Salt diffusion in a temperature field: Application to salinity profiles in solar ponds

In the present investigation, the process of diffusion of salt in a vertical column of liquid, subjected to temperature variations of the types T(x) = constant, linear ( = a + bx) and parabolic ( = a + bx - cx²); with a constant concentration difference between the top and the bottom (0 and 25 per cent, respectively) is studied. It is seen that a linear temperature gradient, T(x) = a + bx, leads to a near convex parabolic salt concentration profile with maximum deviations increasing from 13.5 per cent (at 40°C) to 14.8 per cent (at 70°C) and eventually to 15.7 per cent (at 90°C) with respect to the linear concentration value of 12.5 per cent (by weight) at the midpoint. Conversely, the parabolic temperature profile as well as the modified profile due to the Soret effect leads to near cubic salt profiles which differ only by 2–3 per cent in the upper half of the pond. However, they show a point of inflexion at larger depths near the bottom around which the convex profiles change over and become concave. Subsequently, these studies have been extended to compute the salinity profiles of thermal configurations of the operational solar pond.     

Linear stability analysis of double-diffusive solar pond

In this communication, the stability of the double-diffusive solar ponds has been investigated in the linear approximation. The corresponding linearized system of equations of motion is reduced to a single integro-differential equation using the Green-function technique. In contrast to the conclusions of Veronis that, initially, the instability occurs as an oscillatory mode and at a value of R_T (Rayleigh number for temperature) greater than R_S the motion becomes steady, the present analysis shows that, initially, as R_T increases from zero but remains considerably less than R_S, exponentially growing and decaying modes (steady motion) occur first; for a value of R_T more than a critical value R_T^c, the motion becomes oscillatory. This oscillatory motion may, due to the basic non-linear dynamics of the system, even become aperiodic. Further, for R_S → ∞, the minimum value of R_T for which steady motions can occur tends to $\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{·R}{}_{\mathrm{S}}$, where $\text{K}\text{= K}{}_{\mathrm{S}}\text{/K}{}_{\mathrm{T}}$ where K_S and K_T are diffusivity coefficients for salt and temperature, respectively; as a contrast, according to Veronis, $\text{R}{}_{\mathrm{T}}\text{a}\text{?}\text{σ}{}^{\mathrm{?1}}\text{R}{}_{\mathrm{S}}\text{; σ = v/K}{}_{\mathrm{T}}\text{, v}$ being the kinematic viscosity.     

Some thoughts on solar ponds

Three types of no-salt solar ponds, which do not exhibit environmental or operational problems of the kind observed for salt ponds, are examined on a laboratory scale. The negative temperature gradient necessary for heat storage was obtained by using appropriate arrangements in such a way that narrow passages appear which reduce substantially the heated water currents, or by using two (or more) transparent immiscible liquids which constitute a density gradient serving the same purpose. The influence of the dissolved air in the water mass is discussed.     

The process of loss of internal stability in salt gradient solar ponds

Loss of the bulk stability in salt gradient solar ponds is a rather rare, short duration phenomenon, which can lead to complete mixing of the gradient zone. Laboratory investigations have allowed close observation of this phenomenon and comparison of the derived data with theory. It is shown that there is little or no probability of such instability occurring with the maximum salt concentration normally used (about 20% at the bottom). Boundary erosion of the gradient zone is an entirely unrelated matter.     

Numerical modelling of convective layers in solar ponds

This paper involves the prediction of convective layers on the sidewalls of a solar pond. A three-dimensional finite-volume method for incompressible flows with different initial and boundary conditions is applied for the solution of convective layers generated on solar pond walls. A parametric study was conducted to predict the effects of wall tilt angle and salt concentration on the characteristics of the convective layers.Comparison of the present numerical results with experimental data from previous studies shows that it is possible to capture the flow features of the convective layers. Furthermore, the trends predicted for the effects of the tilt angles and the salt concentrations agrees well with that obtained from experimental data.     

Investigation of solar pond surface zone temperature assumptions

This paper presents the results of tests concerning two assumptions about the surface zone of a solar pond. The first assumption is that the surface zone temperature of the solar pond is equal to the air dry bulb temperature, and the second one is that it is equal to the air wet bulb temperature. The surface zone temperature and the storage zone temperature are predicted by using a lumped-parameter model. The experimental results of the surface zone conform well with theoretical values. The results indicate that the air dry bulb temperature is more accurate in winter-time but that the errors generated by both assumptions are almost equal in the summer-time.     

Thermal analysis of three zone solar pond

This paper presents a periodic analysis of a three zone solar pond as a solar energy collector and long term storage system. We explicitly take into account the convective heat and mass flux through the pond surface and evaluate the temperature and heat fluxes at various levels in the pond during its year round operation by solving the time dependent Fourier heat conduction equation with internal heat generation resulting from the absorption of solar radiation in the pond water. Eventually, an expression, for the transient rate at which heat can be retrieved from the solar pond to keep the temperature of the zone of heat extraction as constant, is derived. Heat retrieval efficiencies of 40.0 per cent, 32.1 per cent, 28.3 per cent and 25.5 per cent are predicted at collection temperatures of 40, 60, 80 and 100°C, respectively. the retrieved heat flux exhibits a phase difference of about 30 to 45 days with the incident solar flux; the load levelling in the retrieved heat flux improves as the thickness of the non-convective zone increases. the efficiency of the solar pond system for conversion of solar energy into mechanical work is also studied. This efficiency is found to increase with collection temperature and it tends to level around 5 per cent at collection temperatures about 90°C.     

Use of clays as liners in solar ponds

An alternative to synthetic materials for use in solar pond liners is to select clayey soils as hydraulic barriers. This option reduces the cost of construction and the risk of contamination of subsoil and groundwater by hot brines. This paper deals with the physical, chemical and hydraulic properties of different soils tested mainly as compacted clay liners. The underdeveloped nations have the option to use this type of liner, but before doing so several tests are recommended, including those for soil and water composition, permeability, plasticity and X-ray diffraction analysis. In this investigation the following samples are analyzed: native clayey soils with illite, montmorillonite and halloysite, treated and non-treated bentonites in powder and granulated form, a mixture of zeolite and sodium bentonite, and industrial minerals composed largely of halloysite, kaolinite and attapulgite selected clays. Neutral salt aqueous solutions (NaCl and KCl) at different concentrations and under temperature gradients were used for compatibility testing conducted on these specimens. Experiment setup and particular testing procedures are also discussed.     

Monitoring and maintaining the water clarity of salinity gradient solar ponds

A common problem encountered in salinity-gradient solar ponds is the growth of various types of algae and bacterial populations, which affects the brine clarity and hence reduces thermal performance. Algae and bacterial populations are enhanced by the presence of organic nutrient such as nitrogen and phosphorus. A comprehensive study was undertaken on three salinity-gradient solar ponds in Australia: a 3000 m² sodium chloride solar pond at Pyramid Hill in Northern Victoria; a 50 m² sodium chloride; and 15 m² magnesium chloride solar pond at RMIT University in Bundoora, Victoria. The experimental study involved monitoring the clarity of these three ponds and testing chemical and biological treatment methods to see their effect on the brine transparency. The sources of turbidity and their impacts on clarity and efficiency of salinity-gradient solar ponds are presented in detail in this paper. The initial observation showed that the amount of sunlight is reduced due to the heavy algal growth creating instability in the solar pond as it absorbs light. Two treatment methods were applied to these solar ponds and experiments were conducted to study the turbidity reduction in the solar ponds. In the RMIT magnesium chloride solar pond, diluted hydrochloric acid was injected in the pond to reduce the pH and turbidity levels. Algal blooms were observed and found in the pond where the pH was between 5.5 and 8. It was observed from the experimental study that pH values should be kept below 4.5 to maintain low turbidity and prevent algae growth. The introduction of brine shrimps was also found to be very effective and economical to control algae, provided the oxygen has not depleted due to advanced heavy algal growth. The investigation concluded that hydrochloric acid could be used initially as a shock treatment to kill all the algae and then brine shrimps could be introduced to control the growth of algal and maintain transparency. This analysis showed that by using a combination of chemical and biological treatment methods, the pond clarity can be maintained and the thermal efficiency of the solar pond can be improved.     

Thermal analysis of honeycomb solar pond

A solar pond consisting of honeycomb panels placed on a thin layer (～ 1 cm) of silicone oil floating on the body of a hot water reservoir is considered and analysed for the heat transfer processes in the system. An explicit expression for the transient rate of heat extraction at constant temperature is derived to obtain the annual variation of retrieved heat flux. The year-round thermal performance of the system has been investigated. For a solar pond with a 10 cm high honeycomb structure, annual average efficiencies of 65, 48, 33 and 24% are predicted for retrieved heat flux at temperatures of 40, 60, 80 and 90°C, respectively. A comparison between honeycomb solar pond and salt-gradient solar pond is also presented.     

Mathematical modelling of salt gradient solar pond performance

This paper presents a mathematical model of the performance of the salt gradient solar pond. A lumped parameter model of the upper convective zone, non-convective zone and lower convective zone is used. This model enables the temperatures of the upper-convective zone and the lower convective zone of the solar pond to be predicted. The experimental results agree well with theoretically predicted values. The major error in the theoretical results is due to the difference between the theoretical value of the solar radiation inside the water and that observed experimentally. It is found that the experimental value of the solar radiation at a depth of 90 cm is approximately 26 per cent of the total solar radiation falling on the solar pond surface, whereas the corresponding theoretical value is found to be 33 per cent. The results conclude that the lumped parameter model can be used as a simple model to predict the performance of the solar pond.     

Constant flow solar pond collector/storage system

This paper presents a periodic analysis of the process of heat extraction by the brine layer circulating at constant flow rate through the bottom convective zone of a solar pond. Explicit expressions for the transient rate of heat extraction and the temperature at which heat can be extracted, as a function of time, depths of convective as well as non-convective zones and the flow rate, are derived. Extensive analytical results for the optimum performance of a pond during its year round operation are presented. In a pond with an upper convective zone depth of 0.2 m optimum heat extraction efficiencies of 24 per cent, 29 per cent and 32 per cent corresponding to heat extraction temperatures of 89, 55 and 42°C are predicted for water flow rates of 2 × 10^?4, 5 × 10^?4 and 10^?3 kg/s m², respectively. The load levelling in the extracted heat flux as well as in its temperature improves as the flow rate is lowered and the non-convective zone is over sized. An increase in the total depth of the solar pond improves the load levelling in extraction temperature, but influences the extracted heat flux differently; shifts its maximum to winter months and deteriorates the load levelling. The variability in flow rate required for the maintenance of constant temperature of the heat extraction zone is also investigated. It is found that the required variability is less for higher temperatures of the heat extraction zone and larger depths of the non-convective zone.     

An experimental study on a modified design compact shallow solar pond

In this study a design of compact shallow solar pond modified from that of Kudish (Kudish and Wof, 1978) is studied experimentally. The difference between this design and that of Kudish is that the water depth is allowed to be changed from 2–15 cm and is not fixed as in the mentioned reference design. The thermal insulation of the cover is installed between the reflector and the inner surface of the wooden cover. In the design of the reference (Kudish and Wof, 1978), the insulation is fixed on the outer surface of the cover, where it will probably be damaged by water, wind, dust etc. Also in our design, the level of water in the bag is measured using a static pressure manometer. The tests were carried out both in winter and in summer whereas they have been done only in summer in the mentioned reference. The results show that the compact shallow solar pond can provide a suitable water temperature to be used for low and moderate temperature applications even in a cold winter and with 10 cm water depth.     

The influence of non-constant diffusivities on solar ponds stability

A solar pond is a basin of water where solar energy is trapped due to an artificially created gradient of salinity that prevents convective motions. The present study intends to clarify the contribution of non-constant diffusion coefficients for the stability of the gradient layer together with the influence of solar radiation absorption, the thermal and molecular diffusivities being assumed to be linear functions of the vertical co-ordinate z. The analysis shows that the consideration of these two effects decreases the margin of stability in comparison with previous studies based on a layer of fluid heated from below with constant diffusivities coefficients and linear profiles for both temperature and salt.     

Single-stage and advanced absorption heat transformers operating with lithium bromide mixtures used to increase solar pond's temperature

Mathematical models of single-stage and advanced absorption heat transformers operating with the water/lithium bromide and water/Carrol™ mixtures were developed to simulate the performance of these systems coupled to a solar pond in order to increase the temperature of the useful heat produced by solar ponds. Plots of coefficients of performance and gross temperature lifts are shown against the temperatures of the heat supplied by the solar pond. The results showed that the single-stage and the double absorption heat transformer are the most promising configuration to be coupled to solar ponds. With single-stage heat transformers it is possible to increase solar pond's temperature until 50°C with coefficients of performance of about 0.48 and with double absorption heat transformers until 100°C with coefficients of performance of 0.33.     

Amorphous silicon solar cells deposited with non-constant silane concentration

The performance and light-soaking behavior of hydrogenated amorphous silicon (a-Si:H) solar cells with absorber layers deposited under non-constant silane concentration (SC) - a measure of silane dilution in hydrogen - using plasma enhanced chemical vapor deposition (PECVD) are investigated. Constant SC values during deposition close to the amorphous to microcrystalline phase transition lead to the formation of crystallites after a certain thickness. To prevent this transition, SC is adjusted during growth to produce an amorphous material that is close to the microcrystalline phase transition without the inclusion of a detectable microcrystalline phase. By adjusting SC during deposition it was possible to achieve an increased open-circuit voltage that is up to 40 mV higher than that for a conventional amorphous silicon solar cell at initial efficiencies above 9%. The best solar cells produced with non-constant SC show improved stability against light induced degradation, which leads to a relative loss in fill factor of only 11.4%, resulting in a stabilized fill factor of 62.5%.     

Physics of shallow solar pond water heater

This communication presents a theoretical analysis of a shallow solar pond water heater, which is in good agreement with the experiments of Kudish and Wolf (1979) and the authors. the heater consists of an insulated metallic rectangular tank with black bottom and sides and a transparent cover at the top. After the collection of solar energy during sunshine hours the heater stores a substantial amount of heat because the top glass cover is covered by an adequate insulation in the night. Analytical expressions for the transient rise of temperature of water in the tank have been derived taking into account the appropriate heat transfer processes during day and night. These experimental results as well as those of Kudish and Wolf (1979) have been found to be in good agreement with the theory presented in this paper. the effects of one more glass cover on the top, and of the thickness of the bottom and side insulation and tank depth on the water temperature have also been studied.