Embed Size (px)
Citation preview
Nuclear Engineering and Design 241 (2011) 1126–1136
Contents lists available at ScienceDirect
Nuclear Engineering and Design
journa l homepage: www.e lsev ier .com/ locate /nucengdes
Development of supercritical water heat-transfer correlation for vertical baretubes
Sarah Mokrya,∗, Igor Pioroa, Amjad Faraha, Krysten Kinga, Sahil Guptaa, Wargha Peimana, Pavel Kirillovb
a Faculty of Energy Systems and Nuclear Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON L1H 7K4, Canadab State Scientific Centre of the Russian Federation – Institute of Physics and Power Engineering (IPPE) named after A.I. Leipunsky, Obninsk, Russia
a r t i c l e i n f o
Article history:Received 1 February 2010Received in revised form 28 May 2010Accepted 6 June 2010Available online 21 July 2010
a b s t r a c t
This paper presents an analysis of heat-transfer to supercritical water in bare vertical tubes. A large set ofexperimental data, obtained in Russia, was analyzed and a new heat-transfer correlation for supercriticalwater was developed. This experimental dataset was obtained within conditions similar to those insupercritical water-cooled nuclear reactor (SCWR) concepts.
The experimental dataset was obtained in supercritical water flowing upward in a 4-m long verticalbare tube with 10-mm ID. The data were collected at pressures of about 24 MPa, inlet temperatures from320 to 350 ◦C, values of mass flux ranged from 200 to 1500 kg/m2 s and heat fluxes up to 1250 kW/m2 forseveral combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocriticaltemperature.
A dimensional analysis was conducted using the Buckingham ˘-theorem to derive the general formof an empirical supercritical water heat-transfer correlation for the Nusselt number, which was final-ized based on the experimental data obtained at the normal and improved heat-transfer regimes. Also,experimental heat transfer coefficient (HTC) values at the normal and improved heat-transfer regimeswere compared with those calculated according to several correlations from the open literature, withCFD code and with those of the proposed correlation.
The comparison showed that the Dittus–Boelter correlation significantly overestimates experimentalHTC values within the pseudocritical range. The Bishop et al. and Jackson correlations tended also todeviate substantially from the experimental data within the pseudocritical range. The Swenson et al.correlation provided a better fit for the experimental data than the previous three correlations at lowmass flux (∼500 kg/m2 s), but tends to overpredict the experimental data within the entrance region anddoes not follow up closely the experimental data at higher mass fluxes. Also, HTC and wall temperaturevalues calculated with the FLUENT CFD code might deviate significantly from the experimental data, forexample, the k–ε model (wall function). However, the k–ε model (low Reynolds numbers) shows betterfit within some flow conditions.
Nevertheless, the proposed correlation showed the best fit for the experimental data within a widerange of flow conditions. This correlation has an uncertainty of about ±25% for calculated HTC valuesand about ±15% for calculated wall temperature. A final verification of the proposed correlation wasconducted through a comparison with other datasets. It was determined that the proposed correlationclosely represents the experimental data and follows trends closely, even within the pseudocritical range.Finally, a recent study determined that in the supercritical region, the proposed correlation showed thebest prediction of the data for all three sub-regions investigated.
Therefore, the proposed correlation can be used for HTC calculations in SCW heat exchangers, forpreliminary HTC calculations in SCWR fuel bundles as a conservative approach, for future comparisonwith other datasets and for the verification of computer codes and scaling parameters between waterand modelling fluids.
© 2010 Elsevier B.V. All rights reserved.
Abbreviations: AECL, Atomic Energy of Canada Limited; CANDU, Canada deuterium uranium (reactor); DHT, deteriorated heat-transfer; GIF, Generation IV InternationalForum; HTC, heat transfer coefficient; ID, inside diameter; NIST, National Institute of Standards and Technology; NPP, nuclear power plant; PT, pressure tube (reactor); PV,pressure vessel (reactor); RMS, root mean square; SCW, supercritical water-cooled; SCWR, supercritical water reactor; SST, shear stress transport (k–ω model); VVER-SCP,water–water power reactor of supercritical pressure (in Russian abbreviations).
∗ Corresponding author. Tel.: +1 905 721 8668x2880.E-mail addresses: sarah [email protected] (S. Mokry), [email protected] (I.
Pioro), [email protected] (P. Kirillov).
0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.nucengdes.2010.06.012
S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136 1127
Nomenclature
C constantcp specific heat at constant pressure, J/kg Kc̄p average specific heat, J/kg K, (Hw − Hb)/(Tw − Tb)D inside diameter, mf functionG mass flux, kg/m2 sH enthalpy, J/kgh heat transfer coefficient, W/m2 Kk thermal conductivity, W/m KL length, mP pressure, Paq heat flux, W/m2
Ra surface roughness, �mT temperature, ◦CV volume, m3
v velocity, m/sx axial location, m
Greek letters� dynamic viscosity, Pa s� density, kg/m3
ı thickness, mm
Dimensionless numbersNu Nusselt number hD/kPr Prandtl number �cp/kPr average Prandtl number (�c̄p/k)Re Reynolds number GD/�
Subscriptsave averageb bulkcalc calculatedcr criticaldht deteriorated heat-transferel electricalexp experimentalh heatedin inletout outletpc pseudocriticalw wall
1
n(o2
icuesif
2007). Fig. 2 shows properties variations in water passing throughthe pseudocritical point at 25 MPa, the proposed operating pres-sure for SCWRs. The most significant changes in properties occur
◦ ◦
. Introduction
Heat-transfer at supercritical pressures is influenced by sig-ificant changes in thermophysical properties at these conditionsPioro and Duffey, 2007). The most significant properties variationsccur within critical and pseudocritical points (Pioro and Duffey,007).
Prior to a discussion on thermophysical properties of supercrit-cal fluids and supercritical water-cooled nuclear reactor (SCWR)oncepts, it is necessary to define special terms and expressionssed at these conditions. General definitions of selected terms andxpressions related to critical and supercritical pressures, as pre-ented in Pioro and Duffey (2007), are listed below. In order tollustrate these terms and expressions a thermodynamic diagram
◦
or water (Pcr = 22.064 MPa and Tcr = 373.95 C) is shown in Fig. 1.Fig. 1. Pressure–temperature diagram for water within critical region.
1.1. General definitions of selected terms and expressions relatedto fluids at critical and supercritical pressures
Compressed fluid is a fluid at a pressure above the critical pres-sure, but at a temperature below the critical temperature.
Critical point (also called a critical state) is the point where thedistinction between the liquid and gas (or vapor) phases disappears,i.e., both phases have the same temperature, pressure and volume.The critical point is characterized by the phase state parameters Tcr,Pcr and Vcr, which have unique values for each pure substance.
Deteriorated heat transfer is characterized with lower values ofthe wall heat transfer coefficient compared to those at the normalheat-transfer regime; and hence, has higher values of wall temper-ature within some part of a test section or within the entire testsection.
Improved heat transfer is characterized with higher values of thewall heat transfer coefficient compared to those at the normal heat-transfer regime; and hence, has lower values of wall temperaturewithin some part of a test section or within the entire test section.
Normal heat transfer can be characterized in general with wallheat transfer coefficients similar to those of subcritical convec-tive heat transfer far from the critical or pseudocritical regions,when are calculated according to the conventional single-phaseDittus–Boelter-type correlations.
Pseudocritical point (characterized with Ppc and Tpc) is a point at apressure above the critical pressure and at a temperature (Tpc > Tcr)corresponding to the maximum value of the specific heat for thisparticular pressure.
Supercritical fluid is a fluid at pressures and temperatures thatare higher than the critical pressure and critical temperature. How-ever, in the present paper, the term supercritical fluid includes bothterms – supercritical fluid and compressed fluid.
Superheated steam is a steam at pressures below the criticalpressure, but at temperatures above the critical temperature.
1.2. Supercritical fluids
Supercritical fluids have unique properties (Pioro and Duffey,
within ±25 C from the pseudocritical temperature (384.9 C). The
1128 S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136
Fig. 2. Profiles of selected properties of supercritical water within pseudocriticalpoint.
Table 1Major parameters of PT SCW CANDU (Canada) and PV SCW VVER-SCP (Russia)nuclear-reactor concepts.
Parameters SCW CANDU® VVER-SCP
Reactor type PT PVReactor spectrum Thermal FastThermal power (MW) 2540 3830Electric power (MW) 1220 1700Thermal efficiency (%) 48 44Pressure (MPa) 25 25Inlet temperature (◦C) 350 280Outlet temperature (◦C) 625 530Mass flow rate (kg/s) 1320 1860
NpdsH(
1
Sawc2
Number of fuel channels 300 241Number of fuel elements in bundle 43 252Length of bundle string (m) 6 4
IST REFPROP software was used to calculate these thermophysicalroperties (NIST, 2007). Crossing from a high-density fluid to low-ensity fluid does not involve a distinct phase change. Phenomenauch as dry-out (critical heat flux) are therefore not applicable.owever, at supercritical conditions, a deteriorated heat-transfer
DHT) regime may exist (Pioro and Duffey, 2007).
.3. SCWR concepts
As part of the Generation IV International Forum (GIF),
CWR concepts (Table 1), which include pressure-vessel (PV)nd pressure-tube (PT) options, are currently under developmentorldwide. Canada is working on the development of a PT-reactoroncept – SCW CANDU reactor (Table 1 and Fig. 3) (Naidin et al.,009a,b; Duffey et al., 2008; Pioro and Duffey, 2007).
Fig. 3. Current Canadian SCWR fuel-channel concept.
Fig. 4. Possible channel layout for 1200-MWel PT SCWR.
One of the main objectives for developing and utilizing SCWRsis that supercritical water (SCW) nuclear power plants (NPPs) offeran increased thermal efficiency, approximately 45–50%, comparedto that of current generation NPPs (30–35%).
The current Canadian SCWR concept (see Fig. 3) includes a fuelchannel comprised of a fuel bundle, liner tube, ceramic layer andpressure tube insulated internally, which would enable the pres-sure tube to operate at temperatures close to that of the moderator(Pioro and Duffey, 2007). The outer surface of the pressure tubewill be in direct contact with the moderator, while the inner sur-face of the pressure tube is covered with a ceramic layer to protectthe pressure tube from exposure to high-temperature coolant. Inaddition, a perforated metal liner covers and protects the insulatorfrom damage during fuelling and/or refuelling and from erosion bythe coolant flow. Fig. 4 provides a schematic of a possible channellayout for a 1200-MWel PT SCWR.
2. Background
Currently, there is just one SCW heat-transfer correlation for fuelbundles, developed by Dyadyakin and Popov (1977). This correla-tion was obtained in a 7-element helically finned bundle. However,heat-transfer correlations for bundles are usually quite sensitive toa particular bundle design. Therefore, this correlation cannot beapplied to other bundle geometries.
To overcome this problem, a wide-range heat-transfer corre-lations based on bare-tube data can be used as a conservativeapproach. The conservative approach is based on the fact that HTCsin bare tubes are generally lower than those in bundle geome-tries, where heat transfer is enhanced with appendages (endplates,bearing pads, spacers, buttons, etc.).
A number of empirical generalized correlations have been pro-
posed to calculate the HTC in forced convection for various fluidsincluding water at supercritical pressures. However, differences incalculated HTC values can be up to several hundred percent (Pioroand Duffey, 2007).
S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136 1129
Table 2Test matrix.
2
aPR2oe
cDnp
2
p(ltt
N
tiatcb
ioTiewamu(t
ctTT
.
P (MPa) Tin (◦C) Tout (◦C)
24 320–350 380–406
.1. Experimental data
The experimental data used in the present paper were obtainedt the State Scientific Centre of Russian Federation – Institute forhysics and Power Engineering supercritical-test facility (Obninsk,ussia) (Pioro et al., 2008; Gospodinov et al., 2008; Pioro and Duffey,007; Kirillov et al., 2005). This set of data was obtained withinperating conditions close to those of SCWRs, including a hydraulic-quivalent diameter.
The data for this study was obtained within the followingonditions: Vertical stainless-steel (12Cr18Ni10Ti) smooth tube:= 10 mm, ıw = 2 mm, and Lh = 4 m; tube internal-surface rough-ess Ra = 0.63–0.8 �m; and upward flow. Table 2 lists test-matrixarameters and Table 3 lists their uncertainties.
.2. Existing correlations
The most widely used heat-transfer correlation at subcriticalressures for forced convection is the Dittus–Boelter correlation1930). McAdams (1942) proposed to use the Dittus–Boelter corre-ation in the following form for forced-convective heat transfer inurbulent flows at subcritical pressures (this statement is based onhe recent study by Winterton, 1998):
ub = 0.0243 Re0.8b Pr0.4
b (1)
Later, Eq. (1) was also used at supercritical conditions. Accordingo Schnurr et al. (1976), Eq. (1) showed good agreement with exper-mental data for supercritical water flowing inside circular tubes atpressure of 31 MPa and at low heat fluxes. However, it was noted
hat Eq. (1) might produce unrealistic results within some flowonditions, especially, near the critical and pseudocritical points,ecause it is very sensitive to properties variations.
In general, experimental HTC values show just a moderatencrease within the pseudocritical region. This increase dependsn flow conditions and heat flux: higher heat flux – less increase.hus, the bulk-fluid temperature might not be the best character-stic temperature at which all thermophysical properties should bevaluated. Therefore, the cross-sectional averaged Prandtl number,hich accounts for thermophysical properties variations withincross-section due to heat flux, was proposed to be used inany supercritical heat-transfer correlations instead of the reg-
lar Prandtl number. Nevertheless, this classical correlation (Eq.1)) was used extensively as a basis for various supercritical heat-ransfer correlations.
Bishop et al. (1964) conducted experiments in supercriti-
al water flowing upward inside bare tubes and annuli withinhe following range of operating parameters: P = 22.8–27.6 MPa,b = 282–527 ◦C, G = 651–3662 kg/m2s and q = 0.31–3.46 MW/m2.heir data for heat transfer in tubes were generalized using theTable 3Uncertainties of primary parameters.
Parameters Uncertainty
Test-section power ±1.0%
Inlet pressure ±0.25%
Wall temperature ±3.0%
Mass-flow rate ±1.5%
Heat loss ≤3.0%
Tw (◦C) q (kW/m2) G (kg/m2 s)
<700 70–1250 200; 500; 1000; 1500
following correlation with a fit of ±15%:
Nub = 0.0069Re0.9b Pr
0.66b
(�w
�b
)0.43 (1 + 2.4
D
x
)(2)
Eq. (2) uses the cross-sectional averaged Prandtl number, andthe last term in the correlation, (1 + 2.4(D/x)), accounts for theentrance-region effect. However, in the present comparison theBishop et al. correlation was used without the entrance-region termas the other correlations (see Eqs. (1), (3) and (4)).
Swenson et al. (1965) found that conventional correlations,which use a bulk-fluid temperature as a basis for calculating themajority of thermophysical properties, were not always accurate.They have suggested the following correlation in which a majorityof thermophysical properties are based on a wall temperature:
Nuw = 0.00459 Re0.923w Pr
0.613w
(�w
�b
)0.231(3)
Eq. (3) was obtained within the following range: pressure22.8–41.4 MPa, bulk-fluid temperature 75–576 ◦C, wall tempera-ture 93–649 ◦C and mass flux 542–2150 kg/m2 s; and predicts theexperimental data within ±15%.
Jackson (2002) modified the original correlation ofKrasnoshchekov et al. (1967) (for details, see Pioro and Duffey,2007) for forced-convective heat transfer in water and carbon diox-ide at supercritical pressures to employ the Dittus–Boelter-typeform for Nu0 as the following:
Nub = 0.0183 Re0.82b Pr0.5
b
(�w
�b
)0.3(
cp
cpb
)n
(4)
where the exponent n is defined as following:
n = 0.4 for Tb < Tw < Tpc and for 1.2 Tpc < Tb < Tw;
n = 0.4 + 0.2
(Tw
Tpc− 1
)for Tb < Tpc < Tw; and
n = 0.4 + 0.2
(Tw
Tpc− 1
)[1 − 5
(Tb
Tpc− 1
)]for Tpc < Tb < 1.2 Tpc and Tb < Tw
An analysis performed by Pioro and Duffey (2007) showed thatthe two following correlations: (1) Bishop et al. (1964) and (2)Swenson et al. (1965); were obtained within the same range ofoperating conditions as those for SCWRs.
The majority of empirical correlations were proposed in the1960s–1970s, when experimental techniques were not at the samelevel (i.e., advanced level) as they are today. Also, thermophysicalproperties of water have been updated since that time (for example,a peak in thermal conductivity in critical and pseudocritical pointswithin a range of pressures from 22.1 to 25 MPa, was not officiallyrecognized until the 1990s (Pioro and Duffey, 2007)).
Therefore, it was necessary to develop a new or an updated cor-relation based on a new set of heat-transfer data and the latestthermophysical properties of water (NIST, 2007) within the SCWRsoperating range.
It should be noted that all heat-transfer correlations presentedin this paper are intended only for the normal and improved heat-transfer regimes.
The following empirical correlation was proposed for calculat-ing the minimum heat flux at which the deteriorated heat-transferregime appears:
qdht = −58.97 + 0.745G, kW/m2 (5)
1130 S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136
Fig. 5. Comparison of data fit with experimental data: (a) for HTC and (b) for Tw (Mokry et al., 2009a; Eq. (9)).
F andP
3
3
ekupaaac
ea
H
l˘
Nub = C × Ren1b Prn2
b
(kw
kb
)n3(�w
�b
)n4(
�w
�b
)n5(7)
Table 4Description of various heat-transfer parameters (Mokry et al., 2009b).
Variable Description SI units Dimensions(M, L, T, K)
HTC Heat transfer coefficient W/m2 K MT−3K−1
D Inside diameter of tube m Lkb Thermal conductivity of fluid at Tb W/m K MLT−3K−1
kw Thermal conductivity of fluid at Tw W/m K MLT−3K−1
� Density of fluid at T kg/m3 ML−3
ig. 6. Comparison of HTC values calculated with proposed correlation (Eq. (9))in = 24.1 MPa and G = 1500 and 200 kg/m2 s.
. Developing new correlation
.1. Dimensional analysis
A dimensional analysis was performed in order to obtain a gen-ral empirical form of a correlation for HTC calculations. It is wellnown that HTC is not an independent variable, and that HTC val-es are affected by velocity, inside diameter and thermophysicalroperties variations. Therefore, a set of the most important vari-bles, which affects the HTC, were identified based on theoreticalnd experimental HTC studies. Table 4 lists parameters identifieds essential for the analysis of heat-transfer processes for forcedonvection at supercritical conditions.
The Buckingham П-theorem for dimensional analysis (Munsont al., 2005) was used to produce the following expression for HTCs a function of the identified heat-transfer parameters.
TC = f (D, kb, kw, �w, �b, �w, �b, cp, v) (6)
Through consideration of the primary dimensions (mass (M),ength (L), time (T) and temperature (K)), six unique dimensionless
-terms were determined. Table 5 lists these terms.
other correlations with experimental data along 4-m circular tube (D = 10 mm):
The resulting relationship based on this analysis is as follows:˘1 = f (˘2, ˘3, ˘4, ˘5, ˘6) or
b b
�w Density of fluid at Tw kg/m3 ML−3
�b Viscosity of fluid at Tb Pa s ML−1T−1
�w Viscosity of fluid at Tw Pa s ML−1T−1
cp Specific heat J/kg K L2T−2K−1
v Velocity m/s LT−1
S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136 1131
Fig. 7. Temperature and HTC profiles at various heat fluxes along 4-m circular tube (D = 10 mm): Pin = 24.1 MPa and G = 200 kg/m2 s.
ng 4-m
3
l
T˘
Fig. 8. Temperature and HTC profiles at various heat fluxes alo
.2. Finalizing correlation
As a result of the experimental-data analysis, the following pre-iminary correlation for heat transfer to supercritical water was
able 5-terms of empirical correlation (Mokry et al., 2009b).
˘-terms Dimensionless group Name
˘1HTC×D
kbNusselt number
˘2�VD�b
Reynolds number
˘3cp�b
kbPrandtl number
˘4kwkb
Thermal conductivity ratio
˘5�w�b
Viscosity ratio˘6
�w�b
Density ratio
circular tube (D = 10 mm): Pin = 24.1 MPa and G = 500 kg/m2 s.
obtained:
Nub = 0.0053 Re0.914b Prb
0.654(
�w
�b
)0.518(8)
To finalize the development of the correlation, the complete setof primary data and Eq. (8) were fed into the SigmaPlot DynamicFit Wizard to perform final adjustments. The final correlation is asfollows:
Nub = 0.0061 Re0.904b Prb
0.684(
�w
�b
)0.564(9)
Fig. 5 shows scatter plots of experimental HTC values versuscalculated HTC values according to Eqs. (8) and (9), and calculatedand experimental values for wall temperatures. Both plots lie alonga 45◦ straight line with an experimental data spread of ±25% for theHTC values and ±15% for the wall temperatures.
1132 S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136
g 4-m
3
HDcfipaflic
lttwvc
Fig. 9. Temperature and HTC profiles at various heat fluxes alon
.3. Verifying proposed correlation
Fig. 6 shows a comparison between experimentally obtainedTC and wall temperature values and those calculated with theittus–Boelter, Jackson, Bishop et al., Swenson et al. and proposedorrelations (Eq. (9)). In order to verify the correlation and the datat, samples of experimental runs from the dataset, with the pro-osed correlation, are shown in Figs. 7–10. The graphs shown are forpressure of ∼24 MPa mass flux from 200 to 1500 kg/m2 s, and heatux up to 729 kW/m2. Fig. 11 shows a comparison between exper-
mentally obtained HTC and wall temperature values and thosealculated with the FLUENT CFD code and the proposed correlation.
An analysis of these plots shows that the Dittus–Boelter corre-ation significantly overestimates experimental HTC values within
he pseudocritical range. The Bishop et al. and Jackson correlationsended also to deviate substantially from the experimental dataithin the pseudocritical range. The Swenson et al. correlation pro-ided a better fit for the experimental data than the previous threeorrelations at low mass flux (∼500 kg/m2 s), but tends to over-
Fig. 10. Temperature and HTC profiles at various heat fluxes along 4-m
circular tube (D = 10 mm): Pin = 24.1 MPa and G = 1000 kg/m2 s.
predict the experimental data within the entrance region and doesnot follow up closely the experimental data at higher mass fluxes.Also, HTC and wall temperature values calculated with the FLU-ENT CFD code might deviate significantly from the experimentaldata (for example, the k–ε model (wall function)). However, the k–εmodel (low Reynolds numbers) shows a better fit within some flowconditions. The k–ω model (shear stress transport (SST)) also pro-vided a reasonable prediction for both HTC values and inside walltemperature, however, it did tend to deviate within the entranceregion.
Nevertheless, the proposed correlation (Eq. (9)) showed the bestfit for the experimental data within a wide range of flow conditions.This correlation has uncertainty of about ±25% for HTC values andabout ±15% for calculated wall temperature.
Therefore, the proposed correlation can be used for a prelimi-nary HTC calculations in SCWR fuel bundles, for future comparisonwith other datasets and for the verification of computer codes andscaling parameters between water and modelling fluids.
circular tube (D = 10 mm): Pin = 24.1 MPa and G = 1500 kg/m2 s.
S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136 1133
Fig. 11. Comparison of HTC and wall temperature values calculated with proposed correlation (Eq. (9)) and FLUENT CFD-code (Vanyukova et al., 2009) with experimentaldata along 4-m circular tube (D = 10 mm): Pin = 23.9 MPa and G = 1000 kg/m2 s.
Fig. 12. Temperature and HTC profiles along circular tube at various heat fluxes: nominal operating conditions – Pin = 23.5 MPa and D = 9.5 mm (Pis’mennyy et al., 2005).
Table 6Other datasets and corresponding test matrices.
Reference P (MPa) q (MW/m2) G (kg/m2 s) Flow geometry
Bishop et al. (1964) 22.8–27.6 0.31–3.46 651–3662 Tube (D = 5 mm) upward flowPis’mennyy et al. (2005) 23.5 Up to 0.515 250; 500 Vertical SS tubes (D = 6.28 mm, Lh = 600; 360 mm, D = 9.50 mm,
Lh = 600; 400 mm)675542–2310–1
ofirw
Polyakov (1975) 29.4 0.50Lee and Haller (1974) 24.1 0.25–1.57Yamagata et al. (1972) 22.6–29.4 0.12–0.93
For the final verification of the correlation, a comparison with
ther datasets was completed (Figs. 12–15). From the presentedgures, it can be seen that the proposed correlation (Eq. (9)) closelyepresents the experimental data and follows trends closely, evenithin the pseudocritical range. Table 6 lists the test matrices forTube (D = 8 mm)441 SS tubes (D = 38.1; 37.7 mm, L = 4.57 m), tube with ribs830 Vertical and horizontal SS tubes (D/L = 7.5/1.5; 10/2 mm/m),
upward, downward and horizontal flows
the datasets against which the proposed correlation was compared.
A recent study was conducted by Zahlan et al. (2010) in orderto develop a heat-transfer look-up table for critical/supercriticalpressures. An extensive literature review was conducted, whichincluded 28 datasets and 6663 trans-critical heat-transfer data.
1134 S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136
Fig. 13. Temperature and HTC profiles along circular tube at various heat fluxes: nominal operating conditions – Pin = 24.5 MPa/Pin = 29.4 MPa and D = 8 mm (Polyakov, 1975).
Fig. 14. Temperature and HTC profiles along circular tube at various heat fluxes: nominal operating conditions – Pin = 24.1 MPa and D = 38 mm (Lee and Haller, 1974).
Table 7Overall weighted average and RMS errors within three supercritical sub-regions (Zahlan et al., 2010).
Correlation Liquid-like region Gas-like region Within critical or pseudocritical regions
Ave. Er (%) RMS (%) Ave. Er (%) RMS (%) Ave. Er (%) RMS (%)
Dittus–Boelter (1930) 32.5 46.7 87.7 131.0 – –5.2
−15.911.5−8.5
Tatd
Bishop et al. (1965) 6.3 24.2Swenson et al. (1965) 1.5 25.2Jackson (2002) 13.5 30.1Proposed Correlation −3.9 21.3
able 7 presents the results of this study, in the form of the over-ll weighted average root mean square (RMS) error, within thehree supercritical sub-regions for the heat-transfer correlationsiscussed in the present paper.
18.4 20.9 28.920.4 5.1 23.028.7 22.0 40.616.5 −2.3 17.0
In their conclusions, Zahlan et al. (2010) determined that in thesupercritical region, the proposed correlation (Eq. (9)) showed thebest prediction for the data within all three sub-regions investi-gated.
S. Mokry et al. / Nuclear Engineering and Design 241 (2011) 1126–1136 1135
F mina
4
vnaGo
ftttwvcpnAEdkfl
tTvvcpfasdtt
licpfl
transfer correlation for vertical bare tubes. In: Proc. ICONE-17, Brussels, Belgium,July 12–16, Paper #76010, p. 8.
ig. 15. Temperature and HTC profiles along circular tube at various heat fluxes: no
. Conclusions
The supercritical-water heat-transfer dataset obtained in aertical bare tube at the Institute for Physics and Power Engi-eering (Obninsk, Russia) was used for the development of
new heat-transfer correlation: P = 24 MPa, Tin = 320–350 ◦C,= 200–1500 kg/m2 s and q ≤ 1250 kW/m2. This dataset wasbtained within the SCWR operating conditions.
The comparison of this dataset with heat-transfer correlationsrom the open literature showed that the Dittus–Boelter correla-ion significantly overestimates experimental HTC values withinhe pseudocritical range. The Bishop et al. and Jackson correlationsended also to deviate substantially from the experimental dataithin the pseudocritical range. The Swenson et al. correlation pro-
ided a better fit for the experimental data than the previous threeorrelations at low mass flux (∼500 kg/m2 s), but tends to over-redict the experimental data within the entrance region and doesot follow up closely the experimental data at higher mass fluxes.lso, HTC and wall-temperature values calculated with the FLU-NT CFD code might deviate significantly from the experimentalata (for example, the k–ε model (wall function)). However, the–ε model (low Reynolds numbers) shows a better fit within someow conditions.
Nevertheless, the proposed correlation showed the best fit forhe experimental data within a wide range of flow conditions.his correlation has an uncertainty about ±25% for calculated HTCalues and about ±15% for calculated wall temperatures. A finalerification of the proposed correlation was conducted through aomparison with other datasets. It was determined that the pro-osed correlation closely represents the experimental data andollows trends closely, even within the pseudocritical range. Finally,recent study conducted by Zahlan et al. (2010) showed that in the
upercritical region, the proposed correlation showed the best pre-iction of the data for all three sub-regions investigated. In addition,he proposed correlation had the best agreement with the data forhe superheated steam region.
Therefore, the proposed correlation can be used for HTC calcu-ations in SCW heat exchangers, for preliminary HTC calculationsn SCWR fuel bundles as the conservative approach, for future
omparison with other datasets and for the verification of com-uter codes and scaling parameters between water and modellinguids.l operating conditions – Pin = 24.5 MPa and D = 7.5 mm (Yamagata et al., 1972).
Acknowledgments
Financial supports from the NSERC Discovery Grant,NSERC/NRCan/AECL Generation IV Energy Technologies Pro-gram and the Ontario Research Excellence Fund are gratefullyacknowledged.
References
Bishop, A.A., Sandberg, R.O., Tong, L.S., 1964. High temperature supercritical pressurewater loop: Part IV. Forced convection heat transfer to water at near-criticaltemperatures and super-critical pressures. Westinghouse Electric Corporation,Pittsburgh, PA.
Bishop, A.A., Sandberg, R.O., and Tong, L.S., 1965, Forced convection heat transferto water at near-critical temperatures and supercritical pressures, A.I.Ch.E.-I.Chem.E Symposium Series No. 2, pp. 77–85.
Dittus, F.W., Boelter, L.M.K., 1930. Heat transfer in automobile radiators of the tubu-lar type. University of California, Berkeley, Publications on Engineering 2 (13),443–461.
Duffey, R., Pioro, I., Zhou, T., et al., 2008. Supercritical water-cooled nuclear reactors(SCWRs): current and future concepts – steam-cycle options. In: Proc. ICONE-16,Orlando, FL, USA, May 11–15, Paper #48869, p. 9.
Dyadyakin, B.V., Popov, A.S., 1977. Heat transfer and thermal resistance of tightseven-rod bundle, cooled with water flow at supercritical pressures. Transac-
tions of VTI ( ) (11), 244–253 (in Russian).Gospodinov, Y., Mokry, S., Pioro, I., Kirillov, P.L., 2008. Supercritical water heat trans-
fer in a vertical bare tube. In: Proc. ICONE-16, Orlando, FL, USA, May 11–15, Paper#48546, p. 11.
Jackson, J.D., 2002. Consideration of the heat transfer properties of supercritical pres-sure water in connection with the cooling of advanced nuclear reactors. In: Proc.13th Pacific Basin Nuclear Conference, Shenzhen City, China, October 21–25.
Kirillov, P., Pometko, R., Smirnov, A., et al., 2005. Experimental study on heat transferto supercritical water flowing in 1- and 4-m-long vertical tubes. In: Proc. GLOBAL‘05, Tsukuba, Japan, October 9–13, Paper No. 518.
Krasnoshchekov, E., Protopopov, V., Van, F., Kuraeva, I., 1967. Experimental investi-gation of heat transfer for carbon dioxide in the supercritical region. In: GazleyJr., C., Harnett, J., Ecker, E. (Eds.), Proc. 2nd All-Soviet Union Conf. on Heat andMass Transfer. Minsk, Belarus, May 1964, vol. 1, pp. 26–35, Published as RandReport R-451-PR.
Lee, R.A., Haller, K.H., 1974. Supercritical water heat transfer developments andapplications. In: Proceedings of the 5th International Heat Transfer Con-ference, Tokyo, Japan, September 3–7, vol. IV Paper No. B7.7, pp. 335–339.
McAdams, W., 1942. Heat Transmission, second ed. McGraw-Hill, New York, NY,USA, 459 pp.
Mokry, S., Gospodinov, Y., Pioro, I., Kirillov, P.L., 2009a. Supercritical water heat-
Mokry, S., Farah, A., King, K., Gupta, S., Pioro, I., Kirillov, P., 2009b. Developmentof supercritical water heat-transfer correlation for vertical bare tubes. In: Pro-ceedings of the Nuclear Energy for New Europe International Conference, Bled,Slovenia, September 14–17, Paper No. 210.
1 ing an
M
N
N
N
P
P
P
fer to supercritical water flowing in tubes. International Journal of Heat and Mass
136 S. Mokry et al. / Nuclear Engineer
unson, B., Young, D., Okiishi, Th., 2005. Fundamentals of Fluid Mechanics, fifth ed.J. Wiley & Sons, New York, NY.
aidin, M., Mokry, S., Baig, F., et al., 2009a. Thermal-design options for pressure-channel SCWRs with co-generation of hydrogen. Journal of Engineering for GasTurbines and Power 131 (January), 8.
aidin, M., Pioro, I., Zirn, U., 2009b. Supercritical water-cooled NPPs with co-generation of hydrogen: general layout and thermodynamic-cycles options. In:Proc. 4th Int. Symp. on Supercritical Water-Cooled Reactors, Heidelberg, Ger-many, March 8–11, Paper No. 78, p. 11.
ational Institute of Standards Technology, 2007. NIST Reference Fluid Thermody-namic and Transport Properties-REFPROP: NIST Standard Reference Database23, Ver. 8.0. Department of Commerce, Boulder, CO, USA.
ioro, I., Duffey, R., 2007. Heat Transfer and Hydraulic Resistance at SupercriticalPressures in Power Engineering Applications. ASME Press, New York, NY, USA,334 pp.
ioro, I.L., Kirillov, P.L., Mokry, S.J., Gospodinov, Y.K., 2008. Supercritical water heattransfer in a vertical bare tube: normal, improved and deteriorated regimes. In:
Proc. ICAPP ‘08, Anaheim, CA, USA, June 8–12, Paper #8333, pp. 1843–1852.is’mennyy, E.N., Razumovskiy, V.G., Maevskiy, E.M., et al., 2005. Experimentalstudy on temperature regimes to supercritical water flowing in vertical tubesat low mass fluxes. In: Proceedings of the International Conference GLOBAL-2005 Nuclear Energy Systems for Future Generation and Global Sustainability,Tsukuba, Japan, October 9–13, Paper No. 519, p. 9.
d Design 241 (2011) 1126–1136
Polyakov, A.F., 1975. Mechanism and limits on the formation of conditions forimpaired heat transfer at a supercritical coolant pressure. High Temperatures 13
(6), 1119–1126 ( 1210–1219).Schnurr, N.M., Sastry, V.S., Shapiro, A.B., 1976. A numerical analysis of heat transfer
to fluids near the thermodynamic critical point including the thermal entranceregion. Journal of Heat Transfer: Transactions of the ASME 98 (4), 609–615.
Swenson, H.S., Carver, J.R., Kakarala, C.R., 1965. Heat transfer to supercritical waterin smooth-bore tubes. Journal of Heat Transfer: Transactions of the ASME SeriesC 87 (4), 477–484.
Vanyukova, G., Kuznetsov, Y., Loninov, A., et al., 2009. Application of CFD-code tocalculations of heat transfer in a fuel bundle of SCW pressure-channel reac-tor. In: Proc. 4th Int. Symp. on Supercritical Water-Cooled Reactors, Heidelberg,Germany, March 8–11, Paper No. 28, p. 9.
Winterton, R.H.S., 1998. Where did the Dittus and Boelter equation come from?International Journal of Heat and Mass Transfer 41 (4–5), 809–810.
Yamagata, K., Nishikawa, K., Hasegawa, S., et al., 1972. Forced convective heat trans-
Transfer 15 (12), 2575–2593.Zahlan, H., Groeneveld, D.C., Tavoularis, S., 2010. Look-up table for trans-critical heat
transfer. In: Proceedings of the 2nd Canada–China Joint Workshop on Supercrit-ical Water-Cooled Reactors (CCSC-2010), Toronto, Ontario, Canada, April 25–28,Paper No. P036.
