Assessing the maximum stability of the non-convective zone in a salinity-gradient solar pond

[+] Author and Article Information
Abdullah A. Abdullah

Department of Mathematical Sciences, Umm Al-Qura University, Makkah

Kenneth Alan Lindsay

Department of Mathematical Sciences, Umm Al-Qura University, Makkah

1Corresponding author.

ASME doi:10.1115/1.4036773 History: Received October 24, 2016; Revised April 13, 2017


The quality of the stability of the non-convective zone of a salinity-gradient solar pond 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 behaviours of the upper and lower convective zones. 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 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.

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