Time-temperature variations in the storage zone of salt-gradient solar ponds

Simplified equations are derived for the time-temperature variations in the storage zone of salt-gradient solar ponds. The temperature distribution in the nonconvective zone was assumed to be approximately linear with water depth. The theoretical results are easy to use. Time-temperature variations in the storage zone of a salt-gradient solar pond in Tainan have been estimated for 4 yr of operation. Comparisons are described with measurements.     

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.     

Thermal performance of a combined packed bed–solar pond system—a numerical study

Solar ponds have recently become an important source of energy that is used in many different applications. The technology of the solar pond is based on storing solar energy in salt-gradient stratified zones. Many experimental and numerical investigations concerning the optimum operational conditions and economical feasibility of solar ponds have been published in the last few decades. In the present study a modified solar pond with a rock bed inserted at the bottom is suggested and investigated. In order to conduct this study and predict the thermal performance of the combined system, a one-dimensional transient numerical model is developed. The boundary conditions are based on measured ambient and ground temperatures at Kuwait city. The model is validated for standard plain salt-gradient solar ponds and is then used to examine the thermal performance of the combined storage system for different rock material and bed geometry. It has been shown that the storage temperature is remarkably increased when low thermal diffusivity rocks (such as Bakelite) are used in the packed bed. Meanwhile, when high conductive rocks are used, the thermal storage temperature considerably deteriorates and the temperature variations amplitudes are almost flattened out. The bed geometry also plays a significant role in the storage process. As expected, an appreciable gain in the storage temperature was obtained for thicker rock beds. Low porosity rock beds, as well, produce higher storage temperatures in the storage zone.     

Solar ponds: A review

This review covers salt-gradient solar ponds and their applications. It traces the historical development since the physical phenomenon of salt-gradient solar ponds was discovered in 1902. It also discusses considerations such as stability criteria and the establishment and maintenance of the salt gradient. It outlines the basic thermophysical processes and considers the three zone configuration of the pond. The paper reviews thermal modelling of solar ponds including analytical and numerical models. It briefly presents construction, operation, end use technology and economics aspects. Note is taken of such innovative concepts as gel or viscosity ponds, membrane ponds and saturated salt ponds.     

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.     

Effect of radiation absorption in saline water on the performance of solar ponds

The effect of the solar radiation absorption characteristics of saline water on the performance of salt-gradient solar ponds under quasi-steady conditions is studied. Several models have been proposed to simulate the absorption of radiation in solar ponds, however, it is shown in this work that experimental data published by many authors militate in favour of representing this absorption simply by a single exponential. Pond performance is strongly influenced by the absorption characteristics. The mean pond temperature of the storage zone and the pond efficiency drop considerably as the turbidity of the water increases. The high values of the extinction coefficient result also in damping the pond temperature fluctuations and increase its time lag with respect to the insolation. The importance of using accurate in-site measured absorption data for pond design and performance prediction is emphasized.     

Comparative performance evaluation of fertiliser solar pond under simulated conditions

An experimental test rig for solar pond simulation was developed to study the chosen fertiliser salt, Muriate of Potash (MOP) for use in a solar pond under simulated conditions with provisions to vary the heating input and maintain a particular lower convective zone temperature. The performance, in terms of temperature and density profiles, was studied for MOP and was compared with that of sodium chloride and saltless solar ponds for different heating regimes and lower convective zone temperatures. The formation of three zones viz., upper convective zone, nonconvective zone, and lower convective zone was distinct at all heating combinations for both MOP and sodium chloride salts under simulated conditions. The temperature and density gradients were not affected significantly by intermittent no-heating spells of the solar ponds. Maintaining lower convective zone temperature of 70 °C and above led to the initiation of minor internal convective zone under simulated conditions. The temperature decay of lower convective zone (LCZ) was at lesser rate for different LCZ temperatures associated with both the heating regimes, for a MOP pond over a 24 h period of cessation of heating as compared to sodium chloride and saltless ponds.     

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.     

Transient performance of a two-dimensional salt gradient solar pond—A numerical study

Solar ponds have recently become an important source of energy that is used in many different applications. The technology of the solar pond is based on storing solar energy in salt-gradient stratified zones. Many experimental and numerical investigations concerning the optimum operational conditions and economical feasibility of solar ponds have been published in the last few decades. In the present study, a novel two-dimensional mathematical model that uses derived variables is developed and presented. This model utilizes vorticity, dilatation, density, temperature and concentration as dependent variables. The resulting governing partial differential equations are solved numerically in order to predict the transient performance of a solar pond in the two-dimensional domain. The boundary conditions are based on measured ambient and ground temperatures at Kuwait city. Based on the present formulation, a computer code has been developed to solve the problem at different operating conditions. The results are compared with the available experimental data and one-dimensional numerical results. Two-dimensionality effects are found to depend mainly on the aspect ratio of the pond. A parametric study is conducted to determine the optimum pond dimensions and operating conditions.     

Saturated solar ponds: 1. Simulation procedure

The mass and energy balances on the upper convective zone, nonconvective zone, and lower convective zone of a saturated solar pond are written to yield a set of nonlinear partial differential equations. These are solved numerically to predict the thermal performance of the pond over a long period of time for various initial and boundary conditions. This model considers external parameters such as hourly variation of incident solar radiation, ambient temperature, air velocity, and relative humidity. Temperature and concentration dependence of density, thermal conductivity, specific heat, and mass diffusivity are taken into account. Heat transfer modes considered between the upper convective zone and the ambient are convection, evaporation, and radiation. Ground heat losses from the lower convective zone are also considered. This model is used to study the development of temperature and concentration profiles inside a saturated solar pond. This model can also be used to predict the long-term performance of a saturated solar pond for various heat extraction temperatures and rates.     

Operation of a commercial solar gel pond

The solar gel pond is an innovative concept which overcomes many of the shortcomings of the conventional salt-gradient solar pond. In this paper, the design, construction and start-up details of a commercial scale pond (400 m²), built for a publishing company in Albuquerque, New Mexico will be presented. A pond with trapezoidal cross section was designed so that shadowing could be minimized and also the ratio of surface area to the volume of the storage zone could be maximized. The publishing company required a minimum of 1 GJ/day (1MBTU/day). Generally it has been noted that in ponds with large volume a lesser percentage of retained energy is lost as edge losses. Based on the above consideration a pond size of 400 m² and 5 m deep with a gel thickness of 60 cm and a mass flow rate (for the heat extraction loop) of 1 × 10⁻⁴ to 1 × 10⁻³ kg/m²·sec was determined to be the optimum size for the publishing company's needs. Two to seven percent salt water was used mainly to keep the gel bags floating on the surface. Tedlar bags were used to contain the gel. During the first year of operation, while the pond was still heating up, the pond obtained a temperature of 60°C and the gel showed no signs of degradation.     

Salt gradient solar pond with reflective bottom: Application to the “saturated” pond

The “saturated” salt gradient solar pond operates near the solubility limit. Consequently, temperature fluctuations may cause precipitation of the salt, which can increase the reflectivity of the bottom. It is shown that this can reduce the width of the nonconvective zone and seriously degrade the performance of the pond. The temperature distribution, efficiency and optimum operating conditions are calculated, taking account of diffusely reflected light from the bottom of the pond. The mechanism for narrowing the nonconvective zone is described. A semiquantitative analysis is made of a known case of simultaneous salt precipitation and nonconvective zone destruction. It is argued that the boundary between the nonconvective zone and the lower convective zone will move to its maximum temperature position if the solubility is a sufficiently strongly increasing function of temperature.     

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 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.     

Computer simulation of solar pond thermal behavior

A computer model of salt gradient solar pond thermal behavior has been developed and used to verify the validity of assuming constant salt solution physical parameters and long term averaging schemes for ambient temperature and insolation in previous solar pond analytical models. A theoretical limit for pond transparency is calculated which is significantly higher than that previously assumed. It is suggested that a transparent membrane be placed just below the air/water interface of solar ponds to maintain pond solution purity and approach the theoretical limit for transparency. A means of estimating the diffuse insolation input into a solar pond is given which utilizes sky color temperatures for different values of the clearness index (K_T). A single sky color temperature is calculated for each average clearness index value ( ).     

Optimum thickness of the nonconvective zone in salt gradient solar ponds

The nonconvective gradient zone of a salt gradient solar pond tends to more effectively transmit incident solar energy to the storage brine below as its thickness is reduced. However, that same gradient zone tends to more effectively reduce heat loss from the warm brines as its thickness is increased. Therefore, there exists an optimum gradient zone thickness for which the net rate of energy collected and retained is a maximum. This report describes a technique for using a numerical simulation model to determine the optimum thickness of the gradient zone in ponds; provided other basic design, operating and climatic factors are specified. Significant improvements in pond efficiency may be obtained if the thickness of the gradient zone is adjusted monthly, seasonally or even if maintained at the annual average optimum thickness as compared with operating the pond with other than an optimum gradient zone thickness.     

A parametric study on solar ponds

A linear relation between the efficiency of solar ponds and factor $\text{θ}{}_{\mathrm{d}}\text{H}$ which is the temperature difference between the pond bottom and the ambient divided by the average insolation is presented. This relation, which has been developed based on a steady state analysis provides valuable information on the relative importance of the parameters involved in the operation of solar ponds. It is found that the existence and the thickness of the top convective zone has a profound negative effect on the yield of solar ponds. The optimum thickness of the density gradient layer under various conditions is also presented. The effect of ground losses is discussed, and it is shown that for the case of wet soil, especially if the level of the underground water is high, the pond should be thermally insulated. It is also shown that the steady state analysis can predict with good accuracy the yearly average response of solar ponds under transient conditions.     

Dependence of speed of sound on salinity and temperature in concentrated NaCl solutions

An ultrasonic velocimeter for salinity measurements in a solar pond has been developed and tested. Calibration of the probe is accomplished by comparing speed of sound measurements in distilled water with accepted values. Speed of sound in NaCl solutions with salinities from 0%–21% by weight has been measured over a temperature range of 7°–88°C. An equation has been developed to compute salinity from the measured speed of sound and the temperature for NaCl solutions. Accuracies better than 0.2% by weight have been demonstrated. The method shows good potential for in situ salinity measurements in salt-gradient solar ponds.     

Membrane stratified solar ponds

The membrane stratified solar pond is a body of liquid utilizing closely spaced transparent membranes to quench convective heat transfer in the top part of the pond. Membranes may be configured as horizontal sheets, vertical sheets or vertical tubes. Several suitable liquids and membrane materials are discussed. Conditions for suppression of convection are described, and transmission of solar radiation through the pond is discussed for each of the three membrane configurations. The steady state thermal efficiency is calculated for the horizontal sheet configuration. Thermal behavior is similar to that of salt gradient solar ponds, but much deeper heat storage layers are feasible. In some cases aquaculture farming may be suitable in the storage layer.     

Freshwater floating-collector-type solar pond

A new type of solar pond is introduced in an effort to provide an inexpensive, renewable heat source, mainly for space-heating purposes. The suggested freshwater solar pond is covered with floating collectors made of insulation boards and thin plastic sheets, and requires very little, if any, constructional work. Forced flow in the collector layer of the pond provides the reduction of the mean collector and pond temperatures and ensures high efficiency. The collectors also provide the necessary thermal and evaporation insulation so that freshwater may be used and the cumbersome and delicate task of salt-gradient maintenance is eliminated.Both simulation and experimental results are reported. A one-dimensional quasi-steady-state simple model is the basis for the simulation. The presented experimental data validate the simulations. Longterm performance characteristics as well as possible modes of seasonal storage utilization of such solar ponds are discussed.