Mathematical modeling and process simulation of perlite grain expansion in a vertical electrical furnace

Expanded perlite is a lightweight material with remarkable thermal and acoustic insulation properties, rendering it widely useful in the construction and manufacturing industries. Currently applied perlite expansion technology suffers numerous technical disadvantages, which adversely affect product quality and limit the range of its applications. To overcome these established drawbacks, a new perlite expansion process has been designed on the basis of a vertical electrically heated expansion furnace. The novel furnace enables precise control of experimental conditions, in order to allow for efficient adjustment of particle residence time and internal temperature. The quality of expanded perlite strongly depends on raw material thermophysical properties as well as furnace operating conditions, and the experimental investigation of the isolated effect of each parameter on expanded product quality is technically cumbersome and extremely time-consuming and expensive.A mathematical model for perlite grain expansion has been developed in order to perform a detailed numerical investigation of process efficiency, toward the optimization of the expansion process in the novel pilot-scale furnace. The dynamic model consists of ordinary differential equations for both air and particle heat and momentum balances, as well as nonlinear algebraic equations for both air and perlite melt thermophysical and transport properties, probing the air temperature distribution within the vertical electrical furnace as well as the particle velocity, temperature and size along its trajectory inside the heating chamber. The effect of raw material physical properties (raw feed origin, initial particle size, effective water content) as well as operating parameters (air inlet temperature and flowrate, furnace wall temperature) on evolution of the particle state variables is presented and discussed. Model results indicate perlite expansion is strongly affected by raw ore feed origin, size and water content. Moreover, operating conditions affect expansion considerably, and furnace wall temperature has the strongest effect on the final particle expansion ratio attained. The new dynamic model is instrumental towards achieving a detailed comprehension of perlite expansion in the vertical electrical furnace towards multi-parametric sensitivity analysis, process optimization and efficient control.     

An anisotropic enhanced thermal conductivity approach for modelling laser melt pools for Ni-base super alloys

Ni-base super alloys are extensively used in high temperature gas turbine engines and energy industries. Due to the high replacement costs of these components, there are huge economic benefits of repairing these components. Laser direct metal deposition processes (LDMD) based on laser cladding, laser fusion welding, and laser surface melting are some of the processes which are used to repair these high value components. Precise control of these processes is important to achieve the desired microstructure, stress distribution, distortions due to thermal stresses and other important output variables. Modelling of these processes is therefore an extremely important activity for achieving any degree of control/optimisation. However, modelling of these processes is not straight-forward due to melt pool flows dominated by Marangoni and buoyancy driven convection. Detailed CFD models are required for accurate prediction of melt pool geometry. But these models are computationally expensive and require greater expertise. To simplify and speed up the modelling process, many researchers have used the isotropic enhanced thermal conductivity approach to account for melt pool convection. A recent study on mild steel has highlighted that isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry. Based on these findings a new approach namely anisotropic enhanced thermal conductivity approach has been developed. This paper presents an analysis on the effectiveness of the isotropic and anisotropic enhanced thermal conductivity approaches for laser melting of Inconel 718 using numerical technique. Experimental melt pool geometry has been compared with modelling results. It has been found that the isotropic enhanced thermal conductivity approach is not able to accurately predict the melt pool geometry, whereas anisotropic enhanced thermal conductivity approach gives good agreement with the experimental results.     

Two-Phase Flow in Single-Screw Extruders

This work concerns numerical simulation of free-surface flows of highly viscous liquids in single-screw extruders.The numerical treatment of a partially filled extruder is a challenging task due to the complex geometry and the large differences in density and viscosity between the two phases, e.g. polymer melt and air. Furthermore, the rotation of the screw leads to a continuous renewing of the free-surface. For this purpose the Volume of Fluid (VOF) method is used. First a simplified two-dimensional model of a single-screw extruder is considered. Good agreement is obtained between the numerical results and experimental data. Finally, the three dimensional free-surface flow in a partially filled single-screw extruder with dynamic mesh motion is presented. In addition, the power characteristics of a conveying screw element with varying degree of filling is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of the non-isothermal flow in a twin-screw extruder

The paper deals with the numerical simulation and experimental validation of transport phenomena in a co-rotating twin screw extruder. We show steady state simulations of conveying elements in a relative system and compare them with transient simulations. With the transient simulation we are able to simulate the temperature development in the twin screw extruder. The results are compared with experimental results and show good agreement. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental validation of a viscoelastic material model for numerical simulation of the extrusion process of rubber blends

The goal of this contribution is the validation of a viscoelastic material model, which allows consideration of the interaction of the typical swelling behavior of viscoelastic fluids and the shear rate dependent viscosity of industrial used rubber blends in the context of an extrusion process. With this knowledge more realistic numerical simulations of the die swell phenomenon and its influence on the resulting profile geometry are possible. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of Degassing Process

This work deals with the modelling and simulation of a degassing process mainly used for extruders in polymer industry. The numerical simulations are done with finite-volume method using OpenFOAM for a 2D single screw extruder. The material parameters have been all chosen for a PDMS-Pentane polymer mixture so that the results could be compared with the available experiments already performed for this mixture [1]. In addition to experiments, the numerical results will be compared with an analytical solution derived from Danckwerts' model [2][3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of functionally graded plates using higher order shear deformation theory

This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.     

Processing,structure, and mechanical properties of alumina-nanofilled polystyrene composites

Binary composites composed of polystyrene (PS) and a synthetic boehmite alumina were produced by using the water-mediated melt compounding (WMC) and direct melt compounding (DMC) techniques. The alumina particles were dispersed in water at ambient temperature. The aqueous alumina suspension was injected into molten PS in a twin-screw extruder to prepare reinforced polymer composites. The dispersion of the alumina was studied by transmission and scanning electron microcopy techniques (TEM and SEM, respectively). The mechanical and thermomechanical properties of the composites were determined by employing a dynamic-mechanical thermal analysis (DMTA) and short-time creep and uniaxial static tensile tests. It was found that the direct melt compounding of the alumina with PS resulted in microcomposites, whereas the water-mediated melt compounding technique gave rise to nanocomposites. The incorporation of alumina into the PS nanocomposites increased their stiffness, tensile strength, and creep resistance. However, the elongation of the PS nanocomposites at break was smaller than that of the PS microcomposites.     

Concerning extruder flow

A criterial equation for determining the energy dissipation in the channel of an extruder screw is obtained analytically for a Newtonian model of the extrudate. It is shown that for actual extruders the dissipation does not depend on the pressure in the die.Moscow Region. Translated from Mekhanika Polimerov, No. 5, pp. 924–927, September–October, 1969.     

Effect of process parameters on injection compression molding of pickup lens

The residual stresses and shrinkages of pickup lens in injection compression molding are investigated in this study. It was realized that the behavior of residual stresses in injection compression molding parts was affected by different process conditions such as melt temperature, mold temperature, compression pressure and time. Moldings under different conditions were numerically investigated to study the effects of the process conditions on the residual stresses and shrinkage of a pickup lens with large thickness variations. The mold temperature and compression were found to be the most important factors that affect the shrinkage of lens in the thickness direction, resulting in surface profile deviation. The effect of heat transfer coefficient of the mold wall used in the molding simulation was also discussed.     

Simulation of a Hybrid-Forming Process using Temperature- and Rate-Dependent Viscoplastic Material Models

Hybrid-forming processes for graded structures are quite innovative methods for the production of components with tailored properties, particularly tailored material properties and geometrical shape. In this contribution a hybrid-forming process based on the utilization of locally varying thermo-mechanical effects is investigated [1]. For process optimization and improvement of the resulting work piece the simulation of the entire forming process is necessary in modern engineering. The main topics of this contribution are the simulation of the cyclic thermal loaded forming tool and the simulation of the work piece treated at large deformations with phase transformations. For both materials temperature- and rate-dependent viscoplastic material models are applied and parameter identification using cyclic tensile-compression tests for the forming tool material and phase transformation tests for a low-alloy steel similar to the work piece material is presented. For validation of finite-element-calculations for the forming tool thermal shock experiments are performed with optical deformation measurements. For validation of finite-element-calculations for the work piece numerical results of geometry and structure after heating, forming and cooling are compared to experimental micro sections. Results concerning the forming tool will be used for future lifetime prediction and results concerning the work piece will be used for future specific setting of graded material properties. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal models for copper-alloyed dies in pressure die casting

A recent innovation in pressure die casting is the use of copper-alloyed dies suitably protected with a thermally sprayed steel layer. The thermal response of copper-alloyed dies is dictated principally by the deposited layer, the cooling arrangement and the casting geometry. This paper is concerned with the development of efficient numerical models for the prediction of both steady-state and transient thermal behaviour of the new die designs. Die temperatures are cyclic but useful information is obtained from a steady-state model, which provides for time-averaged temperatures and energy fluxes. The modelling strategy presented in the paper involves the indirect determination of transient temperatures. A perturbation approach is adopted, where a model for the difference between transient and steady-state temperature is developed. It is shown that this approach can be utilised to determine transient temperature efficiently once steady-state information is available with the transient perturbation model only involving surfaces where a significant variation in temperature occurs.     

Relationship between internal stresses and rheological properties

It is shown that, under practically identical viscous-shear conditions, the correlation between orientation and relaxation processes taking place in an extruder die is different for different brands and batches of shock-resistant polystyrene. It has been found that the material with the the higher orientation tendency in the viscous-fluid state in the die is oriented more strongly at the same conditions in the Mackian elasticity state in the reception and pulling of the extruded polymer. It is shown that the thermal shrinkage of the sheets correlates reasonably well with the degree of swelling and the Mackian elasticity deformation of the polymer."Plastpolimer" Scientific-Industrical Association, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 952–955, September–October, 1972.     

Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation

The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell–Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump across the solid–liquid interface. The jump conditions are derived from the sharp-interface limit of a phase-field model that accounts for variations in the thermal properties between the solid and liquid. The Stefan problem is solved using asymptotic and numerical methods. The analysis reveals that the Fourier-based solution can be recovered from the classical limit of zero relaxation time when either boundary condition is used. However, only the jump condition avoids the onset of unphysical “supersonic” melting, where the speed of the melt front exceeds the finite speed of heat propagation. These results conclusively demonstrate that the jump condition, not the continuity condition, is the most suitable for use in models of phase change based on the Maxwell–Cattaneo equation. Numerical investigations show that thermal relaxation can increase the time required to melt a nanoparticle by more than a factor of ten. Thus, thermal relaxation is an important process to include in models of nanoparticle melting and is expected to be relevant in other rapid phase-change processes.     

FEM analysis for residual stress prediction in hot rolled steel strip during the run-out table cooling

With the increasing demand of higher quality hot rolled strips, flatness defects occurred on the strips during the cooling process on the run-out table have received significant attention and should be considered in the online shape control model. Non-uniform temperature distribution and cooling across the strip width are the main reasons why the strip becomes unflatten after cooling process although the strip is rolled flat at the finishing mill. A thermal, microstructural and mechanical coupling analysis model for predicting flatness change of steel strip during the run-out table cooling process was established using ABAQUS Finite Element Software. In this model, Esaka phase transformation kinetics model was employed to calculate the phase transformation, and coupled with temperature calculation by means of the user subroutine program HETVAL. An elasto-plasticity constitutive model of the material, in which conventional elastic and plastic strains, thermal strain, phase transformation strain and transformation induced plastic strain were taken into account, was derived and realized using the user subroutine program UMAT. The conclusion that the flatness of the steel strip will develop to edge wave defect under the functions of the different thermal and microstructural behaviors across strip width direction during the run-out table cooling procedure was acquired through the analysis results of this model. The calculation results of this analysis model agree with the actual measurements and observation, therefore this model has a high accuracy. To better control the flatness quality of hot rolled steel strip, the shape compensation control strategy of slight center wave rolling is proposed based on the analysis result. This control strategy has been verified by actual measurements, and applied in actual production.     

An integrated thermal model of hot rolling

During the heavy plate rolling process, different production steps, i.e., roll passes, descaling passes, and air cooling periods, influence the temperature evolution of the plate. All these relevant aspects are covered by a one-dimensional thermal model proposed in this paper. Experiments were conducted in a rolling mill under realistic rolling conditions to parametrise and validate the model. Using pyrometer measurements, a simple model adaption strategy is developed, which can cope with uncertainties in the initial temperature profile. The model provides accurate predictions of the temperature evolution of the plate during the whole rolling process from the plate’s exit of the furnace to the last pass. Thus, it can be used for scheduling the production process. Based on the model, an observer can be designed.     

Asymptotic Formulas for Thermography Based Recovery of Anomalies

We start from a realistic half space model for thermal imaging, which we then use to develop a mathematical asymptotic analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design nonit-erative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.AMS subject classifications: 35R20, 35B30