Numerical model building based on XFEM/level set method to simulate ledge freezing/melting in Hall-Héroult cell

Au cours de la production de l'aluminium via le procédé de Hall-Héroult, le bain gelé, obtenu par solidification du bain électrolytique, joue un rôle significatif dans le maintien de la stabilité de la cellule d'électrolyse. L'objectif de ce travail est le développement d'un modèle numérique bidimensionnel afin de prédire le profil du bain gelé dans le système biphasé bain liquide/bain gelé, et ce, en résolvant trois problèmes physiques couplés incluant le problème de changement de phase (problème de Stefan), la variation de la composition chimique du bain et le mouvement de ce dernier. Par souci de simplification, la composition chimique du bain est supposée comme étant un système binaire. La résolution de ces trois problèmes, caractérisés par le mouvement de l'interface entre les deux phases et les discontinuités qui ont lieu à l'interface, constitue un grand défi pour les méthodes de résolution conventionnelles, basées sur le principe de la continuité des variables. En conséquence, la méthode des éléments finis étendus (XFEM) est utilisée comme alternative afin de traiter les discontinuités locales inhérentes à chaque solution tandis que la méthode de la fonction de niveaux (level-set) est exploitée pour capturer, implicitement, l'évolution de l'interface entre les deux phases. Au cours du développement de ce modèle, les problématiques suivantes : 1) l'écoulement monophasique à densité variable 2) le problème de Stefan couplé au transport d'espèces chimiques dans un système binaire sans considération du phénomène de la convection et 3) le problème de Stefan et le mouvement du fluide qui en résulte sont investigués par le biais du couplage entre deux problèmes parmi les problèmes mentionnées ci-dessus. La pertinence et la précision de ces sous-modèles sont testées à travers des comparaisons avec des solutions analytiques ou des résultats obtenus via des méthodes numériques conventionnelles. Finalement, le modèle tenant en compte les trois physiques est appliqué à la simulation de certains scénarios de solidification/fusion du système bain liquide-bain gelé. Dans cette dernière application, le mouvement du bain, induit par la différence de densité entre les deux phases ou par la force de flottabilité due aux gradients de température et/ou de concentration, est décrit par le problème de Stokes. Ce modèle se caractérise par le couplage entre différentes physiques, notamment la variation de la densité du fluide et de la température de fusion en fonction de la concentration des espèces chimiques. En outre, la méthode XFEM démontre sa précision et sa flexibilité pour traiter différents types de discontinuité tout en considérant un maillage fixe.During the Hall-Héroult process for smelting aluminium, the ledge formed by freezing the molten bath plays a significant role in maintaining the internal working condition of the cell at stable state. The present work aims at building a vertically two-dimensional numerical model to predict the ledge profile in the bath-ledge two-phase system through solving three interactive physical problems including the phase change problem (Stefan problem), the variation of bath composition and the bath motion. For the sake of simplicity, the molten bath is regarded as a binary system in chemical composition. Solving the three involved problems characterized by the free moving internal boundary and the presence of discontinuities at the free boundary is always a challenge to the conventional continuum-based methods. Therefore, as an alternative method, the extended finite element method (XFEM) is used to handle the local discontinuities in each solution space while the interface between phases is captured implicitly by the level set method. In the course of model building, the following subjects: 1) one-phase density driven flow 2) Stefan problem without convection mechanism in the binary system 3) Stefan problem with ensuing melt flow in pure material, are investigated by coupling each two of the problems mentioned above. The accuracy of the corresponding sub-models is verified by the analytical solutions or those obtained by the conventional methods. Finally, the model by coupling three physics is applied to simulate the freezing/melting of the bath-ledge system under certain scenarios. In the final application, the bath flow is described by Stokes equations and induced either by the density jump between different phases or by the buoyancy forces produced by the temperature or/and compositional gradients. The present model is characterized by the coupling of multiple physics, especially the liquid density and the melting point are dependent on the species concentration. XFEM also exhibits its accuracy and flexibility in dealing with different types of discontinuity based on a fixed mesh

Smoothed particle hydrodynamics for fluid-solid coupling: modelling fixed and mobile boundaries

Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian numerical method which has undergone extensive development in recent years. SPH has properties which make it especially suited to certain problem types with which traditional methods have struggled. This includes fluid-solid coupled problems, which are particularly relevant for the modelling of coastal dynamics - a domain which is becoming increasingly relevant owing to the changing global infrastructure and climate. SPH, however, is a relatively young method, and suffers drawbacks which have been dubbed its grand challenges. The main one of interest for this work, is the handling of boundary conditions within the method. This thesis aims to present a discussion on SPH in the context of modelling boundaries, both fixed and mobile. Improvements were made to the so-called semi-analytical boundary method, solving the mathematical and numerical problems associated with the method, and presenting the work in such a way that it can easily beported to existing SPH models. Further discussions and adjustments were also made to the boundary method, attempting to tackle some of its inconsistencies and render it more viable for typical use cases. Finally, the coupling of the DEM method for modelling mobile boundaries was addressed, with a particular focus on mesoscale modelling of solids at a similar resolution to the fluid domain. This was previously an unviable problem, but with improvements to the solid fraction calculation presented here, this is no longer the case. This presents the opportunity for full range mesoscale modelling in SPH.Open Acces

An Integrated Nonlinear Wind-Waves Model for Offshore Wind Turbines

This thesis presents a numerical model capable of simulating offshore wind turbines exposed to extreme loading conditions. External condition-based extreme responses are reproduced by coupling a fully nonlinear wave kinematic solver with a hydro-aero-elastic simulator. First, a two-dimensional fully nonlinear wave simulator is developed. The transient nonlinear free surface problem is formulated assuming the potential theory and a high-order boundary element method is implemented to discretize Laplace's equation. For temporal evolution a second-order Taylor series expansion is used. The code, after validation with experimental data, is successfully adopted to simulate overturning plunging breakers which give rise to dangerous impact loads when they break against wind turbine substructures. Emphasis is then placed on the random nature of the waves. Indeed, through a domain decomposition technique a global simulation framework embedding the numerical wave simulator into a more general stochastic environment is developed. The proposed model is meant as a contribution to meet the more and more pressing demand for research in the offshore wind energy sector as it permits taking into account dangerous effects on the structural response so as to increase the global structural safety level

Modelling elevations, inundation extent and hazard risk for extreme flood events

Climate change is expected to result in more frequent occurrences of extreme flood events, such as flash flooding and large scale river flooding. Therefore, there is a need for accurate flood risk assessment schemes in areas prone to extreme flooding. This research study investigates what flood risk assessment tools and procedures should be used for flood risk assessment in areas where the emergence of extreme flood events is possible. The first objective was to determine what type of flood inundation models should be used for predicting the flood elevations, velocities and inundation extent for extreme flood events. Therefore, there different flood inundation model structures were used to model a well-documented extreme flood event. The obtained results suggest that it is necessary to incorporate shock-capturing algorithms in the solution procedure when modelling extreme flood events, since these algorithms prevent the formation of spurious oscillations and provide a more realistic simulation of the flood levels. The second objective was to investigate the appropriateness of the “simplification strategy” (i.e. improving simulation results by increasing roughness parameter) when used as a flood risk assessment modelling tool for areas susceptible to extreme flooding. The obtained results suggest that applying such strategies can lead to significantly erroneous predictions of the peak water levels and the inundation extent, and thus to inadequate flood protection design. The third and final objective was to determine what type of flood hazard assessment methods should be used for assessing the flood hazard to people caused by extreme flooding. Therefore, two different flood hazard assessment criteria were modelled for three extreme flood events. The predicted results suggest that in areas prone to extreme flooding, the flood hazard indices should be predicted with physics-based formulae, as these methods consider all of the physical forces acting on a human body in floodwaters, take into account the rapid changes in the flow regime, which often occur for extreme events, and enable a rapid assessment of the degree of flood hazard to be made in a short time period

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Data analysis and data assimilation of Arctic Ocean observations

Thesis (Ph.D.) University of Alaska Fairbanks, 2019Arctic-region observations are sparse and represent only a small portion of the physical state of nature. It is therefore essential to maximize the information content of observations and bservation-conditioned analyses whenever possible, including the quantification of their accuracy. The four largely disparate works presented here emphasize observation analysis and assimilation in the context of the Arctic Ocean (AO). These studies focus on the relationship between observational data/products, numerical models based on physical processes, and the use of such data to constrain and inform those products/models to di_erent ends. The first part comprises Chapters 1 and 2 which revolve around oceanographic observations collected during the International Polar Year (IPY) program of 2007-2009. Chapter 1 validates pan- Arctic satellite-based sea surface temperature and salinity products against these data to establish important estimates of product reliability in terms of bias and bias-adjusted standard errors. It establishes practical regional reliability for these products which are often used in modeling and climatological applications, and provides some guidance for improving them. Chapter 2 constructs a gridded full-depth snapshot of the AO during the IPY to visually outline recent, previouslydocumented AO watermass distribution changes by comparing it to a historical climatology of the latter 20th century derived from private Russian data. It provides an expository review of literature documenting major AO climate changes and augments them with additional changes in freshwater distribution and sea surface height in the Chukchi and Bering Seas. The last two chapters present work focused on the application of data assimilation (DA) methodologies, and constitute the second part of this thesis focused on the synthesis of numerical modeling and observational data. Chapter 3 presents a novel approach to sea ice model trajectory optimization whereby spatially-variable sea ice rheology parameter distributions provide the additional model flexibility needed to assimilate observable components of the sea ice state. The study employs a toy 1D model to demonstrate the practical benefits of the approach and serves as a proof-of-concept to justify the considerable effort needed to extend the approach to 2D. Chapter 4 combines an ice-free model of the Chukchi Sea with a modified ensemble filter to develop a DA system which would be suitable for operational forecasting and monitoring the region in support of oil spill mitigation. The method improves the assimilation of non-Gaussian asynchronous surface current observations beyond the traditional approach.Chapter 1: Sea-surface temperature and salinity product comparison against external in situ data in the Arctic Ocean -- Chapter 2: Changes in Arctic Ocean climate evinced through analysis of IPY 2007-2008 oceanographic observations -- Chapter 3: Toward optimization of rheology in sea ice models through data assimilation -- Chapter 4: Ensemble-transform filtering of HFR & ADCP velocities in the Chukchi Sea -- General conclusion

Integrated 2D-3D free surface hydro-environmental modelling

An integrated horizontally two- and fully three-dimensional numerical model system has been developed based on a combined unstructured and σ-coordinate grid to simulate the flow and water quality process in large water bodies with a focus on the three dimensional behaviours at specific areas. The model is based on the time dependent Reynolds-Averaged Navier-Stokes equations with a non-hydrostatic pressure distribution and a baroclinic force being incorporated in the three dimensional (3D) model. The two sub models interact dynamically during the solution procedure with no time-step restriction due to integration. The main idea is to use a fractional step algorithm for each model and then integrate the two models fraction by fraction. Hybrid 2D-3D finite volume cells have been introduced for the link nodes which are partly in the 2D domain and partly in the 3D domain. Thus an interpolation/averaging procedure at the interface and domain overlapping is no longer needed. The 3D model uses the projection method for pressure calculation. The advection equation is solved by the semi-Lagrangian method. Other components are solved via the finite element - finite volume (FV) method. The water surface is determined implicitly through a global matrix equation created by assembling the domain's matrices. The cell integrals are calculated analytically to eliminate a common source of numerical diffusion due to the use of approximation techniques for the FV integrals. The horizontal gradients of the density and shear stresses are calculated on true horizontal planes, in order to avoid artificial velocity and diffusion in highly stratified flows. Neumann interpolation elements with virtual nodes have been introduced at Neumann type of boundaries for more accuracy. The integrated model has been verified using analytical solutions and benchmark test cases, including the Ekman velocity distribution, wind driven circulation, lock exchange and integrated 2D-3D flows in basin. The results show the model is capable of the model for accurate simulation and implicit 2D-3D integration. Keywords: integrated modelling, hydrodynamic numerical model, non-hydrostatic, unstructured mesh, hybrid finite element finite volume method.EThOS - Electronic Theses Online ServiceGBUnited Kingdo