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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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O esquema iterativo de fonte de espalhamento (SI) é tradicionalmente aplicado para a convergência da solução numérica de malha fina para problemas de transporte de nêutrons monoenergéticos na formulação de ordenadas discretas com fonte fixa. O esquema SI é muito simples de se implementar sob o ponto de vista computacional; porém, o esquema SI pode apresentar taxa de convergência muito lenta, principalmente para meios difusivos (baixa absorção) com vários livres caminhos médios de extensão. Nesta dissertação descrevemos uma técnica de aceleração baseada na melhoria da estimativa inicial para a distribuição da fonte de espalhamento no interior do domínio de solução. Em outras palavras, usamos como estimativa inicial para o fluxo escalar médio na grade de discretização de malha fina, presentes nos termos da fonte de espalhamento das equações discretizadas SN usadas nas varreduras de transporte, a solução numérica da equação da difusão de nêutrons em grade espacial de malha grossa com condições de contorno especiais, que aproximam as condições de contorno prescritas que são clássicas em cálculos SN, incluindo condições de contorno do tipo vácuo. Para aplicarmos esta solução gerada pela equação da difusão em grade de discretização de malha grossa nas equações discretizadas SN de transporte na grade de discretização de malha fina, primeiro implementamos uma reconstrução espacial dentro de cada nodo de discretização, e então determinamos o fluxo escalar médio em grade de discretização de malha fina para usá-lo nos termos da fonte de espalhamento. Consideramos um número de experimentos numéricos para ilustrar a eficiência oferecida pela presente técnica (DSA) de aceleração sintética de difusão. / The scattering source iterative (SI) scheme is traditionally applied to converge finemesh numerical solutions to fixed-source discrete ordinates neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh average scalar flux in the scattering source terms of the SN discretized equations used in the transport sweeps, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical SN prescribed boundary conditions, including vacuum boundary conditions. To apply this coarse-mesh diffusion solution into the fine-mesh SN transport sweep discretized equations, we first perform within-node spatial reconstruction, and then we determine the fine-mesh average scalar flux for use in the scattering source terms. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Um método numérico nodal livre de erros de truncamento espacial é desenvolvido para problemas adjuntos de transporte de partículas neutras monoenergéticas em geometria unidimensional com fonte fixa na formulação de ordenadas discretas (SN). As incógnitas no método são os fluxos angulares adjuntos médios nos nodos e os fluxos angulares adjuntos nas fronteiras dos nodos, e os valores numéricos gerados para essas quantidades são os obtidos a partir da solução analítica das equações SN adjuntas. O método é fundamentado no uso da convencional equação adjunta SN discretizada de balanço espacial, que é válida para cada nodo de discretização espacial e para cada direção discreta da quadratura angular, e de uma equação auxiliar adjunta não convencional, que contém uma função de Green para os fluxos angulares adjuntos médios nos nodos em termos dos fluxos angulares adjuntos emergentes das fronteiras dos nodos e da fonte adjunta interior. Resultados numéricos são fornecidos para ilustrarem a precisão do método proposto. / A numerical nodal method that is free from all spatial truncation errors is developed for one-speed slab-geometry discrete ordinates (SN) fixed-source adjoint neutral particle transport problems. The unknown in the method are the node-edge and the node-average adjoint angular fluxes, and the numerical values obtained for these quantities are those of the analytic solution of the adjoint SN equations. The method is based on the use of the standard spatially discretized SN balance adjoint equation, which holds in each spatial node and for each discrete ordinates direction, and a nonstandard adjoint auxiliary equation that contains a Greens function for the node-average adjoint angular fluxes in terms of the exiting adjoint angular fluxes from the node edges and the adjoint interior source. Numerical results are given to illustrate the methods accuracy.

Um método de matriz resposta (RM) é descrito para gerar soluções numéricas livres de erros de truncamento espacial para problemas de transporte de nêutrons monoenergéticos e com fonte fixa, em geometria unidimensional na formulação de ordenadas discretas (SN). O método RM com esquema iterativo de inversão parcial por região (RBI) converge valores numéricos para os fluxos angulares nas fronteiras das regiões que coincidem com os valores da solução analítica das equações SN, afora os erros de arredondamento da aritmética finita computacional. Desenvolvemos um esquema numérico de reconstrução espacial, que fornece a saída para os fluxos escalares de nêutrons em qualquer ponto do domínio definido pelo usuário, com um passo de avanço também escolhido pelo usuário. Resultados numéricos são apresentados para ilustrar a precisão do presente método em cálculos de malha grossa. / Presented here is a response matrix (RM) method, which solves numerically fixedsource one-speed slab-geometry neutron transport problems in the discrete ordinates (SN) formulation. The numerical solutions are completely free from spatial truncation errors. Therefore, the RM method with the RBI iterative scheme converges numerical values for the region-edge angular fluxes, which coincide with the numerical values generated from the analytical solution, apart from computational finite arithmetic considerations. A spatial reconstruction scheme has also been developed to yield the detailed profile of the scalar flux using a fixed step defined by the code user. Numerical results are given to illustrate the offered methods accuracy.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Um método de Matriz Resposta (MR) é descrito para gerar soluções numéricas livres de erros de truncamento espacial para problemas multigrupo de transporte de nêutrons com fonte fixa e em geometria unidimensional na formulação de ordenadas discretas (SN). Portanto, o método multigrupo MR com esquema iterativo de inversão nodal parcial (NBI) converge valores numéricos para os fluxos angulares nas fronteiras das regiões que coincidem com os valores da solução analítica das equações multigrupo SN, afora os erros de arredondamento da aritmética finita computacional. É também desenvolvido um esquema numérico de reconstrução espacial, que fornece a saída para os fluxos escalares de nêutrons em cada grupo de energia em um intervalo qualquer do domínio definido pelo usuário, com um passo de avanço também escolhido pelo usuário. Resultados numéricos são apresentados para ilustrar a precisão do presente método em cálculos de malha grossa.

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.

Nuclear nonproliferation research and forensics have a need for improved software solutions, particularly in the estimates of the transmutation of nuclear fuel during burnup and depletion. At the same time, parallel computers have become effectively sized to enable full core simulations using highly-detailed 3d mesh models. In this work, the capability for modeling 3d reactor models is researched with PENBURN, a burnup/depletion code that couples to the PENTRAN Parallel Sn Transport Solver and also to the Monte Carlo solver MCNP5 using the multigroup option. This research is computationally focused, but will also compare a subset of results of experimental Pressurized Water Reactor (PWR) burnup spectroscopy data available with a designated BR3 PWR burnup benchmark. Also, this research will analyze large-scale Cartesian mesh models that can be feasibly modeled for 3d burnup, as well as investigate the improvement of finite differencing schemes used in parallel discrete ordinates transport with PENTRAN, in order to optimize runtimes for full core transport simulation, and provide comparative results with Monte Carlo simulations. Also, the research will consider improvements to software that will be parallelized, further improving large model simulation using hybrid OpenMP-MPI. The core simulations that form the basis of this research, utilizing discrete ordinates methods and Monte Carlo methods to drive time and space dependent isotopic reactor production using the PENBURN code, will provide more accurate detail of fuel compositions that can benefit nuclear safety, fuel management, non-proliferation, and safeguards applications.

Neutron radiation detectors are an integral part of the Department of Homeland Security (DHS) efforts to detect the illicit trafficking of radioactive or special nuclear materials into the U.S. In the past decade, the DHS has deployed a vast network of radiation detection systems at various key positions to prevent or to minimize the risk associated with the malevolent use of these materials. The greatest portion of this detection burden has been borne by systems equipped with 3He because of its highly desirable physical and nuclear properties. However, a dramatic increase in demand and dwindling supply, combined with a lack of oversight for the existing 3He stockpile has produced a critical shortage of this gas which has virtually eliminated its viability for detector applications. A number of research efforts have been undertaken to develop suitable 3He replacements; however, these studies have been solely targeted toward simple detection cases where the overall detection efficiency is the only concern. For these cases, an insertion of additional detectors or materials can produce reaction rates that are sufficient, because the neutron spectral response is essentially irrelevant. However, in applications such as safeguards, non-proliferation efforts, and material control and accountability programs (MC&A), a failure to use detectors that are spectrally matched to 3He can potentially produce dire consequences. This is because these more difficult detection scenarios are associated with fissile material assessments for 239Pu and other actinides and these analyses have almost universally been calibrated to an equivalent 3He response. In these instances, a “simple” detector or material addition approach is neither appropriate nor possible, due to influences resulting from the complex nature of neutron scattering in moderators, cross sections, gas pressure variations, geometries, and surrounding structural interference. These more challenging detection cases require a detailed computational transport analysis be performed for each specific application. A leveraged approach using adjoint transport computations that are validated by forward transport and Monte Carlo computations and laboratory measurements can address these more complex detection cases and this methodology was utilized in the execution of the research. The initial task was to establish the fidelity of a computational approach by executing radiation transport models for existing BF3 and 3He tubes and then comparing the modeling results to laboratory measurements made using these identical devices. Both tubes were 19.6 cm in height, 1-inch in diameter, and operated at 1 and 4 atm pressure respectively. The models were processed using a combination of forward Monte Carlo and forward and adjoint 3-D discrete ordinates (SN) transport methods. The computer codes MCNP5 and PENTRAN were used for all calculations of a nickel-shielded plutonium-beryllium (PuBe) source term that provided a neutron output spectra equivalent to that of weapons-grade plutonium (WGPu). Once the computational design approach was validated, the adjoint SN method was used to iteratively identify six distinct plug-in models that matched the neutron spectral response and reaction rate of a 1-inch diameter 3He tube with a length of 10 cm and operating at 4 atm pressure. The equivalent designs consist of large singular tubes and dual tubes containing BF3 gas, 10B linings, and/or 10B-loaded polyvinyl toluene (PVT). The reaction rate for each plug-in design was also verified using forward PENTRAN and MCNP5 calculations. In addition to the equivalent designs, the adjoint method also yielded various insights into neutron detector design that can lead to additional designs using a combination of different detector materials such as BF3/10B-loaded PVT, 10B-lined tubes/10B-loaded PVT, etc.