Parameter estimation and modeling of lithium and lithium-ion batteries

Specific characteristics of Li-ion batteries (LIBs) make them promising candidates for energy storage systems when compared with the others. High working voltage and energy density as well as green technology of LIBs are the reasons for increasing interest to use these electrochemical systems as the substitute of conventional combustion engine of automobiles. Consequently, the interest to study these technologies has increased recently and several models have been introduced to simulate their behavior. However, it is difficult to model all multiphysics phenomena happening inside such rechargeable batteries. Some important choices need to be made when one wants to select an appropriate model for considering the main physics elements and yet be simple enough for large time scale studies. Combining chemical/electrochemical kinetics and transport phenomena, electrochemical models have been introduced to tackle most important principles inside the cell. These models, however, require known electrochemical parameters which most of the time are hard to get experimentally. Parameter estimation (PE) techniques simplify extracting these representative parameters of the cell behaviour. In this study, a PE methodology has been introduced to estimate the most influential electrochemical parameters of LIBs considering different positive electrode materials. The methodology starts with simplifying the well-known pseudo-two-dimensional (P2D) model, the most complex and the most popular electrochemical engineering models for simulating porous electrodes and introducing an enhanced single particle model (SPM). Neglecting the micro-structure of LIB, major electrochemical parameters are detected at the cell level. Next, the best time domains and discharge current rates to estimate each parameter are estimated by virtue of sensitivity analyses. Owing to the fact that the behavior of LIBs depends on the active materials employed in the electrode, the proposed methodology is verified for three different positive electrode active materials including LiCoO2, LiMn2O4 and LiFePO4. Furthermore, focusing on LiFePO4 (LFP), as the most promising positive electrode active material, a new modification is proposed to the model to address special features of this material. In this regard, a simplified electrochemical model is equipped with a variable resistance equation whose coefficients are estimated by means of PE.Résumé : Les batteries au Li-ion (BLI) figurent parmi les technologies les plus prometteuses pour le design de systèmes de stockage d’énergie à cause de leurs caractéristiques intrinsèques. Leur grand voltage de travail, leur grande densité énergétique et leur impact écologique positif expliquent l’intérêt soutenu de l’utilisation des BLI pour remplacer par exemple les moteurs à explosion dans les applications de transport terrestre. Il n’est donc pas surprenant de constater que ces technologies ont eu une attention scientifique importante et que plusieurs auteurs ont développé des modèles numériques simulant leur comportement. Il reste cependant difficile de représenter tous les phénomènes multiphysiques qui se déroulent à l’intérieur des batteries rechargeables par des modèles mathématiques. Des compromis importants doivent être faits lorsqu’on doit choisir un modèle représentant les principaux phénomènes physico-chimiques tout en restant assez simple pour pouvoir l’utiliser dans des études s’échelonnant sur de larges périodes temps. Représentant à la fois la cinétique électrochimique et le transport de masse, les modèles électrochimiques ont été introduits pour prendre en compte les phénomènes les plus importants. Ces modèles demandent cependant de connaître tous les paramètres électrochimiques, des données qui sont difficiles à obtenir expérimentalement. Les techniques d’estimation de paramètres simplifient l’obtention de ces données critiques pour représenter le comportement de la pile. Dans cette étude, une méthode d’estimation de paramètres a été introduite pour estimer les paramètres électrochimiques des BLI les plus influents, en prenant en compte différents matériaux d’électrode positive. La méthode proposée repose sur une amélioration du modèle à particule unique, qui représente lui-même une simplification du modèle pseudo-2D, le modèle électrochimique le plus connu et le plus complexe dans le domaine de la simulation de piles à électrodes poreuses. Les paramètres électrochimiques les plus importants ont été identifiés en négligeant la micro-structure de la batterie au Li-ion. Une étude de sensibilité a ensuite permis d’identifier les domaines temporels et les courants de décharge les plus favorables pour l’identification de chaque paramètre. Étant donné que le comportement des BLI dépend fortement des matériaux actifs utilisés pour la fabrication des électrodes, la méthodologie proposée a été testée sur 3 matériaux actifs différents (LiCoO2, LiMn2O4 and LiFePO4) employés dans la fabrication industrielle d’électrodes positives. Finalement, une autre amélioration du modèle à particule unique a été proposée et testée afin de mieux représenter le comportement spécifique du LiFePO4 (LFP), un matériau actif parmi les plus prometteurs pour l’électrode positive. Plus précisément, un modèle électrochimique simplifié incluant une équation représentant la variation de résistance en fonction du degré de décharge a été développé et les coefficients de cette équation ont été déterminés au moyen de la méthode d’estimation de paramètres proposée

Inverse Prediction and Application of Homotopy Perturbation Method for Efficient Design of an Annular Fin with Variable Thermal Conductivity and Heat Generation

In the present work, various thermal parameters of an annular fin subjected to thermal loading are inversely estimated using differential evolution (DE) method. In order to obtain the temperature field, the second order nonlinear differential equation for heat transfer with variable thermal conductivity and internal heat generation is solved using Homotopy Perturbation Method (HPM). Classical thermoelasticity approach coupled with an HPM solution for temperature field is employed for the forward solution of thermal stresses. It is interesting that the internal heat generation does not affect the radial stresses, while the temperature field and the tangential stresses are influenced by the heat generation parameters. As the tangential stresses are mainly responsible for mechanical failure due to thermal loading in an annular fin, the unknown thermal parameters are inversely estimated from a prescribed tangential stress field. The reconstructed stress fields obtained from the inverse parameters are found to be in good agreement with the actual solution

Simultaneous estimation of heat flux and heat transfer coefficient in irregular geometries made of functionally graded materials

A numerical inverse analysis based on explicit sensitivity coefficients is developed for the simultaneous estimation of heat flux and heat transfer coefficient imposed on different parts of boundary of a general irregular heat conducting body made of functionally graded materials with spatially varying thermal conductivity. It is assumed that the thermal conductivity varies exponentially with position in the body. The body considered in this study is an eccentric hollow cylinder. The heat flux is applied on the cylinder inner surface and the heat is dissipated to the surroundings through the outer surface. The numerical method used in this study consists of three steps: 1) to apply a boundary-fitted grid generation (elliptic) method to generate grid over eccentric hollow cylinder (an irregular shape) and then solve for the steady-state heat conduction equation with variable thermal conductivity to compute the temperature values in the cylinder, 2) to propose a new explicit sensitivity analysis scheme used in inverse analysis, and 3) to apply a gradient-based optimization method (in this study, conjugate gradient method) to minimize the mismatch between the computed temperature on the outer surface of the cylinder and simulated measured temperature distribution. The inverse analysis presented here is not involved with an adjoint equation and all the sensitivity coefficients can be computed in only one direct solution, without the need for the solution of the adjoint equation. The accuracy, efficiency, and robustness of the developed inverse analysis are demonstrated through presenting a test case with different initial guesses

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Heat Transfer

Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer

Optimal Design of Functionally Graded Parts

Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed

Estimation of the thermal diffusivity in a large electroceramic body by an invere method

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.We investigate the temperature dependence of the thermal diffusivity for a large ceramic body of a cylindrical shape during firing up to 900 °C. The body was made of a ceramic material used in the production of electroporcelain insulators. We describe the corresponding heat transfer by the standard heat equation and solve the inverse problem by the Levenberg-Marquardt method. The results show that the method allows one to detect the physical-chemical processes occurring in the material during firing, namely, the liberation of physically bound water in the range up to 250 °C, the phase transformation of kaolinite into metakaolinite (dehydroxyla-tion) in the range ~ 450 °C – 650 °C, and solid-state sintering starting at ~ 700 °C.cf201

An overview of the proper generalized decomposition with applications in computational rheology

We review the foundations and applications of the proper generalized decomposition (PGD), a powerful model reduction technique that computes a priori by means of successive enrichment a separated representation of the unknown field. The computational complexity of the PGD scales linearly with the dimension of the space wherein the model is defined, which is in marked contrast with the exponential scaling of standard grid-based methods. First introduced in the context of computational rheology by Ammar et al. [3] and [4], the PGD has since been further developed and applied in a variety of applications ranging from the solution of the Schrödinger equation of quantum mechanics to the analysis of laminate composites. In this paper, we illustrate the use of the PGD in four problem categories related to computational rheology: (i) the direct solution of the Fokker-Planck equation for complex fluids in configuration spaces of high dimension, (ii) the development of very efficient non-incremental algorithms for transient problems, (iii) the fully three-dimensional solution of problems defined in degenerate plate or shell-like domains often encountered in polymer processing or composites manufacturing, and finally (iv) the solution of multidimensional parametric models obtained by introducing various sources of problem variability as additional coordinates

A quick review of the applications of artificial neural networks (ANN) in the modelling of thermal systems

Thermal systems play a main role in many industrial sectors. This study is an elucidation of the utilization of artificial neural networks (ANNs) in the modelling of thermal systems. The focus is on various heat transfer applications like steady and dynamic thermal problems, heat exchangers, gas-solid fluidized beds, and others. Solving problems related to thermal systems using a traditional or classical approach often results to near feasible solutions. As a result of the stochastic nature of datasets, using the classical models to advance exclusive designs from the experimental dataset is often a function of trial and error. Conventional correlations or fundamental equations will not proffer satisfactory solutions as they are in most cases suitable and applicable to the problems from where they are generated. A preferable option is the application of computational intelligence techniques focused on the artificial neural network model with different structures and configurations for effective analysis of the experimental dataset. The main aim of current study is to review research work related to artificial neural network techniques and the contemporary improvements in the use of these modelling techniques, its up-and-coming application in addressing variability of heat transfer problems. Published research works presented in this paper, show that problems solved using the ANN model with regression analysis produced good solutions. Limitations of the classical and computational intelligence models have been exposed and recommendations have been made which focused on creative algorithms and hybrid models for future modelling of thermal systems.http://www.etasr.com/index.php/ETASR/indexdm2022Mechanical and Aeronautical Engineerin

Computational Heat Transfer and Fluid Mechanics

With the advances in high-speed computer technology, complex heat transfer and fluid flow problems can be solved computationally with high accuracy. Computational modeling techniques have found a wide range of applications in diverse fields of mechanical, aerospace, energy, environmental engineering, as well as numerous industrial systems. Computational modeling has also been used extensively for performance optimization of a variety of engineering designs. The purpose of this book is to present recent advances, as well as up-to-date progress in all areas of innovative computational heat transfer and fluid mechanics, including both fundamental and practical applications. The scope of the present book includes single and multiphase flows, laminar and turbulent flows, heat and mass transfer, energy storage, heat exchangers, respiratory flows and heat transfer, biomedical applications, porous media, and optimization. In addition, this book provides guidelines for engineers and researchers in computational modeling and simulations in fluid mechanics and heat transfer