Improved modeling for the reheat phase in thermoforming through an uncertainty treatment of the key parameters

This work focuses on the treatment of parameter uncertainty in the simulation of the sheet reheat phase of the thermoforming process. The approach aims to improve the quality of predictions through more accurate evaluation of the input parameters. First, the modeling approach is employed to perform a sensitivity analysis on the reheat phase. Then, a series of specialized experiments with heat flux and temperature sensors are performed on a thermoforming machine. The key parameters identified through the sensitivity analysis are the subject of these experiments. The natural convective heat transfer coefficients are evaluated by two different approaches. Through treatment of the uncertainty associated with the input parameters, the prediction of sheet reheat phase is significantly improved.     

Material modeling and solid phase forming of polycarbonate sheet

The Maxwell-Voigt type mechanical model proposed by Haward and Thackray was further modified to describe the strain rate dependent stress-strain behavior of polycarbonate under the uniaxial loading condition. Major modifications included effects associated with different hardening components of inelastic resistance and the related temperature dependent material behavior. The modified analytical model was shown to describe some of the important features of the stress-strain behavior of polycarbonate specimens tested over the range of strain rates and temperatures. Using the stress-strain relationship as input data; several finite element analyses were made to predict the behavior of polycarbonate sheets under a simple solid phase cup forming process. The computed strain distributions agreed reasonably with the measured values obtained from the gridded polycarbonate sheet that was formed at an elevated temperature. Some of the key assumptions that were used in the analysis are discussed.     

Influence of rheological properties on the sagging of polypropylene and abs sheet for thermoforming applications

The isothermal sagging resistance of different grades of conventional and a high melt strength (HMS) PP has been correlated with the rheological characteristics of the polymers, such as dynamic shear properties, melt strength, and zero shear viscosity. A thermoforming grade of acrylonitrile‐butadiene‐styrene (ABS) was used as a reference material. At 190°C, ABS had the highest viscosity and elastic modulus in the frequency range measured, showing that this polymer is highly elastic. HMS PP had a greater shear thinning behavior than conventional PP because of its broader molecular weight distribution. The tan δ of the polymers showed that conventional PP had a higher tendency to flow than HMS PP and ABS when heated above 172°C. This was confirmed with sagging experiments performed in an air circulating oven, where the rate of sagging decreased as the melt strength and the zero shear viscosity of the polymer increased.     

Improved evidence for the existence of an intermediate phase during hydration of tricalcium silicate

Tricalcium silicate (Ca₃SiO₅) with a very small particle size of approximately 50 nm has been prepared and hydrated for a very short time (5 min) by two different modes in a paste experiment, using a water/solid-ratio of 1.20, and by hydration as a suspension employing a water/solid-ratio of 4000. A phase containing uncondensed silicate monomers close to hydrogen atoms (either hydroxyl groups or water molecules) was formed in both experiments. This phase is distinct from anhydrous tricalcium silicate and from the calcium-silicate-hydrate (C-S-H) phase, commonly identified as the hydration product of tricalcium silicate. In the paste experiment, approximately 79% of silicon atoms were present in the hydrated phase containing silicate monomers as determined from ²⁹Si{¹H} CP/MAS NMR. This result is used to show that the hydrated silicate monomers are part of a separate phase and that they cannot be attributed to a hydroxylated surface of tricalcium silicate after contact with water. The phase containing hydrated silicate monomers is metastable with respect to the C-S-H phase since it transforms into the latter in a half saturated calcium hydroxide solution. These data is used to emphasize that the hydration of tricalcium silicate proceeds in two consecutive steps. In the first reaction, an intermediate phase containing hydrated silicate monomers is formed which is subsequently transformed into C-S-H as the final hydration product in the second step. The introduction of an intermediate phase in calculations of the early hydration of tricalcium silicate can explain the presence of the induction period. It is shown that heterogeneous nucleation on appropriate crystal surfaces is able to reduce the length of the induction period and thus to accelerate the reaction of tricalcium silicate with water.     

A mathematical model of the calendered exiting thickness of micropolar sheet

A theoretical analysis based on the lubrication theory is presented to study the calendering mechanism. The material to be calendered is described by the constitutive relationship of a micropolar fluid. An exact solution and numerical solution of the problem is calculated. The roll‐separating force, power function and exiting sheet thickness are computed numerically using Runge‐Kutta method. The influence of the material parameters on the pressure distribution, pressure gradient and related quantities of engineering interest in calendering process is analyzed through graphs. POLYM. ENG. SCI., 58:327–334, 2018. © 2017 Society of Plastics Engineers     

Prediction of the film thickness distribution and pattern change during film insert thermoforming

Various surface process methods have been developed to decorate plastic or metallic products. Film insert molding (FIM) is one of the methods that enhance the functional and/or aesthetic qualities of a product's surface. However, the drawbacks of FIM are that the thickness of the film can change, depending on the product configuration, and further, the pattern of the decorated film may change. Therefore, this article attempts to quantify the changes in the thickness and in the pattern of the decorated film during the FIM process. G'Sell's viscoelastic constitutive law was adopted to describe the rheological behavior of polymer film. A constant‐velocity uniaxial tensile test at high temperature, which is a new method proposed in this research, was used to obtain the rheological parameters. We also suggested a visual method for predicting pattern change, which was validated by comparing analytical results with those of real products. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Teaching mathematical modeling software for multiobjective optimization in chemical engineering courses

This paper expects to give undergraduate students some guidelines about how to incorporate environmental considerations in a chemical supply chain and how the introduction of these concerns have an important effect on the results obtained in the multiobjective optimization problem where both economic and environmental aspects are considered simultaneously.To extend the economic and environmental assessment outside the chemical plant and to identify the tradeoffs associated with the reality of chemical and petrochemical industries, a simplified problem of a chemical supply chain is proposed as a case study.The inclusion of environmental concerns to this economic problem make this new case study a good example for undergraduate students interested in implementing simultaneous economic and environmental considerations in the chemical process design incorporating mathematical modeling software for solving this multiobjective problem.Thus, the final objective of this paper is to show to undergraduate students how environmental together with economic considerations could have an important impact in the logistics of a supply chain and how multiobjective optimization could be used to make better decisions in the design of chemical processes including its supply chain.To reach our purpose, the Pareto curve of the supply chain is obtained using the ?-constraint method. In addition, the tradeoffs of this multiobjective optimization have been identified and analyzed and ultimately a good decision based on the set of ‘equivalent’ optimal solutions for this chemical supply chain problem determined.     

Evaluation of a mitigation system for leakage accidents using mathematical modeling

Chemical accidents generated during maintenance, repair, and normal operation, such as dispersion, fire, and explosions, can cause massive losses within and outside workplaces. Since a 2012 hydro fluorine leak in Gumi, South Korea, many studies have investigated mitigation systems for reducing accident impact. However, due to potential costs, and lack time and expertise, most companies have hesitated to install mitigation systems without accurate impact evaluations. Therefore, it is essential to analyze mitigation system efficacy under various possible accident scenarios. We considered a mitigation system incorporating a reserve vessel installed next to a storage vessel. When a leakage accident occurs, the chemical in the main vessel is transferred to the reserve vessel by a pump. Simulation results based on Torricellis’ theorem indicate that this mitigation system could significantly reduce leakage, and reduce leakage consequences in terms of maximum diffusion distance and hazardous gas concentrations based on consequence analysis.     

Microchannel reactors for Fischer-Tropsch synthesis: Experimental investigation and mathematical modeling

The Fischer-Tropsch synthesis is a significant technology for converting coal, natural gas, and biomass into synthetic fuels. In recent years, the use of microchannel reactors for the Fischer-Tropsch synthesis has attracted significant attention. Fischer-Tropsch synthesis experiments were carried out in a microchannel reactor and the influences of reaction conditions on the experimental results were investigated in this study. Based on the experimental data, a dynamic multi-component pseudo-homo...     

Development of a multivariable online monitoring system for the thermoforming process

The thermoforming industry has been relatively slow to embrace modern measurement technologies. As a result researchers have struggled to develop accurate thermoforming simulations as some of the key aspects of the process remain poorly understood. For the first time, this work reports the development of a prototype multivariable instrumentation system for use in thermoforming. The system contains sensors for plug force, plug displacement, air pressure and temperature, plug temperature, and sheet temperature. Initially, it was developed to fit the tooling on a laboratory thermoforming machine, but later its performance was validated by installing it on a similar industrial tool. Throughout its development, providing access for the various sensors and their cabling was the most challenging task. In testing, all of the sensors performed well and the data collected has given a powerful insight into the operation of the process. In particular, it has shown that both the air and plug temperatures stabilize at more than 80°C during the continuous thermoforming of amorphous polyethylene terephthalate (aPET) sheet at 110°C. The work also highlighted significant differences in the timing and magnitude of the cavity pressures reached in the two thermoforming machines. The prototype system has considerable potential for further development. POLYM. ENG. SCI., 54:2815–2823, 2014. © 2014 Society of Plastics Engineers     

Biodegradation kinetic modeling of acrylic acid-grafted polypropylene during thermophilic phase of composting

Iranian Polymer Journal - This work aims at modelling and characterizing the kinetics of biodegradation of acrylic acid-grafted polypropylene. Different films of acrylic acid-grafted polypropylene...     

Mathematical modeling of the dispersed phase dynamics

A vector equation of motion in the Lagrangian frame of reference is rearranged into a set of two scalar equations to determine the relative-velocity magnitude of a particle and its direction. The resulting system, written in terms of the Lamé coefficients, is solved jointly with continuum equations of motion in the Eulerian frame of reference. The method is exemplified by the flow of a heterogeneous mixture between permeable parallel walls and the flow of a heterogeneous non-Newtonian fluid over the surface of a sedimentation centrifuge rotor.Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 39, No. 2, 2005, pp. 206–215.Original Russian Text Copyright © 2005 by Kholpanov, Ibyatov.     

Determination of the moisture diffusivity coefficient and mathematical modeling of drying

Drying plays an important role in the production of clay tiles. In the present article, drying process is analyzed taking experimental data for several masonry clays obtained from different clay tile manufacturers and published data for different clay slabs. Calculation methods and computer programs designed for the calculation of the effective diffusion coefficient are developed. The first calculation method represents the analytical solution of the Crank equation, while the second one represents the analytical solution of the Efremov equation with boundary conditions in the form of the flux. Unlike other materials, clay tiles exhibit shrinkage during the drying process. For this reason, a shrinkage correction is included in both calculation methods. Four models (A1, A2, B1 and B2) for predicting the drying behavior are obtained as the result of the calculation cited programs. It is shown that the calculated effective diffusion coefficient determined by the designed computer programs, using experimentally obtained and selected published data sets have similar values to those of the same coefficient reported in the literature. Based on the mathematically determined prognostic values of the effective diffusion coefficient, it was concluded that there is more than 90% agreement between the experimentally recorded and the calculated drying curves.     

Experimental and mathematical modeling of Cr(VI) removal using nano-magnetic Fe3O4-coated perlite from the liquid phase

Modification of perlite using nano-magnetic iron oxide was implemented to produce nano-magneticFe₃O₄-coated perlite composite (Fe₃O₄/Perlite). The prepared composite was characterized using Scanning Electron Microscopy, Fourier-Transform Infrared spectroscopy and Powder X-ray Fluorescence. The potentiality of both perlite and Fe₃O₄/Perlite composite to eliminate Cr(VI) from the environmentally relevant water was investigated. The influence of main factors which could affect the adsorption was studied including; pH of medium, shaking time and Cr(VI) ions concentration. The experimental outcome demonstrated that the modification of perlite by nano-magnetic Fe₃O₄ showed a significantly enhanced Cr(VI) removal efficiency relative to that of unmodified perlite. From the kinetic studies, the experimental data fitted well with the pseudo-second-order model. Moreover, it proposes that Langmuir isotherm is more adequate than the Freundlich isotherm for both perlite and modified perlite. The results recommended that Fe₃O₄/Perlite composite had a great potential as an economic and efficient adsorbent of Cr(VI) from contaminated water, which has huge application potential.     

冷冻干燥过程相迁移和相分布的孔尺度网络模型与模拟

构建了51×51二维孔-喉网络模型对冷冻干燥过程的升华干燥阶段进行模拟。与传统的连续介质模型相比,孔网络模型的特征是具有跟踪干燥过程中物料内部的干燥前沿和相分布的能力。采用网络模型预测了牛肉和火鸡肉的干燥曲线,并模拟了不同冻结速率的火鸡肉在干燥过程中形成的相分布。讨论了模型的计算特性,并分析了孔径分布对相分布特性的影响。结果表明：网络模型可较好地预测升华干燥阶段,可在孔尺度上揭示干燥过程的动力学机理,将为准确地判断升华干燥与解析干燥的转变点提供理论计算基础。