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.

References

1.
Cohen
,
Y.
,
Krumbein
,
W. E.
,
Goldberg
,
M.
, and
Shilo
,
M.
,
2003
, “
Solar Lake (Sinai)—1: Physical and Chemical Limnology
,”
Limnol. Oceanogr.
,
22
(
4
), pp.
597
608
.
2.
Leblanc
,
J.
,
Akbarzadeh
,
A.
,
Andrews
,
J.
,
Lu
,
H.
, and
Golding
,
P.
,
2011
, “
Heat Extraction Methods From Salinity-Gradient Solar Ponds and Introduction of a Novel System of Heat Extraction for Improved Efficiency
,”
Sol. Energy
,
85
(
12
), pp.
3103
3142
.
3.
Giestas
,
M. C.
,
Milhazes
,
J. P.
, and
Pina
,
H. L.
,
2014
, “
Numerical Modeling of Solar Ponds
,”
Energy Procedia
,
57
, pp.
2416
2425
.
4.
Shi
,
Y.
,
Yin
,
F.
,
Shi
,
L.
,
Sun
,
W.
,
Li
,
N.
, and
Liu
,
H.
,
2011
, “
Effects of Porous Media on Thermal and Salt Diffusion of Solar Pond
,”
Appl. Energy
,
88
(
7
), pp.
2445
2453
.
5.
Valderrama
,
C.
,
Gibert
,
O.
,
Arcal
,
J.
,
Solano
,
P.
,
Akbarzadeh
,
A.
,
Larrotcha
,
E.
, and
Cortina
,
J. L.
,
2011
, “
Solar Energy Storage by Salinity Gradient Solar Pond: Pilot Plant Construction and Gradient Control
,”
Desalination
,
279
(13), pp.
445
450
.
6.
Suárez
,
F.
,
Tyler
,
S. W.
, and
Childress
,
A. E.
,
2010
, “
A Fully Coupled, Transient Double-Diffusive Convective Model for Salt-Gradient Solar Ponds
,”
Int. J. Heat Mass Transfer
,
53
(9), pp.
1718
1730
.
7.
Giestas
,
M. C.
,
Pina
,
H. L.
,
Milhazes
,
J. P.
, and
Tavares
,
C.
,
2009
, “
Solar Pond Modeling With Density and Viscosity Dependent on Temperature and Salinity
,”
Int. J. Heat Mass Transfer
,
52
(12), pp.
2849
2857
.
8.
Hill
,
A. A.
, and
Carr
,
M.
,
2013
, “
The Influence of a Fluid-Porous Interface on Solar Pond Stability
,”
Adv. Water Resour.
,
52
, pp.
1
6
.
9.
Boudhiaf
,
R.
,
Moussa
,
A. B.
, and
Baccar
,
M.
,
2012
, “
A Two-Dimensional Numerical Study of Hydrodynamic, Heat and Mass Transfer and Stability in a Salt Gradient Solar Pond
,”
Energies
,
5
(
12
), pp.
3986
4007
.
10.
Karim
,
C.
, and
Jomaa
,
S. M.
,
2012
, “
Experimental Simulation of the Salt Gradient Solar Pond Stability
,”
J. Renewable Sustainable Energy
,
4
(
6
), p.
063143
.
11.
Akrour
,
D.
,
Tribeche
,
M.
, and
Kalache
,
D.
,
2011
, “
A Theoretical and Numerical Study of Thermosolutal Convection: Stability of a Salinity Gradient Solar Pond
,”
Therm. Sci.
,
15
(
1
), pp.
67
80
.
12.
Sodha
,
M. S.
, and
Kumar
,
A.
,
1983
, “
Linear Stability Analysis of Double-Diffusive Solar Pond
,”
Energy Conserv.
,
23
(
2
), pp.
67
71
.
13.
Abdullah
,
A. A.
,
Lindsay
,
K. A.
, and
AbdelGawad
,
A. F.
,
2016
, “
Construction of Sustainable Heat Extraction System and a New Scheme of Temperature Measurement in an Experimental Solar Pond for Performance Enhancement
,”
Sol. Energy
,
130
, pp.
10
24
.
14.
Matti Tukiainen, 2005, “
Mecca, Saudi Arabia - Sunrise, Sunset, Dawn and Dusk Times
,” Ylöjärvi, Finland, accessed May 22, 2017, http://www.gaisma.com/en/location/mecca.html
15.
Weather Atlas, 2002, “
Monthly Weather Forecast and Climate Mecca, Saudi Arabia
,” Yu Media Group d.o.o. Beograd, Belgrade, Serbia, accessed May 22, 2017, http://www.weather-atlas.com/en/saudi-arabia/mecca-climate
16.
Hull
,
J. R.
,
Nielsen
,
C. E.
, and
Golding
,
P.
,
1988
,
Salinity-Gradient Solar Ponds
,
CRC Press
,
Boca Raton, FL
.
17.
Abdullah
,
A. A.
,
Lindsay
,
K. A.
, and
AbdelGawad
,
A. F.
,
2015
, “
Parsimonious Constitutive Expressions With Good Accuracy and Suitable for Modelling the Properties of Aqueous Sodium Chloride in Solar Ponds
,”
Sol. Energy
,
122
, pp.
617
629
.
18.
Bastug
,
T.
, and
Kuyucak
,
S.
,
2005
, “
Temperature Dependence of the Transport Coefficients of Ions From Molecular Dynamics Simulations
,”
Chem. Phys. Lett.
,
408
(1–3), pp.
84
88
.
19.
Swinbank
,
W. C.
,
1963
, “
Long-Wave Radiation From Clear Skies
,”
Q. J. R. Meteorol. Soc.
,
89
(
381
), pp.
339
348
.
20.
Deacon
,
E. L.
,
1970
, “
The Derivation of Swinbank's Long-Wave Radiation Formula
,”
Q. J. R. Meteorol. Soc.
,
96
(
408
), pp.
313
319
.
21.
Holman
,
J. P.
,
1992
,
Heat Transfer
, 7th ed.,
McGraw-Hill
,
New York
.
22.
McAdams
,
W. H.
,
1954
,
Heat Transmission
, 3rd ed.,
McGraw-Hill Kogakusha
,
Tokyo, Japan
, p.
249
.
23.
Bonython
,
C. W.
,
1956
, “
The Influence of Salinity Upon the Rate of Natural Evaporation
,” UNESCO, Canberra, New South Wales, Australia, Report No.
65-71
.
24.
Bonython
,
C. W.
,
1965
, “
Factors Determining the Rate of Solar Evaporation in the Production of Salt
,”
Second Northern Ohio Geological Society Symposium on Salt
, Northern Ohio Geological Society, Cleveland, OH, May 3–5, pp. 152–167.
25.
Turk
,
L. J.
,
1970
, “
Evaporation of Brine: A Field Study on the Bonneville Salt Flats, Utah
,”
Water Resour. Res.
,
6
(
4
), pp.
1209
1215
.
You do not currently have access to this content.