GENERAL ASSESSMENT OF CONVECTION HEAT TRANSFER CORRELATIONS FOR MULTIPLE GEOMETRIES AND FLUIDS AT SUPERCRITICAL PRESSURE

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1 FULL ARTICLE The ojective of this paper is to assess different correlations independently against a diversified dataank the Canadian Nuclear Laoratories multi-fluid and multi-geometry supercritical heat transfer dataank. This dataank was recently expanded y adding compiled and original experimental data otained through collaoration with the Nuclear Power Institute of China. The dataank was sujected to screening for outliers, duplicates, and unreliale data. In addition, inappropriate data, not satisfying certain conditions, were removed. Nevertheless, the used dataank comprised more than measurements of heat transfer to different fluids flowing vertically upward in different geometries. Following a literature review and a compilation of correlations, an assessment of the taulated correlations was performed against the dataank. In total, 24 correlations were considered and applied to the entire dataase for different fluids including water and different flow geometries including tue, annulus, and rod undle. Graphical comparison of est-estimate correlations and representative experimental data is presented in this paper. In addition, statistical error analysis was performed and leading correlations were identified. Although the leading correlation showed a standard deviation of less than 6%, variation of predicted wall temperature and heat transfer coefficient with fluid temperature followed the scatter of the experimental data. GENERAL ASSESSMENT OF CONVECTION HEAT TRANSFER CORRELATIONS FOR MULTIPLE GEOMETRIES AND FLUIDS AT SUPERCRITICAL PRESSURE Hussam Zahlan 1 *, Laurence Leung 1, Yanping Huang 2, and Guangxu Liu 2 1 Canadian Nuclear Laoratories, Chalk River, ON K0J 1J0, Canada 2 Nuclear Power Institute of China, P.O. Box , Chengdu, Sichuan , China Article Info Keywords: SCWR, supercritical fluid, correlation assessment, water, CO 2, tue, rod undle. Article History: Received 3 May 2016, Accepted 19 April 2017, Availale online 2 August DOI: *Corresponding author: hussam.zahlan@cnl.ca Nomenclature c p specific heat capacity at constant pressure (J kg 1 K 1 ) d tue inner diameter G mass flux (kg m 2 s 1 ) H enthalpy (kj kg 1 ) h heat transfer coefficient (kw m 2 K) L heated length (m) k thermal conductivity (W m 1 K 1 ) P pressure (kpa) q heat flux (kw m 2 ) T temperature ( C or K) e a measure of deviation of predicted wall temperature from corresponding measurement = 100 T w,cor T w,exp T w,exp % e 5, e 10, etc. % of data within specified error range (±5%, ±10%, etc.) z axial distance from the inlet of the heated section (m) Greek letters β thermal expansion coefficient β = ð 1 ρ Þð ρ T Þ P μ dynamic viscosity (N s m 2 = kg m 1 s 1 ) ν kinematic viscosity (m 2 s 1 ) ρ fluid density (kg m 3 ) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n i = 1 σ standard deviation 100 ðe i e avg Þ 2 n % Suscripts avg average ulk c critical cor correlation exp experimental f film h, hyd hydraulic pc pseudo-critical w wall 47

2 Dimensionless numers Gr modified Grashof numer ased on q = gβ qd 4 k ν 2 Nu Nusselt numer ( = hd/k) Pr Prandtl numer ( = μc p /k) Pr averaged Prandtl numer ( = (H w H )μ / (k (T w T ))) π q non-dimensional heat flux numer ( = (q/g) (β/c p )) Q thermal loading group Q = β qd k Re Reynolds numer ( = Gdμ 1 ) Areviations CNL Canadian Nuclear Laoratories DHT deteriorated heat transfer HTC heat transfer coefficient HTD heat transfer deterioration NHT normal heat transfer NPIC Nuclear Power Institute of China R-12, 22 refrigerant-12, 22 SC supercritical SCHT supercritical heat transfer SCWR supercritical water-cooled reactor 1. Introduction This investigation was performed in support of the Canadian supercritical water-cooled reactor (SCWR) program. Conceptual design of SCWR requires reliale data/ knowledge aout heat transfer ehaviour of the supercritical (SC) water under normal and postulated accident conditions. Reliale experimental measurements in water are scarce, particularly for rod undle geometry. To study fundamental heat transfer phenomena at a wide range of SC conditions, a large numer of experiments have een performed with model fluids such as CO 2, refrigerant-12 (R-12), and R-22. Such experiments are not only less expensive, ut also more flexile in execution. Tale 1 compares the critical parameters for these 4 fluids. The thermophysical properties of a fluid at near-critical and low-sc pressure ecome highly dependent on temperature and to a much lesser extent on pressure. This is evident in specific heat (c p ), which reaches a value significantly higher than that at standard conditions. Although the maximum change occurs at the critical point, it decreases with increasing pressure; however, the change remains ovious at the pseudo-critical point. This pseudo-critical point corresponds to a thermodynamic state of a fluid when its pressure and temperature ecome larger than or equal to the critical values and is characterized y a maximum specific heat at a given pressure. The implications on momentum and energy transport include significant differences of velocity and temperature fields in the radial direction from those for uniform properties at low-sucritical pressure; under certain flow conditions, uoyancy and acceleration effects attriuted mainly to strong changes in density start influencing heat transfer. Besides the nonlinear dependence of fluid s thermophysical properties on temperature, introducing, for instance, uoyancy to the momentum equation will also implicitly incorporate wall temperature (T w ) dependence, therefore momentum and energy equations ecome strongly coupled. Thus, the description and solution of the turulent mixed-convection flow are further complicated. An example of this intricacy would e the case of application of correlations to data. Churkin and Deev [1] discussed the unavoidale issues in convergence of iterative solutions, which lead some studies to directly apply correlation to data (especially, for example, for a case of application of large numer of correlations to a large size dataase) without the iteration for wall temperature. This complication calls for the need for development of accurate correlations with a different formulation of the convective heat transfer at near critical and SC pressure. Several reviews of convective heat transfer correlations at SC pressure have een pulished, for example, overviews and assessments of supercritical heat transfer (SCHT) correlations against oth SC water and SC CO 2 data for tue [2 7], an assessment of correlations [8 10], and an updated assessment of correlations ased on rod undle water data [11]. The present study focuses on evaluation of correlations independently, regardless of their limitations, such as applicale heat transfer mode (normal/deteriorated). A second study, currently underway, will consider screening of tue data for heat transfer deterioration (HTD) and assessment of different correlations in normal/deteriorated heat transfer regions. TABLE 1. Critical parameters of water, CO 2, R-12, and R-22. Parameter Unit Water CO 2 R-12 R-22 Critical pressure, P c MPa Critical temperature, T c K [ C] [374.1] [31.0] [112.0] [96.15] Critical density, ρ c kg m

3 2. Collaoration and CNL Data Compilation and Selection 2.1. Collaoration with Nuclear Power Institute of China (NPIC) As a result of Canadian Nuclear Laoratories (CNL) collaoration with NPIC in the framework of thermalhydraulics and safety assessment in support of SCWR concept design studies, CNL and its Chinese partner exchanged their corresponding dataases of SCHT for tue geometries. Tale 2 shows the data received from NPIC and the overall data in the updated CNL tue dataases for water and CO CNL data compilation CNL dataases of heat transfer at SC pressure include measurements otained with water, CO 2,refrigerants,and helium in different flow channels including round tues, annuli, and undle suassemlies. The CNL dataases prior to 2015 were organized and descried to show the ranges of flow conditions of the different dataases. Recently, CNL compiled additional rod undle (Tale 3) and tue data. The compiled rod undle data were cross-section average data. It is worth noting that all recently compiled data including the received dataases through the exchange with NPIC were sujected to screening and quality-assurance tests prior to their incorporation into the CNL dataank. This included a heat alance compliance test and duplicate data removal. The CNL dataases were updated with the recently compiled data. As a result, the CNL dataank was expanded y including additional datasets for different fluids and flow geometries. Figure 1 shows the spread of the water and CO 2 dataases for tue over reduced pressure and Reynolds numer. TABLE 2. Numer of data in CNL tue dataase. Tue Water CO 2 NPIC contriution Updated CNL dataase FIGURE 1. Spread of the water and CO 2 dataases for tue over reduced pressure and Reynolds numer Data selection for correlation assessment Data exclusion and rejection As discussed earlier, the compiled data were sujected to quality-assurance tests and screening. This included the rejection and exclusion of unreliale or undesired data for the following main reasons: Fluid: Data for fluids other than water, CO 2, R-12, and R-22 were excluded from this study. Flow direction: Data for flows other than vertical upward were also excluded. Vertical upward is the SCWR coolant direction in the core. TABLE 3. Flow conditions and numers of the recently compiled undle data. Dataset P (MPa) G (kg/m 2 s) q (kw/m 2 ) d hyd (mm) L H (m) T ( C) Data numer Eter et al. [12] Gu et al. [13] Wang et al. [11] Wang et al. [14] Richards [15]

4 Flow geometry: This study is interested in round tue, concentric circular annulus, and rod undle suassemlies; other flow geometries were removed from the correlation assessment dataase. Thermal development region: Data collected at z/d < 30 were left out. Tue diameter: Round tues with sizes d < 2mmwere also excluded. Duplicates Outliers Heat alance inconsistencies. Tale 4 shows a summary of the CNL data used in the current investigation after the data exclusion and rejection, descried aove. 3. Nusselt Numer Correlations Currently, more than 30 correlations for SCHT are availale in the literature. The general form for the SC correlations is Nu= f ðre, Pr, :::Þ. The following sections will descrie the single phase and SCHT correlations used in this study Single phase correlations Single phase correlations were developed for fluids at sucritical pressure. These correlations feature similar parameters to those in the popular Dittus Boelter [16] correlation, ut with different exponents. The Dittus Boelter correlation evaluates the fluid properties at the ulk fluid temperature (T ), whereas the Sieder Tate [17] correlation includes a viscosity ratio term to account for the variation in fluid viscosity at the wall and in the ulk flow. The most recent single phase heat transfer correlation is that of Gnielinski [18] for turulent flows, which includes a friction factor term to account for the increase in heat transfer with an increase in friction factor. All the discussed single phase correlations are ased on water data. These correlations are listed in Tale A1 of Appendix A. TABLE 4. Numers of the screened CNL data used in the present assessment. Flow geometry Water CO 2 Round tue Circular annulus 1078 Rod undle 2 2, plain 3 rods, grid spacer , wire wrap 3 rods, wire wrap rods with R 22 7 rods with R SCHT correlations Water data ased correlations Early SCHT correlations included the Bishop et al. study [20], which was ased on water data for tue and annulus. They modified the Dittus Boelter [16] correlation y including a density ratio to account for the variation of density of the SC fluid at wall and at ulk flow. They replaced the specific heat in the Prandtl numer y the average specific heat capacity c p = H w H T w T,whereH is the fluid enthalpy and the suscripts w and denote that H is evaluated at wall and ulk fluid temperature, respectively. A similar correlation was developed y Swenson et al. [21]; however, T w was used as the reference temperature for Nu, Re, and averaged Pr numer (ased on c p ). Yamagata et al. [22] introduced a correction factor to the Dittus Boelter [16] correlation, which is a function of Eckert numer (E = ( T )/(T w T )) and Prandtl numer at the pseudo-critical temperature or the average specific heat capacity ratio. Watts and Chou [23] correlated mixed convection water data for vertical upward and downward flow. They used a similar deterioration criterion to that y Jackson and Hall [4]. However, density in the averaged Grashof numer is the average density, which was calculated in the present study y integration: 1 ρ avg = T w T T w T ρðtþdt. They proposed correlations for normal and deteriorated heat transfer. Griem [24] modifiedthe Dittus Boelter [16] equation y considering c p at 5 reference temperatures over the range from T to T w ; the selected c p,sel is estimated y excluding the largest 2 c p values and averaging the remaining 3 values. Griem [24] also introduced a correction factor to cover the entire ulk fluid enthalpy range. This factor is a function of H.Thecorrelationof Koshizuka and Oka [25] is ased on their earlier numerical studyonforcedconvectivescflowofwaterina10mm diameter tue. Kuang et al. [26] used their dataank of SCHT to water for vertical upward flow in a tue to develop their correlation. They studied the enhanced and deteriorated heat transfer ased on the normal heat transfer coefficient (HTC) predicted y Dittus Boelter [16]. The correlation y Kuang et al. [26] was developed for normal and deteriorated heat transfer. Mokry et al. [27] usedthe SC water data collected y Kirillov et al. [28] in developing their correlation. For the development of their correlation for normal heat transfer (NHT), Mokry et al. [27] excluded some extrema in wall temperature profile from the correlation dataase including points of minima/maxima and some other points in their vicinity. Cheng et al. [29] developed a simple Nusselt numer ratio correlation ased on the Herkenrath et al. [30] dataase (4599 data points) to predict the deviation from the NHT as predicted y the Dittus Boelter [16] correlation. Unlike other correlations, this correlation was developed to have only explicit dependence on ulk fluid temperature. 50

5 Gupta et al. [31] modified the Swenson et al. [21] correlation descried at the eginning of this section, which evaluates fluid properties in Nu, Re, and average Pr at wall temperature. Gupta et al. [31] added a viscosity ratio term to account for viscosity variations etween wall and ulk flow. They proposed 2 correlations for NHT. In one correlation, Nu, Re, and Pr are evaluated at wall temperature, while in the other correlation they are evaluated at film temperature (T f = (T w + T )/2). Wang et al. [32] modified Jackson s [33] correlationasedoncnlwater data compilation. Wang and Li [9] used Yamagata et al. s [22] criterion for HTD to screen the datasets y Yamagata et al. [22], Kirillov et al. [28], and Zhu et al. [34] for HTD. This categorization resulted in 1916 data points for NHT for water flowing vertically upward in round tues and susequently these data were used for correlation assessment. Wang and Li [9] assessed 15 correlations against the screened NHT data and modified the correlation of Hu [35] for NHT. The modified correlation was evaluated; however, error analysis was performed in terms of Nu numer not HTC. Chen and Fang [10] compiled 5366 data points from 13 sources. The data were for water flowing vertically upward in a round tue. They calculated the ratio of experimental to predicted HTC y Dittus Boelter [16]; ased on the value of this ratio, Chen and Fang [10] classified each experimental data point in 1 of 3 heat transfer modes: normal, enhanced, or deteriorated heat transfer. Then, the categorized data were used for assessing each of the 20 Nusselt numer correlations. Chen and Fang [10] also developed a new correlation: they reviewed functional dependence of known correlations and proposed a general form for a SCHT correlation. The proposed form comprised 8 dimensionless groups. Using regression analysis software, the numer of dimensionless groups was further reduced, and numerical coefficients and exponents of the general form of the correlation were found and optimized ased on the experimental data using the least squares method. Chen and Fang [10] reportedthat their correlation had the est agreement with the data and was superior to Mokry et al. [27]. Chen and Fang [10] did not present parametric trends of the correlation; also the conducted error analysis (though in terms of HTC), in general, did not include a measure of correlation precision error. Similar to Kuang et al. [26], this correlation includes heat flux (q) and wall temperature dependence. Tales of allcorrelationsusedinthisstudyandtheirrangesofflow conditions are presented in Appendix A; the correlations for SCHT to water are listed in Tale A2, andtale A3 taulates flow conditions and dataase characteristics for the water correlations CO 2 data-ased correlations Krasnoscheckov and Protopopov [36] modified their previously derived correlation ased on CO 2 data. The modified correlation was recommended for the following ranges: < Re < < Pr < 65, 0.9 < μ μ w 0.02 < c p c p < 3.6, 0.09 < ρ w ρ < 1.0 < 4 and 46 < q < 2600 kw m 1 Jackson proposed different correlations for SCHT [33, 37]; the original version was ased on the Krasnoscheckov and Protopopov [36] correlation. Later, Wang et al. [32] modified Jackson s[33] correlation ased on the CNL data compilation for CO 2. Gupta et al. [38] proposed 3 correlations for NHT ased on the experimental data collected at Chalk River Laoratories y Pioro and Khartail [39] withtheco 2 loop (MR-1). In each of the 3 correlations, Nusselt, Reynolds, and Prandtl numers are evaluated at 1 of the 3 temperatures (T, T w,ort f ). Gupta et al. [38] showed that the correlation evaluated at T w had est agreement with the data. Yang [40] modified the Petukhov et al. [41] correlation ased on the CO 2 data collected at CNL y Pioro and Khartail [39] and proposed 2 correlations, one for NHT and the other for HTD. Tale A4 lists SCHT correlations for CO 2. Tale A5 lists ranges of flow conditions and correlation-dataase characteristics Rod undle correlations The first reported correlation for rod undles was that y Dyadyakin and Popov [43], ased on water data. They collected experimental data with a tight 7-rod undle. Spacing etween rods was maintained y a helical spacer. Richards [15] analyzed an experimental dataset of SCHT measurements in a 7-rod undle cooled with R-12 flowing vertically upward. Richards [15] applied leading correlations for tue and rod undle to the 7-rod undle dataase and proposed a correlation. The correlation was restricted to NHT of R-12 in a 7-rod undle flow channel. The correlation is applicale to G < 1200 kg m 2 s 1 and fluid temperatures C. Wang et al. [11] conducted an experimental study of SCHT to water flowing vertically upward through a 2 2 rod undle; the 4 rods were inserted into a square channel with rounded corners. They assessed 8 correlations and reoptimized the numerical coefficients and dependencies of Jackson s [33] correlation for est fit of the collected rod undle data. The modified exponent in the density ratio, however, is much higher than the corresponding one in the original correlation which can e sensitive at the pseudocritical point and create scatter in the correlation trend. The correlations and their dataase-characteristics are listed in Tale A6. 51

6 4. Assessment of Correlations Twenty-four correlations were applied directly, without iteration for wall temperature, to the round tue, annulus, and rod undle dataases. Thermophysical properties were estimated from the National Institute of Standards and Technology (NIST) tales [44]. The HTC was calculated from Nu of the correlations. The corresponding wall temperature was calculated ased on the estimated HTC, heat flux and ulk fluid temperature. It is worth reporting that an iteration algorithm was developed for wall temperature, which resulted in convergence issues and produced more than 1 solution. The challenge at this moment is to identify the most realistic solution and decrease the uncertainty Uncertainty assessment The percentage difference of the wall temperature and the corresponding experimental value was calculated y e = 100 T w,cor T w,exp T w,exp % (1) where T w is in C. Then, the average e avg and standard deviation σ values were calculated for all cases. Furthermore, percentage of data predicted y a correlation within an error range of ±5%ðe 5 Þ, ± 10% ðe 10 Þ, 15% ðe 15 Þ, ± 20% ðe 20 Þ,and > j ± 20%jðe >20 Þ of the experimental values was calculated and presented along with the other uncertainty numers Application of correlations to different dataases Round tue and annulus dataases As discussed earlier, present evaluation of correlations used the entire dataases. The round tue data covered the 2 fluids (water and CO 2 ); however, the annulus dataase was for water only Application of the correlations to the rod undle dataases Rod undle flow is very different from simple tue flow. The estimation of ulk fluid enthalpy and mass flux (G) for each suchannel is usually performed with a suchannel code. A different analysis method for rod undle suassemlies is ased on parameters averaged over the flow cross-section and is called cross-section average parameter method. Bulk fluid enthalpy and mass flux are reduced to rod undle cross-section average parameters, which are calculated ased on total power and mass flow rate through all suchannels without the consideration of imalance in flow properties caused y different suchannel effects such as mixing and spacers. Thus, heat transfer in a rod undle is simplified to an equivalent circular tue case rather than an individual suchannel. Wall temperature of interest is the mean temperature and HTC is the average in a cross section, ased on equivalent-hydraulic diameter. Cross-section average calculation of heat transfer enales the use of tue-ased correlations, for instance for preliminary thermalhydraulic analysis of flows in rod undles. 5. Results of Correlation Assessment In total, 8 tales of uncertainty numers are presented in Appendix B. The tales show the assessment results of application of all taulated correlations to all dataases independently, regardless of applicale fluid and (or) heat transfer mode Against round tue and annulus dataase Results for the tue dataases The results of assessment of all correlations against the water dataase for a tue, with a total numer of data points of screened data, are presented in Tale B1. The tale shows that the Chen and Fang [10] correlation has y far the lowest average and standard deviation and the highest percentage of data predicted within the specified error ands discussed in Section 4.1. This correlation also showed similar performancefortheco 2 dataase (Tale B2) with16796 data points. For the tue dataases in water and CO 2,the standard deviation for the Chen and Fang [10] correlation was less than 6% Results for the annulus dataase Tale B3 presents uncertainty numers of all correlations applied to the concentric circular annulus dataase for water 1078 data points, collected y Licht et al. [45]. Results of the assessment of correlations for this dataase show that Jackson s [33] correlation had the est agreement with the data Against rod undle dataases Error analysis of the correlations against the undle data was ased on average wall temperature, ecause most of the data (for different rod undles) were reported in terms of average T w. Also, for general temperature representation and correlation assessment ased on different su-channels and spacers, the average wall temperature was deemed more meaningful than the maximum wall temperature. The latter was reported to e affected y spacer design and measurement location. However, if studying a specific design, the correlations assessment would e more relevant to conduct ased on the maximum wall temperature Water dataases Correlations were also assessed against the rod undle dataases for water. The single phase correlation of Dittus Boelter [16], 20 SC heat transfer correlations for tue and 52

7 FIGURE 2. Comparison of experimental HTC and T w vs. T and leading correlations for water in tue. FIGURE 3. Comparison of experimental HTC and T w vs. T and leading correlations for CO 2 in tue. 53

8 FIGURE 4. Comparison of experimental HTC and T w vs. T and leading correlations for water in concentric annulus. 3correlationsforrodundlewereappliedtotheplain(no spacers in the heated length) 2 2 rod undle dataase (639 data points). The est approximation of the experimental data (Tale B4) was also achieved y Chen and Fang [10], followed y Bishop et al. [20] andgriem[24]. Similarly, the correlations were applied to the wire-wrapped rod undle dataase with 372 data points. Tale B5 shows the results of this assessment: The Chen and Fang [10] correlation had the est agreement with the dataase for wire-wrapped 2 2 rod undle followed y the Wang et al. [32] correlation, originally developed for CO CO 2 dataase The results for the CO 2 dataase (3-rod undle with spacers) with 1155 data points are presented in Tale B6. Here,the uncertainty numers are larger than the ones reported earlier for the plain and spacer-equipped rod undle in water. The est agreement with the data was otained y the Chen and Fang [10] correlation followed y the Wang et al. [32] correlation for water. FIGURE 5. Variation of σ with reduced pressure and reduced fluid temperature for the est-estimate correlations, applied to the water dataase for round tue R-12 and R-22 dataase These dataases are for the 7- and 3-rod undle suassemlies. The results for the 7-rod undle are presented in Tale B7, andtale B8 presents the results for the 3-rod undle. For these 2 dataases, Chen and Fang [10] showed the closest approximation of the experimental data Graphical comparison of leading correlations against data The comparison etween the correlations and the experiment is presented in Figures 2 9. Representative tests for each heat transfer dataase were selected for these figures. Each of the figures is composed of 1 or 2 pairs of plots: Each pair (except Figure 5) includes 1 plot of HTC variations versus ulk fluid temperature and another plot of corresponding wall temperatures versus ulk fluid temperature for the same test data. The HTC plot is positioned on top of the wall temperature plot in a vertical configuration. Where 54

9 FIGURE 6. Comparison of experimental HTC and T w vs. T and leading correlations for water in a 2 2 rod undle. applicale, was presented on the plots with a straight dash-dotted line. Histograms of standard deviation of the est-estimate correlations against reduced pressure and reduced fluid temperature were plotted for the water dataase for the tue Tue and annulus dataases Figure 2 shows the results of the application of different correlations to the water dataase for tue geometries. This figure compares heat transfer as predicted y leading correlations against 2 different experiments. One dataset was collected with the SC water experimental facility at NPIC, while the second dataset was reported y Jackson [46] for natural convection heat transfer experiments performed at the University of Manchester. The left and right plots show predictions of 4 leading correlations against the NPIC test data and the Jackson test data, respectively. The Chen and Fang [10] correlation almost followed the experimental trend. Figure 3 presents a similar comparison for the caron dioxide dataase for tue geometries. The top left plot of this figure shows some scatter in HTC as predicted y the Chen and Fang [10], Wang et al. [32], and Watts and Chou [23] correlations. The correlation scatter resemles the scatter of the experimental data y Zahlan et al. [42]. The right-hand side plots in Figure 3 show a maximum in HTC at the pseudo-critical temperature as demonstrated y the NPIC data. Right plots of Figure 3 show that the correlations approximated experimental T w and HTC in the gas-like region (T > ) closer than that in the liquid-like region where T <. Figure 4 shows similar comparisons for the concentric annulus dataase. It is worth noting that for the present compiled annulus data ylichtetal.[45],theriseoffluidtemperaturealongthe heated length was small. For this dataase, Jackson s [33] correlationshowedtheestoverall results, followed y the Wang et al. [32] correlationforco 2 andbishopetal. [20]. Figure 5 shows the variation of σ with reduced pressure and reduced ulk fluid temperature for the estestimate correlations, applied to the water dataase for a round tue. Performance of the correlations varied along the reduced pressure. Unlike the other 2 correlations presented in Figure 5, ChenandFang[10] showed the minimum changes of σ with P/P c and T /T c.inthelowestt /T c (liquid-like regions) and the correlations showed higher σ, which almost decreased with increasing the reduced ulk fluid temperature. 55

10 FIGURE 7. Comparison of experimental HTC and T w vs. T and leading correlations for CO 2 in a 3-rod undle Rod undle dataases Turulent flow and convective heat transfer in rod undle geometries differ from that in tue geometries. Nevertheless, a preliminary estimation of heat transfer in suchannels can e done with tue-ased correlations. Figures 6 9 show comparisons of HTC and T w versus T etween rod undle data and the selected leading correlations. Figure 6 shows the variation of HTC and T w vs. T for leading correlations against 2 sets of data collected at similar flow conditions for 2 2 rod undles. Figure 6 also compares the experimental heat transfer in a plain 2 2 rod undle from the data y Wang et al. [11] and the corresponding experimental heat transfer coefficient in a wire wrapped 2 2 rod undle from the data y Wang et al. [14]. Although more information is needed aout the location of the wire wrap along the heated length, one oservation can e reported here aout the wire wrap effect on SCHT in the 2 2 rod undle, which is the local increase in HTC just upstream of. The est-estimate correlations ased on the plain rod undle data are the Chen and Fang [10], the Griem [24], and the Bishop et al. [20] correlations. Another oservation is that correlations FIGURE 8. Comparison of experimental HTC and T w vs. T and leading correlations for R-12 in a 7-rod undle. approximated closer experimental heat transfer in the plain rod undle geometry than that in the wire-wrapped rod undle geometry. Similarly, for the wire-wrapped 3-rod undle geometry dataase for CO 2, Figure 7 compares HTC and wall temperature profiles of the test data y Eter et al. [12] and leading correlations. The experimental profiles of HTC and wall temperature show a typical effect of a spacer on heat transfer. Unfortunately, plain rod undle data were unavailale for comparison. Finally, Figures 8 and 9 show the heat transfer profiles of the leading correlations against the Freon data y Richards [15] forr-12ina7-rod undle and Mori et al. [47] for R-22 in a 3-rod undle, respectively. All selected leading correlations showed reasonale representation of the Freon data for oth rod undle geometries. 6. Conclusions and Final Remarks CNL has compiled a diversified dataank of heat transfer data and correlations at SC pressure. The dataank 56

11 includes measurements for different flow geometries including tue, annulus, and rod undle, and different fluids including water, CO 2, R-12, and other fluids. As a result of collaoration with NPIC, the CNL dataases of SCHT for tue were expanded y adding compiled and original experimental data otained in the data exchange. FIGURE 9. Comparison of experimental HTC and T w vs. T and leading correlations for R-22 in 3-rod undle. Appendix A Tales of Correlations TABLE A1. Single phase correlations ased on water data. Performance of selected correlations was assessed against the CNL dataases. In total, 24 correlations were applied to the CNL dataases for tue, annulus, and rod undle. This application was independent of correlations limitation in terms of range of flow conditions, applicale heat transfer mode, and type of fluid for a correlation dataase. Statistical error analysis was performed and leading correlations were identified. Assessment results were presented in tales and graphs. The Chen and Fang [10]correlation showed the est approximation of the experimental wall temperature; it has a strong dependence on oth wall temperature and heat flux and its prediction followed the scatter of the data. Tue-ased correlations were applied to the data for noncircular geometry. This application was performed with the cross section average parameter concept, which uses equivalent hydraulic diameter. This application showed meaningful results. The agreement etween correlations and plain rod undle data was reasonale and etter than that for rod undle data with spacers. Author Single phase correlations Dittus Boelter [16] Nu = 0.023Re 0.8 Pr0.4 Sieder and Tate [17] Nu = 0.027Re 0.8 Pr1=3 ð μ μ w Þ 0.14 Gnielinski [18] f 8 ðre 1000ÞPr Pr Nu = 1 þ 12.7 f 1=2 Pr 2=3 1 Pr w 8 where the Filonenko [19] friction factor f = 1=ð1.82log 10 [Re ] 1.64Þ 2 and T 0.45replaces Pr 0.11for Pr T w > T w þ d 2=3 z 57

12 TABLE A2. Correlations for supercritical heat transfer to water. Author Mokry et al. [27] Nu = Re Pr Gupta et al. [31] Nu f = Re Nu w = Re Nu w,entry = Nu w 1 þ exp ρw ρ f Pr ρw f w Pr ρw w z d Correlation ρ μw μ ρ μw μ Wang and Li [9] Nu = Re Pr ρw kw ρ k Wang et al. [32] Nu = Re 0.82 Pr cp n ρ c 8 p 0.5, T < T w <, or 1.2 < T < T w >< 0.5 þ 0.2 Tw 1 T < < T w n = 0.5 þ 0.2 Tw 1 >: [ 1 5 T 1 ] < T < 1.2 and T < T w T in K Bishop et al. [20] Nu = Re 0.9 Pr 0.66 ρw 0.43 ρ 1 þ 2.4 d z Swenson et al. [21] Nu w = Re w Pr ρw w ρw ρ Yamagata et al. [22] Nu = Re 0.85 Pr 0.8 F c 8 1 E > 1 >< 0.05 cp n1 0.67, Pr F c = pc c p 0 < E < 1 >: cp n2 c p E < 0 E = T T w T n 1 = þ 1 Pr pc þ 1.49 and n 2 = þ 1 Pr pc 0.53 Watts and Chou [23] Nu 0 = 0.021Re 0.8 Pr 0.55 ρw 0.35 ρ for NHT Nu = Nu 0 f Gr Gr = Gr Re 2.7 Pr0.5 Re 2.7 Pr0.5 ð1 3000Gr f ðgr Þ = ð7000gr Griem [24] Nu = Re , Gr = [ρ ρ avg ]gd 3 ρ ν 2, for this study ρ avg = Þ0.295,10 5 Gr 10 4 Þ0.295,Gr Pr sel Φ, here >, NHT Gr 10 4 Pr sel = c p sel μ, k = k þ k w k 2 ( 0.82 H < 1540, Φ = 0.82 þ ðh 1540Þ 1540 H 1740 H in kj=kg: 1.0 H > 1740 Koshizuka and Oka [25] Nu = 0.015Re 0.85 ϕ = q p Pr ϕ þ 10 3 f c q þ 0.11 q p, H < >< f c = >: q p = 200G 1.2 H in J/kg and q in W/m 2 Kuang et al. [26] Nu = Re Pr q p H q p < H π A = q β G c p and Gr = gβ qd 4 k ν 2 kw 1 T w T T w T ρðtþdt < 10 5 k μw μ ρw ρ 0.31ðGr Þ ðπ A Þ (continued) 58

13 TABLE A2. (Continued). Author Cheng et al. [29] Correlation F = Nu Nu 0 = minðf 1,F 2 Þ,Nu 0 = 0.023Re 0.8 Pr1=3 2.4, F 1 = 0.85 þ π A F2 = þ π A ðπ A,pc 10 3 Þ 1.55 π A,pc Chen and Fang [10] Nu = 0.46 Re 0.16 Prw 0.1 νw 0.55 cp Pr ν 0.88 Gr c p Gr 0.81 TABLE A3. Flow conditions and dataase characteristics for the water correlations. Correlation P (MPa) G (kg m 2 s) q (kw m 2 ) d (mm) Dataase Dittus Boelter [16] Constant properties flow Mokry et al. [27] and Gupta et al. [31] NHT Griem [24] , 14, 20 NHT Yamagata et al. [22] , 10 Koshizuka and Oka [25] Up to 1800 H 4000 kj/kg Wang and Li [9] NHT Kuang et al. [26] Wide range Chen and Fang [10] Cheng et al. [29] 22.5, 23.5, 24.0, , 1000, 1500, 2250, , 20 Swenson et al. [21] Bishop et al. [20] , 5.1 Watts and Chou [23] , 32.2 Fully developed flow Wang et al. [32] TABLE A4. Correlations for supercritical heat transfer to CO 2. Author Krasnoscheckov and Protopopov [36] Jackson [33, 37] Nu = Re 0.82 Correlation Nu = Nu ρw 0.3 cp n,nu0 ð8þre 0 ρ c p = f Pr 12.7ð8Þ f 1=2 ðpr 2=3 1Þþ1.07 f is the Filonenko [19] friction factor descried earlier. 8 T 0.4, w 1, or T 1.2 >< n n = 1 = 0.22 þ 0.18 T w 1 T w 2.5, T in K n >: 1 þð5n 1 2Þ 1 T 1 T 1.2 Nu = 0.021Re >< n = >: Pr 0.5 ρw Pr0.4 ρw 0.4 þ 0.2 Tw 1 T in K Gupta et al. [38] Nu = 0.01Re 0.89 Nu f = Re 0.94 f 0.3 cp n ρ c p [36] 0.3 cp n ρ c p [37] 0.4, T < T w <, or 1.2 < T < T w 0.4 þ 0.2 Tw 1 T < < T w [ 1 5 T 1 ] < T < 1.2 and T < T w 0.14 Pr ρw ρw 0.52 k ρ 0.57 kw Nu w = Re 0.96 w Pr w 0.14 agreement with data. ρ 0.93 kw k 0.22 μw μ 1.13 ρw ρ 0.84 kw k 0.75 μw μ 0.22, authors showed that the previous correlation had est (continued) 59

14 TABLE A4. (Continued). Author Correlation Wang et al. [32] Nu = Re 0.79 Pr 0.66 ρw 0.38 cp n ρ c 8 p 0.66, T < T w <, or 1.2 < T < T w >< 0.66 þ 0.2 Tw T n = pc 1 T < < T w 0.66 þ 0.2 Tw >: 1 [ 1 5 T 1 ] < T < 1.2 and T < T w T in K Yang [40] Nu = Nu P T P c TABLE A5. Flow conditions and dataase characteristics for the CO 2 correlations. Correlation P (MPa) G (kg m 2 s) q (kw m 2 ) d (mm) Dataase Krasnoshchekov and Protopopov [36] 7.85, Also verified in water Jackson [33] a Based on Kranoshchekov and Protopopov correlation [36] Gupta et al. [38] CNL CO 2 dataase [39] Wang et al. [32] CNL CO 2 dataase [39] Yang [40] 7.6, 8.4, Up to CNL CO 2 dataase [39] a Modification of the [3] correlation. TABLE A6. Rod undle correlations and main characteristics of their dataases. Author Correlation Dataase Richard [15] a Nu = 9.23Re Pr1.1 w c p Wang et al. [11] Nu = 0.01 Re 0.88 Pr 0.64 ρf 1.76 cp 0.49 ρ c p Dyadyakin and Popov [43] Nu = Re 0.8 Pr 0.7 ρw 0.45 μ 0.2 ρ 0.1 ρ μ in ρ in 1 þ 2.5 d hyd z Appendix B cpw a Valid for NHT of R-12 in 7-rod undle and a G < 1200 kg m 2 s q GH μ k cp μ w k w c p and for HTD: Nu = Nu P T P c 10 4 q GH μ k cp μ w k w c p R-12, 7-rod undle with grid spacers, vertical upward flow Water, plain 2 2 rod undle, vertical upward flow Water, tight 7-element undle, helically wrapped Statistical Error Analysis This appendix taulates uncertainties of correlations for all dataases. The numers in rackets in the tale caption show numer of data points used in a particular assessment. TABLE B1. Correlation uncertainty against water dataase for tue (20 825). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] (continued) 60

15 TABLE B1. (Continued). Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Sieder and Tate [17] Gnielinski [18] Dittus Boelter [16] TABLE B2. Correlation uncertainty against CO 2 dataase for tue (16 796). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Sieder and Tate [17] Gnielinski [18] Dittus Boelter [16]

16 TABLE B3. Correlation uncertainty against water dataase for annulus (1078). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Richards [15] Wang et al. [11] Dittus Boelter [16] TABLE B4. Correlation uncertainty against 2 2 rod undle dataase for water (639). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Dyadyakin and Popov [43] Richards [15] Wang et al. [11] Dittus Boelter [16]

17 TABLE B5. Correlation uncertainty against wire-wrapped rod undle dataase for water (2 2/3-rod; 353/19 data points, respectively). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Dyadyakin and Popov [43] Richards [15] Wang et al. [11] Dittus Boelter [16] TABLE B6. Correlation uncertainty against 3-rod undle dataase for CO 2 (1155). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] (continued) 63

18 TABLE B6. (Continued). Cheng et al. [29] Dyadyakin and Popov [43] Richards [15] Wang et al. [11] Dittus Boelter [16] TABLE B7. Correlation uncertainty against 7-rod undle dataase for R-12 (129). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Dyadyakin and Popov [43] Richards [15] Wang et al. [11] Dittus Boelter [16] TABLE B8. Correlation uncertainty against 3-rod undle dataase for R-22 (192). Bishop et al. [20] Swenson et al. [21] Chen and Fang [10] Wang and Li [9] Gupta et al. [31] Gupta et al. [38] Krasnoschekov and Protopopov [36] Yamagata et al. [22] Wang et al. [32]; water (continued) 64

19 TABLE B8. (Continued). Wang et al. [32]; CO Watts and Chou [23] Yang [40]; NHT Yang [40]; DHT Griem [24] Koshizuka and Oka [25] Jackson [33] Jackson [37] Mokry et al. [27] Kuang et al. [26] Cheng et al. [29] Dyadyakin and Popov [43] Richards [15] Wang et al. [11] Dittus Boelter [16] REFERENCES [1] A.N. Churkin and V.I. Deev, 2013, Amiguity of Calculation Results of Heat Transfer to Water Using Empirical Correlations in the Region of Supercritical Pressure, Proceedings of the 6th International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-6), Shenzen, Guangdong, China, 3 7 March 2013, Paper ISSCWR [2] W.B. Hall, J.D. Jackson, and A. Watson, 1968, A ReviewofForced Convection Heat Transfer to Fluids at Supercritical Pressures, Proceedings of the Institution of Mechanical Engineers, 182, Part 3I, pp [3] J.D. Jackson and W.B. Hall, 1979a, Forced Convection Heat Transfer to Fluids at Supercritical Pressure, In: Turulent Forced Convection in Channels and Bundles, Edited y S. Kakaç and D.B. Spalding, vol. 2, Hemisphere Pulishing Corp., Washington, DC, USA, pp [4] J.D. Jackson and W.B. Hall, 1979, Influences of Buoyancy on Heat Transfer to Fluids Flowing in Vertical Tues Under Turulent Conditions, In: Turulent Forced Convection in Channels and Bundles, Edited y S. Kakaç and D.B. Spalding, vol. 2, Hemisphere Pulishing Corp., Washington, DC, USA, pp [5] X. Cheng and T. Schulenerg, 2001, Heat Transfer at Supercritical Pressures Literature Review and Application to an HPLWR, Technical Report FZKA 6609, Forschungszentrum Karlsruhe, Germany. [6] I.L.Pioro,H.F.Khartail,andR.B.Duffey,2004, Heat Transfer to Supercritical Fluids Flowing in Channels Empirical Correlations (Survey), Nuclear Engineering and Design, 230(1 3), pp doi: /j. nucengdes [7] B.S. Petukhov and A.F. Polyakov, 1988, Heat Transfer at Supercritical Pressures, In: Heat Transfer in Turulent Mixed Convection, Edited y B. Launder, Hemisphere Pulishing Corp., New York, NY, USA, Chapter 7.1, pp [8] H. Zahlan, D.C. Groeneveld, S. Tavoularis, S. Mokry, and I. Pioro, 2011, Assessment of Supercritical Heat Transfer Prediction Methods, Proceedings of the 5th International Symposium on Supercritical-Water- Cooled Reactors (ISSCWR-5), Vancouver, BC, Canada, March [9] C. Wang and H. Li, 2014, Evaluation of the Heat Transfer Correlations for Supercritical Pressure Water in Vertical Tues, Heat Transfer Engineering, 35(6 8), pp doi: / [10] W. Chen and X. Fang, 2014, A New Heat Transfer Correlation for Supercritical Water Flowing in Vertical Tues, International Journal of Heat and Mass Transfer, 78, pp doi: /j. ijheatmasstransfer [11] H. Wang, Q. Bi, L. Wang, H. Lv, and L.K.H. Leung, 2014, Experimental Investigation of Heat Transfer from a 2 2 Rod Bundle to Supercritical Pressure Water, Nuclear Engineering and Design, 275, pp doi: /j.nucengdes [12] A. Eter, D.C Groeneveld, and S. Tavoularis, 2016, An Experimental Investigation of Supercritical Heat Transfer in a Three-Rod Bundle Equipped with Wire-Wrap and Grid Spacers and Cooled y Caron Dioxide, Nuclear Engineering and Design, 303, pp doi: / j.nucengdes [13] H.Y. Gu, H.B. Li, Z.X. Hu, D. Liu, and M. Zhao, 2015, Heat Transfer to Supercritical Water in a 2 2 Rodundle, Annals of Nuclear Energy, 83, pp doi: /j.anucene [14] H. Wang, Q. Bi, and L.K.H. Leung, 2016, Heat Transfer from a 2 2 Wire-Wrapped Rod Bundle to Supercritical Pressure Water, International Journal of Heat and Mass Transfer, 97, pp doi: /j. ijheatmasstransfer [15] G. Richards, 2012, Study of Heat Transfer in a 7-Element Bundle Cooled with the Upward Flow of Supercritical Freon-12, Master Thesis, University of Ontario Institute of Technology, Oshawa, ON, Canada. [16] F.W Dittus and L.M.K. Boelter, 1930, Heat Transfer in Automoile Radiators of the Tuular Type, Pulications on Engineering, University of California, Berkeley, CA, USA, vol. 2(13), pp [17] E.N. Sieder and G.E. Tate, 1936, Heat Transfer and Pressure Drop of Liquids in Tues, Industrial & Engineering Chemistry, 28(12), pp doi: /ie50324a027. [18] V. Gnielinski, 1976, New Equations for Heat and Mass Transfer in Turulent Pipe and Channel Flow, International Chemical Engineering, 16(2), pp [19] G.K. Filonenko, 1954, Gidravlicheskoye soprotivleniye v truakh, Teploenergetika, 1(4), pp (in Russian). [20] A.A. Bishop, R.O. Sanderg, and L.S. Tong, 1965, Forced Convection Heat Transfer to Water at Near-Critical Temperatures and Supercritical Pressures, Chemical Engineering under Extreme Conditions, Proceedings of the A.I. Ch.E.-I. Chem.E, Symposium. Series No. 2, London, UK, June 1965, pp [21] H.S. Swenson, J.R. Carver, and C.R. Kakarala, 1965, Heat Transfer to Supercritical Water in Smooth-Bore Tues, Journal of Heat Transfer, Transactions of the ASME Series C, 87(4), pp doi: /