Symbolic computation and the Rayleigh-Bénard stability problem

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)

Modelos de turbulência aplicados a armazenamento de energia com THERMOCLINE

CIES2020 - XVII Congresso Ibérico e XIII Congresso Ibero-americano de Energia SolarRESUMO: Neste trabalho são considerados os modelos de simulação em 2D de um tanque com thermocline, aplicando uma nova abordagem, considerando a modelação de várias camadas. Esta nova abordagem resulta das características de conceção do tanque que o tornam diferente dos usualmente utilizados. Após ter sido constatado que o modelo k−ε, usualmente utilizado, se revelava inapropriado para descrever os fenómenos que ocorrem neste tanque, resolveu-se optar por um modelo de turbulência SST k – ω mais sensível no caso de domínios complexos e malhas variáveis. Este modelo foi testado e comparado com novas hipóteses, nomeadamente a nível das fronteiras viabilizando quer o tempo computacional de resolução do problema quer a sua convergência e precisão. Três parâmetros estiveram sempre em consonância, o time step, a dimensão da malha e a velocidade inicial.ABSTRACT: In this work, 2D simulation models of a thermocline tank are considered applying a new approach, considering the modeling of several layers, boundary contour and more complex mesh. This new approach results from the design characteristics of the tank that make it different from the ones usually used. Considering all these phenomena that occur in this tank, it was decided to opt for a more sensitive SST k - ω turbulence model in the case of complex domains and variable meshes. This model was tested and compared with new hypotheses, namely at the boundaries, making possible both the computational time to solve the problem and its convergence and precision. Three parameters were always in mind, the time step, the mesh size and the initial speed of the velocity.info:eu-repo/semantics/publishedVersio

Numerical modeling of solar ponds

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

Available CFD models assessment

ABSTRACT: The partial differential equations that govern fluid flow and heat transfer are not usually amenable to analytical solutions, except for very simple cases. Therefore, in order to analyze fluid flows, flow domains are split into smaller subdomains (made up of geometric primitives like hexahedron and tetrahedron in 3D and quadrilaterals and triangles in 2D). The governing equations are then discretized and solved inside each of these subdomains. In the present situation, a finite volume method will be used to solve the approximate representation of the equations’ system. Care must be taken to ensure proper continuity of solution across the common interfaces between two subdomains, so that the approximate solutions inside various portions can be put together to give a complete picture of fluid flow in the entire domain. The subdomains are often called elements or cells and the collection of all elements or cells is called a mesh or grid. The origin of the term mesh (or grid) goes back to early days of CFD when most analyses were 2D in nature. For 2D analyses, a domain split into elements resembles a wire mesh, hence the name.N/

Thermal energy production by a dual solar pound

A Salt Gradient Solar Pond (SGSP) is a salt water basin that collects and stores solar energy. These devices rely on the existence of a non-convective zone (NCZ) that functions as a transparent thermal insulation zone, created by a salt gradient. Salinity and temperature gradients in this zone can give rise to double diffusive problems that can decrease the insulation properties of this zone. The stability of this zone is thus crucial in a SGSP. Stability control, analysis of energy extraction, device efficiency and maintenance strategies are determinant for the correct performance of the SGSP. The implementation of these strategies can be expensive and not sufficient to prevent instability problems. This paper intends to give a contribution to the maintenance problem presenting a new concept of a SGSP utilisation: The Dual Solar Pond (DSP

Modeling in TRNSYS of a single effect evaporation system powered by a Rankine cycle

The paper presents an analysis of a Single Effect Evaporation (SEE) system as a pre-study to the feasibility of concentrated solar power plants (CSP) powering desalination units for cogeneration of water and electricity. An algorithm to model a SEE system in steady-state operation was made and is described in this work. This algorithm was implemented in TRNSYS environment, and a simple analysis was conducted of a SEE system powered by a Rankine cycle used in CSP plants

Dinâmica da dupla difusão : aplicação a lagos solares

Tese apresentada para obtenção do Grau de Doutor em Ciências da EngenhariaN/

Dinamica da dupla difusao: Aplicacao a lagos solares

This work presents a stability analysis and a model of Solar Ponds. This type of solar energy device prevents convection in a body of water by creating a vertical negative salt gradient, that counteracts the thermal gradient. The performance of the Pond depends on the stability of the gradient zone where both thermal and molecular diffusion are present. Due to the fact that thermal diffusion coefficient is greater then the saline diffusion coefficient "double diffusion" instabilities may occur, leading to the onset of a convective process. The first part of this work establishes the limits for the maintenance of a diffusive heat transfer process in the gradient zone considering the effect of solar radiation absorption, the variation of the diffusion coefficients and both effects coupled. The analysis is made considering the Boussinesq approximation of the Navier Stokes system of equations, solved using a semi-analytical process. In the second part of the work a 2D semi-analytical model is made in order to analyse the evolution of temperature, salinity and velocity fields and the transition from diffusion to convection, being possible to validate the stability criteria previously obtained. It is possible to conclude that the onset of convection in a Solar Pond is function of pond's geometry, of the imposed initial saline profile and of pond's transparency. The transition from diffusive to convective flow occurs through oscillatory motion depending on pond's characteristicsAvailable from Fundacao para a Ciencia e a Tecnologia, Servico de Informacao e Documentacao, Av. D. Carlos I, 126, 1249-074 Lisboa, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga

NewSOL Project: Implementation and validation tests for Fluent : Case 0

ABSTRACT: The present report was made according to the implementation of “Fluent: Case 0”1 of the NewSol Project (Grant nº 720985). The Ansys computational package software was used for the conducted simulations. A 2D geometry symmetrical at the middle axis was constructed. Several meshes were both made and simulated for the minimum computational cost. For simplicity of the problem and at this early stage of development of the model, the ullage space was taken to be filled with HTF (Heat Transfer Fluid). Although HTF fills the ullage space in the tank, this is not in good agreement with the condition described in Case 0 which considers air as the medium. All the simulations were performed with steady state conditions. However, in the future transient state would be used.N/