The flow and heat transfer phenomena inside an underground thermal storage tank, initially filled with hot water at an almost uniform temperature and then left to interact with the cold surroundings, are studied numerically. The purpose of the study is to gain insight into how these phenomena affect the heat losses to the surroundings, before a new charging process takes place. A two-dimensional numerical model to solve for the transient flow and thermal fields within the tank coupled with the heat transport through the tank walls and within the ground are employed. Natural convection is found to dominate at the early transients when a strong recirculation develops, with a Rayleigh number characteristic of turbulent flow. A low-Re kε turbulence model is used for the computation. As time proceeds and the temperature differences between water and surroundings decrease, the recirculation decays and the heat transfer is dominated by thermal diffusion. The ground properties are varied, mainly in order to account for different moisture contents in the ground. Comparisons are made under realistic conditions with preliminary experimental results showing satisfactory agreement.

1.
ASHRAE Handbook of Applications, 1995, American Society of Heating, Refrigeration and Air-conditioning Engineers Inc., Atlanta, GA, Chap. 40.
2.
Duffie, J. A., and Beckman, W., 1991, Solar Engineering of Thermal Processes, 2nd ed., John Wiley & Sons, New York, Chap. 8.
3.
Givoni
,
B.
,
1977
, “
Underground Longterm Storage of Solar Energy Storage—An Overview
,”
Sol. Energy
,
19
, pp.
617
623
.
4.
Garg, H. P., Mullick, S. C., and Bhargava, A. K., 1985, Solar Thermal Energy Storage, D. Reidel Publishing Company, Dordrecht, Holland, Chap. 5.
5.
Jaluria
,
Y.
, and
Gupta
,
S. K.
,
1982
, “
Decay of Thermal Stratification in a Water Body for Solar Energy Storage
,”
Sol. Energy
,
28
(
2
), pp.
137
143
.
6.
Cotter
,
M. A.
, and
Charles
,
M. E.
,
1993
, “
Transient Cooling of Petroleum by Natural Convection in Cylindrical Storage Tanks: I—Development and Testing of a Numerical Simulator
,”
Int. J. Heat Mass Transfer
,
36
(
8
), pp.
2165
2174
.
7.
Cotter
,
M. A.
, and
Charles
,
M. E.
,
1993
, “
Transient Cooling of Petroleum by Natural Convection in Cylindrical Storage Tanks: II—Effect of Heat Transfer Coefficient, Aspect Ratio and Temperature-Dependent Viscosity
,”
Int. J. Heat Mass Transfer
,
36
(
8
), pp.
2175
2182
.
8.
Nicolette
,
V. F.
,
Yang
,
K. T.
, and
Lloyd
,
J. R.
,
1985
, “
Transient Cooling by Natural Convection in a Two-Dimensional Square Enclosure
,”
Int. J. Heat Mass Transfer
,
28
(
9
), pp.
1721
1732
.
9.
Robillard
,
L.
, and
Vasseur
,
P.
,
1982
, “
Convective Response of a Mass of Water near 4°C to a Constant Cooling Rate Applied on its Boundaries
,”
J. Fluid Mech.
,
118
, pp.
123
141
.
10.
Mihalakakou
,
G.
,
Santamouris
,
M.
,
Asimakopoulos
,
D.
, and
Argiriou
,
A.
,
1995
, “
On the Ground Temperature below Buildings
,”
Sol. Energy
,
55
(
5
), pp.
355
362
.
11.
Sobotka
,
P.
,
Yoshino
,
H.
, and
Matsumoto
,
S.
,
1995
, “
The Analysis of Deep Basement Heat Loss by Measurements and Calculations
,”
ASHRAE Trans.
,
101
(
2
), pp.
186
197
.
12.
Adjali
,
M. H.
,
Davies
,
M.
,
Riain
,
C. Ni.
, and
Littler
,
J. G.
,
2000
, “
In situ Measurements and Numerical Simulation of Heat Transfer beneath a Heated Ground Floor Slab
,”
Build. Environ.
,
33
, pp.
75
83
.
13.
Zhou
,
Z.
,
Rees
,
S. W.
, and
Thomas
,
H. R.
,
2002
, “
A Numerical and Experimental Investigation of Ground Heat Transfer Including Edge Insulation Effects
,”
Build. Environ.
,
37
, pp.
67
78
.
14.
Gauthier
,
C.
,
Lacroix
,
M.
, and
Bernier
,
H.
,
1997
, “
Numerical Simulation of Soil Heat Exchanger-Storage Systems for Greenhouses
,”
Sol. Energy
,
60
(
6
), pp.
333
346
.
15.
Parrini
,
F.
,
Vitale
,
S.
, and
Castellano
,
L.
,
1992
, “
Rational Analysis of Mass, Momentum and Heat Transfer Phenomena in Liquid Storage Tanks under Realistic Operating Conditions, 2. Application to a Feasibility Study
,”
Sol. Energy
,
49
(
2
), pp.
95
106
.
16.
Inalli
,
M.
,
1998
, “
Design Parameters for a Solar Heating System with an Underground Cylindrical Tank
,”
Energy (Oxford)
,
23
(
12
), pp.
1015
1027
.
17.
Inalli
,
M.
,
U¨nsal
,
M.
, and
Tanyildizi
,
V.
,
1997
, “
A Computational Model of a Domestic Solar Heating System with Underground Spherical Thermal Storage
,”
Energy (Oxford)
,
22
(
12
), pp.
1163
1172
.
18.
Papanicolaou
,
E.
, and
Belessiotis
,
V.
,
2002
, “
Transient Natural Convection in a Cylindrical Enclosure at High Rayleigh Numbers
,”
Int. J. Heat Mass Transfer
,
45
(
7
), pp.
1425
1444
.
19.
Papanicolaou
,
E.
, and
Jaluria
,
Y.
,
1995
, “
Computation of Turbulent Flow in Mixed Convection in a Cavity with a Localized Heat Source
,”
ASME J. Heat Transfer
,
117
(
3
), pp.
649
658
.
20.
Cheesewright, R., King, K. J., and Ziai, S., 1986, “Experimental Data for the Validation of Computer Codes for the Prediction of Two-Dimensional Buoyant Cavity Flows,” in Significant Questions in Buoyancy Affected Enclosure or Cavity Flows, J. A. C. Humphrey et al., eds., ASME, New York, HTD-Vol. 60, pp. 75–81.
21.
Launder
,
B. E.
, and
Sharma
,
B. I.
,
1974
, “
Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow near a Spinning Disc
,”
Lett. Heat Mass Transfer
,
1
, pp.
131
138
.
22.
Henkes
,
R. A. W. M.
, and
Hoogendoorn
,
C. J.
,
1995
, “
Comparison Exercise for Computations of Turbulence Natural Convection in Enclosures
,”
Numer. Heat Transfer, Part B
,
28
, pp.
59
78
.
23.
Heindel
,
T. J.
,
Ramadhyani
,
S.
, and
Incropera
,
F. P.
,
1994
, “
Assessment of Turbulence Models for Natural Convection in an Enclosure
,”
Numer. Heat Transfer, Part B
,
26
, pp.
147
172
.
24.
Papanicolaou
,
E.
, and
Jaluria
,
Y.
,
1993
, “
Mixed Convection from a Localized Heat Source in a Cavity with Conducting Walls: A Numerical Study
,”
Numer. Heat Transfer, Part A
,
23
, pp.
463
484
.
25.
Zhu
,
J.
,
1991
, “
A Low-Diffusive and Oscillation-Free Convection Scheme
,”
Commun. Appl. Numer. Methods
,
7
, pp.
225
232
.
26.
Papanicolaou
,
E.
,
Giebert
,
D.
,
Koch
,
R.
, and
Schulz
,
A.
,
2001
, “
A Conservation-Based Discretization Approach for Conjugate Heat Transfer Calculations in Hot-Gas Ducting Turbomachinery Components
,”
Int. J. Heat Mass Transfer
,
44
(
18
), pp.
3413
3429
.
27.
Timma
,
J.
, and
Padet
,
J.-P.
,
1985
, “
Etude The´orique du Couplage Convection-Conduction en Convection Libre Laminaire sur une Plaque Verticale
,”
Int. J. Heat Mass Transfer
,
28
(
6
), pp.
1097
1104
.
28.
Pozzi
,
A.
, and
Lupo
,
M.
,
1988
, “
The Coupling of Conduction with Laminar Natural Convection along a Flat Plate
,”
Int. J. Heat Mass Transfer
,
31
(
9
), pp.
1807
1814
.
29.
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, 2nd ed., Oxford University Press.
30.
Hyun, J. M., 1994, “Unsteady Buoyant Convection in an Enclosure,” Advances in Heat Transfer, 24, Academic Press, San Diego, pp. 277–321.
31.
Vliet
,
G. C.
, and
Liu
,
C. K.
,
1969
, “
An Experimental Study of Turbulent Natural Convection Boundary Layers
,”
ASME J. Heat Transfer
,
91, pp.
517
531
.
32.
Qureshi
,
Z. H.
, and
Gebhart
,
B.
,
1978
, “
Transition and Transport in Buoyancy Driven Flow in Water Adjacent to a Vertical Uniform Flux Surface
,”
Int. J. Heat Mass Transfer
,
21
, pp.
1467
1479
.
33.
Gray
,
D. D.
, and
Giorgini
,
A.
,
1976
, “
The Validity of the Boussinesq Approximation for Liquids and Gases
,”
Int. J. Heat Mass Transfer
,
19
, pp.
545
551
.
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