Convección natural en cavidades tridimensionales
- Autores: Odalys Sánchez Casals
- Directores de la Tesis: Oriol Batiste Boleda (dir. tes.), Maria Isabel Mercader Calvo (dir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2015
- Idioma: español
- Tribunal Calificador de la Tesis: Henar Herrero Sanz (presid.), Laureano Ramírez de la Piscina Millán (secret.), Jordi Pallarès Curto (voc.)
- Programa de doctorado: Programa Oficial de Doctorado en Física Computacional y Aplicada
- Materias:
- Enlaces
- Tesis en acceso abierto en: TDX
- Resumen
The modelling of convective transport processes involving heat and mass transfer in an incompressible Newtonian fluid in cylindrical domains is a relevant research subject both for theoretical research and for industry. However, many of the available studies up to present are two-dimensional, and three-dimensional models using laterally heated cylindrical geometries are scarce. Although the two-dimensional approaches with lateral heating give some significant results, they cannot capture the fully three-dimensional nature of the velocity and temperature fields in three-dimensional geometries in bounded domains; besides, the wall effect in transport problems cannot be neglected. As an example, two-dimensional simulations predict solutions with multiple rolls for aspect ratio boxes greater than 2 that are not observed in three-dimensional studies, and fail to reproduce the nature of the first instability and the associated critical values. In this PhD thesis, we simulate numerically three problems in which the convective transport is produced either by temperature differences in the cylinder lids or by concentration differences within the fluid, as happens in the diffusion experiments in liquid metal mixtures or semiconductors. The system analyzed in the first two problems consists of a horizontal cylinder laterally heated; in the first case, the cylinder remains at rest, while in the second a rotation about its axis is included. Fluid behaviour under different heating intensities (Rayleigh number), materials (Prandtl number) and container size (shape parameter) is investigated. The effect of the rotation of the cylinder on the convective motion is discussed in detail. The values of the angular velocity have been kept low in order to analyze the transition from a fluid flow dominated by convection to a flow in which the fluid rotates as a solid-body with the walls. Much of the work is devoted to analyzing the basic solutions and their stability diagram, and to describing some of the secondary solutions. The aim of the third problem is to analyze the influence of convective pollution in the measurements of the diffusion coefficients when using the method of long capillary in low gravity. We will compare our numerical results with those of the experimental technique called shear cells implemented with a finite volume method and with the previously existing two-dimensional results. The influence on the diffusion coefficients measurements of other factors such as, the low gravity levels, the effects of the tilting and rotation of the capillary, the fluctuations of the gravitational field and the actual accelerometer signals g-jitter, will be also assessed. We numerically solve the Navier-Stokes equation in Boussinesq approximation for an incompressible viscous fluid, which is coupled to an equation for temperature or concentration in cylindrical coordinates. The equations are written in the laboratory reference frame, spatially discretized with a pseudospectral Chebyshev method for radial and axial dependence and with a Fourier-Galerkin method in the azimuthal direction and solved with a second order semi-implicit time splitting method.
