Dissertations / Theses on the topic 'Mass transfer – Mathematical models'

Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Garimella, Srinivas; Committee Member: Fuller, Tom; Committee Member: Jeter, Sheldon; Committee Member: Lieuwen, Tim; Committee Member: Wepfer, William. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Orientador: Julian Martínez
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos
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Resumo: Este projeto utilizou a tecnologia supercrítica no processo de extração, usando o dióxido de carbono como solvente. Esta tecnologia apresenta-se como uma alternativa para processos que usam solventes orgânicos tóxicos, além de respeitar os princípios da química verde, pautada nos conceitos de desenvolvimento sustentável. Com o objetivo de compreender melhor todos os mecanismos fenomenológicos envolvidos neste processo, bem como poder controlá-los visando à sua otimização, a modelagem matemática é uma opção bastante atrativa. As substâncias capsaicinoides, presente em grandes quantidades em várias espécies de pimenta, responsáveis pela sensação pungente e que, no entanto, possuem comprovadas ações benéficas ao organismo, foram definidas como substâncias alvo. Desta forma, para os estudos dos fenômenos de transferência de massa, três espécies de pimentas, Capsicum frutescens, Capsicum chinense, Capsicum boccatum, foram analisadas quanto aos seus teores de capsaicinoides. A espécie Capsicum frutescens apresentou o maior concentração destas substâncias e foi escolhida como a matéria-prima para etapas posteriores. Um planejamento experimental de extração supercrítica desta espécie de pimenta foi realizado variando a pressão e a temperatura. A partir destas extrações foi observado que a condição de extração de 15MPa e 313 K apresentou a melhor combinação entre rendimento e concentração de capsaicina. Cinéticas de extração realizadas nesta condição, porém variando a vazão de solvente, o diâmetro de partícula e o volume de extração, foram estudadas. Maiores taxas de extração foram obtidas nas maiores vazões e nos menores diâmetros de partícula e volume de leito de extração devido à maior importância do fenômeno convectivo. O modelo de partículas intactas e rompidas de Sovová (1994) foi usado para ajustar os dados experimentais das curvas e obter os parâmetros do modelo. Três tipos de modelagem foram realizadas: ajuste de cada curva individualmente; ajuste simultâneo gerando um conjunto de parâmetros para os pares das duplicatas; ajuste múltiplo que ajustou um valor único do parâmetro XK para cada conjunto de curvas com o mesmo diâmetro de partícula. Com os ajustes foi possível calcular o coeficiente convectivo de transferência de massa de cada condição e o respectivo valor do número de Sherwood experimental. Com os dados experimentais de cada condição foram calculados os números adimensionais de Reynolds e Schimdt. Com estes novos conjuntos de dados de números adimensionais foram realizadas novas modelagens matemáticas e, através destas, propostas novas correlações. Estas novas equações foram baseadas tanto na existência única da convecção forçada quanto na existência, mesmo que pouco significativa, da convecção natural. A eficácia destes novos modelos foi avaliada com a comparação dos coeficientes de transferência de massa convectivos calculados com aqueles ajustados das curvas experimentais, apresentando, em geral, boa similaridade. Por fim, uma extração em escala piloto realizada deu indícios, através dos resultados calculados das novas correlações, que a convecção natural nestas escalas não pode ser desprezada
Abstract: This workt used the supercritical technology in the process of extraction, using carbon dioxide as solvent. This technology is based on concepts of sustainable development and respects the principals of green chemistry. It appears as an alternative to processes that use toxic organic solvents. Mathematical modeling is an interesting tool to understand better all phenomenological mechanisms involved in this process and to be able to control and optimize them. Capsaicinoids, which are responsible for the pungent sensation caused by peppers, have well-known beneficial properties for human organism. These substances are present in large quantities in several pepper species. Capsaicinoids were chosen as target substances for the study of mass transfer phenomena. Capsaicinoid contents were analyzed for three pepper species: Capsicum frutescens, Capsicum chinense, Capsicum boccatum. The species Capsicum frutescens showed higher concentration of these substances and was chosen as raw material for further steps. An experimental design of supercritical extraction from this pepper species was carried out varying pressure and temperature. These extractions showed that the extraction condition of 15 MPa and 313 K gave the best combination of yield and capsaicin concentration. Therefore, extraction kinetics was studied under this condition, varying solvent flow rate, particle diameter and extraction bed volume. The highest extraction rates were obtained for high solvent flow rates, low particle diameters and low extraction bed volume. This can be explained by the greater importance of the convective phenomenon under these conditions. The Sovová¿s model (1994) for intact and broken particles was used to fit experimental data to curves and obtain model parameters. Three types of mathematical modeling were established: (1) fitting of each individual curve, (2) simultaneous fitting creating a set of parameters for pairs of duplicates, (3) multiple fitting that adjsuts a single value for the parameter XK for each set of curves with the same particle diameter. These fits allowed calculating the convective mass transfer coefficient for each condition and the respective values of the experimental Sherwood number. Experimental data was used to calculate dimensionless numbers of Reynolds and Schmidt for of each condition. Other mathematical modelings were performed using these new data sets of dimensionless numbers, which allowed proposing new correlations. These new equations were based on the existence of forced and free convection, even though the importance of the second phenomenon was considered small. The efficiency of these new models was assessed with a comparison of calculated convective mass transfer coefficients to those fitted from experimental curves. A good coherence was found between both. Finally, a pilot scale extraction was performed and the results obtained using the proposed correlations suggested that free convection cannot be neglected at such scales
Mestrado
Engenharia de Alimentos
Mestra em Engenharia de Alimentos

Hollow fibre and spiral wound membrane (SWM) modules are the most common commercially available membrane modules. The latter dominate especially for RO, NF and UF and are the focus of this study. The main difficulty these types of modules face is concentration polarisation. In SWM modules, the spacer meshes that keep the membrane leaves apart also help reduce the effects of concentration polarisation. The spacer filaments act as flow obstructions, and thus encourage flow destabilisation and increase mass transfer enhancement. One of the detrimental aspects of the use of spacers is an increase of pressure losses in SWM modules. This study analyses the mechanisms that give rise to mass transfer enhancement in narrow spacer-filled channels, and investigates the relationship between flow destabilisation, energy losses and mass transfer. It shows that the regions of high mass transfer on the membrane surface correlate mainly with those regions where the fluid flow is towards the membrane. Based on the insights gained from this analysis, a series of multi-layer spacer designs are proposed and evaluated. In this thesis, a Computational Fluid Dynamics (CFD) model was used to simulate steady and unsteady flows with mass transfer in two- and three-dimensional narrow channels containing spacers. A solute with a Schmidt number of 600 dissolving from the wall and channel Reynolds numbers up to 1683 were considered. A fully-developed concentration profile boundary condition was utilised in order to reduce the computational costs of the simulations. Time averaging and Fourier analysis were performed to gain insight into the dynamics of the different flow regimes encountered, ranging from steady flow to vortex shedding behind the spacer filaments. The relationships between 3D flow effects, vortical flow, pressure drop and mass transfer enhancement were explored. Greater mass transfer enhancement was found for the 3D geometries modelled, when compared with 2D geometries, due to wall shear perpendicular to the bulk flow and streamwise vortices. Form drag was identified as the main component of energy loss for the flow conditions analysed. Implications for the design of improved spacer meshes, such as extra layers of spacer filaments to direct the bulk flow towards the membrane walls, and filament profiles to reduce form drag are discussed.

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2006.
Garimella, Srinivas, Committee Chair ; Ghiaasiaan, S. Mostafa, Committee Member ; Graham, Samuel, Committee Member ; Breedveld, Victor, Committee Member ; Fuller,Tom, Committee Member.

Heat actuated adsorption heat pumps offer the opportunity to improve overall energy efficiency in waste heat applications by eliminating shaft work requirements accompanying vapor compression cycles. The coefficient of performance (COP) in adsorption heat pumps is generally low. The objective of this thesis is to model the adsorption system to gain critical insight into how its performance can be improved. Because adsorption heat pumps are intermittent devices, which induce cooling by adsorbing refrigerant in a sorption bed heat/mass exchanger, transient models must be used to predict performance. In this thesis, such models are developed at the adsorbent particle level, heat/mass exchanger component level and system level. Adsorption heat pump modeling is a coupled heat and mass transfer problem. Intra-particle mass transfer resistance and sorption bed heat transfer resistance are shown to be significant, but for very fine particle sizes, inter-particle resistance may also be important. The diameter of the adsorbent particle in a packed bed is optimized to balance inter- and intra-particle resistances and improve sorption rate. In the literature, the linear driving force (LDF) approximation for intra-particle mass transfer is commonly used in place of the Fickian diffusion equation to reduce computation time; however, it is shown that the error in uptake prediction associated with the LDF depends on the working pair, half-cycle time, adsorbent particle radius, and operating temperatures at hand. Different methods for enhancing sorption bed heat/mass transfer have been proposed in the literature including the use of binders, adsorbent compacting, and complex extended surface geometries. To maintain high reliability, the simple, robust annular-finned-tube geometry with packed adsorbent is specified in this work. The effects of tube diameter, fin pitch and fin height on thermal conductance, metal/adsorbent mass ratio and COP are studied. As one might expect, many closely spaced fins, or high fin density, yields high thermal conductance; however, it is found that the increased inert metal mass associated with the high fin density diminishes COP. It is also found that thin adsorbent layers with low effective conduction resistance lead to high thermal conductance. As adsorbent layer thickness decreases, the relative importance of tube-side convective resistance rises, so mini-channel sized tubes are used. After selecting the proper tube geometry, an overall thermal conductance is calculated for use in a lumped-parameter sorption bed simulation. To evaluate the accuracy of the lumped-parameter approach, a distributed parameter sorption bed simulation is developed for comparison. Using the finite difference method, the distributed parameter model is used to track temperature and refrigerant distributions in the finned tube and adsorbent layer. The distributed-parameter tube model is shown to be in agreement with the lumped-parameter model, thus independently verifying the overall UA calculation and the lumped-parameter sorption bed model. After evaluating the accuracy of the lumped-parameter model, it is used to develop a system-level heat pump simulation. This simulation is used to investigate a non-recuperative two-bed heat pump containing activated carbon fiber-ethanol and silica gel-water working pairs. The two-bed configuration is investigated because it yields a desirable compromise between the number of components (heat exchangers, pumps, valves, etc.) and steady cooling rate. For non-recuperative two-bed adsorption heat pumps, the average COP prediction in the literature is 0.39 for experiments and 0.44 for models. It is important to improve the COP in mobile waste heat applications because without high COP, the available waste heat during startup or idle may be insufficient to deliver the desired cooling duty. In this thesis, a COP of 0.53 is predicted for the non-recuperative, silica gel-water chiller. If thermal energy recovery is incorporated into the cycle, a COP as high as 0.64 is predicted for a 90, 35 and 7.0°C source, ambient and average evaporator temperature, respectively. The improvement in COP over heat pumps appearing in the literature is attributed to the adsorbent particle size optimization and careful selection of sorption bed heat exchanger geometry.

Continental and submarine hydrothermal systems are commonly found around the world. Similar systems that sustain water or other fluids are also likely to exist in planetary bodies throughout the solar system. Also, terrestrial submarine systems have been suggested as the locations of the first life on Earth and may, therefore, provide indications of where to find life on other planetary bodies. The study of these systems is vital to the understanding of planetary heat transfer, chemical cycling, and biological processes; hence hydrothermal processes play a fundamental role in planetary evolution. In this thesis, three particular types of hydrothermal systems are investigated through the development of mathematical models: (1) terrestrial low-temperature diffuse flows at mid-oceanic ridges (MORs), (2) submarine near-axis convection on Earth, and (3) convection driven by magmatic intrusives on Mars. Model set-ups for all systems include a two-dimensional space with a vertical, hot wall, maintained at constant temperature, located adjacent to a water-saturated porous medium at a lower temperature. By assuming that convection occurs vigorously and within a thin layer next to the hot wall, boundary layer theory is applicable. The models provide steady-state, single-phase estimates of the total heat and mass transfer rates in each scenario over permeability ranges of 10^-14 m² to 10^-10 m² for the submarine systems and 10^-14 m² to 10^-8 m² for the Martian systems. Heat output results derived from the boundary layer model suggest that diffuse flow on MORs contributes 50% or less of heat output to the ridge system, which falls at the low end of observations. For the near-axis model, results found that heat transfer in the hydrothermal boundary layer was greater than the input from steady state generation of the oceanic crust by seafloor spreading. This suggests that the size of the mushy zone evolves with time. Heat output and fluid flux calculations for Martian systems show that fluid outflow adjacent to a single intrusion is too small to generate observed Martian surface features in a reasonable length of time.

On envisage deux types de configuration du systeme de sechage suivant la nature du generateur d'air chaud. Dans la premiere configuration, le sechoir est ventile par de l'air chaud sortant d'un capteur solaire du type multi-masse. La seconde configuration utilise un rechauffeur d'air constitue de resistances electriques. Pour chaque sous-systeme de la chaine, on propose une modelisation fine et originale; une etude systematique de l'etat thermique, massique et des performances du systeme de captation multi-passes et du systeme de sechage en fonction des parametres externes et internes est realisee. On envisage aussi l'effet d'un recyclage de l'air sur le comportement dynamique du systeme de sechage. Enfin, une conformation entre les resultats experimentaux obtenus sur un prototype construit et teste en laboratoire avec des resistances electriques permet une validation du modele theorique propose pour le sechage d'un lit epais des feves de cacao

La determination de l'evolution de l'etat hygrothermique d'un toit experimental de tuiles de terre cuite durant son sechage est effectuee a partir du modele mathematique de luikov et des equations des conditions aux limites de type fourier. On determine les coefficients thermophysiques et de transfert de masse de la terre cuite. Les coefficients de transferts de chaleur et de masse, dus a la convection en surface et en sous-face de la couverture, sont etudies en fonction des donnees meteorologiques. La resolution numerique du probleme de sechage suppose unidimensionnel est effectuee par une methode de differences finies

CAPES
Na indústria do petróleo existe um grande interesse no entendimento dos fenômenos de formação de hidratos já que eles podem danificar a tubulação, colocar vidas em risco e diminuir a produção de óleo e gás pelo bloqueio da linha. Ou seja, conhecer os fenômenos associados à formação de hidratos reflete diretamente no custo operacional da indústria petrolífera. Diversos grupos de pesquisa já propuseram diferentes modelos para predizer o crescimento de hidratos na interface líquido-gás e na parede das tubulações de produção de petróleo em águas profundas. Entretanto, os modelos baseados unicamente na transferência de calor não foram adequados para explicar os dados experimentais pois os consumos de água e gás não eram considerados. Assim, esta dissertação tem como objetivo desenvolver um modelo, matemático e numérico, que permita prever o crescimento dos hidratos de metano e de dióxido de carbono na parede da tubulação por meio das equações de conservação de massa e energia de forma acoplada. Como nenhuma solução analítica é possível, foi utilizado o método numérico dos volumes finitos com o esquema totalmente implícito. A verificação da implementação computacional foi realizada utilizando um modelo de dissociação de hidratos existente na literatura. A partir dos resultados numéricos, foi avaliado como as condições termodinâmicas, a porosidade e a condutividade térmica do hidrato, o diâmetro da tubulação e a disponibilidade de gás influenciam na taxa de crescimento de hidrato. Como principais resultados, verificou-se que a porosidade e a disponibilidade de gás representaram grande importância no cálculo da taxa de crescimento da camada de hidrato.
The study of the clathrate-hydrate formation processes in pipelines is very important to the oil and gas industry because these structures can stop production and it represents a safety risk due to the pressure build-up in the pipelines. Several research groups have proposed different models to predict how a hydrate film grows. However, the models based only on heat transfer could not explain satisfactorily the experimental data because the water and gas consumption were disregarded. So, in order to predict the hydrate growth phenomenon in tube wall, the current work presents a mathematical and numerical model for the coupled mass and energy balance problem for CO2 and CH4 hydrates. As a result of the coupling equations, no analytical solution is possible. So, a computational algorithm has been proposed based on the finite volume method and fully implicit scheme. The verification of the code was conducted through a dissociation model which has been presented by the literature. Although, its validation was not possible since no experimental data is currently available. The hydrate growth rate was evaluated by studying the influence of the thermodynamic conditions, the hydrate porosity and thermal conductivity, the pipe diameter and the gas availability. As a result, it has been noticed that the hydrate porosity and the gas availability had great influence in the hydrate growth rate.

Cette thèse porte sur le développement d’une approche pratique de modélisation/simulation des systèmes solaires combinés Photovoltaïques/Thermiques PV/T. Il s’agit d’une approche basée sur un modèle d’ordre réduit en représentation d’état (ORRE). En effet, les systèmes solaires thermiques, électriques et combinés intégrés aux bâtiments possèdent des spécificités permettant de s’affranchir des méthodes numériques classiques (mécanique des fluides numérique et thermique numérique). Ces méthodes sont réputées dans le domaine de l’aérodynamique, de l’aéraulique…etc. Par contre, dans le domaine du mix-énergétique tels que celui considéré dans ce mémoire, l’application directe de ce modèle peut conduire à des dépassements des capacités mémoire ou des temps de calcul exorbitants. Une alternative est de développer des méthodes adaptées au problème physique considéré, en traitant l’aspect multi-physique toute en restant dans une taille de données raisonnable et du temps de calcul réduit. La méthodologie de modélisation consiste à réduire les dimensions des équations qui régissent le problème. En se basant sur la symétrie du système, puis en découpant le système en zones de contrôle basées sur une valeur moyenne gouvernée par les nombres adimensionnels de Biot (Bi) et de Fourier (Fo). Les résultats obtenus en fonctionnement dynamique pourront nous fournir des paramètres de sorties, plus particulièrement, les rendements électrique, thermique et la puissance de circulation du fluide caloporteur. L’avantage de l’approche proposée réside dans la simplification du modèle résultant, qui est représenté par un seul système d’équations algébriques en représentation d’état regroupant tous les éléments physiques du système en fonctionnement dynamique (conditions aux limites variables dans le temps). Ce modèle regroupe la variable fondamentale qui est la température, et les deux types de contrôle et de conception. De plus, le modèle d’ORRE est intégrable dans le fonctionnement en temps réel des systèmes PV/T intégrés aux bâtiments (PV/T-Bât) afin d’accompagner leurs régulation et gestion des flux mise en jeu. Le modèle ainsi proposé a fait l’objet d’une validation où les résultats numériques ont été comparés aux résultats expérimentaux. En effet, quatre configurations ont été étudiées et évoquées dans une approche linéaire. Les résultats obtenus montrent une cohérence tolérable entre les résultats expérimentaux, et numériques. Cette cohérence a été évaluée en termes d’incertitude entre les résultats du modèle et le cas étudié expérimentalement. Le cas d’un système non-linéaire a été également abordé. En effet, rares sont les travaux qui ont été publiés mettant en valeur les phénomènes non-linéaires dans les systèmes complexes PV/T-Bât, Ainsi, on a développé avec la même stratégie, des modèles bilinéaires qui modélise le mieux possible le comportement thermique dans les systèmes PV/T-Bât. Une étude d’optimisation du système multi-physique en introduisant une étude paramétrique est menée en terme afin d’étudier la sensibilité des paramètres sur le rendement énergétique. Cependant, les études d’optimisation paramétriques restent limitées et insuffisantes à cause de la résolution mono-objectif du problème d’optimisation, alors que notre système manifeste un comportement combiné et multi-physique de nature contradictoire. Pour ce faire, une optimisation multi-objectifs est introduite avec trois fonctions objectif en employant l’algorithme génétique NSGA-II. L’originalité de notre méthode est d’employer l’algorithme en régime dynamique afin de choisir la conception du système la plus optimale. Les résultats trouvés peuvent contribuer à améliorer la conception des systèmes PV/T-Bât et l’optimisation de leur fonctionnement
This thesis consists to develop a simplified model approach for Photovoltaic / Thermal (PV / T) combined solar system based on state-space reduced order model. The building integrated solar systems are getting high attention in these last decencies, as well as the performance increasing which require high numerical methods to improve the design and reducing the costs. In one hand, the CFD methods are useful tool to predict the energy (mechanical and thermal) of combined PV/T systems, but it requires an expensive computing capacities and exorbitant calculation times, On the other hand, the PV/T systems can generate both the electrical and thermal flows, and requires an easily and performant optimization model. An alternative is to develop methods that are adapted to the physical problem under consideration, treating the multi-physics aspect while remaining in a reasonable data size and reduced computing time. The first part of the current thesis consists to develop a mathematical model which consists of reducing the dimensions of the governed equations. Based on the symmetry of the geometry, the system is subdivided into control areas which governed by the dimensionless Biot (Bi) and Fourier (Fo) numbers. The obtained results in dynamic mode can provide output key parameters, more particularly the electrical and thermal efficiencies and the dissipated hydrodynamic power. The advantage of this approach lies in the simplification of the resulting model, which is represented by a single state-space representation that groups all the physical elements of the system into dynamic mode, i.e. in continuous variation of the boundary condition. This model groups the fundamental variable, which is the temperature, and two type parameters, which are the control parameters and the design parameters. In addition, the reduced order model can be integrated into real-time operation of building-integrated PV / T (BIPV/T) systems in order to support their regulation and management of intervening flows. In order to validate the use of our model, it is necessary to test it for several cases of Building Integrated PV/T systems (BIPV/T). For this, four major configurations were studied and discussed in a linear approach; the found results show a good agreement with experimental works. A second level has been developed as part of our thesis work, which is the non-linearity in combined PV / T and BIPV/T systems; in particular, bilinear models have been developed with the same strategy which best models the thermal behavior in BIPV/T systems. The second issue, related to Multi-physics aspect. Furthermore, in order to evaluate the sensitivity of the parameters, a parametric optimization has been made with dimensionless numbers. However, parametric optimization studies remain limited and insufficient because of the single-objective resolution of the optimization problem, whereas our system manifests a mixed and multi-physics behavior with contradictory nature. To do this, a multi-objective optimization is introduced with three objective functions using the NSGA-II genetic algorithm. The originality of our method is to use the algorithm in dynamic mode in order to choose the design of the optimal system. The found results can contribute to the design of BIPV/T systems and optimize their operation

Forster theory of energy transfer is applied in diluted systems, and yet it remains unknown if it can be applied to the dense media. We have studied the exciton transfer in one-dimensional (1-D) close-packed pure and mixed quantum dot (QD) array under different models and two-dimensional (2-D) perfect lattice. Our approach is based on the master equation created by treating the exciton relaxation as a stochastic process. The random parameter has been used to describe dot-to-dot distance variations. The master equation has been investigated analytically for 1-D and 2-D perfect lattices and numerically for 1-D disordered systems. The suitability of Forster decay law on the excitation decay of close-packed solid has been discussed. The necessity to consider the effect of the further nearest interdot interactions has been checked.
Department of Physics and Astronomy

Following melt alloying and chlorine fluxing in reverberatory-like aluminum holding furnaces, it is common practice to allow the melt to settle for about an hour prior to casting operations. The purpose of this procedure is to allow inclusions to settle to the surface bottom or to float out to an overlying layer of dross. Mathematical modelling of this process reveals that significant natural convection currents are generated, particularly during the early part of this holding period, and that as these currents gradually diminish, so does the rate of precipitation of inclusions. A 6.25 ton pilot scale holding furnace was used to test the model's predictions of changes in metal quality with holding time. Satisfactory agreement was observed between predicted and "LiMCA"$ sp1$ measured changes in inclusion density levels of (Ti-V)B$ sb2$. Both approaches revealed exponential-like decays in inclusion density levels, with time constants in order of 10 to 60 minutes. ftn$ sp1$LiMCA--Liquid Metal Cleanliness Analyzer

Proposition d'un modele et d'un code de calcul pour suivre l'evolution longitudinale de la concentration en matiere organique dissoute dans une galerie d'evacuation au rhone des effluents des stations d'epuration de chambery et d'aix-les bains, la pollution organique etant consommee par un film biologique fixe sur les parois du canal

Model order reduction (MOR) is one of the general techniques in the fields of computeraided design (CAD) and electronic design automation (EDA) which accelerates the flow of electronic simulations and verifications. By MOR, the original circuit, which is described by a set of ordinary differential equations (ODEs), can be trimmed into a much smaller reduced-order model (ROM) in terms of the number of state variables, with approximately the same input-output (I/O) characteristics. Hence, simulations using this ROM will be much more efficient and effective than using the original system. In this thesis, a novel and fast approach of computing the projection matrices serving high-order Volterra transfer functions in the context of weakly and strongly nonlinear MOR is proposed. The innovation is to carry out an association of multivariate Laplace-domain variables in high-order multiple-input multiple-output (MIMO) transfer functions to generate univariate single-s transfer functions. In contrast to conventional projection-based nonlinear MOR which finds projection subspaces about every si in multivariate transfer functions, only that about a single s is required in the proposed approach. This translates into much more compact nonlinear ROMs without compromising accuracy. Different algorithms and their extensions are devised in this thesis. Extensive numerical examples are given to prove and verify the algorithms.
published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy

The analytical solution to a model time-dependent continuous lethargy photon transport equation is evaluated numerically to obtain a benchmark solution using the Laplace transforms coupled with the multiple collision expansion method. The benchmark solution is then used to check the accuracy of the multigroup approximation. Excellent agreement between continuous lethargy benchmarks and multigroup approximation is obtained.

Monte Carlo radiation transfer provides an efficient modelling tool for probing the dusty local environment of young stars. Within this thesis, such theoretical models are used to study the disk structure of objects across the mass spectrum - young low mass Brown Dwarfs, solar mass T-Tauri stars, intermediate mass Herbig Ae stars, and candidate B-stars with massive disks. A Monte Carlo radiation transfer code is used to model images and photometric data in the UV - mm wavelength range. These models demonstrate how modelling techniques have been updated in an attempt to reduce the number of unknown parameters and extend the diversity of objects that can be studied.

Le bicarbonate de soude raffiné, produit industriellement par la société Solvay, est fabriqué dans des colonnes à bulles de grande taille, appelées les colonnes BIR.

Dans ces colonnes, une phase gazeuse contenant un mélange d’air et dioxyde de carbone (CO2) est dispersée sous forme de bulles dans une solution aqueuse de carbonate et de bicarbonate de sodium (respectivement Na2CO3 et NaHCO3). Cette dispersion donne lieu à un transfert de CO2 des bulles vers la phase liquide. Au sein des colonnes, la phase gazeuse se répartit dans deux populations de bulles :des petites bulles (diamètre de quelques mm) et des grandes bulles (diamètre de quelques cm). Le transfert bulle-liquide de CO2 est couplé à des réactions chimiques prenant place en phase liquide, qui conduisent à la conversion du Na2CO3 en NaHCO3. Une fois la concentration de saturation dépassée le NaHCO3 précipite sous forme de cristaux et un mélange liquide-solide est recueilli à la sortie de ces colonnes.

Ce travail, réalisé en collaboration avec la société Solvay, porte sur l’étude et la modélisation mathématique des phénomènes de transfert de matière entre phases, couplés à des réactions chimiques, prenant place au sein d’une colonne BIR. L’association d’études sur des colonnes à bulles à l’échelle industrielle ou réduite (pilote) et d’études plus fondamentales sur des dispositifs de laboratoire permet de développer une meilleure compréhension du fonctionnement des colonnes BIR et d’en construire un modèle mathématique détaillé.

L’objectif appliqué de ce travail est la mise au point d’un modèle mathématique complet et opérationnel d’une colonne BIR. Cet objectif est supporté par trois blocs de travail, dans lesquels différents outils sont développés et exploités.

Le premier bloc est consacré à la modélisation mathématique du transfert bulle-liquide de CO2 dans une solution aqueuse de NaHCO3 et de Na2CO3. Ce transfert est couplé à des réactions chimiques en phase liquide qui influencent sa vitesse. Dans un premier temps, des modèles sont développés selon des approches unidimensionnelles classiquement rencontrées dans la littérature. Ces approches passent par une idéalisation de l’écoulement du liquide autour des bulles. Une expression simplifiée de la vitesse du transfert bulle-liquide de CO2, est également développée et validée pour le modèle de colonne BIR.

Dans un second temps, une modélisation complète des phénomènes de transport (convection et diffusion), couplés à des réactions chimiques, est réalisée en suivant une approche bidimensionnelle axisymétrique. L’influence de la vitesse de réactions sur la vitesse de transfert est étudiée et les résultats des deux approches sont également comparés.

Le deuxième bloc est consacré à l’étude expérimentale du transfert gaz-liquide de CO2 dans des solutions aqueuses de NaHCO3 et de Na2CO3. A cette fin, un dispositif expérimental est développé et présenté. Du CO2 est mis en contact avec des solutions aqueuses de NaHCO3 et de Na2CO3 dans une cellule transparente. Les phénomènes provoqués en phase liquide par le transfert de CO2 sont observés à l’aide d’un interféromètre de Mach-Zehnder.

Les résultats expérimentaux sont comparés à des résultats de simulation obtenus avec un des modèles unidimensionnels développés dans le premier bloc. De cette comparaison, il apparaît qu’une mauvaise estimation de la valeur de certains paramètres physico-chimiques apparaissant dans les équations de ce modèle conduit à des écarts significatifs entre les grandeurs observées expérimentalement et les grandeurs estimées par simulation des équations du modèle.

C’est pourquoi une méthode d’estimation paramétrique est également développée afin d’identifier les valeurs numériques de ces paramètres physico-chimiques sur base des résultats expérimentaux. Ces dernières sont également discutées.

Dans le troisième bloc, nous apportons une contribution à l’étude des cinétiques de précipitation du NaHCO3 dans un cristallisoir à cuve agitée. Cette partie du travail est réalisée en collaboration avec Vanessa Gutierrez (du service Matières et Matériaux de l’ULB).

Nous contribuons à cette étude par le développement de trois outils :une table de calcul Excel permettant de synthétiser les résultats expérimentaux, un ensemble de simulations de l’écoulement au sein du cristallisoir par mécanique des fluides numérique et une nouvelle méthode d’extraction des cinétiques de précipitation du NaHCO3 à partir des résultats expérimentaux. Ces trois outils sont également utilisés de façon combinée pour estimer les influences de la fraction massique de solide et de l’agitation sur la cinétique de germination secondaire du NaHCO3.

Enfin, la synthèse de l’ensemble des résultats de ces études est réalisée. Le résultat final est le développement d’un modèle mathématique complet et opérationnel des colonnes BIR. Ce modèle est développé en suivant l’approche de modélisation en compartiments, développée au cours du travail de Benoît Haut. Ce modèle synthétise les trois blocs d’études réalisées dans ce travail, ainsi que les travaux d’Aurélie Larcy (du service Transferts, Interfaces et Procédés de l’ULB) et de Vanessa Gutierrez. Les équations modélisant les différents phénomènes sont présentées, ainsi que la méthode utilisée pour résoudre ces équations. Des simulations des équations du modèle sont réalisées et discutées. Les résultats de simulation sont également comparés à des mesures effectuées sur une colonne BIR. Un accord raisonnable est observé.

A l’issue de ce travail, nous disposons donc d’un modèle opérationnel de colonne BIR. Bien que ce modèle doive encore être optimisé et validé, il peut déjà être utilisé pour étudier l’effet des caractéristiques géométriques des colonnes BIR et des conditions appliquées à ces colonnes sur le comportement des simulations des équations du modèle et pour identifier des tendances.

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The refined sodium bicarbonate is produced by the Solvay company using large size bubble columns, called the BIR columns.

In these columns, a gaseous phase containing an air-carbon dioxyde mixture (CO2) is dispersed under the form of bubbles in an aqueous solution of sodium carbonate and sodium bicarbonate (Na2CO3 and NaHCO3, respectively). This dispersion leads to a CO2 transfer from the bubbles to the liquid phase. Inside these columns, the gaseous phase is distributed in two bubbles populations :small bubbles (a few mm of diameter) and large bubbles (a few cm of diameter).

The bubble-liquid CO2 transfer is coupled with chemical reactions taking places in the liquid phase that leads to the conversion of Na2CO3 to NaHCO3. When the solution is supersaturated in NaHCO3, the NaHCO3 precipitates under the form of crystals and a liquid-solid mixture is extracted at the outlet of the BIR columns.

This work, realized in collaboration with Solvay, aims to study and to model mathematically the mass transport phenomena between the phases, coupled with chemical reactions, taking places inside a BIR column. Study of bubble columns at the industrial and the pilot scale is combined to a more fundamental study at laboratory scale to improve the understanding of the BIR columns functioning and to develop a detailed mathematical modeling.

The applied objective of this work is to develop a complete and operational mathematical modeling of a BIR column. This objective is supported by three blocks of work. In each block, several tools are developed and used.

The first block is devoted to the mathematical modeling of the bubble-liquid CO2 transfer in an NaHCO3 and Na2CO3 aqueous solution. This transfer is coupled with chemical reactions in liquid phase, which affect the transfer rate.

In a first time, mathematical models are developed following the classical one-dimensional approaches of the literature. These approaches idealize the liquid flow around the bubbles. A simplified expression of the bubble-liquid CO2 transfer rate is equally developed and validated for the BIR column model.

In a second time, a complete modeling of the transport phenomena (convection and diffusion) coupled with chemical reactions is developed, following an axisymmetrical twodimensional approach. The chemical reaction rate influence on the bubble-liquid transfer rate is studied and the results of the two approaches are then compared.

The second block is devoted to the experimental study of the gas-liquid CO2 transfer to NaHCO3 and Na2CO3 aqueous solutions. An experimental set-up is developed and presented. CO2 is put in contact with NaHCO3 and Na2CO3 aqueous solutions in a transparent cell. The phenomena induced in liquid phase by the CO2 transfer are observed using a Mach-Zehnder interferometer.

The experimental results are compared to simulation results that are obtained using one of the one-dimensional model developed in the first block. From this comparison, it appears that a wrong estimation of some physico-chemical parameter values leads to significative differences between the experimentally observed quantities and those estimated by simulation of the model equations. Therefore, a parametric estimation method is developed in order to estimate those parameters numerical values from the experimental results. The found values are then discussed.

In the third block is presented a contribution to the NaHCO3 precipitation kinetic study in a stirred-tank crystallizer. This part of the work is realized in collaboration with Vanessa Gutierrez (Chemicals and Materials Department of ULB).

Three tools are developed :tables in Excel sheet to synthetize the experimental results, a set of simulations of the flow inside the crystallizer by Computational Fluid Dynamic (CFD) and a new method to extract the NaHCO3 precipitation kinetics from the experimental measurements. These three tools are combined to estimate the influences of the solid mass fraction and the flow on the NaHCO3 secondary nucleation rate.

Finally, the synthesis of all these results is realized. The final result is the development of a complete and operational mathematical model of BIR columns. This model is developed following the compartmental modeling approach, developed in the PhD thesis of Benoît Haut. This model synthetizes the three block of study realized in this work and the studies of Aurélie Larcy (Transfers, Interfaces and Processes Department of ULB) and those of Vanessa Gutierrez. The equations modeling the phenomena taking place in a BIR column are presented as the used method to solve these equations. The equations of the model are simulated and the results are discussed. The results are equally compared to experimental measurement realized on a BIR column. A reasonable agreement is observed.

At the end of this work, an operational model of a BIR column is thus developed. Although this model have to be optimized and validated, it can already be used to study the influences of the geometrical characteristics of the BIR columns and of the conditions applied to these columns on the behaviour of the model equation simulations and to identity tendencies.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

There is a growing recognition in design professions that lighting is a significant factor in energy consideration. This has generated an interest in daylighting; the bringing of direct and diffuse daylight into buildings to reduce the use of artificial lighting. Many methods exist for quantifying diffuse daylight distribution for use in the design of buildings, but the methods vary widely both in technique and capability. Moreover, no present method deals with direct daylight (sunshine) distribution. Additionally, none have taken advantage of improvements in computer technology that make feasible more complex mathematical computational models for dealing with direct and diffuse daylight together. This dissertation describes the theoretical development and computer implementation of a new mathematical approach to analyzing the distribution of direct and diffuse daylight. This approach examines light transfer from extraterrestrial space to the inside of a room based on the principles of astrometry, solid geometry, and radiation transfer. This study discusses and analyzes certain aspects critical to develop a mathematical model for evaluating daylight performance and compares the results of the proposed model with 48 scale model studies to determine the validity of using this mathematical model to predict the daylight distribution of a room. Subsequent analysis revealed no significant variation between scale model studies and this computer simulation. Consequently, this mathematical model with the attendant computer program, has demonstrated the ability to predict direct and diffuse daylight distribution. Thus, this approach does indeed have the potential for allowing designers to predict the effect of daylight performance in the schematic design stage. A microcomputer program has been developed to calculate the diffuse daylight distribution. The computation procedures of the program use the proposed mathematical model method. The program was developed with a menu-driven format, where the input data can be easily chosen, stored, and changed to determine the effects of different parameters. Results can be obtained through two formats. One data format provides complete material for analyzing the aperture size and location, glass transmission, reflectance factors, and room orientation. The other provides the graphic displays which represent the illuminance in plan, section, and 3-dimensional contour. The program not only offers a design tool for determining the effects of various daylighting options quickly and accurately in the early design stage, but also presents the daylight distribution with less explanation and with more rapid communication with the clients. The program is written in BASICA language and can be used with the IBM microcomputer system.
Ph. D.

Dissertation (PhD)--University of Stellenbosch, 2000.
ENGLISH ABSTRACT: A mathematical model is presented which conceptualises fluid flow and heat transfer in cellular metallic foams completely saturated with a fluid in motion. The model consists of a set of elliptic partial differential governing equations describing, firstly, a momentum balance in the fluid by the spatial distribution of its locally mean velocity, and secondly, an energy balance in the fluid and in the solid matrix of the metallic foam, by the spatial and temporal distribution of their locally mean temperatures. The separate energy balance descriptions for the fluid and the solid matrix extend the application of the model to conditions of thermal equilibrium and thermal non-equilibrium between the fluid and the solid matrix. A computational solution algorithm is presented which allows the universal application of the model to porous domains of arbitrary shape, with spatially and temporally variable heat loads in a variety of forms.
AFRIKAANSE OPSOMMING: 'n Wiskundige model word voorgestel wat vloei en warmteoordrag voorspel in sellulêre metaalsponse wat in geheel gevul is deur 'n bewegende vloeier. Die vloeier kan in gasof vloeistoffase verkeer. Die model bestaan uit 'n stel elliptiese parsiële differensiaalvergelykings wat in die eerste plek 'n momentum-ewewig in die vloeier beskryf in terme van 'n ruimtelike, lokaal-gemiddelde snelheidsveld, en wat tweedens 'n energie-ewewig in die vloeier en in die soliede matriks van die metaalspons beskryf in terme van ruimtelike en tydelike lokaal-gemiddelde temperatuur verspreidings. Die aparte energie-ewewig beskrywings vir die vloeier en vir die soliede matriks van die metaalspons brei die aanwending van die model uit na gevalle waar die vloeier en die soliede matriks in termiese ewewig of in termiese onewewig verkeer. 'n Numeriese oplossingsalgoritme word ook voorgestel vir die universele toepassing van die model op ruimtelik-arbitrêre metaalspons geometrië wat onderwerp word aan 'n aantal verskillende ruimtelik-en tydveranderlike termiese laste.

L'agent actif considéré a été l'éthoprophos, principe nématicide utilisé en agrochimie, mais dans un premier temps, l'aniline a été utilisé comme agent simulant. Les processus d'absorption et de désorption dans l'eau, ont été modélisés, dans le cas d'un granulé composé d'EVA pur, à l'aide d'une solution analytique de l'équation de Fick. Un modèle mathématique basé sur une méthode numérique a été construit pour décrire les transferts à travers un granulé composé par un noyau et une enveloppe

Bibliography: leaves 100-106. Studies different models of "quintessence", in particular, a quintessence arising from an ultra-light pseudo Nambu-Goldstone boson. Overviews dynamical properties for these models using phase-space analyses to study attractor and tracker solutions. Studies high-redshift type Ia supernovae constraints on these models. Studies the impact of a simple phenomenological model for supernovae luminosity evolution on the PNGB models and the potentials of a future supernovae data set to discriminate the PNGB models over the other quintessence models. Studies gravitational lensing statistics of high luminosity quasars upon the quintessence models.

Fossil fuel is an important energy source, but is unavoidabiy running out. Since the cellulosic material is the most abundant source of organic matter, the ethanol, which is produced from cellulosic waste materials, is gaining more and more attention. These materials are cheap, renewable and their availability makes them superior compared to other raw materials. The cellulose must be hydrolyzed to glucose before it can be fermented to ethanol. The enzymatic hydrolysis of cellulose using cellulase enzymes is the most widely used method. The production cost of cellulase enzymes is the major cost in ethanol manufacture. To optimize the cost of ethanol production, enzyme stability needs to be improved through maintaining the activity of the enzymes and by optimizing the production of the cellulase. The aim of researchers, engineers and industrials is to get more biomass for the same cost. The filamentous fungus Trichoderma reesei has a long history in the production of the cellulase enzymes. This production can be influenced strongly by varying the growth media and culture conditions (pH, temperature, DO, agitation,... ). At present, it is my opinion that no modelling study has included both the hydrodynamic and kinetic aspects to investigate the effect of shear and mass transfer on the morphology of microorganisms that influence the rheology of the broth and production of cellulase. This thesis presents the development of a mathematical model for cellulase production and the growth of biomass in an airlift bioreactor. The kinetic model is coupled with the methodology of two-phase flow using mathematical models based on the bubble break-up and coalescence to predict mass transfer rate, which is one of the critical factor in the fermentation. A comparison between the results obtained by the developed model and the experimental data is given and discussed. The design proposed for the airlift geometry by Ahamed and Vermette enables us to get a high mass transfer and production rate. The results are very promising with respect to the potential of such a model for industrial use as a prediction tool, and even for design.

Hawking radiation, despite its presence in theoretical physics for over thirty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to systems which model the spacetime geometry of black holes, and which, by analogy, are also thought to emit Hawking radiation. These analogue systems typically exhibit dispersion, which regularizes the wave behaviour at the horizon but does not lend itself well to analytic treatment, thus rendering Hawking’s prediction less secure. A general analytic method for dealing with Hawking radiation in dispersive systems has proved difficult to find. This thesis presents new numerical and analytic results for Hawking emission spectra in dispersive systems. It examines two black-hole analogue systems: it begins by introducing the well-known acoustic model, presenting some original results in that context; then, through analogy with the acoustic model, goes on to develop the lesser-known fibre-optical model. The following original results are presented in the context of both of these models: • an analytic expression for the low-frequency temperature is found for a hyperbolic tangent background profile, valid in the entire parameter space; it is well-known that the spectrum is approximately thermal at low frequencies, but a universally valid expression for the corresponding temperature is an original development; • an analytic expression for the spectrum, valid over almost the entire frequency range, when the velocity profile parameters lie in the regime where the low-frequency temperature is given by the Hawking prediction; previous work has focused on the low-frequency thermal spectrum and the characterization of the deviations from thermality, rather than a single analytic expression; and • a new unexplored regime where no group-velocity horizon exists is examined; the Hawking spectra are found to be non-zero here, but also highly non-thermal, and are found, in the limit of small deviations, to vary with the square of the maximum deviation; the analytic expression for the case with a horizon is found to carry over to this new regime, with appropriate modifications. Furthermore, the thesis examines the results of a classical frequency-shifting experiment in the context of fibre-optical horizons. The theory of this process is presented for both a constant-velocity and a constantly-decelerating pulse, the latter case taking account of the Raman effect. The resulting spectra are at least qualititively explained, but there is a discrepancy between theory and experiment that has not yet been accounted for.

Forced convection cooling process is the most widely used method of cooling to extend shelf life of horticultural produce after harvest. However, heterogeneous cooling of produce inside different parts of ventilated packages is a serious problem. Therefore, it is essential to design packages that facilitate air circulation throughout the entire package to provide uniform cooling. Selection of appropriate combinations of air temperature and velocity for a given vent design is currently done largely by experimental trial and error approach. A more logical approach in designing new packages, to provide uniform cooling, is to develop mathematical models that would be able to predict package performance without requiring costly experiments.
In this study, mathematical models of simultaneous airflow, heat and mass transfer during forced convection cooling process were developed and validated with experimental data. The study showed that produce cooling is strongly influenced by different ventilated package designs. Generally, cooling uniformity was increased by increasing number of vents from 1 (2.4% vent area) to 5 (12.1% vent area). More uniform produce cooling was obtained at less cooling time when vents were uniformly distributed on package walls with at least 4.8% opening areas. Aerodynamic studies showed that heterogeneity of airflow distribution during the process is strongly influenced by different package vent configurations. The highest cooling heterogeneity index (108%) was recorded at 2.4% vent area whereas lowest heterogeneity index (0%) was detected in a package with 12.1% vent area.
The magnitudes of produce evaporative cooling (EC) and heat generation by respiration (HG) as well as the interactive effects of EC, HG and package vent design on produce cooling time were also investigated. Considerable differences in cooling times were obtained with regard to independent and simultaneous effects of EC and HG in different package vent configurations. Cooling time was increased to about 47% in a package with 1 vent compared to packages with 3 and 5 vents considering simultaneous effects of EC and HG. Therefore, the effects of EC and HG can be influential in designing the forced-air precooling system and consequently, in the accurate determination of cooling time and the corresponding refrigeration load.

Atherogenesis is the leading cause of death in the developed world, and is putting considerable monetary pressure on health systems the world over. Although the risk factors are well understood, unfortunately, the initiation and development of this disease still remains relatively poorly understood, but it is becoming increasingly identifiable as a dysfunction of the endothelial cells that line the walls of arteries. The prevailing haemodynamic environment plays an important role in the focal nature of atherosclerosis to very specific regions of the human vasculature. Disturbed haemodynamics lead to very low wall shear stress, and inhibit the transport of important blood borne chemicals. The present study models, both computationally and mathematically, the transport and hydrolysis of important blood borne adneosine nucleotides in physiologically relevant arterial geometries. In depth analysis into the factors that affect the transport of these low diffusion coefficient species is undertaken. A mathematical model of the complex underlying endothelial cell dynamics is utilised to model production of key intracellular molecules that have been implicated into the complex initiation processes of atherosclerosis; hence regions of the vasculature can be identified as being 'hot spots' for atherogenesis. This model is linked into CFD software allowing for the assessment of how 3D low yields and mass transfer affect the underlying cell signalling. Three studies are undertaken to further understand nucleotide variations at the endothelium and to understand factors involved in determining the underlying cell dynamics. The major focus of the first two studies is geometric variations. This is primarily due to the plethora of evidence implicating the geometry of the human vasculature, hence the haemodynamics, as an influential factor in atherosclerosis initiation. The final model looks at a physiologically realistic geometry to provide a more realistic reproduction of the in vivo environment.

Research is performed to assess the potential of surface moisture evaporative cooling from composite plates as a means of reducing the external temperature of military aircraft. To assess the feasibility of evaporative cooling for this application, a simplified theoretical model of the phenomenon is formulated. The model consists of a flat composite plate at an initial uniform temperature, T0. The plate also possesses an initial moisture (molecular water) content, M0. The plate is oriented vertically and at t=0 s, one surface is exposed to a free stream of air at an elevated temperature. The other surface is exposed to stagnant air at the same temperature as the plate’s initial temperature. The equations associated with energy and mass transport for the model are developed from the conservation laws per the continuum mechanics hypothesis. Constitutive equations and assumptions are introduced to express the two nonlinear partial differential equations in terms of the temperature, T, and the partial density of molecular water, ρw. These equations are approximated using a weak form Galerkin finite element formulation and the α–family of time approximation. An algorithm and accompanying computer program written in the Matlab programming language are presented for solving the nonlinear algebraic equations at successive time steps. The Matlab program is used to generate results for plates possessing a variety of initial moisture concentrations, M0, and diffusion coefficients, D. Surface temperature profiles, over time, of moisture bearing specimens are compared with the temperature profiles of dry composite plates. It is evident from the results that M0 and D affect the surface temperature of a moist plate. Surface temperature profiles are shown to decrease with increasing M0 and/or D. In particular, dry and moist specimens are shown to differ in final temperatures by as much as 30°C over a 900 s interval when M0 = 30% and D is on the order of 10–8m2/s (T0 = 25°C, h = 60 W/m2°C, T∞ = 90°C).

La méthode couplant l'expérimentation et la modélisation est utilisée pour étudier le processus d'absorption et de désorption du méthanol avec un transfert tridimensionnel dans le bois. Le méthanol est un bon solvant pour fixer certains produits fongicides à l'intérieur du bois, car le bois est un matériau qui peut être attaqué par des champignons, c'est pourquoi on le soumet à un traitement en profondeur par des produits fongicides, ce qui lui permet d'être utilisé dans les milieux les plus défavorables. Le traitement du bois est indispensable mais pas suffisant car un problème apparait lorsque l'échantillon de bois traité est placé dans l'eau, il s'agit de la libération qui prend place, avec deux inconvénients ; une pollution de l'eau et une diminution de la résistance du bois envers les champignons. Des modèles mathématiques basés sur une méthode numérique aux différences finies ont été construits pour décrire les transferts du méthanol dans le bois et d'autres pour décrire la libération du produit chimique dans l'eau. Ces modèles permettent de simuler les cinétiques de transfert et fournir plus d'information que les expériences

The primary focus of the present work is the development of macro-models for numerical simulation of binary alloy solidification processes, consistent with microscopic phase-change considerations, with a particular emphasis on capturing the effects of non-equilibrium species redistribution on overall macrosegregation behaviour. As a first step, a generalised macroscopic framework is developed for mathematical modelling of the process. The complete set of equivalent single-phase governing equations (mass, momentum, energy and species conservation) are solved following a pressure-based Finite Volume Method according to the SIMPLER algorithm. An algorithm is also developed for the prescription of the coupling between temperature and the melt-fraction. Based on the above unified approach of solidification modelling, a macroscopic numerical model is devised that is capable of capturing the interaction between the double-diffusive convective field and a localised fluid flow on account of solutal undercooling during non-equilibrium solidification of binary alloys. Numerical simulations are performed for the case of two-dimensional transient solidification of Pb-Sn alloys, and the simulation results are also compared with the corresponding experimental results quoted in the literature. It is observed that non-equilibrium effects on account of solutal undercooling result in an enhanced macrosegregation. Next, the model is extended to capture the effects of dendritic arm coarsening on the macroscopic transport phenomena occurring during a binary alloy solidification process. The numerical results are first tested against experimental results quoted in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom-cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation can be predicted as compared to that dictated by shrinkage-induced fluid flow alone. For an order-of-magnitude assessment of predictions from the numerical models, a systematic approach is subsequently developed for scaling analysis of momentum, heat and species conservation equations pertaining to the case of solidification of a binary mixture. A characteristic velocity scale inside the mushy region is derived, in terms of the morphological parameters of the two-phase region. A subsequent analysis of the energy equation results in an estimation of the solid layer thickness. It is also shown from scaling principles that non-equilibrium effects result in an enhanced macro-segregation compared to the case of an equilibrium model For the sake of assessment of the scaling analysis, the predictions are validated against computational results corresponding to the simulation of a full set of governing equations, thus confirming the trends suggested by the scale analysis. In order to analytically investigate certain limiting cases of unidirectional alloy solidification, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. The results are tested for the problem of solidification of an ammonium chloride-water solution, and are compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. An excellent agreement between the present solutions and results from the computational simulation can be observed. The generalised numerical model is subsequently utilised to investigate the effects of laminar double-diffusive Rayleigh-Benard convection on directional solidification of binary fluids, when cooled and solidified from the top. A series of experiments is also performed with ammonium chloride-water solutions of hypoeutectic and hypereutectic composition, so as to facilitate comparisons with numerical predictions. While excellent agreements can be obtained for the first case, the second case results in a peculiar situation, where crystals nucleated on the inner roof of the cavity start descending through the bulk fluid, and finally settle down at the bottom of the cavity in the form of a sedimented solid layer. An eutectic solidification front subsequently progresses from the top surface vertically downwards, and eventually meets the heap of solid crystals collected on the floor of the cavity. However, comparison of experimental observations with corresponding numerical results from the present model is not possible under this situation, since the associated transport process involves a complex combination of a number of closely interconnected physical mechanisms, many of which are yet to be resolved. Subsequent to the development of the mathematical model and experimental arrangements for macroscopic transport processes during an alloy solidification process, some of the important modes of double-diffusive instability are analytically investigated, as a binary alloy of any specified initial composition is directionally solidified from the top. By employing a close-formed solution technique, the critical liquid layer heights corresponding to the onset of direct mode of instability are identified, corresponding two a binary alloy with three different initial compositions. In order to simulate turbulent transport during non-equilibrium solidification processes of binary alloys, a modified k-8 model is subsequently developed. Particular emphasis is given for appropriate modelling of turbulence parameters, so that the model merges with single-phase turbulence closure equations in the pure liquid region in a smooth manner. Laboratory experiments are performed using an ammonium chloride-water solution that is solidified by cooling from the top of a rectangular cavity. A good agreement between numerical and experimental results is observed. Finally, in order to study the effects of three-dimensionality in fluid flow on overall macrosegregation behaviour, the interaction between double-diffusive convection and non-equilibrium solidification of a binary mixture in a cubic enclosure (cooled from a side) is numerically investigated using a three-dimensional transient mathematical model. Investigations are carried out for two separate model systems, one corresponding to a typical metal-ally analogue system and other corresponding to an actual metal-alloy system. As a result of three-dimensional convective flow-patterns, a significant solute macrosegregation is observed in the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.

Severe declines in the number of some songbirds over the last 40 years have caused heated debate amongst interested parties. Many factors have been suggested as possible causes for these declines, including an increase in the abundance and distribution of an avian predator, the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a predator effect on the abundance of its prey, we analyse data on 10 species visiting garden bird feeding stations monitored by the British Trust for Ornithology in relation to the abundance of sparrowhawks. We apply Bayesian hierarchical models to data relating to averaged maximum weekly counts from a garden bird monitoring survey. These data are essentially continuous, bounded below by zero, but for many species show a marked spike at zero that many standard distributions would not be able to account for. We use the Tweedie distributions, which for certain areas of parameter space relate to continuous nonnegative distributions with a discrete probability mass at zero, and are hence able to deal with the shape of the empirical distributions of the data. The methods developed in this thesis begin by modelling single prey species independently with an avian predator as a covariate, using MCMC methods to explore parameter and model spaces. This model is then extended to a multiple-prey species model, testing for interactions between species as well as synchrony in their response to environmental factors and unobserved variation. Finally we use a relatively new methodological framework, namely the SPDE approach in the INLA framework, to fit a multi-species spatio-temporal model to the ecological data. The results from the analyses are consistent with the hypothesis that sparrowhawks are suppressing the numbers of some species of birds visiting garden feeding stations. Only the species most susceptible to sparrowhawk predation seem to be affected.

The kinetics of reduction by free flavin semiquinones of the individual components of 1:1 complexes of yeast cytochrome c peroxidase and the cytochrome c from horse, tuna, and yeast, including several site-specific mutants of either the cytochrome c or cytochrome c peroxidase, have been studied. The orientations of the various cytochromes c within electrostatically-stabilized complexes with the peroxidase are not equivalent. This is shown by differential decreases in the rate constants for cytochrome reduction by neutral flavin semiquinones upon complexation which are in the order: tuna ≫ horse > yeast iso-2 > yeast iso-1. We have also directly measured the physiologically-significant intracomplex one-electron transfer rate constants from the ferrous cytochromes c to the peroxide-oxidized species of the peroxidase at several ionic strengths. The rate constants at low ionic strength are highly species dependent, again consistent with the contention that the orientations of the various cytochromes within the complex with CcP are not the same. Increasing the ionic strength in all cases resulted in an increase in the rate constant for the first-order process which controls electron transfer from cytochrome c to the peroxidase Compound I species of the peroxidase. When the two proteins are immobilized by covalent cross-linking, no such rate enhancement is observed, suggesting that the ionic strength effect is manifested by an increase in the number of geometric orientations between the two proteins which results in more rapid electron transfer. Similar rate enhancing effects are observed when positively charged residues on the surface of cytochrome c are converted to electrostatically neutral amino acids by site-specific mutagenesis. The effect of site-specific mutagenesis of two residues of cytochrome c peroxidase have also been studied. His-181, when converted to a glycine has little effect on the electron transfer rate constant, whereas when Trp-191 is converted to a phenylalanine no intracomplex electron transfer could be observed, indicating an obligatory role of this residue in the electron transfer process.

A theoretical study of convective heat transfer is presented for a laminar flow subjected to an axial variation in the external heat transfer coefficient (or dimensionless Biot number). Since conventional techniques fail for a variable boundary condition parameter, a variable eigenfunction approach is developed. An analysis is carried out for a periodic heat transfer coefficient, which serves as a model for heat transfer from a duct fitted with an array of evenly spaced fins. Three solution methods for the variable eigenfunction technique are examined: an Nth order approximation method, an iterative method and a stepwise periodic method. The stepwise periodic method provides the most convenient and accurate solution for a stepwise periodic Biot number. Graphical results match exactly to ones obtained by Charmchi and Sparrow from a finite-difference scheme. A connected region technique is also developed to provide limited exact results to test the validity of the three solution methods. The study of a finned duct by a stepwise periodic Biot number is carried out via a parametric study, an average (constant) Biot number approximation and an assumed velocity profile analysis. Results for the parametric study show that external finning yields substantial heat transfer enhancement over an unfinned duct, especially when the Biot number of the unfinned regions is low. A decrease in the interfin spacing causes increased enhancement. Variations of the period of the Biot number causes relatively small changes in enhancement as long as the ratio of finned to unfinned surface remains unchanged. An average (constant) Biot number approximation for a specified finned tube is compared to the stepwise periodic Biot number solution. The results show that the constant Biot number approximation provides accurate results. Finally, the results for the influence of the assumed velocity profile demonstrate that a constant velocity flow provides increased heat transfer and more effective enhancement by external finning than a laminar fully developed flow, especially at high Biot numbers. This study provides insight into heat transfer enhancement due to finning and also develops a solution methodology for problems involving variable boundary condition parameters.
M.S.

The atmospheres of exoplanets are being characterised in increasing detail by observational facilities and will be examined with even greater clarity with upcoming space based missions such as the James Webb Space Telescope (JWST) and the Wide Field InfraRed Survey Telescope (WFIRST). A major component of exoplanet atmospheres is the presence of cloud particles which produce characteristic observational signatures in transit spectra and influence the geometric albedo of exoplanets. Despite a decade of observational evidence, the formation, dynamics and radiative-transport of exoplanet atmospheric cloud particles remains an open question in the exoplanet community. In this thesis, we investigate the kinetic chemistry of cloud formation in hot Jupiter exoplanets, their effect on the atmospheric dynamics and observable properties. We use a static 1D cloud formation code to investigate the cloud formation properties of the hot Jupiter HD 189733b. We couple a time-dependent kinetic cloud formation to a 3D radiative-hydrodynamic simulation of the atmosphere of HD 189733b and investigate the dynamical properties of cloud particles in the atmosphere. We develop a 3D multiple-scattering Monte Carlo radiative-transfer code to post-process the results of the cloudy HD 189733b RHD simulation and compare the results to observational results. We find that the cloud structures of the hot Jupiter HD 189733b are likely to be highly inhomogeneous, with differences in cloud particle sizes, number density and composition with longitude, latitude and depth. Cloud structures are most divergent between the dayside and nightside faces of the planet due to the instability of silicate materials on the hotter dayside. We find that the HD 189733b simulation in post-processing is consistent with geometric albedo observations of the planet. Due to the scattering properties of the cloud particles we predict that HD 189733b will be brighter in the upcoming space missions CHaracterising ExOPlanet Satellite (CHEOPS) bandpass compared to the Transiting Exoplanet Space Survey (TESS) bandpass.

The investigations presented in the thesis are theoretical studies of magnetohydrodynamic flows, heat and mass transfer in Newtonian/non-Newtonian cooling liquids, due to horizontal/vertical stretching sheet. The theoretical studies include the effect of magnetic field, uniform and non-uniform heat source/sink (flow and temperature dependent heat source/sink) effects. The considered problems include flow of viscous fluids in the presence of applied magnetic field and electric field with first order chemical reactions. The viscous incompressible Newtonian fluid flow in porous medium with Darcy-Forchheimmer model, electrically conducting fluid and nanofluid is studied. We introduce innovative techniques for finding solutions of highly nonlinear coupled boundary value problems such as Runge-Kutta method, Perturbation method and Differential Transform Method (DTM).   Chapter 1-2 gives a brief introduction. Chapter 3 focuses on Lie group analysis of MHD flow and heat transfer over a stretching sheet. The effects of viscous dissipation, uniform heat source/sink and MHD on heat transfer are addressed. In Chapter 4-6 we examined the laminar flow, thermocapillary flow of a nanoliquid thin film over an unsteady stretching sheet in presence of MHD and thermal Radiation in different situations. An effective medium theory (EMT) based model is used for the thermal conductivity of the nanoliquid.  Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) - water base liquid. In Chapter 7-9 we analyzed, heat and mass transfer in MHD, mixed convection, viscoelastic fluid flow, non-Darcian flow due to stretching sheet in presence of viscous dissipation, non-uniform heat source/sink and porous media have been investigated in different situations.  MHD and viscous dissipation have a significant influence on controlling of the dynamics.    In Chapter 10 the linear stability of Maxwell fluid-nanofluid flow in a saturated porous layer is examined theoretically when the walls of the porous layers are subjected to time-periodic temperature modulations. A modified Darcy-Maxwell model is used to describe the fluid motion, and the nanofluid model used includes the effects of the Brownian motion. The thermal conductivity and viscosity are considered to be dependent on the nanoparticle volume fraction. In Chapter 11 we studied MHD flow in a vertical double passage channel taking into account the presence of the first order chemical reactions. The governing equations are solved by using a regular perturbation technique valid for small values of the Brinkman number and a DTM valid for all values of the Brinkman number.

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Bachelors
Engineering and Computer Science
Computer Engineering

One of the most significant challenges faced when modeling mass transfer from contaminant source zones is uncertainty regarding parameter estimates. These rate parameters are of particular importance because they control the connectivity between a simulated contaminant source zone and the aqueous phase. Where direct observation has fallen short, this study attempts to interpret field data using an inverse modeling technique for the purpose of constraining mass transfer processes which are poorly understood at the field scale. Inverse modeling was applied to evaluate parameters in rate-limited models for mass transfer. Two processes were analyzed: (i) desorption of hydrophobic contaminants and (ii) multicomponent Non-Aqueous Phase Liquid (NAPL) dissolution. Desorption was investigated using data obtained from elution experiments conducted with weathered sediment contaminated with 2,4,6 trinitrotoluene (TNT) (Sellm and Iskandar, 1994). Transport modeling was performed with four alternative source models, but predictive error was minimized by two first-order models which represented sorption/desorption using a Freundlich isotherm. The results suggest that first-order/Freundlich models can reproduce dynamic desorption attributed to high-and-low relative energy sorption sites. However, additional experimentation with the inversion method suggests that mass constraints are required in order to appropriately determine mass transfer coefficients and sorption parameters. The final portion of this research focused on rate-limited mass transfer from multicomponent NAPLs to the aqueous phase. Previous work has been limited to bench and intermediate scale findings which have been shown to inadequately translate to field conditions. Two studies were conducted in which numerical modeling was used to reproduce dissolution from multicomponent NAPL sources. In the first study, a model was generated to reproduce dissolution of chloroform (TCM), trichloroethylene (TCE) and tetrachloroethylene (PCE) observed during an emplaced-source field experiment conducted within a flow cell (Broholm et al., 1999). In the second study, a methodology was developed for analyzing benzene, toluene, ethylbenzene and xylene (BTEX) data during a field-scale mass transfer test conducted within a vertically-smeared source zone (Kavanaugh, 2010). The findings suggest that the inversion technique, when provided appropriate characterization of site and source parameters and when given appropriate dataset resolution, represents a viable method for parameter determination. Furthermore, the findings of this research suggest that inversion-based modeling provides an innovative predictive method for determining mass transfer parameters for multicomponent mixtures at the field scale.
Ph. D.