A medição de vazão de escoamentos multifásicos é uma necessidade constante em diversas atividades industriais como exploração de óleo e gás, controle de linhas de transporte de vapor e monitoramento de sistemas de resfriamento de usinas nucleares. Dentre os meios disponíveis para a realização da medição de vazão mássica, os dispositivos de medição de pressão diferencial constituem um dos métodos mais simples, sendo sua construção, aplicação e operação em escoamentos monofásicos bem conhecidas e definidas por normas técnicas. No entanto, sua aplicação tem sido estendida a escoamentos multifásicos, geralmente estando aliada a uma técnica adicional de medição de fração de vazio ou fração volumétrica das fases. Este trabalho descreve o estudo numérico de escoamentos multifásicos através de medidores de vazão baseados em pressão diferencial como placas de orifício e bocais de vazão de raio longo. Para tal, primeiramente foram conduzidas simulações de escoamentos monofásicos através de placas de orifício e bocais de vazão de raio longo na faixa de número de Reynolds 15.000 500.000. Os resultados de coeficiente de descarga obtidos foram quantitativamente comparados com os valores preditos por norma ISO, apresentando desvio máximo de aproximadamente 4, 9% para as placas e de 1,0% para os bocais. Em uma segunda etapa, escoamentos do tipo gás úmido (wet gas) através de placas de orifício foram simulados através de três abordagens diferentes. Os resultados de vazão mássica total obtidos foram comparados com dados experimentais fornecidos pela PETROBRAS. As abordagens que consideram o escorregamento entre as fases apresentaram previsões mais próximas dos experimentos, com desvio relativo médio de 3,9%, enquanto a modelagem homogênea apresentou um desvio médio de 6, 6%. Nestes estudos, foram também avaliadas as estruturas desenvolvidas no escoamento através de visualizações da distribuição de fases. São também apresentadas duas sugestões para complementação da caracterização de um escoamento multifásico: (1) a introdução da informação de fração de vazio na formulação apresentada por Paz (2011) e (2) a análise estatística do sinal de pressão diferencial em placas de orifício. Com relação ao primeiro item, comparações quantitativas com dados experimentais sugeriram que a alternativa apresentada é viável para operações de monitoramento da produção. Já o último estudo mostrou qualitativamente a influência da quantidade de líquido na flutuação da pressão diferencial / The flowrate measurement of multiphase flows is a constant need at many industrial activities such as oil and gas exploration, steam transport lines control and monitoring of nuclear plants cooling systems. Within the available means for performing flowrate measurement, the differential pressure devices constitute one of the simplest methods, with their construction, application and operation in single phase flows being well known and defined by technical standards. However, their application has been extended to multiphase flows, usually being allied to a void fraction or phase volume fraction measurement technique. This work describes a numerical study of multiphase flows through differential pressure-based flowrate meters such as orifice plates and long radius nozzles. Firstly simulations of single phase flows through orifice plates and long radius nozzles were conducted in the Reynolds number range 15.000500.000. The obtained results of discharge coefficients were quantitatively compared to ISO Standard predicted values, showing a maximum deviation of approximately 4,9% for the orifice plates and of 1,0% for the nozzles. In a second stage, wet gas flows through orifice plates were simulated by means of three approaches. The calculated results of total mass flowrate were compared to experimental data provided by PETROBRAS. The approaches that considered the slip between phases provided the closest results to the experiments, with a mean relative error of 3, 9%, while the homogeneous modeling presented an error of 6, 6%. In these studies, the structures developed within the domain were also evaluated through the visualization of the phases distribution. Two suggestions for complementing the characterization of a multiphase flow are presented: (1) the introduction of void fraction information into the formulation presented by Paz (2011) and (2) the statistical analysis of the orifice plate pressure drop signal. Regarding the first item, quantitative comparison with experimental data suggested that the presented alternative is viable for production monitoring operations. The last study qualitatively revealed the influence of the liquid loading in the pressure drop fluctuation.

Esta tese apresenta um modelo matemático para simulação numérica do escoamento com turbilhonamento (swirl) em tochas de plasma térmico de arco não transferido que operam em corrente contínua, assim como os resultados obtidos com as simulações para estudo de casos. O modelo magneto-hidrodinâmico (modelo MHD) bidimensional permitiu simular a interação entre o escoamento e o arco elétrico usando uma configuração axissimétrica, que abrange as seguintes regiões: entrada do gás; interior da tocha; jato de plasma livre no ambiente. O modelo foi implementado num código numérico baseado no Método dos Volumes Finitos para a solução numérica das equações governantes. Para os estudos foram simulados casos com diferentes condições operacionais (vazão de gás; intensidade de corrente elétrica; gases plasmogênicos: ar e argônio; intensidade de turbilhonamento). A fim de verificar a qualidade do modelo, alguns resultados foram comparados com a literatura e apresentaram boa concordância: a maior diferença obtida entre valores de temperatura experimentais e valores calculados foi -10%, e a média das diferenças obtidas nas comparações foi de aproximadamente ±3,2%. Os perfis de temperatura e de velocidade obtidos para a região do arco e para o jato de plasma resultante permitiram o estudo do comportamento do escoamento na tocha de plasma em diferentes condições. Conclui-se que o modelo desenvolvido é apto à realização de investigações numéricas do escoamento em tochas de plasma e dos efeitos do turbilhonamento na interação arco/escoamento. / This thesis presents a mathematical model for numerical simulation of swirling flow in DC non-transferred arc thermal plasma torches, as well as the results obtained from simulations to case studies. The two-dimensional magnetohydrodynamic model (MHD model) allowed simulate the interaction between the flow and the electric arc using an axisymmetric configuration, covering the following areas: gas inlet; inside the torch; free jet of plasma in the environment. The model was implemented in a computer code based on the Finite Volume Method (FVM) to enable the numerical solution of the governing equations. For the study, cases were simulated with different operating conditions (gas flow rate; electric current intensity; plasmogenic gases: air and argon; swirl intensity). In order to verify the quality of the model, some results were compared with the literature and showed good agreement: the biggest difference between experimental temperature values and calculated values was 10%, and the average of the differences obtained in the comparisons was approximately ±3.2%. The resulting profiles of temperature and velocity obtained for the region of the arc and the plasma jet allowed the study of the flow behavior in the plasma torch in different conditions. It is concluded that the model developed is able to carry out numerical investigations of the flow in plasma torches and the effects of swirl in the interaction arc/flow.

A medição de vazão de escoamentos multifásicos é uma necessidade constante em diversas atividades industriais como exploração de óleo e gás, controle de linhas de transporte de vapor e monitoramento de sistemas de resfriamento de usinas nucleares. Dentre os meios disponíveis para a realização da medição de vazão mássica, os dispositivos de medição de pressão diferencial constituem um dos métodos mais simples, sendo sua construção, aplicação e operação em escoamentos monofásicos bem conhecidas e definidas por normas técnicas. No entanto, sua aplicação tem sido estendida a escoamentos multifásicos, geralmente estando aliada a uma técnica adicional de medição de fração de vazio ou fração volumétrica das fases. Este trabalho descreve o estudo numérico de escoamentos multifásicos através de medidores de vazão baseados em pressão diferencial como placas de orifício e bocais de vazão de raio longo. Para tal, primeiramente foram conduzidas simulações de escoamentos monofásicos através de placas de orifício e bocais de vazão de raio longo na faixa de número de Reynolds 15.000 500.000. Os resultados de coeficiente de descarga obtidos foram quantitativamente comparados com os valores preditos por norma ISO, apresentando desvio máximo de aproximadamente 4, 9% para as placas e de 1,0% para os bocais. Em uma segunda etapa, escoamentos do tipo gás úmido (wet gas) através de placas de orifício foram simulados através de três abordagens diferentes. Os resultados de vazão mássica total obtidos foram comparados com dados experimentais fornecidos pela PETROBRAS. As abordagens que consideram o escorregamento entre as fases apresentaram previsões mais próximas dos experimentos, com desvio relativo médio de 3,9%, enquanto a modelagem homogênea apresentou um desvio médio de 6, 6%. Nestes estudos, foram também avaliadas as estruturas desenvolvidas no escoamento através de visualizações da distribuição de fases. São também apresentadas duas sugestões para complementação da caracterização de um escoamento multifásico: (1) a introdução da informação de fração de vazio na formulação apresentada por Paz (2011) e (2) a análise estatística do sinal de pressão diferencial em placas de orifício. Com relação ao primeiro item, comparações quantitativas com dados experimentais sugeriram que a alternativa apresentada é viável para operações de monitoramento da produção. Já o último estudo mostrou qualitativamente a influência da quantidade de líquido na flutuação da pressão diferencial / The flowrate measurement of multiphase flows is a constant need at many industrial activities such as oil and gas exploration, steam transport lines control and monitoring of nuclear plants cooling systems. Within the available means for performing flowrate measurement, the differential pressure devices constitute one of the simplest methods, with their construction, application and operation in single phase flows being well known and defined by technical standards. However, their application has been extended to multiphase flows, usually being allied to a void fraction or phase volume fraction measurement technique. This work describes a numerical study of multiphase flows through differential pressure-based flowrate meters such as orifice plates and long radius nozzles. Firstly simulations of single phase flows through orifice plates and long radius nozzles were conducted in the Reynolds number range 15.000500.000. The obtained results of discharge coefficients were quantitatively compared to ISO Standard predicted values, showing a maximum deviation of approximately 4,9% for the orifice plates and of 1,0% for the nozzles. In a second stage, wet gas flows through orifice plates were simulated by means of three approaches. The calculated results of total mass flowrate were compared to experimental data provided by PETROBRAS. The approaches that considered the slip between phases provided the closest results to the experiments, with a mean relative error of 3, 9%, while the homogeneous modeling presented an error of 6, 6%. In these studies, the structures developed within the domain were also evaluated through the visualization of the phases distribution. Two suggestions for complementing the characterization of a multiphase flow are presented: (1) the introduction of void fraction information into the formulation presented by Paz (2011) and (2) the statistical analysis of the orifice plate pressure drop signal. Regarding the first item, quantitative comparison with experimental data suggested that the presented alternative is viable for production monitoring operations. The last study qualitatively revealed the influence of the liquid loading in the pressure drop fluctuation.

Large-eddy simulation (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) calculations have been performed to investigate the effects of different mathematical models for scalar variance and its dissipation rate as applied to both a non-reacting bluff-body turbulent flow and an extension to a reacting case. In the conserved scalar formalism, the mean value of a thermo-chemical variable is obtained through the PDF-weighted integration of the local description over the conserved scalar, the mixture fraction. The scalar variance, one of the key parameters for the determination of a presumed β-function PDF, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modelled using either an algebraic expression or a transport equation. The proposed approach is first applied to URANS and then extended to LES. Velocity, length and time scales associated with the URANS modelling are determined using the standard two-equation k-ε transport model. In contrast, all three scales required by the LES modelling are based on the Smagorinsky subgrid scale (SGS) algebraic model. The present study proposes a new algebraic and a new transport LES model for the scalar dissipation rate required by the transport equation for scalar variance, with a time scale consistent with the Smagorinsky SGS model.

A three dimensional, Navier-Stokes finite volume flow solver which uses Roe&rsquo / s upwind flux differencing scheme for spatial and Runge-Kutta explicit multi-stage time stepping scheme and implicit Lower-Upper Symmetric Gauss Seidel (LU-SGS) iteration scheme for temporal discretization on unstructured and hybrid meshes is developed for steady rocket internal viscous flow applications. The spatial accuracy of the solver can be selected as first or second order. Second order accuracy is achieved by piecewise linear reconstruction. Gradients of flow variables required for piecewise linear reconstruction are calculated with both Green-Gauss and Least-Squares approaches. The solver developed is first verified against the three-dimensional viscous laminar flow over flat plate. Then the implicit time stepping algorithms are compared against two rocket motor internal flow problems. Although the solver is intended for internal flows, a test case involving flow over an airfoil is also given. As the last test case, supersonic vortex flow between concentric circular arcs is selected.

This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.

Large-eddy simulation (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) calculations have been performed to investigate the effects of different mathematical models for scalar variance and its dissipation rate as applied to both a non-reacting bluff-body turbulent flow and an extension to a reacting case. In the conserved scalar formalism, the mean value of a thermo-chemical variable is obtained through the PDF-weighted integration of the local description over the conserved scalar, the mixture fraction. The scalar variance, one of the key parameters for the determination of a presumed β-function PDF, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modelled using either an algebraic expression or a transport equation. The proposed approach is first applied to URANS and then extended to LES. Velocity, length and time scales associated with the URANS modelling are determined using the standard two-equation k-ε transport model. In contrast, all three scales required by the LES modelling are based on the Smagorinsky subgrid scale (SGS) algebraic model. The present study proposes a new algebraic and a new transport LES model for the scalar dissipation rate required by the transport equation for scalar variance, with a time scale consistent with the Smagorinsky SGS model.

For turbulent flow calculations, some of the well-known turbulence models in the literature are applied on a previously developed Navier-Stokes solver designed to handle laminar flows. A finite volume formulation, which is cell-based for inviscid terms and cell-vertex for viscous terms, is used for numerical discretization of the Navier-Stokes equations in conservative form. This formulation is combined with one-step, explicit time marching Lax-Wendroff numerical scheme that is second order accurate in space. To minimize non-physical oscillations resulting from the numerical scheme, second and fourth order artificial smoothing terms are added. To increase the convergence rate of the solver, local time stepping technique is applied. Before applying turbulence models, Navier-Stokes solver is tested for a case of subsonic, laminar flow over a flat plate. The results are in close agreement with Blasius similarity solutions. To calculate turbulent flows, Boussinesq eddy-viscosity approach is utilized. The eddy viscosity (also called turbulent viscosity), which arises as a consequence of this approach, is calculated using Cebeci-Smith, Michel et. al., Baldwin-Lomax, Chien&rsquo / s k-epsilon and Wilcox&rsquo / s k-omega turbulence models. To evaluate the performances of these turbulence models and to compare them with each other, the solver has been tested for a case of subsonic, laminar - transition fixed - turbulent flow over a flat plate. The results are verified by analytical solutions and empirical correlations.

The aim of this study is to extend a parallel Fortran90 code to compute three&ndash / dimensional laminar and turbulent flowfields over rotary wing configurations. The code employs finite volume discretization and the compact, four step Runge-Kutta type time integration technique to solve unsteady, thin&ndash / layer Navier&ndash / Stokes equations. Zero&ndash / order Baldwin&ndash / Lomax turbulence model is utilized to model the turbulence for the computation of turbulent flowfields. A fine, viscous, H type structured grid is employed in the computations. To reduce the computational time and memory requirements parallel processing with distributed memory is used. The data communication among the processors is executed by using the MPI ( Message Passing Interface ) communication libraries. Laminar and turbulent solutions around a two bladed UH &ndash / 1 helicopter rotor and turbulent solution around a flat plate is obtained. For the rotary wing configurations, nonlifting and lifting rotor cases are handled seperately for subsonic and transonic blade tip speeds. The results are, generally, in good agreement with the experimental data.

Made available in DSpace on 2016-12-12T20:25:12Z (GMT). No. of bitstreams: 1 Maico Jeremias da Silva.pdf: 5502697 bytes, checksum: 292822b79334828b19d2d99087aae96b (MD5) Previous issue date: 2015-07-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work discusses the behaviour of the convection heat transfer coefficient in plane fins with variation of air flow velocity and fin spacing. The differential equation that governs heat transfer in fins is discretized by the finite volume method, which enables computation of the fin thermal characteristics, such as temperature distribution, heat transfer and fin efficiency. The determination of the convection coefficient, important parameter for thermal analysis, is performed by applying a heuristic optimization method, known as Particle Swarm Optimization, which combines data measured from experimental analysis conducted in wind tunnel with the aforementioned heat transfer numerical approximation of fins. / Este trabalho analisa os efeitos da velocidade do escoamento de ar e do espaçamento entre aletas no coeficiente de convecção forçada sobre as superfícies de aletas planas. As equações diferenciais que definem a transferência de calor em aletas são discretizadas pela técnica de volumes finitos possibilitando a determinação das características térmicas da aleta, tais como perfil de temperatura, calor transferido e eficiência térmica. A determinação do coeficiente de convecção, parâmetro fundamental para análises térmicas, é realizada mediante a aplicação de um método de otimização heurístico, conhecido como Método do Enxame de Partículas, que combina os dados obtidos da análise experimental realizada em túnel de vento com a aproximação numérica da troca de calor na aleta descrita acima