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.

Submitted by Dilene Paulo (dilene.fatima@ufcg.edu.br) on 2018-02-07T13:41:46Z No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5) / Made available in DSpace on 2018-02-07T13:41:46Z (GMT). No. of bitstreams: 1 VERA SOLANGE DE OLIVEIRA FARIAS – TESE PPGEP 2011.pdf: 7179434 bytes, checksum: 4a30c9a95f4a089e00fa550fbf1b42b8 (MD5) Previous issue date: 2011-04-29 / CNPq / Este trabalho apresenta a solução numérica da equação de difusão tridimensional em regime transiente, para um domínio arbitrário. Para atingir os objetivos, a equação de difusão foi discretizada usando coordenadas generalizadas via método dos volumes finitos com uma formulação totalmente implícita, para condições de contorno de equilíbrio e convectiva. Para cada passo no tempo, o sistema de equações obtido para uma dada malha estruturada foi resolvido pelo método de Gauss-Seidel. O código computacional foi desenvolvido em FORTRAN, usando o estúdio CVF 6.6.0, na plataforma Windows Vista. A solução proposta foi validada usando soluções analíticas e numéricas da equação de difusão para várias geometrias, permitindo validar malhas ortogonais e não-ortogonais. A análise e comparação dos resultados mostraram que a solução proposta forneceu resultados coerentes para todos os casos investigados. O código computacional desenvolvido foi aplicado na simulação, a partir de dados experimentais da secagem de telhas cerâmicas para as seguintes condições experimentais: temperaturas de 55,6 °C, 69,7 °C, 82,7 °C e 98,6 °C e teor de umidade inicial variando de 0,2345 até 0,2405 (b.s.). A simulação tornou possível determinar o coeficiente de difusão efetivo em função da razão de umidade e da temperatura do ar de secagem e também o valor do coeficiente de transferência convectivo de massa correspondente para cada temperatura. / This work presents a three-dimensional numerical solution for the diffusion equation in transient state, in an arbitrary domain. The diffusion equation was discretized using the finite volume method with a fully implicit formulation and generalized coordinates, for the equilibrium and convective boundary condition. For each time step, the system of equations obtained for a given structured mesh was solved by the Gauss-Seidel method. A computational code in FORTRAN, using the CFV 6.6.0 Studio, in a Windows Vista platform was developed. The proposed solution was validated by analytical and numerical solutions of the diffusion equation for several geometries. The geometries tested enabled to validate both orthogonal and non-orthogonal meshes. The analysis and comparison of the results showed that the proposed solution provides correct results for all cases investigated. The developed computational code was applied in the simulation, using experimental data of the drying of ceramic roof tiles, for the following experimental conditions: temperature from 55.6; 69.7; 82.7; 72.8 and 98.7 °C, initial moisture content from 0.2345 up to 0.2405 (d.b.). The simulation makes it possible to determine an expression for the diffusion coefficient as a function of the moisture content and temperature of the drying air, and also the value of the convective mass transfer coefficient corresponding to each temperature.

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

Ce travail est une contribution à la simulation numérique d'écoulements turbulents autour de corps non profilés. Après avoir précisé les ingrédients numériques et les modèles de turbulence utilisés dans nos simulations, nous présentons une étude sur l'évaluation des effets de la procédure dynamique des modèles de sous-maille dans un modèle VMS-LES et une approche hybride RANS/VMS-LES. Des problèmes d'écoulements autour d'un cylindre seul et en tandem sont considérés. Nous étudions ensuite le comportement de modèles de turbulence hybrides pour la simulation d'écoulements en régime sous-critique autour d'un cylindre circulaire. Le calcul de l'écoulement autour d'un cylindre de section rectangulaire par l'approche VMS-LES est aussi présenté. Enfin, dans une dernière partie, après avoir fait une revue des travaux importants sur les schémas d'avancement en temps multirate, nous proposons une nouvelle approche explicite multirate par agglomération de volumes finis que nous appliquons à des calculs d'écoulements turbulents complexes en utilisant un modèle de turbulence hybride. / This work is a contribution to the numerical simulation of turbulent flows around bluff bodies. After specifying the numerical ingredients and the turbulence models used in our simulations, we present a study on the impact of the dynamic sub-grid scale modeling in VMS-LES model and a RANS/VMS-LES hybrid turbulence approach. Simulations of flows around a cylinder and a tandem are performed. Next, we assess the behaviour of some hybrid turbulence models for the simulation of flows around a circular cylinder in the subcritical regime. The computation of the flow around a rectangular cylinder with the VMS-LES approach is also presented. At last, after a review of some important works on multirate time advancing schemes, we propose a new volume-agglomeration explicit multirate approach that is applied to the computation of complex turbulent flows by a hybrid turbulence model.

Title: Numerical Solution of the Three-dimensional Compressible Flow Author: Martin Kyncl Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Jiří Felcman, CSc. Abstract: This thesis deals with a fluid flow in 3D in general. The system of the equations, describing the compressible gas flow, is solved numerically, with the aid of the finite volume method. The main purpose is to describe particular boundary conditions, based on the analysis of the incomplete Riemann problem. The analysis of the original initial-value problem shows, that the right hand-side initial condition, forming the Riemann problem, can be partially replaced by the suitable complementary condition. Several modifications of the Riemann problem are introduced and analyzed, as an original result of this work. Algorithms to solve such problems were implemented and used in code for the solution of the compressible gas flow. Numerical experiments documenting the suggested methods are performed. Keywords: compressible fluid flow, the Navier-Stokes equations, the Euler equations, boundary conditions, finite volume method, the Riemann problem, numerical flux, tur- bulent flow

Les matériaux granulaires multiphasiques occupent une place très importante dans notre environnement qui suscitent un grand intérêt de nombreuses communautés scientifiques, notamment celles de la mécanique des sols ou de la géotechnique. Le caractère divisé permet les milieux granulaires multiphasiques d'avoir un comportement mécanique global qui trouve leur origine, leur distribution et interactions entre les phases de composition. Un modèle de couplage hydromécanique est présenté dans ce travail de thèse pour l'application à la modélisation microscopique des couplages hydromécaniques dans les matériaux granulaires saturés. Le modèle numérique est basé sur un couplage de la méthode des éléments discrets (DEM) avec une formulation en volumes finis, à l'échelle des pores (PFV), du problmème de l'écoulement d'un fluide visqueux incompressible. Le solide est modélisé comme un arrangement de particules sphériques avec des interactions de type élasto-plastique aux contacts solide-solide. On considère un écoulement de Stokes incompressible, en supposant que les forces inertielles sont négligeables par rapport aux forces visqueuses. La géométrie des pores et leur connectivité sont définies sur la base d'une triangulation régulière des sphères, qui aboutit à un maillage tétrahédrique. La définition des conductivités hydrauliques à l'échelle des pores est un point clef du modèle, qui se rapproche sur ce point à des modèles de type pore-network. Une importance particulière réside dans les lois d'interactions fluide-solide permettant de déterminer des forces de fluide appliquées sur chacune des particules, tout en assurant un coût de calcul acceptable pour la modélisation en trois dimensions avec plusieurs millieurs des particules. Des mesures de perméabilités sur des assemblages bidisperses de billes de verre sont présentées et comparées aux prédictions du modèle et aux formules empiriques/semi-empiriques dans la littérature, ce qui valide la définition de la conductivité locale et met en évidence le rôle de la distribution granulométrique et la porosité. Une approche numérique pour analyser l'interaction mécanique fluide-solide et les mécanismes d'érosion interne est finalement présentée. / Multiphase granular materials occupy a very important place in our environment that are of great interest to many scientific communities, including those of soil mechanics or geotechnical engineering. The divided nature allows multiphase granular media to have a global mechanical behaviour which originates from all component phases, their distribution and interactions. Acoupled hydromechanical model is presented in this work for the application to microscopic modeling of coupled hydromechanical in saturated granular materials. The numerical model uses a combination of the discrete element method (DEM) with a pore-scale finite volume (PFV) formulation of flow problem of an incompressible viscous fluid. The solid is modeled as an assembly of spherical particles, where contact interactions are governed by elasto-plasticrelations. Stokes flow is considered, assuming that inertial forces are small in comparison with viscous forces. Pore geometry and pore connections are defined locally through regular triangulation of spheres, from which a tetrahedral mesh arises. The definition of pore-scale hydraulic conductivities is a key aspect of this model. In this sense, the model is similar to a pore-network model. The emphasis of this model is, on one hand the microscopic description of the interaction between phases, with the determination of the forces applied on solid particles by the fluid, on the other hand, the model involves affordable computational costs, that allow the simulation of thousands of particles in three dimensional models. Permeability measurements on bidispersed glass beads are reported and compared with model predictions and empirical formulas/semi-empirical in the literature, validating the definition of local conductivities and bringing out the role of particle size distribution and porosity. A numerical approach to analyze the fluid-solid mechanical interaction and mechanisms of internal erosion is finally presented.

Made available in DSpace on 2016-08-31T13:24:10Z (GMT). No. of bitstreams: 1 AndreHFB_DISSERT.pdf: 2463155 bytes, checksum: 1554ed6a6d87b8a8535d92ad7432b8e5 (MD5) Previous issue date: 2012-01-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Drip irrigation is one of the most efficient methods for applying water to a crop, capable of delivering water at a rate close to the demand. Many efforts have been required to estimate the amount of water needed by plants. Therefore studying soil water extraction by plants linked to mathematical modeling for behavior prediction, and linked to computational resources to allow complex mathematical procedures to be realized in a short space of time, becomes a powerful and necessary alternative for the understanding and quantification of the involved processes. This work aims to simulate soil water movement under conditions of drip irrigation, including the quantification of soil evaporation and crop transpiration of soil water. The finite volumes method was used to numerically solve the Richards equation for the simulation of soil water movement. Equations from literature were used to estimate transpiration and evaporation, adjusting them for use in finite volumes and modifying them, when necessary, to adapt them to the used model. A software was developed to perform the simulations of soil water movement, formation of a wet bulb and quantification of transpiration and evaporation. Concerning mass conservation, the results of the lesser simulations presented a relative error smaller than 0.001%. The results of the simulations of water losses by evaporation and transpiration were very similar to observed data from a lysimeter experiment, making the model results satisfactory. However, more tests and comparisons with more robust models are suggested. / A irrigação por gotejamento superficial é um dos métodos mais eficientes na aplicação de água por poder fornecer água às plantas numa taxa mais próxima a da demanda hídrica da cultura quando comparado com outros métodos. Tem-se demandado muitos esforços na tentativa de se estimar a quantidade de água necessária às plantas. Dessa forma, o estudo da extração de água do solo pelas plantas aliado à modelagem matemática para a predição de comportamentos, e aos recursos computacionais para a realização de cálculo matemáticos complexos num curto espaço de tempo, se torna uma alternativa poderosa e necessária no entendimento e quantificação dos processos envolvidos. O presente trabalho tem por objetivo simular o movimento da água no solo sob condições de irrigação por gotejamento superficial, incluindo a quantificação da evaporação da água do solo e da transpiração da cultura. Foi utilizado o método dos volumes finitos na resolução numérica da equação de Richards para a simulação do movimento de água no solo. Utilizaram-se equações já desenvolvidas na literatura para abordar a transpiração e a evaporação, adequando-as para utilização em volumes finitos e modificando-as, quando necessário, para adaptá-las ao modelo proposto neste trabalho. Um software foi desenvolvido com a finalidade de se realizar as simulações de movimento de água, formação do bulbo molhado e quantificação da transpiração e da evaporação. Quanto à conservação de massa, os resultados das simulações apresentaram erro relativo menores que 0,001%. Os resultados das simulações das perdas de água por evaporação e transpiração foram bastante similares aos de um experimento realizado com lisímetro, tornando os resultados do modelo satisfatórios. Porém, sugere-se que sejam efetuados mais testes e comparações com modelos mais robustos.

Dans cette thèse, nous nous intéressons à l'étude d'un modèle de transport de sédiments en nous plaçant sous deux angles d'approche différents. L'un concerne la modélisation numérique du problème et propose une méthode de résolution numérique basée sur un solveur de Riemann approché pour le système de Saint-Venant-Exner qui reste un des systèmes les plus répandus pour traiter le transport sédimentaire par charriage. Ce dernier repose sur un couplage du modèle hydraulique de Saint-Venant et du modèle morphodynamique d'Exner. Le point essentiel de la méthode proposée se situe au niveau du traitement du couplage de ce système. En effet, il existe deux stratégies; la première consiste à découpler la résolution de la partie fluide de la partie solide et les faire interagir à des instants donnés alors que la seconde considère une résolution couplée du système en mettant à jour conjointement les grandeurs hydrauliques et solides aux mêmes instants. Se posera alors la question du choix de la stratégie de résolution pour laquelle nous apporterons des éléments de réponses en comparant les deux approches. L'autre se concentre sur la mise en place d'une méthodologie pour l'étude des incertitudes liées au même modèle. Pour ce faire, nous proposons une formulation stochastique du système de Saint-Venant-Exner et nous cherchons à caractériser la variabilité des sorties par rapport aux paramètres d'entrée naturellement aléatoires. Cette première étude révélera la nécessité de revenir à un système de Saint-Venant avec un fond bruité pour étudier la sensibilité des grandeurs hydrauliques par rapport aux perturbations topographiques. / In this thesis, we are interested on the study of a sediment transport model through two different approaches. One of them concerns the numerical modelling of the problem and proposes a numerical problem-solving method based on an approximate Riemann solver for the Saint-Venant-Exner system which is one of the most common model to deal with sedimentary bed-load transport. This last one is based on a coupling between the hydraulic model of Saint-Venant and the morphodynamic model of Exner. The key point of the proposed method is the treatment of the coupling issue. Indeed, there exists two strategies; the first one consists on decoupling the resolution of the fluid part from the solid part and making them interact at fixed times whereas the second one considers a coupled approach to solve the system by jointly updating the hydraulic and solid quantities at same times. We then raise the issue of the choice of the strategy for which we suggest answers by comparing both approaches. The other one focuses on the development of a methodology to study the uncertainties related to the model previously mentioned. To this end, we propose a stochastic formulation of the Saint-Venant-Exner system and we look for characterizing the variabilities of the outputs in relation to the naturally random input parameters. This first study reveals the need for a return to the Saint-Venant system with a perturbed bed to understand the sensitivity of the hydraulic quantities on the topographical perturbations.