to diameter ratio and enables flow curves to be calculated independent of the capillary dimensions and the swell properties of the polymer.     

Flow distribution and velocity measurement in a radial flow fixed bed reactor using electrical resistance tomography

Electrical resistance tomography is a relatively simple and inexpensive technique for imaging electrically conducting systems. It has been applied to visualise the flow pattern and distribution inside a radial flow packed bed of novel design for improving reactor performance with lower pressure drop. The density of information yielded by electrical tomography is suitable for validation of Computational fluid dynamics. Sets of tomographic images representing slices through a packed bed have been obtained for a 8-plane × 16-electrode sensor configuration which produces of the order 10³ conductivity measurements in three-dimensions. Pulse injections of high conductivity tracer, both uniformly in the feed and localised, can be imaged as multiple tomographic images or 3D solid-body images, revealing the internal flow pattern. Differentiation of the motion of the tracer peak conductivity within pixels in the sensing planes and between the planes allows the local flow velocities and directions to be determined. This quantifies the flow pattern for uniformity and radial distributive properties.     

并行微通道内气液相分配规律

微反应器的集成放大对于微化工技术的工业应用具有重要意义。利用高速摄像仪对4个并行微通道内气液两相流动状况及相分配规律进行了研究,考察了气液两相流量及液相黏度对两相分布均匀性的影响。实验所用液相为含0.3%表面活性剂十二烷基硫酸钠（SDS）的蒸馏水-甘油溶液,气相为氮气（N₂）。实验观察到了6种典型的两相流型。对各支通道均为弹状流情况下气泡长度和气泡速度的分布规律进行了研究。在一定气相流率下,各支通道气泡长度的相对标准偏差随液相流率的增大而增大,气泡速度的相对标准偏差值随液相流率的增大先升高到一定值然后逐渐减小。气相分配不均匀性随液相流率和黏度的增大而增大,液相分配不均匀性随液相黏度的增大而减小,气相流率的变化对于两相分布影响不明显。研究结果有助于并行微通道的结构设计与优化,以实现更为均匀的气液两相流动分配。     

立式分层并联径向流吸附器流场数值模拟

为降低径向流吸附器高度对均布的影响,提出了径向流吸附器的分层并联设计方法,并建立了径向流分层并联吸附器的数值计算模型。应用计算流体力学方法对分层并联式径向流吸附器中流体在床层内的流场进行了数值模拟计算,并在相同条件下与增高改进后的径向流吸附器的流场分布进行对比。结果表明,分层并联设计方法的均匀度相比于增高方法的均匀度提高了80%,有效清除了径向流吸附器过高对床层内流体均布的负面影响,且对分层并联径向流吸附器上部单元床层厚度进一步优化,达到了上下单元同时穿透的目的。     

Experimental measurement of temperature profiles of molten flowing polymers in a heat exchanger

Molten polymer was pumped through an isothermal-wall heat exchanger and the temperature at four radial positions was measured with a hypodermic thermocouple. Temperature profiles were obtained for heating, cooling, and isothermal flow of polyethylene, polystyrene and polypropylene at Graetz numbers from 1.7 to 9.2. The results show large viscous heating effects, particularly for cooling.     

Dispersion in electrochemical cells with radial flow between parallel electrodes. I. A dispersive plug flow mathematical model

The conventional relations for dispersion in tubes and ducts are inappropriate for radial flows such as are found in the disc-stack and pump cells. A first-order mathematical model is therefore developed for radial flow between infinite parallel planes. The shapes of the predicted responses to pulses of injected material are shown to be in qualitative agreement with experimental curves, however the form of the mathematical expression is inappropriate for routine data analysis. Nevertheless simple relationships are derived which enable the dispersion coefficient and mean residence time of an electrogenerated species to be determined from the first and second moments of the response and a knowledge of the geometry of the system. In Part II experimental data are analysed in detail with the aid of the model; however, it is clear that an improved model is of a three-phase flow, a slow phase creeping along either plane with a faster ‘core’ flow in between.     

Optimization design research of air flow distribution in vertical radial flow adsorbers

Non-uniform flow distribution usually exists in a vertical radial flow adsorber, which significantly decreases the utilization of adsorbents. We adopted numerical simulation methods based on the ANSYS Fluent 15.0 software to study the flow pattern in vertical radial flow adsorber, where programs of user-defined functions (UDF) were set up to interpret component equation, momentum equation and energy equation. To solve the problem of non-uniform air distribution, the relationship between the radial pressure drop across the bed and the ratio of cross-sectional area of the central pipe to that of the annular channel was studied, and optimization design of the distributor inserted in the central channel was given by parametric method at the same time. Through comparative analysis in the given experimental condition, the uniformity reached about 99.1% and the breakthrough time extended from 564 s to 1,175 s under the present optimized design method.     

Modeling flow distribution and pressure drop in redox flow batteries

The combination of interdigitated flow fields (IDFF) with porous electrodes offers lower pressure drop and better performance than conventional flow‐through porous electrodes in redox flow batteries. Comprehensive three‐dimensional and simplified one‐dimensional + two‐dimensional models describing flow uniformity and pressure losses within flow through, parallel, and interdigitated flow fields were developed and used to demonstrate the benefits of IDFF. Analytical solutions for IDFF that compare favorably with computational fluid dynamics quantify the trade between pressure loss and velocity maldistribution both along the channels and within the electrode. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3746–3755, 2018     

微细平行流通道换热器流量均布性试验研究

以水为工质,用试验的方法研究了不同进出口结构和Re数下微细平行流通道内流体的流动,使用高速摄影系统拍摄,得到流体在Z型和U型微细通道内的流动情况,并通过Image-pro plus软件提取各通道流体的流速。结果表明:在试验涵盖Re数下,Z型和U型结构换热器流量分配均匀性随着Re数的减小而变好,其中Z型换热器的整体流量分配均匀性提高了约80.4%,U型换热器的整体流量分配均匀性提高了约64.3%;进出口结构对微细平行流通道的流量分配和压降有很大的影响,Z型换热器整体均匀性比U型换热器高约2%—44%,Z型换热器进出口压降比U型减小了约1.2%—19.9%。因此Z型换热器的综合性能更好。     

Thermodynamics of gas solubilities in molten polymers

Perturbed-hard-chain theory is extended to mixtures of polymers and volatile fluids, including supercritical gases. This extension is used to derive an expression for Henry's constant for a solute in a molten polymer. Theoretical calculations and data reduction are reported for a variety of solutes in polyethylene, polyisobutylene, and poly(dimethyl siloxane) in the temperature region 25–300°C. Calculated Henry's constants and their temperature dependence are generally in good agreement with the limited experimental data now available.