Heat transfer to water at supercritical pressure within the core of a supercritical water reactor must be predicted accurately to ensure safe design of the reactor and prevent overheating of the fuel cladding. In the previous work (Laurien, 2012, “Semi-Analytic Prediction of Hydraulic Resistance and Heat Transfer for Pipe Flows of Water at Supercritical Pressure,” Proceedings of the International Conference on Advances in Nuclear Power Plants, ICAPP’12, Chicago, June 24–28), we have demonstrated that the wall shear stress and the wall temperature can be computed in a coupled way by a finite-difference method, taking the wall roughness into account. In the present paper, the classical two-layer model, consisting only of a laminar sublayer and a turbulent wall layer, is extended toward the same task. A set of implicit algebraic equations for the wall shear stress and the wall temperature is derived. It is consistent with the well-established Colebrook equation for rough pipes, which is included as a limiting case for constant properties. The accuracy of the prediction for strongly heated pipe flow is tested by comparison to experiments (Yamagata et al., 1972, “Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes,” Int. J. Heat Mass Transfer, 15(12), 2575–2593) with supercritical water. The high accuracy and the generality of Laurien (2012) “Semi-Analytic Prediction of Hydraulic Resistance and Heat Transfer for Pipe Flows of Water at Supercritical Pressure,” Proceedings of the International Conference on Advances in Nuclear Power Plants, ICAPP’12, Chicago, June 24–28 are not achieved, but with the help of correction factors, the two-layer model has a potential for improved predictions of the hydraulic resistance and the heat transfer of pipe and channel flows at supercritical pressure.

References

References
1.
Schulenberg
,
T.
,
Starflinger
,
J.
,
Marault
,
P.
,
Bittermann
,
D.
,
Maraczy
,
C.
,
Laurien
,
E.
,
Lycklama a Niejeholt
,
J. A.
,
Anglart
,
H.
,
Andreani
,
M.
,
Ruzikowa
,
M.
, and
Toivonen
,
A.
,
2011
, “
European Supercritical Water Cooled Reactor
,”
Nucl. Eng. Des.
,
241
(
9
), pp.
3505
3513
. 0029-549310.1016/j.nucengdes.2010.09.039
2.
Pioro
,
I. L.
,
Khartabil
,
H. F.
, and
Duffey
,
R. B.
,
2004
, “
Heat Transfer to Supercritical Fluids flowing in Channels—Empirical Correlations (Survey)
,”
Nucl. Eng. Des.
,
230
(
1–3
), pp. 
69
91
. 0029-549310.1016/j.nucengdes.2003.10.010
3.
Lycklama a Niejeholt
,
J. A.
,
Visser
,
D. C.
,
Laurien
,
E.
,
Anglart
,
H.
, and
Chandra
,
L.
,
2011
, “
Development of a Heat Transfer Correlation for the HPLWR Fuel Assembly by Means of CFD Analyses
,”
5th International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-4)
,
Vancouver, CA
,
Mar. 13–16
,
T. Schulenberg and J. Starflinger
,
Heidelberg, Germany
.
4.
Löwenberg
,
M. F.
,
Laurien
,
E.
,
Class
,
A.
, and
Schulenberg
,
T.
,
2008
, “
Supercritical Water Heat Transfer in Vertical Tubes: A Look-Up Table
,”
Prog. Nucl. Energy
,
50
(
2–6
), pp.
532
538
. 0149-197010.1016/j.pnucene.2007.11.037
5.
Zahlan
,
H.
,
Groeneveld
,
D. C.
, and
Tavoularis
,
S.
,
2011
, “
Derivation of a Look-Up Table for Trans-Critical Heat Transfer for Water-Cooled Tubes
,”
Proceedings of the 14th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-14)
,
Sept. 25–30
,
American Nuclear Society
,
Toronto, Canada
.
6.
Laurien
,
E.
,
2012
, “
Semi-Analytic Prediction of Hydraulic Resistance and Heat Transfer for Pipe Flows of Water at Supercritical Pressure
,”
Proceedings of the International Conference on Advances in Nuclear Power Plants, ICAPP’12
,
Chicago
,
June 24–28
,
American Nuclear Society
,
Chicago, IL
.
7.
Laurien
,
E.
,
2014
, “
Prediction of Hydraulic Resistance and Heat Transfer of Super-Critical Water Pipe Flows with Wall Roughness
,”
Workshop on Heat Transfer at Supercritical Pressure in Nuclear Reactors and Solar Energy Systems
,
Manchester, UK
,
June 30–July 1
,
D. Jackson
,
Manchester, GB
.
8.
He
,
S.
,
Kim
,
W. S.
, and
Bae
,
J. H.
,
2008
, “
Assessment of Performance of Turbulence Models in Predicting Supercritical Pressure Heat Transfer in Vertical Tube
,”
Int. J. Heat Mass Transfer
,
51
(
19–20
), pp. 
4659
4675
. 0017-931010.1016/j.ijheatmasstransfer.2007.12.028
9.
Zhu
,
Y.
,
2010
, “
Numerical Investigation of the Flow and Heat Transfer within the Core Cooling Channel of a Supercritical Water Reactor
,” Dissertation,
University of Stuttgart
, IKE-8-122.
10.
Kiss
,
A.
,
Laurien
,
E.
,
Aszodi
,
A.
, and
Zhu
,
Y.
,
2010
, “
Numerical Simulation on a HPLWR Fuel Assembly Flow with One Revolution of Wrapped Wire Spacers
,”
Kerntechnik
,
75
(
4
), pp. 
148
157
. 0932-390210.3139/124.110080
11.
Kays
,
W.
,
Crawford
,
M.
, and
Weigand
,
B.
,
2005
,
Convective Heat and Mass Transfer (Int. ed.)
,
McGraw-Hill
,
New York
.
12.
Behr
,
H. D.
, and
Stephan
,
K.
,
1998
,
Heat and Mass Transfer
,
Springer
,
Berlin, Heidelberg
.
13.
Petukhov
,
B. S.
,
1970
, “
Heat Transfer and Friction in Turbulent Pipe Flow with Variable Properties
,”
Adv. Heat Transfer
,
6
, pp. 
503
564
. 0065-271710.1016/S0065-2717(08)70153-9
14.
Colebrook
,
C. F.
,
1939
, “
Turbulent Flow in Pipes with particular Reference to the Transition Region between Smooth and Rough Pipe
,”
J. Inst. Civ. Eng.
,
11
(
4
), pp.
133
156
.10.1680/ijoti.1939.13150
15.
Moody
,
L. F.
, and
Princeton
,
L. J.
,
1944
, “
Friction Factors for Pipe Flows
,”
Trans. ASME
, pp. 
671
684
. 0097-6822
16.
Bronstein
,
I. N.
, and
Semendjajew
,
K. A.
,
1991
,
Taschenbuch der Mathematik
,
25th ed.
,
Teubner
,
Stuttgart, Leipzig
.
17.
Kader
,
B. A.
,
1981
, “
Temperature and Concentration Profiles in Fully Turbulent Boundary Layers
,”
Int. J. Heat and Mass Transfer
,
24
(
9
), pp.
1541
1544
. 0017-931010.1016/0017-9310(81)90220-9
18.
Lemmon
,
E. W.
,
Huber
,
M. L.
, and
McLinden
,
M. O.
,
2010
, “
REFPROP, NIST Standard Reference Database
,”
Thermophysical Properties Division, National Institute of Standards and Technology
, Boulder, CO.
19.
Avci
,
A.
, and
Karagoz
,
I.
,
2009
, “
A Novel Explicit Equation for Friction Factor for Smooth and Rough Pipes
,”
J. Fluids Eng.
,
131
(
6
), pp. 
061203-1
061203-4
. 0098-220210.1115/1.3129132
20.
Yamagata
,
K.
,
Nishikawa
,
K.
,
Hasegawa
,
S.
,
Fujii
,
I.
, and
Yoshida
,
S.
,
1972
, “
Forced Convective Heat Transfer to Supercritical Water Flowing in Tubes
,”
Int. J. Heat Mass Transfer
,
15
(
12
), pp. 
2575
2593
. 0017-931010.1016/0017-9310(72)90148-2
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