Experimental Thermal and Fluid Science

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1 Experimental Thermal and Fluid Science 33 (2009) Contents lists availale at ScienceDirect Experimental Thermal and Fluid Science journal homepage: Convective heat transfer to CO 2 at a supercritical pressure flowing vertically upward in tues and an annular channel Yoon-Yeong Bae *, Hwan-Yeol Kim Korea Atomic Energy Research Institute, 1045 Daedeokdaero, Yuseong, Daejeon , Repulic of Korea article info astract Article history: Received 4 July 2008 Received in revised form 2 Octoer 2008 Accepted 2 Octoer 2008 Keywords: Forced convection heat transfer Supercritical pressure Upward flow Tues Annulus Caron dioxides The Super-Critical Water-Cooled Reactor (SCWR) has een chosen y the Generation IV International Forum as one of the candidates for the next generation nuclear reactors. Heat transfer to water from a fuel assemly may deteriorate at certain supercritical pressure flow conditions and its estimation at degraded conditions as well as in normal conditions is very important to the design of a safe and reliale reactor core. Extensive experiments on a heat transfer to a vertically upward flowing CO 2 at a supercritical pressure in tues and an annular channel have een performed. The geometries of the test sections include tues of an internal diameter (ID) of 4.4 and 9.0 mm and an annular channel (8 10 mm). The heat transfer coefficient (H) and Nusselt numers were derived from the inner wall temperature converted y using the outer wall temperature measured y adhesive K-type thermocouples and a direct (tue) or indirect (annular channel) electric heating power. From the test results, a correlation, which covers oth a deteriorated and a normal heat transfer regime, was developed. The developed correlation takes different forms in each interval divided y the value of parameter Bu. The parameter Bu (referred to as Bu hereafter), a function of the Grashof numer, the Reynolds numer and the Prandtl numer, was introduced since it is known to e a controlling factor for the occurrence of a heat transfer deterioration due to a uoyancy effect. The developed correlation predicted the Hs for water and HCFC-22 fairly well. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction * Corresponding author. Tel.: ; fax: address: yyae@kaeri.re.kr (Y.-Y. Bae). 1 At a critical temperature and a critical pressure physical properties experience sustantial changes. Over the critical pressure a temperature still can e found where the physical properties changes with a lesser degree. It is called a pseudo-critical temperature. After the introduction of supercritical fossil fuel fired power plants, convective heat transfer at a supercritical pressure has een a never-ending suject of many researchers. Heat transfer at a supercritical pressure is totally different from that at a sucritical pressure due to the sustantial variations of the physical properties of fluids at around a pseudo-critical temperature. 1 The convective heat transfer correlations developed ased on the test data otained at a sucritical pressure are no longer valid at a supercritical pressure since the non-dimensional parameters ased on the ulk temperature or the averaged temperature are not sufficient to interpret the dynamic and thermal fields at a supercritical pressure. In this regime the properties at a wall temperature egin to play an important role and should e reflected in a heat transfer correlation. A change of the temperature and a resulting change of the physical properties primarily occur near a wall. When the location of the pseudo-critical temperature appears at a near-wall region, the variation of the physical properties would e sustantial around this location and the heat transfer rate must e a function of these varying properties. In this context, a simple ulk or wall temperature can not e a representative temperature for this heat transfer and a conventional heat transfer correlation ased on a ulk fluid condition is no longer valid for a heat transfer to supercritical fluids. Therefore it is necessary to develop a new heat transfer correlation reflecting a property variation near a wall in order to correctly estimate a heat transfer rate at a supercritical pressure. At a sucritical pressure, as the coolant temperature exceeds the oiling point, the occurrence of a oiling crisis causes an arupt decrease of the heat transfer rate and an increase of the fuel rod temperature eyond its limit. This is one of the major concerns for a nuclear system design. On the contrary at a supercritical pressure, a fluid does not oil ut its density changes sustantially, and it causes a decrease of the heat transfer rate, which is called a heat transfer deterioration. In spite of a great deal of efforts in experimental and theoretical studies, the precise mechanism of a heat transfer deterioration is not well understood. An attempt to measure the hydrodynamic and thermal fields of a caron dioxide flowing vertically upward has een made y Kurganov and Kaptil nyi [1]. They experimentally verified that an M-shape velocity distriution and a distortion of the shear stress are the major causes of a heat transfer deterioration. However, a quantitative analysis is still necessary to estimate the exact condition for the /$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi: /j.expthermflusci

2 330 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) Nomenclature Bu Bu ¼ Gr = Re 2:7 Pr0:5 C f Fanning friction factor C p specific heat (kj kg 1 ) C p C p ¼ R Tw T dt=ðt w T Þ¼ðh w h Þ=ðT w T Þ d, D tue diameter (m) f Darcy Weisach friction factor (=4C f ) G mass flux (kg m 2 s 1 ) Gr Grashof numer ( ), Gr ¼ q ðq qþgd3 l 2 k thermal conductivity (W m 2 ) Nu Nusselt numer p pressure (Pa) Pr Prandtl numer ( ) Pr Pr ¼ l Cp =k q heat flux (kw m 2 ) r radial coordinate (m) Re Reynolds numer ( ) R:E: mean error, Eq. (14) T temperature (K) u axial velocity (m s 1 ) v radial velocity (m s 1 ) x axial coordinate (m) Greek symols q density (kg R m 3 ) q q ¼ 1 Tw Tw T T qdt l dynamic viscosity (kg s 1 m 1 ) r standard deviation, Eq. (15) Suscripts and superscripts 0 at constant physical properties mass averaged value cr at critical condition d, D ased on diameter i at the inlet, inner m spatially averaged quantity pc at pseudo-critical temperature var p at variale physical properties w at the wall inception of a deterioration, and no more reports on this have een pulished since then. The criteria for an onset of a heat transfer deterioration are given in [2 4]. A consensus for the criterion has not een reached yet though. Heat transfer correlations have een proposed for decades y many researchers with water [2,5 7], caron dioxide [8 11], and HCFC-22 (also known as Freon-22 or R-22) [12,13]. Every researcher has proposed his/her own heat transfer correlation ased on their experimental data ut they reveal sustantial differences from each other. To the authors knowledge there is no single correlation covering oth a normal heat transfer regime and a deteriorated heat transfer regime. Watt and Chou [14] suggested a set of correlations from a test with water, and Komita et al. [12] recently modified them ased on their test data from a test with HCFC-22. They oth treated the deterioration regime separately and provided an independent correlation in addition to one for a normal regime, ut the suggested set of correlations is not continuous, and results in two values on a given condition. Furthermore the correlations y Watt and Chou were ased on a natural circulation and the main focus was given to a mixed convection. Jackson recently [15] proposed a correlation after analyzing extensive experimental data from various sources ut it does not address a deterioration regime. A versatile convective heat transfer correlation is required for an accurate estimation of a heat transfer rate, covering not only a normal regime ut also a deterioration regime, since the heat transfer rate is one of the important inputs to a numerical analysis for a nuclear reactor s safety and performance, especially in the suchannels of a fuel assemly. Considering the initiation of a SCWR development program under the Gen IV International Forum [16] the acquisition of a reliale heat transfer correlation is urgently required. In this paper an attempt will e made to develop a convective heat transfer correlation, which can e used for a deterioration regime as well as a normal regime 2. Review of existing correlations The convective heat transfer correlations at a supercritical pressure can e categorized into three groups. The first one is a Dittus Boelter type such as Nu ¼ ARe C1 Pr C2 ðq w =q Þ C3 Cp =C p C4 l w =l C5 ðk w =k Þ C6 ð1þ where constants A, C1 C6 may e constants or variales of the physical properties. Another type, which is attriuted to Petukhov [17], is ðf =8ÞRePr Nu ¼ 1 þ 900=Re þ 12:7ðf =8Þ 1=2 ðpr 2=3 1Þ The last one was first suggested y Watt and Chou [14]. It incorporated the effect of a uoyancy and a thermal acceleration y adding a factor and it takes the following form: q C9 h. i Nu ¼ ARe C7 Pr C8 w q f Gr Re 2:7 Pr 0:5 ð3þ The term in the square racket of Eq. (3) is a parameter representing a uoyancy effect and f here implies a function, not Darcy-Weisach friction factor. We will review it in detail later. There is no priority for one type or another. Each type has its own advantages and disadvantages. The selection of one type from another wholly depends on the preference of the users. In this work we chose the third type as a reference correlation with a slight modification as follows: Nu varp ¼ 0:021Re 0:82 Pr 0:5 ðq w =q Þ0:3 ð C p =C p Þ n ð4þ where n ¼ 0:4 for T ht w ht pc ; and for 1:2T pc ht ht w n ¼ 0:4 þ 0:2 ðt w =T pc Þ 1 for T ht pc ht w ; n ¼ 0:4 þ 0:2½ðT w =T pc Þ 1Šf1 5½ðT =T pc Þ 1Šg for T pc ht h1:2t pc and T ht w ðt ; T pc ; T w are in K:Þ The index n has een introduced in [10] and found to e very effective for reflecting the effect of a temperature increase in a thermal oundary layer near a wall. Watt and Chou [14] were the first to introduce two groups of correlations for a normal and a deteriorated heat transfer regime y using. a parameter introduced in Ref. [18] such as Bu ¼ Gr Re 2:7 Pr0:5. Their correlations result in two values according to the type of regime, nevertheless Bu is the same. It is a natural reasoning that if Bu is a proper parameter descriing the flow and heat transfer ehavior of a fluid, a single value should ð2þ

3 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) Coolant Pump TG PSV Outside Chiller Coolant Pump Chilled Coolant Storage Cooler PG PG PT Bypass Valve PT PG Accumulator N 2 TG Air-driven Boosting Compressor CO 2 Tank Test Section (3m) Heating Region (2.1m) Teflon plate for electrical insulation DP Gear-type CO 2 Circulation Pump Corioli-type Flowmeter Liquid-like CO 2 Electric Preheater Vapor-like CO 2 Cooling water PT Fig. 1. Supercritical heat transfer test facility SPHINX with CO 2 as a medium. e produced for one value of Bu. Considering their test was otained from a natural circulation experiment and the data may cover only a part of a flow regime, the applicaility of their correlation is doutful. In their test the minimum value of Bu was 10 6, which is way aove the convective heat transfer regime. Komita et al. [12] also followed Ref. [14] with a slight modification to correlate their data otained for HCFC-22. It is our understanding that if we can find a proper parameter, which descries the heat transfer ehavior in an agreeale manner, a more competent correlation including a function of that parameter may e developed. 3. Experiment 3.1. Test facility Since the critical condition of water is MPa, C, and a heat transfer test under such a condition requires a high heating power and cost, CO 2 has een widely used as a surrogate fluid, which has a much milder critical condition (7.38 MPa, C) than water. In our test we have chosen CO 2 as a medium to take advantage of its low critical condition and low experimental cost. Fig. 1 shows a schematic diagram of the test facility. The design pressure and temperature of the main loop are 12.0 MPa and 80 C, respectively. The test loop is initially charged with CO 2 y an air-driven reciprocating compressor. The charged CO 2 is pumped y two gear pumps installed in parallel at the ottom of the test section through an electric heater, which heats up the fluid to the preset fluid temperature at the test section inlet. The CO 2 leaving the test section enters the heat exchanger and cools down to the pre-set temperature. The heat exchanger is cooled y chilled water, and its temperature is controlled y a cooler. A gear type pump is adopted to minimize the inevitale flow fluctuation. An accumulator filled with gaseous nitrogen, which is located at the discharge of the pumps, also reduces any fluctuation in a flow. The pre-heater and the power supply unit control the inlet and outlet temperatures of the fluid, respectively. The test section is heated y a direct electric heating (tues) or indirect heating (annulus) to provide a uniform heat flux on the test section surface. The mass flow rate is regulated y adjusting the ypass valve and/or the pump speed. A Corioli type flow meter, manual flow control and isolation valves, pressure transmitters, and thermocouples are installed in the test facility. The inner diameter of the main loop is aout 20 mm. The main loop is insulated to minimize any heat loss to the atmosphere Test sections Fig. 2 shows the test sections and the locations of the measuring points. The test section at the left is a circular tue with an inside diameter of 4.4 mm and heated y a direct current power supply to impose a uniform heat flux on the tue internal surface. 41 K-type thermocouples, each 5 cm apart, are soldered onto the external surface of the tue to measure the wall temperatures. The middle one is a 9 mm ID tue test section. The details are the same as those for the 4.4 mm ID tue, except for the heated length. The right one is the test section for an annular channel. A heater rod with an outside diameter (OD) of 8 mm is centered in the 10 mm ID tue. Twelve thermocouples are TIG welded spirally onto the surface of the heater rod with an axial distance of 100 or 200 mm, and separated circumferentially at 60. The hydraulic diameter 2 of the annulus channel is the same as the 4.4 mm tue. The supercritical CO 2 flows upward, and the fluid temperatures are measured in the mixing chamers at the inlet and the outlet of the test section as well as along the tue surface. The tests were conducted with a change of the mass flux and the heat flux at a given pressure. In order to investigate the effects of the pressure on a heat transfer, the experiments were performed at three different pressures: 1.05, 1.1 and 1.2 times the critical pressure. The outlet temperature of the test section was restricted to elow 100 C for safety reasons. For each test, the heat flux was determined for the given mass flux and pressure so that the fluid temperature passes the pseudo-critical point well ahead of the exit of the test section. This constraint was imposed to guarantee the occurrence of a heat transfer deterioration in the test section. Tale 1 shows the range of the test conditions. The range of the Reynolds 2 The concept of heated perimeter is introduced for the design of single heater rod with annulus channel. With this concept the hydraulic diameter is calculated y d h = 4A/P heated.

4 332 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) Total length : 3000 Heated length : Ø4.4 T0.89 Total length : Heated length : Ø9.0 T Thermocouples 41 Thermocouples Total length : 2440 Heated length : thermocouples (100 mm apart) O Ø8 Ø10 6 thermocouples ( 200 mm apart) Fig. 2. Test sections: tue of 4.4 and 9 mm ID and an annular channel of 8 10 mm. Tale 1 Test conditions. Condition Unit Value Inlet pressure MPa 7.75, 8.12, 8.85 (1.05, 1.10, 1.15 Pcr) Inlet temperature C 5 27 Mass flux kg/m 2 s 400, 500, 750, 1000, 1200 Heat flux kw/m 2 Up to 150 numer is , which was carefully chosen to cover the operating range of the proposed SCWR concepts Data collection A PC-ased DAS collects the data (Fig. 3). The assemly of a VXIased multiplexer and multimeter, scans and digitizes the process variales from the loop, and then transfers them to the PC over an IEEE1394 us. This equipment can scan 64 channels at a rate of 300 Hz. The numer of process variales in the loop is 52 and the experiments were implemented under a steady state. The accuracies and ranges of the measuring devices are shown in Tale 2. Near a pseudo-critical temperature, the wall temperature approaches the fluid temperature to as close as a few degree Celsius. Such a small temperature difference is comparale with the standard accuracy of a K-type thermocouple, and may cause a considerale error in an estimated H. Thus, a specific in-situ caliration was performed to clarify the error ound of the test results. The thermocouples were calirated, oth at cooled and heated conditions, y using a thermometer and the maximum error was less than 2.0%. Since the H is calculated y dividing the heat flux y the temperature difference etween the wall and ulk temperatures, the total uncertainty of the measured data is a square root of [(thermocouple accuracy) 2 + (DAS accuracy) 2 ] = 2.14%. The error in the electric heating power was neglected. 4. Development of the correlations 4.1. Buoyancy parameter By reviewing our test data it was found that the data could not e predicted properly y the existing correlation types given y Eqs. (1) (3) and an additional function of a non-dimensional parameter was required. We repeated the procedure for a derivation of the uoyancy parameter given in [18] for a completeness. Under a non-isothermal condition the Reynolds-averaged equation of motion in cylindrical coordinates is as follows: qu ou ou þ qv ox or ¼ dp dx qg þ 1 oðrsþ r or where s ¼ l ou or qu0 v 0 and the variales with an over ar imply the Reynolds-averaged values. After integrating them over the tue cross section and utilizing the fact that the radial velocity v is negligile for a pipe flow and ou ox can e replaced y dum dx dp dx ¼ _m du m dx q mg þ 2s w R, Eq. (5) ecomes The pressure gradient is alanced y three terms in the right hand side of Eq. (6) which are a thermal acceleration, a uoyancy force, and a wall shear stress, respectively. By adding Eqs. (5) and (6) we otain the following equation: qu ou ou þ qv ox or ¼ _m du m dx ðq m qþg þ 1 r oðrsþ þ 2s w or R At a near-wall region Eq. (7) is approximated as follows: _m du m dx ðq m qþg þ 1 r ð5þ ð6þ ð7þ oðrsþ þ 2s w or R ¼ 0 ð8þ A useful parameter can e derived y alancing the uoyancy force and the wall shear stress gradient. It was experimentally confirmed that the profiles of a shear stress distriution and a velocity distriution are distorted sustantially in the region of a heat transfer deterioration. The velocity distriution deformed into an M-shape and the gradient of the shear stress ecomes very steep near a wall and even a negative shear stress occurs in some regions as shown in Fig. 4 [1]. As evident in Fig. 4, a change of the shear stress distriution is clearly related to a change of the velocity distriution, which is closely related to a thermal acceleration and a uoyancy force. The first and fourth terms in Eq. (8) do not vary significantly. Therefore we can conclude that the value of the uoyancy force divided y the gradient of a shear stress is an indicator of the occurrence of a heat transfer deterioration. Using an approximation near a wall

5 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) DAS Operation and Data Transfer over IEEE-1394 Serial Bus PC for DAS control Data transfer over the VXI ackplane Control Panel Measured Signal T/S wall temperature T/S diff. pressure T/S up- & down- stream pressure Preheater outlet temperature CO2 Flowrate Circ. pump speed Circ. pump discharge pressure Circ. pump discharge temperature E8491B E1411B Multimeter E1476A Multiplexer To 1476A Terminal Block Test Loop Control Circ. pump power Preheater power Main DC power trip (Emergency) Fig. 3. PC-ased data acquisition system. Tale 2 Accuracies and ranges of the measuring instruments (vendor supplied). Measuring instrument Range Accuracy K-type thermocouple o C ±0.75% or ±2.2 o C Pressure transmitter ar ±0.25% of full scale (0 16 MPa) Differential pressure transmitter mm H 2 O ±0.055% of span ( kpa) Mass flow meter kg/h ±0.15% 1 r oðrsþ ffi 1 RDs dt ¼ Ds d t or R d t d t we otain the criterion for the occurrence of heat transfer deterioration as follows: ðq q w Þgd t Ds dt ffi Oð1Þ ð10þ ð9þ where q m and q were replaced with q and q w without a loss of a generality, since our interest is focused on the near-wall region. Eq. (10) can e transformed into a comination of several nondimensional parameters on the condition of a vanishing shear stress across a turulent thermal oundary layer (su-layer and uffer layer) corresponding to y þ ¼ 30 (The readers are asked to refer to Ref. [18] for a more detailed derivation.) Ds db s w ¼ 104 Gr Re 2:7 Pr0:5 0:5 q ð11þ l w l q w where d t is effectively replaced y d B since we deal with a fluid of a moderate Prandtl numer. The value of the product of a viscosity ratio and a density ratio is an order of unity as shown in Fig. 5 and Bu ¼ Gr =ðre 2:7 Pr0:5 Þ ecomes the major parameter for heat transfer deterioration at a supercritical pressure. Bu is plotted against the enthalpy in Fig. 6 for two typical cases. Bu decreases monotonically except around the pseudo-critical temperature and the region of heat transfer deterioration. Bu varies sustantially along the tue. The upper curve is for the heat transfer deterioration Fig. 4. Axial evolution of the velocity and shear stress distriution across a channel. Please note that the appearance of an M-shape profile of the velocity and negative shear stress aove the pseudo-critical temperature [1].

6 334 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) l 0:5 Fig. 5. Variation of w q along the channel axis. l q w Fig. 7. Variation of the Nusselt numer calculated from the test data and normalized y a correlation for a variale property as shown in Eq. (4), as a function of the uoyancy parameter Bu. regime and the lower one is for the normal heat transfer regime. It is noteworthy that there is a large difference etween the two curves in addition to the variations along the tue. Kurganov and Zeigarnik [19] categorized a heat transfer regime into six groups ased on the values of a uoyancy force divided y a wall friction. However their proposed correlations are extremely complicated, and they are not user-friendly A new correlation Fig. 6. Variation of Bu along the channel axis. For three geometries, tues of 4.4 and 9.0 mm ID and an annulus channel etween an 8 mm OD heater rod and a 10 mm ID tue, 8316 test data points have een collected. The data was converted to a Nusselt numer and reduced y dividing y the values calculated y Eq. (4) which only differs y a constant from the correlation suggested in [15]. For the calculation of the physical properties, the NIST Standard Reference Dataase 23, Version 7.1 was used. The details of the experimental results for various geometries can e found in references [20 24]. The reduced Nusselt numers are plotted against Bu in Fig. 7. When Bu is small enough, that is Bu < , a heat transfer can e predicted y the Dittus Boelter equation or Eq. (4). When Bu ecomes very large, that is, Bu > , the flow recovers from a deterioration and the Nusselt numer egins to increase. In this region the heat transfer seems to e enhanced y the uoyancy effect. The test matrix of this paper does not cover the range eyond Bu = , and it may e premature to derive any correlation in this range, ut its initial stage can e seen, if not clearly, in Fig. 7. More data needs to e collected to support a prediction in this regime. In Ref. [18] an increasing trend of the Nusselt numer eyond a normal value has een oserved when the parameter representing the uoyancy effect is very strong. As Bu increases up to , the Nusselt numer decreases monotonically and smoothly. When Bu exceeds the Nusselt numer decreases aruptly to a value of 0.75 until Bu reaches When Bu lies etween and the reduced Nusselt numer remains constant at When Bu reaches the Nusselt numer experiences another sharp decrease, and at around , it egins to increase, presumaly due to the evolution of the velocity distriution from an M-shape to a normal velocity distriution in a turulent flow. As the fluid flows upward along the tue, the point of the pseudo-critical temperature may travel from the wall to the center since the fluid temperature rises continuously y heat supply from the wall. The existence of the point of the pseudo-critical temperature near the wall may cause an M-shape velocity distriution, and a steep shear stress distriution, and this is said to e one of the major reasons for a heat transfer deterioration. As the fluid continues to move upward, and the point of the pseudo-critical temperature merges with the channel center, it makes the temperature of the whole fluid supercritical, and the velocity peak of the M-shape distriution seems to start smoothing out and the gradient of the shear stress also returns

7 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) to its original state. Consequently the heat transfer rate will return, if not completely, to its normal state. This is the phenomenon we can deduce from the lowermost plate of Fig. 7. InFig. 4 it can e seen that the peak in the M-shape velocity distriution relaxes at a far down stream (x/d = 107.5) after showing a sharp peak at x/d = This argument is solely deduced from the presumption of a direct relation etween a heat transfer deterioration and a velocity distriution (or shear stress distriution). Additional experiments are necessary to support this argument, which was not possile in our test facility due the limit of the power supply. By reviewing the data plotted in Fig. 7, it was found that systematic overshoots of the H for certain values of Bu occurred. As shown in Fig. 6, Bu monotonically decreases except for a certain region, and an overshoot seems to occur downstream of the tues, where the temperature reaches a pseudo-critical value. It was assumed to come from an inaccuracy of the thermocouples or a strange heat transfer phenomena, which needs further study. This overshoot is significant for the case of a tue and an annular channel, which have the same hydraulic diameter of 4.4 mm. At this moment no exact explanation can e given ecause many factors may have influenced that phenomena, and it is not possile to single out one factor as a major cause. In this paper we will neglect the overshoot, ecause as we will see in the next section of this paper, it will not affect the development of a correlation as much as expected. The data plotted in Fig. 7 can e est represented y the following set of correlations for relevant ranges of Bu. The function Fig. 8. Comparison of the estimation against the experimental data. f ðbuþ ¼Nu exp =Nu varp which is to e multiplied y Nu varp to result in a new correlation, was otained y a trial and error procedure rather than a rigorous regression method in order to exclude inaccurate data points around the pseudo-critical point. If we define a function 5: < Bu < 7: f ðbuþ ¼ð1 þ 1: BuÞ 0:032 7: < Bu < 1: f ðbuþ ¼0:0185 Bu 0: : < Bu < 1: f ðbuþ ¼0:75 1: < Bu < 3: f ðbuþ ¼0:0119 Bu 0:36 3: < Bu < 1: f ðbuþ ¼32:4 Bu 0:40 finally the suggested correlation will take the form as Nu ¼ Nu varp f ðbuþ ð12aþ ð12þ ð12cþ ð12dþ ð12eþ ð13þ Eqs. (12a), (12), (12c), (12d), (12e) are plotted with thick green lines at the top of the data in Fig. 7. The estimated Hs were compared with the test data, and are plotted in Fig. 8. The solid lines represent ±30% error ounds. Out of the 8312 data points 7148 data points are within the ±30% error ound, which is 86.0%. Most of the errors might have resulted from an inaccuracy of the thermocouples, whose accuracy is aout 0.75% or 2.2 C whichever is greater. When the heat flux is less than 20 kw/m 2 and accordingly the temperature difference etween the wall and ulk temperatures is less than 5 C, approximately a 40% uncertainty is unavoidale. It is inevitale in an experiment using CO 2 as a medium. Fig. 9 shows the distriution of the data points within several error ounds. The mean error is 10.5% and the standard deviation of the developed correlation against the experimental data is 20.8%. The mean error and the standard deviation are defined as Fig. 9. Fractional numers of the data points within specified error ounds. " #, X R:E: ¼ ðnu cor Nu exp Þ100=Nu exp datapoints N total and ( X ), r 2 2 ¼ ðnu cor Nu exp Þ100=Nu exp datapoints N total ð14þ ð15þ The positive value for the mean error implies that the correlation overestimates the experimental data. 5. Examination of the new correlation A new set of correlations given y Eq. (13) was tested against the test data otained with water, CO 2 and HCFC-22. For a reference, several well known correlations such as Dittus Boelter (DB) [25], Bishop et al. (BI) [5], Griem (GR) [26], Jackson (JA) [15], and Komita et al. (JK) [12], were additionally plotted in each graph for the purpose of a comparison. The reference correlations are summarized in Tale 3. Henceforth, the correlations will e referred to as the areviations in the parenthesis for simplicity. The values calculated y Eq. (13) will e referred to as KC. Throughout the figures, the continuous lines with symols are the predictions y the various correlations including the proposed

8 Tale 3 Selected heat transfer correlations. Authors Correlation Conditions Medium Dittus and Boelter (DB) [25] Nu D ¼ 0:023Re 0:8 D Prn 0:7 6 Pr 6 16 n = 0.4 for heating Re D P 10; 000 n = 0.3 for cooling L=D P 10 (Valid only for sucritical pressure fluids) Bishop et al. (BI) [5] Nu ¼ 0:0069Re 0:9 Pr 0:66 ðq w =q Þ 0:43 ½1 þ 2:4=ðx=dÞŠ P = MPa Water Pr ¼ l Cp=k G = kg/m 2 s C p ¼ R Tw T dt=ðt w T Þ¼ðh w h Þ=ðT w T Þ q = kw/m 2 Griem (GR) [26] Nu ¼ hd k ¼ 0:0169Re 0:8356 Pr 0:432 / P = MPa Water k ¼ðk þ k wþ=2 G = kg/m 2 s Re ¼ _md=m q = kw/m 2 Pr ¼ C p;sel m = k 8 < 0:82 if h kJ=kg / ¼ 0:82 þ 0:18 h if h kJ=kg : h 1 if h kj=kg C p;sel ¼ 1 P i 5 3 i¼1 CpðT iþ C p;max C p;2;max Jackson (JA) [15] After review of the existing literatures and data WaterCO 2 Komita et al.(jk) [12] Nu ¼ 0:0183Re 0:82 Pr 0:5 ðq =q w Þ0:3 ðc p =C p Þ n n ¼ 0:4 for T ht w ht pc ; and for 1:2T pc ht ht w n ¼ 0:4 þ 0:2½ðT w =T pc Þ 1Š for T ht pc ht w ; n ¼ 0:4 þ 0:2½ðT w =T pc Þ 1Šf1 5½ðT =T pc Þ 1Šg for T pc ht h1:2 T pc and T ht w T ; T pc ; T w are in K: For normal heat transfer For Gr =ðre 2:7 Pr 0:5 Þh10 4 Nu h i 0:295 ¼ Gr =ðre 2:7 Nu Pr 0:5 Þ varp For Gr =Re 2:7 Pr 0:5 P 10 4 Nu h i 0:295 ¼ 7000Gr =ðre 2:7 Nu Pr 0:5 Þ varp For deteriorated heat transfer For Gr =Re 2:7 Pr 0:5 h2: Nu ¼½0: Gr =Re 2:7 Nu Pr 0:5 Š 0:7 varp For Gr =Re 2:7 Pr 0:5 P 2: Nu ¼½5141Gr =Re 2:7 Nu Pr 0:5 Š 0:41 varp Nu varp ¼ 0:021Re 0:8 Pr 0:55 ð q w Þ q 0:35 Gr ¼ q ðq qþgd3 1 q ¼ T w T l 2 Z Tw T qdt Modification of Watt and Chou s correlationg = kg/m 2 sq = kw/m mm, 13 mmp = 5.5 MPa HCFC Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009)

9 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) Fig. 10. Comparison of the estimated heat transfer coefficient y various correlations against the experimental data: p = 8.12 MPa, G = 1200 kg/m 2 s, q = 50 kw/m 2, d i = 4.4 mm. Fig. 13. Comparison of the estimated heat transfer coefficient y various correlations against the experimental data: p = 8.12 MPa, G = 400 kg/m 2 s, q = 50 kw/m 2, d i = 9 mm. Fig. 11. Comparison of the estimated heat transfer coefficient y various correlations against the experimental data: p = 8.12 MPa, G = 1200 kg/m 2 s, q = 50 kw/m 2, d i = 9 mm. Fig. 14. Application of the correlations including the one otained from the CO 2 test for the Freon condition; p = 5.5 MPa, G = 400 kg/m 2 s, q = 10 kw/m 2, d i = 4.4 mm. Fig. 12. Comparison of the estimated heat transfer coefficient y various correlations against the experimental data: p = 8.12 MPa, G = 400 kg/m 2 s, q = 50 kw/m 2, d i = 4.4 mm. Fig. 15. Application of the correlations including the one otained from the CO 2 test for the Freon condition; p = 5.5 MPa, G = 400 kg/m 2 s, q = 25 kw/m 2, d i = 4.4 mm.

10 338 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) Fig. 16. Application of the correlations including the one otained from the CO 2 test for the water condition; p = 24.5 MPa, G = 1260 kg/m 2 s, q = 233 kw/m 2, d i = 7.5 mm. Fig. 17. Application of the correlations including the one otained from the CO 2 test for the water condition; p = 24.5 MPa, G = 375 kg/m 2 s, q = 348 kw/m 2, d i =12 mm. one, and the scattered open round symols are the experimental data otained from the test at SPHINX or digitized from pulished papers. In Figs , the Hs are plotted against the corresponding ulk enthalpy. The ulk enthalpy was calculated from the inlet enthalpy with an assumption of a constant heat flux on the tue surface or heater rod. Figs compare the predictions y various correlations including the proposed correlation with the test data otained at SPHINX. At a condition of p = 8.12 MPa, G = 1200 kg/m 2 s, q =50kW/m 2 in the tues of 4.4 mm and 9.0 mm ID (Figs. 10 and 11), the proposed correlation predicts the data reasonaly well when compared with the existing correlations except for DB, BI and JK. The inaccurate prediction y DB is natural, since it was developed for constant physical properties and plotted for the purpose of a reference. Graezhnaya and Kirillov [27] also noted that the Bishop s correlation overestimated the experimental values and a 25% reduction of the constant (from 6.5 to 5.2) was required to predict their data with an acceptale error. The good prediction of JA is also understandale since it was developed y reviewing many data points for various geometries and mediums. The difference in the diameter does not seem to affect the prediction accuracy of the correlations. Figs. 12 and 13 show comparisons of the predictions y the correlations with the data otained at SPHINX at p = 8.12 MPa, G = 400 kg/m 2 s, q = 50 kw/m 2, which corresponds to the condition for a heat transfer deterioration. Oviously all the correlations except for KC and JK failed to predict the test data, as expected. The outstanding prediction capaility of the proposed correlation is clear as can e seen in Figs 12 and 13. Although JK was developed with HCFC-22 as a medium to cover oth a deterioration and a normal regime it was unale to properly predict the test data otained for the 4.4 mm ID tue with CO 2 as a medium, on the other hand it predicted the data for the 9.0 mm ID tue, strikingly well. In Figs. 14 and 15, the predictions y the proposed correlation are compared with the data otained with HCFC-22 y Mori et al.[13]. At a condition of p = 5.5 MPa, G = 400 kg/m 2 s, q = 10 kw/m 2 (Fig. 14), which corresponds to a normal heat transfer, KC slightly underestimated the data when compared with those y the other correlations. At a condition of p = 5.5 MPa, G = 400 kg/m 2 s, q =25kW/m 2 (Fig. 15), which corresponds to a deteriorated heat transfer, KC predicted the data satisfactorily. While KC predicted the inception point of a deterioration with a great accuracy, it overestimated the data when the heat transfer recovered from a deterioration. In Fig. 16 the data otained y Yamagata et al. [2] with water flowing vertically upward in a 7.5 mm ID tue at p = 24.5 MPa, G = 1260 kg/m 2 s, q = 233 kw/m 2 was compared with the prediction y the proposed correlation. As is evident, it slightly overestimated the data, while the other correlations slightly underestimated the data. However, the overall assessment seems to e satisfactory. Finally, in Fig. 17, the prediction y the proposed correlation was compared with the data otained y Shitsman [28] with water flowing vertically upward in a 12 mm ID tue at p = 24.5 MPa, G = 375 kg/ m 2 s, q = 348 kw/m 2. When the flow was in the deterioration regime, the prediction y KC followed the data satisfactorily ut it started deviating as soon as the flow recovered from a deterioration. From the discussions aove, it can e concluded that the proposed correlation predicts the experimental data reasonaly well. Especially, the proposed correlation predicted the inception point of a deterioration exceptionally well for some cases, although it was not successful for all the cases, for instance for HCFC-22. For the deterioration regime the proposed correlation generally overestimated the H, however, the extent of the overestimation was not very wild. Nevertheless a further study is necessary efore we can reach a consensus; the proposed correlation may e regarded as a first step for the formulation of a reliale universal correlation for heat transfer at a supercritical pressure, equally applicale to oth a normal heat transfer regime and a deteriorated heat transfer regime. 6. Conclusion A series of experiments for a convective heat transfer to CO 2 at a supercritical pressure flowing upward in tues and an annular channel has een performed, and as a result, a set of heat transfer correlations was developed. The resulting correlations are categorized y the uoyancy parameter Bu and the range of the prediction covers oth a normal and a deterioration regime. The developed set of correlations has een tested against pulished data for water and HCFC-22. A fairly good agreement etween the predictions and the data was shown even though it was developed from an experiment using CO 2 as a medium. The prediction y the proposed correlation showed a good ehavior especially when the uoyancy effect is severe, in other words near a deterioration regime. Acknowledgement The authors would like to acknowledge the financial support provided y the Ministry of Education, Science and Technology

11 Y.-Y. Bae, H.-Y. Kim / Experimental Thermal and Fluid Science 33 (2009) through I-NERI program and the Korea Atomic Energy Research Institute for its continuing support and encouragement in SCWR research. References [1] V.A. Kurganov, A.G. Kaptil nyi, Velocity and enthalpy fields and eddy diffusivities in a heated supercritical fluid flow, Experimental Thermal and Fluid Science 5 (4) (1992) [2] K. Yamagata, K. Nishikawa, S. Hasegawa, T. Fujii, S. Yoshida, Forced convection heat transfer to supercritical water flowing in tues, International Journal of Heat and Mass Transfer 15 (1972) [3] M. Okawa, H. Komita, S. Shiga, S. Yoshida, H. Mori, K. Moriya, Supercritical pressure fluid heat transfer study for supercritical water cooled power reactor development, in: Proceedings of the 13th Pacific Basin Nuclear Conference, Shenzhen, China, Octoer 21 25, [4] H.K. Jeon, J.K. Kim, J.Y. Yoo, J.S. 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