Assessing the Maximum Stability of the Nonconvective Zone in a Salinity-Gradient Solar Pond

Abstract

The quality of the stability of the nonconvective zone of a salinity-gradient solar pond (SGSP) is investigated for an operating protocol in which the flushing procedure exactly compensates for evaporation losses from the solar pond and its associated evaporation pond. The mathematical model of the pond uses simplified, but accurate, constitutive expressions for the physical properties of aqueous sodium chloride. Also, realistic boundary conditions are used for the behaviors of the upper and lower convective zones (LCZs). The performance of a salinity-gradient solar pond is investigated in the context of the weather conditions at Makkah, Saudi Arabia, for several thickness of upper convective zone (UCZ) and operating temperature of the storage zone. Spectral collocation based on Chebyshev polynomials is used to assess the quality of the stability of the pond throughout the year in terms of the time scale for the restoration of disturbances in temperature, salinity, and fluid velocity underlying the critical eigenstate. The critical eigenvalue is found to be real and negative at all times of year indicating that the steady-state configuration of the pond is always stable, and suggesting that stationary instability would be the anticipated mechanism of instability. Annual profiles of surface temperature, salinity, and heat extraction are constructed for various combinations for the thickness of the upper convective zone and storage zone temperature.