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     

Design and optimization of an extrusion die for the production of wood–plastic composite profiles

In this work, the optimization of an extrusion die designed for the production of a wood–plastic composite (WPC) decking profile is investigated. The optimization was performed with the help of numerical tools, more precisely, by solving the continuity and momentum conservation equations that govern such flow, and aiming to balance properly the flow distribution at the extrusion die flow channel outlet. To capture the rheological behavior of the material, we used a Bird‐Carreau model with parameters obtained from a fit to the (shear viscosity versus shear‐rate) experimental data, collected from rheological tests. To yield a balanced output flow, several numerical runs were performed by adjusting the flow restriction at different regions of the flow‐channel parallel zone cross‐section. The simulations were compared with the experimental results and an excellent qualitative agreement was obtained, allowing, in this way, to attain a good balancing of the output flow and emphasizing the advantages of using numerical tools to aid the design of profile extrusion dies. POLYM. ENG. SCI., 55:1849?1855, 2015. © 2014 Society of Plastics Engineers     

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     

基于流动平衡的塑料挤出模优化设计

在构建流道三维参数化模型的基础上,将有限元数值分析和优化技术相结合,以口模出口处型材截面上各子区域平均流速相等为优化目标,以压缩段入口壁厚和平直段长度为设计变量,对挤出模优化设计进行了研究。并以实例说明了优化设计的具体过程,验证了所用方法的正确性和有效性。     

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.     

Optimization‐driven design of dies for profile extrusion: Parameterization,strategy, and performance

A computational design optimization environment is developed, handling, for the first time, streamline dies used for profiles in unplasticized polyvinyl chloride (uPVC) having multiple complex features, as well as simpler designs. Die cavity cross sections are described by planar contours, such as the cutting paths for wire electrical discharge machining of the plates from which streamline profile dies are constructed. Contours are parameterized using key points, and by joining the contours with ruled surfaces, the three‐dimensional geometry can be reconstructed. For the optimization a developed flow analysis on each die cross section is used with the avoid‐cross‐flow strategy. Cross sections are partitioned and the die is balanced to obtain the required flow rate through each. A robust and efficient parallel decoupled optimization strategy is developed. In application to a uPVC window profile, five cross sections were optimized. The number of design variables on each ranged from 2 to 46, and the cross section optimizations converged within one to seven cycles. Compared with the work of an experienced designer making manual changes to the computer‐aided design model, guided by computational fluid dynamics analyses, the design quality was comparable or better and computational demands similar; however, the time required from the designer was reduced seven times. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Extents of reaction and flow for homogeneous reaction systems with inlet and outlet streams

For homogeneous reaction systems with inlet and outlet streams, this article proposes a linear transformation of the number of moles vector into three distinct parts, namely, the reaction variants, the inlet‐flow variants, and the reaction and inlet‐flow invariants. The transformed states can be interpreted physically as (i) the amount of material contributed by each reaction and still present in the reactor (extents of reaction), (ii) the amount of material contributed by each inlet stream and still present in the reactor (extents of inlet flow), and (iii) the fraction of the initial conditions that has left the reactor (extent of outlet flow). Furthermore, several implications of being able to compute the extents of reaction and inlet flow are discussed. The methodology is illustrated in simulation via the ethanolysis of phthalyl chloride. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

An optimization method with experimental validation for the design of extrusion wire coating dies for a range of different materials and operating conditions

The objective of this article is to determine a wire coating‐hanger melt distributor geometry to ensure a homogenous exit velocity distribution that will best accommodate a wide material range and multiple operating conditions (i.e., die wall temperature and flow rate change). The computational approach incorporates finite element (FE) analysis to evaluate the performance of a die design and includes a nonlinear constrained optimization algorithm based on the Kriging interpolation and sequential quadratic programming algorithm to update the die geometry. Two optimization problems are then solved, and the best solution is taken into account to manufacture the optimal distributor. The Taguchi method is used to investigate the effect of the operating conditions, i.e., melt and die wall temperature, flow rate and material change, on the velocity distribution for the optimal die. In the example chosen, the wire coating die geometry is optimized by taking into account the geometrical limitations imposed by the tool geometry. Finally, the FE analysis and optimization results are validated by comparison with the experimental data obtained with the optimal die. The purpose of the experiments described below is to investigate the effect of material change. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

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.     

Optimal temperature profile in methanol synthesis reactor

An optimal temperature profile is determined for a methanol synthesis reactor of LURGI type. The temperature profile is estimated so that methanol production rate in the reactor outlet will be maximized. First, the reactor is simulated based on heterogeneous one- and two-dimensional models. The comparison of the simulation results and plant data shows that the heterogeneous one-dimensional model can reliably be used for determining optimal temperature profile. Since optimal temperature profile for reversible exothermic reaction in tubular reactors is a decreasing function of reactor length, the technique of control variable parameterization is used for determining optimal temperature profile in a methanol reactor. In this way, a third order polynomial is considered for the temperature profile and the polynomial coefficients are as decision variables. The optimization is based on a Quasi-Newton's method (BFS technique), and the objective function is methanol flow rate at the reactor outlet. The results of optimization indicate that if optimal temperature profile is implemented in the reactor, methanol production will significantly be increased.     

OPTIMAL TEMPERATURE PROFILE IN METHANOL SYNTHESIS REACTOR

An optimal temperature profile is determined for a methanol synthesis reactor of LURGI type. The temperature profile is estimated so that methanol production rate in the reactor outlet will be maximized. First, the reactor is simulated based on heterogeneous one- and two-dimensional models. The comparison of the simulation results and plant data shows that the heterogeneous one-dimensional model can reliably be used for determining optimal temperature profile. Since optimal temperature profile for reversible exothermic reaction in tubular reactors is a decreasing function of reactor length, the technique of control variable parameterization is used for determining optimal temperature profile in a methanol reactor. In this way, a third order polynomial is considered for the temperature profile and the polynomial coefficients are as decision variables. The optimization is based on a Quasi-Newton's method (BFS technique), and the objective function is methanol flow rate at the reactor outlet. The results of optimization indicate that if optimal temperature profile is implemented in the reactor, methanol production will significantly be increased.     

某燃煤电厂300MW机组SCR烟气脱硝装置结构优化

SCR烟气脱硝装置中烟气流场的分布及还原剂（NH3）与NOx的混合效果对脱硝效果起着重要作用,因此,采用数值模拟技术对于初步设计的SCR烟气脱硝装置进行结构优化是目前国内外SCR烟气脱硝装置设计必不可少的一部分。本研究采用Fluent软件对某燃煤电厂300MW机组SCR烟气脱硝装置内的烟气流动、第一层催化剂入口NH3与NOx的混合和系统压降等方面进行模拟,结果表明：BMCR工况下,结构优化后的SCR烟气脱硝装置AIG上（下）游、第一层催化剂入口和装置出口截面烟气流速相对标准偏差不超过15%;第一层催化剂入口截面NH3/NOx摩尔比相对标准偏差不超过10%;第一层催化剂入口截面烟气进入最大偏差角度处于±10°范围之间;系统压降低于800Pa。合理的设计导流板能够起到抑制弯管以及变截面所引起的流场分离现象、消除大旋流的产生使烟气更加流畅地进入催化剂等作用。     

Optimization of air flow field of the melt blowing slot die via numerical simulation and genetic algorithm

The air flow field plays a key role in melt blowing. In this article, an optimal design procedure that improves the airflow field of melt blowing is proposed. A parameter, stagnation temperature which is a combination of static temperature and kinetic temperature, is proposed to evaluate the air flow field. The stagnation temperature is obtained via computer simulation, while optimization is accomplished by genetic algorithm. Four main geometry parameters of the slot die: slot width, nose piece width, slot angle, and setback are investigated. The optimal results were achieved in the 40th generation. The results also show that the smaller slot angle and larger slot width can result in the higher stagnation temperature. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

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.     

Investigation of the flow of molten tellurite glass in a double-crucible die

The viscoplastic flow of molten tellurite glass realized during the process of the drawing of an optical fiber through a double-crucible die was numerically investigated. The procedure for the computational experiment and the results of the simulation, including those obtained under local temperature disturbances, regarding the interactions between the melts in the die outlet part during the starting and stationary flow stages were described. The computational investigations were performed with the use of the ANSYS CFX software.     

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     

衣架式流延模头内熔体流动与模具变形的三维耦合数值模拟

利用Polyflow软件对一种衣架式流延模头内熔体的流动和模具变形进行了三维耦合数值模拟。结果表明:衣架式模头中熔体的流动可视为歧管内(沿歧管方向)和狭缝中(沿挤出方向)的压力流的组合;模头狭缝表面在模具厚度方向的变形沿挤出方向近似为线性增加,而沿模具宽度方向为非线性减小;模具变形后的熔体出口流率由狭缝的实际间隙和扇形区出口处的压力共同决定,单位宽度的出口流率沿模具宽度方向先增加后减小。     

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。     

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