Saturated solar ponds: 2. Parametric studies

The effects of following parameters on the performance of saturated solar ponds are studied: thickness of upper convective zone, nonconvective zone, and lower convective zone; starting time of the pond; water table depth below the pond; ground thermal conductivity; transmissivity of salt solution; incident radiation; ambient air temperature, humidity, and velocity; thermophysical properties of salt solution; pond bottom reflectivity; convection, evaporation, radiation, and ground heat losses; temperature and rate of heat removal; type of salt. Magnesium chloride and potassium nitrate salt ponds located at Madras (India) are considered for the parametric study. A comparison is also made with an unsaturated solar pond.     

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.     

Performance assessment of a magnesium chloride saturated solar pond

This paper deals with the experimental investigation of a magnesium chloride saturated solar pond and its performance evaluation through energy and exergy efficiencies. The solar pond system is filled with magnesium chloride containing water to form layers with varying densities. A solar pond generally consists of three zones, and the densities of these zones increase from the top convective zone to the bottom storage zone. The incoming solar radiation is absorbed by salty water (with magnesium chloride) which eventually increases the temperature of the storage zone. The high-temperature salty water at the bottom of the solar pond remains much denser than the salty water in the upper layers. Thus, the convective heat losses are prevented by gradient layers. The experimental temperature changes of the solar pond are measured by using thermocouples from August to November. The densities of the layers are also measured and analysed by taking samples from at the same point of the temperature sensors. The energy and exergy content distributions are determined for the heat storage zone and the non-convective zone. The maximum exergy destructions and losses appear to be 79.05 MJ for the heat storage zone and 175.01 MJ for the non-convective zone in August. The energy and exergy efficiencies of the solar pond are defined as a function of solar radiation and temperatures. As a result, the maximum energy and exergy efficiencies are found to be 27.41% and 26.04% for the heat storage zone, 19.71% and 17.45% for the non-convective zone in August, respectively.     

Thermal behavior of a small salinity-gradient solar pond with wall shading effect

The thermal behavior of a small-scale salinity-gradient solar pond has been studied in this paper. The model of heat conduction equation for the non-convective zone has been solved numerically with the boundary conditions of the upper and lower convective zones. The variation of the solar radiation, during a year, and its attenuation in the depth of the pond has been discussed. The wall shading area for a vertical wall square pond has been elaborated and its effect on the reduction of the sunny area has been included in the model. The temperature variation of the storage zone has been calculated theoretically and compared with the experimental results. The sensitivity analysis demonstrates the importance of the side and bottom insulation and the thickness of the non-convective zone, as well as the wall shading effect on the performance of the pond. The application of several loading patterns gives an overall efficiency of 10% for the small pond.     

A parametric study of the small-scale solar pond (SSSP)

A parametric study of salt-gradient solar ponds of size less than 100 m² is presented. The study is based on a dynamic model of the pond which takes into account the variation of solar radiation, ambient temperature and the amount of heat extracted with time. Furthermore3 it considers a small-scale pond whose top is covered by a transparent cover, thus considerably reducing the thickness of the top convective zone. The parameters investigated include: pond dimensions, depths of the different layers, starting dates for pond operation and load application, pond insulation and the value of the thermal load.     

Numerical Simulation of Double-diffusive Dynamical Model of a Solar Pond Considering the Effect of Turbidity and Wind

A solar pond, typical double-diffusive system, is a stable heat source that can collect and store the solar energy. When the thermal stable condition is not satisfied at the interface, the upper and lower convective zone (UCZ and LCZ) will erode the middle non-convective zone (NCZ), resulting in a drop or even a collapse of the thermal performance of solar pond. Wind strongly affects the erosion of NCZ from the entrainment of UCZ. The double-diffusion of heat and salt plays an important role in the erosion of NCZ from the entrainment of the lower-con vective zone (LCZ). The turbidity of saline water in the pond not only could lower the thermal performance of solar pond, but have effect on the entrainment mechanism. In this paper, based on the double-diffusive model along with the wind-driven turbulent entrainment model, the effects of turbidity and external wind etc. on the thermal performance of solar pond and the entrainment mechanism are analyzed with the numerical simulation.     

Modeling and testing a salt gradient solar pond in northeast Ohio

A dynamic computer model of a salt gradient solar pond as an annual-cycle solar energy collection and storage system was developed. The model was validated using experimental results of a solar pond located at the Ohio Agricultural Research and Development Center (OARDC), Wooster, Ohio. The model was then used to analyze the transient energy phenomena which occurred within the storage zone of the pond. Generalized daily weather functions used were the incident solar radiation upon a horizontal surface, the daylight length and the daily maximum and minimum ambient air temperatures.Various simulations were performed to evaluate the OARDC solar pond and to improve its overall effective capacity of heat storage. It was found that 4–6 weeks variation in start-up time and 5–10°C variation in start-up temperature had no effect on late summer peak storage temperature. The pond operated at a 20 per cent collection efficiency with a 1.5-m deep gradient. Insulating the pond in the winter would be beneficial if no heat was removed during the fall. Reducing the gradient zone thickness to 1 m and enlarging the storage zone could improve the performance of a 3-m deep pond. The model could be used to predict and analyze the transient thermal response of large storages associated with solar heating system for a variety of purposes and climatic conditions.     

A parametric design study of solar ponds

The salt stratified solar pond is found to be a reliable solar collector and storage system. This paper discusses the effect of varying certain design parameters on pond steady-state temperatures. These significant parameters are sizing parameters—pond surface area and depth of the pond; operating parameters—storage volume and the heat extraction fraction; and geo-climatic parameters3s?olar radiation, water table depth and upper convective zone thickness. Studies indicate that there is an optimum depth and storage volume of the pond for each application in terms of temperature and heat load desired.     

Performance of Shallow Solar Ponds

This investigation is devoted to study the performance of a shallow solar pond composed of two zones, a convective zone and a non-convective zone. Finite difference techniques and a comprehensive iterative procedure were employed to solve the realistic transient energy equations subjected to temperature dependent heat transfer coefficients. Actual solar insolation, wind speed, and ambient temperature were used to evaluate the performance of this shallow solar pond at various time intervals for Alexandria all the year round. Lastly, the effect of varying the percentage of the non-convective zone was also investigated under various environmental and operating conditions.     

A fully coupled,transient double-diffusive convective model for salt-gradient solar ponds

A fully coupled two-dimensional, numerical model that evaluates, for the first time, the effects of double-diffusive convection in the thermal performance and stability of a salt-gradient solar pond is presented. The inclusion of circulation in the upper and lower convective zone clearly shows that erosion of the non-convective zone occurs. Model results show that in a two-week period, the temperature in the bottom of the solar pond increased from 20 °C to approximately 52 °C and, even though the insulating layer is being eroded by double-diffusive convection, the solar pond remained stable. Results from previous models that neglect the effect of double-diffusive convection are shown to over-estimate the temperatures in the bottom of the solar pond. Incorporation of convective mixing is shown to have profound impacts on the overall stability of a solar pond, and demonstrates the need to actively manage the mixing and heat transfer to maintain stability and an insulating non-convective zone.     

Salt gradient stabilized solar pond collector

This paper presents a theoretical analysis of a salt gradient solar pond as a steady state flat plate solar energy collector. 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 by solving the Fourier heat conduction equation with internal heat generation resulting from the absorption of solar radiation as it passes through the pond water. These evaluations, in combination with energy balance considerations, enable the derivation of the expressions for solar pond efficiency of heat collection as well as the efficiency of heat removal. The efficiency expressions are Hottel-Whillier-Bliss type, prevalent for flat plate collectors. Numerical computations are made to investigate the optimization of geometrical and operational parameters of the solar pond. For given atmospheric air temperature, solar insolation and heat collection temperature, there is an optimum thickness of nonconvective zone for which the heat collection efficiency is maximum. The heat removal factor is also similar to that of a flat plate collector and the maximum efficiency of heat removal depends on both the flow rate and the temperature in the nonconvective zone.     

A transient model of a laboratory-scale carnalite salt gradient solar pond

The thermal performance of a laboratory-scale salt gradient solar pond has been modeled as a one-dimensional unsteady conduction heat transfer problem with heat generation. The pond is assumed to be cut into horizontal slices and finite difference heat balance equations are solved simultaneously to predict the temperature of each slice at any time. The initial conditions were the temperature profile data. The boundary conditions were determined by studying the heat balance at the bottom of the pond and by assuming the pond surface temperature to be equal to the ambient temperature. Solar radiation attenuation is calculated by the Bryant and Colbeck formula. A computer program is constructed to perform the calculations. In addition, Kooi's model was compared with our model. Similarly the salinity behavior was studied by writing the one-dimensional differential mass balance equation over a small slice with the appropriate boundary and initial conditions. The resultant set of linear equations was solved simultaneously for the unknown new concentrations. A computer program has been constructed to perform the calculations. Fair agreement between experimental and predicted profiles was obtained.     

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.     

Computer simulation of salt gradient solar pond’s thermal behaviour

This paper investigates a few mathematical aspects of computer simulation of salt gradient solar pond’s thermal behavior. The basic equation governing heat flow in the non-convective zone of solar pond is solved by finite difference approach using the Crank–Nicholsen method. Stability and convergence of the method, specifically for the case of solar pond, is examined over a wide range of depth difference (Δx) and time difference (Δt). It is observed that the mesh ratio parameter ( ) which is used to define the stability and convergence of the method does not have an absolute value, rather its value varies with Δx. While using an actual set of Δx and Δt, the stability must be tested with reference to the set being used. Few other mathematical aspects pertaining to the actual application of the method are also investigated. Also, the effect of fineness of ambient input data on long term performance of the pond is investigated. It is observed that the diurnal variation of ambient input data yields the same accuracy as the hourly variation. Different approaches of calculating the heat losses from upper convective zone are compared for long term performance of the pond. A simple method is suggested to calculate the radiation flux at a depth which results due to multiple reflections between bottom and surface of the pond. The method saves computational time when used for simulation and is also suitable for hand calculations.     

Influence of thermal emittance on the performance of laminated solar control glazing

Influence of thermal emittance on the performance of laminated solar control glazing is presented. A transient one-dimensional mathematical model allowing the prediction of conductive heat transfer within the glazing and convective and radiative heat transfer from the glazing towards the interior and exterior are considered separately. A constant normal incidence of air mass 2 solar radiation of 750 W/m² was assumed. The redistribution of the component of the solar radiation absorbed by the laminated glass and the shading coefficient (SC) were calculated for solar transmittance, 0.05 to 0.35; thermal emittance of the inner surface of the glazing, 0.15 to 0.85; convective heat transfer coefficient for the exterior surface, 10–100 W/m² K and exterior ambient temperatures of 15°C, 32°C and 45°C. The results indicate that as the emittance decreases, the SC decreases by 10–20% for all cases of ambient temperatures considered. The contribution from the convective mechanisms to the heat transfer to the interior is always higher than that from radiative process in the range of ambient temperatures considered. The results presented in this paper would help to decide whether for a given location of interest, the incorporation of a heat mirror glazing would make a meaningful reduction in the cooling load in enclosures with single glazed windows.     

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.     

Enhancing the thermal efficiency of solar ponds by extracting heat from the gradient layer

An alternative method of heat extraction from salinity-gradient solar ponds is investigated with the aim of increasing the overall energy efficiency of collecting solar radiation, storing heat and delivering this heat to an application. In this alternative method, heat is extracted from the non-convecting gradient layer of a solar pond as well as, or instead of, from the lower convective zone (LCZ). A theoretical analysis of combined gradient-layer and LCZ heat extraction is conducted to obtain expressions for the variation of temperature with depth in the pond, and the temperature gradient with depth. The dependence of the overall energy efficiency of the pond on thickness of the gradient-layer, temperature of delivered heat, and various combinations of gradient layer and LCZ heat extraction rates, including the limiting cases of gradient-layer heat extraction only, and LCZ heat extraction only, is then explored. This theoretical analysis suggests that heat extraction from the gradient layer has the potential to increase the overall energy efficiency of a solar pond delivering heat at a relatively high temperature by up to 50%, compared with the conventional method of heat extraction solely from the LCZ. The potential gain in efficiency using gradient-layer heat extraction is attributed to the lowering of heat losses by conduction to the upper convective (surface) zone that can be achieved with this method. Experimental investigations are proposed to test the predictions of the theoretical analysis in practice, and assess the impact of a number of idealized assumptions made on the findings reported here.     

Analytical model of solar pond with heat exchanger

This paper presents an analytical model of a three zone solar pond with heat exchange pipes laid in its bottom convective zone. Explicit expressions for the transient rate of heat extraction and the temperature at which heat can be extracted are derived as a function of geometrical and operational parameters of the system. The transfer of heat from the pond bottom convective zone to the heat exchange fluid is expressed in terms of a heat removal factor, F_R. Analytical results, characteristic of the optimum performance of the pond, are presented and the criteria for the size and heat transfer characteristics of the heat exchanger are investigated. The annual average efficiency of heat extraction exhibits the asymptotic increase with the increase of length per unit pond area of heat exchange pipe.     

Correlations for the yearly or seasonally optimum salt-gradient solar pond in Greece

Simple correlations and corresponding nomographs are presented, which express the maximum useful heat received from salt-gradient solar ponds throughout the year or during a specified season of the year, and the corresponding optimum depth of the nonconvective zone in terms of the thickness of the upper convective zone and the temperature under which the maximum useful heat is received. The correlations are valid for the Athens (Greece) area or for regions with a similar climate, because solar radiation and ambient temperature values for Athens have been employed, obtained by a statistical process of hourly measurements over a period of about 20 years. For other climates, it is easy to develop similar correlations using the same methodology. Development of the proposed correlations is based on a method, which simulates the transient operation of the salt-gradient pond using finite-differences, and calculates the useful heat received hourly along the typical year. Thus, the useful heat received during a period or throughout the year is calculated as a sum of hourly values. Calculations of the useful heat are performed for a great number of values of the parameters of the problem, and the combinations of values that maximize useful heat are selected and used for developing correlations and corresponding nomographs. The correlations presented may be employed in the design of the optimum solar pond under the specific requirements of each application.     

A study on the thermal storage of the ground beneath solar ponds by computer simulation

A salt gradient solar pond is a large scale solar collector having built-in heat storage capability. This is in part due to the mass of water in the pond and in part to the ground beneath the pond. Some scholars have already paid attention to the ground thermal storage. In this work, emphasis has been put upon the un-steady state performance and the transient behavior of SGSPs. A simple computer simulation method is adopted to study the ground heat loss and the heat recovery rate under varied combinations of the depth of the underground water table, the thickness of the lower convective zone, the heat withdrawal pattern, and the thermal properties of the soil. The effect of an insulation layer between the pond and the ground is also examined.