Hillel Rubin

Modeling the performance of a solar pond as a source of thermal energy

Abstract The use of solar ponds is becoming more attractive in todays energy scene. A major advantage of solar ponds over other collectors is the ability to store thermal energy for long periods of time. The solar pond comprises a hydraulic system subject to processes of heat and mass transfer. The design of this system and the related equipment requires a thorough knowledge of the pond heating-up process and expected thermohaline structure within the pond. The current study considers that convection currents in the pond are inhibited by the salinity distribution, and applies a finite difference implicit model in order to investigate the interaction among physical variables represented by various dimensionless parameters. Variables which are included in the analysis comprise the solar radiation input and absorption as it passes through the pond; diffusion and dispersion of heat within the pond; absorption of heat at the bottom of the pond; and withdrawal of heat from layers within the pond. The physical variables generate 3 dimensionless variables associated with the ponds heating-up process. A 4 dimensionless variable is associated with the heat utilization. The analysis represented in this paper concerns the interaction between these dimensionless parameters and its implications.

Thermal convection in a nonhomogeneous aquifer

Abstract Geothermal activity creates destabilizing temperature gradients in groundwater. Very often stabilizing salinity gradients also exist in the aquifer. The combination of temperature and salinity distributions in the aquifer may induce various kinds of hydrodynamic instability. Such instabilities are possible mainly in thick aquifers, which usually consist of various nonhomogeneous formations. In this study we investigate the effect of the aquifer nonhomogeneity on the stability of the flow field as well as on heat and salinity transport through the aquifer. By Galerkin expansion the criteria of the flow field stability were identified and calculated quantitatively. It was found that the point of instability is demonstrated by marginal stability or overstability. The nonhomogeneity of the aquifer leads to asymmetry of the convection cells.

On the application of the boundary layer approximation for the simulation of density stratified flows in aquifers

Abstract Stratification of the density in groundwater flow stems from the contact between water which contains minerals in low concentration with water containing a high concentration of minerals. The flow in such a flow field should be simulated by solving simultaneously the equations of continuity, motion and solute transport, because solute concentration affects the dynamics of the flow. Such an approach is generally associated with complicated calculations and numerical schemes subject to problems of convergence and stability, as the basic equations are highly nonlinear. This study applies the phenomenological boundary layer approximation, and suggests a reference to three different zones in the flow field: (a) fresh water zone, (b) transition zone, and (c) mineralized water zone. In zones (a) and (c) it is assumed that the potential flow theory can be applied. In zone (b) the flow is nonpotential but the basic similarity conditions typical to boundary layers exist. The approach suggested in this study simplifies the mathematical models that should be used for the flow field simulation. This approach is especially attractive in cases where the Dupuit approximation is applicable. In such cases very often analytical solutions can be obtained for unidirectional flows. In cases that are too complicated for representation by analytical solutions, the method can be used for the creation of simplified numerical schemes. Various examples in this study demonstrate the application of the method for various field problems associated with steady state as well as unsteady state conditions. The simplicity of the method makes it useful for variety of problems. It can be used even by small institutions and small consulting firms, who have usually access to minicomputers and microprocessors.

Application of the aquifer's average characteristics for determining the onset of thermohaline convection in a heterogeneous aquifer

Abstract Due to layered deposition of sedimentary rocks, the aquifers characteristics usually vary with the depth. Such variations are mainly significant in thick aquifers. The variable characteristics cause the aquifer to be heterogeneous. The basic equations used for the simulation of transport phenomena in the heterogeneous aquifer are nonlinear. Therefore, simulation of thermohaline convection in such a stratum requires complicated mathematical models. The present study considers the application of the aquifers average characteristic method for such a simulation. According to this method, the model considers constant average characteristics of the aquifer, instead of considering variable local characteristics of the saturated porous medium. Such an approach considerably simplifies the calculations. The study verifies the applicability of the method for the predictions concerning diffusive thermohaline convection in a heterogeneous aquifer. On this basis the study presents an analysis of important features of dispersive thermohaline convection in a heterogeneous aquifer by applying the method of the aquifers average characteristics.

AN ANALYSIS OF INSTABILITIES CAUSED BY SALINITY GRADIENTS IN GROUNDWATER

Salinity gradients in groundwaters may lead to convection currents. The present study concerns stability criteria of the flow field as well as an analysis of the salinity transport due to finite amplitude disturbances. It was found that convection cells are always two dimensional rolls whose axes are parallel to the unperturbed velocity vector. Salinity transport through the aquifer is considerably increased due to the convection motion. Mechanical dispersion due to the convection motion reduces the intensity of salinity transport.