Numerical results show that at supercritical pressures, once the buoyancy force increases, the effect of the turbulent Prandtl number, Prt, on convective heat transfer becomes considerable. This phenomenon has not been adequately addressed in the literature. In this study, the effect of the turbulent Prandtl number on the rate of heat transfer in both enhanced and deteriorated regimes of heat transfer to supercritical fluid flows has been extensively investigated. Having realized that variations of the turbulent Prandtl number can affect the model predictions so greatly, a new correlation to express the changes of Prt with respect to flow conditions in a supercritical environment is developed. Effects of various important parameters such as heat flux, mass flux, and fluid pressure are included in the proposed correlation. This correlation has been modified to be applicable for different supercritical fluids. The comparison with various experimental data shows that by implementing the new correlation of Prt in the numerical code, it is possible to significantly improve the simulation results. Such a correlation seems to be the first one introduced in the literature for a supercritical fluid flow.

References

References
1.
Kraan
,
M.
,
Peeters
,
M. M. W.
,
Cid
,
M. V. F.
,
Woerlee
,
G. F.
,
Veugelers
,
W. J. T.
, and
Witkamp
,
G. J.
,
2005
, “
The Influence of Variable Physical Properties and Buoyancy on Heat Exchanger Design for Near- and Supercritical Conditions
,”
J. Supercrit. Fluids
,
34
(
1
), pp.
99
105
.
2.
Yamaguchi
,
H.
,
Sawada
,
N.
,
Suzuki
,
H.
,
Ueda
,
H.
, and
Zhang
,
X. R.
,
2010
, “
Preliminary Study on a Solar Water Heater Using Supercritical Carbon Dioxide as Working Fluid
,”
ASME J. Sol. Energy Eng.
,
132
(
1
), p.
011010
.
3.
Pecnik
,
R.
,
Rinaldi
,
E.
, and
Colonna
,
P.
,
2012
, “
Computational Fluid Dynamics of a Radial Compressor Operating With Supercritical CO2
,”
ASME J. Eng. Gas Turbines Power
,
134
(
12
), p.
122301
.
4.
Lee
,
Y.
, and
Lee
,
J. I.
,
2014
, “
Structural Assessment of Intermediate Printed Circuit Heat Exchanger for Sodium-Cooled Fast Reactor With Supercritical CO2 Cycle
,”
Ann. Nucl. Energy
,
73
, pp.
84
95
.
5.
Serrano
,
I. P.
,
Cantizano
,
A.
,
Linares
,
J. I.
, and
Moratilla
,
B. Y.
,
2014
, “
Modeling and Sizing of the Heat Exchangers of a New Supercritical CO2 Brayton Power Cycle for Energy Conversion for Fusion Reactors
,”
Fusion Eng. Des.
,
89
(
9–10
), pp.
1905
1908
.
6.
Besarati
,
S. M.
,
Goswami
,
D. Y.
, and
Stefanakos
,
E. K.
,
2015
, “
Development of a Solar Receiver Based on Compact Heat Exchanger Technology for Supercritical Carbon Dioxide Power Cycles
,”
ASME J. Sol. Energy Eng.
,
137
(
3
), p.
031018
.
7.
Bakhromkina
,
A. A.
,
Shvarts
,
A. L.
, and
Chugreev
,
A. A.
,
2015
, “
Development and Application of a New Type of Separators for Supercritical and Ultra-Supercritical Once-Through Boilers
,”
Power Technol. Eng.
,
48
(
6
), pp.
47
52
.
8.
Chen
,
Z.
,
Wang
,
G.
,
Yin
,
F.
,
Chen
,
H.
, and
Xu
,
Y.
,
2015
, “
A New System Design for Supercritical Water Oxidation
,”
Chem. Eng. J.
,
269
, pp.
343
351
.
9.
Bazargan
,
M.
, and
Fraser
,
D.
,
2009
, “
Heat Transfer to Supercritical Water in a Horizontal Pipe: Modeling, New Empirical Correlation, and Comparison Against Experimental Data
,”
ASME J. Heat Transfer
,
131
(
6
), p.
061702
.
10.
Mokry
,
S.
,
Pioro
,
I.
,
Farah
,
A.
,
King
,
K.
,
Gupta
,
S.
,
Peiman
,
W.
, and
Kirillov
,
P.
,
2011
, “
Development of Supercritical Water Heat Transfer Correlation for Vertical Bare Tubes
,”
Nucl. Eng. Des.
,
241
(
4
), pp.
1126
1136
.
11.
Gupta
,
S.
,
Saltanov
,
E.
,
Mokry
,
S. J.
,
Pioro
,
I.
,
Trevani
,
L.
, and
McGillivray
,
D.
,
2013
, “
Developing Empirical Heat Transfer Correlations for Supercritical CO2 Flowing in Vertical Bare Tubes
,”
Nucl. Eng. Des.
,
261
, pp.
116
131
.
12.
Chen
,
W.
, and
Fang
,
X.
,
2014
, “
A New Heat Transfer Correlation for Supercritical Water Flowing in Vertical Tubes
,”
Int. J. Heat Mass Transfer
,
78
, pp.
156
160
.
13.
Chen
,
W.
,
Fang
,
X.
,
Xu
,
Y.
, and
Su
,
X.
,
2015
, “
An Assessment of Correlations of Forced Convection Heat Transfer to Water at Supercritical Pressure
,”
Ann. Nucl. Energy
,
76
, pp.
451
460
.
14.
Wang
,
H.
,
Wang
,
W.
,
Bi
,
Q.
, and
Wang
,
L.
,
2015
, “
Experimental Study of Heat Transfer and Flow Resistance of Supercritical Pressure Water in a SCWR Sub-Channel
,”
J. Supercrit. Fluids
,
100
, pp.
15
25
.
15.
Hall
,
W. B.
, and
Jackson
,
J. D.
,
1969
, “
Laminarization of a Turbulent Pipe Flow by Buoyancy Force
,”
ASME
Paper No. 69-HT-55.
16.
Jackson
,
J. D.
, and
Hall
,
W. B.
,
1979
, “
Influences of Buoyancy on Heat Transfer to Fluids Flowing in Vertical Tubes Under Turbulent Conditions
,”
Turbulent Forced Convection in Channels and Bundles
, Vol.
2
,
S.
Kakac
and
D. B.
Spalding
, eds.,
Hemisphere
,
New York
, pp.
613
640
.
17.
Bazargan
,
M.
,
Fraser
,
D.
, and
Chatoorgan
,
V.
,
2005
, “
Effect of Buoyancy on Heat Transfer in Supercritical Water Flow in A Horizontal Round Tube
,”
ASME J. Heat Transfer
,
127
(
8
), pp.
897
902
.
18.
Lei
,
X.
,
Li
,
H.
,
Zhang
,
Y.
, and
Zhang
,
W.
,
2013
, “
Effect of Buoyancy on the Mechanism of Heat Transfer Deterioration of Supercritical Water in Horizontal Tubes
,”
ASME J. Heat Transfer
,
135
(
7
), p.
071703
.
19.
Sadr
,
K. X.
,
2015
, “
Experimental Investigation of Buoyancy Effects on Convection Heat Transfer of Supercritical CO2 Flow in a Horizontal Tube
,”
Heat Mass Transfer
,
52
(
4
), pp.
713
726
.
20.
He
,
S.
,
Kim
,
W. S.
,
Jiang
,
P.-X.
, and
Jackson
,
J. D.
,
2004
, “
Simulation of Mixed Convection Heat Transfer to Carbon Dioxide at Supercritical Pressure
,”
J. Mech. Eng. Sci.
,
218
(
11
), pp.
1281
1296
.
21.
He
,
S.
,
Jiang
,
P. X.
,
Xu
,
Y. J.
,
Shi
,
R. F.
,
Kim
,
W. S.
, and
Jackson
,
J. D.
,
2005
, “
A Computational Study of Convection Heat Transfer to CO2 at Supercritical Pressures in a Vertical Mini Tube
,”
Int. J. Therm. Sci.
,
44
(
6
), pp.
521
530
.
22.
Sharabi
,
M.
,
Ambrosini
,
W.
,
He
,
S.
, and
Jackson
,
J. D.
,
2008
, “
Prediction of Turbulent Convective Heat Transfer to a Fluid at Supercritical Pressure in Square and Triangular Channels
,”
Ann. Nucl. Energy
,
35
(
6
), pp.
993
1005
.
23.
Jiang
,
P. X.
,
Zhang
,
Y.
, and
Shi
,
R. F.
,
2008
, “
Experimental and Numerical Investigation of Convection Heat Transfer of CO2 at Supercritical Pressures in a Vertical Mini-Tube
,”
Int. J. Heat Mass Transfer
,
51
(
11–12
), pp.
3052
3056
.
24.
Jiang
,
P. X.
,
Zhang
,
Y.
,
Xu
,
Y. J.
, and
Shi
,
R. F.
,
2008
, “
Experimental and Numerical Investigation of Convection Heat Transfer of CO2 at Supercritical Pressures in a Vertical Tube at Low Reynolds Numbers
,”
Int. J. Therm. Sci.
,
47
(
8
), pp.
998
1011
.
25.
He
,
S.
,
Kim
,
W. S.
, and
Bae
,
J. H.
,
2008
, “
Assessment of Performance of Turbulence Models in Predicting Supercritical Pressure Heat Transfer in a Vertical Tube
,”
Int. J. Heat Mass Transfer
,
51
(
19–20
), pp.
4659
4675
.
26.
He
,
S.
,
Kim
,
W. S.
, and
Jackson
,
J. D.
,
2008
, “
A Computational Study of Convective Heat Transfer to Carbon Dioxide at a Pressure Just Above the Critical Value
,”
Appl. Therm. Eng.
,
28
(
13
), pp.
1662
1675
.
27.
Sharabi
,
M.
, and
Ambrosini
,
W.
,
2009
, “
Discussion of Heat Transfer Phenomena in Fluids at Supercritical Pressure With the Aid of CFD Models
,”
Ann. Nucl. Energy
,
36
(
1
), pp.
60
71
.
28.
Licht
,
J.
,
Anderson
,
M.
, and
Corradini
,
M.
,
2009
, “
Heat Transfer and Fluid Flow Characteristics in Supercritical Pressure Water
,”
ASME J. Heat Transfer
,
131
(
7
), p.
072502
.
29.
Mohseni
,
M.
, and
Bazargan
,
M.
,
2010
, “
The Effect of the Low Reynolds Number k-ε Turbulence Models on Simulation of the Enhanced and Deteriorated Convective Heat Transfer to the Supercritical Fluid Flows
,”
Heat Mass Transfer
,
47
(
5
), pp.
609
619
.
30.
Kruizenga
,
A.
,
Li
,
H.
,
Anderson
,
M.
, and
Corradini
,
M.
,
2012
, “
Supercritical Carbon Dioxide Heat Transfer in Horizontal Semicircular Channels
,”
ASME J. Heat Transfer
,
134
(
8
), p.
081802
.
31.
Bazargan
,
M.
, and
Mohseni
,
M.
,
2012
, “
Algebraic Zero-Equation Versus Complex Two-Equation Turbulence Modeling in Supercritical Fluid Flows
,”
Comput. Fluids
,
60
, pp.
49
57
.
32.
Yang
,
Z.
,
Bi
,
Q.
,
Wang
,
H.
,
Wu
,
G.
, and
Hu
,
R.
,
2013
, “
Experiment of Heat Transfer to Supercritical Water Flowing in Vertical Annular Channels
,”
ASME J. Heat Transfer
,
135
(
4
), p.
042504
.
33.
Yu
,
S.
,
Li
,
H.
,
Lei
,
X.
,
Feng
,
Y.
,
Zhang
,
Y.
,
He
,
H.
, and
Wang
,
T.
,
2013
, “
Influence of Buoyancy on Heat Transfer to Water Flowing in Horizontal Tubes Under Supercritical Pressure
,”
Appl. Therm. Eng.
,
59
(
1–2
), pp.
380
388
.
34.
Gang
,
W.
,
Pan
,
J.
,
Bi
,
Q.
,
Yang
,
Z.
, and
Wang
,
H.
,
2014
, “
Heat Transfer Characteristics of Supercritical Pressure Water in Vertical Upward Annuli
,”
Nucl. Eng. Des.
,
273
, pp.
449
458
.
35.
Zhang
,
S.
,
Gu
,
H.
,
Xiong
,
Z.
, and
Gong
,
S.
,
2014
, “
Numerical Investigation on Heat Transfer of Supercritical Fluid in a Vertical 7-Rod Bundle
,”
J. Supercrit. Fluid
,
92
, pp.
8
15
.
36.
Wang
,
K.
,
Xu
,
X.
,
Wu
,
Y.
,
Liu
,
C.
, and
Dang
,
C.
,
2015
, “
Numerical Investigation on Heat Transfer of Supercritical CO2 in Heated Helically Coiled Tubes
,”
J. Supercrit. Fluid
,
99
, pp.
112
120
.
37.
Podila
,
K.
, and
Rao
,
Y. F.
,
2015
, “
CFD Analysis of Flow and Heat Transfer in Canadian Supercritical Water Reactor Bundle
,”
Ann. Nucl. Energy
,
75
, pp.
1
10
.
38.
Xiong
,
J.
,
Cheng
,
X.
, and
Yang
,
Y.
,
2015
, “
Numerical Analysis on Supercritical Water Heat Transfer in a 2 × 2 Rod Bundle
,”
Ann. Nucl. Energy
,
80
, pp.
123
134
.
39.
Lee
,
S. H.
, and
Howell
,
J. R.
,
1998
, “
Turbulent Developing Convective Heat Transfer in a Tube for Fluids near the Critical Point
,”
Int. J. Heat Mass Transfer
,
41
(
10
), pp.
1205
1218
.
40.
Howell
,
J. R.
, and
Lee
,
S. H.
,
1999
, “
Convective Heat Transfer in the Entrance Region of a Vertical Tube for Water Near The Thermodynamic Critical Point
,”
Int. J. Heat Mass Transfer
,
42
(
7
), pp.
1177
1187
.
41.
Dang
,
C.
, and
Hihara
,
E.
,
2004
, “
In-Tube Cooling Heat Transfer of Supercritical Carbon Dioxide, Part 2, Comparison of Numerical Calculation With Different Turbulence Models
,”
Int. J. Refrig.
,
27
(
7
), pp.
748
760
.
42.
Antonia
,
R. A.
, and
Kim
,
J.
,
1991
, “
Turbulent Prandtl Number in the Near-Wall Region of a Turbulent Channel Flow
,”
Int. J. Heat Mass Transfer
,
34
(
7
), pp.
1905
1908
.
43.
Kays
,
W. M.
, and
Crawford
,
M. E.
,
1993
,
Convective Heat and Mass Transfer
,
3rd ed.
,
McGraw-Hill
, New York.
44.
McEligot
,
D. M.
, and
Taylor
,
M. F.
,
1996
, “
The Turbulent Prandtl Number in the Near-Wall Region for Low-Prandtl-Number Gas Mixtures
,”
Int. J. Heat Mass Transfer
,
39
(
6
), pp.
1287
1295
.
45.
Kays
,
W. M.
,
1994
, “
Turbulent Prandtl Number—Where Are We?
,”
ASME J. Heat Transfer
,
116
(
2
), pp.
284
295
.
46.
Hollingsworth
,
D. K.
,
Kays
,
W. M.
, and
Moffat
,
R. J.
,
1989
, “
Measurement and Prediction of the Turbulent Thermal Boundary Layer in Water on Flat and Concave Surface
,” Thermosciences division, Department of Mechanical Engineering, Stanford University, Stanford, CA, Report No. HMT-41.
47.
Mohseni
,
M.
, and
Bazargan
,
M.
,
2011
, “
Effect of Turbulent Prandtl Number on Convective Heat Transfer to Turbulent Flow of a Supercritical Fluid in a Vertical Round Tube
,”
ASME J. Heat Transfer
,
133
(
7
), p.
071701
.
48.
Oosthuizen
,
P. H.
, and
Naylor
,
D.
,
1999
,
An Introduction to Convective Heat Transfer Analysis
,
McGraw-Hill
,
New York
.
49.
Myong
,
H. K.
, and
Kasagi
,
N.
,
1990
, “
A New Approach to the Improvement of k-ε Turbulence Model for Wall Bounded Shear Flows
,”
JSME Int. J.
,
33
, pp.
63
72
.
50.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Taylor and Francis
, Oxford, UK.
51.
Versteeg
,
H. K.
and
Malalasekera
,
W.
,
2007
,
An Introduction to Computational Fluid Dynamic, The Finite Volume Method
,
2nd ed.
,
Longman Group Ltd.
, Harlow, UK.
52.
Song
,
J. H.
,
Kim
,
H. Y.
,
Kim
,
H.
, and
Bae
,
Y. Y.
,
2008
, “
Heat Transfer Characteristics of a Supercritical Fluid Flow in a Vertical Pipe
,”
J. Supercrit. Fluid
,
44
(
2
), pp.
164
171
.
53.
Shiralkar
,
B. S.
, and
Griffith
,
P.
,
1970
, “
The Effect of Swirl, Inlet Condition, Flow Direction and Tube Diameter on Heat Transfer to Fluids at Supercritical Pressure
,”
ASME J. Heat Transfer
,
92
(
3
), pp.
465
474
.
54.
Jackson
,
J. D.
,
Hall
,
W. B.
,
Fewster
,
J.
,
Watson
,
A.
, and
Watts
,
M. J.
,
1975
, “
Heat Transfer to Supercritical Pressure Fluids
,” Design Report No. 34.
55.
Grabezhnaya
,
V. A.
, and
Kirillov
,
P. L.
,
2006
, “
Heat Transfer Degradation Boundary in Supercritical Pressure Flow
,”
At. Energy
,
101
(
4
), pp.
262
270
.
56.
Grabezhnaya
,
V. A.
, and
Kirillov
,
P. L.
,
2006
, “
Heat Transfer Under Supercritical Pressures and Heat Transfer Deterioration Boundaries
,”
Therm. Eng.
,
53
(
4
), pp.
296
301
.
57.
Kim
,
J. K.
,
Jeon
,
H. K.
,
Yoo
,
J. Y.
, and
Lee
,
J. S.
,
2005
, “
Experimental Study on Heat Transfer Characteristics of Turbulent Supercritical Flow in Vertical Circular/Non-Circular Tubes
,” 11th
NURETH-11
, Avignon, France, Oct. 2–6, 2005.
58.
Yamagata
,
K.
,
Nishikawa
,
K.
,
Hasegawa
,
S.
,
Fujii
,
T.
, and
Yoshida
,
S.
,
1972
, “
Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes
,”
Int. J. Heat Mass Transfer
,
15
(
12
), pp.
2575
2593
.
59.
Lemmon
,
E. W.
,
Peskin
,
A. P.
,
LcLinden
,
M. O.
, and
Friend
,
D. G.
,
2003
, “
NIST 12: Thermodynamic and Transport Properties of Pure Fluids
,” National Institute of Standards and Technology, Gaithersburg, MD, NIST Standard Reference Database Number 12, Version 5.1.
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