Neste trabalho, o fenômeno de evaporação em gases rarefeitos e analisado, para o caso de uma espécie de gás bem como de misturas binárias. Evaporação fraca e forte são consideradas para escoamentos de gases em canal e semi-espaco. Também e investigado o fenômeno conhecido como reverso de temperatura, típico de gases em estado de rarefação. O método ADO, uma versão analítica do método de ordenadas discretas, é utilizado para construção de soluções em forma fechada para os diversos problemas e quantidades de interesse, como perfis de temperatura e fluxos de calor. Para o caso de um gás, uma solução unificada e desenvolvida para problemas formulados a partir dos modelos cinéticos, derivados da equação de Boltzmann, BGK, S, Gross- Jackson e MRS. No caso de mistura binária de gases, a formulação matemática e baseada no modelo McCormack. Particularmente, quando a evaporação forte e abordada, e aspectos não lineares devem ser incluídos, a versão não linear do modelo BGK e utilizada. Neste caso, a solução ADO do modelo linear e utilizada em um processo chamado de pós-processamento para inclusão dos termos não lineares do problema e reavaliação das quantidades de interesse, evidenciando melhoria dos resultados obtidos pela formulação linear. Uma serie de resultados numéricos são listados e é observada, de forma geral, excelente exatidão e eficiência computacional. / In this work, evaporation phenomena in rarefied gas flow, for one gas case and binary mixtures, are analyzed. Weak and strong evaporation are considered in channel and half-space problems. The reverse of temperature problem, typical in rarefied gas dynamics, is also investigated. The ADO method, an analytical version of the discrete ordinates method, is used to develop closed form solutions, to several problems and quantities of interest, as temperature profiles and heat flows. For the one gas case, an unified solution is developed for the BGK, S, Gross-Jackson and MRS models, derived from the Boltzmann equation. For binary mixtures, the mathematical formulation is based on the McCormack model. Particularly, when strong evaporation is investigated, and nonlinear aspects have to be included, the nonlinear BGK model is used. In this case, the ADO solution, provided by the linear model, is considered in a post-processing procedure which takes into account the nonlinear terms to evaluate the quantities of interest, and improved results are obtained, in comparison with the linear version. A series of numerical results are listed and, in general, an excellent accuracy and good computational efficiency are observed.

Afin de modéliser l'absorption dans le traitement des transferts radiatifs en milieu atmosphérique, de nombreuses méthodes plus précises et plus rapides ont été développées. La modélisation de la formation du brouillard, où le rayonnement infrarouge joue un rôle très important, nécessite des méthodes numériques suffisamment précises pour calculer le taux de refroidissement. Le brouillard radatif se forme après des conditions de ciel clair, où l'absorption est le processus radiatif dominant, en raison d'un fort refroidissement nocturne. Avec l'augmentation des ressources de calcul et le développement du Calcul Haute Performance, les modèles à bandes, pour effectuer l'intégration sur la longueur des grandeurs radiométriques, sont les plus utilisés. Toutefois, le couplage entre les transferts radiatifs 3-D et la dynamique des fluides reste très coûteux en temps de calcul. Le rayonnement augmente d'environ cinquante pourcent le temps de la simulation pour la dynamique des fluides uniquement. Pour réduire le temps passé dans une itération radiative, une nouvelle paramétrization basée sur les modèles en émissivité a été développée. Cette approche nécessite seulement une résolution de l'ETR contre $N_{text{bandes}} times N_{text{gauss}}$ pour un modèle à $N_{text{bandes}}$ avec $N_{text{gauss}}$ points de quadratures sur chaque bande. Une comparaison avec des données de simulation a été effectuée et cette nouvelle paramétrisation de l'absorption infrarouge a montré sa capacité à prendre en compte les variations des concentrations gazeuses et d'eau liquide. Une étude à travers le couplage entre le modèle développé et le code de CFD Code_Saturne a été réalisée afin valider dynamiquement notre paramétrisation. Enfin une simulation exploratoire a été effectuée sur un domaine 3-D en présence de bâti idéalisé, pour capter les effets radiatifs 3-D dûs aux hétérogénéités horizontales du champ d'eau liquide et des bâtiments / The Atmospheric Radiation field has seen the development of more accurate and faster methods to take into account absorption. Modelling fog formation, where Infrared Radiation is involved, requires accurate methods to compute cooling rates. Radiative fog appears with clear sky condition due to a significant cooling during the night where absorption is the dominant processus. Thanks to High Performance Computing, multi-spectral approaches of Radiative Transfer Equation resolution are often used. Nevertheless, the coupling of three-dimensional radiative transfer with fluid dynamics is very computationally expensive. Radiation increases the computation time by around fifty percent over the pure Computational Fluid Dynamics simulation. To reduce the time spent in radiation calculations, a new method using the broadband emissivity has been developed to compute an equivalent absorption coefficient (spectrally integrated). Only one resolution of Radiative Transfer Equation is needed against $N_{text{band}} times N_{text{gauss}}$ for an $N_{text{band}}$ model with $N_{text{gauss}}$ quadrature points on each band. A comparison with simulation data has been done and the new parameterization of Radiative properties shows the ability to handle variations of gases concentrations and liquid water. A dynamical study through the coupling between the infrared radiation model and Code_Saturne has been done to validate our parametrization. Finally the model was tested on a 3-D domain with idealized buildings to catch 3-D infrared radiative effects due to horizontally inhomogenities of the liquid water content field and buildings

This thesis discusses the development of an improved microbial inactivation model for analyzing continuous flow UV-LED air treatment systems and use of the model to evaluate the impact of several treatment system design parameters on inactivation. Model development includes three submodels: a radiation submodel, a fluid flow submodel, and an inactivation kinetics submodel. Radiation modeling defines the UV irradiance throughout the system. Fluid flow modeling provides the residence times that microbes spend exposed to the UV irradiation while passing through the system. Inactivation modeling combines irradiance and residence times with inactivation kinetics to calculate species-specific inactivation in a treatment system. The most significant development focuses on the radiation submodel as it is key to linking the UV intensity emissions to treatment system properties and inactivation rates. Various radiation transfer models previously developed by other researchers are evaluated for computational efficiency and effectiveness in modeling non-uniform LED emission and diffuse and specular wall reflections. The Discrete Ordinates Method (DOM) with Legendre-Chebyshev quadrature sets is selected for use in this research due to its ability to represent both non-uniform LED emission profiles and combined specular and diffuse surface reflection. The DOM and associated quadrature schemes are reviewed in detail and limitations in representing LED emissions discussed. Sensitivity to spatial and directional discretization is evaluated. The radiation submodel is combined with a well-accepted inactivation kinetics correlation and two simple fluid flow models: a uniform flow model and a fully-developed flow model. The use and validity of these submodels is explained and their limitations discussed. Predicted microbial inactivation from the overall model is shown to compare well with limited data from a test system. Model flexibility in evaluating several system operating and design parameters is illustrated. These analyses show that for a similar number of LEDs, highly reflective surfaces (diffuse or specular) produce higher inactivation. Other parameters are shown to impact inactivation but to a lesser degree. Square ducts result in higher inactivation than non-square ducts, a fully-developed flow profile slightly increases inactivation over a uniform flow profile, positioning LEDs on all four duct walls slightly increases inactivation when surfaces are non-reflective or diffuse, and positioning LEDs closer together results in slightly higher inactivation.

Dans les fours de raffinerie, l'efficacité du transfert énergétique vers le pétrole brut avant sa distillation est altérée par la formation d'un composé carboné dans les tubes, appelé coke. Cela conduit à l'augmentation des coûts de production et de maintenance, et exige une compréhension accrue ainsi qu'un meilleur contrôle de ce phénomène. Cet encrassement est de type chimique et induit par les fortes températures. Dans les fours de cette dimension, le transfert de chaleur s'effectue principalement par rayonnement des produits de combustion. Le flux radiatif net sur les surfaces d'échange des tubes dépend de la température de toutes les surfaces solides et a donc besoin d'être prédit avec une précision suffisante. La température sur les tubes est le résultat d'un équilibre entre le rayonnement thermique et la conduction. Le comportement thermique de l'ensemble du système est un problème de couplage entre le rayonnement et la conduction. Une méthodologie complète de couplage est exposée et validée de la manière suivante. Dans ce problème, la flamme est décrite par un modèle analytique axisymétrique avec chimie complexe. Le couplage avec la conduction dans les tubes est réalisé par l'utilisation d'une méthode aux ordonnées discrètes (DOM) avec un modèle spectral de type bandes étroites pour le rayonnement des gaz de combustion. Un bilan énergétique confirme que les transferts de chaleur sont dominés par le rayonnement thermique. Un bon accord avec les mesures disponibles sur un four réel montre que l'approche proposée est capable de prédire le rayonnement thermique. L'étape suivante consiste à coupler le calcul de la température du tube à une loi d'encrassement. Un modèle chimique simple est utilisé. Il est validé à l'aide d'une expérience de laboratoire. La comparaison entre les températures obtenues avec la simulation et celles mesurées par des sondes thermiques montre que la simulation est capable de capturer l'évolution de la température dans le tube avec précision. Enfin, un modèle d'encrassement pour la configuration réelle est trouvé puis appliqué dans une simulation couplée complète. Cette simulation montre un bon accord entre l'évolution de la température sur site et dans la simulation. Une analyse plus poussée est réalisée sur les profils de température, de flux radiatif et de dépôt de coke et montre l'impact de ce dépôt sur l'installation / In industrial refinery furnaces, the efficiency of the thermal transfer to heat crude oil before distillation is often altered by coke deposition inside the process pipes. This leads to increased production and maintenance costs, and requires better understanding and control. Crude oil fouling is a chemical reaction that is, at first order, thermally controlled. In such large furnaces, the predominant heat transfer process is thermal radiation by the hot combustion products, which directly heats the pipes. As radiation fluxes depend on temperature differences, the pipe surface temperature also plays an important role and needs to be predicted with sufficient accuracy. This temperature results from the energy balance between thermal radiation and conduction in the solid material of the pipe, meaning that the thermal behavior of the whole system is a coupled radiation-conduction problem. In this work, this problem is solved in a cylindrical furnace, using the Discrete Ordinate Method (DOM) with accurate spectral models for the radiation of combustion gases, described by a complex chemistry flame model, and coupled to heat conduction in the pipe to predict its wall temperature. An energy balance confirms that heat transfers are effectively dominated by thermal radiation. Good agreement with available measurements on a real furnace shows that the proposed approach is able to predict the heat transfer to the pipe. The method gives an accurate prediction of the radiative source term and temperature fields in the furnace and on the pipe surface, which are key parameters for liquid fouling inside the pipe. Although reasonably accurate results are obtained with simple models, they still can be easily improved by more sophisticated models for turbulence, combustion and radiation. The next step is to couple the calculation of the pipe temperature to a fouling law. Since exact composition of crude oil is not available, one needs to model coke deposition with simple fouling law. The idea is to model the deposition rate by a thermal resistance added to the heated pipe and allows to coupling the calculation of the pipe temperature to a fouling law. A simple chemical model is used, and validated against a labscale experiment, prior to apply it to a furnace configuration. Comparing the temperature obtained with the simulation to the temperature measured by thermal probes at selected locations shows that the simulation is able to capture the temperature variation at these points. It is shown that coking occurs when the temperature has remained high on both sides of the pipe for a sufficient length. We explain how to extract a fouling law in controlled condition when the deposit is induced by thermal stressing of the crude. Finally, the whole system, including radiation,conduction and deposition, is coupled. Results are compared to the real furnace and show relatively good agreement in terms of external skin pipe temperature prediction. This observation validates the methodology exposed in this script

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for the prediction of radiative heat transfer in nongray absorbing-emitting media was developed by incorporation of two different gas spectral radiative property models, namely wide band correlated-k (WBCK) and spectral line-based weighted sum of gray gases (SLW) models. Predictive accuracy and computational efficiency of the developed code were assessed by applying it to the predictions of source term distributions and net wall radiative heat fluxes in several one- and two-dimensional test problems including isothermal/non-isothermal and homogeneous/non-homogeneous media of water vapor, carbon dioxide or mixture of both, and benchmarking its steady-state predictions against line-by-line (LBL) solutions and measurements available in the literature. In order to demonstrate the improvements brought about by these two spectral models over and above the ones obtained by gray gas approximation, predictions obtained by these spectral models were also compared with those of gray gas model. Comparisons reveal that MOL solution of DOM with SLW model produces the most accurate results for radiative heat fluxes and source terms at the expense of computation time when compared with MOL solution of DOM with WBCK and gray gas models. In an attempt to gain an insight into the conditions under which the source term predictions obtained with gray gas model produce acceptable accuracy for engineering applications when compared with those of gas spectral radiative property models, a parametric study was also performed. Comparisons reveal reasonable agreement for problems containing low concentration of absorbing-emitting media at low temperatures. Overall evaluation of the performance of the radiation code developed in this study points out that it provides accurate solutions with SLW model and can be used with confidence in conjunction with computational fluid dynamics (CFD) codes based on the same approach.

Climate models are the primary tools used for understanding past climate variations and for future projections. The atmospheric radiation is the key component of these models. Accurate modeling of atmosphere necessitates reliable evaluation of the medium radiative properties and accurate solution of the radiative transfer equation in conjunction with the time-dependent multi-dimensional governing equations of atmospheric models. Due to difficulty in solving the equations of atmospheric and radiation models simultaneously, radiation equations have been solved when input data such as concentration, temperature etc. were made available upon solution of equations of atmospheric models. Generally, time step of conservation equations are 10-30 minutes but radiative transfer equation is called only once every 1-3 hours. However, there is inaccuracy due to the fixed radiation fluxes over the intervening time steps. To overcome this problem, the equations of atmospheric and radiation models have to be solved simultaneously and the solution methods have to be compatible. For this purpose, a radiative-convective model with radiation model based on method of lines (MOL) solution of discrete ordinate method (DOM) with wide band correlated-k (WBCK) was developed. To achieve this objective, a previously developed MOL solution of DOM with WBCK model was adapted to 1-D longwave clear sky atmosphere and its predictive accuracy and computational efficiency was examined on the test problem by using benchmark solution obtained from Line-by-line Radiative Transfer Model (LBLRTM). The radiation code was then coupled with radiative-convective model and the predictive accuracy of this model was examined for several coupling intervals. Comparisons reveal that as coupling interval increases, although the computation time of the model decreases, the predicted temperature profiles diverge from the one obtained when equations of radiative-convective model and the radiation model are solved simultaneously and percentage relative error in temperature increases an order of magnitude when coupling time between radiative-convective model and the radiation model increases from 2 to 10 hours. Therefore, it can be concluded that the equations of the radiation model have to be solved simultaneously with the equations of the climate model. Overall evaluation of the performance of the radiation model used in this study points out that it provides accurate and computationally efficient solutions and can be used with confidence in conjunction with the climate models for simultaneous solution of governing equations with radiation transfer equation.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The method discrete ordinates is used to solve problems involving rarefied gas dynamics. In this work, a version of the analytical method discrete ordinates (ADO) is used to solve problems in a semi-infinite. The complete analytical development, in cartesian coordinates, the solution of the Thermal-Slip and Viscous-Slip problems is presented, for four kinetic models: BGK model, S model, Gross Jackson model and MRS model in a unified approach. In addition, to describe the interaction between gas and surface, we use the Cercignani-Lampis boundary condition defined in terms of the coefficients of accommodation of tangential momentum and energy accommodation coefficient kinetic corresponding the velocity normal. Numerical results are presented, where we obtain quantities of interest, such as: velocity profile and heat flow profile, which were implemented computationally through the FORTRAN program. / O método de ordenadas discretas é utilizado na solução de alguns problemas envolvendo a dinâmica de gases rarefeitos. Neste trabalho, uma versão analítica do método de ordenadas discretas (ADO) é usada para resolver problemas em meio semiinfinito. O desenvolvimento analítico completo, em coordenadas cartesianas, da solução dos problemas Deslizamento Térmico e Deslizamento Viscoso é apresentada, para quatro modelos cinéticos: modelo BGK, modelo S, modelo Gross Jackson e modelo MRS em uma abordagem unificada. Além disso, para descrever o processo de interação entre o gás e a parede utiliza-se o núcleo de Cercignani-Lampis definido em termos do coeficiente de acomodação do momento tangencial e do coeficiente de acomodação da energia cinética correspondendo a velocidade normal. Resultados numéricos são apresentados, onde obtém-se grandezas de interesse, tais como: perfil de velocidade e perfil de fluxo de calor, os quais foram implementados computacionalmente através do programa FORTRAN.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this paper, we present numerical results for macroscopic quantities of interest (velocity profile, the heat ow profile and shear stress) for the ow of a binary mixture of rarefied gases in microchannels of arbitrary planes, defined by two infinite parallel lates without symmetry condition. The ow of gas mixture is due to a constant pressure gradient (Poiseuille's Problem), a temperature gradient (Problem Thermal-Creep) and a density gradient (Fuzzy Problem) in the direction parallel to the surface surrounding gases. The kinetic theory for the ow of gas mixture is described by a linearized model of the Boltzmann equation, the McCormack model. To better describe the interaction between gas and wall is used by Maxwell kernel in the terms of a single accommodation coefficient and the Cercignani-Lampis kernel defined in terms of the coefficients of accommodation of tangential momentum accommodation coefficient and the kinetic energy corresponding to normal velocity, which according to literature is a more appropriate model than the usual model that involves specular and diffuse. In seeking solutions to the problem proposed, it uses a analytical version of the discrete ordinates method (ADO), based an arbitrary quadrature scheme, whereby it is determined a problem of eigenvalues and their constant separation. The numerical calculations are performed for three mixtures of noble gases: Neon-Argon, Helium-Argon and Helium-Xenon, and computationally implemented using the FORTRAN computer program. / Neste trabalho, apresenta-se resultados numéricos para grandezas macroscropicas de interesse (perfil de velocidade, perfil do fluxo de calor e tensão de cisalhamento) relativas ao fluxo de uma mistura binária de gases de rarefação arbitrária em microcanais planos, definidos por duas placas paralelas infinitas sem condição de simetria. O fluxo da mistura gasosa ocorre devido a um gradiente constante de pressão (Problema de Poiseuille), um gradiente de temperatura (Problema Creep-Térmico) e um gradiente de densidade (Problema Difuso), na direção paralela a superfície que cerca os gases. A teoria cinética para o fluxo da mistura gasosa é descrita por um modelo linearizado da equação de Boltzmann, o modelo de McCormack. Para melhor descrever o processo de interação entre o gás e a parede utiliza-se o núcleo de Maxwell em termos de um único coeficiente de acomodação e o núcleo de Cercignani-Lampis definido em termos dos coeficientes de acomodação do momento tangencial e o coeficiente de acomodação da energia cinética correspondendo a velocidade normal, que segundo a literatura é um modelo mais apropriado do que o usual modelo que envolve reflexão especular e difusa. Na busca de soluções do problema proposto, usa-se uma versão analítica do método de ordenadas discretas (ADO), baseada num esquema de quadratura arbitrário, segundo a qual determina-se um problema de autovalores e respectivas constantes de separação. Os cálculos numéricos são realizados para três misturas de gases nobres: Neônio-Argônio, Hélio-Argônio e Hélio-Xenônio, e implementados computacionalmente através do programa computacional FORTRAN.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A formulação explícita matricial desenvolvida nesta tese de doutorado foi proposta visando ser uma alternativa na solução de Problemas Inversos de estimativa de propriedades radiativas em meios participantes homogêneos unidimensionais usando a Equação de Transferência Radiativa para modelar a interação da radiação com o meio participante. A equação de transporte é formulada em forma matricial e o domínio angular é discretizado usando conceitos do método de ordenadas discretas e a expansão da função de fase do espalhamento anisotrópico em uma série de polinômios de Legendre. A formulação proposta consiste em uma formulação explícita para o problema inverso. Um arranjo apropriado das condições de contorno prescritas (fluxos incidentes) e dos fluxos emergentes nos contornos de uma placa permitem o cálculo direto do operador de transmissão, do operador albedo e do operador de colisão. A partir do operador de colisão calculado são obtidos os valores estimados dos coeficientes de extinção total e de espalhamento. São apresentadas as formulações para problemas em regime estacionário e em regime transiente, bem como os resultados para alguns casos-teste. / The explicit matrix formulation developed in the present thesis has been proposed as an alternative for the solution of Inverse Problems for radiative properties estimation in one-dimensional homogeneous participating media using Radiative transfer equation for the modeling of the radiation interaction with the participating medium. This transport equation is formulated in a matrix form and the angular domain is discretized using concepts of the discrete ordinates methods and the expansion of the function of phase function of anisotropic scattering in a series of Legendre polynomial. The formulation proposed consists on an explicit formulation for the inverse problem. An adequate assembly of the prescribed boundary conditions (incidents flux) and of the emerging flux at the boundaries of the slab allows the direct computation of the transmission, albedo and collision operators. From the computed collision operator estimated values for total extinction and scattering coefficients are obtained. The formulations for steady state and transient situations are presented, as well as test case results.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação o método espectronodal SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, é utilizado para a determinação dos fluxos angulares médios nas faces dos nodos homogeneizados em domínio heterogêneo. Utilizando esses resultados, desenvolvemos um algoritmo para a reconstrução intranodal da solução numérica visto que, em cálculos de malha grossa, soluções numéricas mais localizadas não são geradas. Resultados numéricos são apresentados para ilustrar a precisão do algoritmo desenvolvido. / In this dissertation the spectral nodal method SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, is used to determine the angular fluxes averaged along the edges of the homogenized nodes in heterogeneous domains. Using these results, we developed an algorithm for the reconstruction of the node-edge average angular fluxes within the nodes of the spatial grid set up on the domain, since more localized numerical solutions are not generated by coarse-mesh numerical methods. Numerical results are presented to illustrate the accuracy of the algorithm we offer.