DEVELOPMENT OF A HEAT-TRANSFER CORRELATION FOR SUPERCRITICAL WATER FLOWING IN A VERTICAL BARE TUBE

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1 Proceedings of the of 14th the International Heat Transfer Conference IHTC14 August 8-13, 10, Washington, DC, USA IHTC IHTC14-2 DEVELOPMENT OF A HEAT-TRANSFER CORRELATION FOR SUPERCRITICAL WATER FLOWING IN A VERTICAL BARE TUBE Sarah Mokry, Amjad Farah, Krysten King, Sahil Gupta and Igor Pioro Faculty of Energy Systems and Nuclear Science University of Ontario Institute of Technology 00 Simcoe Street North, Oshaa, Ontario, L1H 7K4 Sarah_Mokry@hotmail.com; Amjad.Farah@yahoo.com; KrystenKing@gmail.com; Sahil.UOIT@gmail.com; Igor.Pioro@uoit.ca Pavel Kirillov State Scientific Center of the Russian Federation Institute of Physics and Poer Engineering (IPPE) named after A.I. Leipunsky, Oninsk, Russia Kirillov@ippe.ru ABSTRACT This paper presents an analysis of heat-transfer to SuperCritical Water (SCW) in are vertical tues. A large set of eperimental data, otained in Russia, as analyzed and a ne heat-transfer correlation for SCW as developed. This eperimental dataset as otained ithin conditions similar to those for proposed SuperCritical Water-cooled nuclear Reactor (SCWR) concepts. Thus, the ne correlation presented in this paper can e used for preliminary heat-transfer calculations in SCWR fuel channels. The eperimental dataset as otained for SCW floing upard in a 4-m-long vertical are tue. The data as collected at pressures of aout 24 MPa for several cominations of all and ulk-fluid temperatures that ere elo, at, or aove the pseudocritical temperature. The values ranged for mass flu from kg/m 2 s, for heat flu up to 1250 kw/m 2 and for inlet temperatures from 3 to 350 C. Previous studies have confirmed that there are three heattransfer regimes for forced convective heat transfer to ater floing inside tues at supercritical pressures: (1) Normal Heat-Transfer (NHT) regime; (2) Deteriorated Heat-Transfer (DHT) regime, characterized y loer than epected Heat Transfer Coefficients (HTCs) (i.e., higher than epected all temperatures) than in the NHT regime; and (3) Improved Heat- Transfer (IHT) regime ith higher-than-epected HTC values, and thus loer values of all temperature ithin some part of a test section compared to those of the NHT regime. Also, previous studies have shon that the HTC values calculated ith the Dittus-Boelter and Bishop et al. correlations deviate quite sustantially from those otained eperimentally. In particular, the Dittus-Boelter correlation significantly over predicts the eperimental data ithin the pseudocritical range. A ne heat-transfer correlation for forced convective heattransfer in the NHT regime to SCW in a are vertical tue is presented in this paper. It has demonstrated a relatively good fit for HTC values (±25%) and for all temperature calculations (±15%) for the analyzed dataset. This correlation can e used for supercritical ater heat echangers linked to indirect-cycle concepts and the co-generation of hydrogen, for future comparisons ith other independent datasets, ith undle data, as the reference case, for the verification of computer codes for SCWR core thermalhydraulics and for the verification of scaling parameters eteen ater and modeling fluids. 1. INTRODUCTION TO SCWR CONCEPTS Supercritical ater-cooled nuclear reactors are highpressure (~25 MPa) and high-temperature (outlet temperatures up to 625 C) reactors that ill operate aove the thermodynamic critical point of ater (22 MPa and 374 C). As part of the Generation IV International Forum (GIF), SCWR concepts are currently under development orldide. The concept of the SCWR dates ack to the late 1950s. Research for the SCWR, conducted in the United States and the former USSR, provided significant contriution to the preliminary conceptual design phase (late 1950s 1960s). Currently, to main SCWR conceptual designs are under consideration. The first design involves a reactor Pressure- 1 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

2 T1, P1 T 2, P 2 T3, P3 Vessel (PV) concept, hile the second design is a Pressure- Tue (PT) concept. Canada is participating in the development of a PT SCWR, hich is a natural evolution of the current Canadian CANDU 1 technology (see Figure 1). Sustainale Fuel input Multiple products are key to sustainale future and competitive designs Pump Generator Core H.P Turine Turin e H.P. Electric poer Hydrogen and process heat Heat for Co- Generation or IP/LP Turines S C ON DEN SER Industrial isotopes Figure 1. Pressure-Tue Supercritical Water CANDU Nuclear Reactor Concept (courtesy of Dr. R. Duffey (AECL)) [1]. Brine Drinking ater shon that PT SCWRs are feasile. A possile channel layout of 10-MW el PT SCWR is presented in Figure 2c. A further study on conceptual thermal-design options for pressure-tue SCWRs can e found in [5]. Tale 1. Major parameters of SCW CANDU and KP-SKD 2 nuclear-reactor concepts [1]. Parameters SCW CANDU KP-SKD Reactor type PT PT Reactor spectrum Thermal Thermal Thermal poer, MW Electric poer, MW Thermal efficiency, % Pressure, MPa Inlet temperature, C Outlet temperature, C Mass flo rate, kg/s Numer of fuel channels Numer of fuel elements in undle Length of undle string, m 6 Maimum cladding temperature, C One of the main ojectives for developing and utilizing SCWRs is that SCW Nuclear Poer Plants (NPPs) offer an increased thermal efficiency, approimately 45 50%, compared to that of current generation NPPs (30 35%). Additionally, they allo for a decrease in capital and operational costs. Generation IV reactor concepts [1] under development at Atomic Energy of Canada Limited (AECL) [2] and the Research and Development Institute of Poer Engineering (RDIPE) [3] have a main design ojective of achieving major reductions in unit energy cost relative to eisting Pressurized Water Reactor (PWR) designs [4]. This approach uilds on using eisting SCW eperience in operating fossil-fired thermal poer plants. A major contriution to this energy cost reduction ould result from oosting the outlet coolant temperature, therey increasing the thermal efficiency of the NPP. Tale 1 lists parameters of current PT SCWR concepts eing developed y AECL (Canada) and RDIPE (Russia). The current Canadian SCWR concept includes a fuel channel comprised only of a pressure tue insulated internally, hich ould enale the pressure tue to operate at temperatures close to that of the moderator (see Figure 2a). This fuel-channel design ould e used for SCW heating from 350 to 625 C. A re-entrant fuel-channel design (see Figure 2), alloing the pressure tue to operate at the SCW inlet temperature, might e used for nuclear steam superheat at sucritical pressures. The current heat-transfer evaluation has Coolant (a) () Ceramic Insulator Fuel Bundle Pressure Tue Liner 1 CANDU (CANada Deuterium Uranium) is a registered trademark of Atomic Energy of Canada Limited (AECL). 2 KP-SKD - Pressure-tue nuclear reactor at supercritical pressure (in Russian areviations). 2 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

3 Supercritical fluids have unique properties [7], [8]. It is ell estalished that thermophysical properties of any fluid, including ater, eperience significant changes ithin critical and pseudocritical regions. Figure 3 illustrates these variations for ater passing through the pseudocritical point at 25 MPa, the proposed operating pressure for SCWRs. The most significant changes in properties occur ithin ±25 C from the pseudocritical temperature (384.9 C). The National Standards Institute of Technology (NIST) Reference Fluid Properties (REFPROP) softare [9] as used to calculate these thermophysical properties. Crossing from high-density fluid to lo-density fluid does not involve a distinct phase change. Phenomena such as dryout (critical heat flu) are therefore not applicale. Hoever, at supercritical conditions, a DHT regime may eist [1] ~ 50 o C Water, P=25 MPa Thermal Conductivity, W/m-K Density, kg/m T pc = o C Fluid Density c p Thermal Conductivity Viscosity c p, kj/kg-k Viscosity Pa-s Temperature, o C Figure 3. Selected Properties for Supercritical Water at Pseudocritical Point. (c) Figure 2. (a) 3-D Vie of SCW CANDU Ceramic-Insulated Fuel-Channel (ased on AECL design [1,6]); () 3-D Vie of SCWR Re-entrant Fuel-Channel; and (c) Possile Channel Layout of 10-MWel PT SCWR. In support of developing SCWRs, studies are eing conducted on heat transfer at supercritical conditions. This paper presents an analysis of heat transfer to SCW floing in are vertical tues as a first step toards thermalhydraulic calculations in a fuel-channel. A large set of eperimental data, otained in Russia, as analyzed and an updated heat-transfer correlation for supercritical ater as developed. 2. SUPERCRITICAL FLUIDS Compared to eisting PWRs, SCWRs ould involve increasing the coolant pressure from MPa to aout 25 MPa, the inlet temperature to aout 350C, and the outlet temperature to 625C. The coolant ould pass through the pseudocritical region efore reaching the channel outlet [1]. 3. HEAT TRANSFER CORRELATIONS AT SUPERCRITICAL PRESSURES Currently, there is just one supercritical-ater heat-transfer correlation for fuel undles, developed y Dyadyakin and Popov [10], [1]. Nu 0.021Re 0.8 Pr in 0.2 in D hy, (Eq. 1) here is the aial location along the heated length in meters, and D hy is the hydraulic-equivalent diameter (equals four times the flo area, divided y the etted perimeter) in meters. This correlation as otained through eperimentation ith a tight-lattice 7-element helically-finned undle (see Figure 4) cooled ith ater. Five test undles ith different flo areas ere eamined. Hoever, heat-transfer correlations for undles are generally very sensitive to undle design, and the investigated design appears to e for a moile-type (i.e. sumarine or ship) reactor. Therefore, this correlation cannot e applied to other undle geometries and used for fuel undles of SCWRs. 3 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

4 (a) () Figure 4. Cross-Section (a) and 3-D Image () of the Dyadyakin and Popov Test Bundle Installed Inside Pressure Tue. To overcome this prolem, a ide-range heat-transfer correlation ased on are-tue data should e developed, as a conservative approach. This process is ased on the fact that HTC values for are tues are generally loer than those having undle geometries here heat transfer is enhanced ith appendages (endplates, earing pads, spacers, utton, etc.). A numer of empirical generalized correlations, ased on eperimentally otained datasets, have een proposed to calculate HTCs in forced convection for various fluids, including ater, at supercritical pressures. These are-tueased correlations are availale in various literature sources. Hoever, analysis and comparison of these correlations y Pioro and Duffey [1] has shon that differences in HTC values can e up to several hundred percent. 3.1 Eisting Heat Transfer Correlations The most idely used heat-transfer correlation at sucritical pressures for forced convection is the Dittus-Boelter correlation [11]. McAdams [12] proposed the use of the Dittus- Boelter correlation in the folloing form for forced-convective heat transfer in turulent flos at sucritical pressures (this statement as ased on the recent study y Winterton [13]: Nu Re Pr (Eq. 2) Later, Eq. (2) as also used at supercritical conditions. According to Schnurr et al. [14], Eq. (2) shoed good agreement ith eperimental data for SCW, floing inside circular tues, at a pressure of 31 MPa ith lo heat flues. Hoever, it as noted that Eq. (2) might produce unrealistic results ithin some flo conditions, especially ithin the critical and pseudocritical points, ecause it is very sensitive to properties variations. In general, this classical correlation as used etensively as a asis for various supercritical heattransfer correlations. An analysis performed y Pioro and Duffey [1] shoed that the to folloing correlations: 1) Bishop et al. [15] and 2) Senson et al. [16] ere otained ithin the same range of operating conditions as those for SCWRs. Bishop et al. [15] conducted eperiments in SCW floing upard inside are tues and annuli ithin the folloing range of operating parameters: pressure MPa, ulk-fluid temperature ºC, mass flu kg/m 2 s and heat flu MW/m 2. Their data for heat transfer in tues as generalized using the folloing correlation ith a fit of ±15%: D Nu Re Pr (Eq. 3) here > 0. Equation (3) uses the cross-sectional averaged Prandtl numer, for details, see [1]. The last term in the correlation accounts for entrance-region effects. The Bishop et al. correlation is often used ithout the entrance-region term (Eq. 4), ecause this term depends significantly on the particular design of the inlet of the are test section: Nu Re Pr (Eq. 4) In addition, the Dittus-Boelter correlation as used in the folloing form, for reference purposes: Nu 023 Re Pr (Eq. 5) Senson et al. [16] found that conventional correlations, hich use the ulk-fluid temperature as a asis for calculating the majority of thermophysical properties, did not ork ell. They suggested the folloing correlation in hich thermophysical properties are ased mainly on all temperature: Nu Re Pr (Eq. 6) Equation (6) as otained ithin the folloing range: pressure MPa, ulk-fluid temperature ºC, all temperature ºC and mass flu kg/m 2 s; and predicts the eperimental data ithin ±15%. Jackson [17] modified the original correlation of Krasnoshchekov et al. [18] (for details, see [1]), for forcedconvective heat transfer in ater and caron dioide at supercritical pressures, to employ the Dittus-Boelter type form for Nu o. Finally, the folloing correlation as otained: 4 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

5 0.3 c p Nu Re Pr c p Where the eponent n is defined as folloing: n 0.4 for T T T pc and for 1.2T pc T T ; T n for T T pc T ; and T pc T T n for T pc T pc T T 1. 2T and T T. pc pc n (Eq. 7) 3.2 Comparison of Heat Transfer Correlations Figure 5 shos to sample eperimental runs at supercritical pressures and provides eperimentally measured HTC values. A comparison eteen eperimental HTCs and the calculated HTCs using the Dittus-Boelter, Bishop et al., Jackson, and Senson et al. correlations are plotted. As can e seen from Figure 5, the Dittus-Boelter correlation provides a significant overestimation of the HTCs ithin the pseudocritical region, and thus, this correlation is unusale ithin a ide range of parameters. The Bishop et al. and Jackson correlations also tend to deviate sustantially from the eperimental data ithin the pseudocritical range. The Senson et al. correlation provides a etter fit for the eperimental date than the previous three correlations ithin some flo conditions, ut does not closely follo the eperimental data ithin others [19]. It should e noted that all heat-transfer correlations presented in this paper are intended only for normal heattransfer regime calculations. Neither the Dittus-Boelter nor the Bishop et al. correlations can e used for the prediction of HTCs ithin the deteriorated heat-transfer regime. An empirical correlation as proposed for heat flu calculations at hich the deteriorated heat-transfer regime appears (for details, see []): P q dht G (Eq. 8) Pcr A more thorough discussion and comparison of heattransfer correlations can e found in Pioro and Duffey [1]. Temperature, o C Temperature, o C Bulk-Fluid Enthalpy, kj/kg T in P in = 24.1 MPa G = 1495 kg/m 2 q ave = 884 kw/m 2 q dht = 1055 kw/m 2 Bishop et al. corr. H pc Senson et al. corr. Heat transfer coefficient Bulk-fluid temperature Heated length Dittus-Boelter corr. Jackson corr. T pc = 382 o C Aial Location, m (a) Bulk-Fluid Enthalpy, kj/kg Aial Location, m T out T in P in = 24.2 MPa G = 500 kg/m 2 s q ave = 335 kw/m 2 q dht = 314 kw/m 2 Bishop et al. corr. Senson et al. corr. H pc Heated length Dittus-Boelter corr. Jackson corr. Heat transfer coefficient Bulk-fluid temperature T pc = 382 o C () Figure 5. Temperature and HTC (Eperimental and Calculated Values) Profiles along Heated Length of Bare Vertical Tue: (a) G = 1500 kg/m 2 s and q = 884 kw/m 2 ; () G = 500 kg/m 2 s and q = 335 kw/m 2 [21]. 4. EXPERIMENTAL DATASET The eperimental data used in the current paper as otained at the State Scientific Center of Russian Federation Institute for Physics and Poer Engineering Supercritical-Test Facility (Oninsk, Russia). This set of data as otained ithin operating conditions close to those of SCWRs, including the hydraulic-equivalent diameter (D hy ) [19], [21]. In addition, this dataset as collected recently, thus eperimental techniques ould have een at a more advanced level than those of the correlations previously discussed. T out HTC, kw/m 2 K HTC, kw/m 2 K 5 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

6 4.1 Test Facility The Supercritical-Pressure Test Facility SKD-1 loop [22] is a high-temperature and high-pressure pumped loop. This loop as intended for supercritical ater heat-transfer testing in are tues and other flo geometries, ithin a ide range of parameters (operating pressures up to 28 MPa at outlet ater temperatures up to 500ºC and poer up to 0.6 MW). All components of the eperimental setup ere made of stainless steel and distilled and de-ionized ater as used as a coolant in the loop. Water passes from a pump through a flometer, a preheater, a test section, a miing cooler, main coolers and ack to the pump. Pressurization as achieved ith a high-pressure gas (N 2 ) (see Figure 6). The test section is installed vertically ith an upard flo. Poer as delivered to the test section y a 600 kw (AC) poer supply, and cooling as achieved just donstream of the test section using a miing cooler. While some of the heat from the test section as removed using this miing cooler, a large portion as removed using the main loop heat echangers in the discharge circuit of the pump. test section proved to e very limited and as determined to e insufficient for analysis. Therefore, only the dataset collected ith the 4-m-long test section is presented in this paper. Water as heated y means of an AC electric current passing through the tue all from the inlet to the outlet poer terminals (copper clamps). In order to minimize heat losses, the test section as rapped ith thermal insulation. A schematic of the test section is provided in Figure 7. Figure 7. SKD-1 Loop Test Section Schematic (courtesy of Professor P.L. Kirillov) [22]. Figure 6. Schematic of the SKD-1 Loop [6], [22]. 4.2 Test-Section Design The test section as a vertical stainless steel (12Cr18Ni10Ti) smooth circular tue ith upard flo (10- mm ID, 2-mm all thickness and tue internal arithmeticaveraged surface roughness R a = µm). The diameter of the test section is close to the proposed hydraulic-equivalent diameter of an SCWR fuel undle. To heated lengths ere utilized: 1) 1-m-long and 2) 4-m-long. Upon evaluation, the eperimental dataset collected through use of the 1-m-long 4.3 Eperimental Procedure The test-section as heated y the application of an alternating current through the tue. The specified operating parameters (pressure, mass flu and ater temperature at the tue inlet) ere set at the test section. The eperimental dataset as recorded y a Data Acquisition System (DAS) hen the desired flo conditions and poer level had een reached and stailized. Net, a ne poer level and/or ne set of flo conditions ere setup. The test matri covered in the eperiments is listed in Tale 2. These test matri values are close to the operating conditions of SCWRs (pressure of MPa, inlet temperature of up to 350ºC, outlet temperature of up to 625ºC, mass flu ithin kg/m 2 s and heat flu of up to kw/m 2 ). The eperimental runs ere carried out under steady-state operating conditions, at forced ater circulation, ith vertical upard flo in the test section. 6 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

7 Tale 2. Dataset Test Matri [19], [21], [22]. P T in T out T q G MPa C C C kw/m 2 kg/m 2 s < ; 500; 1000; 1500 outlet ulk-fluid temperatures (see Figure 8). This effect seems to e due to the increased measurement uncertainty at lo mass-flo rates. The heat-loss tests, conducted at the eginning of the eperimental program, ere used to determine the heat-loss characteristics of the test section. Heat loss as estimated y comparing the electrical heat input against the actual heat transfer to ater. The test results shoed that heat-loss from the test section as minor, ithin 3% of the electrical heat input. The poer used in the heat-transfer calculations ere adjusted for this heat loss. 5. EXPERIMENTAL RESULTS Selected eperimental results [23], [24] in SCW floing upard in the vertical are circular tue are summarized in Figures 8, to illustrate the key findings. In general, the folloing supercritical heat-transfer cases ere covered: Within a certain heated length: (a) 1. in in in T Tpc, T Tpc, T Tpc and (a) or () and and 2. (a) and or () and Typically, at the entrance region (i.e., L/D 30), the all temperature rises sharply (Figure 8). In general, this temperature profile is due to the thermal-oundary-layer development. At the inlet and outlet, poer clamps may have affected the neary heated-all temperature. Therefore, any data, i.e., affected ith poer-clamp effect, ere eliminated from consideration. The same applies to some data points, hich ere outliers of the general trend due to various reasons such as faulty thermocouples and points in the IHT and DHT regimes. Eperimental data for supercritical ater otained at higher mass flues (G = kg/m 2 s) (see Figure 8a) shoed good agreement eteen the calculated value of the last donstream ulk-fluid temperature, hich as calculated through incremental heat-alances, and the measured outlet ulk-fluid temperature just donstream of the outlet miing chamer. Hoever, at loer mass flu (G = 0 kg/m 2 s), there is a noticeale difference eteen the measured and calculated () Figure 8. Temperature and HTC Variations along a 4- m Circular Tue at Various Heat Flues: Nominal Flo Conditions P in = 24.0 MPa and (a) G = 1500 kg/m 2 s; () G = 0 kg/m 2 s [23]. A comparison of the HTC eperimental data (some unreliale points ere not considered, for details, see [21]) ith those calculated according to the heat-transfer correlations y Bishop et al. (Eq. (4)) and Dittus-Boelter (Eq. (5)) shos that, in general, the Bishop et al. correlation has a good agreement ith the eperimental HTCs outside the pseudocritical region. Hoever, this correlation over predicts the eperimental HTCs ithin the pseudocritical region. Figure 9 shos a comparison of all eperimental HTC values ith those calculated. 7 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

8 The Dittus-Boelter correlation can also predict the eperimental HTCs outside the pseudocritical region, ut deviates significantly from the eperimental data ithin the pseudocritical region. It should e noted that usually oth these correlations cannot e used for prediction of HTCs ithin the deteriorated heat-transfer regime. All these oservations are similar to those reported and revieed in the literature y Pioro and Duffey [1]. HTC cal, kw/m 2 K HTC ep, kw/m 2 K +25% -25% G = 1500 kg/m 2 s G = 1000 kg/m 2 s G = 500 kg/m 2 s G = 0 kg/m 2 s Figure 9. Comparison of Eperimental Heat Transfer Coefficient Values ith Those Calculated Through Bishop et al. Correlation [15], [23]. Later, Kirillov [22] proposed a ne constant to e used in the Bishop et al. Correlation* (Eq. 9): Nu Pr Re (Eq. 9) A comparison of the HTC eperimental data ith those calculated according to the modified Bishop et al. correlation* (Eq. (4)) and Dittus-Boelter correlation (Eq. (5)) shos that, in general, the Bishop et al. correlation* has a good agreement ith the eperimental HTCs outside the pseudocritical region. Hoever, this correlation as also found to slightly under predict the eperimental HTCs ithin the pseudocritical region. Therefore, the modified Bishop et al. correlation* (i.e. ith Kirillov s coefficient) can e used for a preliminary calculations of HTCs at supercritical pressures ithin the range of operating conditions of supercritical ater nuclear reactors. Results for this correlation are shon in Figure 10 [25]. Hoever this correlation is still insufficient for the design-development calculations that are necessary for SCWRs. Therefore it is necessary for a ne correlation to e developed. Temperature, o C Temperature, o C Bulk Fluid Enthalpy, kj/kg T in P in =24.0 MPa, G=1494 kg/m 2 s, q ave =582 kw/m 2 Dittus-Boelter corr. Heat transfer coefficient Inside all temperature Bulk fluid temperature Heated length H pc = 2139 kj/kg Improved HT Bishop et al. corr.* T pc = 381 o C Aial Location, m (a) Bulk Fluid Enthalpy, kj/kg T in P in =24.0 MPa, G=1494 kg/m 2 s, q ave =874 kw/m 2 Heat transfer coefficient Bishop et al. corr.* DIttus-Boelter corr. Inside all temperature Heated length Aial Location, m H pc Improved HT T pc = 381 o C Bulk fluid temperature T out T out () Figure 10. Temperature and Heat Transfer Coefficient Variations Along a 4-m Circular Tue at Various Heat Flues: Nominal Flo Conditions P in = 24.0 MPa and G = 1500 kg/m 2 s [25]. 6. DEVELOPING THE CORRELATION In order to otain a general empirical form of an equation governing heat transfer coefficients, a dimensional analysis as conducted. It is ell knon that HTC is not an independent variale, and that HTC values are affected y fluid velocity, inside diameter and thermophysical properties variations. A revie of trends in correlating heat transfer data at supercritical pressures determined that there are nine parameters affecting HTC, kw/m 2 K HTC, kw/m 2 K 8 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

9 heat transfer [1]. Tale 3 lists the parameters identified as essential for the analysis of heat-transfer processes for forced convection at supercritical conditions. Tale 3. Description of Various Parameters of Heat Transfer [19]. Variale Description SI units Dimensions HTC Heat Transfer coefficient W/(m 2 K) MT -3 K -1 D Diameter of the tue m L ρ Density of ater kg/m 3 ML -3 ρ µ µ k k Density of ulk fluid Dynamic viscosity of ater Dynamic viscosity of ulk fluid Thermal conductivity of ater Thermal conductivity of ulk-fluid kg/m 3 ML -3 Pa s ML -1 T -1 Pa s ML -1 T -1 W/(m K) MLT -3 K -1 W/(m K) MLT -3 K -1 c p Specific heat J/(kg K) L 2 T -2 K -1 V Characteristic velocity m/s LT -1 The Buckingham П-Theorem [26], using dimensionless pi terms, as chosen for this analysis. This theorem is ased on dimensional homogeneity, in hich dimensionless pi terms can e formed from the correlation variales. Thus, the folloing epression as produced for HTCs as a function of the identified heat-transfer parameters: HTC = f (D, ρ, ρ, µ, µ, k,, k, c p, V) (Eq. 10) Each of the identified parameters as roken don into the four primary dimensions of mass (M), length (L), time (T), and temperature (K) (see Tale 3). Through consideration of these primary dimensions, si unique dimensionless П terms ere determined. These terms are listed in Tale 4. Tale 4. Π Terms of the Empirical Correlation [19]. Π Terms Dimensionless Group Name HTC D Nusselt numer Π 1 Π 2 Π 3 Π 4 Π 5 Π 6 k V D c p k k k Reynolds numer Prandtl numer Density ratio Viscosity ratio Thermal conductivity ratio The resulting relationship ased on this analysis is as follos: Π 1 = f (Π 2, Π 3, Π 4, Π 5, Π 6 ) or, (Eq. 11) Nu C Re Pr n1 n2 n3 n4 k k (Eq. 12) Equation (12) provided a starting point for the development of a correlation, here HTC can e calculated from the folloing equation: k HTC Nu D hy (Eq. 13) here D hy and k denote hydraulic diameter and thermal conductivity of ater, respectively. The various coefficients for the resulting relationship needed to e determined for the final correlation. As a result of the eperimental-data analysis, the folloing preliminary correlation for heat transfer to supercritical ater as otained: Nu Re Pr (Eq. 14) To finalize the development of the correlation, the complete set of primary data and Eq. (14) ere fed into the SigmaPlot Dynamic Fit Wizard to perform final adjustments. The final correlation is as follos: Nu Re Pr (Eq. 15) The test matri shon in Tale 5 provides the range of applicaility for the ne Mokry et al. correlation. This matri is the result of comparison ith Kirillov s [22] eperimental data, in addition to a comparison ith other datasets for supercritical ater n5 9 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

10 uncertainty of aout ±25% for HTC values and aout ±15% for calculated all temperature. 7. VERIFYING THE CORRELATION In order to verify the correlation and the data fit, samples of eperimental runs from the dataset, ith the final correlation, are shon in Figure 12. The graphs shon are for a pressure of ~24 MPa and vary in mass flu from kg/m 2 s. 8. CONCLUSION G= 500 kg/m 2 s G=1000 kg/m 2 s G=1500 kg/m 2 s (a) +15% -15% Supercritical ater heat-transfer data for a vertical are circular tue ere otained ithin the proposed SCWR operating conditions: pressure of ~24 MPa, mass flues from 0 to 1500 kg/m 2 s, heat flues up to 1250 kw/m 2 and inlet temperatures from 3 to 350ºC. Supercritical heat transfer as investigated for several cominations of all and ulkfluid temperatures, i.e., internal all temperatures and ulkfluid temperatures elo, at, or aove the pseudocritical temperature. The otained correlation for forced convective heat transfer to supercritical ater in a are vertical tue shoed a good fit (±25%) for the analyzed dataset. In addition, the calculated all temperature resulted in a slightly more accurate fit for the analyzed dataset (±15%). T calc T ep () Figure 11. Comparison of Data Fit ith Eperimental Data: (a) for Heat Transfer Coefficient and () for T [19]. Tale 5: Test Matri for Mokry et al. Correlation. Pressure, MPa Heat Flu, kw/m 2 Mass Flu, kg/m 2 s Diameter, mm Even though the final eponents slightly deviate from the preliminary correlation, oth correlations fit the data in nearly the same manner. Figure 11 provides scatter plots of the eperimentally otained HTC values versus the calculated HTC values for each of the aove mentioned correlations. The final correlation (Eq. (15), Mokry et al. correlation) has an Thus, this ne correlation can e used: (1) for preliminary calculations of supercritical-ater-cooled fuel undles, as a conservative approach in relation to SCWRs; (2) for calculations of supercritical ater heat-transfer in heat echangers in SCWR indirect cycle concepts; (3) for calculations of heat-transfer in heat echangers for the cogeneration of hydrogen at supercritical ater NPPs; (4) for calculations of supercritical ater heat-transfer in heat echangers for other Generation IV reactor concepts ith an indirect cycle; (5) for future comparison ith other independent datasets; (6) for comparison ith undle data, as the reference case; (7) for the verification of computer codes for SCWR core thermalhydraulics; and (8) for verification of scaling parameters eteen ater and modeling fluids such as caron dioide, refrigerant R134a, and others. ACKNOWLEDGEMENTS Financial supports from the NSERC Discovery Grant, NSERC/NRCan/AECL Generation IV Energy Technologies Program (NNAPJ) and AECL are gratefully acknoledged. 10 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

11 (a) () (c) (d) Figure 12. Temperature and Heat Transfer Coefficient Variations at Various Heat Flues along a 4-m Circular Tue: Nominal Operating Conditions P in = 24.0 MPa, (a)g = 500 kg/m 2 s; (), (c)g = 1000 kg/m 2 s; (d)g = 1500 kg/m 2 s [19]. NOMENCLATURE c p specific heat at constant pressure (J/kg K) H c p average specific heat, J/kg K, H T T D f G H h k inner diameter, m function mass flu, kg/m 2 s enthalpy, J/kg heat transfer coefficient, W/m 2 K thermal conductivity, W/m K L heated length, m P pressure, MPa Q heat transfer rate, W q heat flu, W/m 2 R a surface roughness, µm T temperature, o C V velocity, m/s Greek letters dynamic viscosity, Pa s density, kg/m 3 11 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

12 Dimensionless numers h D Nu Nusselt numer k c Pr Prandtl numer p k Pr averaged Prandtl numer c p k Re G D Reynolds numer Suscripts ave average ulk calc calculated cr critical dht deteriorated heat transfer ep eperimental hy hydraulic in inlet conditions out outlet conditions pc pseudocritical all aial location, m Areviations AECL Atomic Energy of Canada Limited CANDU CANada Deuterium Uranium (reactor) DAS Data Acquisition System DHT Deteriorated Heat-Transfer (regime) GIF Generation IV International Forum HTC Heat Transfer Coefficient ID Internal Diameter IHT Improved Heat-Transfer (regime) KP-SKD Pressure-tue nuclear reactor at supercritical pressure (in Russian areviations) NHT Normal Heat-Transfer (regime) NIST National Institute of Standards and Technology NPP Nuclear Poer Plant PT Pressure Tue PV Pressure Vessel PWR Pressurized Water Reactor RDIPE Research and Development Institute of Poer Engineering (Mosco) (NIKIET in Russian areviations) REFPROP REFerence PROPerties SCW SuperCritical Water SCWR SuperCritical Water-cooled Reactor REFERENCES [1] Pioro, I.L. and Duffey, R.B., 07. Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Poer Engineering Applications, ASME Press, Ne York, NY, USA, 334 pages. [2] Khartail, H.F., Duffey, R.D., Spinks, N., and Diamond, W., 05. The pressure-tue concept of Generation IV Supercritical Water-Cooled Reactor (SCWR): Overvie and status, Proceedings of the 05 International Congress on Advances in Nuclear Poer Plants (ICAPP 05), Seoul, Korea, May 15-19, Paper #5564, 7 pages. [3] Duffey, R.B., Pioro, I.L., Gaaraev, B.A., and Kuznetsov, Yu.N., 06. SCW pressure-channel nuclear reactors: Some design features, Proc. ICONE-14, July 17-, Miami, FL, USA, Paper # [4] Duffey, R.D., Khartail, H.F., Pioro, I.L., and Hopood, J.M., 03. The future of nuclear: SCWR Generation IV high performance channels, Proc. ICONE-11, Shunjuku, Tokyo, Japan, April -23, Paper No , 8 pages. [5] Mokry, S., Naidin, M., Baig, F., Gospodinov, Ye., Zirn, U., Bakan, K., Pioro, I. and Naterer, G., 08. Conceptual Thermal- Design Options for Pressure-Tue SCWRs ith Thermochemical Co-Generation of Hydrogen, Proceedings of the 16 th International Conference on Nuclear Engineering (ICONE-16), Orlando, FL, USA, May 11 15, Paper #48313, 13 pages. [6] Pioro, I.L, Kirillov, P.L., Mokry, S.J. and Gospodinov, Y.K., 10. Supercritical Water Heat Transfer in a Vertical Bare Tue: Normal, Improved and Deteriorated Regimes, to e pulished in Nuclear Technology, 31 pages. [7] Pioro, I.L., Khartail, H.F. and Duffey, R.B., 04. Heat Transfer to Supercritical Fluids Floing in Channels Empirical Correlations (Survey), Nuclear Engineering and Design, 230(1 3), pp [8] Pioro, I.L. and Duffey, R.B., 03. Literature Survey of the Heat Transfer and Hydraulic Resistance of Water, Caron Dioide, Helium and Other Fluids at Supercritical and Near- Critical Pressures, Report AECL-12137/FFC-FCT-409, CRL AECL, April, ISSN , 182 pages. [9] National Institute of Standards and Technology, 07. NIST Reference Fluid Thermodynamic and Transport Properties- REFPROP. NIST Standard Reference Dataase 23, Ver Boulder, CO, U.S.: Department of Commerce. [10] Dyadyakin, B.V. and Popov, A.S., Heat transfer and thermal resistance of tight seven-rod undle, cooled ith ater flo at supercritical pressures, (In Russian), Transactions of VTI (Труды ВТИ), No. 11, pp [11] Dittus, F.W. and Boelter, L.M.K., Heat Transfer in Automoile Radiators of the Tuular Type, University of California, Berkeley, Pulications on Engineering, Vol. 2(13), pp [12] McAdams, W.H., Heat Transmission, 2 nd edition, McGra-Hill, Ne York, NY, USA, 459 pages. [13] Winterton, R.H.S., Where did the Dittus and Boelter equation come from? International Journal of Heat and Mass Transfer, 41 (4 5), pp [14] Schnurr, N.M., Sastry, V.S. and Shapiro, A.B., A Numerical Analysis of Heat Transfer to Fluids near the Thermodynamic Critical Point Including the Thermal Entrance 12 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use:

13 Region, Journal of Heat Transfer, Transactions of ASME, 98 (4), pp [15] Bishop, A.A., Sanderg, R.O. and Tong, L.S., Forced Convection Heat Transfer to Water at Near-Critical Temperatures and Super-Critical Pressures, Report WCAP-56, Westinghouse Electric Corporation, Atomic Poer Division, Pittsurgh, PA, USA, Decemer, 85 pages. [16] Senson, H.S., Carver, J.R. and Kakarala, C.R., Heat transfer to supercritical ater in smooth-ore tues, Journal of Heat Transfer, Transactions of the ASME, Series C, 87 (4), pp [17] Jackson, J.D., 02. Consideration of the heat transfer properties of supercritical pressure ater in connection ith the cooling of advanced nuclear reactors, Proceedings of the 13 th Pacific Basin Nuclear Conference, Shenzhen City, China, Octoer 21 25, 6 pages. [18] Krasnoshchekov, E.A., Protopopov, V.S., Van, F. and Kuraeva, I.V., Eperimental investigation of heat transfer for caron dioide in the supercritical region, Proceedings of the 2 nd All-Soviet Union Conference on Heat and Mass Transfer, Minsk, Belarus, May, 1964, Pulished as Rand Report R-451-PR, Edited y C. Gazley, Jr., J.P. Hartnett and E.R.C. Ecker, Vol. 1, pp [19] Mokry, S., Farah, F., King, K., Gupta, S, Pioro, I. and Kirillov, P., 09. Development of Supercritical Water Heat- Transfer Correlation for Vertical Bare Tues, Proceedings of the Nuclear Energy for Ne Europe 09 International Conference, Bled, Slovenia, Septemer 14-17, Paper#210, 13 pages. [] Gaaraev, B.A., Kuznetsov, Yu.N., Pioro, I.L. and Duffey, R.B., 07. Eperimental Study on Heat Transfer to Supercritical Water Floing in 6-m Long Vertical Tues, Proceedings of the 15 th International Conference on Nuclear Engineering (ICONE-15), April 22-26, Nagoya, Japan, Paper #10692, 8 pages. [21] Mokry, S., Gospodinov, Ye., Pioro, I. and Kirillov, P., 09a. Supercritical Water Heat-Transfer Correlation for Vertical Bare Tues, Proceedings of the 17 th International Conference on Nuclear Engineering (ICONE-17), Brussels, Belgium, July 12-16, Paper#76010, 8 pages. [22] Kirillov, P., Pometko, R., Smirnov, A., Graezhnaia, V., Pioro, I., Duffey, R., and Khartail, H., 05. Eperimental study on heat transfer to supercritical ater floing in 1- and 4-m-long vertical tues, Proceedings of GLOBAL 05 International Conference, Nuclear Energy Systems for Future Generation and Gloal Sustainaility (GLOBAL 05), Tsukua, Japan, Oct. 9-13, Paper No. 518, 8 pages. [23] Mokry, S., Pioro, I., Kirillov, P. and Gospodinov, Ye., 10. Supercritical-Water Heat-Transfer in a Vertical Bare Tue, to e pulished in Nuclear Engineering and Design, 9 pages. [24] Gospodinov, Ye., Mokry, S., Pioro, I. and Kirillov, P.L., 08. Supercritical Water Heat Transfer in a Vertical Bare Tue, Proceedings of the 16 th International Conference on Nuclear Engineering (ICONE-16), Orlando, FL, USA, May 11 15, Paper #48546, 11 pages. [25] Pioro, I.L, Kirillov, P.L., Mokry, S.J. and Gospodinov, Y.K., 08a. Supercritical Water Heat Transfer in a Vertical Bare Tue: Normal, Improved and Deteriorated Regimes, Proceedings of the 08 International Congress on Advances in Nuclear Poer Plants (ICAPP 08), Anaheim, CA, USA, June 8 12, Paper #8333, 10 pages. [26] Munson, Bruce R., Young, Donald F., and Okiishi, Theodore H., 05. Fundamentals of Fluid Mechanics. 5 th ed. Ne York: Wiley, 816 pages. 13 Copyright 10 y ASME Donloaded From: on 09/19/16 Terms of Use: