References of "Peters, Bernhard 50002840"
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See detailThree-dimensional CFD-DEM simulation of raceway transport phenomena in a blast furnace
Aminnia, Navid UL; Adhav, Prasad UL; Darlik, Fateme UL et al

in Fuel (2023), 334(2),

Improving energy efficiency in a blast furnace (BF) has a significant effect on energy consumption and pollutant emission in a steel plant. In the BF, the blast injection creates a cavity, the so-called ... [more ▼]

Improving energy efficiency in a blast furnace (BF) has a significant effect on energy consumption and pollutant emission in a steel plant. In the BF, the blast injection creates a cavity, the so-called raceway, near the inlet. On the periphery of the raceway, a ring-type zone is formed which is associated with the highest coke combustion rate and temperatures in the raceway. Therefore, predicting the raceway size or in other words, the periphery of the ring-type zone with accuracy is important for estimating the BF’s energy and coke consumption. In the present study, Computational Fluid Dynamics (CFD) is coupled to Discrete Element Method (DEM) to develop a three-dimensional (3D) model featuring a gas–solid reacting flow, to study the transport phenomena inside the raceway. The model is compared to a previously developed two-dimensional (2D) model and it is shown that the assumptions associated with a 2D model, result in an overestimation of the size of the raceway. The 3D model is then used to investigate the coke particles’ combustion and heat generation and distribution in the raceway. It is shown that a higher blast flow rate is associated with a higher reaction rate and a larger raceway. A 10% increase in the inlet velocity (from 200 m/s to 220 m/s) caused the raceway volume to grow by almost 40%. The DEM model considers a radial discretization over the particle, therefore the heat and mass distributions over the particle are analyzed as well. [less ▲]

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See detailDeveloping a DEM-Coupled OpenFOAM solver for multiphysics simulation of additive manufacturing process
Aminnia, Navid UL; Estupinan Donoso, Alvaro Antonio UL; Peters, Bernhard UL

in Scipedia.com (2022, December)

Powder-based additive manufacturing technologies, specifically selective laser melting, are challenging to model due to the complex, interrelated physical phenomena that are present on multiple spatial ... [more ▼]

Powder-based additive manufacturing technologies, specifically selective laser melting, are challenging to model due to the complex, interrelated physical phenomena that are present on multiple spatial scales, during the process. A key element of such models will be the detailed simulation of flow and heat transfer throughout the melt pool that is formed when the powder particles melt. Due to the high temperature gradients that are rised inside the melt pool, Marangoni force plays a key role in governing the flows inside the melt pool and deciding its shape and dimensions[1]. On the other hand the mass and heat transfer between the melt and the powder also has a signifacnt role in shaping the melt pool at the edges. In this study we modified an OpenFOAM solver(icoReactingMultiphaseInterFoam) cou- pled with an in-house developed DEM code known as eXtended Discrete Element Method or XDEM which models the dynamics and thermodynamics of the particles[2]. By adding the Marangoni force to the momentum equation and also defining a laser model as a boundary Condition for Liquid-Gas Interface, the solver is capable of modeling selective laser melting process from the moment of particle melting to the completion of the so- solidified track. The coupled solver was validated with an ice-packed bed melting case and was used to simulate a multi-track selective laser melting process. [less ▲]

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See detailLocal Verlet buffer approach for broad-phase interaction detection in Discrete Element Method
Mainassara Chekaraou, Abdoul Wahid UL; Besseron, Xavier UL; Rousset, Alban UL et al

E-print/Working paper (2022)

The Extended Discrete Element Method (XDEM) is an innovative numerical simulation technique that extends the dynamics of granular materials known as Discrete Element Method (DEM) by additional properties ... [more ▼]

The Extended Discrete Element Method (XDEM) is an innovative numerical simulation technique that extends the dynamics of granular materials known as Discrete Element Method (DEM) by additional properties such as the thermodynamic state, stress/strain for each particle. Such DEM simulations used by industries to set up their experimental processes are complexes and heavy in computation time. At each time step, those simulations generate a list of interacting particles and this phase is one of the most computationally expensive parts of a DEM simulation. The Verlet buffer method, initially introduced in Molecular Dynamic (MD) (and also used in DEM), allows keeping the interaction list for many time steps by extending each particle neighbourhood by a certain extension range, and thus broadening the interaction list. The method relies on the temporal coherency of DEM, which guarantees that no particles move erratically from one time step to the next. In the classical approach, all the particles have their neighbourhood extended by the same value which leads to suboptimal performances in simulations where different flow regimes coexist. Additionally, and unlike in MD, there is no comprehensive study analysing the different parameters that affect the performance of the Verlet buffer method in DEM. In this work, we propose a new method for the dynamic update of the neighbour list that depends on the particles individual displacement and define a particle-specific extension range based on the local flow regime. The interaction list is analysed throughout the simulation based on the particle's displacement allowing a flexible update according to the flow regime conditions. We evaluate the influence of the Verlet extension range on the execution time through different test cases and analyse empirically the extension range value giving the best performance. [less ▲]

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See detailParallel Multi-Physics Simulation of Biomass Furnace and Cloud-based Workflow for SMEs
Besseron, Xavier UL; Rusche, Henrik; Peters, Bernhard UL

in Practice and Experience in Advanced Research Computing (PEARC '22) (2022, July)

Biomass combustion is a well-established process to produce energy that offers a credible alternative to reduce the consumption of fossil fuel. To optimize the process of biomass combustion, numerical ... [more ▼]

Biomass combustion is a well-established process to produce energy that offers a credible alternative to reduce the consumption of fossil fuel. To optimize the process of biomass combustion, numerical simulation is a less expensive and time-effective approach than the experimental method. However, biomass combustion involves intricate physical phenomena that must be modeled (and validated) carefully, in the fuel bed and in the surrounding gas. With this level of complexity, these simulations require the use of High-Performance Computing (HPC) platforms and expertise, which are usually not affordable for manufacturing SMEs. In this work, we developed a parallel simulation tool for the simulation of biomass furnaces that relies on a parallel coupling between Computation Fluid Dynamics (CFD) and Discrete Element Method (DEM). This approach is computation-intensive but provides accurate and detailed results for biomass combustion with a moving fuel bed. Our implementation combines FOAM-extend (for the gas phase) parallelized with MPI, and XDEM (for the solid particles) parallelized with OpenMP, to take advantage of HPC hardware. We also carry out a thorough performance evaluation of our implementation using an industrial biomass furnace setup. Additionally, we present a fully automated workflow that handles all steps from the user input to the analysis of the results. Hundreds of parameters can be modified, including the furnace geometry and fuel settings. The workflow prepares the simulation input, delegates the computing-intensive simulation to an HPC platform, and collects the results. Our solution is integrated into the Digital Marketplace of the CloudiFacturing EU project and is directly available to SMEs via a Cloud portal. As a result, we provide a cutting-edge simulation of a biomass furnace running on HPC. With this tool, we demonstrate how HPC can benefit engineering and manufacturing SMEs, and empower them to compute and solve problems that cannot be tackled without. [less ▲]

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See detailAn Innovative Partitioning Technology for Coupled Software Modules
Peters, Bernhard UL; Besseron, Xavier UL; Peyraut, Alice et al

in Proceedings of the 12th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH (2022, July)

Multi-physics simulation approaches by coupling various software modules is paramount to unveil the underlying physics and thus leads to an improved design of equipment and a more efficient operation ... [more ▼]

Multi-physics simulation approaches by coupling various software modules is paramount to unveil the underlying physics and thus leads to an improved design of equipment and a more efficient operation. These simulations are in general to be carried out on small to massively parallelised computers for which highly efficient partitioning techniques are required. An innovative partitioning technology is presented that relies on a co-located partitioning of overlapping simulation domains meaning that the overlapping areas of each simulation domain are located at one node. Thus, communication between modules is significantly reduced as compared to an allocation of overlapping simulation domains on different nodes. A co-located partitioning reduces both memory and inter-process communication. [less ▲]

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See detailHEAT AND MASS TRANSFER BETWEEN XDEM & OPENFOAM USING PRECICE COUPLING LIBRARY
Adhav, Prasad UL; Besseron, Xavier UL; Estupinan Donoso, Alvaro Antonio UL et al

Scientific Conference (2022, June 09)

This work demonstrates the rapid development of a simulation environment to achieve Heat and Mass Transfer (HMT) between Discrete Element Methods (DEM) and Computa- tional Fluid Dynamics (CFD). The HMT ... [more ▼]

This work demonstrates the rapid development of a simulation environment to achieve Heat and Mass Transfer (HMT) between Discrete Element Methods (DEM) and Computa- tional Fluid Dynamics (CFD). The HMT coupling can be employed to simulate processes such as drying, pyrolysis, combustion, melting, solid-fluid reactions etc and have indus- trial applications such as biomass furnaces, boilers, heat exchangers, and flow through packed beds. This shows that diverse CFD features and solvers need to be coupled with DEM in order to achieve various applications mentioned above. The proposed DEM-CFD Eulerian-Lagrangian coupling for heat and mass transfer is achieved by employing the preCICE coupling library[1] on volumetric meshes. In our prototype, we use the eXtended Discrete Element Method (XDEM)[2] for handling DEM calculations and OpenFOAM for the CFD. The XDEM solver receives various CFD data fields such as fluid properties, and flow conditions exchanged through preCICE, which are used to set boundary conditions for particles. Various heat transfer and mass transfer laws have been implemented in XDEM to steer HMT source term computations. The heat and mass source terms computed by XDEM are transferred to CFD solver and added as source. These source terms represent particles in CFD. The generic coupling interface of preCICE, XDEM and its adapter allows to tackle a di- verse range of applications. We demonstrate the heat, mass & momentum coupling capa- bilities through various test cases and then compared with our legacy XDEM-OpenFOAM coupling and experimental results. [less ▲]

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See detailDevelopment of an HPC Multi-Physics Biomass Furnace Simulation and Integration in a Cloud-based Workflow
Besseron, Xavier UL; Henrik, Rusche; Peters, Bernhard UL

Scientific Conference (2022, June 09)

Biomass combustion offers a credible alternative to reduce the consumption of fossil fuels. To optimize the biomass combustion process and improve the design of biomass furnaces numerical simulation is a ... [more ▼]

Biomass combustion offers a credible alternative to reduce the consumption of fossil fuels. To optimize the biomass combustion process and improve the design of biomass furnaces numerical simulation is a less expensive and time-effective approach as opposed to the experimental method. However, the combustion in a biomass furnace involves intricate physical phenomena that must be modeled (and validated) carefully, in the fuel bed (with particle motion and shrinking, heat transfer, drying, pyrolysis, gasification) and in the surrounding gas (with turbulence, combustion, radiation). With this level of complexity, and to be conducted in a reasonable time, the simulation of industrial biomass furnaces requires the use of High-Performance Computing (HPC) platforms and expertise, which is usually not affordable for manufacturing SMEs. To address this issue, we developed a configurable digital twin of a biomass furnace running on HPC and we designed a cloudified easy-to-use end-to-end workflow. This fully automated workflow, from user input to results analysis, has been integrated into the digital marketplace of the CloudiFacturing EU project and is now directly available to SMEs via a Cloud portal. With this presentation, we want to offer a glance at the internal details and enabling technologies used in our parallel coupled application and scientific workflow. Our parallel simulation tool for biomass furnaces combines OpenFOAM (for the gas phase) parallelized with MPI and XDEM (for the solid wood particles) parallelized with OpenMP. The two libraries are coupled in parallel using an original approach based on the co-located partitioning strategy which has been tailored to minimize communications. As for the cloud workflow, it is based on an all-in-one Singularity image containing all the software, scripts, and data required to prepare the simulation input, execute the computation-intensive simulation, and analyze the results. Finally, we present the lessons learned from the development of this complex workflow and highlight the remaining challenges related to HPC multi-physics coupled simulations. [less ▲]

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See detailMATERIAL MODELLING AND FINITE ELEMENT ANALYSIS IN METAL ADDITIVE MANUFACTURING
Mashhood, Muhammad UL; Baroli, Davide; Wyart, Eric et al

Poster (2022, May 31)

The additive manufacturing (AM) is competent method for the manufacturing of complex metal parts with wider process flexibility. During manufacturing, the metal part repetitively undergoes heating and ... [more ▼]

The additive manufacturing (AM) is competent method for the manufacturing of complex metal parts with wider process flexibility. During manufacturing, the metal part repetitively undergoes heating and cooling under the influence of laser passes and ambient conditions respectively. In turn, the material experiences the thermal strain and residual stress. The aim of the work is to predict them using certain material model. Where the solidified metal part from melt-pool is considered in current analysis. For numerical simulation, Finite Element Method (FEM) is chosen. The heat equation is first solved for thermal profile of AM Process. Afterwards, the structural analysis is performed with such thermal load. The non linear constitutive material model is utilised. For concerned material model, the temperature dependence upon the material properties is also implemented. The resulting Finite Element Analysis (FEA) platform offers the macro-scale thermal solution and the prediction of resulting plastic distortion in material. This prediction however has become more accurate when the variable material property, depending upon the temperature of analysis zone, is introduced. [less ▲]

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See detailXDEM study of burden distribution in iron ore pellet firing
Estupinan Donoso, Alvaro Antonio UL; Peters, Bernhard UL; Amani, H et al

in Ironmaking and Steelmaking (2022), 49(6), 615-625

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See detailTHE EVOLUTION OF THERMAL DISTORTION AND STRESSES AT MACRO SCALE FOR METAL ADDITIVELY MANUFACTURED PART
Mashhood, Muhammad UL; Zilian, Andreas UL; Peters, Bernhard UL et al

Scientific Conference (2022, February 05)

[1] R.K. Ganeriwala, M. Strantza, W.E. King, B. Clausen, T.Q. Phan, L.E. Levine, D.W. Brown, N.E. Hodge, Evaluation of a thermomechanical modelfor prediction of residual stress during laser powder bed ... [more ▼]

[1] R.K. Ganeriwala, M. Strantza, W.E. King, B. Clausen, T.Q. Phan, L.E. Levine, D.W. Brown, N.E. Hodge, Evaluation of a thermomechanical modelfor prediction of residual stress during laser powder bed fusion of Ti-6Al- 4V, Additive Manufacturing(2019), Vol. 27., 489–502. [2] M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes and G. N. Wells, The FEniCS Project Version 1.5, Archive of Numerical Software(2015), Vol. 3., 100:9–23. [less ▲]

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See detailThermo-mechanical modelling for metal additive manufacturing
Mashhood, Muhammad UL; Baroli, Davide; Wyart, Eric et al

Scientific Conference (2021, October 27)

[1] Alnaes, M. S. Blechta, J. Hake, J. Johansson, A. Kehlet, B. Logg, A. Richardson, C. Ring, J.Rognes, M. E. and Wells, G. N. The FEniCS Project Version 1.5. Archive of Numerical Software(2015), Vol. 3 ... [more ▼]

[1] Alnaes, M. S. Blechta, J. Hake, J. Johansson, A. Kehlet, B. Logg, A. Richardson, C. Ring, J.Rognes, M. E. and Wells, G. N. The FEniCS Project Version 1.5. Archive of Numerical Software(2015), Vol. 3., 100:9–23. [2] Carraturo, M. and Kollmannsberger, S. and Reali, A. and Auricchio, F. and Rank, E. An immersed boundary approach for residual stress evaluation in SLM processes. [less ▲]

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See detailAWJC Nozzle simulation by 6-way coupling of DEM+CFD+FEM using preCICE coupling library
Adhav, Prasad UL; Besseron, Xavier UL; ROUSSET, Alban et al

Scientific Conference (2021, June 16)

The objective of this work is to study the particle-laden fluid-structure interaction within an Abrasive Water Jet Cutting Nozzle. Such coupling is needed to study the erosion phenomena caused by the ... [more ▼]

The objective of this work is to study the particle-laden fluid-structure interaction within an Abrasive Water Jet Cutting Nozzle. Such coupling is needed to study the erosion phenomena caused by the abrasive particles inside the nozzle. So far, the erosion in the nozzle was predicted only through the number of collisions, using only a simple DEM+CFD[1] coupling. To improve these predictions, we extend our model to a 6-way Eulerian-Lagrangian momentum coupling with DEM+CFD+FEM to account for deformations and vibrations in the nozzle. Our prototype uses the preCICE coupling library[2] to couple 3 numerical solvers: XDEM[3] (for the particle motion), OpenFOAM[4] (for the water jet), and CalculiX[5] (for the nozzle deformation). XDEM handles all the particle motions based on the fluid properties and flow conditions, and it calculates drag terms. In the fluid solver, particles are modeled as drag and are injected in the momentum equation as a source term. CalculiX uses the forces coming from the fluid solver and XDEM as boundary conditions to solve for the displacements. It is also used for computing the vibrations induced by particle impacts. . The preliminary 6-way DEM+CFD+FEM coupled simulation is able to capture the complex particle-laden multiphase fluid-structure interaction inside AWJC Nozzle. The erosion concentration zones are identified and are compared to DEM+CFD coupling[1]. The results obtained are planned to be used for predicting erosion intensity in addition to the concentration zones. In the future, we aim to compare the erosions predictions to experimental data in order to evaluate the suitability of our approach. The FEM module of the coupled simulation captures the vibration frequency induced by particles and compares it with the natural frequency of the nozzle. Thus opening up opportunities for further investigation and improvement of the Nozzle design. [less ▲]

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See detailA Discrete Element Framework for Modeling the Mechanical Behaviour of Snow PART I: Mechanical Behaviour and Numerical Model
Kabore, Brice Wendlassida UL; Peters, Bernhard UL; Michael, Mark et al

in Granular Matter (2021), 23(2), 42

A framework for investigating the mechanics of snow is proposed based on an advanced micro-scale approach. Varying strain rates, densities and temperatures are taken into account. Natural hazards i.e ... [more ▼]

A framework for investigating the mechanics of snow is proposed based on an advanced micro-scale approach. Varying strain rates, densities and temperatures are taken into account. Natural hazards i.e. snow avalanches are triggered by snow deforming at low rates, while a large group of industrial applications concerning driving safety or winter sport activities require an understanding of snow behaviour under high deformation rates. On the micro-scale, snow is considered to consist of ice grains joined by ice bonds to build a porous structure. Deformation and failure of bonds and the inter-granular collisions of ice grains determine the macroscopic response under mechanical load. Therefore, this study proposes an inter-granular bond and collision model for snow based on the discrete element method (DEM) to describe interaction on a grain-scale. It aims at predicting the mechanical behaviour of ice particles under different strain rates using a unified approach. Thus, the proposed algorithm predicts the displacement of each individual grains due to inter-granular forces and torques that derive from bond deformation and grain collision. For this purpose, the inter-granular characteristics are approximated by an elastic viscous-plastic material law which is based on the temperature-dependent properties of poly-crystalline ice Ih. [less ▲]

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See detailA Discrete Element Framework for Modeling the Mechanical Behaviour of Snow PART II: Model Validation
Peters, Bernhard UL; Kabore, Brice Wendlassida UL; Mark, Michael et al

in Granular Matter (2021), 23(2), 43

A micro-scale modelling approach of snow based on the extension of the classical discrete element method (DEM) has been presented in the first part of this study. This modelling approach is employed to ... [more ▼]

A micro-scale modelling approach of snow based on the extension of the classical discrete element method (DEM) has been presented in the first part of this study. This modelling approach is employed to predict the mechanical response of snow under compression dependent on strain rate, initial density and temperature. Results obtained under a variety of conditions are validated with experimental data for both micro- and macro-scale, in particular the broad range between ductile i.e.~low deformation rates and brittle i.e.~high deformation rates regimes are investigated. For this purpose snow is assumed to be composed of ice grains that are inter-connected by a network of bonds between neighbouring grains. This arrangement represents the micro-scale of which the interaction is described by inter-granular collision and bonding. Hence, the response on a macro-scale is largely determined by inter-granular collisions and deformation and failure of bonds during a loading cycle. Consequently, validation was first carried out on micro-scale deformations at different loading rates and temperatures. Hereafter, macro-scale simulations of confined and unconfined, deformation-controlled compression tests have been predicted and were successfully compared to experimental data reported in literature. [less ▲]

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See detailOpenMP optimisation of the eXtended Discrete Element Method (XDEM)
Ojeda-May, Pedro; Eriksson, Jerry; Rousset, Alban UL et al

Report (2021)

The eXtended Discrete Element Method (XDEM) is an extension of the regular Discrete Element Method (DEM) which is a software for simulating the dynamics of granular material. XDEM extends the regular DEM ... [more ▼]

The eXtended Discrete Element Method (XDEM) is an extension of the regular Discrete Element Method (DEM) which is a software for simulating the dynamics of granular material. XDEM extends the regular DEM method by adding features where both micro and macroscopic observables can be computed simultaneously by coupling different time and length scales. In this sense XDEM belongs the category of multi-scale/multi-physics applications which can be used in realistic simulations. In this whitepaper, we detail the different optimisations done during the preparatory PRACE project to overcome known bottlenecks in the OpenMP implementation of XDEM. We analysed the Conversion, Dynamic, and the combined Dynamics-Conversion modules with Extrae/Paraver and Intel VTune profiling tools in order to find the most expensive functions. The proposed code modifications improved the performance of XDEM by ~17% for the computational expensive Dynamics-Conversion combined modules (with 48 cores, full node). Our analysis was performed in the Marenostrum 4 (MN4) PRACE infrastructure at Barcelona Supercomputing Center (BSC). [less ▲]

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See detailEvaluation of erosion inside AWJC Nozzle by 6-way coupling of DEM+CFD+FEM using preCICE
Adhav, Prasad UL; Besseron, Xavier UL; Rousset, Alban et al

Presentation (2021, February 23)

The objective of this work is to study the particle‐induced erosion within a nozzle for abrasive cutting. So far, the erosion in the nozzle was predicted only through the number of collisions, using only ... [more ▼]

The objective of this work is to study the particle‐induced erosion within a nozzle for abrasive cutting. So far, the erosion in the nozzle was predicted only through the number of collisions, using only a simple DEM+CFD coupling. To improve these predictions, we extend our model to a 6‐way momentum coupling with DEM+CFD+FEM to account for deformations and vibrations in the nozzle. Our prototype uses preCICE to couple 3 numerical solvers: XDEM (for the particle motion), OpenFOAM (for the water jet), and CalculiX (for the nozzle deformation). The OpenFOAM adapter has been adapted to add particles drag, which is modeled as semi‐implicit porosity, implicit and explicit drag terms injected to OpenFOAM solver through fvOptions. This 6‐way coupling between DEM+CFD+FEM brings the simulation of the particle‐laden multiphase flow inside the abrasive cutting nozzle close to the real‐life conditions. Thus opening up opportunities for further investigation and improvement of the Nozzle design. [less ▲]

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See detailMathematical modeling of thermal behavior of single iron ore pellet during heat hardening oxidation
Amani, Hafez; Alamdari, E.K; Ale Ebrahim, H. et al

in Journal of Thermal Analysis and Calorimetry (2021)

In this study, a one-dimensional generic model capable of being integrated with reactor scale models is proposed for a single pellet through solving the transient diferential conservation equations ... [more ▼]

In this study, a one-dimensional generic model capable of being integrated with reactor scale models is proposed for a single pellet through solving the transient diferential conservation equations. Predicted results comparison with the experimental data showed close agreement. In addition, the model was used to investigate the relevance of physical characteristics of pellet, reacting gas composition, difusion factors, and prevailing regime. It was found that the pure magnetite pellet could achieve a temperature rise of about 245 K at oxygen concentration of 40 vol.%, whereas the maximum temperature diference inside the pellet was approximately 24 K. Moreover, increasing pellet size, the maximum attainable temperature reached a peak and then leveled out. Furthermore, by decreasing the pore diameter, the pellet size with peak temperature shifted to the smaller pellet sizes. Analyzing the numerical results also showed that for the small pellet sizes, shortening the difusion path leads to the spreading of the reaction interface. The modeling methodology herein can be applied to any particulate processes and is not limited to the aforementioned case. [less ▲]

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See detailThermo-mechanical coupling and part-level analysis for additive manufacturing processes
Mashhood, Muhammad UL; Baroli, Davide; Zilian, Andreas UL et al

Scientific Conference (2021, January 13)

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design ... [more ▼]

[1] Hussein, A. and Hao, L. and Yan, C. and Everson, R. Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Materials & Design (1980-2015), (2013), 52:638–647. [2] Bangerth, W. and Hartmann, R. and Kanschat, G. deal.II – a General Purpose Object Oriented Finite Element Library. ACM Trans. Math. Softw.(2007), Vol. 33., 4:24/1–24/27. [less ▲]