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Research Papers

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

[+] Author and Article Information
A. A. Abdullah, K. A. Lindsay

Department of Mathematical Sciences,
Umm Al-Qura University,
Makkah 24382, Saudi Arabia

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received October 24, 2016; final manuscript received April 13, 2017; published online June 8, 2017. Assoc. Editor: Carlos F. M. Coimbra.

J. Sol. Energy Eng 139(4), 041010 (Jun 08, 2017) (12 pages) Paper No: SOL-16-1454; doi: 10.1115/1.4036773 History: Received October 24, 2016; Revised April 13, 2017

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.

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Figures

Grahic Jump Location
Fig. 1

The configuration of a salt-gradient solar pond is shown including the primary mechanisms governing its interactions with its surroundings. In the case of a large pond, thermal losses from the retaining walls of the pond may be ignored.

Grahic Jump Location
Fig. 2

The experimental SGSP at Makkah, Saudi Arabia, showing floating rings to reduce wave action

Grahic Jump Location
Fig. 4

The upper curve shows the average daily Celsius temperature at the Makkah solar pond throughout the year. The lower curves represent the average daily Celsius temperature of the UCZ for a thickness of 0.25 m (bottom curve), 0.50 m (middle curve), and 0.75 m (top curve) with the LCZ maintained at95 °C.

Grahic Jump Location
Fig. 3

The upper curve shows the average insolation (kWh/m2/day) received by the Makkah solar pond throughout the year. The lower curves represent the average rate of heat extraction (kWh/m2/day) for a UCZ of thickness 0.25 m (top curve), 0.50 m (middle curve), and 0.75 m (bottom curve) with the LCZ maintained at 95 °C.

Grahic Jump Location
Fig. 5

The annual profile of the average daily salinity of the UCZ of the Makkah solar pond is shown for a UCZ of thickness 0.75 m (top curves), for a UCZ of thickness 0.50 m (middle curves), and for a UCZ of thickness of 0.25 m (bottom curves). Solid and dashed lines are associated with LCZ temperatures of 95 °C and 80 °C, respectively.

Grahic Jump Location
Fig. 6

The value of τ=|σ|−1 is shown for the Makkah solar pond for UCZs of thickness 0.25 m, 0.50 m, and 0.75 m when the LCZ is operated at 95 °C (solid lines) and at 80 °C (dashed lines)

Grahic Jump Location
Fig. 7

The annual profile of the insolation is shown based on expression (A8) with M = 5 (dashed line) and M = 2 (dotted line)

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