Auswahl der wissenschaftlichen Literatur zum Thema „Coupled volumes“

L'utilisation croissante des sources d'énergie renouvelable avec une grande volatilité de production, comme l'énergie éolienne et solaire, conduit à des fluctuations dans le réseau électrique qui doivent être compensées. Pour cette raison les machines hydrauliques, turbines et pompes, sont plus souvent opérées dans les régimes de fonctionnement hors fonctionnement nominal et la fréquence des phases de démarrage et arrêt augmente. Ce type de fonctionnement peut avoir des conséquences importantes sur le cycle de vie des machines. Il est donc essentiel de prendre en compte l'écoulement dans les phases transitoires lors de la conception de la machine et la simulation numérique des écoulements est un outil adapté pour cela. La présente étude a pour objectif de développer une méthode de couplage flexible qui combine la méthode à maillage volumes finis (VF) et la méthode sans maillage Smoothed Particle Hydrodynamics - Arbitrary Lagrange Euler (SPH-ALE). Cette méthode couplée peut être utilisée comme outil pour l'investigation des phénomènes transitoires dans les machines hydrauliques. SPH-ALE est particulièrement bien adapté aux simulations des écoulements fortement dynamiques avec des géométries mobiles mais elle a des difficultés pour calculer des forts gradients de pression et vitesse. Un raffinement de particules est difficile à implémenter, surtout si les particules doivent être raffinées de manière anisotrope. Les méthodes volumes finis (VF) sont établies pour les simulations numériques d'écoulements grâce à leur stabilité et précision. Par contre, elles peuvent être lourdes pour les simulations avec des géométries mobiles et demandent souvent une interface entre des parties mobiles et statiques du maillage ce qui génère des erreurs supplémentaires. Pour combiner les deux approches complémentaires, une méthode de couplage a été développée qui décompose le domaine de calcul en zones où la vitesse et la pression sont calculées par la méthode VF, en zones où elles sont obtenues par SPH-ALE et en zones de recouvrement où les informations sont transférées de la zone VF à la zone SPH et inversement. Dans les zones de recouvrement les points de calcul VF sont utilisés comme voisins pour l'intégration en espace des particules SPH. Aux limites du maillage VF la vitesse et la pression sont interpolées des particules SPH, similairement aux méthodes Chimére des maillages recouvrants. Un logiciel SPH-ALE existant du groupe ANDRITZ est utilisé pour cette étude. Un solveur VF faiblement compressible est implémenté dans ce logiciel. Le solveur discrétise la même forme des équations de Navier-Stokes que le solveur SPH-ALE. Des solveurs de Riemann avec des états reconstruits par la méthode MUSCL sont employés. En outre, le solveur SPH-ALE est amélioré et adapté aux écoulements internes. Pour cette raison des conditions à l'entrée et à la sortie du type subsonique sont implémentées. Du plus, une méthode de correction du gradient de la fonction kernel est présentée qui améliore la précision du champ de pression, notamment si les particules ne sont pas distribuées régulièrement. La méthode couplée est validée à l'aide des cas test académiques en unidimensionnel et en bidimensionnel, comme le cas de tube à choc, les tourbillons de Taylor-Green et l'écoulement autour d'une aube symétrique du type NACA avec des particules en description eulérienne. En outre, le couplage offre la possibilité d'imposer des conditions à la sortie aux particules lagrangiennes. La méthode est appliquée aux simulations d'écoulement transitoire en 2D avec des particules qui se déplacent en suivant les géométries mobiles<br>The increased use of intermittent forms of renewable energy like wind and solar energy produces fluctuations in the electric grid that have to be compensated. For this reason, hydraulic machines like turbines and pumps are more often operated under non-conventional operating conditions and are submitted to frequent starts and stops. This type of operating conditions has important consequences on the life cycle of the machines. It is thus of paramount importance that transient flows at off-design conditions are properly taken into account in the design phase and numerical simulation is an appropriate way to do so. The present study aims at developing a flexible coupling method of the meshbased Finite Volume Method (FVM) and the meshless Smoothed Particle Hydrodynamics - Arbitrary Lagrange Euler (SPH-ALE) method, which can be used as a tool for the investigation of transient phenomena in hydraulic machines. SPH-ALE is very well adapted for the simulation of highly dynamic flows with moving geometries but has difficulties to correctly represent rapidly changing gradients of the field variables. Particle refinement is difficult to implement, especially if particles are refined in an anisotropic way. FV methods are well established in CFD because of their accuracy and stability. However, they can be tedious for simulations with moving geometries and often necessitate an interface between moving and static parts of the mesh which introduces additional errors. To overcome the shortcomings of both methods, a coupling method is developed that uses a decomposition of the computational domain into regions where the physical field variables are computed by the FV method, regions where they are computed by SPH-ALE and overlapping regions where the information is transferred from the FV domain to the SPH domain and vice versa. In the overlapping regions FV calculation points are used as neighbors for the SPH integration in space. At the boundaries of the FV mesh, velocity and pressure are interpolated from the SPH particles by means of scattered data interpolation techniques, similarly to Chimera methods for overlapping grids. For this study, an existing SPH-ALE software of the ANDRITZ Group is used. A weakly compressible FV solver is implemented into this software that discretizes the same form of the Navier-Stokes equations than the SPH-ALE solver. Similar to the present SPH-ALE method, Riemann solvers with reconstructed states, obtained by a MUSCL scheme, are employed. Moreover, adaptations and improvements of the SPH-ALE solver itself are made, which are important for the coupling and for the simulation of internal flows in general. Thus, subsonic inlet and outlet conditions are implemented. Furthermore, a correction method of the kernel gradient is presented that ensures zeroth order consistency of the SPH-ALE approximation of the divergence of the convective fluxes. The correction improves greatly the SPH pressure field on non-uniform particle distributions. The implemented coupled method is successfully validated by means of inviscid academic one-dimensional and two-dimensional testcases like a shock tube case, Taylor-Green vortices and the flow around a symmetric NACA airfoil with particles in Eulerian description. Furthermore, the coupling provides a possibility to implement outlet boundary conditions to Lagrangian moving SPH particles. It is then applied to the simulation of transient flows in rotor stator systems in 2D with moving particles

The overall aim of the work described in this thesis is to bring a number of contributions to hydrology and hydrological modeling in the framework of a specific physically-based numerical model for integrated surface subsurface and flow-transport processes, the CATchment-HYdrology Flow-Transport (CATHY_FT) model. These contributions revolve around three main themes: the enhancement of the numerical performance of hydrological models for flow and transport phenomena, the improvement of our current understanding of complex boundary conditions in order to reduce the errors associated with their modeling, and the testing and benchmarking of distributed physically-based models for groundwater flow and transport processes. The work to achieve the general objective is elaborated into four stages. First, the Larson-Niklasson post-processing algorithm is implemented in CATHY_FT to reconstruct mass-conservative velocities from a linear, or P1, Galerkin solution of Richards' equation. This is done to improve the accuracy and mass balance properties of the companion advective transport model (finite volume-based), which rely on accurate velocity fields as input. Through a comparison between the results from the reconstructed velocities and the P1 Galerkin velocities, it is shown that a locally mass-conservative velocity field is necessary to obtain accurate transport results. Second, a detailed and novel analysis of the behavior of seepage face boundaries is performed with the flow model of CATHY_FT. The numerical simulations examine the model's performance under complex conditions such as heterogeneity and coupled surface/subsurface flow. It is shown that the overall numerical solution can be greatly affected by the way seepage face boundaries are handled in hydrological models and that careful considerations are required when using simple approximations, in the presence of heterogeneous slopes, and for seepage faces forming on a portion of the land surface. Third, CATHY_FT is implemented and run at the Landscape Evolution Observatory of the Biosphere 2 facility, Arizona. A detailed modeling analysis is performed of the experimental data collected during an isotope tracer experiment and from an intensively-measured hillslope, including quantity and quality of groundwater discharge and point-scale flow and transport data. This flow and tracer data is used to incrementally explore complex phenomena and associated hypotheses (e.g., heterogeneity, fractionation, and dispersion), progressing from flow to transport and from integrated to point-scale response analysis. This incremental approach highlights the challenges in testing and validating the new generation of integrated hydrological models when considering many types and levels of observation data. Finally, a concluding analysis is performed that relates to all three themes of the thesis, describing some of the features of the CATHY_FT model, discussing key issues associated to its further development, and testing its physical and numerical behavior for both real and synthetic scenarios. This final stage of the thesis addresses the myriad challenges faced in accurately and efficiently resolving the difficult behavior of the advection-dispersion equation for subsurface solute transport, in properly handling the complex boundary conditions for solute interactions across the land surface, and generally in capturing process interactions and feedbacks between flow and transport phenomena in surface and subsurface environments.<br>Lo scopo di questa tesi e' fornire dei contributi all'idrologia e alla modellazione idrologica nell'ambito di un modello numerico specifico, il modello CATchment HYdrology Flow-Transport (CATHY_FT), utilizzato per simulare processi integrati di superficie e sotterranei e di flusso e trasporto. Questi contributi riguardano tre temi principali: il miglioramento del comportamento numerico di modelli idrologici che simulano fenomeni di flusso e trasporto, l'approfondimento di condizioni al contorno complesse con l'obbiettivo di ridurre gli errori relativi alla loro modellazione e il test e l'analisi comparativa di modelli a base fisica utilizzati per simulare processi di flusso e trasporto sotterranei. Il lavoro per raggiungere l'obbiettivo generale viene diviso in quattro step. Nel primo step l'algoritmo di Larson-Niklasson e' implementato in CATHY_FT per ricostruire velocita' conservatrici della massa a partire da una soluzione lineare (o P1) di Galerkin dell'equazione di Richards, in modo da permettere al modello di trasporto avvettivo (basato sui volumi finiti) di conservare la massa, cosa che dipende strettamente dall'accuratezza del campo di velocita' che questo utilizza. Confrontando i risultati ottenuti con le velocita' derivanti dalla soluzione P1 di Galerkin e quelle ricostruite, viene mostrato che un campo di velocita' localmente conservativo e' necessario per ottenere risultati accurati con il trasporto. Nella seconda fase viene effettuata un'analisi dettagliata del comportamento delle condizioni ai limiti nella zona del fronte di infiltrazione con il modello di flusso di CATHY_FT. Le simulazioni numeriche esaminano il comportamento del modello in condizioni complesse come quelle di eterogeneita' e di flusso di superficie e sotterraneo accoppiato. Viene dimostrato che la soluzione numerica puo' essere fortemente influenzata dal modo in cui la zona di infiltrazione viene trattata nei modelli idrologici e che considerazioni accurate sono sempre necessarie quando si usano approssimazioni, in presenza di versanti eterogenei e per le zone di infiltrazione che si formano nella superficie terrestre. Come terzo step, CATHY_FT viene testato al Landscape Evolution Observatory del Biosphere 2 in Arizona. Viene eseguita un'analisi dettagliata di dati sperimentati raccolti durante un esperimento di tracciante isotopico e da un versante artificiale intensivamente controllato. Le informazioni comprendono la qualita' e la quantita' della portata sotterranea e dati puntuali di flusso e trasporto. Questi dati di flusso e tracciante sono utilizati per esplorare fenomeni complessi e le ipotesi associate (e.g., eterogeneita', frazionamento e dispersione), procedendo dalla risposta di flusso a quella di trasporto e dalla risposta integrata a quella puntuale. Questo approccio incrementale evidenzia le sfide legate alla validazione della nuova generazione di modelli idrologici integrati quando si guarda a diversi tipi e livelli di dati osservati. Infine, viene eseguita un'analisi conclusiva che si lega a tutti e tre i temi della tesi, descrivendo alcune caratteristiche del modello CATHY_FT, discutendo problemi chiave legati al suo sviluppo futuro e testando il suo compertamento fisico e numerico sia per scenari sintetici che reali. Questo step finale della tesi affronta la miriade di sfide legate alla risoluzione accurata ed efficace del comportamento difficile dell'equazione di avezione-dispersione per processi di trasporto di soluto sotterraneo, alla risoluzione appropriata delle condizioni ai limiti complesse per rappresentare le interazioni di soluto attraverso la superficie terrestre e, in generale, alla rappresentazione delle interazioni tra i fenomeni di flusso e trasporto nell'ambiente superficiale e sotterraneo.

Orientador: Jose Roberto Nunhez<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica<br>Made available in DSpace on 2018-08-11T08:15:27Z (GMT). No. of bitstreams: 1 Lopes_GabrielaCantarelli_M.pdf: 1710566 bytes, checksum: efab0c6308734536b15c2ef91d4d8337 (MD5) Previous issue date: 2008<br>Resumo: Processos que envolvem escoamentos de fluidos no interior de dutos estão presentes em muitas aplicações industriais. Na indústria petroquímica um desses processos que vem se tornando cada vez mais importante é o craqueamento catalítico de frações pesadas do petróleo, já que as converte em frações leves e mais nobres. Por causa da crescente demanda mundial por gasolina e GLP e à sua alta rentabilidade para uma refinaria de petróleo, unidades de craqueamento catalítico em leito fluidizado (FCC) estão presentes em todo o mundo. Testes experimentais costumam ser usados no estudo dos fenômenos envolvidos nesse processo. Porém esse tipo de análise possui alto custo, que pode ser reduzido com o uso de simulações computacionais em seu estudo inicial. Assim, o objetivo deste trabalho foi desenvolver um modelo tridimensional e elíptico, em linguagem Fortran, capaz de fornecer dados para a análise preliminar de escoamentos no interior de reatores de FCC. Na modelagem desses problemas são usadas equações diferenciais parciais, e essas não possuem solução analítica conhecida, sendo necessário o emprego de métodos numéricos para esse fim. Neste trabalho foi usado o Método dos Volumes Finitos, que tem a função de substituir as equações diferenciais parciais por equações algébricas aplicadas a pequenos volumes de controle finitos pertencentes ao domínio. Uma das maiores dificuldades encontradas no tratamento numérico de escoamentos incompressíveis é a determinação de um campo de pressão que satisfaça a Equação da Continuidade. Esse problema foi resolvido fazendo-se uso da abordagem acoplp.da de solução. Para análise do modelo foram obtidos perfis numéricos de velocidade e pressão para fluidos escoando em regimes laminar e turbulento, que foram validados usando-se os dados obtidos com a solução analítica das equações, por correlações (semi-) empíricas ou por dados experimentais, conforme cada um dos casos. Notou-se que o modelo representa muito bem casos laminares, e gue 11.oS casos turbulentos foi necessário um maior refino da malha próximo a parede do tubo. Também foram feitas simulações para que se pudessem observar as características tridimensionais, elípticas e transientes da modelagem do escoamento. De maneira geral o modelo se mostrou bastante rápido, convergindo em poucas iterações. Palavras-Chave: Fluidodinâmica computacional; dutos cilíndricos; modelo tridimensional e elíptico; método dos Volumes Finitos; solução acoplada; turbulência<br>Abstract: Processes involving fluid flow in tubes are present in many industrial applications. In petrochemical industry one of these processes that are becoming more and more important is the fluid catalytic cracking of heavy petroleum fractions. This fact is due to the process capacity to convert heavy fractions in light and valuable ones. Because of the increasingly worldwide demand for gasoline and LPG and its high yield for a petroleum refinery, fluid catalytic cracking (FCC) units are present in the whole world. Experimental tests are used in the study of the phenomena involved in this processo However this kind of analysis has high cost which can be reduced by using computational simulations in its initial study. Thus, the aim of this work was the development of a three-dimensional and elliptical mo dei in Fortran language in order to provide data for fluid flow preliminary analysis in FCC reactors. Partial differential equations were used in the modeling of these problems. These equations do not have known analytical solution, being necessary therefore the use of numerical methods. In this work the Finite Volume Method were applied with this purpose. This method has as a role to substitute the partial differential equations of the mo dei for algebric equations applied to small finite control volumes of the domain. One of the biggest difficulties found in the numerical treatment of incompressible fluid flows is the determination of apressure field that satisfies the Continuity Equation. This problem was solved using the coupled solution approach. For model analysis, numerical velocity and pressure proJ:iles for laminar and turbulent flows were obtained, that had been validated using the data obtained through the analytical solution of the equations, by empirical correlations or by experimental data, according to each one of the cases. The model represented well laminar cases, and in the turbulent ones the mesh had to be more refined near the tube wall. Other simulations were performed, in aQalyzing the three-dimensional, elliptical and transient model characteristics. In general, the mo dei was very fast, converging in a few interations. Keywords: Computational fluid dyn~mic; cylindrical ducts; three-dimensional and elliptical model; Finite Volume Method; coupled solution; turbulence<br>Mestrado<br>Desenvolvimento de Processos Químicos<br>Mestre em Engenharia Química