Critical heat flux under zero flow conditions in vertical annulus with uniformly and non-uniformly heated sections

Nuclear Engineering and Design 205 (2001) 265– 279 www.elsevier.com/locate/nucengdes

Critical heat flux under zero flow conditions in vertical annulus with uniformly and non-uniformly heated sections Se-Young Chun a,*, Sang-Ki Moon a, Heung-June Chung a, Sun-Kyu Yang a, Moon-Ki Chung a, Masanori Aritomi b b

a Korea Atomic Energy Research Institute, 150 Dukjin-dong, Yusong-gu, Taejon, 305 -353, South Korea Research Laboratory for Nuclear Reactor, Tokyo Institute of Technology, 2 -12 -1 Ohokayama, Meguro-ku, Tokyo, 152 Japan

Received 30 May 2000; received in revised form 10 August 2000; accepted 15 August 2000

Abstract The experimental study of water CHF (critical heat flux) under zero flow conditions has been carried out in an annulus flow channel with uniformly and non-uniformly heated sections over a pressure range of 0.52– 14.96 MPa. In the present boiling system, the CHFs occur in the upper region of the heated section, in contrast to the results in the experiments for boiling tubes conducted by several investigators. The general trend of the CHF with pressure is that the CHF increases up to a medium pressure of about 6 – 8 MPa and decreases as the pressure is further increased. A comparison of the present data with the existing flooding CHF correlations shows that the correlations depend greatly on the effect of the heat flux distribution. When the correction terms with the density ratio and the effect of the heat flux distribution proposed in the present work are used with the CHF correlation based on the Wallis flooding correlation, it predicts the measured flooding CHF within an RMS error of 9.0%. © 2001 Elsevier Science B.V. All rights reserved.

1. Introduction Correct characterization of the critical heat flux (CHF) is of particular interest when predicting nuclear reactor core behavior for accident situations, including a flow transient such as reactor circulation pump failure and a loss of coolant accident (LOCA). The core coolant flow is reduced during a large portion of several types of

* Corresponding author. Tel.: +82-42-8682948; fax: + 8242-8688362. E-mail address: [email protected] (S.-Y. Chun).

accident scenarios, and the reactor core encounters a stagnant or reverse flow. The understanding of the fundamental nature of CHF in the vertical flow channel under stagnant or zero flow conditions will be important for reactor safety, as is the case with low flow CHF. In the case of a vertical channel with a larger liquid volume or shorter heated section, it may be inferred easily that the CHF mechanism becomes similar to the departure from nucleate boiling (DNB) in pool boiling. The CHF mechanism for a narrow and long vertical channel under a zero flow condition may be different from that of the pool boiling CHF.

0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S0029-5493(00)00377-0

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Several investigators (Barnard et al., 1974; Mishima and Nishihara, 1987; El-Genk et al., 1988; Chang et al., 1991; Park, J.W. et al., 1997) have conducted experiments on CHF under very low flow conditions from several hundred kg m − 2 s − 1 to a zero inlet flow with a completely closed bottom end. They have observed that a countercurrent flow is formed in the vertical flow channel at zero and very low flow rates, and subsequently the CHF occurs due to the countercurrent flow limitation (CCFL) or flooding. The CHF in these boiling systems was considerably smaller than that of normal pool boiling (Mishima and Nishihara, 1987; El-Genk et al., 1988). The experiments of El-Genk et al. (1988) indicated that the CHF values with zero flow were about 30% lower than those with net water upward flow when extrapolated to zero flow. For practical applications in the non-nuclear industry, many studies on the CHF phenomenon of the countercurrent flow of a heated vertical tube closed at the bottom end have been made with respect to the design and performance of closed two-phase thermosyphons (Sakhuja, 1973; Tien and Chung, 1979; Nejat, 1981; Imura et al., 1983; Dobran, 1985; Reed and Tien, 1987; Casarosa and Dobran, 1988; Katto and Hirao, 1991; Katto and Watanabe, 1992). In these references, flooding in the countercurrent flow was regarded and discussed by many investigators as one of the CHF mechanisms, and empirical flooding equations were employed in the development of the correlations for prediction of the CHF. Hence, the CHF of this sort is called the flooding CHF. The flooding CHF correlations were based on the Wallis empirical equation (Wallis, 1969) obtained from the countercurrent flow in water and air two-phase system or the Kutateladze criterion for the onset of flooding, with the assumption of mass and energy balance. The thermal hydraulics system codes most widely used for analyzing accidents in nuclear power plants are RELAP5/MOD3 (RELAP5 Code Manual, 1995) and TRAC-PF1 (Liles et al., 1984). In these codes, the Biasi correlation (Biasi et al., 1967) and the AECL-UO CHF Look-up table (Groeneveld et al., 1986), which are based on the data base of normal upward flow CHFs in tubes, are employed for the prediction of CHF.

To provide the CHF value for the zero flow conditions, the Biasi correlation is evaluated at a mass flux of 200 kg m − 2 s − 1 and the CHF Look-up table uses the Zuber pool boiling CHF correlation (Zuber, 1959) with a void fraction correction suggested by Griffith et al. (1977). It is obvious that the codes adopt inappropriate methods to predict the CHF under zero flow conditions. The experimental studies of the CHF in closed two-phase thermosyphons have been made using a uniformly heated vertical tube without a liquid reservoir at the top of the heated section. The conditions of the nuclear reactor may require a vertical test channel with the non-uniformly heated section and the liquid reservoir. In the above references, the CHF experiments were carried out under near atmospheric pressure conditions. The authors have conducted the CHF experiments for zero inlet flow in a uniformly heated vertical annulus with a liquid reservoir under high pressure conditions (Chun et al., 2000). Until now, to the authors’ knowledge, CHF experiments in a flow channel with a nonuniformly heated section under high pressure conditions have not been carried out. Therefore, this paper presents the results from CHF experiments carried out at zero inlet flow in the annulus flow channel with uniformly and non-uniformly heated sections and with the water reservoir under extended pressure conditions. Several existing correlations for the countercurrent flooding CHF are compared with the CHF data obtained in the present experiments to examine the applicability of the correlations.

2. Experimental descriptions

2.1. Experimental facility The CHF experiments reported in this paper have been conducted in Reactor Coolant System thermal hydraulics loop facility (RCS loop facility) of the Korea Atomic Energy Research Institute (KAERI). A description of the facility can be found in Chun et al. (2000). The test section used in this experimental work is described here in detail.

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Fig. 1. Test section geometry and the locations of measuring sensors — ( with non-uniform heat flux distribution.

Fig. 1 shows the details of the test section used in the present experiments. The test section consists of a vertical annulus flow channel and upper and lower plenums. The upper plenum is connected to a steam/water separator. The annulus flow channel is constituted by an outer pipe with an inside diameter of 19.4 mm and an inner heater rod with an outer diameter of 9.54 mm, having a heating length of 1842 mm at room temperature. The inner heater rod is heated indirectly by electricity. The sheath and heating element of the heater rod are made of Inconel 600 and Nichrome, respectively. Heater rods with uniform and non-uniform axial power distributions are used in the present work. For measuring the heater rod surface temperature and detecting the CHF occurrence, six Chromel – Alumel thermocouples with a sheath outer diameter of 0.5 mm are embedded on the outer surface of the heater rod. As shown in Fig. 2, in the heater rod with non-uniform axial power, the power level is divided into 10 steps with a minimum and maxi-

267

) denote the thermocouple locations of the heater rod

mum power ratio of 0.448 and 1.400, respectively, to simulate a symmetric chopped cosine heat flux profile. The temperature sensing points on the heater rod surface are located at 10, 30, 110, 310, 510 and 910 mm for the uniform power heater rod and at 10, 200, 301, 400, 510 and 740 mm for

Fig. 2. Heat flux distribution of the non-uniform heater rod.

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the non-uniform power heater rod from the top end of the heated section. The main parameters measured in the experiments are the water temperatures and pressures at the inlet and outlet plenums, and the water temperatures at the bottom and top of the heated section, the surface temperatures of the heater rod, the differential pressures in the test section, and the power applied to the test section. All the electrical signals from the sensors and transmitters are treated and analyzed by a data acquisition and control system consisting of the A/D and D/A converter and a workstation computer. The uncertainties of the measuring system were estimated from the calibration of sensors and the accuracy of the equipment, according to a propagation error analysis based on Taylor’s series method (ANSI/ASME PTC 19.1, 1985). The evaluated maximum uncertainties of pressures and temperatures were less than 9 0.3% and 9 0.7 K of the readings in the range of interest, respectively. The uncertainties of the heat flux calculated from the applied power were always less than 91.8% of the readings. The heat loss in the heated section should be taken into account in the calculation of the heat flux. The heat losses were estimated by the pretests (i.e. heat balance tests) for each pressure condition and were less than 3% of the power input.

2.2. Experimental procedure and conditions The CHF experiments have been performed by the following procedure. First, the circulation pump, preheater and pressurizer are operated for raising the temperature of the loop and establishing inlet subcooling and pressure of the test section at the desired levels, and the isolation valve located at the upper stream of the test section is fully closed. Power is applied to the heater rod of the test section and increased gradually in small steps. The period between the power steps is chosen to be sufficiently long (about 15 min) so that the loop could stabilize at the steady-state conditions. The water temperatures (T/CW 4 and 5; Fig. 1) in the upper plenum of the test section and the connecting pipe between the upper plenum and the steam/water separator reach the

saturated temperature as the power to the heater rod increases. A countercurrent flow is then formed in the heated section. A balance is kept between the steam generation in the heated section and the falling saturated water into the heated section from the upper plenum due to gravity. As the loop approaches a CHF condition, the temperature fluctuation of the heater rod surface is detected. The CHF condition in the present experiments is determined when the surface temperature of the heater rod continuously rises and then becomes 100 K higher than the saturation temperature. Whenever the CHF was detected, the heater power was automatically reduced or tripped to prevent any damage to the heater rod. In the present experimental conditions, the water temperature (T/CW 2) at the bottom end of the heated section remained in a subcooled condition during a run of the experiment, in spite of the fact that power was applied to the heater rod and the water of the heated section was being heated. This is due to the existence of relatively large heat loss and convective heat transfer toward the lower plenum in the present test section arrangement. A pressure rise at the upper plenum was not observed during a run of the experiment, since the amount of steam generated in the heated section is considerably smaller, compared to the volume of the steam/water separator. A total of 135 CHF data were obtained in the ranges of the water subcooling enthalpies from 85 to 413 kJ kg − 1 at the bottom end of the heated section and system pressures from 0.52 to 14.96 MPa. The pressure at the top end of the heated section is specified as the system pressure and is used for the analysis of the experimental data.

3. Experimental results and discussions

3.1. Data reduction In the flooding phenomenon for countercurrent flow, the vapor flow rate is the most important parameter. As mentioned above, the water at the bottom part of the heated section is under a subcooled condition at the occurrence of a CHF. In this situation, the amount of steam generated

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Fig. 3. Physical model of the present boiling system.

in the heated section cannot be evaluated directly from the mass and energy balances. The information for the locations of the onset of saturated boiling is required to evaluate the vapor flow rate at the top end of the heated section. We can consider a countercurrent annular flow as illustrated in Fig. 3. In order to search for the locations of the onset of saturated boiling in the present boiling system, it is assumed that the pressure losses due to friction and acceleration can be neglected for the pressure difference DP between the bottom end of the heated section (Z=0) and location Z, and that the void fraction in the subcooled boiling region is negligibly small. The pressure difference DP is equal to the static head from the bottom end of the heated section to location Z. Consequently, the average void fraction h from the bottom end (Z = 0) to location Z is given as h=

zl,satgZ+ (zl,sub −zl,sat)gZsat −DP (zg −zl,sat)g(Z −Zsat)

269

For the present test section, the pressure difference DPm − 2 measured by the differential pressure transmitter DP-2 (Fig. 1) are plotted as a function of subcooling temperature DTsub at the bottom end of the heated section for a given system pressure in Fig. 4. In the present conditions, it was observed that the relationship between DPm − 2 and DTsub is linear for a fixed system pressure. The pressure difference DPm − 2,sat for DTsub = 0 (i.e. Zsat = 0) at the bottom end of the heated section can be given from the extrapolation of the liner relationship between DPm − 2 and DTsub. Substituting the value of DPm − 2,sat, Z (in the present case, Z= 1.042 m) and Zsat = 0 into Eq. (1), the average void fraction ho for the saturated condition at the bottom end of the heated section is calculated for each system pressure. When it is assumed that h decreases linearly in proportion to the increase of distance Zsat from the bottom end of the heated section to the saturation point, the void fraction h is expressed as follows:



h= ho 1−

Zsat Z



(2)

Location Zsat of the onset of saturated boiling is given from Eqs. (1) and (2) and the measured pressure difference DPm − 2. For calculating Eq. (1), the subcooled liquid density zl,sub in the bottom region of the heated section uses that for an average of the temperature at the bottom end of the heated section and the saturated temperature.

(1)

where zl and zg are the liquid and vapor densities, and g is the gravitational acceleration. The subscripts ‘sub’ and ‘sat’ denote the subcooling and saturation conditions, respectively.

Fig. 4. Relationship of the pressure drop (DPm − 2) and the subcooling temperature at the bottom end of the heated section.

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270

Subsequently, the boiling length LB at CHF conditions is defined using the heated length Lh as follows: LB = Lh − Zsat

(3)

The average CHF qC,B over the boiling length is expressed by qC,B =

1 LB

&

Lh

q(z) dz

(4)

Zsat

where q(z) is the axial heat flux profile of the heater rod. In the present work, the experimental data are discussed and analyzed with the boiling length LB and the average CHF qC,B.

3.2. Obser6ation of CHF beha6iors In the present experiments, the power input to the heater rod was carefully increased. If the power was rapidly increased and the periods between the power steps were short before the water temperature in the upper plenum reached the saturation temperature, rapid temperature rises (i.e. dryout) throughout the surface of the heater rod at the same time were frequently observed in low heat flux conditions (about one half of qC,B). This phenomenon is due to the sudden evaporation of water in all regions of the heated surface area under unstable conditions, while the stable countercurrent flow does not form yet. This situation is not desired in the present work, because it is an irregular event related to an imbalance between the fall of condensed water from the upper plenum and rising vapor in the heated section. Fig. 5(a) shows the typical surface temperature variation of the heater rod at CHF conditions. As the power level approaches the CHF, the fluctuations of the surface temperature start in the upper region of the heated section (i.e. T/C 1, 2 or 3). When the power level reaches the CHF condition, the magnitude of the temperature fluctuations becomes large and after a while, CHF occurs in the upper region of the heated section. The surface temperature variation shown in Fig. 5(b) is different from Fig. 5(a). The surface temperatures rise monotonously without the fluctuations after a small temperature fluctuation starts. This type of temperature behavior was observed only at high

Fig. 5. (a) Typical behavior of the heated surface temperature with time. (b) Temperature behavior of the heated surface at high pressure conditions.

pressures of 12.08 and 14.96 MPa. In the present experiments, the CHF always occurred at the locations of 10 and 30 mm (T/C 1 and 2) from the top end of the heated section for the uniform heat flux. For the non-uniform heat flux, the CHF occurred mainly at the locations of 200 mm, and sometimes 10 or 301 mm (T/C 2 and sometimes T/C 1, 3) for the non-uniform heat flux. In the middle positions (T/C 5 and 6), the surface temperatures of the heater rod maintained a constant superheat and the temperature fluctuation was not observed during a run of the experiment. The surface temperature behavior illustrated in Fig. 5 is closely similar to that observed in the experiment of Katto and Hirao (1991), which was conducted in uniformly heated tubes with a liquid reservoir at the top of the heated section. The boiling length varies with the water subcooling condition at the bottom end of the heated section. In Fig. 6, the CHF values qC,B are given as a

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function of boiling length to hydraulic equivalent diameter ratio LB/Dhy. The CHF values monotonously decrease with LB/Dhy, although the values for the non-uniform heat flux scatter due to the effect of pressure. This trend is consistent with the analytical and experimental study of Katto and Watanabe (1992), which indicated that the magnitude of the CHF is approximately inversely proportional to the heated length of the tube under a fixed condition of the tube diameter. However, several experimental studies (Barnard et al., 1974; Imura et al., 1983; El-Genk et al., 1988; Katto and Hirao, 1991) indicated that the CHF in the heated vertical channel with closed bottom occurs at the middle or lower position of the heated section, in contrast to the results from the observations of the present experiments. For example, Katto and Hirao (1991) reported that the location of the onset of CHF lies between the middle and the bottom end of the heated tubes over a range of LB/Dhy =30 – 112.5. Hwang and Chang (1994) considered a physical model similar to Fig. 3 for a boiling tube with a closed bottom. They then predicted the CHF locations on the basis of the assumption that dryout occurs at the boundary between the two-phase mixture and the countercurrent annular flow regions, i.e. the location of the minimum liquid film thickness, owing to the evaporation of the falling film. In the annulus, if the falling liquid film is formed on both the heated and unheated surface almost uni-

Fig. 6. Flooding CHF as a function of boiling length to hydraulic equivalent diameter ratio.

271

Fig. 7. Effect of pressure on flooding CHF.

formly such as that pointed out by Mishima and Nishihara (1987), the amount of downward flow on the unheated surface is two times as large as that on the heated surface at the top end of the heated section. In the present boiling system, the reason that the CHF occurs at the upper portion of the heated section is presumed to be as follows. The liquid film is formed at the part above the heated section, and the liquid film flow on the unheated surface reaches a mixture level without evaporation. Even if the flooding begins at the part above the heated section and the falling film flow rate decreases, the mixture level does not go down so much because enough water is continuously supplied by the liquid film flow on the unheated surface. The two-phase mixture level exists in higher position above a location of 510 mm (T/C 5) from the top end of the heated section. As a result, the CHF occurs in the upper region of the heated section. In order to illustrate the effect of pressure on the CHF in the present boiling system, the measured CHF are plotted as a function of pressure in Fig. 7. The scattering of the CHF values for a fixed pressure is due to the effect of the boiling length (i.e. the variation of the subcooling at the bottom end of the heated section). The CHFs for the non-uniform heat flux show, over a pressure range of 0.52 –9.82 MPa, values about 30% higher than those for the uniform heat flux. For the high pressure region of 12.08 –14.96 MPa, the trend on the difference of the CHF values between the

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uniform and non-uniform heat fluxes cannot be recognized due to the insufficiency of the experimental data. In the case of pool boiling, it is known that CHF reaches a maximum at one-third of the critical pressure (about 8 MPa) (Morozov, 1962). As can be seen in Fig. 7, the general trend of the CHF with pressure is that the CHF increases up to a medium pressure of about 6–8 MPa with increasing pressure and decreases as the pressure is further increased. This indicates that the CHF behavior with pressure in the present boiling system is closely similar to that of pool boiling, although the magnitude of the CHF variation with pressure is smaller, compared to the case of pool boiling.

3.3. Existing correlations for flooding CHF The empirical flooding correlations have been useful to estimate the CHF in a heated vertical channel closed at the bottom end. One of the most frequently used correlations for flooding was given by Wallis (1969), in the following expression: j*g 1/2 +mj*l 1/2 =Cw

(5)

where j *g and j *l are the dimensionless superficial velocities of vapor and liquid, respectively, and Cw is a constant, mainly depending upon the tube end conditions. Cw has values from 0.725 to 1.0, from the flooding experimental results in the countercurrent flow. The constant m is set to unity in the conditions of the present work. The dimensionless superficial velocities j *g and j *l are defined by − 1/2 j *g = jgz 1/2 g (gDDz)

(6)

− 1/2 j *l = jlz 1/2 l (gDDz)

(7)

where jg and jl are the superficial velocities of gas and liquid, respectively, D is the inner diameter of the tube, and Dz is the density difference (zl − zg) between the liquid and vapor phases. For the boiling system shown in Fig. 3, when the heated area AB over the boiling length is employed, the following mass and energy balance equation holds under steady-state conditions:

jgzgAf = jlzlAf =

qC,BAB hlg

(8)

where Af is the flow area of the channel, and hlg is the latent heat of vaporization. Substituting Eq. (8) into Eq. (5) and using a hydraulic equivalent diameter Dhy in Eqs. (6) and (7) for the annulus channel, the CHF due to flooding is expressed in a dimensionless form as the following equation:

    n

qC,B C 2 Dhe = w 1/2 hlg(gDhyzgDz) 4 LB

1+

zg zl

1/4

−2

(9) In the above equation, the heated equivalent diameter to the boiling length ratio Dhe/(4LB) was used instead of the term Af/AB. The CHF qC,B and the boiling length LB are calculated from Eqs. (4) and (3), respectively. Sakhuja (1973) showed that Eq. (9) agreed with his experimental data for tubes. Mishima and Nishihara (1987) rewrote Eq. (9) as follows:

   n

qC,B z C 2w Dhe = D* 1/2 1+ g 1/2 hlg(guzgDz) 4 LB zl

1/4

−2

(10) where D* is the dimensionless diameter, defined by D* =Dhy/u. The length scale u of the Taylor instability is given by u= (|/gDz)1/2, where | is the surface tension. Therefore, D* used by Mishima and Nishihara is equal to the Bond number, Bo = Dhy(gDz/|)1/2. They reported that the flooding CHF was well reproduced by Eq. (10) with C 2w = 0.96 for an annulus. Nejat (1981) proposed a flooding CHF correlation based on Eq. (9). The original form of the Nejat correlation for the tube is as follows:

     n

qC,ax LB hlgzg(gD)1/2 D = C 2w

Dz zg

− 0.1

1/2

1+

zg zl

1/4

−2

(11)

where qC,ax is the CHF in an axial direction, defined by qC,ax =

yD Af

&

Lh

q(z) dz

Zsat

Nejat added the correction term (LB/D) − 0.1 in the correlation in order to reduce the scatter of the

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experimental data points on the tubes, and then showed that Eq. (11) with C 2w =0.36 satisfactorily correlates with the experimental data. Using the CHF qC,B in the heated surface and the heated equivalent diameter Dhe in the correction term, Eq. (11) is rewritten as

  Dz 1+ z  n

C2 D qC,B = w he 1/2 hlgzg(gDhy) 4 LB

1/2

1/4

g

−2

zl

zg

(12) where C 2w is 0.36(LB/Dhe)0.1. Several investigators have employed Kutateladze’s criterion for the onset of flooding, given by the following expression: 1/2 K 1/2 g +mK l =Ck

(13)

where Kg and Kl are defined by Kg = jgz 1/ g − 1/4 2(g|Dz) − 1/4 and Kl =jlz 1/2 , respecl (g|Dz) tively, and Ck is a constant. Pushkina and Sorokin gave m = 0, C 2k =3.2 for the flooding condition (Bankoff and Lee, 1983). Substituting jg and jl into Eq. (13) and setting the value of m to unity, a correlation for the flooding CHF is given by the following expression:

    n

qC,B C2 D = k he 1/4 2 hlg(g|z gDz) 4 LB

1+

zg zl

1/4

−2

(14)

Tien and Chung (1979) gave the form of Ck including a correction term with a function of the Bond number Bo as follows: C 2k =3.2[tanh(B 1/4 o / 2)]2. The empirical correlation with a similar form to Eq. (14) was derived by Imura et al. (1983). The correlation is expressed by

  

2 k

qC,B C Dhe = 1/4 2 hlg(g|z gDz) 4 LB

zg zl

− 0.13

(15)

Imura et al. reported that Eq. (15) with C 2k = 0.64 correlated with the experimental data within 9 30% accuracy. Mishima and Nishihara (1987) reported that the flooding CHF is correlated using Eq. (10) with Cw =1.66, 0.98 and 0.73 for tubes, annuli and rectangular channels, respectively. In Nejat’s Eq. (11), Cw was modified with the term of LB/D, and Tien and Chung proposed Eq. (14) with a correction term relating to the Bond number Bo for Ck.

273

This implies that the values of Cw and Ck are not constant and vary with the geometry and thermodynamic conditions. Eqs. (9) and (14) show that the flooding CHF is a function of LB/Dhe, Bo and zg/zl. Park, C. et al. (1997) examined the effects of the terms LB/Dhe, Bo and zg/zl on C 2w using Eq. (9) based on the Wallis flooding equation and proposed the empirical correlation for C 2w as follows:

  

C 2w = 1.22

LB Dhe

0.12

zg zl

0.064

× (1+ 0.055Bo − 4.08× 10 − 3B 2o)

(16)

They reported that the flooding CHF is predicted within a RMS (root mean square) error of 18.8% when Eq. (16) for C 2w is used with Eq. (9).

3.4. Comparison with existing correlations The left-hand sides of Eqs. (14) and (15) are sometimes called the Kutateladze number, which is employed in many CHF correlations for pool boiling. Additionally, the left-hand side of Eq. (10) by Mishima and Nishihara is also equal to the Kutateladze number. Only Nejat’s Eq. (12) does not include the Kutateladze number and is independent of surface tension The present data are compared with Eqs. (10), (12), (14) and (15), using the dimensionless parameters as follows: q*C,w =

qC,B , hlg(gDhyzgDz)1/2

q*C,k =

q*C,N =

qC,B , hlgzg(gDhy)1/2

qC,B and hlg(g|z 2gDz)1/4

x =[1+ (zg/zl)1/4] − 2 The results of the comparison are shown in Figs. 8–11. Figs. 8, 10 and 11 show that Eqs. (10), (14) and (15) greatly depend on the axial heat flux distribution of the heated section. In Fig. 8 for the Mishima and Nishihara equation, the experimental data points have a large scatter in both heat flux distributions. The Kutateladze flooding CHF correlation (Eq. (14)) and Imura et al.’s correlation (Eq. (15)) reasonably correlate with the experimental data for the uniform heat flux, but the

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Fig. 8. Comparison of the present data with Mishima and Nishihara’s equation (Eq. (10)).

Fig. 10. Comparison of the present data with Tien and Chung’s equation (Eq. (14)).

experimental data for the non-uniform heat flux are considerably scattered as shown in Figs. 10 and 11. On the other hand, Fig. 9 shows that the Nejat Eq. (12) better correlates the experimental data in the range of pressures from 3.02 to 14.96 MPa. The discrepancy between the uniform and non-uniform heat fluxes tends to become large as the pressure decreases, particularly in the low pressure region (from 0.52 to 1.79 MPa). When C 2w and C 2k suggested by each investigator are used, the dimensionless parameters q*c calculated by Eqs. (10), (12), (14) and (15) give considerably lower values than the present data. In the comparison with Eq. (14), the value of 3.2 is used as C 2k, because the use of the Bond number term of

Tien and Chung produces a large difference between the present data and the calculated values. The form of the Bond number term of Tien and Chung may not be appropriate. Actually, Katto and Watanabe (1992) and Park, C. et al. (1997) discussed and examined Eq. (14) with [tanh(B 1/4 o / 2)]2 = 1, and then used C 2k = 3.2, so as to correspond better to their CHF data. Eqs. (10) and (12) and the Park, C. et al. (1997) correlation for C 2w were derived using Eq. (9) based on the Wallis flooding equation. When C 2k in Eq. (14) is set to 3.2C 2w and Eq. (16) for C 2w is used, Eq. (14) essentially has the same form as Eq. (10) because Eq. (16) includes the Bond number term. The original correlation of Imura et al.

Fig. 9. Comparison of the present data with Nejat’s equation (Eq. (12)).

Fig. 11. Comparison of the present data with Imura et al.’s correlation (Eq. (15)).

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(1983) was derived independently of the flooding correlation. The density ratio (zg/zl) − 0.13 and the constant value of 0.64 for C 2k in the right-hand side of Eq. (15) were determined empirically from their experimental results that the effect of Bo on the CHF is not recognized at a constant zg/zl condition. Katto and Hirao (1991) pointed out that the right-hand side of Eq. (15) is nearly equivalent to the right-hand side of Eq. (9) except for the value of C 2w. Therefore, C 2w of Park, C. et al. (1997) can be applied for Eqs. (10), (12), (14) and (15). As shown in Figs. 8 and 9, the values calculated by Eqs. (10) and (12) with C 2w of Park, C. et al. (1997) draw tolerably toward the present data. Eq. (10) with C 2w of Park, C. et al. (1997) gives a large scattering of the calculated q*C,k. Figs. 10 and 11 show that the parameter q*C,k calculated by Eqs. (14) and (15) with C 2w of Park, C. et al. (1997) appear in a region between the data points for uniform and non-uniform heat fluxes. The use of C 2w of Park, C. et al. (1997) in the flooding CHF equations yields better agreement than C 2w and C 2k suggested by each investigator. However, the discrepancy due to the effect of the heat flux distribution cannot be improved. As can be seen from Fig. 9, the present data are linearly correlated with Nejat’s Eq. (12) and the parameter q*C,N calculated using C 2w of Park, C. et al. (1997) do not scatter, although the effect of the heat flux distribution is large in the low pressure region. The range of zg/zl used in the development of Imura et al.’s correlation covers the present experimental conditions. This means that the influence of the functional form of the density ratio term is large. The comparison of the ranges of the present conditions and the experimental data used by Park, C. et al. (1997) is listed in Table 1. In the range of the experimental data used in the development of C 2w of Park, C. et al. (1997), the density ratio zg/zl does not cover the present experimental conditions. Therefore, the term (zg/zl)0.064 in Eq. (16) should be reformed as corresponds to the present conditions. In Eq. (9), the variation of C 2w (= 4q*C,w LB/(Dhex)) for zg/zl can be obtained for the present data, and then, from the best fitting of the relation between C 2w and zg/zl, the functional form of zg/zl in Eq. (16) is obtained. As a result,

275

Table 1 Ranges of the present experimental data and applicable ranges of the correlation of Park, C. et al. (1997) (Eq. (16)) for C 2w Present work

Park, C. et al. (1997)

Test section geometry

Annulus

Fluid

Water

Round tubes, annuli and rectangular channels Water and Freon 113 4.8–17.2

Hydraulic 9.86 equivalent diameter (mm) (Dhy) Length to diameter 48.0–59.8 ratio (LB/Dhe) Liquid to vapor 6.2–335.6 ratio (zl/zg) Bond number (Bo) 4.25–10.0

8.1–120.0 200–1600 1.79–17.3

the correlation of Park, C. et al. (1997) is rewritten as follows: C 2w = 1.22

   LB Dhe

0.12

zg zl

− 0.032

×(1 + 0.055Bo − 4.08× 10 − 3B 2o)

(17)

In order to take into account the effect of the heat flux distribution on the CHF, the length LC,B from the location of the onset of saturated boiling to the location of the CHF occurrence is introduced. Using Eq. (17) for C 2w and the ratio Dhe/ LC,B instead of the term Dhe/LB in Eqs. (9) and (14), and then plotting the terms 4q*C,w/(C 2w j) and 4q*C,k/(C 2wj) as a function of Dhe/LC,B, respectively, the functional forms of Dhe/LC,B for the present data are determined as follows: 4(Dhe/LC,B)1.396 for Eq. (9) based on the Wallis flooding equation, and 4(Dhe/LC,B)1.160 for Eq. (14) based on the Kutateladze flooding criterion. Eqs. (9) and (14) including the above terms give the results as shown in Figs. 12 and 13. These figures indicate that a pertinent use of the term Dhe/LC,B can reduce the effect of the heat flux distribution on the CHF. In particular, Eq. (9) with (Dhe/LC,B)1.396 is scarcely influenced by the heat flux distribution. Consequently, Eq. (9) based on the Wallis flooding equation is rewritten as the following expression:

S.-Y. Chun et al. / Nuclear Engineering and Design 205 (2001) 265–279

276

Fig. 12. Comparison of the present data with the modified Wallis flooding CHF correlation.

   n

qC,B = C 2w

Dhe LC,B

× 1+

1.396

zg zl

hlg(gDhyzgDz)1/2

1/4

−2

(18)

where C 2w uses Eq. (17). In Fig. 14, the present data are compared with Nejat’s Eq. (12) with the term 4(Dhe/LC,B)1.396, since the values obtained by using Eqs. (9) and (10) scatter slightly as shown in Figs. 8 and 12. The values of Nejat’s parameter q*C,N for the flooding CHF predicted using Eq. (17) for C 2w is represented by a solid line in the figure because it does not quite present the scattering of the calculated values. The solid line

Fig. 14. Comparison of the present data with the modified Nejat equation.

shows excellent agreement with the present data. Fig. 15 shows the comparison of the CHF predicted by Eq. (18) with the present CHF data. Eq. (18) with Eq. (17) for C 2w predicts the present flooding CHF within an RMS error of 9.0%. In practical application, since Eq. (18) includes the unknown parameter LC,B, for a given pressure, the axial heat flux distribution shape and geometry, the CHF value may be calculated by iteration using the relationship

Fig. 15. Comparison of the present CHF with the CHF predicted by Eq. (18) with Eq. (17) for C 2w RMS error= Fig. 13. Comparison of the present data with the modified Kutateladze flooding CHF correlation.

' 

1 N qC,B,pred −qC,B,exp % N i=1 qC,B,exp

where N is the total number of data.



2

qZ =

1 Z− Zsat

&

S.-Y. Chun et al. / Nuclear Engineering and Design 205 (2001) 265–279

277

Z

q(z) dz

the Wallis flooding equation with Eq. (17) for C 2w predicts the measured flooding CHF within the RMS error of 9.0%.

Zsat

where qZ is the average heat flux from Zsat to location Z. However, the term Dhe/LC,B in Eq. (18) may become the different functional form according to the axial heat flux shape condition. Hence, further analytical studies are required to predict the location of the flooding CHF.

4. Conclusions The experimental study of water CHF under zero flow conditions has been carried out in an annulus flow channel with uniformly and non-uniformly heated sections over a pressure range of 0.52 –14.96 MPa. The present experimental data are compared with several existing flooding CHF expressions. The following conclusions can be drawn from this study: 1. In this experiment, the CHFs occur in the upper region of the heated section, in contrast to the results from the observations in the experiments for boiling tubes conducted by several investigators. This discrepancy can be interpreted from the geometry effect on the difference between the annulus and the tube. 2. The flooding CHFs for the non-uniform heat flux have about 30% higher values than those for uniform heat flux, in the range of pressures from 0.52 to 9.82 MPa. The general trend of the CHF with pressure is that the CHF increases up to a medium pressure of about 6–8 MPa and decreases as the pressure is further increased. 3. When Eq. (14), based on the Kutateladze flooding criterion, and Imura et al.’s correlation are used with the correlation of Park, C. et al. (1997) for C 2w, the parameter q*C,k gives reasonable agreement with the present data. However, the discrepancy due to the effect of the heat flux distribution cannot be improved. 4. The density term in the correlation of Park, C. et al. (1997) for C 2w was corrected corresponding to the present condition and the correction term (Dhe/LC,B)1.396 was proposed in order to take into account the effect of the heat flux distribution on the CHF. Eq. (18) based on

Acknowledgements The authors would like to thank the Ministry of Science and Technology of Korea for their financial support of the Long-term Nuclear R & D Program. Appendix A AB Af Bo Ck Cw D Dhe Dhy D* d g hlg Dhsub

J J* K LC,B

LB Lh LZ

heated area of the boiling length, m2 cross-sectional flow area of a channel, m2 Bond number, Dhy(gDz/|)1/2 constant in the Kutateladze flooding criterion constant in the Wallis flooding equation tube inner diameter, m heated equivalent diameter, m hydraulic equivalent diameter, m dimensionless diameter, Dhy/u heater rod diameter, m gravitational acceleration, m s−2 latent heat of evaporation, kJ kg−1 subcooling enthalpy at the bottom end of the heated section, K superficial velocity, m s−1 dimensionless superficial velocity, jz 1/2(gDDz)−1/2 Kutateladze number, jz 1/2 (g|Dz)−1/4 length from the onset of saturated boiling to the location of CHF occurrence, m boiling length in the heated section, m heated length, m length from the bottom end of the heated section to location Z, m

278

m

P DP q(z) qave qC,B qC,ax qZ q*C,k

q*C,N q*C,w DTsub

Z

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constant in the Wallis equation and Kutateladze criterion for flooding pressure, MPa differential pressure, kPa axial heat flux profile of the heater rod, kW m−2 average heat flux over the heated section, kW m−2 average critical heat flux over the boiling length, kW m−2 critical heat flux in the axial direction, kW m−2 average heat flux from Zsat to location Z, kW m−2 dimensionless CHF parameter in Eqs. (10), (14) and (15), qC,B/ [hlg(g|z 2gDz)1/4] dimensionless CHF parameter in Eq. (12), qC,B/[hlgzg(gDhy)1/2] dimensionless CHF parameter in Eq. (9), qC,B/[hlg(gDhyzgDz)1/2] subcooling temperature at the bottom end of the heated section, K distance from the bottom end of the heated section, m

Greek symbols h average void fraction from the bottom end of the heated section to location Z h average void fraction for the saturated condition at the bottom end of the heated section u length scale of Taylor instability, (|/gDz)1/2, m density, kg m−3 z Dz density difference of liquid and vapor phase, zl−zg, kg m−3 | surface tension, N m−1 x dimensionless parameter in the flooding CHF equations, [1+ (zg/zl)1/4]−2 Subscripts C B

critical heat flux boiling length

G Exp K L N Pred Sat Sub W Z

vapor phase experiment Kutateladze’s flooding criterion liquid phase Nejat’s correlation prediction saturation condition subcooled condition Wallis’s flooding equation location in the axial direction from the bottom end of the heated section

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