A methodology to reduce thermal gradients due to the exothermic reactions in composites processing

In resin transfer molding (RTM) process, a polymer composite part is fabricated by injecting a thermoset resin into a fiber preform placed in a closed mold cavity. After the infiltration of the resin into the empty spaces in the mold, the manufacturing process is characterized by a curing reaction, which is an exothermic resin polymerization phenomenon that cross-links the resin and results in a solid structure. In most cases, the resin cure is initiated by heating the mold. The heat released during the reaction can cause temperature gradients in the composite, which leads to residual stresses in the part. Residual stresses are undesirable as they can cause shrinkage and warpage. By controlling the temperature of the mold walls, one can control the cure reaction and reduce the thermal gradients through the composite part. In this paper, we present a methodology based on scaling analysis of the energy balance equation to manage the heat generated by the cure reaction that minimizes the temperature gradients before the resin solidifies. The method capability is demonstrated with a highly reactive polyester resin infiltrated into different types of glass fiber preforms in a rectangular mold.     

Numerical simulation of filling and solidification of permanent mold castings

Filling of a mold is an essential part of the permanent mold casting process and affects significantly the heat transfer and solidification of the melt. For this reason, accurate prediction of the temperature field in permanent mold castings can be achieved only by including simulation of filling in the analysis. In this work we model filling and solidification of a casting of an automotive piston produced from an aluminum alloy. Filling of the three-dimensional mold is modeled by using the volume-of-fluid method. Fluid mechanics and heat transfer equations are solved by a finite element method. Comparisons of numerical results to available experimental data show that the formulated model provides a solution of acceptable accuracy despite some uncertainty in material properties and boundary and initial conditions. This implies that the model can be a viable tool to design permanent molds.     

Using differential mold temperatures to improve the residual wall thickness uniformity around curved sections of fluid assisted injection molded tubes

Fluid assisted injection molding technology, including gas assisted injection molding and water assisted injection molding, has been used to manufacture plastic tubes in recent years, due to the light weight of molded parts, relatively lower resin cost per part and faster cycle time. However, the non-uniform residual wall thickness distribution usually occurs around curved sections and can significantly affect the molded product quality. This aim of this report was to improve the uniformity of residual wall thickness distribution at curved sections of fluid assisted injection molded tubes by adopting differential mold temperatures. Experiments were carried out on an 80-ton injection molding machine equipped with gas and water injection units. The material used was semi-crystalline polypropylene. It was found that the water assisted molded parts exhibit a more uniform thickness distribution at curved sections than the gas assisted molded parts. The uniformity of residual wall thickness in fluid assisted injection molded parts could be improved by adopting differential mold temperatures. In addition, a numerical simulation using commercially available software was carried out to simulate the melt temperature distributions during the filling process, so as to better interpret the fluid penetration behavior in fluid assisted injection molded parts.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

Parabolic modeling of the pultrusion process with thermal property variation

Pultrusion is a manufacturing method for fiber-reinforced composite with constant cross-section. In this process, a fiber creel is impregnated in a resin bath and passes through a heated die with a constant pulling force and the elevated die temperature induces the curing-resin process. At the present work the effect of variable properties (thermal conductivity and volumetric heat capacity) during the pultrusion process of thermosetting composite materials is numerically studied. The thermal properties are considered as a function of both temperature and degree of cure distributions inside the carbon/epoxy matrix composites. A two-dimensional parabolic model using the finite element method to solve the energy and degree of cure transport equations was used. These two equations are coupled by a source term from resin curing exothermic reaction. The resin cure kinetics and the properties that are temperature-dependent are both modeled by expressions obtained from the literature. The computational domain is discretized using an unstructured mesh with triangular elements and an adaptive refinement. Iterative algorithms are used to solve the algebraic equation system. Results showed that as the temperature and degree of cure along the die extension increase the volumetric heat capacity and the thermal conductivity also elevate. The influence of the pulling speed and the die temperature in the thermal property variation is also analyzed. It is verified that the temperature profile at the pultruded bar centerline for the variable property case is smoother than the constant one, similarly when the pulling speed is increased. The degree of cure development is delayed for the variable property simulation, requiring a larger die length to reach a suitable degree of cure design value. Moreover, the proper knowledge of these characteristics allows a better pultrusion process design.     

Numerical simulation of the casting process of a wind turbine rotor hub

An integrated numerical model was applied to simulate the mold filling and solidification process as well as predict the occurrence of relative casting defects for a rotor hub casting. The goal was to conduct a numerical experimentation to obtain an optimal alloy design of ductile cast iron for the rotor hub casting. A computer‐aided engineering software based on the finite element method was employed in this study. Numerical simulations were conducted for the rotor hub casting with two different types of alloy composition for ductile cast iron. The mold filling and solidification process were examined to predict the occurrence and extent of casting defects and a better alloy design was then proposed based on the simulated results to alleviate casting defects of the rotor hub casting. Copyright © 2010 John Wiley & Sons, Ltd.     

Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying

The drying behavior of a moist object subjected to convective drying is analyzed numerically by solving heat and moisture transfer equations. A 3-D numerical model is developed for the prediction of transient temperature and moisture distribution in a rectangular shaped moist object during the convective drying process. The heat transfer coefficients at the surfaces of the moist object are calculated with an in-house computational fluid dynamics (CFD) code. The mass transfer coefficients are then obtained from the analogy between the thermal and concentration boundary layer. Both these transfer coefficients are used for the convective boundary conditions while solving the simultaneous heat and mass transfer governing equations for the moist object. The finite volume method (FVM) with fully implicit scheme is used for discretization of the transient heat and moisture transfer governing equations. The coupling between the CFD and simultaneous heat and moisture transfer model is assumed to be one way. The effect of velocity and temperature of the drying air on the moist object are analyzed. The optimized drying time is predicted for different air inlet velocity, temperature and moisture content. The drying rate can be increased by increasing the air flow velocity. Approximately, 40% of drying time is saved while increasing the air temperature from 313 to 353 K. The importance of the inclusion of variable surface transfer coefficients with the heat and mass transfer model is justified.     

Autoclave curing of thermosetting composites: Process modeling for the cure assembly

The heat transfer process involved in the autoclave curing of fiber-reinforced thermosetting composites is investigated numerically. In the analysis, the cure assembly is assumed to consist of a tool plate, composite laminate, and bleeder/vacuum bag. Thus, the heat transfer between the composite and the autoclave environment takes place through materials of different thermal properties. The temperature distribution thus obtained is utilized in conjunction with the models formulated by Loos and Springer [2] to calculate the cure parameters such as degree of cure, resin viscosity, and ply compaction. Four important issues arise from the process control and optimization (i.e., the effects of heating rate, laminate thickness, bleeder material, and convective heating) are addressed in this study. Based on the results obtained, recommendations for possible process improvement are made.     

A foam ablation model for lost foam casting of aluminum

A model is developed for heat transfer, polymer vaporization, and gas diffusion at the interface between the advancing liquid metal and the receding foam pattern during mold filling in lost foam casting of aluminum. Most of the pattern interior decomposes by ablation, but the boundary cells decompose by a collapse mechanism, which creates an undercut in the pattern next to the coating. By regulating how much of the pattern coating is exposed to gas diffusion, the undercut controls the overall filling speed of the metal through the mold. Computed values for the foam decomposition energy from this model compare very well with experimental data on foam pyrolysis, and predicted filling speeds are consistent with observations in published experiments. In addition, the model explains several unusual observations about mold filling that until now have not been understood.     

Use of non local equilibrium theory to predict transient temperature during non-isothermal resin flow in a fibrous medium

Liquid composite molding processes generally involve injection of a polymeric resin in a fibrous preform previously placed in a closed mold. Resin kinetics largely depend on the temperature cycle applied and, as far as thick composites parts are concerned, they can greatly impact on the temperature profile, especially in the core of the part where high temperature range can be reached, affecting the part mechanical properties. Thermal analysis of the system is usually done at the macro-scale level. However, at micro level and because of resin flow across the fibrous preform, local thermal effects have to be considered. A heat dispersion coefficient for instance will account for the hydrodynamic effects so as to improve significantly the accuracy of the temperature profile prediction at steady state. To improve prediction of transient temperature profiles, local heat transfer between resin and fibers needs to be considered. The characterization of this coefficient is conducted following an inverse method, numerical solutions parametered by this coefficient being derived from a non local thermal equilibrium (or two-equation model) and compared with experimental temperature profiles drawn for several injection velocity cases in a sensored mold. Significant improvement in the prediction of transient temperature profile is then obtained. Correlation between the injection velocity and the local heat exchange coefficient is also shown.     

A FINITE ELEMENT METHOD FOR CASTING SIMULATIONS

This paper presents a finite element model for the three-dimensional simulation of industrial mold filling and solidification problems. The finite element solutions of mold filling problems involve highly convective fluid flow coupled with free surface, heat transfer, nonconstant material properties, and complex three-dimensional geometries. They present unusual challenges for both the finite element modeling and numerical solution algorithms. In this work a segregated algorithm is proposed to solve Navier-Stokes, energy, and front tracking equations. The streamline upwind Petrov-Galerkin formulation is used to obtain stable solutions. The position of the free surface is modeled using a level-set approach. The whole procedure is shown to present the accuracy, robustness, and cost-effectiveness needed for complex three-dimensional industrial applications.     

辐射离散传播法在三维圆柱腔体辐射传热计算中的应用

运用空间解析几何理论与数值计算相结合的方法,实现了辐射离散传播法（OTM）在三维圆柱腔体内辐射传热计算的应用。采用坐标转换建立了辐射射线方程,通过直接求解所有发射点上各立体角内的辐射射线与各辐射单元体的交点,确定射线经过的路径及各交点与发射点的距离,然后按距离远近对交点进行排序,得到适合DTM法求解辐射能量传递方程的交点顺序。运用该方法对圆柱腔体内辐射换热进行三维计算,得到与精确解基本相符的结果;将DTM法运用于煤粉燃烧火焰辐射换热的计算,得到的温度场与实验结果基本一致,表面辐射热流密度分布合理,由此表明本文设计的方法是可行的。     

The Improved Direct Collocation Meshless Approach for Radiative Heat Transfer in Participating Media

The moving least-squares (MLS) direct collocation meshless method (DCM) is an effective numerical scheme for solving the radiative heat transfer in participating media. In this method the trial function is constructed by a MLS approximation and the radiative transfer equation (RTE) is discretized directly at nodes by collocation. The main drawback of this method is that, like most of the other numerical methods, the solution to the RTE by the DCM also suffers much from nonphysical oscillations in some cases caused by the convection-dominated property of the RTE. To overcome the numerical oscillations, special stabilization techniques are usually adopted, which increases the complexity and computation time of problem. In the present work a new scheme based on the outflow-boundary intensity interpolation correction is proposed that can easily ensure a large reduction in numerical oscillations of results without any complex stabilization technique. Adaptive support domain technique is also adopted, and the size of the support domain of each evaluated point changes with the density of nodes with irregular distribution. Five cases are studied to illustrate the numerical performance of these improvements. The numerical results compare well with the benchmark approximate solutions, and it is shown that the improved moving least-square direct collocation meshless method (iDCM) is easily implemented, efficient, of high accuracy, and excellent stability, to solve radiative heat transfer in homogeneous participating media.     

A new LRBFCM-GBEM modeling algorithm for general solution of time fractional-order dual phase lag bioheat transfer problems in functionally graded tissues

The main objective of this article is to propose a new hybrid modeling algorithm based on combining local radial basis function collocation method (LRBFCM) and general boundary element method (GBEM) for solving time fractional-order dual phase lag bioheat transfer problems in functionally graded tissues. The LRBFCM was developed and implemented using an implicit time-stepping technique and Caputo time fractional derivative for solving the fractional-order governing equation without dual phase lags. Due to suitability of the GBEM for modeling of bioheat transfer in functionally graded tissues. Therefore, GBEM is applied for solving the dual phase lags governing equation without fractional-order derivative. The numerical results are depicted graphical forms to show the effects of functionally graded parameter, fractional-order parameter and anisotropy on the nonlinear temperature distribution. Also, these numerical results demonstrate the validity and accuracy of the proposed algorithm and technique.     

Quality inspection in polymer processing by a thermophysical handy tester

This paper presents the applicability of a thermophysical handy tester for quality inspection and diagnostic technique such as in situ measurement of polymeric resin products. Influence of crystallinity known as a rating factor of quality, or filler concentration upon thermal conductivity is determined for the case of unsaturated polyester resin products by using the tester. Consequently, good correlations between the thermal conductivity and the crystallinity or the filler concentration are certified. The variation or the distribution of thermal conductivity of products molded under various conditions can be detected nondestructively using the tester. As an example, the thermal conductivity distribution around the forming gate is demonstrated, indicating the density‐uniformity of the resin product. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(6): 421–433, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20124     

新型定形板状相变材料的蓄/放热特性

对填充了新型定形板状相变材料的蓄热槽的蓄／放热特性进行了数值计算分析和实验比较。根据数值计算，对影响蓄热槽蓄／放热特性的主要因素——相变材料的几何尺寸、相变材料的导热系数、流体流速、对流放热系数、相变材料填充率等的影响规律进行了分析研究，计算出了蓄热槽内温度分布随时间的变化；并在实验台上测试了蓄热槽初始温度、流人和流出蓄热槽流体温度、作为蓄热体的相变材料测点温度随时间的变化，计算结果与实验结果具有较好的一致性。     

Approximate analytic solution of heat conduction in hollow semi-spheres flying at hypersonic speed

Heat transfer in blunt noses of hypersonic vehicles with coolant inside can be approximately considered as heat conduction in hollow semi-sphere with aerodynamic heating on the outer boundary and enhanced cooling on the inner boundary. Theoretical investigations of temperature field in hollow semi-spheres were carried out by solving the two-dimensional axsymmetric conduction equation, which could be transformed into Legendre equation when the separation of variables is applied. However, for such a semi-sphere flying at hypersonic speed, the distribution of heat transfer rates as an outer boundary condition is so complex that the integration in the Legendre solution is nearly impossible to be completed. In this paper, a 4th order Legendre polynomial, derived by the method of undetermined coefficients, was adopted to approach the local similarity solution of hypersonic aerodynamic heating and simplify the integration process, by which an approximate solution could be set up for the temperature field. The approximate solution is also validated by comparing the analytical results with data from numerical simulations, in which the conduction equation is solved with the improved Richardson scheme. Both analytical and numerical results are compared to each other and match quite well.     

Numerical Procedure for Heat Transfer Coefficient Identification in Solidification of Binary Alloys and Its Experimental Verification

In this article the inverse problem consisting of determination of the heat transfer coefficient in the process of binary alloy solidification is considered. Additional information on the inverse problem is delivered by measurements of temperature at selected points of the cast. In the model discussed, the distribution of temperature is described by means of the heat conduction equation with the substitute thermal capacity, with the liquidus and solidus temperatures varying in dependence on the concentration of the alloy component. For describing the concentration, the Scheil model is used. For solving the direct problem, the finite-difference method supplemented by the generalized alternating phase truncation method is applied. For minimization of the properly constructed functional, the artificial bee colony algorithm is employed. Additionally, the article contains the results of a numerical experiment as well as the results of an experimental verification illustrating the usefulness of the proposed procedure.     

Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.     

Numerical analysis on the effects of different inlet gates and gap heights in TQFP encapsulation process

Finite volume method (FVM) based simulation of encapsulation process in thin quad flat pack (TQFP) packages is presented in this paper. The 3D model of TQFP package is built and meshed with tetrahedral elements using GAMBIT, and simulated by FLUENT software. Castro–Macosko viscosity model and volume of fluid (VOF) technique are applied for flow front tracking of the encapsulant. Curing kinetics is taken into consideration in the simulation using Kamal’s equation. To solve the Castro–Macosko and Kamal models, suitable user defined functions (UDFs) are developed using MS VISUAL STUDIO.NET software and incorporated into the FLUENT. The parameters such as mold filling time, flow front profiles, pressure distribution in the package and void formation, for three different inlet gate arrangements and gap heights, are analyzed. The degree of conversion of the molding compound during the encapsulation process is also studied for different number of inlet gates. It is found that the filling time and void occurrence could be reduced by increasing the number of inlet gates, and the variation of gap height within the cavity is crucial in controlling the peak pressure. Moreover, the combined effect to two competing events, such as, reduction of viscosity with shear rate due to non-Newtonian behavior of the polymer fluid and increase in viscosity during the curing reaction, are effectively demonstrated. The simulation results are compared with previous experimental results and found in good conformity.