Browsing by Author "Pina, H.L."
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- Numerical modeling of solar pondsPublication . Lima, Maria Margarida de Lemos Canedo Giestas; Milhazes, Jorge P.; Pina, H.L.A SGSP is a basin of water where solar energy is trapped due to an artificially imposed salinity gradient. In a SGSP three zones can be identified: the surface and bottom zones that are both convective and an intermediate zone in between which is intended to be non-convective. This zone acts as a transparent insulation and allows the storage of solar energy at the bottom where it is available for use. A numerical model where the SGSP dynamics is described in terms of velocity, pressure, temperature and salt concentration is presented. It is based on the Navier-Stokes equations for an incompressible fluid coupled to one advection-diffusion equation for and one advection-diffusion equation for . The fluid density is taken to depend on and and the Boussinesq hypothesis is adopted: the fluid density appearing in the LHS of the Navier-Stokes equation is supposed constant and equal to some reference value whereas it is assumed to be variable in the RHS. The space discretization of the governing equations is based on the respective weak formulations and the discretization employs finite elements with a pressure correction method used to decouple velocity and pressure. Integration in time is accomplished by a BDF (Backward Differentiation Formula) method with the above PDEs treated sequentially within each time step. A computer code was developed employing the finite element class library deal.II. Comparisons with available experimental results are made to validate this numerical model.
- Symbolic computation and the Rayleigh-Bénard stability problemPublication . Lima, Maria Margarida de Lemos Canedo Giestas; Pina, H.L.This paper analyzes the linear stability of an horizontal layer of fluid consisting of a mixture of water and salt. The layer is hotter at the bottom and cooler at the top thus having a tendency to destabilize. To counteract this a salt concentration gradient (denser at the bottom and lighter at the top) is sometimes present, either naturally as in the ocean or created artificially as in solar ponds. The relevant governing equations are the linearized continuum mechanics balance laws applied to an incompressible, heat-conducting and salt-diffusing fluid, leading to a system of partial differential equations, from which the stability of a given base state has to be assessed with respect to arbitrary initial perturbations. This problem involves intensive symbolic computations that can be much facilitated by the use of a Computer Algebra System (CAS).