Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

Rotated Versions of the Jablonowski Steady‐State and Baroclinic Wave Test Cases: A Dynamical Core Intercomparison

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95316/1/jame31.pd

Numerical analysis of air-water flows in hydraulic structures using computational fluid dynamics (CFD)

Tesis por compendioThe new legal regulations derived from climate change dictate that hydraulic structures must be designed to handle flood events associated with return periods up to 10,000 years. This obviously involves adapting the existing infrastructure to meet such requirements. In order to avoid risks in the restitution of the flow discharged to rivers, such as bank overflows or streambed erosion and scour processes, hydraulic design must be supported by reliable tools capable of reproducing the behavior of hydraulic structures. In the work presented herein, a fully three-dimensional CFD model to reproduce the behavior of different types of air-water flow in hydraulic structures is presented. The flow is assumed to be turbulent, isotropic and incompressible. Several RANS turbulence models are tested and structured rectangular meshes are employed to discretize the analyzed domain. The presence of two fluids is modeled using different VOF approaches and simulations are run using the PIMPLE algorithm. The model is implemented using the open-source platform OpenFOAM and its performance is compared to the commercial code FLOW-3D. The analysis is conducted separately on two different parts of hydraulic structures, namely: the spillway and the stilling basin. Additionally, a case of practical application, where the model reproduces the flow of a real-life case, is also presented in order to prove the suitability of the model to actual design cases. Mesh independence and model validation using experimental data are checked in the results of all the case studies. The sensitivity of the presented model to certain parameters is extensively discussed using different indicator variables. Among these parameters are turbulence closure, discretization scheme, surface tracking approach, CFD code or boundary conditions. Pros and contras of each of them are addressed. The analyzed turbulence models are the Standard k ¿ ¿, the Realizable k ¿ ¿, the RNG k ¿ ¿, and the SST k ¿ ¿. The discretization schemes under study are: a first-order upwind method, the second-order limited Van Leer method, and a second-order limited central difference method. The VOF approaches analyzed are the Partial VOF, as implemented in OpenFOAM, and the TruVOF, as implemented in FLOW-3D. In most cases, the Standard k ¿ ¿ model provides the most accurate estimations of water free surface profiles, although the rest of variables, with few exceptions, are better predicted by the RNG k ¿ ¿. The latter model generally requires slightly longer computation times. The SST k ¿ ¿ reproduces correctly the phenomena under study, although it generally turned out to be less accurate than its k ¿ ¿ counterparts. As regards the comparison among VOF approaches and codes, it is impossible to determine which one performs best. E.g. OpenFOAM, using the Partial VOF, managed to reproduce the in- ternal hydraulic jump structure and all derived variables better than FLOW-3D, using the TruVOF, although the latter seems to capture better the momentum transfer and so all derived variables. In the case of flow in stepped spillways, OpenFOAM captures better the velocity profiles, although FLOW-3D is more accurate when estimating the water free surface profile. It is worth remark- ing that not even their response to certain model parameters is comparable. E.g. FLOW-3D is significantly less sensitive to mesh refinement than OpenFOAM. Given the result accuracy achieved in all cases, the proposed model is fully applicable to more complex design cases, where stilling basins, stepped spillways and hydraulic structures in general must be investigated.Las nuevas disposiciones legales derivadas del cambio climático dictaminan que las estructuras hidráulicas sean capaces de funcionar correctamente con eventos de inundación asociados a periodos de retorno de hasta 10,000 años. Esto, obviamente, implica adaptar la infraestructura existente para satisfacer dichos requerimientos. A fin de evitar riesgos en la restitución de los caudales vertidos al río, como desbordamientos o procesos erosivos y de socavación, el diseño hidráulico ha de sustentarse en herramientas fiables capaces de reproducir el comportamiento de las estructuras hidráulicas. En este trabajo, se presenta un modelo numérico CFD completamente tridimensional para reproducir el comportamiento de diferentes tipos de flujo aire-agua en estructuras hidráulicas. Se asume que el flujo es turbulento, isotrópico e incompresible. Diversos modelos de turbulencia RANS son contrastados y se emplean mallas estructuradas rectanuglares para discretizar el dominio analizado. La presencia de dos fluidos es modelada utilizando diferentes enfoques VOF y las simulaciones son ejecutadas empleando el algoritmo PIMPLE. El modelo es implementado mediante la plataforma de código abierto OpenFOAM y su respuesta es comparada con la del modelo comercial FLOW-3D. El análisis se lleva a cabo sobre dos partes diferentes de una estructura hidráulica, a saber, el aliviadero y el cuenco amortiguador, de forma separada. Además, un caso de aplicación práctica, donde el modelo reproduce el flujo en una estructura real, es presentado también a fin de probar la adecuación del modelo a casos de diseño aplicado. Se comprueban la independencia de la malla y la validación con datos experimentales de los resultados de todos los casos de estudio. La sensibilidad del modelo presentado a ciertos parámetros es analizada de forma exhaustiva empleando diferentes variables indicadoras. Los pros y contras de cada uno de éstos son planteados. Los modelos de turbulencia analizados son el Standard k-epsilon, el Realizable k-epsilon, el RNG k-epsilon y el SST k-omega. Los esquemas de discretización estudiados son: un método de primer orden upwind, uno de Van Leer de segundo orden y un esquema de segundo orden limitado de diferencias centradas. Los enfoques VOF analizados son el Partial VOF, implementado en OpenFOAM, y el TruVOF, implementado en FLOW-3D. En la mayoría de casos, el modelo k-epsilon aporta las estimaciones más precisas de perfiles de lámina libre de agua, pese a que el resto de variables, con alguna excepción, son mejor predichas por el RNG k-epsilon. Este modelo generalmente requiere mayores tiempos de cálculo. El k-omega reproduce correctamente los fenómenos bajo estudio, pese a que su precisión es generalmente más baja que la de los modelos k-epsilon. En lo que respecta a la comparación entre enfoques VOF y códigos, es imposible determinar cuál es el mejor. Por ejemplo, OpenFOAM, empleando el Partial VOF, logra reproducir la estructura interna del resalto hidráulico y todas las variables derivadas mejor que FLOW-3D, empleando el TruVOF, a pesar de que este último parece capturar mejor la transferencia de cantidad de movimiento y, por tanto, todas las variables derivadas. En el caso del flujo en aliviaderos escalonados, OpenFOAM captura mejor los perfiles de velocidad, pese a que FLOW-3D es más preciso en la estimación de los perfiles de lámina libre de agua. Conviene recalcar que ni tan sólo su respuesta a ciertos parámetros del modelo es comparable. Por ejemplo, FLOW-3D es significativamente menos sensible al refinado de malla que OpenFOAM. A la luz de la precisión de los resultados obtenidos en todos los casos, el modelo propuesto es completamente aplicable a casos de diseño más complejos, donde cuencos amortiguadores, aliviaderos escalonados y estructuras hidráulicas en general han de ser investigadas.Les noves disposicions legals derivades del canvi climàtic dictaminen que cal que les estructures hidràuliques siguen capaces de funcionar correctament amb esdeveniments d'inundació associats a períodes de retorn de fins a 10,000 anys. Això, òbviament, implica adaptar la infraestrctura existent per satisfer aquests requeriments. A fi d'evitar riscs en la restitució dels cabals vessats al riu, com desbordaments o processos erosius i de socavació, el disseny hidràulic ha de recolzar-se en ferramentes fiables capaces de reproduir el comportament de les estructures hidràuliques. En aquest treball, es prsenta un model numèric CFD completament tridimensional per a reproduir el comportament de diferents tipus de flux aire-aigua en estructures hidràuliques. S'assumeix que el flux és turbulent, isotròpic i incompressible. Diferents models de turbulència RANS són contrastats i s'empren malles estructurades rectangulars per discretitzar el domini analitzat. La presència de dos fluids és modelada utilitzant diferents enfocaments VOF i les simulacions són executades emprant l'algorisme PIMPLE. El model és implementat mitjançant la plataforma de codi obert OpenFOAM i la seua resposta és comparada amb la del codi comercial FLOW-3D. L'anàlisi es du a terme sobre les diferents parts d'una estructura hidràulica, a saber, sobreeixidors esgraonats i vas esmorteïdor, de forma separada. A més, un cas d'aplicació pràctica, on el model reprodueix el flux a una estructura real, és presentat també a fi de provar l'adequació del model a casos de disseny aplicat. Es comproven la independència de la malla i la validació amb dades experimentals dels resultats de tots els casos d'estudi. La sensibilitat del model presentat a certs paràmetres és analitzada de forma exhaustiva emprant diferents variables indicadores. Els pros i contres de cadascun d'aquests són plantejats. Els models de turbulència analitzats són l'Standard k-epsilon, el Realizable k-epsilon, el RNG k-epsilon i l'SST k-omega. Els esquemes de discretització estudiats són: un mètode de primer ordre upwind, un de Van Leer de segon ordre i un esquema de segon ordre limitat de diferències centrades. Els enfocaments VOF analitzats són el Partial VOF, implementat en OpenFOAM, i el TruVOF, implementat en FLOW-3D. En la majoria de casos, el model Standard k-epsilon aporta les estimacions més precises de perfils de làmina lliure d'aigua, tot i que la resta de variables, amb alguna excepció, són millor predites pel RNG k-epsilon. Aquest model generalment requereix majors temps de càlcul. El k-omega reprodueix correctament els fenòmens sota estudi, tot i que la seua precisió és generalment més baixa que la dels models k-epsilon. Pel que fa la comparació entre enfocaments VOF i codis, és impossible determinar quin és el millor. Per exemple, OpenFOAM, emprant el Partial VOF, aconsegueix reproduir l'estructura interna del ressalt hidràulic i totes les variables derivades millor que FLOW-3D, emprant el TruVOF, tot i que aquest últim pareix capturar millor la transferència de quantitat de moviment i, per tant, totes les variables derivades. En el cas del flux en sobreeixidors esgraonats, OpenFOAM captura millor els perfils de velocitat, tot i que FLOW-3D és més precís en estimar els perfils de làmina lliure d'aigua. Cal deixar palès que ni tan sols la seua resposta a certs paràmetres del model és comparable. Per exemple, FLOW-3D és significativament menys sensible al refinament de malla que OpenFOAM. En base a la precisió dels resultats obtinguts en tots els casos, el model proposat és completament aplicable a casos de disseny més complexos, on vassos esmorteïdors, sobreeixidors esgraonats i estructures hidràuliques en general han de ser investigades.Bayón Barrachina, A. (2017). Numerical analysis of air-water flows in hydraulic structures using computational fluid dynamics (CFD) [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90440TESISCompendi

High-pressure elastic properties of major materials of Earth's mantle from first principles

The elasticity of materials is important for our understanding of processes ranging from brittle failure, to flexure, to the propagation of elastic waves. Seismologically revealed structure of the Earth's mantle, including the radial (one-dimensional) profile, lateral heterogeneity, and anisotropy are determined largely by the elasticity of the materials that make up this region. Despite its importance to geophysics, our knowledge of the elasticity of potentially relevant mineral phases at conditions typical of the Earth's mantle is still limited: Measuring the elastic constants at elevated pressure-temperature conditions in the laboratory remains a major challenge. Over the past several years, another approach has been developed based on first-principles quantum mechanical theory. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. A review of high-pressure theoretical studies of major mantle phases shows a wide diversity of elastic behavior among important tetrahedrally and octahedrally coordinated Mg and Ca silicates and Mg, Ca, Al, and Si oxides. This is particularly apparent in the acoustic anisotropy, which is essential for understanding the relationship between seismically observed anisotropy and mantle flow. The acoustic anisotropy of the phases studied varies from zero to more than 50% and is found to depend on pressure strongly, and in some cases nonmonotonically. For example, the anisotropy in MgO decreases with pressure up to 15 GPa before increasing upon further compression, reaching 50% at a pressure of 130 GPa. Compression also has a strong effect on the elasticity through pressure-induced phase transitions in several systems. For example, the transition from stishovite to CaCl2 structure in silica is accompanied by a discontinuous change in the shear (S) wave velocity that is so large (60%) that it may be observable seismologically. Unifying patterns emerge as well: Eulerian finite strain theory is found to provide a good description of the pressure dependence of the elastic constants for most phases. This is in contrast to an evaluation of Birch's law, which shows that this systematic accounts only roughly for the effect of pressure, composition, and structure on the longitudinal (P) wave velocity. The growing body of theoretical work now allows a detailed comparison with seismological observations. The athermal elastic wave velocities of most important mantle phases are found to be higher than the seismic wave velocities of the mantle by amounts that are consistent with the anticipated effects of temperature and iron content on the P and S wave velocities of the phases studied. An examination of future directions focuses on strategies for extending first-principles studies to more challenging but geophysically relevant situations such as solid solutions, high-temperature conditions, and mineral composites

Numerical Analysis of a Single Droplet Impinging upon Liquid Films using the VOF Method

Over the last few decades, developing alternatives to fossil fuels has become increasingly important. Biofuels, in particular, have attracted interest not only as an alternative to expensive fossil fuels but also by providing a solution to several challenges that the modern world currently faces, which include worries regarding energy security, economic development, the need to mitigate climate change and achieving lower greenhouse gas emissions. The major objective of this dissertation is numerically simulating the vertical impact of a single droplet upon a liquid surface with the same liquid properties and surrounded by air. Four fluids were taken into account: water, 100% Jet A-1 and 75%/25% and 50%/50% of Jet A-1 and NEXBTL, respectively. Particularly, multiphase flows are complicated phenomena in nature due to the difficulty in accurately predicting the interface between the phases. The numerical model consists of solving the Navier-Stokes equations by means of the explicit Volume of Fluid (VOF) method for a 2D axisymmetric assumption. This analysis considers several parameters and models that define this phenomenon. The physical properties of the liquid and gas, which are density and viscosity, surface tension, gravity and the contact angles of the different fluids represent our physical model. For the solution approach, the Fractional Step Method (FSM) numerically solves the Navier-Stokes incompressible equations, the Geometric Reconstruction scheme tracks the interface between the liquid and the gas phase and the Continuum Surface Force (CSF) model includes the effects of surface tension. The numerical results are validated both qualitatively and quantitatively with available experimental results. Six different outcomes were numerically simulated: Prompt Splash, Crown Splash, Spreading, Jetting, Fingering and Bubbling. The numerical results for the initial four outcomes are in good agreement with the experimental results in terms of the initial impact and crown expansion. The fingering phenomenon displayed several issues concerning crown development due to the 3D nature of the instabilities formed at the crown rim. The bubbling phenomenon was not possible to numerically recreate. Information regarding the dynamics of this phenomenon is scarce and more research is required to understand the peculiarities of dome formation. It was also visualized prompt splash for the crown splash and bubbling initial stages, which did not correspond to the experimental results. There are several reasons that justify this discrepancy, such as the difficulty in capturing very tiny ejected droplets or the solution approach forcing prompt splash on some of the cases. Overall, 3D simulations are required for future analysis to accurately predict secondary atomization. Work toward the bubbling phenomenon must also be considered.Nas últimas décadas, o desenvolvimento de alternativas aos combustíveis fósseis tem-se tornado gradualmente mais relevante. Os biocombustíveis, em particular, atraem interesse, não apenas como uma alternativa ao elevado custo dos combustíveis fósseis, mas também como solução para vários desafios que o mundo moderno enfrenta atualmente. Estes desafios incluem preocupações com a segurança energética, desenvolvimento económico, a necessidade de mitigar a mudança climática e redução das emissões de gases de efeito de estufa. O principal objetivo desta dissertação é simular numericamente o impacto vertical de uma gota sobre uma superfície líquida com iguais propriedades e envolvida por ar. Foram considerados quatro fluidos: água, 100% Jet A-1 e 75%/25% e 50%/50% de Jet A-1 e NEXBTL, respectivamente. Particularmente, os modelos multifásicos são fenómenos complicados na natureza devido à dificuldade em prever, com precisão, a interface entre as diferentes fases. O modelo numérico consiste em resolver as equações de Navier-Stokes a partir do método explícito do Volume de Fluido (do inglês, Volume of Fluid) para um modelo bidimensional (2D) axissimétrico. Esta análise considera vários parâmetros e métodos para caracterizar a dinâmica do impacto de gotas. As propriedades físicas dos fluidos, a gravidade e os ângulos de contacto são utilizados para clarificar este modelo. Em termos de abordagem dos métodos de solução, o Método de Etapa Fracionária (em inglês, Fractional Step Method) resolve numericamente as equações incompressíveis de Navier-Stokes, o esquema de Reconstrução Geométrica (em inglês, Geometric Reconstruction) delimita a interface entre o líquido e a gás e o modelo de Força de Superfície Contínua (em inglês, Continuum Surface Force) inclui os efeitos da tensão superficial. Os resultados numéricos são validados qualitativa e quantitativamente com os resultados experimentais disponíveis. Seis cenários diferentes foram simulados numericamente: Prompt Splash, Crown Splash, Spreading, Jetting, Fingering e Bubbling. Os primeiros quatro fenómenos referidos estão de acordo com os resultados experimentais em termos do impacto inicial e da expansão da coroa. O fenómeno de fingering apresentou vários problemas relativos ao desenvolvimento da coroa devido à natureza tridimensional (3D) das instabilidades formadas nos limites externos da coroa. O fenómeno de bubbling não foi possível de recriar numericamente. É necessário compreender a dinâmica deste fenómeno e como, atualmente, a pesquisa atual é escassa, estudos devem ser feitos para entender as peculiaridades da formação deste tipo de cúpulas. Também foi visualizado a ocorrência de prompt splash para as fases iniciais do crown splash e do bubbling, que não correspondiam aos resultados experimentais. Há várias razões que justificam essa discrepância, como a dificuldade de capturar as gotas extremamente pequenas provenientes da atomização secundária ou os métodos de solução forçarem o splash inicial em alguns casos. Em termos de análises futuras, simulações 3D são necessárias para averiguar o número, tamanho e velocidade das gotas provenientes da atomização secundária. O fenómeno de bubbling também requer um estudo mais exaustivo no comportamento da dinâmica do impacto das gotas

Mathematical Theory and Modelling in Atmosphere-Ocean Science

Mathematical theory and modelling in atmosphere-ocean science combines a broad range of advanced mathematical and numerical techniques and research directions. This includes the asymptotic analysis of multiscale systems, the deterministic and stochastic modelling of sub-grid-scale processes, and the numerical analysis of nonlinear PDEs over a broad range of spatial and temporal scales. This workshop brought together applied mathematicians and experts in the disciplinary fields of meteorology and oceanography for a wide-ranging exchange of ideas and results in this area with the aim of fostering fundamental interdisciplinary work in this important science area