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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
441

Comparação numérica e experimental entre um ensaio de swirl estático e contí­nuo. / Numerical and experimental comparisons between static and continuous Swirl tests.

Cruciani, Eduardo Henrique 03 May 2019 (has links)
O presente trabalho tem como escopo validar qualitativa e quantitativamente o ensaio de swirl em cabeçotes de motores Diesel realizado de maneira contínua, comparando-o com o padrão estático amplamente aplicado na indústria no controle de qualidade deste componente. A modificação metodológica do ensaio permite ensaios muito mais velozes do que os atuais, podendo, com todas as verificações necessárias, ser extensível a uma linha de montagem, permitindo controle de qualidade diretamente após o processo de usinagem do fundido ou antes de montar o cabeçote no bloco do motor. O presente trabalho apresenta a metodologia aplicada para o tratamento do problema bem como os resultados obtidos até o momento, indicando também os que ainda serão obtidos. No escopo do projeto, apresenta-se de maneira sucinta todo o procedimento utilizado para as simulações estáticas e transiente dos métodos de medição a partir do método do volume finitos de um código comercial, destacando a metodologia para determinação das malhas, seleção dos modelos e esquemas de discretização utilizados, destacando por fim uma comparação entre diferentes aberturas de válvula do ensaio estático e os primeiros resultados da simulação com abertura de válvula ao longo do tempo de simulação. Do ponto de vista experimental, descreveu-se o equipamento utilizado bem como as adaptações realizadas, principalmente no que tangem a automação do controle de válvula, no escopo do presente projeto, apresentando por fim alguns resultados do ensaio contínuo na bancada em comparação com o estático. Os ensaios e simulações numéricas estática e transientes apresentaram coerência em seus resultados. As simulações, quando comparadas entre si e com os resultados do PIV, mostram que os perfis de escoamento são bastante parecidos em todas as situações, o que permite concluir que existe a possibilidade de se realizar o ensaio de swirl de forma dinâmica para esta configuração específica. / The present work aims to validate qualitatively and quantitatively the swirl test in diesel engine heads performed continuously, comparing it with the static standard widely applied in industry in the quality control of this component. The methodological modification of the test allows for tests much faster than the current ones and can be extensible to an assembly line, allowing quality control directly after the cast machining process or before mounting the engine block. The present work presents the applied methodology for the treatment of the problem as well as the results obtained so far, also indicating the ones that will be obtained. In the scope of the project, the whole procedure used for the static and transient simulations of the measurement methods based on the finite volume method of a commercial code is presented, highlighting the methodology for determining the meshes, selection of models and schemes of discretization. At last, a comparison between different valve openings of the static test and the first results of the simulation with valve opening during the simulation time will be presented. From the experimental point of view, the equipment used was described, as well as the adaptations made, mainly in what concerns the automation of valve control, within the scope of the present project. Some results of the continuous test in the bench are presented and compared with the static ones. The static and dynamic tests and simulations presented good coherence among their results. The simulations, when compared one with each other and to the PIV test results, showed great similarities among the in-cylinder flow velocity profiles, what might lead to the conclusion that it is possible to test cylinder heads dynamically, at least with the presented configuration.
442

Computational Fluid Dynamics Simulations of Radial Dispersion in Low N Fixed Bed Reactors

Medeiros, Nicholas J 20 April 2015 (has links)
Fixed bed reactors are widely applicable in a range of chemical process industries. Their ease of use and simplified operation make them an attractive and preferred option in reactor selection, however the geometric complexities within the bed as a result of the unstructured packing has made the design of such beds historically based on pseudo-homogenous models together with correlation-based transport parameters. Low tube-to-particle diameter ratio (N) beds, in particular, are selected for highly exothermic or endothermic reactions, such as in methane steam reforming or alkane dehydrogenation. Due to the large fraction of tube to catalyst particle contact in these low N beds, wall effects induce a mass transfer boundary layer at the wall, and in the case of thermal beds, a simultaneous resistance to heat transfer. Computational Fluid Dynamics (CFD) has been shown to be an accurate tool for experimental validation and predictive analysis of packed beds, and may be used to derive more accurate design parameters for fixed bed reactors. More specifically, the elucidation of dispersion, or the transport of reactant and product within the bed due to molecular diffusion and convective flow is of fundamental interest to the design of fixed beds. Computational Fluid Dynamics was used in this research to study solute dispersion in eight beds of varying N at a range of particle Reynolds numbers in the laminar flow regime. In the first stage of research, flow development was simulated in three-dimensional packed beds of spheres. Then, the reactor wall was sectioned to include a boundary condition of pure methane, from which the solute could laterally disperse into the bed. In the second stage, a two-dimensional representation of the bed was created using the commercial Finite Element Analysis software COMSOL Multiphysics. In these models, axial velocity profiles and radial methane concentration profiles taken from the 3-D models were supplied, and a fitting procedure by use of the Levenberg-Marquardt Least-Squares optimization algorithm was completed to fit radial dispersion coefficients and near-wall mass transfer coefficients to the CFD data. These optimization runs were conducted for all N at a number of bed depths in each case. Two sub-studies were conducted in which a constant velocity profile and a local velocity profile were supplied to the 2-D model, and the optimization re-run. It was found that this two parameter model did not fully account for various mechanisms of dispersion in the bed, namely the increasing rate of dispersion from the tube wall boundary layer up to the bed center, but only accounted for a diffusive-dispersion at the wall and a constant-rate, convective-dispersion everywhere else in the bed. Length dependency of dispersion coefficients were also noted, particularly in the developing sections of the bed. Nevertheless, the combined CFD and optimization procedure proved to be an accurate and time-efficient procedure for the derivation of dispersion coefficients, which may then lend themselves to the standard design of packed bed reactors.
443

Computational Fluid Dynamics Simulations of Radial Dispersion in Low N Fixed Bed Reactors

Medeiros, Nicholas J 20 April 2015 (has links)
Fixed bed reactors are widely applicable in a range of chemical process industries. Their ease of use and simplified operation make them an attractive and preferred option in reactor selection, however the geometric complexities within the bed as a result of the unstructured packing has made the design of such beds historically based on pseudo-homogenous models together with correlation-based transport parameters. Low tube-to-particle diameter ratio (N) beds, in particular, are selected for highly exothermic or endothermic reactions, such as in methane steam reforming or alkane dehydrogenation. Due to the large fraction of tube to catalyst particle contact in these low N beds, wall effects induce a mass transfer boundary layer at the wall, and in the case of thermal beds, a simultaneous resistance to heat transfer. Computational Fluid Dynamics (CFD) has been shown to be an accurate tool for experimental validation and predictive analysis of packed beds, and may be used to derive more accurate design parameters for fixed bed reactors. More specifically, the elucidation of dispersion, or the transport of reactant and product within the bed due to molecular diffusion and convective flow is of fundamental interest to the design of fixed beds. Computational Fluid Dynamics was used in this research to study solute dispersion in eight beds of varying N at a range of particle Reynolds numbers in the laminar flow regime. In the first stage of research, flow development was simulated in three-dimensional packed beds of spheres. Then, the reactor wall was sectioned to include a boundary condition of pure methane, from which the solute could laterally disperse into the bed. In the second stage, a two-dimensional representation of the bed was created using the commercial Finite Element Analysis software COMSOL Multiphysics. In these models, axial velocity profiles and radial methane concentration profiles taken from the 3-D models were supplied, and a fitting procedure by use of the Levenberg-Marquardt Least-Squares optimization algorithm was completed to fit radial dispersion coefficients and near-wall mass transfer coefficients to the CFD data. These optimization runs were conducted for all N at a number of bed depths in each case. Two sub-studies were conducted in which a constant velocity profile and a local velocity profile were supplied to the 2-D model, and the optimization re-run. It was found that this two parameter model did not fully account for various mechanisms of dispersion in the bed, namely the increasing rate of dispersion from the tube wall boundary layer up to the bed center, but only accounted for a diffusive-dispersion at the wall and a constant-rate, convective-dispersion everywhere else in the bed. Length dependency of dispersion coefficients were also noted, particularly in the developing sections of the bed. Nevertheless, the combined CFD and optimization procedure proved to be an accurate and time-efficient procedure for the derivation of dispersion coefficients, which may then lend themselves to the standard design of packed bed reactors.
444

Studies on Aboveground Storgae Tanks Subjeected to Wind Loading: Static, Dynamic, and Computational Fluid Dynamics Analyses

Yen-Chen Chiang (6620447) 14 May 2019 (has links)
<p>Due to the slender geometries of aboveground storage tanks, maintaining the stability under wind gusts of these tanks has always been a challenge. Therefore, this thesis aims to provide a through insight on the behavior of tanks under wind gusts using finite element analysis and computational fluid dynamic (CFD) analysis. The present thesis is composed of three independent studies, and different types of analysis were conducted. In Chapter 2, the main purpose is to model the wind loading dynamically and to investigate whether a resonance can be triggered. Research on tanks subjected to static wind load have thrived for decades, while only few studies consider the wind loading dynamically. Five tanks with different height (<i>H</i>) to diameter (<i>D</i>) ratios, ranging from 0.2 to 4, were investigated in this chapter. To ensure the quality of the obtained solution, a study on the time step increment of an explicit dynamic analysis, and a on the mesh convergence were conducted before the analyses were performed. The natural vibration frequencies and the effective masses of the selected tanks were first solved. Then, the tanks were loaded with wind gusts with the magnitude of the pressure fluctuating at the frequency associating with the most effective mass and other frequencies. Moreover, tanks with eigen-affine imperfections were also considered. It was concluded that resonance was not observed in any of these analyses. However, since the static buckling capacity and the dynamic buckling capacity has a relatively large difference for tall tanks (<i>H</i>/<i>D </i>≥ 2.0), a proper safety factor shall be included during the design if a static analysis is adopted. </p> <p> </p> <p>Chapter 3 focus on the effect of an internal pressure generated by wind gusts on open-top tanks. Based on boundary layer wind tunnel tests (BLWT), a significant pressure would be generated on the internal side of the tank shell when a gust of wind blow through an open-top tank. This factor so far has not been sufficiently accounted for by either ASCE-7 or API 650, despite the fact that this internal pressure may almost double the design pressure. Therefore, to investigate the effect of the wind profile along with the internal pressure, multiple wind profiles specified in different design documents were considered. The buckling capacities of six tanks with aspect ratios (<i>H</i>/<i>D</i>) ranging from 0.1 to 4 were analyzed adopting geometrically nonlinear analysis with imperfection using an arc-length algorithm (Riks analysis). Material nonlinearity was also included in some analyses. It was observed that the buckling capacity of a tank obtained using ASCE-7/API 650 wind profile is higher than buckling capacities obtained through any other profiles. It was then concluded that the wind profile dictated by the current North American design documents may not be conservative enough and may need a revision. </p> <p> </p> <p>Chapter 4 investigates how CFD can be applied to obtain the wind pressure distribution on tanks. Though CFD has been widely employed in different research areas, to the author’s best knowledge, only one research has been dedicated to investigate the interaction between wind gusts and tanks using CFD. Thus, a literature review on the guideline of selecting input parameter for CFD and a parametric study as how to choose proper input parameters was presented in Chapter 4. A tank with an aspect ratio of 0.5 and a flat roof was employed for the parametric study. To ensure the validity of the input parameters, the obtained results were compared with published BLWT results. After confirming that the selected input parameters produces acceptable results, tanks with aspect ratio ranging from 0.4 to 2 were adopted and wind pressure distribution on such tanks were reported. It was concluded that the established criteria for deciding the input parameters were able to guarantee converged results, and the obtained pressure coefficients agree well with the BLWT results available in the literature. </p>
445

Experimental and Numerical Investigations of Wind-Induced Effects on Ground-Mounted Solar Panels at the WDS Facility

Massaad, Charly 25 June 2019 (has links)
The usage of ground-mounted photovoltaic solar panels is increasing, and it is essential to fully understand the wind behavior and loading on the panels, since there is no specific code or guideline for their design in the present. In addition, the University of Ottawa and Carleton University recently developed a new facility, called the Wind Damage Simulator (WDS). This study will allow to understand the flow behavior in the facility, along with the effects of different blower rpm settings on the flow. A CFD study was also conducted, in order to examine the methodology and turbulence models suitable for the flow replicated in this facility, for future research. The newly developed Wind Damage Simulator (WDS) facility was used to examine wind-induced effects on two solar panels attached to a frame. The mean pressure coefficient distribution on the photovoltaic panels was examined for several wind angles of incidence (AOI) and wind speeds. The wind AOI considered were the 0°, 30°, 45°, 180°, 210° and 225°, along with wind speeds ranging from 14 m/s to 42 m/s, with increments of around 2 m/s. The experimental results showed fluctuations in the Cp distribution on the panels, due to the WDS wind flow being highly unstable. The 180° wind AOI led to the highest uplift mean Cp equivalent (Cpeq) value on the panels. The 45° and 180° wind AOI were found to induce a Cpeq of significantly higher magnitude on the first panel compared to the second panel, whereas the 0° and 210° wind AOI induced a significantly higher Cpeq magnitude on the second panel compared to the first panel Cpeq. Moreover, the CFD study provided pressure coefficient distribution on the panels and flow visualization when interacting with the panels surfaces. The LES Dynamic Smagorinsky subgrid scale model was found to be more suitable for the WDS numerical replication than the RANS shear stress transport k-ω turbulence model. The LES model showed the fluctuating pressure coefficients on the panels’ surfaces, induced by the swirls that were formed post interaction of the wind with the panels.
446

Wind effect on super-tall buildings using computational fluid dynamics and structural dynamics

Unknown Date (has links)
Super-tall buildings located in high velocity wind regions are highly vulnerable to large lateral loads. Designing for these structures must be done with great engineering judgment by structural professionals. Present methods of evaluating these loads are typically by the use of American Society of Civil Engineers 7-10 standard, field measurements or scaled wind tunnel models. With the rise of high performance computing nodes, an emerging method based on the numerical approach of Computational Fluid Dynamics has created an additional layer of analysis and loading prediction alternative to conventional methods. The present document uses turbulence modeling and numerical algorithms by means of Reynolds-averaged Navier-Stokes and Large Eddy Simulation equations applied to a square prismatic prototype structure in which its dynamic properties have also been investigated. With proper modeling of the atmospheric boundary layer flow, these numerical techniques reveal important aerodynamic properties and enhance flow visualization to structural engineers in a virtual environment. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2015. / FAU Electronic Theses and Dissertations Collection
447

Estudo numérico do escoamento ao redor de cilindros alinhados. / Numerical investigation of the flow around two circular cylinders in tandem.

Carmo, Bruno Souza 20 May 2005 (has links)
Este trabalho lida com o escoamento incompressível ao redor de pares de cilindros rígidos e imóveis, posicionados de forma alinhada em relação a uma corrente uniforme. São dois os objetivos desta pesquisa: o primeiro é estabelecer relações de causalidade entre características físicas do escoamento e as mudanças observadas nas forças e no campo fluido com as variações do número de Reynolds (Re) e do espaçamento entre os corpos; e o segundo consiste em compreender a influência mútua entre tridimensionalidades e interferência no escoamento. Utilizou-se o método de elementos espectrais para realizar simulações bi e tridimensionais do escoamento. Os espaçamentos entre centros (lcc) analisados vão de 1,5 a 8 diâmetros, e eles são comparados com o caso de um cilindro isolado. A faixa de Re vai de 160 a 320, compreendendo a transição na esteira. O foco foi dado nas instabilidades de pequena escala (modos A e B). Dados referentes ao número de Strouhal, coeficiente de arrasto médio, flutuação do coeficiente de sustentação e correlação axial são apresentados. Com auxílio de visualizações do escoamento, são propostos mecanismos que explicam o fenômeno de interferência, refletido no comportamento das curvas. Os resultados mostraram que simulações bidimensionais são insuficientes para se prever a combinação (Re, lcc) de inversão do arrasto. Verificou-se também que, quando o espaçamento é menor do que o crítico, o processo de transição na esteira se dá de forma diferente do observado para um cilindro isolado. / This work deals with the incompressible flow around pairs of rigid and immovable circular cylinders in tandem arrangements. There are two goals in this research: the first one is to find causality relationships between physical characteristics of the flow and the changes that are observed in the forces and in the flow field with the variation of the Reynolds number (Re) and the distance between the bodies; and the second one is to comprehend the mutual influence between three-dimensional structures and interference. The spectral element method was employed to carry out two- and three-dimensional simulations of the flow. The centre-to-centre distance (lcc) of the investigated configurations varies between 1.5 and 8 diameters, and they are compared to the isolated cylinder case. The Re range goes from 160 to 320, covering the transition in the wake. We focused in the small scale instabilities (modes A and B). Data of Strouhal number, mean drag coefficient, RMS of the lift coefficient and axial correlation are presented. With aid of flow visualizations, we propose mechanisms to explain the interference phenomenon, which is reflected in the behaviour of the graphics. The results show that two-dimensional simulations are not sufficient to predict the (Re, lcc) pair correspondent to the drag inversion point. We also verified that, in the cases where lcc is lower than the critical spacing, the transition in the wake happens in a way different from the one observed in the flow around a single cylinder.
448

Simulação numérica do escoamento em um túnel de cavitação. / Numerical simulation of flow in a cavitation tunnel.

Silva, Angelo Augusto Negrão da 25 May 2015 (has links)
A presente dissertação investiga o comportamento do escoamento em um túnel de cavitação, através de simulações fluido-dinâmicas computacionais, excluindo a bomba de circulação. Para tanto um extenso estudo buscou selecionar a abordagem numérica e configurações de simulação mais adequadas, de uma forma a reproduzir as características hidrodinâmica inerentes à operação do túnel. Portanto, as informações referentes à perda de carga, uniformidade no perfil de velocidade, tendência de cavitação, descolamento e altura da camada limite foram apreciadas. Esse estudo foi direcionado por dados provenientes de métodos empíricos da literatura, resultados experimentais do próprio túnel pesquisado e de outros túneis. Em geral, os resultados foram satisfatórios, pois a perda de carga estimada foi semelhante ao obtido experimentalmente. Além de serem identificados os trechos com efeito desfavorável na uniformidade do escoamento, foram determinadas a distribuição de pressão nas aletas e o perfil de velocidade incidente na bomba. / This study deals with a cavitation tunnel flow (except the pump region) through computational fluid dynamic simulations. Therefore, previously one made a literature survey to aid the selection of the most appropriate techniques and simulation settings to simulate the hydrodynamic characteristics of the tunnel. The pressure drop, uniformity of the velocity profile, existence of cavitation, detachment and height of the boundary layer were evaluated. This study used empirical methods and also experimental results. The results were satisfactory, as long as the estimated pressure drop was close to the one obtained experimentally. In addition, it was forecasted low flow uniformity in some parts of the tunnel, the pressure distribution on the fins and the incident velocity profile at the pump.
449

Modelagem do escoamento em reator catalítico de membrana cerâmica para hidrogenação parcial trifásica. / Modeling flow in ceramic catalytic membrane reactor for partial three-phase hydrogenation.

Costa, Isis Santos 25 November 2011 (has links)
No presente trabalho, foi desenvolvido um modelo para o escoamento em reator de membrana do tipo contator ativo, através da abordagem de dinâmica dos fluidos computacional (CFD), utilizando o código comercial ANSYS FLUENT. O modelo incluiu todo o módulo de membrana constituído por uma membrana tubular e um casco metálico. A reação modelo estudada foi a hidrogenação parcial de 1,5-ciclooctadieno, realizada pelo bombeamento da mistura reacional, dissolvida em n-heptano, através da membrana, a partir das extremidades do tubo. Como catalisador, considerou-se a presença de nanopartículas de Pd impregnadas na membrana. O meio poroso foi aproximado por leito granular representado pela equação de Ergun, tendo como parâmetros a porosidade e o tamanho de grão da membrana de alfa-Al2O3 . O valor para o tamanho de grão foi adotado como equivalente ao diâmetro de partícula determinado com uso do código aberto de estereologia ImageJ, do instituto Nacional de Saúde dos Estados Unidos. O modelo de turbulência adotado foi o RNG k-epsilon. Um estudo de sensibilidade incluiu simulações comparando escoamento desprezando reações como escoamento reativo, variação da velocidade, alteração da saída do fluxo e ativação de modelo de turbulência no meio poroso. Foram realizadas simulações de defeitos estruturais na membrana, correspondendo a regiões de porosidade alterada, com e sem perda de sua uniformidade azimutal. Conclui-se que a presença de defeitos estruturais que afetem a uniformidade azimutal da membrana pode resultar em sensível alteração do escoamento em CMRs. / This study focused on the development of a model for the flow in a reactor membrane of the type active contactor, approached through computational fluid dynamics (CFD), using the commercial code ANSYS FLUENT. The model included the entire membrane module, consisted of a tubular membrane and a metal shell. The model reaction studied was the partial hydrogenation of 1,5-cyclooctadiene initiated by the pumping of the reaction mixture, dissolved in n-heptane, through the membrane, from the ends of the tube. As a catalyst, the study considered the presence of impregnated Pd nanoparticles in the membrane. The porous medium was approximated by a granular bed as represented by the Ergun equation, having as parameters the porosity and the grain size of the alfa-Al2O3 membrane. The value for the grain size was adopted as equivalent to particle diameter determined through the open source stereology software ImageJ, of the National Institute of Health USA. The turbulence model used was the RNG k-epsilon. A sensitivity study included simulations of flow neglecting and including reactions, speed variation, change the flow outlet and activation of turbulence model in the porous media. Simulations of structural defects in the membrane were performed, defining regions of porosity changes with and without loss of azimuthal uniformity. The conclusion was that the presence of structural defects that affect the azimuthal uniformity of the membrane can result in marked alteration of the flow regime in CMRs.
450

Mecânica dos fluidos computacional integrada com modelo térmico do corpo humano para análise de ambientes térmicos. / Integration of computational fluid dynamics with human body thermal model for thermal environment analysis.

Castelli, Fábio Alexandre 22 October 2012 (has links)
Neste trabalho é proposta uma metodologia numérica como ferramenta para avaliação de ambientes térmicos com manequins. A simulação de CFD do ambiente térmico em simulador comercial é integrada à simulação do sistema térmico do corpo humano realizada em código acadêmico. As soluções dos fluxos de calor e temperaturas nas peles são retroalimentadas e a transferência de informações é realizada via arquivo. A geometria do ambiente térmico é simplificada para minimizar os efeitos de problemas com a malha computacional na simulação de CFD, permitindo uma melhor análise do método interativo proposto. O manequim é separado em 15 segmentos cilíndricos representando cabeça, pescoço, tronco, braços, antebraços, mãos, coxas, pernas e pés. Cada segmento é subdividido em quatro quadrantes, totalizando 60 zonas, para capturar assimetrias térmicas e aerodinâmicas. Foi conduzido estudo de validação geométrica de manequim virtual pela comparação de resultados dos coeficientes térmicos obtidos com CFD e resultados obtidos de ensaios experimentais da literatura. A qualidade da malha e o tratamento de parede são discutidos. Os resultados tornam evidente que uma geometria simplificada do manequim é suficiente para estudos e avaliações de ambiente térmico e de conforto térmico quando se utiliza técnicas numéricas de CFD. Os resultados a partir da integração dos simuladores mostram que o método numérico pode ser instável nos segmentos com baixo metabolismo e baixa vazão de sangue, como nos pés e mãos. Pretende-se introduzir na metodologia proposta algum mecanismo que identifique automaticamente este fenômeno, para evitar a divergência do método e tornar a ferramenta mais robusta. / In this work is proposed a new numerical methodology as a tool for thermal comfort evaluation. This method promotes the interaction of the thermal environment simulation and the thermal system of the human body simulation. The commercial CFD simulator FLUENT R and an academician code for human body simulation are used. The solutions are fed back and the transfer is made by file. The geometry of the room is simplified to minimize the effects of problems with the computational mesh in the CFD simulation, allowing a better analysis of the proposed interactive method. The dummy is separated into 15 cylindrical segments representing head, neck, trunk, arms, forearms, hands, thighs, legs and feet. Each segment is subdivided into four quadrants, totaling 60 zones, to capture asymmetries in the heat flux field and temperature field. Was conducted a geometric validation of virtual dummy by comparing results of heat transfer coefficients from literature and CFD simulation. The mesh quality and near wall treatment are discussed. The results show that a simplified geometry of the dummy is sufficient for thermal environment studies and evaluations in CFD simulations. The results from coupled simulations show that the numerical method can be unstable in the segments with low metabolism and low blood flow, as the feet and hands. So, its intended to introduce mechanisms in the methodology to automatically identify this phenomenon and to avoid the divergence of the method to make more robust this methodology.

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