Flow analysis network (FAN)—A method for solving flow problems in polymer processing

A finite element method is proposed for solving two dimensional flow problems in complex geometrical configurations commonly encountered in polymer processing. The method is applicable to flow in relatively narrow gaps of variable thickness and any desired shape. It was developed for analyzing flow in injection molding dies and certain extrusion dies. The fluid can be any non-Newtonian fluid which is incompressible, inelastic, and time independent. The flow field is divided into an Eulerian mesh of cells. Around each node, located at the center of the cell, a local flow analysis is made. The analysis around all nodes results in a set of linear algebraic equations with the pressures at the nodes as unknowns. The simultaneous solution of these equations results in the required pressure distribution, from which the flow rate distribution is obtained. Solution for the isothermal Newtonian flow problem is obtained by a one-time solution of the equations, whereas solution of a non-Newtonian problem requires iterative solution of the equations.     

Non-newtonian flow modeling in the mixing section of a single-screw extruder with flow analysis network method

The flow of non-Newtonian fluids obeying the power-law relation through the mixing sections of a single-screw extruder is analyzed with a modified flow analysis network (FAN) method. Three types of mixing elements, the Maddock, the dulmage, and the blister ring elements, are studied. The Maddock and the blister ring elements are dispersive type elements. They generate high pressure drop, and yield a negative pressure gradient which indicates poor pumping capability. The flow fields are rather regular in these elements. On the other hand, the dulmage element is a distributive type element. It generates a low pressure drop, and yields a positive pressure gradient at low extrusion rate which indicates better pumping capability than the dispersive type elements. Extensive flow splitting and reorientation is observed in this element. The power-law exponent has significant effect on pumping characteristics. However, the overall flow patterns of Newtonian fluids and power-law fluids in these mixing elements are quite similar.     

环形D模机头流道有限元数值模拟

通过有限元分析软件POLYFLOW建立了环形口模机头的三维等温流场模型.在改变机头流道结构参数以及工艺条件的情况下,对流道的压力场、黏度场及翦切场进行了研究.模拟的数字结果显示,随着口模间隙的增大,流道内的压力场减弱并随着间隙的增大而迅速降低,容易导致聚丙烯在机头内提前发泡.     

环形口模机头流道有限元数值模拟

通过有限元分析软件POLYFLOW建立了环形口模机头的三维等温流场模型。在改变机头流道结构参数以及工艺条件的情况下,对流道的压力场、黏度场及剪切场进行了研究。模拟的数字结果显示,随着口模间隙的增大,流道内的压力场减弱并随着间隙的增大而迅速降低,容易导致聚丙烯在机头内提前发泡。     

Experiments and flow analysis of a micropelletizing die

A study has been performed to examine the process of micropelletization on four different polyethylenes with melt index values between 1 and 5 g/10 min. The experiments were done on a 50‐mm 30:1 L/D extruder with an underwater micropelletizer attached. The average micropellet size that was produced ranged from 0.4 to 0.5 mm in diameter depending on whether a plastomer or high‐density grade was selected. The dimensions of the pellets were influenced strongly by the occurrence of die‐hole freeze‐off. Minor sharkskin was observed on the surface of the micropellets, a result of the high stresses experienced in the pelletizer die. A non‐isothermal, axisymmetric flow model was used to assist in the analysis by comparing the observed results to the predicted shear stresses in the die. The calculations revealed that extremely high shear rates were present in the die holes, resulting in a significant degree of wall slip. The measured rheological properties of the micropellets did not show any change in comparison to their virgin resins, likely because of the presence of wall slippage and the short residence time of the polymer in the die holes. Polym. Eng. Sci. 44:1391–1402, 2004. © 2004 Society of Plastics Engineers.     

Design,optimization, and manufacturing of a multiple‐thickness profile extrusion die with a cross flow

This article presents a procedure to achieve a uniform outlet flow of molten polymer for a complex die profile with various thicknesses in die outlet cross section. According to a specific optimization methodology, the die was optimized based on varying die land length. The scope of this article includes: 3D flow simulation, optimization of the die velocity outputs based on the results of simulation process, and comparison of numerical predictions with the experimental data. Finally a significant result obtained by this work indicates higher ratio of the land length to the height of the zone with cross flow rather than the zones that are directly fed by the extruder. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers.     

Improvement of ethylene cracking reaction network with network flow analysis algorithm

Reaction network model is central to ethylene cracking process simulation. Studying an ethylene cracking reaction (ECR) network, which involves hundreds of components and thousands of reactions, becomes a difficult task. To facilitate a rapid and comprehensive reaction network analysis and improve ECR network, this paper introduced a ranking algorithm called network flow analysis algorithm (NFAA) to a reaction network analysis procedure. NFAA analyses the reaction network with comprehensive information such as network topological structure, reaction mechanism, and process model data. Following NFAA, reactions and species are ranked based on their significances. According to the ranking of reactions, unimportant reactions (lower ranking) in ECR network are removed to reduce ECR network complexity and decrease computational scale without loss of prediction accuracy. On the other hand, rankings provide guidance on adjusting parameters of ECR network. The application of NFAA makes a progress in improvement of ECR reaction network in an industrial case.     

Analysis of flux decline during ultrafiltration of sugarcane juice (Limed) using cross flow cell

Experimental and theoretical studies were carried out to analyse the flux decline behaviour of limed sugarcane juice and retention characteristics of its components (total dissolved solids, sucrose and colour) in a rectangular cross flow ultrafiltration cell. Retentions of sucrose and total dissolved solids were found to increase with increase in pressure and feed bulk concentration. A theoretical model was developed to describe flux decline, combining the effects of formation of a gel‐like porous layer (constituting high molecular weight substances) and osmotic pressure controlled layer (constituting low molecular weight substances). Predictions were observed to be in good agreement.     

Experimental and CFD analysis of two-phase cross/countercurrent flow in the packed column with a novel internal

The pressure drop and liquid hold-up for the G-L cross/counter-current flow in a packed column with a novel internal was simulated using a Eulerian/Eulerian two-fluid model solved by a commercial CFD software CFX4.4. Simulation results are in good agreement with the experimental data of pressure drop. The internal significantly increases the gas radial velocity and lower the gas axial velocity, which lowers the pressure drop and improves operational flexibility. To minimize bypass flow caused by the internal, optimum baffle thickness and width of the internal's passage are proposed.     

Analysis and simulation of non-Newtonian flow in the coat-hanger die of a meltblown process

Meltblown is one of the fastest growing processes for nonwoven production. The design of the coat-hanger geometry of a die is very important for meltblown technology. In this article, melt rheological properties were studied based on capillary rheometry, followed by analysis and simulation of the melt flow in the die and its experimental verification. It is essential for the optimal design of the die and helps to better understand the meltblown process as well. The result of this research showed that the rheological properties of melt flow in the die obey the power-law equation very well in the meltblown process. The coat-hanger die has a good operation feasibility for different resins and various operation conditions from the view of web uniformity. The pressure drop through the orifices is the major contribution to the pressure drop in the die. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 67: 193–200, 1998     

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.     

Analysis of slot coating flow under tilted die

Slot coating is a high precision coating method, where the film thickness is controlled by the flow rate fed to the die and the production speed. The range of desirable operating conditions for uniform coating is limited by the shape and locations of upstream and downstream menisci, which are controlled by the pressure gradient within the coating flow. The gradient can be controlled by the shape and orientation of the slot coating die, that is, die configuration. Here, the tilted die, the so‐called angle‐of‐attack configuration is considered. The configuration is similar to underbite and overbite configurations, but it has a sloped die lip due to tilting. Coating flows with such a configuration are examined by computer‐aided analysis using the Galerkin/finite element method. Using steady‐state analysis, the effect of the angle of attack on the upstream meniscus location is discussed. In transient analysis, the amplitude of the thickness variation is predicted under different types of disturbances, namely flow rate and gap oscillations. The analysis shows that die lip configurations affect the thickness uniformity under periodic disturbances. The effect of die tilting can be similar to or different from the underbite/overbite configurations, depending on the type of oscillation. During the analysis, the flow rate apportioning inside the coating flow and decomposing thickness variations into two separating oscillations are useful in understanding the results is found. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1745–1758, 2015     

横流环境中压电风扇耦合射流流动换热特性

利用激光多普勒测振仪分别测定攻角和横流速度对压电风扇振幅的影响。基于相应的振动测试结果利用动网格技术对横流环境中不同安装角度下压电风扇冷却加热壁面的三维非定常流动和传热特性进行了数值模拟,同时应用红外热像仪对相同横流条件工况下加热表面的局部对流传热系数分布进行了测量。研究结果显示,攻角为90°时,作用在风扇上的气动载荷最小,风扇振幅最大,而随着攻角的减小风扇振幅也逐渐减小;安装角为90°时,压电风扇振动以及横流作用所诱导形成的耦合涡结构冲击加热表面,并在下游区域具有明显的脱落、破碎过程,对于叶尖包络区对应的壁面局部对流换热有显著的强化作用,此时风扇耦合换热性能最强,高于45°和135° 2倍以上;且时均对流传热系数的实验结果与数值模拟具有良好的一致性。     

A network flow analysis of extrusion dies and other flow systems

A method is presented to calculate the slow viscous flow distribution in systems of passages, for which the major velocity components are substantially parallel to the axes of those passages. That condition is generally satisfied in flat extrusion dies, disc filters, in-line filters, and other now devices. A finite difference matrix method is initially used to determine the flow distribution for an assumed viscosity distribution. That flow distribution is next used to determine a new distribution of resistances, now based on a specified rheological equation. This process is iterated until there is no significant change in the flow distribution. The passages are subdivided in this method and replaced by a network of resistances. A few unknowns are introduced at one end of the network, which are solved at the other end, using a matrix marching routine. The method is described for newtonian flow through a flat die with equalizing channel, for which the analytic solution is known. Results are shown for that die for flow of power law liquids.     

Pressure drop through a tapered die with optimized flow characteristics

The flow of power-law liquids through tapered dies has been analyzed in an earlier paper.¹ We now consider a taper which is additionally streamlined so as to make the transition from a broad and sluggish flow to a flow which is narrow and fast and as smooth as possible. This involves (1) the rational selection of an appropriate taper function within the relevant flow geometry and (2) the integration, between limits, of that function.     

Modelling of bubble dynamics in a venturi flow with a potential flow method

A simple model for cavitation bubble dynamics has been developed using a combination of boundary element methods and one-dimensional bubble dynamic equations. Each bubble is assumed to be spherical and is modelled using a potential source. The strength of the source is governed by one-dimensional bubble dynamic equations so that the velocity of the growing bubble at the interface between the vapour and liquid is correctly represented. The model has been implemented into computer program to study the growth, collapse, and interaction of cavitating bubbles as they flow through a venturi. Interactions between a bubble starting as a nucleus of gas, the surrounding liquid and the venturi boundaries are described. Although this is a simple model, surprisingly complex interactions can be studied with short computational times and limited computer resources. Thus, insights have been gained which otherwise would have been extremely difficult to obtain. These are described in terms of the bubble history, instantaneous velocity maps and instantaneous stream function contours.     

Fluid-dynamic experimental study in a slurry bubble column with a tube bank in cross flow

In this work, the fluid-dynamic of a slurry bubble column provided with a tube bank operating in cross flow was studied. The main objective was to determine the influence of the air velocity, the slurry velocity, and the solid concentration in the gas holdup and solid distribution inside a bed with internals. Pilot scale equipment with a column of square traverse section (0.144 m 2 ) of stainless steel with 2.20 m height was used. The column base has a truncated pyramidal shape with an inclination angle to the vertical of 20°. In the central part of the equipment, there is a bank of 49 tubes ( D =2.54 cm and L =38 cm) in an aligned arrangement ( S_L=S_T=4.4,rm cm ). The three-phase system used was compressed air, tap water, and sieved sand ( D_p=0.0505,rm cm ). The velocities of liquid and gas phases were varied in the range from 0.31 to 1.24 cm/s and from 1.41 to 3.15 cm/s, respectively, and the solids load concentration from 0 to 30% w/w. According to the results, when the liquid and gas phase velocities increase, the gas holdup, varepsilon_G , increases, while when the solids load concentration increases, varepsilon_G presents a local maximum at intermediate values, varepsilon_G being the largest for the two-phase system. Analogously, the axial profiles of solids concentration showed a local maximum in the central region of the column, exactly in the area of the tube bank. In the traverse direction, the solids concentration increases gradually heading to the center of the column. These profiles, axial and traverse, become more uniform as the air velocity increases and the slurry as well. In addition, according to expectations, the solids concentration increases in each point of the column as the load concentration is increased in the system.     

基于收敛交叉映射的化工过程扰动因果分析方法

当化工装置出现异常情况,操作工人往往无法及时准确地定位故障发生的原因。基于数据的方法能够通过化工过程数据,分析异常工况中的扰动传播路径,确定异常工况出现的根本原因。针对化工动态系统,提出了具有时间特性的收敛交叉映射方法（CCM）,和基于赤池信息准则的维度选择方法。为了验证提出算法的有效性,在简单的生态系统,因果检测基准系统和全混釜反应器（CSTR）中进行验证,并与原有的收敛交叉映射算法进行对比,体现出具有时间特性的收敛交叉映射算法的优越性。