Unsteady laminar convection in cylindrical domains: numerical studies and application to solar water storage tanks

Los dispositivos de almacenamiento de energía térmica son ampliamente usados en diversos sistemas térmicos caracterizados por un desfase temporal entre la producción de energia y su consumo, como es el caso de los sistemas de energía solar térmica. El diseño optimizado de estos equipos puede representar un considerable aumento en el rendimiento térmico de la instalación de la cual forman parte. En la línea de optimización de sistemas y equipos térmicos, en los últimos años la Mecánica de Fluidos Computacional (CFD) se ha consolidado como una herramienta básica, proporcionando a investigadores e ingenieros un método para ensayar virtualmente sus diseños, disminuyendo los costes en términos de tiempo, recursos y personal. Es en esta línea se encuentran las principales aportaciones de esta tesis, la cual tiene como principal objetivo la simulación numérica de procesos de convección laminar en régimen transitorio y dominios cilíndricos para su aplicación al estudio de los fenómenos de transferencia de calor y dinámica de fluidos que tienen lugar en los tanques de almacenamiento de energía.Se presenta la metodología seguida para la resolución de las ecuaciones gobernantes de la transferencia de calor y dinámica de fluidos en coordenadas cilíndricas, mostrando las principales particularidades de su discretización para este tipo de geometrías y se detalla el tratamiento realizado para resolver estas singularidades dentro del código numérico. Posteriormente, se expone la metodología para la solución de flujos transitorios e incompresibles y se realiza un riguroso proceso de verificación del código y las soluciones numéricas obtenidas. Esta metodología se aplica al estudio del comportamiento de los tanques de almacenamiento de energía estratificados. Un aspecto básico del funcionamiento de estos equipos es la calidad de la energía almacenada. Esta calidad viene determinada por el grado de estratificación térmica, en la cual influyen diferentes factores como la mezcla que ocurre debido a las corrientes de fluido que entran durante los procesos de carga y descarga térmica y también debido al intercambio de calor con el ambiente. En este sentido, en este trabajo se analiza la estratificación térmica para diferentes condiciones de trabajo y configuraciones por medio de las simulaciones numéricas multidimensionales. Para medir el grado de estratificación se han tenido en cuenta diferentes parámetros y como resultado del estudio, se propone un parámetro adimensional basado en un análisis exergético. Esta exergía adimensional ha permitido comparar el funcionamiento de los tanques en las diferentes situaciones analizadas y se ha mostrado útil para cuantificar la calidad de la energía almacenada.Por otra parte, se estudia el comportamiento térmico de los tanques de almacenamiento durante su modo de operación estático y considerando las pérdidas de energía al ambiente. Este estudio tiene como objetivo fundamental caracterizar el proceso de enfriamiento del fluido en tanques que forman parte de sistemas solares térmicos para el rango de bajas y medianas temperaturas. Se presenta la metodología seguida para el análisis, desde la identificación de los números adimensionales que definen el problema, la formulación de un modelo zonal para la predicción del comportamiento térmico, el estudio paramétrico llevado a cabo y el posterior post-proceso de los resultados con el objetivo de proporcionar los parámetros necesarios para alimentar el modelo zonal. El modelo propuesto, junto con las correlaciones obtenidas, predicen correctamente el comportamiento del fluido, constituyendo una alternativa interesante para reproducir el proceso de enfriamiento del fluido en los tanques durante largos periodos de tiempo.Thermal storage devices are widely used in many thermal systems and applications that are characterised by the delay between energy production and consumption, such as thermal solar systems. The improvement in their design and optimisation is a key aspect in the thermal optimisation of the system, where a good preformance of the storage tank can represent a considerable increase in the overall efficiency of the installation. In the subject of optimisation of thermal equipment, Computational Fluid Dynamics have been consolidated as an indispensable tool providing researchers and engineers with a method to test virtually their prototypes with low effort in time, personnel and resources. This thesis is focused in the numerical simulation of unsteady laminar convection in cylindrical domains and its application to the study of the heat transfer and fluid flow that take place in stratified storage tanks. The first part of this document is devoted to present the methodology followed for the numerical resolution of the governing equation of heat and fluid flow in cylindrical coordinates. The main particularities of the discretisation of the equations in these geometries, as well as the solution procedure for incompressible and transient flow problems are also presented. Special emphasis is given to the verification of the code, the appropriateness of the discretisation adopted and the verification of the numerical solution obtained.The second part of this thesis is focused on the study of the heat transfer and fluid flow phenomena that take place in stratified storage tanks, including the performance measures and modeling efforts of these devices. The quality of the energy stored is determined by the degree of the thermal stratification of the storage tank, which is affected by several factors such as the mixing due to the inlet streams during load and unload, the heat losses to the environment, among others. In this sense, thermal stratification analysis is carried out by means of the virtual prototyping of the tanks for different working conditions and configurations. In order to measure the performance of the tanks, different parameters are considered. The analysis led to the proposition of a new exergy-based parameter as a tool for assessing and comparing storage tanks. The usefulness of this parameter for quantifying the quality of the energy stored is also shown.Furthermore, the thermal behaviour of storage tanks during the static mode of operation considering the heat losses to the environment is also analysed. The study is addressed to characterise the cool down of the fluid inside storage tanks for solar thermal systems in the low-to-medium temperature range. The methodology followed, from the identification of the significant non-dimensional parameters that define the problem, the formulation of a zonal prediction model, a parametric numerical study by means of detailed multidimensional CFD computations and the post-processing of the results in order to feed the global model are exposed in detail. Zonal model presented, together with the correlations given are in good agreement with the numerical results and constitute an alternative for the prediction of the long-term performance of the storage tanks during the cooling process

Spectral methods in fluid dynamics

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome

Poloidal-toroidal decomposition in a finite cylinder. II. Discretization, regularization and validation

The Navier-Stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility. Regularity of the solutions is ensured in several ways: First, the potentials are represented using a spectral basis which is analytic at the cylindrical axis. Second, the non-physical discontinuous boundary conditions at the cylindrical corners are smoothed using a polynomial approximation to a steep exponential profile. Third, the nonlinear term is evaluated in such a way as to eliminate singularities. The resulting pseudo-spectral code is tested using exact polynomial solutions and the spectral convergence of the coefficients is demonstrated. Our solutions are shown to agree with exact polynomial solutions and with previous axisymmetric calculations of vortex breakdown and of nonaxisymmetric calculations of onset of helical spirals. Parallelization by azimuthal wavenumber is shown to be highly effective

Magnetohydrodynamic experiments on cosmic magnetic fields

It is widely known that cosmic magnetic fields, i.e. the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. It is less well known that cosmic magnetic fields play also an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI). Considerable theoretical and computational progress has been made in understanding both processes. In addition to this, the last ten years have seen tremendous efforts in studying both effects in liquid metal experiments. In 1999, magnetic field self-excitation was observed in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently, self-excitation was also obtained in the French "von Karman sodium" (VKS) experiment. An MRI-like mode was found on the background of a turbulent spherical Couette flow at the University of Maryland. Evidence for MRI as the first instability of an hydrodynamically stable flow was obtained in the "Potsdam Rossendorf Magnetic Instability Experiment" (PROMISE). In this review, the history of dynamo and MRI related experiments is delineated, and some directions of future work are discussed.Comment: 25 pages, 26 figures, to appear in ZAM

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows

Superfluid spherical Couette flow

We solve numerically for the first time the two-fluid, Hall--Vinen--Bekarevich--Khalatnikov (HVBK) equations for a He-II-like superfluid contained in a differentially rotating, spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor--Couette flow. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as \Rey increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for \Rey > 10^3. The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall--Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to "pinch" meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the flow appreciably, but it does alter the cores of the circulation cells, especially at lower \Rey. As \Rey increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In nonaxisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants.Comment: Accepted for publication in the Journal of Fluid Mechanic

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

Experimental and numerical study of Taylor-Couette flow

Taylor-Couette flow between in a gap of two coaxial cylinders is studied using a combination of particle image velocimetry (PIV) experimental data and computational fluid dynamics (CFD). Wavy vortex flow and modulated wavy vortex flow which are two flow regimes of Taylor-Couette flow are investigated using the PIV technique and power spectral density. In addition, the turbulent Taylor-Couette flow is studied by means of Reynolds-average Navier-Stokes (RANS) simulations and stereo-PIV. Two main turbulence models of Reynolds-average Navier-Stokes simulations are used in the investigation and verified with the PIV experimental data. The investigations provide in-depth evaluation of the simulation schemes. This work shows that computational fluid dynamics in combination with PIV data is an excellent tool to study turbulent structures in the Taylor-Couette flow. Furthermore, this work demonstrates the in-depth evaluation of RANS simulation