C. F. Tavares1*, J. M.P. Coelho2, D. Castro Alves2, M. Abreu2, A. M. Joyce1, E. C. Fernandes3

1 INETI, Dept. of Renewable Energies, Campus do Lumiar do INETI, 1649-038 Lisbon, Portugal
2 INETI, Dept. of Optics and Laser, Campus do Lumiar do INETI, 1649-038 Lisbon, Portugal
3 IST, Dept. of Mechanical Engineering, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
* Corresponding Author, :elia. tavares@.ineti. pt

Abstract

The gradient zone of salt gradient solar pond is a double diffusive system where instabilities can appear leading to the reduction of the performance of the pond. To better understand double diffusive instabilities a double diffusive layer was studied in laboratory. An initial stable salt stratified layer was heated from bellow to a prescribed temperature and the evolution of the system was analysed. Shadowgraph and Particle Image Velocimetry (PIV) techniques were used to identify and to study the evolution of convective and diffusive zones, to obtain instantaneous whole field velocities measurement and to analyse the effect of convection on the behaviour of the neighbouring densities interfaces. The evolution of the temperature and salinity profiles was also recorded along time to analyse the stability criteria that lead to the transition of diffusive regime to convective regime. Experimental buoyancy ratios show good agreement with Veronis’ stability criteria. For high imposed temperature and a comparative weak density gradient, vigorous convective layers separated by thin interfaces produce great instabilities and a rapid destruction of the diffusive zones. On the other hand, when the linear solute gradient is strong the system develops quasi-stationary states where the interfaces remain stable for a significant period of time.

Keywords: solar pond, double-diffusive convection, flow visualization, stability

1. Introduction

A salt gradient solar pond is an artificial device used to collect and store solar thermal energy. A non-convective zone in the middle of the solar pond allows a significant rise of temperature in the lower zone where the solar thermal energy is stored. This is an attractive and low cost solution to capture and store solar thermal energy, in a seasonal way, due to easy construction with few resources needed. The surface area of a solar pond can vary between few square meters to thousands of square meters. Nowadays, solar ponds with a surface area of few square meters and few centimetres of depth are being developed for different thermal application like, for instance, desalination [1].

The main key to the working of a solar pond is the non-convective zone, also named gradient zone. The gradient zone works like an optical thermal insulator reducing the loss of heat collected in the lower zone of the pond (the storage zone), since the water has low thermal conductivity and is opaque to infra-red radiation.

The non-convective zone is characterized by the presence of two gradients, the salinity and the temperature gradients, both having an opposite effect to the stability of the non-convective layer. The salinity gradient increases the density with depth, promoting the stability of the layer, while the temperature gradient has an adverse effect that counteracts the density gradient. The different
molecular diffusivities of heat and mass and the opposing effects on the vertical density distribution of the temperature and salinity gradients can lead to local destabilization that could cause local convective motions, even with a statically stable density gradient. This kind of instabilities is named double-diffusive convection. The appearance of these convective zones weakens the insulator feature of the solar pond and reduces pond’s efficiency. To predict and prevent the onset of convective motion in the gradient zone it is important to understand double diffusive process and the condition for the change of diffusive regime to convective regime.

It should be remarked that double (or multiple) diffusive convection phenomenon takes place in other engineering systems and processes like crystal growth, liquefied natural gas storage tanks and nuclear engineering, in different domains, like oceanography, astrophysics and geology and in several practical applications like pollution and thermal environment control of buildings [2].

One of the topics of double diffusive systems is the study of the behaviour of the double diffusive layer under stability criteria, i. e., the physical conditions, regarding temperature and salinity profiles, from which instabilities can appear leading to oscillatory movements that could produce convective regimes. Veronis [3] defined that stability depends essentially on the following dimensional numbers: the thermal and salinity Rayleigh numbers, Ra and Rs, respectively, the Prandtl number, Pr, and the Schmidt number, Sc. The ratio between the Pr and Sc, t, is for NaCl aqueous solution equal to approximately 10-2, (t = Pr/Sc => t = KS/KT) showing that the thermal diffusivity (KT) of this salt is one hundred greater than the molecular diffusivity (KS). The relation between Rs and Ra is named density stability ratio, or buoyancy ratio, Rp, and is defined as:

Rs 0AS

— ^ RP =——

Ra p aAT

where AS and AT are the salinity and temperature differences between the top and the bottom of the gradient zone, and a and p are the coefficient of thermal and saline expansion coefficient. The theoretical analysis of Veronis of the behaviour of double diffusive layers under stability criteria gave the following marginal states equations: for the onset of instabilities Ra=0.809Rs (i. e., Rp= 1.236), and for the onset of steady convective motion: Ra=43.16Rs (i. e., Rp= 0.023). More recent studies [4], which consider variation of flow properties and the effect of solar radiation absorption, led to the definition of some different stability conditions, more restrictive when non-constant diffusivities of molecular heat and salt and solar radiation absorption is considered simultaneously in the theoretical analysis.

Experimental studies of double diffusive layers were usually performed by heating from bellow an initial stable salt gradient which has a similar effect to solar radiation absorption in salt stratified layer. When a stable salt gradient layer is heated from below, a series of convective layers separated by thin density interfaces could be formed. Turner [5] was the first to perform, in laboratory, quantitative studies of this phenomenon, concentrating on the dynamics of the first mixed layer which appears near the heating surface, and the formation of the second layer above it. Huppert and Linden [6] extended this formulation to predict the evolution of the following layers. The density interfaces that separate convective layers from gradient zones, this last with more or less thickness, are subject not only to double diffusive instabilities but also to other types of instabilities, namely the effect of the adjacent convective motions. The rates of salt transported diffusively from the density interface and convectively into the mixed regions determine the evolution of the thickness and stability of these interfaces [7], and consequently the growth rate of convective zones.

The present work consists on the laboratory study of double diffusive systems. A salt stratified layer with an initial linear concentration gradient was heated from bellow at a prescribed temperature. With the present work the flow visualization technique Particle Image Velocimetry (PIV) [8] was implemented to obtain the velocity fields and the patterns of convective zones and Shadowgraph technique was used to identify the position of the interfaces. We present results of the evolution of a double diffusive layer, namely, the evolution of the salinity and temperature vertical profiles, and we compare these profiles with Veronis’s stabilities criterions. The effects of convective zones on the behaviour of densities interfaces are also analysed.