In direct sensible thermal storage systems, both the energy discharging and charging processes are inherently time-dependent as well as rate-dependent. Simplified models which depict the characteristics of this transient process are therefore crucial to the sizing and rating of the storage devices. In this paper, existing models which represent three distinct classes of models for thermal storage behavior are recast into a common formulation and used to predict the variations of discharge volume fraction, thermal mixing factor, and entropy generation. For each of the models considered, the parametric dependence of key performance measures is shown to be expressible in terms of a Peclet number and a Froude number or temperature difference ratio. The thermal mixing factor for each of the models is reasonably well described by a power law fit with Fr2Pe for the convection-dominated portion of the operating range. For the uniform and nonuniform diffusivity models examined, there is shown to be a Peclet number which maximizes the discharge volume fraction. In addition, the cumulative entropy generation from the simplified models is compared with the ideally-stratified and the fully-mixed limits. Of the models considered, only the nonuniform diffusivity model exhibits an optimal Peclet number at which the cumulative entropy generation is minimized. For each of the other models examined, the cumulative entropy generation varies monotonically with Peclet number.

1.
Wildin
,
M. W.
, and
Truman
,
C. R.
, 1989, “
Performance of Stratified Vertical Cylindrical Thermal Storage Tanks, Part I: Scale Model Tank
,”
ASHRAE Trans.
0001-2505,
95
, pp.
1086
1095
.
2.
Yoo
,
J.
,
Wildin
,
M. W.
, and
Truman
,
C. R.
, 1986, “
Initial Formation of a Thermocline in Stratified Thermal Storage Tanks
,”
ASHRAE Trans.
0001-2505,
92
, pp.
280
292
.
3.
Musser
,
A.
, and
Bahnfleth
,
W. P.
, 1998, “
Evolution of Temperature Distributions in a Full-Scale Stratified Chilled Water Storage Tank With Radial Diffusers
,”
ASHRAE Trans.
0001-2505,
104
, pp.
55
67
.
4.
Wildin
,
M. W.
, 1989, “
Performance of Stratified Vertical Cylindrical Thermal Storage Tanks, Part II: Prototype Tank
,”
ASHRAE Trans.
0001-2505,
95
, pp.
1096
1105
.
5.
Wildin
,
M. W.
, 1991, “
Flow Near the Inlet and Design Parameters for Stratified Chilled Water Storage
,” ASME Paper No. 91-HT-27.
6.
Tarawneh
,
C.
, 1999, “
Experiments With a Mass Transfer Analog for the Filling of Stratified Thermal Energy Storage
,” Master’s thesis, University of Nebraska-Lincoln. Advisor: K. O. Homan.
7.
Truman
,
C. R.
,
Wildin
,
M. W.
, and
Yoo
,
J.
, 1985, “
Scale Modeling of Stratified Water Thermal Storage Tanks
,”
Proceedings of Symposium on Modeling Environmental Flows, ASCE/ASME Mechanics Conference
.
8.
Wildin
,
M. W.
, and
Truman
,
C. R.
, 1985, “
A Summary of Experience With Stratified Chilled Water Tanks
,”
ASHRAE Trans.
0001-2505,
92
, pp.
956
976
.
9.
Cole
,
R. L.
, and
Bellinger
,
F. O.
, 1982, “
Natural Thermal Stratification in Tanks, Phase 1 Final Report
,” Report No. ANL-82-5, Argonne National Laboratory.
10.
Han
,
S. M.
,
Wu
,
S. T.
,
Reid
,
W.
, and
Christenson
,
D. L.
, 1978, “
Experimental and Numerical Study of Liquid Thermal Storage Tank Models
,”
Proceedings of the Annual Meeting, American Section of ISES
.
11.
Mavros
,
P.
,
Belessiotis
,
V.
, and
Haralambopoulos
,
P.
, 1994, “
Stratified Energy Storage Vessels: Characterization of Performance and Modeling of Mixing Behavior
,”
Sol. Energy
0038-092X,
52
, pp.
327
336
.
12.
Oppel
,
F. J.
,
Ghajar
,
A. J.
, and
Moretti
,
P. M.
, 1986, “
A Numerical and Experimental Study of Stratified Thermal Storage
,”
ASHRAE Trans.
0001-2505,
92
, pp.
293
309
.
13.
Truman
,
C. R.
, and
Wildin
,
M. W.
, 1989, “
Finite Difference Model for Heat Transfer in a Stratified Thermal Storage Tank With Throughflow
,” ASME/AIChE National Heat Transfer Conference, Vol. 110 of ASME HTD.
14.
Zurigat
,
Y. H.
,
Liche
,
P. R.
, and
Ghajar
,
A. J.
, 1991, “
Influence of Inlet Geometry on Mixing in Thermocline Thermal Energy Storage
,”
Int. J. Heat Mass Transfer
0017-9310,
34
, pp.
115
125
.
15.
Cabelli
,
A.
, 1977, “
Storage Tanks—A Numerical Experiment
,”
Sol. Energy
0038-092X,
19
, pp.
45
54
.
16.
Cai
,
L.
,
Stewart
,
W. E.
, Jr.
, and
Sohn
,
C. W.
, 1993, “
Turbulent Buoyant Flows into a 2D Storage Tank
,”
Int. J. Heat Mass Transfer
0017-9310,
36
, pp.
4247
4256
.
17.
Guo
,
K. L.
, and
Wu
,
S. T.
, 1985, “
Numerical Study of Flow and Temperature Stratification in a Liquid Storage Tank
,”
ASME J. Sol. Energy Eng.
0199-6231,
107
, pp.
15
20
.
18.
Hahne
,
E.
, and
Chen
,
Y.
, 1998, “
Numerical Study of Flow and Heat Transfer Characteristics in Hot Water Stores
,”
Sol. Energy
0038-092X,
64
, pp.
9
18
.
19.
Mo
,
Y.
, and
Miyatake
,
O.
, 1996, “
Numerical Analysis of the Transient Turbulent Flow Field in a Thermally Stratified Thermal Storage Water Tank
,”
Numer. Heat Transfer, Part A
1040-7782,
30
, pp.
649
667
.
20.
Spall
,
R. E.
, 1998, “
A Numerical Study of Transient Mixed Convection in Cylindrical Thermal Storage Tanks
,”
Int. J. Heat Mass Transfer
0017-9310,
41
, pp.
2003
2011
.
21.
Bejan
,
A.
, 1978, “
Two Thermodynamic Optima in the Design of Sensible Heat Units for Energy Storage
,”
ASME J. Heat Transfer
0022-1481,
100
, pp.
708
712
.
22.
Bejan
,
A.
, 1996,
Entropy Generation Minimization
,
CRC Press
.
23.
Krane
,
R. J.
, 1987, “
A Second Law Analysis of the Optimum Design and Operation of Thermal Energy Storage Systems
,”
Int. J. Heat Mass Transfer
0017-9310,
30
, pp.
43
57
.
24.
Moran
,
M. J.
, and
Keyhani
,
V.
, 1982, “
Second Law Analysis of Thermal Energy Storage System
,”
Proceedings of the Seventh International Heat Transfer Conference
,
Vol.
6
.
25.
Krane
,
R. J.
, and
Krane
,
M. J. M.
, 1992, “
The Optimum Design of Stratified Thermal Energy Storage Systems - Part II: Completion of the Analytical Model, Presentation and Interpretation of the Results
,”
ASME J. Energy Resour. Technol.
0195-0738,
114
, pp.
204
208
.
26.
Homan
,
K. O.
, 2003, “
Integral Solutions for Transient Temperature Profiles in Stably-Stratified Open Enclosures
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
273
281
.
27.
Homan
,
K. O.
, 2003, “
Internal Entropy Generation Limits for Direct Sensible Thermal Storages
,”
ASME J. Energy Resour. Technol.
0195-0738,
125
, pp.
85
93
.
28.
Bahnfleth
,
W. P.
, and
Musser
,
A.
, 1999, “
Parametric Study of Charging Inlet Diffuser Performance in Stratified Chilled Water Storage Tanks With Radial Diffusers
,” Technical Report No. ASHRAE.
29.
Lavan
,
Z.
, and
Thompson
,
J.
, 1977, “
Experimental Study of Thermally Stratified Hot Water Storage Tanks
,”
Sol. Energy
0038-092X,
19
, pp.
519
524
.
30.
Homan
,
K. O.
, and
Soo
,
S. L.
, 1998, “
Laminar Flow Efficiency of Stratified Chilled-Water Storage Tanks
,”
Int. J. Heat Mass Transfer
0017-9310,
19
, pp.
69
78
.
31.
Cole
,
R. L.
, and
Bellinger
,
F. O.
, 1982, “
Thermally Stratified Tanks
,”
ASHRAE Trans.
0001-2505,
88
, pp.
1005
1017
.
32.
Schlichting
,
H.
, 1987,
Boundary Layer Theory
,
7th ed.
,
McGraw-Hill
.
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