La descripción del flujo de fluidos involucra la solución de las ecuaciones de Navier-Stokes compresible, un problema muy complejo cuya estructura matemática no es del todo comprendida. Por lo tanto, mediante análisis asintótico, se pueden derivar modelos simplificados bajo ciertas hipótesis sobre el problema hechas en términos de parámetros adimensionales que miden la importancia relativa de los diferentes procesos físicos. Los flujos a baja velocidad se pueden describir por diferentes modelos que incluyen las ecuaciones de Navier Stokes incompresible cuya matemática es mucho mas conocida. Sin embargo, algunos flujos importantes no se pueden considerar incompresibles debido a la presencia de efectos térmicos. En esta clase de problemas se pueden derivar otra clase de ecuaciones simplificadas: las ecuaciones de Boussinesq y las ecuaciones de bajo numero de Mach.La complejidad de estos problemas matemáticos hace que su solución numérica sea muy difícil. En estos problemas el método de los elementos finitos es inestable, lo que en la práctica implica soluciones numéricas que presentan oscilaciones nodo a nodo de naturaleza no física. En las ecuaciones de Navier Stokes incompresible, dos fuentes bien conocidas de inestabilidad son la condición de incompresibilidad y la presencia del término convectivo. Muchas técnicas de estabilización utilizadas hoy en día se basan en la separación de escalas, descomponiendo la incógnita en una parte gruesa inducida por la discretización del domino y una parte fina de subescala. Modelar la subescala y su influencia conduce a un problema modificado para la escala gruesa que resulta estable.Aunque las técnicas de estabilización son ampliamente utilizadas hoy en día, importantes problemas permanecen abiertos. Contribuyendo a su comprensión, en este trabajo se analizan varios aspectos del modelado de las subescalas. Para problemas escalares de segundo orden, se encuentra la dependencia de la subescala con el tamaño de la malla en el caso general de mallas anisótropas. Estas ideas son extendidas a sistemas de ecuaciones para considerar el problema de Oseen. También se analiza el modelado de las subescalas en problemas transitorios, obteniendo un mejor esquema de integración temporal para el problema de escala gruesa. Para considerar flujos a baja velocidad, se presenta la extensión de estas técnicas a problemas no lineales acoplados, lo que esta íntimamente relacionado con el problema del modelado de la turbulencia, que es un tema en si mismo.Los flujos acoplados térmicamente, aparte del interés intrínseco que merecen, son importantes desde un punto de vista ingenieril. Una solución precisa del problema de flujo es necesaria para definir las cargas térmicas sobre las estructuras, que en muchos casos responden fuertemente, haciendo el problema acoplado. Esta clase de problemas, que motivaron este trabajo, incluyen la respuesta estructural en el caso de un incendio. / A general description of a fluid flow involves the solution of the compressible Navier-Stokes equations, a very complex problem whose mathematical structure is not well understood. Therefore, simplified models can be derived by asymptotic analysis under some assumptions on the problem, made in terms of dimensionless parameters that measure the relative importance of different physical processes. Low speed flows can be described by several models including the incompressible Navier Stokes equations whose mathematical structure is much better understood. However many important flows cannot be considered as incompressible, even at low speed, due to the presence of thermal effects. In such kind of problems another class of simplified equations can be derived: the Boussinesq equations and the Low Mach number equations.The complexity of these mathematical problems makes their numerical solution very difficult. For these problems the standard finite element method is unstable, what in practice means that node to node oscillations of non physical nature may appear in the numerical solution. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective terms. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modelling of the subgrid scale and its influence leads to a modified coarse scale problem that now can be shown to be stable. Although stabilization techniques are nowadays widely used, important problems remain open. Contributing to their understanding, several aspects of the subgrid scale modelling are analyzed in this work. For second order scalar problems, the dependence of the subgrid scale on the mesh size, in the general anisotropic case, is clarified. These ideas are extended to systems of equations to consider the Oseen problem. The modelling of the subgrid scales in transient problems is also analyzed, leading to an improved time discretization scheme for the coarse scale problem. To consider low speed flow models, the extension of these techniques to nonlinear and coupled problems is presented, something that is intimately related to the problem of turbulence modelling, which a entire subject on its own right. Thermally coupled flow problems, despite the intrinsic interest they deserve, are important from an engineering point of view. An accurate solution of a flow problem is needed to define thermal loads on structures which, in many cases have a strong response, making the problem coupled. This kind of problems, that motivated this work, include the problem of a structural response in the case of fires.

This dissertation consists of two parts, i.e. dynamic approaches for subgrid-scale (SGS) stress modelling for large eddy simulation and advanced assessment of the resolved scale motions related to turbulence geometrical statistics and topologies. The numerical simulations are based on turbulent Couette flow. The first part of the dissertation presents four contributions to the development of dynamic SGS models. The conventional integral type dynamic localization SGS model is in the form of a Fredholm integral equation of the second kind. This model is mathematically consistent, but demanding in computational cost. An efficient solution scheme has been developed to solve the integral system for turbulence with homogeneous dimensions. Current approaches to the dynamic two-parameter mixed model (DMM2) are mathematically inconsistent. As a second contribution, the DMM2 has been optimized and a modelling system of two integral equations has been rigorously obtained. The third contribution relates to the development of a novel dynamic localization procedure for the Smagorinsky model using the functional variational method. A sufficient and necessary condition for localization is obtained and a Picard's integral equation for the model coefficient is deduced. Finally, a new dynamic nonlinear SGS stress model (DNM) based on Speziale's quadratic constitutive relation [J. Fluid Mech., 178, p.459, 1987] is proposed. The DNM allows for a nonlinear anisotropic representation of the SGS stress, and exhibits a significant local stability and flexibility in self-calibration. In the second part, the invariant properties of the resolved velocity gradient tensor are studied using recently developed methodologies, i.e. turbulence geometrical statistics and topology. The study is a posteriori based on the proposed DNM, which is different than most of the current a priori approaches based on experimental or DNS databases. The performance of the DNM is further validated in terms of its capability of simulating advanced geometrical and topological features of resolved scale motions. Phenomenological results include, e.g. the positively skewed resolved enstrophy generation, the alignment between the vorticity and vortex stretching vectors, and the pear-shape joint probability function contour in the tensorial invariant phase plane. The wall anisotropic effect on these results is also examined.

The research network “Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models” was organized with European funding (COST Action ES0905) for the period of 2010–2014. Its extensive brainstorming suggests how the subgrid-scale parameterization problem in atmospheric modeling, especially for convection, can be examined and developed from the point of view of a robust theoretical basis. Our main cautions are current emphasis on massive observational data analyses and process studies. The closure and the entrainment–detrainment problems are identified as the two highest priorities for convection parameterization under the mass–flux formulation. The need for a drastic change of the current European research culture as concerns policies and funding in order not to further deplete the visions of the European researchers focusing on those basic issues is emphasized.

Multiphase flows are ubiquitous across engineering disciplines: water-sediment river flows in civil engineering, oil-water-sand transportation flows in petroleum engineering; and sorbent-flue gas reactor flows in chemical engineering. These multiphase flows can include a combination of momentum, heat, and mass transfer. Studying and understanding the behavior of multiphase, multiphysics flow configurations can be crucial for safe and efficient engineering design. In this work, a framework for the development and validation, verification and uncertainty quantification (VVUQ) of subgrid models for heat transfer in multiphase flows is presented. The framework is developed for a carbon capture reactor; however, the concepts and methods described in this dissertation can be generalized and applied broadly to multiphase/multiphysics problems. When combined with VVUQ methods, these tools can provide accurate results at many length scales, enabling large upscaling problems to be simulated accurately and with calculable errors. The system of interest is a post-combustion solid-sorbent carbon capture reactor featuring a solid-sorbent bed that is fluidized with post-combustion flue gas. As the flue gas passes through the bed, the carbon dioxide is exothermically adsorbed onto the sorbent particle’s surface, and the clean gas is passed onto further processes. To prevent overheating and degradation of the sorbent material, cooling cylinders are immersed in the flow to regulate temperatures. Simulating a full-scale, gas-particle reactor using traditional methods is computationally intractable due to the long time scale and variations in length scales: reactor, O(10 m); cylinders, O(1 cm); and sorbent particles, O(100 um). This research developed an efficient subgrid method for simulating such a system. A constitutive model was derived to predict the effective suspension-cylinder Nusselt number based on the local flow and material properties and the cylinder geometry, analogous to single-phase Nusselt number correlations. This model was implemented in an open source computational fluid dynamics code, MFIX, and has undergone VVUQ. Verification and validation showed great agreement with comparable highly-resolved simulations, achieving speedups of up to 10,000 times faster. Our model is currently being used to simulate a 1 MW, solid-sorbent carbon capture unit and is outperforming previous methods in both speed and physically accuracy. / 2017-06-21T00:00:00Z

京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第13108号 / 論理博第1556号 / 新制||理||1620(附属図書館) / (主査)准教授 重 尚一, 教授 余田 成男, 教授 石川 裕彦 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DGAM

The aim of the present study is to develop subgrid-scale models that are relevant for complex flows and combustion. A stochastic model based on a stochastic Smagorinsky constant with adjustable variance and time scale is proposed. The stochastic model is shown to provide for backscatter of both kinetic energy and scalar variance without causing numerical instabilities. A new subgrid-scale scalar flux model is developed using the same kind of methodology that leads to the explicit algebraic scalar flux model, EASFM, for RANS. The new model predicts the anisotropy of the subgrid-scales in a more realistic way than the eddy diffusion model. Both new models were tested in rotating homogeneous shear flow with a passive scalar. Rogallo’s method of moving the frame with the mean flow to enable periodic boundary conditions was used to simulate homogeneous shear flow. / QC 20101119

No description available.

Ce travail a pour objectif d'améliorer la prédictivité des modèles à deux fluides pour la description des lits fluidisés gaz-solide pour les particules du groupe A dans la classification de Geldart. La première partie traite de l'incorporation de nouveaux phénomènes physiques dans le formalisme statistique utilisé : collisions induites par le cisaillement, phénomènes de lubrification lors des chocs et forces inter-particulaires. La deuxième partie traite de la résolution numérique du modèle. Il est montré que la simulation des lits de particules de type A présente une très forte sensibilité au maillage, conduisant à une surestimation de la hauteur du lit. L'introduction du formalisme filtré permet d'identifier la traînée filtrée comme étant l'origine principale du problème. Deux modèles de sous-maille sont proposés pour la prédiction de celle-ci et sont testés à la fois sur une configuration académique et sur une expérience de laboratoire. / This work aims to increase the predictivity of the two-fluid model in gas-solid fluidized beds of Geldart A particles. The first part deals with the integration of physical phenomena into the two-fluid model: shear-induced collisions, lubrication between particles and inter-particular forces. The second part deals with the practical resolution of the two-fluid model using numerical codes. It is shown that bed expansion for Geldart A particles have a strong dependance on the mesh size used to compute the flow, leading to a major overestimation. The filtered approach is used and points up the filtered drag as the key of the problem. Two subgrid drag models are proposed and tested on both academic and laboratory configurations.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.

This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.