AN ASSESSMENT OF ROUND TUBE CORRELATIONS FOR CONVECTIVE HEAT TRANSFER AT SUPERCRITICAL PRESSURE

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1 FULL ARTICLE The ojective of this study is to evaluate round-tue dataased correlations depending on their applicaility conditions including heat transfer mode and fluid. The present assessment of correlations was performed against the round-tue dataases for vertical upward flow of water and CO 2 from the Canadian Nuclear Laoratories multifluid, multigeometry dataank of supercritical heat transfer. To categorize the data according to a representative heat mode, various criteria for onset of heat transfer deterioration were proposed. However, there is no consensus in the literature on a single approach. Two popular, semi-empirical criteria were chosen for screening the data for uoyancy- and acceleration-induced heat transfer deterioration. The experimental conditions of the data were screened for specified ranges of the 2 criteria indicating heat transfer deterioration. However, in many cases, the corresponding heat transfer mode of the experimental data was not appropriately predicted. In light of this inadequacy, improving accuracy of this method was deemed necessary. Therefore, each of the 2 criteria was empirically modified twice, once for water and once again for CO 2. This paper presents these 2 original modifications for each of the fluids. Ultimately, each experimental data point was categorized y the modified criteria into 1 of 2 heat transfer modes, either normal or deteriorated. In total, 21 round-tue correlations were selected and applied to the categorized dataases of normal and deteriorated heat transfer for water and CO 2. Details of the assessment results are presented in this paper in tales of uncertainty numers for each of the correlations and dataases and in graphs, comparing est-estimate correlations with representative experimental data. AN ASSESSMENT OF ROUND TUBE CORRELATIONS FOR CONVECTIVE HEAT TRANSFER AT SUPERCRITICAL PRESSURE Hussam Zahlan* and Laurence Leung Canadian Nuclear Laoratories, Chalk River, ON K0J 1J0, Canada Article Info Keywords: SCWR, supercritical, heat transfer deterioration, correlation assessment, water, CO2. Article History: Received 24 Novemer 2016, Accepted 13 June 2017, Availale online 15 Septemer DOI: *Corresponding author: hussam.zahlan@cnl.ca Nomenclature C B uoyancy coefficient c p specific heat capacity at constant pressure (J kg 1 K 1 ) d tue inner diameter (mm, m) f friction factor G mass flux (kg m 2 s 1 ) g gravitational acceleration (m s 2 ) H enthalpy (kj kg 1 ) L heated length (m) K 1 a coefficient in the empirical equation for friction factor K 1 = k thermal conductivity (Wm 1 K 1 ) P pressure (kpa) q heat flux (kw m 2 ) T temperature ( CorK) 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 Greek letters β thermal expansion coefficient β = axial distance from the inlet of the heated section (m) 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 ) σ standard deviation (%) Suscripts avg average ulk c critical cor correlation exp experimental f film pc pseudo-critical w wall Dimensionless numers Ac modified acceleration numer ( = f ðq, Re, PrÞ) 1 ρ ρ T P 67

2 Bo modified uoyancy numer ( = f ðgr, Re, PrÞ) 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 nondimensional 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 OHTD onset of heat transfer deterioration SC supercritical SCHT supercritical heat transfer SCWR supercritical water-cooled reactor 1. Introduction Leung et al. [1] descried the conceptual design of the core of the Canadian supercritical water-cooled reactor (SCWR), which is a pressure-tue type nuclear system with the fuel cooled with water at supercritical pressures. The coolant enters the fuel channel at an approximate temperature and pressure of 325 C and 26 MPa, respectively. While flowing up through fuel elements, light-water temperature increases gradually and exceeds the critical temperature. The outlet coolant temperature and pressure are 625 C (on average) and 25 MPa, respectively. An accurate prediction of cladding temperature is an essential requirement for design and safety analysis of SCWRs. Supercritical heat transfer (SCHT) correlations are generally circumscried y conditions of their dataases. In addition, most correlations were developed for normal heat transfer (NHT). Generally, application of SCHT correlations outside their valid range poses risks and is generally not recommended. To properly apply supercritical (SC) correlations, experimental dataases should e first screened for heat transfer deterioration (HTD). The screening will separate data under conditions of HTD from the rest of the data. In fact, most HTD criteria were developed ased on water or CO 2 for a circular tue geometry; therefore, the choice was made to screen the round-tue dataases for water and CO 2. This investigation was performed in support of the Canadian program for the SCWR. The HTD phenomenon has found a particular interest in the SCWR design studies. The literature revealed many different approaches for the identification of HTD in a round tue. A common approach assumes the occurrence of HTD when the measured heat transfer coefficient (HTC) is deviated from the predicted value y a correlation that is ased on NHT data. However, studies showed that such approaches are indirect, have little physical significance, and often lead to inconsistent conclusions. Similarly, onset of heat transfer deterioration (OHTD) has een descried y different types of empirical criteria correlating heat flux (q) at OHTD to a specified mass flux (G). However, studies also showed that this type of dimensional criteria is necessarily specific to particular experiments and does not seem to e of general validity. In contrast, Jackson s[2,3] criteria provided physical insight and identified key nondimensional parameters characterizing this heat transfer phenomenon. It is noted, however, that these criteria include numerical coefficients, whose values have not yet een determined conclusively. In this study, Jackson s [2,3] heat transfer criteria for uoyancy and acceleration, respectively, were selected for the identification of HTD in the water and CO 2 dataases for tues from the Canadian Nuclear Laoratories (CNL) dataank. Recently, Zahlan et al. [4] assessed availale correlations against entire dataases from the CNL dataank. In contrast to that study, the present work separated the HTD data from the entire tue dataase, and assessed all tue correlations against normal and deteriorated heat transfer (DHT) dataases separately. The study y Zahlan et al. [4] also revealed that some of the applied CO 2 correlations approximated experimental water data closer than most of the investigated water data-ased correlations and vice versa. In addition, some correlations, originally developed for NHT, approximated well the entire dataase. To complete the correlation assessment study, it was decided to assess the water and CO 2 correlations ased on fluid type and heat transfer mode. Applicale conditions usually originate from those conditions of a correlation dataase used for its development/ validation. Therefore, in this study, the correlation assessment was performed against the water and CO 2 dataases of normal and deteriorated heat transfer. Thus, allowing for a separate comparison etween different correlations at conditions within and outside their applicale range. Also, the results of the assessment were presented for each dataase. This included normal and DHT dataases for water and CO CNL Dataank of SCHT and Assessed Correlations The CNL multifluid, multigeometry supercritical pressure heat transfer dataank consists of 10 datasets. In addition to water and CO 2, the dataank comprises measurements collected with refrigerants and helium for round tues, annuli, and rod undle suassemlies. Zahlan et al. [4] reported a description of the CNL dataank compiled prior to 2016 and showed ranges of flow conditions of the dataases Tue dataases for water and CO 2 The tue dataases for water and CO 2 include more than screened data points, of which the water data 68

3 constitute more than 50%. The dataases were sujected to screening and quality assurance tests, as discussed in Zahlan et al [4], where duplicates, outliers, and data not complying with heat alance were removed Data exclusion and rejection Inappropriate data, not falling in the interest of the present assessment, were excluded. The criteria for the selection of appropriate data included fluid type, flow orientation, flow geometry, thermal development length, and tue diameter size. To meet these criteria, the data correspond to either water or CO 2 flowing vertically upward in a round tue with a diameter greater than or equal to 2 mm. Also, the axial location of the measurement point is greater than or equal to 30 in lengthto-diameter ratio (i.e., z/d) from the start of the heated length Assessed tue data-ased correlations Zahlan et al. [4] discussed and taulated more than 20 round-tue correlations for single phase and SCHT. They also reported a compilation of availale SCHT correlations for rod undle geometries. In addition, the ranges of the flow conditions of the taulated correlations as well as the characteristics of their dataases were reported y Zahlan et al. [4]. In this paper, the assessed tue data-ased correlations are presented in tales (Appendix A) according to the applicale heat transfer mode and fluid as follows NHT correlations The Dittus Boelter [5] correlation was included in the present assessment and added to the NHT correlations. Tales A1 and A3 of Appendix A show NHT correlations for water and CO 2 flow, respectively Correlations for the comined mode of normal and deteriorated heat transfer Water-data-ased correlations for the comined mode of normal and deteriorated heat transfer are presented in Tale A2 of Appendix A DHT correlations The Yang CO 2 correlation for DHT [6] is shown in Tale A4. 3. Identification of HTD 3.1. Selected HTD criteria Studies on prediction of HTD, in terms of conditions, location, and amount of decrease in heat transfer are ongoing. As discussed in Section 1, Jackson s [2, 3] HTDcriteriawere chosen, as they provided physical insight and identified key nondimensional parameters characterizing this heat transfer phenomenon. However, these criteria include numerical coefficients, which were optimized with the experimental data A criterion for uoyancy-induced HTD Jackson [2] proposed the following criterion for HTD y uoyancy Bo = Gr Re Pr 0.8 Gr = gβ qd 4 k ν Pr ; β = 1 ρ ρ T Pr = H w H T w T Re = Gd μ μ k Pr 0.4 where the suscripts and w refer to ulk and wall, respectively, indicating the temperature, at which properties are evaluated. This criterion was developed ased on Jackson s [2] mixed convection model. The constant in the limit of the uoyancy numer in the inequality Equation (1) resulted from p setting the uoyancy coefficient C B = ffiffiffi 2 δ þ K 3=2 1 and was assigned a value of 10 5.C B is ased on δ +,theuniversalturulent uffer layer thickness 1,whichhasanapproximated magnitude of 30. K 1 = is the coefficient in the empirical equation for the friction coefficient f = K 1 Re m 1,where m 1 = The value of the uoyancy coefficient is not universal and inconclusive. The lower limit in Equation (1) represents around 2% reductions in the Nusselt numer ratio Nu Nu 0 downstream of the thermal entry length [2]. In this ratio Nu 0 is the Nusselt numer for normal variale property heat transfer. The lower limit is viewed as OHTD y uoyancy. Jackson [2] pointed out that as the uoyancy force develops, it continues causing deterioration in the heat transfer up to an upper limit ðbo Þ. The value of the upper limit indicates partial laminarization of the mixed convection flow where the corresponding reduction in Nusselt numer ratio 50%. Note that the upper limit could include the region of recovery where heat transfer starts restoration, ut its value is still elow the corresponding normal heat transfer for forced convective variale property flow. Incorporating this upper limit to Equation (1) yields Pr Bo (2) Pr In the range of this inequality, the modified uoyancy numer Bo specifies a reduction of 2% 50% of heat transfer due to uoyancy A criterion for acceleration-induced HTD Similar to the uoyancy criterion, Jackson [3] proposedthe following criterion for HTD y acceleration Ac = Q Re P (1) Pr Q = (3) β qd k Similar to C B, the limit of the acceleration numer in Equation (3) was ased on the estimated value of the 1 δ + = ρ 1 2τ 1 2 δt δ= μ, the overar indicates integrated average, δ is the turulent uffer layer thickness and the suscript δ T is the thermal layer thickness [2]. 69

4 acceleration coefficient p C A of 10 4,whichwasalsoasedon δ + = 30. C A = 18 ffiffiffi 2 δ + =3K 3=2 1 : The limit Ac = represents aout 2% reduction in the Nusselt numer ratio. This limit is also viewed as OHTD y acceleration. As discussed earlier, the numerical values in Equations (2) and (3) can e optimized. 4. Screening of the Water Dataase for HTD Equations (2) and (3) were used for screening the experimental dataase of heat transfer to water flowing vertically upward in a round tue at supercritical pressure. In this investigation, the conditions at the onset of HTD in the experimental data were defined as those for the case with the lowest heat flux (among test series performed at fixed flow conditions except heat flux), for which the wall temperature profile showed a tendency to have one or more peaks, as was shown in Zahlan et al. [7]. To generalize this definition for different fluids, this temperature rise may e scaled with the critical or pseudo-critical temperature of the fluid. As the critical pressure and temperature of water are much higher than those for model fluids of interest, it is expected that the temperature peak corresponding to the onset of HTD would e more ovious in water than in CO 2 and R 134a Application of Jackson s uoyancy criterion to the water dataase Equation (2) was applied to the experimental dataase for water [4]. However, some of the data in NHT mode were predicted in HTD. The lower limit of this criterion corresponding to the OHTD y uoyancy is shifted down. To illustrate this ehaviour, variations of T w and HTC are shown against H for the Ackerman test data [8]. Figures 1a 1 and 1a 2 show variations of T w and HTC vs: H, and of the uoyancy criterion, respectively. These figures manifest this issue in the uoyancy criterion. The test data of Ackerman [8] exhiited little changes in wall temperature and HTC. Relatively small wall temperature peaks have een encountered and associated with a small reduction in HTC and a minimum at the location of the wall-temperature peak. Experimental conditions of this test and the ehaviour of the experimental wall temperature and HTC are elieved to correspond to the onset of HTD due to uoyancy. To further investigate the limits of Equation (2), more datasets at conditions of significant uoyancy were considered and examined. Tale 1 shows 2 representative datasets of Ackerman [8] and Alferov et al. [9]. For verification of the validity of the limits of Equation (2), the 2 datasets were examined and plotted as follows: 1 dataset represented strong HTD (Figure 1 1 ), whereas the other dataset showed transitional heat transfer mode (Figure 1c 1 ). The 3 cases of Figure 1 correspond to mild HTD, strong HTD, and restoration/enhancement, respectively. Buoyancy numers for the 3 rd case were eyond the upper limit of Equation (2) Modification of Jackson s criterion for uoyancy As discussed earlier, Equation (2) was used to screen the water dataase for uoyancy-induced HTD [2]. Unfortunately, the criterion did not accurately identify the corresponding experimental heat transfer mode, whether deteriorated or not. It s worth reporting that, in data selection, care was taken to have the value of the acceleration numer for the selected data sufficiently far from the range of the acceleration criterion for HTD. Jackson s criterionforheat transfer deterioration due to uoyancy [2] was empirically modified. The experimental data representative of OHTD, significant HTD, and restoration and enhancement of mixed convection heat transfer were examined and plotted in the form of Bo 107 and Bo ðpr Pr Þ vs: H. These 3 heat transfer regions are presented in Figure 1. Figure 1a 2, representing OHTD, as evidently seen on Figure 1a 1, showed a value of Bo 107 larger ðpr Pr Þ 0.4 than the numerical constant in the lower limit of Equation (2) viewed as Bo 107 = 4. The illustrated lower limit ðpr Pr Þ 0.4 on Figure 1a 2 was considered as the new lower limit for the Equation (2). Next mode is the significant HTD presented on Figure 1 1. For this case, Figure 1 2 shows that Bo 107 varied ðpr Pr Þ 0.4 over a numerical range wider than that for the previous case ut within the HTD range of Equation (2). Lastly,Figure 1c 1,2 plots present a different case where heat transfer started recovery, as manifested y the continuous improvement of HTC. Here, the uoyancy numer was slightly larger than the upper limit of Equation (2). Thus, only the lower limit of Equation (2) was modified to remove the variance etween the value in the lower limit of Equation (2) and that limit ased on experimental data. The modified constant in the lower limit is and the modified criterion ecomes Pr Bo (4) Pr 4.3. Application of Jackson s acceleration criterion to the water dataase Equation (3) was applied to the water dataase for tues [4]. However, data showing HTD due to acceleration were not accurately identified y Equation (3). The lower limit in this criterion corresponding to the OHTD y acceleration is shiftedupyroughlyanorderofmagnitude.thisdata categorization did not include some of the experimentally oserved HTD data evidently affected y acceleration (e.g., the Domin [10] data shown in Figure 2a 1 ). To study this discrepancy, more test data were examined. Tale 2 shows the flow conditions of selected tests for verifying the variation of the acceleration numer. The selected tests represent mild and significant HTD due to acceleration. As discussed earlier, data of vertical upward flow direction are of interest to the current study. Figure 2a 1,2 shows the results 70

5 FIGURE 1. Wall temperature and HTC profiles for the Ackerman [8] data(figures 1a 1,2 and 1 1,2 )andthealferov[9] data (Figure 1c 1,2 ), and the corresponding variation of the uoyancy numer. TABLE 1. Selected Datasets of Figure 1 for Studying the Limits of Equation (2). Reference Plot d mm P MPa G Kg/m 2 s q kw/m 2 Ackerman [8] a 1,a , Alferov et al. [9] c 1,c of this data categorization for the test data y Domin [10]. This test was performed with a round tue of 4 mm in inner diameter at high mass and heat fluxes. The wall temperature profileofthedomindata[10] (Figure 2a 1 )showsasignificant gloal peak with a sharp rise in T w, whereas the corresponding HTC profile shows an ovious gloal minimum point with a sharp drop at the corresponding location of the wall-temperature peak. The calculated acceleration numer 71

6 FIGURE 2. Wall temperature and HTC profiles (left) for the Domin [10] data(figure 2a 1,2 )andtheackerman[8] data (Figures 2 1,2 and 2c 1,2 ), and the corresponding variation of the acceleration numer (right). TABLE 2. Selected Datasets of Figure 2 for Studying the Limit of Equation (3). Reference Plot d mm P MPa G Kg/m 2 s q kw/m 2 Domin [10] a 1,a Ackerman [8] 1, c 1,c (Figure 2a 2 ) was oviously lower than the lower limit of the acceleration numer ðac Þ of Equation (3). On the other hand, the calculated uoyancy numer was always an order of magnitude lower than the minimum value of the lower limit of the uoyancy criterion indicating undoutedly negligile uoyancy effects on heat transfer for this test. Similarly, for the Ackerman data [8] at q = 1260 and 631 kw/m 2, the calculated uoyancy numer 72

7 was always much lower than the lower limit of the uoyancy criterion, which is also indicative of a weak uoyancy force. Ackerman s testdata[8] (Figure 2 1,2 )atq = 1260 kw/m 2 correspond to a significant HTD. Unlike these 2 plots, Figure 2c 1,2 represents a much milder case Modification of the acceleration criterion for water Based on the minimum values of the Ac in Figures 2a 2, 2 2, and 2c 2, the lower limit of Ac in Equation (3), corresponding to the onset of HTD due to acceleration, is estalished as Ac (5) Similar to uoyancy, acceleration effect develops. The plots of Ac versus H show that as Ac developed following a deterioration mode, a region of restoration was noted. However, the heat transfer can stay less efficient than the corresponding mode of NHT with variale properties. 5. Screening of the CO 2 Dataase for HTD Similar to water-data-ased correlations, CO 2 -data-ased correlations are applicale to specific heat transfer modes. Assessing these correlations requires screening of the CO 2 data for HTD, which have een applied to verify limits of Jackson s criteria [2, 3] Application of the HTD criteria to the CO 2 dataase Buoyancy criterion Jackson s criterion for uoyancy-induced HTD [2] was applied to the CO 2 dataase for vertical upward flow in round tues. However, the criterion did not successfully categorize all the CO 2 experimental data to deteriorated or normal heat transfer. Results showed that some of the data with nearly linear temperature profiles were categorized as HTD. Similar to the approach followed in Section 4 for the water dataase, the limits of Equation (2) were evaluated. The systematic experimental study y Zahlan et al. [7] madethe detection of OHTD easier than the previous case with the water dataase. Two tests with a 22 mm inner-diameter tue at low to moderate mass fluxes are presented in Figure 3, in which the suplots for each of the 2 tests are configured vertically. While maintaining similar flow conditions, HTD onset was detected with a gradual increase in heat flux. This is shown graphically in terms of wall temperature and HTC variations with ulk fluid enthalpy for the 2 test series Acceleration criterion The application of Jackson s acceleration criterion [3] to the CO 2 dataase for tues also followed the same approach applied to the water dataase. Figure 4 shows the wall temperature and HTC profiles of the experimental data y Zahlan et al. [7] and Shiralkar and Griffith [11], and the corresponding variation of the acceleration numer. In the 2 test series of Figure 4, CO 2 flowed in tues with relatively small size diameters at high mass and heat fluxes Modification of the HTD criteria for CO Modification of the uoyancy criterion Verification of the limits of the uoyancy criterion followed a similar approach descried earlier for the water dataase in Section 4. Left-hand side plots of Figure 3 show how the lower limit was verified and determined. And, the right-hand side plots of the Figure 3 show how the upper limit was estalished. The modified uoyancy criterion ased on the CO 2 dataase is Pr Bo (6) Pr Modification of the acceleration criterion Analysis was done on the 2 datasets y Zahlan et al. [7] and Shiralkar and Griffith [11], discussed earlier. Results, compared with the water dataase, showed a different value of the lower limit of the acceleration numer, which was less than the one deduced earlier for water. The modified Ac is Ac (7) PleasenotethatforCO 2, the lower limit of the modified uoyancy and acceleration numers also represents around 2% reductions in the Nu Nu 0. Tale 3 summarizes the results of the modifications and the final values of the limits of the HTD criteria for water and CO Discussion One may notice some differences etween the deduced values of the corresponding constants of the modified criteria for heat transfer to water and CO 2. The difference can e attriuted to the imperfection in scaling of the involved forces, etween the 2 fluids, y the nondimensional numers of the criteria. During the study of experimental variations of uoyancy and acceleration numers and the corresponding wall temperature and HTC profiles, it was oserved that some test data at high wall temperatures showed flat temperature profiles. Such flattened high wall temperature profiles were reported y Petukhov and Polyakov [12]. These profiles in fact occurred when convective heat transfer was simultaneously affected y significant uoyancy and acceleration. The plots in Figures 2a 2 and 2 2,showingvariationofAc versus H, revealed that acceleration effect develops. As Ac develops following a deterioration mode, a transition mode is noted. However, heat transfer in transition would stay less efficient than the corresponding one for normal variale property heat transfer. 73

8 FIGURE 3. Variation of wall temperature, HTC, and uoyancy numer with ulk fluid enthalpy in CO 2. The solid line is the fluid temperature. From the experimental data y Zahlan et al. [7]. TABLE 3. Modified Limits of Jackson s[2, 3] Criteria for HTD. Fluid Buoyancy 6. Correlation Assessment Acceleration Lower limit Upper limit Lower limit Water Pr Pr CO Pr Pr Method In total, 21 tue-data-ased correlations (11 for NHT and 10 for comined normal and DHT) were applied directly to the round tue dataases of NHT and DHT for water and CO 2 flows. Correlation restrictions in terms of applicale heat transfer mode and fluid were considered in this study. On the other hand, the correlations were applied independently of their applicale conditions, for the reasons descried earlier. Correlation assessment was performed for each dataase of NHT and DHT for water in addition to CO 2, in total, 4 dataases. Thus, each correlation was evaluated within its applicale range of conditions, as well as outside the range of the applicaility. Also, results are presented for each correlation and individually for each dataase of normal and deteriorated heat transfer. Thermophysical properties were estimated from NIST tales [13]. HTC was calculated from the Nusselt numer of the correlations. Based on the correlation HTC, 74

9 FIGURE 4. Variation of wall temperature, HTC, and acceleration numer with ulk fluid enthalpy in CO 2. The solid line is the fluid temperature. The data in Figure 4a 1 3 are from Zahlan et al. [7] and in Figure are from Shiralkar and Griffith [11]. and the known heat flux and ulk fluid temperature, the wall temperature was calculated using each correlation Uncertainty numers The percentage difference etween the correlation-predicted wall temperature and the corresponding experimental value (T w in C) was calculated y e = 100 T w,cor T w,exp T w,exp % (8) Thus, the average e avg and standard deviation σ were calculated. Furthermore, the numer 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. 7. Results of the Assessment 7.1. Against the NHT dataase for water and CO 2 All of the taulated correlations, listed in Tales A1 A4 for oth normal and DHT, were assessed against the water dataase of NHT (8372 data points). The results of the assessment are presented in Appendix B in Tale B1. Similarly, the results for the CO 2 dataase of NHT (4441 data points) are presented in Tale B3. In terms of the calculated average and standard deviation and error ands, Tales B1 and B3 75

10 FIGURE 5. Comparison etween leading correlations and experiments in terms of T w and HTC vs.t from the NHT dataases for water and CO 2 for tue. show that the correlation y Chen and Fang [14] has y far the closest approximation of the NHT data for the 2 fluids Against the DHT dataase for water and CO 2 The results of the application of the correlations to the water dataase of DHT (12453 data points)arepresentedin Tale B2. In this paper, the term leading correlation and est-estimate correlation are used interchangealy to refer to those correlations, which approximated experimental data closer than others in terms of the different uncertainty numers, descried in Section 6.2. The leading correlation was Chen and Fang [14], followed y Wang and Li [15]. And, the results of the assessment for the CO 2 dataase of DHT (12355 data points) are listed in Tale B4. This tale also shows that the Chen and Fang [14] correlation had the est uncertainty numers. It s worth noting that a valid correlation for normal/dht predicted the NHT data closer than the DHT data. In other words, the present correlations approximated the NHT data closer than the DHT data Graphical comparison of the leading correlations against tue data Graphical comparison etween the leading correlations and the corresponding experimental data is presented in Figure 5 for NHT and in Figure 6 for DHT. Two pairs of plots constitute each of the Figures 5 and 6: one for water (left) and the other for CO 2 (right). Each pair shows the variation of wall temperature (ottom) and corresponding HTC (top) with ulk fluid temperature. Representative tests were selected in each figure for water and CO 2. Figure 5 compares leading correlations and 2 experiments from the water and CO 2 dataases for tue in NHT mode. One can note that Jackson s[16] water data were in the supercritical liquid-like region, i.e., (T and T w ) <. The water data, in terms of wall temperature, were generally under predicted, and the Chen and Fang [14] correlation followed the slope of the experimental data. The vertical right pair of plots in Figure 5 compares leading correlations with the experimental data y Zahlan et al. [7]. Although CO 2 in this test experienced the condition T < < T w, the monotonic increase in T w is still evident. This temperature ehavior indicates that the encountered heat transfer mode is not deteriorated. In fact, the modified criteria were successful in predicting NHT mode for these test data. Figure 6 also shows a comparison etween est-estimate correlations and data, categorized y the modified criteria into HTD mode. The water data y Herkenrath et al. [17] were approximated fairly well y different correlations. However, at, differences appeared clearly etween the predictions of the correlations and the data. Wall temperature was significantly overpredicted y 76

11 FIGURE 6. Comparison etween leading correlations and experiment in terms of T w and HTC vs. T from the DHT dataases for water and CO 2 for tue. the Chen and Fang [14] and the rest of the correlations. The correlation trend in the proximity of was not smooth. This is most likely due to the high dependencies of some wall-temperature-dependent parameters in the correlation. This correlation showed some scatter and a sharp rise in T w and a sudden drop in HTC at this point. A comparison etween est-estimate correlations and the CO 2 data y Shiralkar and Griffith [11] is also presented in Figure 6. In the tuular test section, CO 2 encountered oth heat transfer conditions: near-pseudocritical point region, i.e., T < < T w and, further downstream from the inlet of the heated section, the ehaviour of gas-like, i.e., < (T and T w ). The heat transfer mode for these data was classified as DHT. The Chen and Fang [14] correlation showed good agreement with the heat transfer data y Shiralkar and Griffith [11]. 8. Conclusions and Final Remarks The CNL tue dataases of heat transfer to water and CO 2 at supercritical pressure were screened for uoyancy and acceleration effects on heat transfer using the physically ased criteria of Jackson [2, 3]. However, these criteria could not accurately categorize the data with the corresponding experimental heat transfer mode. This study presents 4 original modifications of the Jackson s [2, 3] criteria for heat transfer deterioration y uoyancy and acceleration applicale to water and CO 2. The modifications were ased on experimental data at different heat transfer modes, including those at onset of heat transfer deterioration and heat transfer restoration following deterioration. The details of the empirical modification of the criteria were discussed for water as well as CO 2. Differences were found etween the corresponding constants of the modified criteria for water and CO 2.Thediscrepancy might e attriuted to the imperfection of the nondimensional numers of the criteria in scaling of the involved effects etween the 2 fluids. The present correlation assessment evaluated the tue dataased correlations in agreement with applicale heat transfer mode and fluid, and independently of them. Detailed statistical error analysis was performed. Best-estimate correlations were identified for the normal and deteriorated heat transfer dataases for a circular tue geometry. The Chen and Fang [14] correlation showed the est approximation of the experimental wall temperature for the normal and deteriorated heat transfer data for water and CO 2. 77

12 However, the correlation followed, and sometimes exceeded, the scatter of the data. The flattened high wall temperature profiles, descried in the literature, did occur when convective heat transfer was simultaneously affected y significant uoyancy and acceleration. As with uoyancy, the acceleration effect develops. The plots of the acceleration numer against ulk fluid enthalpy revealed that as the acceleration numer develops following a deterioration mode a transition mode is noted. However, the heat transfer in transition would stay less efficient than the corresponding one in a normal mode of heat transfer. Appendix A Tales of Correlations TABLE A1. Correlations for normal heat transfer to water. Author Dittus Boelter [15] Nu = 0.023Re 0.8 Pr0.4 Mokry et al. [18] Nu = Re Pr ρw Gupta et al. [19] Nu f = Re Nu w = Re Nu w,entry = Nu w 1 + exp ρ f Pr ρw f w Pr ρw w z d Wang and Li [16] Nu = Re Pr Correlation ρ μw μ ρ μw Wang et al. [20] Nu = Re 0.82 Pr 0.5 ρw 0.3 cp n ρ c p 8 TABLE A2. Author μ ρw ρ kw k , T < T w < T pc, or 1.2 < T < T w >< Tw 1, T < < T w n = >: Tw 1 [ 1 5 T 1 ], < T < 1.2 and T < T w T in K Correlations for normal/deteriorated heat transfer to water. Bishop et al. [21] Nu = Re 0.9 Pr 0.66 ρw Swenson et al. [22] Nu w = Re w Pr w Correlation ρw ρ ρ d z Yamagata et al. [23] Nu = Re 0.85 Pr 0.8 F c 8 1, >< E > 1 F c = 0.67, Pr 0.05 cp n1 pc c p 0 < E < 1 >: cp n2, c p E < 0 E = T T w T n 1 = Pr pc and n 2 = Pr pc 0.53 Watts and Chou [24] 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 f ðgr Re 2.7 Pr0.5, Gr = [ρ ρ avg ]gd 3 1, for this study ρ ρ ν 2 avg = T w T T w ρðtþdt T ð1 3000Gr Þ = Þ0.295,10 5 Gr 10 4 ð7000gr Þ0.295,Gr > 10 4, NHT: Gr < 10 5 (continued) 78

13 TABLE A2. (Continued). Author Griem [25] Nu = Re Pr sel Koshizuka and Oka [26] Nu = 0.015Re 0.85 Pr Φ Φ, here Correlation Pr sel = c p sel μ, k = k + k w k 2 : 8 >< 0.82, H < 1540 Φ = >: 4 ðh 1540Þ, 1540 H 1740, H in kj/kg. 1.0, H > Φ = 0.69 q p f c q q p, H < >< q f c = p, H q p, < H >: q p = 200G 1.2 H in J/kg and q in W/m 2 Kuang et al. [27] Nu = Re Pr kw μw ρw 0.31 k μ ρ Gr π A Cheng et al. [28] π A = q β G c p and Gr = gβ qd 4 k ν 2 F = Nu Nu 0 = minðf 1, F 2 Þ,Nu 0 = 0.023Re 0.8 Pr1=3 F 1 = ðπ A 10 3 Þ , F 2 = π ðπ A,pc 10 3 Þ 1.55 A Chen and Fang [13] Nu = 0.46Re 0.16 Prw 0.1 νw 0.55 cp 0.88 Gr Pr ν c p TABLE A3. Correlations for normal heat transfer to CO 2. Author Krasnoscheckov and Protopopov [29] Nu = Nu 0 ρw ρ 0.3 cp c p n,nu0 = >< n = >: 12.7 f 8 f 8 Re Pr 1=2 Pr 2=3 1 Gr 0.81 Correlation f is the Filonenko [30] friction factor descried earlier , T w 1, or T 1.2 n 1 = , T w 1 T w 2.5 n 1 + 5n T,1 T 1.2, T in K π A,pc Jackson [31, 32] Nu = Re 0.82 Pr 0.5 ρw ρ 0.3 cp c p n [31] Nu = 0.021Re 0.8 Pr0.4 ρw 0.3 cp n ρ c p [32] 8 0.4, T < T w < T pc, or 1.2 < T < T w >< Tw n = 1, T < < T w >: Tw 1 [ 1 5 T 1 ], < T < 1.2 and T < T w T in K (continued) 79

14 TABLE A3. (Continued). Author Correlation Gupta et al. [33] Nu = 0.01Re 0.89 Nu f = Re 0.94 f 0.14 Pr ρw ρw 0.52 k ρ 0.57 kw Nu w = Re 0.96 w Pr w 0.14 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 agreement with data. Wang et al. [20] Nu = Re 0.79 Pr 0.66 ρw 0.38 cp n ρ c 8 p 0.66, T < T w < T pc, or 1.2 < T < T w >< Tw n = 1, T < < T w >: Tw 1 [ 1 5 T 1 ], < T < 1.2 and T < T w Appendix B Results of Statistical Error Analysis T in K Yang [6] Nu = Nu TABLE A4. A correlation for deteriorated heat transfer to CO 2. P P c T q GH μ μ w k k w cp c p Author Correlation Yang [6] Nu = Nu P T P c 10 4 q GH μ k cp μ w k w c p 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 NHT (8372). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Bishop et al. [21] Swenson et al. [22] Chen and Fang [13] Wang and Li [16] Gupta et al. [19] Gupta et al. [33] Krasnoschekov and Protopopov [29] Yamagata et al. [23] Wang et al. [20]; water Wang et al. [20]; CO Watts and Chou [24] Yang [14]; NHT Yang [14]; DHT Griem [25] Koshizuka and Oka [26] Jackson [31] (continued) 80

15 TABLE B1. (Continued). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Jackson [32] Mokry et al. [18] Kuang et al. [27] Cheng et al. [28] Dittus-Boelter [15] TABLE B2. Correlation uncertainty against water dataase for DHT (12453). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Bishop et al. [21] Swenson et al. [22] Chen and Fang [13] Wang and Li [16] Gupta et al. [19] Gupta et al. [33] Krasnoschekov and Protopopov [29] Yamagata et al. [23] Wang et al. [20]; water Wang et al. [20]; CO Watts and Chou [24] Yang [14]; NHT Yang [14]; DHT Griem [25] Koshizuka and Oka [26] Jackson [31] Jackson [32] Mokry et al. [18] Kuang et al. [27] Cheng et al. [28] Dittus-Boelter [15] TABLE B3. Correlation uncertainty against CO 2 dataase for NHT (4441). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Bishop et al. [21] Swenson et al. [22] Chen and Fang [13] Wang and Li [16] Gupta et al. [19] Gupta et al. [33] Krasnoschekov and Protopopov [29] Yamagata et al. [23] Wang et al. [20]; water Wang et al. [20]; CO Watts and Chou [24] (continued) 81

16 TABLE B3. (Continued). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Yang [14]; NHT Yang [14]; DHT Griem [25] Koshizuka and Oka [26] Jackson [31] Jackson [32] Mokry et al. [18] Kuang et al. [27] Cheng et al. [28] Dittus Boelter [15] TABLE B4. Correlation uncertainty against CO 2 dataase for DHT (12355). Correlation e avg,% σ, % e 5,% e 10,% e 15,% e 20,% e >20,% Bishop et al. [21] Swenson et al. [22] Chen and Fang [13] Wang and Li [16] Gupta et al. [19] Gupta et al. [33] Krasnoschekov and Protopopov [29] Yamagata et al. [23] Wang et al. [20]; water Wang et al. [20]; CO Watts and Chou [24] Yang [14]; NHT Yang [14]; DHT Griem [25] Koshizuka and Oka [26] Jackson [31] Jackson [32] Mokry et al. [18] Kuang et al. [27] Cheng et al. [28] Dittus Boelter [15] REFERENCES [1] L.K.H.Leung,M.Yetisir,W.Diamond,D.Martin,J.Pencer,B.Hyland, et al., 2011, A Next Generation Heavy Water Nuclear Reactor with Supercritical Water as Coolant, International Conference on Future of HWRs, Ottawa, ON, Canada, 2 5 Octoer 2011, Paper No [2] J.D. Jackson, 2011, A Model of Developing Mixed Convection Heat Transfer in Vertical Tues to Fluids at Supercritical Pressure, Proceedings of the 5th International Symposium on SCWR (ISSCWR-5), Vancouver, BC, Canada, March 2014, Paper P104. [3] J.D. Jackson, 2013, Fluid Flow and Convective Heat Transfer to Fluids at Supercritical Pressure, Nuclear Engineering and Design, 264, pp doi: /j.nucengdes [4] H. Zahlan, L. Leung, Y. Huang, and G. Liu, 2016, General Assessment of Convection Heat Transfer Correlations for Multiple Geometries and Fluids at Supercritical Pressure, CNL Nuclear Review. Forthcoming. Also availale as CNL report CW CONF-027, Rev.0. [5] F.W. Dittus and L.M.K. Boelter, 1930, Heat Transfer in Automoile Radiators of the Tuular Type, University of California Pulications in Engineering, vol. 2, University of California Press, Berkeley, CA, USA, pp [6] S.-K. Yang, 2013, Heat Transfer Modes in Supercritical Fluids, the 15th International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-15),Pisa,Italy,12 17 May 2013, Paper NURETH Also availale as AECL report, CW CONF-003, Rev.0. [7] H. Zahlan, D. Groeneveld, and S. Tavoularis, 2015, Measurements of Convective Heat Transfer to Vertical Upward Flows of CO 2 in Circular Tues at Near-Critical and Supercritical Pressures, Nuclear Engineering and Design, 289, pp doi: /j.nucengdes

17 [8] J.W. Ackerman, 1970, Pseudooiling Heat Transfer to Supercritical Pressure Water in Smooth and Ried Tues, Journal of Heat Transfer, 92(3), pp (ASME Paper No. 69 WA/HT-2). doi: / [9] N.S. Alferov, R.A. Ryin, and B.F. Balunov, 1969, Heat Transfer with Turulent Water Flow in a Vertical Tue under Conditions of Appreciale Influence of Free Convection, Thermal Engineering, 16 (12), pp (1969, Translated from Teploenergetika, 16(12), pp ). [10] G. Domin, 1963, Warme uergang in kritischen und üerkritischen Bereichen von Wasser in Rohren. Brennstoff-Warme-Fraft (BWK), 15(11), pp (in German). [11] B.S. Shiralkar and P. Griffith, 1969, Deterioration in Heat Transfer to Fluids at Supercritical Pressure and High Heat Fluxes, Journal of Heat Transfer, 91(1), pp doi: / [12] B.S. Petukhov and A.F. Polyakov, 1988, Heat Transfer at Supercritical Pressures, Heat Transfer in Turulent Mixed Convection, Hemisphere Pulishing Corp., New York, NY, USA, Chapter 7.1, pp [13] E.W. Lemmon, M.O. McLinden, and D.G. Friend, 2002, Thermophysical Properties of Fluid Systems, NIST Standard Reference Dataase Numer 23, Version 7.0. NIST Reference Fluid Thermodynamic and Transport Properties Dataase. [14] 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.ijheatmass transfer [15] 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: / [16] J.D. Jackson, 2009, Heat Transfer Studies at Manchester with Caron Dioxide at Supercritical and Near-critical Pressures, Report produced for AECL in connection with the dataase on SCWR Heat Transfer eing estalished y IAEA, Ref. JDJ/IAEA/CRP/Report No. 1, Octoer, [17] H. Herkenrath, P. Mörk-Mörkenstein, U. Jung, and F.J. Weckermann, 1967, Wärmeuergung an Wasser ei Erzwungener Strömung im Drückereich von 140 is 250 Bar, EURATOM report, EUR-3658 d (in German). [18] S. Mokry, Ye. Gospodinov, I. Pioro, and P. Kirillov, 2009, Supercritical Water Heat-Transfer Correlation for Vertical Bare Tues, Proceedings of the 17th International Conference on Nuclear Engineering (ICONE-17), Brussels, Belgium, July 2009, Paper # ICONE , 8 pages. [19] S. Gupta, S. Mokry, and I. Pioro, 2011, Developing a Heat-Transfer Correlation for Supercritical-Water Flowing in Vertical Tues and its Application in SCWRs, Proceedings of the 19th International Conference On Nuclear Engineering (ICONE-19), Chia, Japan, May 2011, Paper# ICONE , 11 pages. [20] S. Wang, L.Q. Yuan, and L.K.H. Leung, 2010, Assessment of Supercritical Heat-Transfer Correlations against AECL Dataase for Tues, The 2nd Canada-China Joint Workshop on Supercritical Water-Cooled Reactors (CCSC-2010), Toronto, ON, Canada, April [21] A.A. Bishop, R.O. Sanderg, and L.S. Tong, 1965, Forced Convection Heat Transfer to Water at Near-Critical Temperatures and Supercritical Pressures, Symposium on Chemical Engineering under Extreme Conditions, Proceedings of the AIChE Symposium Series No. 2, London, UK, June 1965, pp Also availale under report WCAP [22] H.S. Swenson, J.R. Carver, and C.R. Kakarala, 1965, Heat Transfer to Supercritical Water in Smooth-Bore Tues, Journal of Heat Transfer, 87(4), pp doi: / [23] K. Yamagata, K. Nishikawa, S. Hasegawa, T. Fugii, and S. Yoshida, 1972, Forced Convective Heat Transfer to Supercritical Water Flowing in Tues, International Journal of Heat and Mass Transfer, 15(12), pp doi: / (72) [24] M.J. Watts and C.T. Chou, 1982, Mixed Convection Heat Transfer to Supercritical Pressure Water, Heat Transfer 1982: Proceedings of the 7th International Heat Transfer Conference, Munich, Germany, 6 10 Septemer 1982, Vol. 3, pp [25] H. Griem, 1996, A NewProcedureforthePredictionofForced Convection Heat Transfer at Near- and Supercritical Pressure, Heat and Mass Transfer, 31(5), pp doi: /BF [26] S. Koshizuka and Y. Oka, 2000, Computational Analysis of Deterioration Phenomena and Thermal-hydraulic Design of SCR, Proceedings of the 1st International Symposium on Supercritical Water- Cooled Reactors, Design and Technology (SCR-2000), Tokyo, Japan, 6 8 Novemer 2000, Paper No [27] B. Kuang, Y.Q. Zhang, and X. Cheng, 2008, A New, Wide-Ranged Heat Transfer Correlation of Water at Supercritical Pressures in Vertical Upward Ducts, Proceedings of the 7th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-7), Seoul, South Korea, 5 9 Octoer 2008, Paper 189. [28] X. Cheng, Y.H. Yang, and S.F. Huang, 2009, A Simple Heat Transfer CorrelationforSCFluidFlowinCircularTues, Proceedings of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-13), Kanazawa City, Ishikawa Prefecture, Japan, 27 Septemer 2 Octoer 2009, Paper N13P1047. [29] E.A. Krasnoshchekov and V.S. Protopopov, 1966, Experimental Study of Heat Exchange in Caron Dioxide in the Supercritical Range at High Temperature Drops, High Temperatures, 4(3), pp (1966, Translated from Teplofizika Vysokikh Temperatur, 4(3), pp ). [30] G.K. Filonenko, 1954, Hydraulic Resistance of Pipes, Teploenergetika, 1(4), pp (in Russian). [31] J.D. Jackson, 2002, Consideration of the Heat Transfer Properties of Supercritical Pressure Water in Connection with the Cooling of Advanced Nuclear Reactors, Proceedings of the 13th Pacific Basin Nuclear Conference (PBNC 2002), Shenzhen City, China, Octoer [32] J.D. Jackson, 2009, Validation of an Extended Heat Transfer Equation for Fluids at Supercritical Pressure, Proceedings of the 4th International Symposium on Supercritical Water-Cooled Reactors (ISSCWR-4), Heidelerg, Germany, 8 11 March 2009, Paper 24. [33] S. Gupta, E. Saltanov, S.J. Mokry, I. Pioro, and L. Trevani, 2013, Developing Empirical Heat-Transfer Correlations for Supercritical CO 2 Flowing in Vertical Bare Tues, Nuclear Engineering and Design, 261, pp doi: /j.nucengdes