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An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions
Nuclear Engineering and Design 235 (2005) 2295–2309
An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions Sang-Ki Moon ∗ , Se-Young Chun, Seok Cho, Won-Pil Baek Thermal-Hydraulic Safety Research Department, Korea Atomic Energy Research Institute, 150 Deokjin-dong, Yuseong-gu, Daejeon 305-353, Republic of Korea Received 27 October 2004; received in revised form 7 March 2005; accepted 17 April 2005
Abstract An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m2 s). © 2005 Elsevier B.V. All rights reserved.
1. Introduction The critical heat flux (CHF) is a thermal hydraulic phenomenon of great importance for the development and safety analysis of nuclear reactors. Most of the ∗ Corresponding author. Tel.: +82 42 868 2229; fax: +82 42 868 8362. E-mail address: [email protected] (S.-K. Moon).
0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.04.004
CHF studies have been concentrated into the development of the design correlations for CHF prediction at high flow rate and high pressure conditions as expected in light water reactors. Now many aspects of the CHF phenomenon are well understood and reasonable CHF prediction methods are available to predict the CHF at high flow rate conditions corresponding to the normal operating ranges of the light water reactors.
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Nomenclature Af AhB D D* G G* g hfg j j* Ku N Nf P QC,loc
QBC q (Z) qBCT qC,avg,T qC,loc
XC Z ZC
flow area (m2 ) heated area from saturation location to the CHF location (m2 ) hydraulic diameter (m) dimensionless hydraulic diameter (D/λ) (–) mass flux (kg/(m2 s)) dimensionless mass flux (–) gravitational acceleration (m/s2 ) latent heat of vaporization (kJ/kg) superficial velocity (m/s) dimensionless superficial velocity (–) Kutateladze number (–) number of data (–) viscosity number (–) pressure (MPa) critical power (total power at CHF from bottom of the heated length to CHF location) (kW) boiling critical power (critical power from the saturation location to the CHF location) (kW) local heat flux at axial distance Z from the bottom of the heated length (kW/m2 ) boiling length CHF (average heat flux for boiling length) (kW/m2 ) average CHF (average heat flux at CHF for whole heated section) (kW/m2 ) local CHF (local heat flux at CHF location) (kW/m2 ) local critical quality at CHF location (–) axial distance from the bottom of the heated length (m) CHF location (m)
Greeks letters α void fraction (–) hi inlet subcooling (kJ/kg) ρ density difference between liquid and steam (kg/m3 ) ε relative prediction error (predicted value/measure value − 1) (–)
λ µ ρ σ
wave length scale of Taylor instability (m) viscosity (N s/m2 ) density (kg/m3 ) surface tension (N/m)
Subscripts avg average B boundary C CHF f saturated liquid g saturated steam loc local m measured p predicted T total for the whole test section The importance of the critical heat flux at low flow conditions has been generally well known in relation to the nuclear safety during the operational transients and accidents such as a loss-of-coolant accident (LOCA). The CHF phenomenon at low flow conditions is more complicated due to the remarkable effects of buoyancy and flow instabilities. A lot of CHF experiments using round tubes and annuli have been carried out in low flow conditions and the low flow CHF studies using round tubes and annuli show quite good advancements (Mishima and Nishihara, 1986; El-Genk et al., 1988; Park et al., 1997; Schoesse et al., 1997; Kim et al., 2000; Chun et al., 2000, 2001, 2003). However, a lot of these experimental studies have been performed under low (nearly atmospheric) pressure conditions. Thus, in spite of these CHF experiments in low flow conditions, the CHF behavior at low flow conditions is not so well understood, especially at high pressure conditions. Nuclear reactor core consists of fuel rod bundles and there exist some unheated walls such as the control rod and in-core instrumentation guide tubes. It is known that these unheated walls affect the fluid enthalpy distribution and the CHF value. The CHF tests using rod bundles can simulate more closely the nuclear reactor core than round tube or annulus test sections. Therefore, for a practical application of the CHF data to nuclear reactor safety analysis, it is necessary to broaden the CHF data base for rod bundles. Extensive CHF studies using rod bundles have been performed
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mostly for the normal operating conditions of nuclear reactors. However, at low flow conditions, CHF data for rod bundles are very limited, and the applicable design correlations are almost non-existent (El-Genk and Rao, 1991). Although a lot of CHF correlations are available for rod bundles, these correlations would be inappropriate to predict the CHF at low flow conditions because they were developed based mostly on high flow CHF data. During a main steam line break (MSLB) of nuclear reactor, an increased steam flow resulting from a pipe break in the main steam system causes an increased energy removal from the affected steam generator, and consequently the reactor coolant system. One of the important concerns with the MSLB is a return-to-power event after the reactor trip due to reactivity addition caused by increased core cooling. There is a potential to exceed the departure from nucleate boiling (DNBR) at the return-to-power conditions during the main steam line break, especially at the end of the core life (Lee et al., 1996). The reactor power level, DNBR and other safety parameters must not exceed allowable limits for a nuclear reactor safety. We need a reliable CHF correlation to estimate a safety margin of the DNBR limit. The return-to-power conditions in the steam line break accident is characterized by a low mass flux less than about 250 kg/(m2 s), an intermediate pressure, and a high inlet subcooling (Lee et al., 1996). However, there are few available CHF data and no CHF correlations that are reliable and applicable to the low flow and intermediate pressure conditions. Lee et al. (1996) used the Macbeth CHF correlation (1963) to estimate the safety margin of the Korean Standard Nuclear Power plant (KSNP) because it has some conservatism compared with other CHF correlations such as the Biasi correlation (Biasi et al., 1967) and the 1986 AECLUO CHF look-up table (Groeneveld et al., 1986). This analysis raises some questions about the conservatism of the Macbeth correlation because the correlation itself was not compared with actual CHF data in return-topower conditions. Thus, rod bundle CHF data in low flow, intermediate pressure and high inlet subcooling conditions are indispensable for a reliable estimation of the safety margin under the return-to-power conditions during a steam line break accident. For the reasons mentioned above, an experimental study has been performed for water flowing in a 3 × 3 rod bundle with cosine axial heat flux distribution at low
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flow and a wide range of pressure conditions including return-to-power conditions. This paper provides the CHF test results and some considerations on the CHF predictions in relation to the return-to-power conditions during the main steam line break accident. The obtained CHF data are used to analyze the effect of various parameters on the return-to-power CHF, and to estimate the prediction capability and application feasibility of the conventional CHF correlations.
2. Experimental description 2.1. Experimental facility The CHF experiments have been carried out in the reactor coolant system thermal hydraulics loop facility (RCS loop facility) of the Korea Atomic Energy Research Institute (KAERI). The principal operating conditions of the RCS loop facility are: -
operating pressure: 0.5–16.0 MPa; test section flow rate: 0.03–0.3 kg/s; maximum water temperature: 620 K; available heating power of test section: 970 kW.
Fig. 1 shows a schematic diagram of the RCS loop facility (Chun et al., 2001, 2003). It basically consists of a main circulation pump, preheater, CHF test section, steam/water separator, condenser, pressurizer and cooler. The loop is filled with de-ionized water. The flow rate at the test section inlet is controlled by adjustments of the motor speed of the circulating pump and the flow control valves. Water flow rate at the test section is measured by one of three orifices with different measuring ranges. Flow oscillations that are usually observed in low flow conditions are effectively suppressed by a throttle valve installed upstream of the test section. The preheater with a power of 40 kW adjusts the degree of the inlet subcooling of the water entering the test section. The inlet plenum pressure of the test section is maintained at nearly constant values using the pressurizer with an immersion heater of 40 kW. As shown in Fig. 2, the test section has a flow housing (39.8 mm × 39.8 mm) inside the pressure vessel where nine heater rods having a heated length of 3673 mm are located. The heater rods have a symmetric cosine axial heat flux and have a diameter of 9.52 mm and pitch of 12.6 mm. The heater rods are indirectly
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Fig. 1. KAERI RCS thermal hydraulic loop.
heated by alternating current (ac) power. The sheath and heating element of the heater rods are made of Inconel 600 and Nichrome, respectively. Eleven spacer grids with a simple geometry are installed to support
the heater rods in the test section. The spacer grid effects on the CHF might be small in this experiment, because the spacer grids have no mixing vanes and the thermocouples for measurement of the wall tempera-
Fig. 2. Test section and instrumentation.
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Fig. 3. Axial heat flux distribution.
ture are installed just upstream of the spacer grids. To measure the heater rod surface temperatures and detect a CHF occurrence, six or four thermocouples with a sheath diameter of 0.5 mm are embedded on the surface of the heater rods. The temperature measuring points of these thermocouples are located just upstream of the spacer grids at 10, 225, 625, 1025, 1425 and 1825 mm from the top end of the heated section. Sixteen thermocouples of the same type are located in both the inlet and outlet of the heated section to measure the subchannel water temperatures. As shown in Fig. 3, the heated section of the heater rods is evenly divided into 15 steps to simulate a symmetric cosine axial heat flux profile with a minimum and maximum heat flux ratios to an average heat flux of 1.37 and 0.44, respectively. The radial power distribution is uniform so that heater rods have the same power. The system pressure should be defined as the pressure at the exit of the test section because the CHF occurs generally in the upper part of the test section. However, the pressure at the outlet plenum of the test section becomes unstable as the exit quality of the test section becomes large. The flow rates in the present experiments are so low that the pressure drop through the test section is negligible compared with the system pressure. Thus, in the present experiments, the pressures at the inlet plenum of the test section are used as test parameters. In general, the local thermal hydraulic conditions are different among subchannels inside a rod bundle. For exact calculation of the local thermal hydraulic conditions such as local mass flux and quality of subchannels, we need a subchannel analysis code such as COBRA-
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IV-1 (Wheeler et al., 1976). It is said that the existing subchannel codes tend to have an advantage in predicting local conditions at low quality conditions. However, it is difficult to obtain reliable local conditions at high quality conditions using existing subchannel codes. Therefore, in this study, the cross-sectional average values of mass flux and local quality are used for the analysis of the CHF. The critical quality at the CHF location is defined as the cross-sectional average value calculated by using heat balance equation. The measured data such as the pressure, fluid temperature, mass flux, heater rod surface temperature and power to the heater rods are recorded, processed and stored in a data acquisition and control unit. According to a propagation error analysis based on Taylor’s series method (ANSI/ASME PTC 19.1, 1985), the uncertainties of the measured data are estimated from the calibration of the measurement sensors and the accuracy of the related equipments. The estimated maximum uncertainties are less than ±0.3%, ±1.5%, ±0.7 K of the reading values for the pressure, mass flux and temperature, respectively. The uncertainties of the power measurements supplied to the heater rods are less than ±1.8% of the reading values. Before starting a set of experiments, pretests (i.e. heat balance tests) are carried out to estimate a heat loss in the test section. The heat loss in the heated section estimated by the pretests for pressure conditions are less than 2% of the total applied power to the test section. 2.2. Experimental procedure and conditions The CHF experiments are carried out by the following procedures. After setting the water flow rate, inlet subcooling and inlet pressure at the desired values, the electric power to the heater rods is increased gradually in small steps while the test section inlet conditions are kept at constant values. At each power level, the main parameters are allowed to stabilize for several minutes to achieve a steady-state condition before raising the power level again. This process continues until a sharp increase of the wall temperature is observed in the heater rod surface. The CHF conditions are determined to be reached when one of the wall temperatures of the heater rods shows a continuous sharp increase and then become 100 K higher than the saturation water temperature. Whenever the CHF is detected, the heater power is automatically reduced to small val-
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Table 1 Experimental conditions Parameter
Total database
Return-to-power conditions
Pressure, P (MPa) Mass flux, G (kg/(m2 s)) Inlet subcooling, hi (kJ/kg) Critical quality, XC (−) (kW/m2 ) Average CHF, qC,avg,T Total critical power, QC,loc (kW) No. of data
0.47–15.06 49.66–654.44 67.90–729.76 0.34–1.29 77.02–834.62 76.69–828.36 299
5.97–12.08 49.66–250.58 206.59–722.70 0.68–1.27 88.81–470.29 88.37–466.78 93
ues or tripped to prevent any damage of the heater rods. A total of 299 CHF data including 93 CHF data in return-to-power conditions are obtained as shown in Table 1. Considering Lee et al.’s analysis results (1996), in this study, we defined the thermal hydraulic conditions at the return-to-power conditions as those of a low mass flux less than 250 kg/(m2 s), intermediate pressure between 6.0 and 12.0 MPa, and a high inlet subcooling greater than 200 kJ/kg.
Above this pressure and mass flux conditions, most of the CHFs occurred at thermocouple No. 3. Fig. 4 shows the effect of the mass flux on the average CHF for the whole heated section at a CHF
3. Experimental results and discussion 3.1. Characteristics of CHF data In general, a CHF for a vertical flow with uniformly heated rods occurs at the end of the heated section. On the other hand, the CHF with non-uniformly heated rods occurs at the upstream location rather than the end of the heated section. In the present experiment, most of the first CHFs occurred in the heater rods of R1, R2, R7 and R5, and about 60 and 32% of the CHFs occurred at thermocouples No. 3 and 2 (see Fig. 2), respectively. The present CHF data shows that the CHF is more probable in corner regions rather than in the central region since the flow velocity tends to be low and an unheated wall exists in the corner regions (known as “cold wall effect”). In the corner regions, the liquid film in annular flow is distributed on the unheated wall as well as the heater rod surfaces. The liquid film on the heater rod is only directly related to an evaporation process and accordingly to the CHF, although the liquid film exists on the unheated wall. This phenomenon, generally called cold wall effect, affects the CHF. For a pressure and mass flux less than 7.0 MPa and 350 kg/(m2 s), the CHFs occurred evenly at thermocouples No. 2 and 3.
Fig. 4. Effect of the mass flux on the average CHF based on the present measurements: (a) P = 6.0 MPa and (b) P = 12.0 MPa.
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Fig. 5. Effect of the pressure on the average CHF based on the present measurements.
occurrence. As shown in the figure, the average CHF increases as the mass flux increases. The increase rate of the average CHF becomes large with decreasing the pressure so that the effect of the mass flux on the average CHF becomes large at lower pressures. For a low mass flux or high inlet subcooling, the average CHF increases linearly with a steep slope. However, the increase rate of the average CHF becomes small as the mass flux increases, so the average CHF increases slowly. The effect of the inlet subcooling on the CHF becomes small at very low mass flux conditions and this is consistent with the previous understandings (Chun et al., 2001, 2003). Fig. 5 shows the effect of the pressure on the average CHF. At high mass flux conditions, there is a peak CHF value near 3 MPa while at very low mass flux conditions, the effect of the pressure on the CHF is small and hardly appears. In the medium mass flux conditions, the average CHF decreases monotonously as the pressure increases. On the whole, the average CHF for the pressures greater than 3 MPa decreases monotonously or is nearly constant as the pressure increases. Fig. 6 shows the relationship between the critical quality and local CHF at a CHF occurrence location. As the mass flux becomes high, the CHF occurs at a low critical quality, and the local CHF decreases largely with the critical quality. As the mass flux increases, the local CHF decreases for the same critical quality. However, at a low mass flux, the CHF occurs at a high critical quality and the increase rate of the local CHF
Fig. 6. Effect of the local critical quality on the local CHF based on the present measurements: (a) P = 6.0 MPa and (b) P = 12.01 MPa.
is not large as the critical quality increases. As mentioned above, the critical quality was calculated based on the heat balance considering the inlet conditions and applied total heat up to the CHF location. The calculated thermodynamic equilibrium critical quality can be higher than 1 for very low mass flux where countercurrent flow exists at the CHF location. It is somewhat difficult to clearly observe the effect of the local critical quality on the CHF at very low flow conditions, because the thermodynamic equilibrium critical quality used in these analyses is different from an actual flow quality. For a very low mass flux and a critical quality greater than 1, the CHF might occur at a counter-current flow such as flooding. For the high critical quality conditions greater than about 0.9, the local CHF converges into a single curve nearly independent of the mass flux.
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Most of the present CHF data belong to annular flows for which the CHF occurs due to dryout of the liquid film. In general, for a low quality annular flow, the CHF occurs mainly through the balance between droplet entrainment and liquid film evaporation, because the droplet deposition is suppressed by a strong vapor effusion from the liquid film due to high heat fluxes. The low critical quality and high CHF region is characterized by a sharply decreasing curve of the CHF versus the critical quality. In the case of a high quality annular flow, the effects of the entrainment and evaporation of the liquid film on the CHF are small due to a thin liquid film, and the CHF is governed mainly by the deposition of the liquid droplet. Previous analyses (Katto, 1984; Levy et al., 1981) show that in this high quality and low heat flux region, the CHF decreases slowly with increasing the critical quality. Finally, the CHF curve flattens out tending to become horizontal. The CHF versus critical quality curve as shown in Fig. 6 is quite similar to the previous postulation or analysis result using the liquid film dryout model by Katto (1984) and Levy et al. (1981). 3.2. Flow pattern transition and the CHF mechanism
- flow pattern transition from a slug or a churn turbulent flow to an annular flow, and an annular to annular-mist flow; - dryout or breakup of the liquid film in an annular flow; - complete evaporation of liquid (or high quality CHF, critical quality is about 1.0). Mishima and Nishihara (1986) proposed a dimensionless heat flux qC ∗ and a dimensionless mass flux G∗ to provide some understanding on the CHF under low flow and low pressure conditions as follows: ∗
qC =
- flooding-limited CHF at stagnant or extremely very low flow conditions;
(1)
G , λρg gρ
(2)
G∗ =
where the wave √ length scale, λ, is the Taylor instability defined as λ = σ/gρ. For a non-uniform heat flux profile, the dimensionless CHF can be defined as the following equation using the critical power based on the boiling length, QBC , i.e. critical power from the saturation location to the CHF location: ∗
The CHF mechanism and characteristics are closely related to the two-phase flow pattern. Mishima and Nishihara (1986) observed that the CHF for an internally heated annulus occurred when the flow regime changed from a churn flow to an annular flow at low flow rates and low pressure conditions. El-Genk et al. (1988) observed that while the CHF in his smallest annulus always occurred at the transition from an annular to an annular-mist flow, the CHF in the larger annuli occurred either at the churn-to-annular flow transition or at the slug-to-churn flow transition. Since these CHF experiments were performed near atmospheric pressure conditions, there were no experimental observation and analysis for the CHF mechanism at low mass flow and high pressure conditions. The CHF mechanisms are roughly classified as follows in a very low flow region where the mass flux is between several 10 and 100 kg/(m2 s) (Mishima and Nishihara, 1986; El-Genk et al., 1988):
q C hfg λρg gρ
qBC =
QBC , AhB hfg λρg gρ
(3)
where AhB is the total heated area from the saturation location to the CHF location. The heat balance equation for the boiling length can be expressed as ∗
qBC ·
√ AhB = G∗ XC = D∗ jg∗ = Ku. Af
(4)
Dimensionless flooding-limited CHF can be derived using the simple flooding correlation by Wallis, the mass balance in counter-current flow conditions and the heat balance equations as follows: √ C 2 D∗ ∗ AhB qBC · = . (5) 2 Af [1 + (ρg /ρf )1/4 ] As mentioned above, one of the CHF mechanisms in a very low flow region is the flow pattern transition to annular flow. Ishii (1977) developed the flow transition criterion between the annular and annular-mist flow by using the onset of a droplet entrainment as follows:
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jg ≥
σgρ ρg2
1/4
∗
· qBC
−0.2 Nf ,
GD for Ref = (1 − X) > 1635, µf jg ≥
σgρ ρg2
(6)
1/4
for Ref = (1 − X)
−1/3
−0.2 Nf × 11.78Ref
GD ≤ 1635. µf
∗
GD ≤ 1635 (9) µf The dimensionless churn-to-annular flow transition criterion can be obtained using the existing flow transition criterion as follows:
,
Mishima and Ishii (1984): ∗
jg∗ ≥ (α − 0.11) → qBC ·
(7)
AhB −0.2 = Nf , Af
for Ref = (1 − X)
GD > 1635, µf
AhB −1/3 −0.2 = 11.78Nf Ref , Af
for Ref = (1 − X)
In terms of the dimensionless parameters and heat balance equation (4), these entrainment induced flow transition criterion can be expressed as following dimensionless equations: · qBC
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(8)
√ AhB = D∗ (α − 0.11) Af (10)
Taitel et al. (1980): 3.1 ∗ AhB jg∗ ≥ √ → qBC · = Ku = 3.1 Af D∗
(11)
For high pressure conditions, Mishima and Ishii’s churn-to-annular flow transition criterion has no solution. In this study, Taitel et al.’s churn-to-annular flow transition criterion is used to obtain the dimensionless
Table 2 Dimensionless parameters and equations Dimensionless parameters Taylor wave length scale Hydraulic diameter Mass flux Critical heat flux Boiling critical heat flux Steam superficial velocity Kutateladze number Viscosity number Heat balance equation Flooding-limited CHF at G = 0
√ λ = σ/gρ ∗ D = D/λ G∗ = G/ λρg gρ qC ∗ = qC ∗ / hfg
λρg gρ
∗ = Q /A h qBC BC hB fg
λρg gρ
jg∗ = jg ρg /gρD √ ρg /[gσρ]1/4 Ku = jg √ Nf = µf / ρf σ σ/gρ
√ ∗ · A ∗ ∗ ∗ ∗ qBC hB = GAf XC hfg → qBC · AhB /Af = G XC = D jg = Ku √ 2 2 h ρ gρD C fg g AhB C D∗ ∗ AhB = → qBC · = q · 2 2 1/4 Af Af [1 + (ρg /ρf ) ] [1 + (ρg /ρf )1/4 ]
Onset of droplet entrainment (Mishima and Ishii, 1984) 1/4
For Ref > 1635
jg = [σgρ/ρg2 ]
For Ref ≤ 1635
jg = [σgρ/ρg2 ]
Churn-to-annular transition Mishima and Ishii (1984)
Taitel et al. (1980)
−0.2 ∗ · Nf → qBC
AhB −0.2 = Nf Af
AhB −1/3 −0.2 = Nf × 11.78Ref Af ∗ · A /A )D∗ N −1 where Ref = (1 − X)GD/µf = (G∗ − qBC ρg /ρf hB f f 1/4
−1/3
−0.2 Nf × 11.78Ref
∗ · → qBC
∗ · A /A = ρgD/ρg (α − 0.11) → qBC hB f jg where α = √ 1/4 Co j + 2(σgρ/ρf2 ) 1/4 ∗ jg = 3.1[σgρ/ρg2 ] → qBC · AhB /Af = 3.1
jg =
√
D∗ (α − 0.11) =
√ D∗ jg∗
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heat balance equations at the transition boundary. Detailed dimensionless parameters and equations used in this paper to analyze the flow pattern transition are shown in Table 2. In order to identify the CHF mechanism at low flow conditions mentioned above, dimensionless flow pattern transition lines and a flooding-limited CHF are plotted in Fig. 7. This figure shows that except for the very low mass flux conditions, the measured CHF is far above the churn-to-annular flow transition boundary of Taitel et al. (1980) and the onset of droplet entrainment of Mishima and Ishii (1984). At a low pressure of 0.51 MPa, the dimensionless critical boiling power, ∗ · A /A , under very low mass flux conditions qBC hB f is close to the onset of the entrainment criterion of
Mishima and Ishii (1984). However, at a high pressure of 15.00 MPa under very low mass flux conditions, the critical boiling power is close to the churn-toannular flow transition lines. As the mass flux increases, the CHF mechanism changes consecutively from the flooding, the churn-to-annular flow transition, the onset of the droplet entrainment, and finally to the liquid film dryout in annular flow. The CHF mechanism due to the complete evaporation of the liquid (high quality CHF) is overlapped approximately with the churnto-annular flow transition and the onset of droplet entrainment. The rough maximum mass flux of the CHF occurrence by the churn-to-annular flow transition criterion can be found from the extrapolation of the onset of the droplet entrainment criterion in the turbulent region, Eq. (8), to the complete evaporation line (XC = 1), Eq. (4), as follows: −0.2 G∗B = Nf .
Fig. 7. Flow pattern transition and the present CHF data: (a) P = 0.51 MPa and (b) P = 15.00 MPa.
(12)
Fig. 8 shows that the CHF data are correlated well by the churn-to-annular flow transition criterion of Taitel et al. (1980) for a dimensionless mass flux less than Eq. (12). This result agrees with the experimental results of Mishima and Nishihara (1986), who observed that the CHF data for an internally heated annulus at low flow and low pressure conditions are correlated well by the churn-to-annular flow transition lines of Mishima and Ishii (1984). The churn-to-annular flow transition criterion of Taitel et al. (1980) was derived from the hypothesis that an annular flow cannot exist, unless the vapor velocity in the vapor core is sufficient to lift the entrained droplets. When the vapor flow rate is insufficient, the droplets fall back, accumulate, form a bridge and a churn or slug flow takes place. The churn-to-annular flow transition criterion, Eq. (11), is almost identical to the empirical results for the flow reversal phenomena by Pushkina and Sorokin (1969), who determined the air velocity necessary to lift the liquid film for flooding experiments in tubes varying from 6 to 309 mm in diameter. They correlated the experimental results in terms of the Kutateladze number, except for the constant 3.1 of Eq. (11), which is replaced by the constant 3.2. In general, the flow reversal is defined as the change in flow direction of liquid initially in co-current upflow with a gas as the gas flow rate decreases sufficiently, while the flooding
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Fig. 8. Flow pattern transition criterion of Taitel et al. and the present CHF data: (a) mass flux vs. churn-to-annular flow pattern transition and (b) pressure vs. churn-to-annular flow pattern transition.
is defined as the stalling of a liquid downflow by a sufficient rate of gas upflow in counter-current flow conditions. As shown in Fig. 8, the CHF at a very low flow rate is closely related to the flow reversal phenomena or the churn-to-annular flow transition criterion, which is different with the CHF occurrence due to the flooding. Fig. 9 shows that the current CHF data also are correlated roughly by the complete evaporation criterion of the liquid for the dimensionless mass flux less than Eq. (12). Therefore, the present CHF data are well correlated with the churn-to-annular flow transition criterion of Taitel et al. and the complete evaporation of the liquid for very low mass flux conditions. This trend becomes clearer as the pressure increases. In general,
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Fig. 9. Complete evaporation of the liquid and the present CHF data: (a) mass flux vs. the complete evaporation criterion and (b) pressure vs. the complete evaporation criterion.
the churn-to-annular flow transition criterion underestimates slightly the CHF data while the complete evaporation criterion of the liquid overestimates slightly the CHF data. Thus, the present CHF data fall between the two criteria. 3.3. Comparison with conventional CHF correlations In order to investigate the applicability and prediction capability of the existing CHF correlations on the return-to-power CHF, four existing CHF correlations are used to predict the CHF data in return-to-power conditions. The four CHF correlations are the 1995 CHF look-up table (Groeneveld et al., 1996), EPRI
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rod bundle correlation (Reddy and Fighetti, 1983), Macbeth correlation (1963), and the CHF correlations developed by the present authors (Moon et al., 2002). The CHF look-up table was developed by using extensive worldwide CHF data for round tubes, and is known to predict the CHF reasonably well for most of the conditions. However, it is known that the prediction capability becomes worse in the low flow and low pressure conditions because sufficient CHF data for those conditions are not used in the development of the table. The EPRI rod bundle correlation was developed based on a lot of rod bundle CHF data generated in HTRF at the Columbia University and, at present, it is the most reliable rod bundle CHF correlation which can be used for extensive experimental conditions. Since the applicable range of mass flux is 270–5560 kg/(m2 s), it is necessary to estimate the applicability of the EPRI correlation in return-to-power CHF conditions of very low mass flux conditions. The CHF correlation developed by the present authors uses the dimensionless parameters proposed by Mishima and Nishihara (1986) and predicted well the rod bundle CHF data generated by the present authors (Moon et al., 2002). The CHF correlation of the present authors is as follows: AH ∗ qC,avg,T Af C3 hi = C1 + C2 1 + G∗ + C4 G∗2 , (13) hfg
where C1 = 2.249, C2 = 0.72465, C3 = 0.91215 and C4 = −42.19535 × 10−4 . The local CHF values by the look-up table, EPRI and Macbeth correlations are calculated by assuming a total power applied to the heated section and using the local conditions at various axial locations. If the local heat flux at any axial location is equal to the local CHF value at that position predicted by the correlations, it is assumed that the CHF occurs at that axial location. Table 3 and Figs. 10–12 show the prediction results of the four correlations for the present total data and return-to-power CHF conditions. In general, the look-up table and KAERI correlation predict the av erage CHF, qC,avg,T , reasonably well for the present data including return-to-power conditions. Although the Macbeth correlation shows a large RMS error for the present total data, it predicts the average CHF well for the return-to-power conditions. As shown in Fig. 12, the Macbeth correlation overestimates highly the average CHF for mass fluxes greater than about 350 kg/(m2 s). The EPRI correlation overestimates the average CHF for low mass flux conditions smaller than about 250 kg/(m2 s). This is due to that the applicable range of the EPRI correlation is greater than about 270 kg/(m2 s) as mentioned above. However, the EPRI correlation predicts the average CHF within ±15% for mass fluxes greater than 250 kg/(m2 s). From this comparison, the following consequences are derived: the look-up table, KAERI and Macbeth
Table 3 CHF prediction results of the conventional CHF correlations Parameter
Correlation Look-up table Meana
KAERI
RMS error
Mean error
RMS error
Total database (no. of data = 299) qC,avg,T −0.035 0.128 −0.310 0.440 qC,loc QC,loc 0.045 0.136 ZC 0.157 0.184
0.087 −0.254 0.183 0.160
0.178 0.364 0.269 0.183
0.151 −0.225 0.255 0.164
0.291 0.368 0.390 0.188
0.017 – – –
0.114 – – –
Return-to-power conditions (no. of data = 93) qC,avg,T −0.090 0.124 qC,loc −0.286 0.396 QC,loc −0.031 0.087 0.130 0.160 ZC
0.183 −0.110 0.266 0.132
0.231 0.282 0.333 0.160
−0.052 −0.262 0.009 0.132
0.119 0.383 0.105 0.160
−0.004 – – –
0.114 – – –
a
1 N
N
RMS error
Macbeth
Mean error
Mean error =
error
EPRI
ε , RMS error = i=1 i
N 1 N
ε2 , i=1 i
N = no. of data.
Relative prediction error ε = (predicted value − measured value)/measured value.
Mean error
RMS error
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Fig. 10. Prediction results of the CHF correlations for the present average CHF: (a) total data and (b) return-to-power condition only.
correlations are recommended for the prediction of the average CHF for the return-to-power conditions except very low mass flux conditions. For very low mass flux of about 50 kg/(m2 s), the look-up table and Macbeth correlation underestimate slightly the average CHF while the KAERI correlation overestimates slightly the average CHF. In the viewpoint of the CHF analysis by system codes and subchannel codes, it is important to predict the local CHF value using local conditions parameters such as local quality. Since the look-up table, EPRI and Macbeth correlations are based on the local conditions, they can predict the CHF occurrence location and the local CHF value. On the other hand, the CHF correlation developed by the present authors is based on the inlet conditions, so it is not able to predict the CHF location but only the average CHF for the whole
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Fig. 11. Prediction errors for the present average CHF in the returnto-power condition: (a) mass flux and (b) inlet subcooling.
Fig. 12. Comparison of the CHF correlations with the present CHF data.
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test section. Table 3 shows the prediction results for the local CHF value, qC,loc , critical power up to the CHF location, QC,loc , and the CHF location, ZC , by the lookup table, EPRI and Macbeth correlations. In the present CHF experiment, an accurate first CHF location could not be obtained because the limited numbers of the wall thermocouples were welded to the heater rod surface and immovable. The predicted CHF locations by the look-up table and the two correlations are almost all at the end of the heated section. Thus, the local CHF values are highly underestimated. As examined above, the look-up table, Macbeth and KAERI correlations predict reliably the average CHF value for the return-to-power conditions. Thus, it is possible to use them for the analysis of the return-topower CHF in a steam line break accident. However, the Macbeth correlation is not recommended at high mass flux conditions due to the overestimation of the average CHF. If more accurate values of the total critical power and average CHF are required, the CHF correlation developed by the authors can be used with a further improvement at very low mass flux conditions. The prediction of the CHF location and the local CHF value by the look-up table, Macbeth and EPRI correlations was not satisfactory. Thus, we must draw attention when these correlations are used for the local CHF analysis using system codes and subchannel codes. More CHF data should be generated in low mass flux conditions less than about 100 kg/(m2 s) in order to improve the CHF prediction capabilities of the existing CHF correlation in the return-to-power CHF conditions.
(2)
(3)
(4)
(5)
As the mass flux decreases, the effects of the inlet subcooling and pressure on the CHF become small. The local CHF versus critical quality curve shows two distinct regions due to the change of the main governing process that are quite similar to the previous postulation or analysis result using liquid film dryout model. The low critical quality and high CHF region is characterized by a sharp slope while the high critical quality and low CHF region is characterized by a small slope or nearly constant local CHF with increasing critical quality. The CHF mechanism changes consecutively from the flooding, churn-to-annular flow transition, the onset of a droplet entrainment, and finally to a liquid film dryout in an annular flow as the mass flux increases. The CHF mechanism by the complete evaporation of the liquid (high quality CHF) is overlapped with the CHF occurrence by the churnto-annular flow transition criterion. For a dimensionless mass flux less than Eq. (12), the present CHF data are correlated well by the churn-to-annular flow transition criterion of Taitel et al. (1980). Thus, the CHF at a very low flow and high pressure conditions is closely related to the flow transition and flow reversal phenomena. Although look-up table, Macbeth and KAERI CHF correlations predict reasonably the average CHF in return-to-power conditions, the prediction capability becomes worse at a low mass flux less than about 100 kg/(m2 s). Therefore, it is necessary to improve the CHF correlations by using more CHF data generated in very low mass flux conditions.
4. Conclusions Using a 3 × 3 rod bundle, 3.673 m long, with a symmetric cosine axial heat flux distribution, a CHF experiment has been carried out for water flow under low mass flux and a wide range of pressure conditions. Also, the applicability and prediction capability of the existing CHF correlations for the return-to-power conditions were estimated. From these studies, the following conclusions were obtained: (1) The effects of the mass flux, inlet subcooling and pressure on the CHF are consistent with the general understanding. The effect of mass flux on the CHF is relatively large at low pressure conditions.
Acknowledgement The work presented in this paper was performed under the Long-Term Nuclear R&D Program sponsored by the Ministry of Science and Technology of Korea.
References ANSI/ASME PTC 19.1, 1985. Performance Test Codes, Supplement on Instruments and Apparatus, Part 1, Measurement Uncertainty. ASME, New York.
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309 Biasi, L., Clerici, G.C., Garibba, S., Sala, R., Tozzi, A., 1967. Studies on burnout. Part 3—a new correlation for round ducts and uniform heating and its comparison with world data. Energia Nucl. 14, 530–537. Chun, S.Y., Chung, H.J., Moon, S.K., Yang, S.K., et al., 2001. Effect of pressure on critical heat flux in uniformly heated vertical annulus under low flow conditions. Nucl. Eng. Design 203, 159–174. Chun, S.Y., Chung, H.J., Hong, S.D., Yang, S.K., Chung, M.K., 2000. Critical heat flux in uniformly heated vertical annulus under a wide range of pressures 0.57 to 15.0 MPa. J. Korean Nucl. Soc. 32 (2), 128–141. Chun, S.Y., Moon, S.K., Baek, W.P., Chung, M.K., Aritomi, M., 2003. An experimental study of critical heat flux in nonuniformly heated vertical annulus under low flow conditions. KSME Int. J. 17 (8), 1171–1184. El-Genk, M.S., Haynes, S.J., Kim, S.H., 1988. Experimental studies of critical heat flux for low flow of water in vertical annuli at near atmospheric pressure. Int. J. Heat Mass Transfer 31 (11), 2291–2304. El-Genk, M.S., Rao, D., 1991. On the predictions of critical heat flux in rod bundles at low flow and low pressure conditions. Heat Transfer Eng. 12 (4), 48–57. Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng. 7, 46–62. Groeneveld, D.C., Leung, L.K.H., Kirillov, P.L., et al., 1996. The 1995 look-up table for critical heat flux in tubes. Nucl. Eng. Design 163, 1–23. Ishii, M., 1977. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various twophase flow regimes. ANL Report ANL-77-47. Katto, Y., 1984. Prediction of critical heat flux for annular flow in tubes taking into account the critical liquid film thickness concept. Int. J. Heat Mass Transfer 27 (6), 883–891. Kim, H.C., Baek, W.P., Chang, S.H., 2000. Critical heat flux of water in vertical round tubes at flow pressure and low flow conditions. Nucl. Eng. Design 199, 49–73. Lee, C.S., Kim, H.C., Kim, J.J., Baek, S.S., Lee, B.I., Chun, T.H., Lee, C.C., 1996. A Feasibility Study on the Extended Cycle From the
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Point of View of Non-LOCA Safety Analysis. KAERI Report, KAERI/TR-699/96. Levy, S., Healzer, J.M., Abdollahian, D., 1981. Prediction of critical heat flux in vertical pipe flow. Nucl. Eng. Design 65, 131–140. Macbeth, R.V., 1963. Burn-Out Analysis. Part-4. Application of a Local Condition Hypothesis to World Data for Uniformly Heated Round Tubes and Rectangular Channels. UKAEA Report, AEEW-R267, Winfrith. Mishima, K., Ishii, M., 1984. Flow regime transition criteria for upward two-phase flow in vertical tubes. Int. J. Heat Mass Transfer 27 (5), 723–737. Mishima, K., Nishihara, H., 1986. Critical heat flux at low velocity and pressure conditions. In: Proceedings of the 2nd International Topical Meeting on Nuclear Power Plant Thermal Hydraulics and Operations, April 1986, Tokyo, Japan. Moon, S.K., Chun, S.Y., Choi, K.Y., Park, J.K., Baek, W.P., 2002. Experimental study on the low flow CHF in vertical rod bundle with axial heat flux distribution. In: Proceedings of the Korean Nuclear Society Spring Meeting, May 2002. Park, J.W., Baek, W.P., Chang, S.H., 1997. Critical heat flux and flow pattern for water flow in annular geometry. Nucl. Eng. Design 172, 137–155. Pushkina, O.L., Sorokin, Y.L., 1969. Breakdown of liquid film motion in vertical tubes. Heat Transfer Sov. Res. 1 (5), 56– 64. Reddy, D.G., Fighetti, C.F., 1983. Parametric Study of CHF Data, vol. 2. A Generalized Subchannel CHF Correlation for PWR and BWR Fuel Assemblies. EPRI Report, NP-2609. Schoesse, T., Aritomi, M., Kataoka, Y., Lee, S.R., Yoshioka, Y., Chung, M.K., 1997. Critical heat flux in a vertical annulus under low upward flow and near atmospheric pressure. J. Nucl. Sci. Technol. 34 (6), 559–570. Taitel, Y., Bornea, D., Dukler, A.E., 1980. Modelling flow pattern transitions for steady upward gas–liquid flow in vertical tubes. AIChE J. 26 (3), 345–354. Wheeler, C.L. et al., 1976. COBRA-IV-I: An Interim Version of COBRA for Thermal Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements and Cores, BNWL-1962.
An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions Sang-Ki Moon ∗ , Se-Young Chun, Seok Cho, Won-Pil Baek Thermal-Hydraulic Safety Research Department, Korea Atomic Energy Research Institute, 150 Deokjin-dong, Yuseong-gu, Daejeon 305-353, Republic of Korea Received 27 October 2004; received in revised form 7 March 2005; accepted 17 April 2005
Abstract An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m2 s). © 2005 Elsevier B.V. All rights reserved.
1. Introduction The critical heat flux (CHF) is a thermal hydraulic phenomenon of great importance for the development and safety analysis of nuclear reactors. Most of the ∗ Corresponding author. Tel.: +82 42 868 2229; fax: +82 42 868 8362. E-mail address: [email protected] (S.-K. Moon).
0029-5493/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2005.04.004
CHF studies have been concentrated into the development of the design correlations for CHF prediction at high flow rate and high pressure conditions as expected in light water reactors. Now many aspects of the CHF phenomenon are well understood and reasonable CHF prediction methods are available to predict the CHF at high flow rate conditions corresponding to the normal operating ranges of the light water reactors.
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Nomenclature Af AhB D D* G G* g hfg j j* Ku N Nf P QC,loc
QBC q (Z) qBCT qC,avg,T qC,loc
XC Z ZC
flow area (m2 ) heated area from saturation location to the CHF location (m2 ) hydraulic diameter (m) dimensionless hydraulic diameter (D/λ) (–) mass flux (kg/(m2 s)) dimensionless mass flux (–) gravitational acceleration (m/s2 ) latent heat of vaporization (kJ/kg) superficial velocity (m/s) dimensionless superficial velocity (–) Kutateladze number (–) number of data (–) viscosity number (–) pressure (MPa) critical power (total power at CHF from bottom of the heated length to CHF location) (kW) boiling critical power (critical power from the saturation location to the CHF location) (kW) local heat flux at axial distance Z from the bottom of the heated length (kW/m2 ) boiling length CHF (average heat flux for boiling length) (kW/m2 ) average CHF (average heat flux at CHF for whole heated section) (kW/m2 ) local CHF (local heat flux at CHF location) (kW/m2 ) local critical quality at CHF location (–) axial distance from the bottom of the heated length (m) CHF location (m)
Greeks letters α void fraction (–) hi inlet subcooling (kJ/kg) ρ density difference between liquid and steam (kg/m3 ) ε relative prediction error (predicted value/measure value − 1) (–)
λ µ ρ σ
wave length scale of Taylor instability (m) viscosity (N s/m2 ) density (kg/m3 ) surface tension (N/m)
Subscripts avg average B boundary C CHF f saturated liquid g saturated steam loc local m measured p predicted T total for the whole test section The importance of the critical heat flux at low flow conditions has been generally well known in relation to the nuclear safety during the operational transients and accidents such as a loss-of-coolant accident (LOCA). The CHF phenomenon at low flow conditions is more complicated due to the remarkable effects of buoyancy and flow instabilities. A lot of CHF experiments using round tubes and annuli have been carried out in low flow conditions and the low flow CHF studies using round tubes and annuli show quite good advancements (Mishima and Nishihara, 1986; El-Genk et al., 1988; Park et al., 1997; Schoesse et al., 1997; Kim et al., 2000; Chun et al., 2000, 2001, 2003). However, a lot of these experimental studies have been performed under low (nearly atmospheric) pressure conditions. Thus, in spite of these CHF experiments in low flow conditions, the CHF behavior at low flow conditions is not so well understood, especially at high pressure conditions. Nuclear reactor core consists of fuel rod bundles and there exist some unheated walls such as the control rod and in-core instrumentation guide tubes. It is known that these unheated walls affect the fluid enthalpy distribution and the CHF value. The CHF tests using rod bundles can simulate more closely the nuclear reactor core than round tube or annulus test sections. Therefore, for a practical application of the CHF data to nuclear reactor safety analysis, it is necessary to broaden the CHF data base for rod bundles. Extensive CHF studies using rod bundles have been performed
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mostly for the normal operating conditions of nuclear reactors. However, at low flow conditions, CHF data for rod bundles are very limited, and the applicable design correlations are almost non-existent (El-Genk and Rao, 1991). Although a lot of CHF correlations are available for rod bundles, these correlations would be inappropriate to predict the CHF at low flow conditions because they were developed based mostly on high flow CHF data. During a main steam line break (MSLB) of nuclear reactor, an increased steam flow resulting from a pipe break in the main steam system causes an increased energy removal from the affected steam generator, and consequently the reactor coolant system. One of the important concerns with the MSLB is a return-to-power event after the reactor trip due to reactivity addition caused by increased core cooling. There is a potential to exceed the departure from nucleate boiling (DNBR) at the return-to-power conditions during the main steam line break, especially at the end of the core life (Lee et al., 1996). The reactor power level, DNBR and other safety parameters must not exceed allowable limits for a nuclear reactor safety. We need a reliable CHF correlation to estimate a safety margin of the DNBR limit. The return-to-power conditions in the steam line break accident is characterized by a low mass flux less than about 250 kg/(m2 s), an intermediate pressure, and a high inlet subcooling (Lee et al., 1996). However, there are few available CHF data and no CHF correlations that are reliable and applicable to the low flow and intermediate pressure conditions. Lee et al. (1996) used the Macbeth CHF correlation (1963) to estimate the safety margin of the Korean Standard Nuclear Power plant (KSNP) because it has some conservatism compared with other CHF correlations such as the Biasi correlation (Biasi et al., 1967) and the 1986 AECLUO CHF look-up table (Groeneveld et al., 1986). This analysis raises some questions about the conservatism of the Macbeth correlation because the correlation itself was not compared with actual CHF data in return-topower conditions. Thus, rod bundle CHF data in low flow, intermediate pressure and high inlet subcooling conditions are indispensable for a reliable estimation of the safety margin under the return-to-power conditions during a steam line break accident. For the reasons mentioned above, an experimental study has been performed for water flowing in a 3 × 3 rod bundle with cosine axial heat flux distribution at low
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flow and a wide range of pressure conditions including return-to-power conditions. This paper provides the CHF test results and some considerations on the CHF predictions in relation to the return-to-power conditions during the main steam line break accident. The obtained CHF data are used to analyze the effect of various parameters on the return-to-power CHF, and to estimate the prediction capability and application feasibility of the conventional CHF correlations.
2. Experimental description 2.1. Experimental facility The CHF experiments have been carried out in the reactor coolant system thermal hydraulics loop facility (RCS loop facility) of the Korea Atomic Energy Research Institute (KAERI). The principal operating conditions of the RCS loop facility are: -
operating pressure: 0.5–16.0 MPa; test section flow rate: 0.03–0.3 kg/s; maximum water temperature: 620 K; available heating power of test section: 970 kW.
Fig. 1 shows a schematic diagram of the RCS loop facility (Chun et al., 2001, 2003). It basically consists of a main circulation pump, preheater, CHF test section, steam/water separator, condenser, pressurizer and cooler. The loop is filled with de-ionized water. The flow rate at the test section inlet is controlled by adjustments of the motor speed of the circulating pump and the flow control valves. Water flow rate at the test section is measured by one of three orifices with different measuring ranges. Flow oscillations that are usually observed in low flow conditions are effectively suppressed by a throttle valve installed upstream of the test section. The preheater with a power of 40 kW adjusts the degree of the inlet subcooling of the water entering the test section. The inlet plenum pressure of the test section is maintained at nearly constant values using the pressurizer with an immersion heater of 40 kW. As shown in Fig. 2, the test section has a flow housing (39.8 mm × 39.8 mm) inside the pressure vessel where nine heater rods having a heated length of 3673 mm are located. The heater rods have a symmetric cosine axial heat flux and have a diameter of 9.52 mm and pitch of 12.6 mm. The heater rods are indirectly
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Fig. 1. KAERI RCS thermal hydraulic loop.
heated by alternating current (ac) power. The sheath and heating element of the heater rods are made of Inconel 600 and Nichrome, respectively. Eleven spacer grids with a simple geometry are installed to support
the heater rods in the test section. The spacer grid effects on the CHF might be small in this experiment, because the spacer grids have no mixing vanes and the thermocouples for measurement of the wall tempera-
Fig. 2. Test section and instrumentation.
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Fig. 3. Axial heat flux distribution.
ture are installed just upstream of the spacer grids. To measure the heater rod surface temperatures and detect a CHF occurrence, six or four thermocouples with a sheath diameter of 0.5 mm are embedded on the surface of the heater rods. The temperature measuring points of these thermocouples are located just upstream of the spacer grids at 10, 225, 625, 1025, 1425 and 1825 mm from the top end of the heated section. Sixteen thermocouples of the same type are located in both the inlet and outlet of the heated section to measure the subchannel water temperatures. As shown in Fig. 3, the heated section of the heater rods is evenly divided into 15 steps to simulate a symmetric cosine axial heat flux profile with a minimum and maximum heat flux ratios to an average heat flux of 1.37 and 0.44, respectively. The radial power distribution is uniform so that heater rods have the same power. The system pressure should be defined as the pressure at the exit of the test section because the CHF occurs generally in the upper part of the test section. However, the pressure at the outlet plenum of the test section becomes unstable as the exit quality of the test section becomes large. The flow rates in the present experiments are so low that the pressure drop through the test section is negligible compared with the system pressure. Thus, in the present experiments, the pressures at the inlet plenum of the test section are used as test parameters. In general, the local thermal hydraulic conditions are different among subchannels inside a rod bundle. For exact calculation of the local thermal hydraulic conditions such as local mass flux and quality of subchannels, we need a subchannel analysis code such as COBRA-
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IV-1 (Wheeler et al., 1976). It is said that the existing subchannel codes tend to have an advantage in predicting local conditions at low quality conditions. However, it is difficult to obtain reliable local conditions at high quality conditions using existing subchannel codes. Therefore, in this study, the cross-sectional average values of mass flux and local quality are used for the analysis of the CHF. The critical quality at the CHF location is defined as the cross-sectional average value calculated by using heat balance equation. The measured data such as the pressure, fluid temperature, mass flux, heater rod surface temperature and power to the heater rods are recorded, processed and stored in a data acquisition and control unit. According to a propagation error analysis based on Taylor’s series method (ANSI/ASME PTC 19.1, 1985), the uncertainties of the measured data are estimated from the calibration of the measurement sensors and the accuracy of the related equipments. The estimated maximum uncertainties are less than ±0.3%, ±1.5%, ±0.7 K of the reading values for the pressure, mass flux and temperature, respectively. The uncertainties of the power measurements supplied to the heater rods are less than ±1.8% of the reading values. Before starting a set of experiments, pretests (i.e. heat balance tests) are carried out to estimate a heat loss in the test section. The heat loss in the heated section estimated by the pretests for pressure conditions are less than 2% of the total applied power to the test section. 2.2. Experimental procedure and conditions The CHF experiments are carried out by the following procedures. After setting the water flow rate, inlet subcooling and inlet pressure at the desired values, the electric power to the heater rods is increased gradually in small steps while the test section inlet conditions are kept at constant values. At each power level, the main parameters are allowed to stabilize for several minutes to achieve a steady-state condition before raising the power level again. This process continues until a sharp increase of the wall temperature is observed in the heater rod surface. The CHF conditions are determined to be reached when one of the wall temperatures of the heater rods shows a continuous sharp increase and then become 100 K higher than the saturation water temperature. Whenever the CHF is detected, the heater power is automatically reduced to small val-
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Table 1 Experimental conditions Parameter
Total database
Return-to-power conditions
Pressure, P (MPa) Mass flux, G (kg/(m2 s)) Inlet subcooling, hi (kJ/kg) Critical quality, XC (−) (kW/m2 ) Average CHF, qC,avg,T Total critical power, QC,loc (kW) No. of data
0.47–15.06 49.66–654.44 67.90–729.76 0.34–1.29 77.02–834.62 76.69–828.36 299
5.97–12.08 49.66–250.58 206.59–722.70 0.68–1.27 88.81–470.29 88.37–466.78 93
ues or tripped to prevent any damage of the heater rods. A total of 299 CHF data including 93 CHF data in return-to-power conditions are obtained as shown in Table 1. Considering Lee et al.’s analysis results (1996), in this study, we defined the thermal hydraulic conditions at the return-to-power conditions as those of a low mass flux less than 250 kg/(m2 s), intermediate pressure between 6.0 and 12.0 MPa, and a high inlet subcooling greater than 200 kJ/kg.
Above this pressure and mass flux conditions, most of the CHFs occurred at thermocouple No. 3. Fig. 4 shows the effect of the mass flux on the average CHF for the whole heated section at a CHF
3. Experimental results and discussion 3.1. Characteristics of CHF data In general, a CHF for a vertical flow with uniformly heated rods occurs at the end of the heated section. On the other hand, the CHF with non-uniformly heated rods occurs at the upstream location rather than the end of the heated section. In the present experiment, most of the first CHFs occurred in the heater rods of R1, R2, R7 and R5, and about 60 and 32% of the CHFs occurred at thermocouples No. 3 and 2 (see Fig. 2), respectively. The present CHF data shows that the CHF is more probable in corner regions rather than in the central region since the flow velocity tends to be low and an unheated wall exists in the corner regions (known as “cold wall effect”). In the corner regions, the liquid film in annular flow is distributed on the unheated wall as well as the heater rod surfaces. The liquid film on the heater rod is only directly related to an evaporation process and accordingly to the CHF, although the liquid film exists on the unheated wall. This phenomenon, generally called cold wall effect, affects the CHF. For a pressure and mass flux less than 7.0 MPa and 350 kg/(m2 s), the CHFs occurred evenly at thermocouples No. 2 and 3.
Fig. 4. Effect of the mass flux on the average CHF based on the present measurements: (a) P = 6.0 MPa and (b) P = 12.0 MPa.
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Fig. 5. Effect of the pressure on the average CHF based on the present measurements.
occurrence. As shown in the figure, the average CHF increases as the mass flux increases. The increase rate of the average CHF becomes large with decreasing the pressure so that the effect of the mass flux on the average CHF becomes large at lower pressures. For a low mass flux or high inlet subcooling, the average CHF increases linearly with a steep slope. However, the increase rate of the average CHF becomes small as the mass flux increases, so the average CHF increases slowly. The effect of the inlet subcooling on the CHF becomes small at very low mass flux conditions and this is consistent with the previous understandings (Chun et al., 2001, 2003). Fig. 5 shows the effect of the pressure on the average CHF. At high mass flux conditions, there is a peak CHF value near 3 MPa while at very low mass flux conditions, the effect of the pressure on the CHF is small and hardly appears. In the medium mass flux conditions, the average CHF decreases monotonously as the pressure increases. On the whole, the average CHF for the pressures greater than 3 MPa decreases monotonously or is nearly constant as the pressure increases. Fig. 6 shows the relationship between the critical quality and local CHF at a CHF occurrence location. As the mass flux becomes high, the CHF occurs at a low critical quality, and the local CHF decreases largely with the critical quality. As the mass flux increases, the local CHF decreases for the same critical quality. However, at a low mass flux, the CHF occurs at a high critical quality and the increase rate of the local CHF
Fig. 6. Effect of the local critical quality on the local CHF based on the present measurements: (a) P = 6.0 MPa and (b) P = 12.01 MPa.
is not large as the critical quality increases. As mentioned above, the critical quality was calculated based on the heat balance considering the inlet conditions and applied total heat up to the CHF location. The calculated thermodynamic equilibrium critical quality can be higher than 1 for very low mass flux where countercurrent flow exists at the CHF location. It is somewhat difficult to clearly observe the effect of the local critical quality on the CHF at very low flow conditions, because the thermodynamic equilibrium critical quality used in these analyses is different from an actual flow quality. For a very low mass flux and a critical quality greater than 1, the CHF might occur at a counter-current flow such as flooding. For the high critical quality conditions greater than about 0.9, the local CHF converges into a single curve nearly independent of the mass flux.
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Most of the present CHF data belong to annular flows for which the CHF occurs due to dryout of the liquid film. In general, for a low quality annular flow, the CHF occurs mainly through the balance between droplet entrainment and liquid film evaporation, because the droplet deposition is suppressed by a strong vapor effusion from the liquid film due to high heat fluxes. The low critical quality and high CHF region is characterized by a sharply decreasing curve of the CHF versus the critical quality. In the case of a high quality annular flow, the effects of the entrainment and evaporation of the liquid film on the CHF are small due to a thin liquid film, and the CHF is governed mainly by the deposition of the liquid droplet. Previous analyses (Katto, 1984; Levy et al., 1981) show that in this high quality and low heat flux region, the CHF decreases slowly with increasing the critical quality. Finally, the CHF curve flattens out tending to become horizontal. The CHF versus critical quality curve as shown in Fig. 6 is quite similar to the previous postulation or analysis result using the liquid film dryout model by Katto (1984) and Levy et al. (1981). 3.2. Flow pattern transition and the CHF mechanism
- flow pattern transition from a slug or a churn turbulent flow to an annular flow, and an annular to annular-mist flow; - dryout or breakup of the liquid film in an annular flow; - complete evaporation of liquid (or high quality CHF, critical quality is about 1.0). Mishima and Nishihara (1986) proposed a dimensionless heat flux qC ∗ and a dimensionless mass flux G∗ to provide some understanding on the CHF under low flow and low pressure conditions as follows: ∗
qC =
- flooding-limited CHF at stagnant or extremely very low flow conditions;
(1)
G , λρg gρ
(2)
G∗ =
where the wave √ length scale, λ, is the Taylor instability defined as λ = σ/gρ. For a non-uniform heat flux profile, the dimensionless CHF can be defined as the following equation using the critical power based on the boiling length, QBC , i.e. critical power from the saturation location to the CHF location: ∗
The CHF mechanism and characteristics are closely related to the two-phase flow pattern. Mishima and Nishihara (1986) observed that the CHF for an internally heated annulus occurred when the flow regime changed from a churn flow to an annular flow at low flow rates and low pressure conditions. El-Genk et al. (1988) observed that while the CHF in his smallest annulus always occurred at the transition from an annular to an annular-mist flow, the CHF in the larger annuli occurred either at the churn-to-annular flow transition or at the slug-to-churn flow transition. Since these CHF experiments were performed near atmospheric pressure conditions, there were no experimental observation and analysis for the CHF mechanism at low mass flow and high pressure conditions. The CHF mechanisms are roughly classified as follows in a very low flow region where the mass flux is between several 10 and 100 kg/(m2 s) (Mishima and Nishihara, 1986; El-Genk et al., 1988):
q C hfg λρg gρ
qBC =
QBC , AhB hfg λρg gρ
(3)
where AhB is the total heated area from the saturation location to the CHF location. The heat balance equation for the boiling length can be expressed as ∗
qBC ·
√ AhB = G∗ XC = D∗ jg∗ = Ku. Af
(4)
Dimensionless flooding-limited CHF can be derived using the simple flooding correlation by Wallis, the mass balance in counter-current flow conditions and the heat balance equations as follows: √ C 2 D∗ ∗ AhB qBC · = . (5) 2 Af [1 + (ρg /ρf )1/4 ] As mentioned above, one of the CHF mechanisms in a very low flow region is the flow pattern transition to annular flow. Ishii (1977) developed the flow transition criterion between the annular and annular-mist flow by using the onset of a droplet entrainment as follows:
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309
jg ≥
σgρ ρg2
1/4
∗
· qBC
−0.2 Nf ,
GD for Ref = (1 − X) > 1635, µf jg ≥
σgρ ρg2
(6)
1/4
for Ref = (1 − X)
−1/3
−0.2 Nf × 11.78Ref
GD ≤ 1635. µf
∗
GD ≤ 1635 (9) µf The dimensionless churn-to-annular flow transition criterion can be obtained using the existing flow transition criterion as follows:
,
Mishima and Ishii (1984): ∗
jg∗ ≥ (α − 0.11) → qBC ·
(7)
AhB −0.2 = Nf , Af
for Ref = (1 − X)
GD > 1635, µf
AhB −1/3 −0.2 = 11.78Nf Ref , Af
for Ref = (1 − X)
In terms of the dimensionless parameters and heat balance equation (4), these entrainment induced flow transition criterion can be expressed as following dimensionless equations: · qBC
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(8)
√ AhB = D∗ (α − 0.11) Af (10)
Taitel et al. (1980): 3.1 ∗ AhB jg∗ ≥ √ → qBC · = Ku = 3.1 Af D∗
(11)
For high pressure conditions, Mishima and Ishii’s churn-to-annular flow transition criterion has no solution. In this study, Taitel et al.’s churn-to-annular flow transition criterion is used to obtain the dimensionless
Table 2 Dimensionless parameters and equations Dimensionless parameters Taylor wave length scale Hydraulic diameter Mass flux Critical heat flux Boiling critical heat flux Steam superficial velocity Kutateladze number Viscosity number Heat balance equation Flooding-limited CHF at G = 0
√ λ = σ/gρ ∗ D = D/λ G∗ = G/ λρg gρ qC ∗ = qC ∗ / hfg
λρg gρ
∗ = Q /A h qBC BC hB fg
λρg gρ
jg∗ = jg ρg /gρD √ ρg /[gσρ]1/4 Ku = jg √ Nf = µf / ρf σ σ/gρ
√ ∗ · A ∗ ∗ ∗ ∗ qBC hB = GAf XC hfg → qBC · AhB /Af = G XC = D jg = Ku √ 2 2 h ρ gρD C fg g AhB C D∗ ∗ AhB = → qBC · = q · 2 2 1/4 Af Af [1 + (ρg /ρf ) ] [1 + (ρg /ρf )1/4 ]
Onset of droplet entrainment (Mishima and Ishii, 1984) 1/4
For Ref > 1635
jg = [σgρ/ρg2 ]
For Ref ≤ 1635
jg = [σgρ/ρg2 ]
Churn-to-annular transition Mishima and Ishii (1984)
Taitel et al. (1980)
−0.2 ∗ · Nf → qBC
AhB −0.2 = Nf Af
AhB −1/3 −0.2 = Nf × 11.78Ref Af ∗ · A /A )D∗ N −1 where Ref = (1 − X)GD/µf = (G∗ − qBC ρg /ρf hB f f 1/4
−1/3
−0.2 Nf × 11.78Ref
∗ · → qBC
∗ · A /A = ρgD/ρg (α − 0.11) → qBC hB f jg where α = √ 1/4 Co j + 2(σgρ/ρf2 ) 1/4 ∗ jg = 3.1[σgρ/ρg2 ] → qBC · AhB /Af = 3.1
jg =
√
D∗ (α − 0.11) =
√ D∗ jg∗
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heat balance equations at the transition boundary. Detailed dimensionless parameters and equations used in this paper to analyze the flow pattern transition are shown in Table 2. In order to identify the CHF mechanism at low flow conditions mentioned above, dimensionless flow pattern transition lines and a flooding-limited CHF are plotted in Fig. 7. This figure shows that except for the very low mass flux conditions, the measured CHF is far above the churn-to-annular flow transition boundary of Taitel et al. (1980) and the onset of droplet entrainment of Mishima and Ishii (1984). At a low pressure of 0.51 MPa, the dimensionless critical boiling power, ∗ · A /A , under very low mass flux conditions qBC hB f is close to the onset of the entrainment criterion of
Mishima and Ishii (1984). However, at a high pressure of 15.00 MPa under very low mass flux conditions, the critical boiling power is close to the churn-toannular flow transition lines. As the mass flux increases, the CHF mechanism changes consecutively from the flooding, the churn-to-annular flow transition, the onset of the droplet entrainment, and finally to the liquid film dryout in annular flow. The CHF mechanism due to the complete evaporation of the liquid (high quality CHF) is overlapped approximately with the churnto-annular flow transition and the onset of droplet entrainment. The rough maximum mass flux of the CHF occurrence by the churn-to-annular flow transition criterion can be found from the extrapolation of the onset of the droplet entrainment criterion in the turbulent region, Eq. (8), to the complete evaporation line (XC = 1), Eq. (4), as follows: −0.2 G∗B = Nf .
Fig. 7. Flow pattern transition and the present CHF data: (a) P = 0.51 MPa and (b) P = 15.00 MPa.
(12)
Fig. 8 shows that the CHF data are correlated well by the churn-to-annular flow transition criterion of Taitel et al. (1980) for a dimensionless mass flux less than Eq. (12). This result agrees with the experimental results of Mishima and Nishihara (1986), who observed that the CHF data for an internally heated annulus at low flow and low pressure conditions are correlated well by the churn-to-annular flow transition lines of Mishima and Ishii (1984). The churn-to-annular flow transition criterion of Taitel et al. (1980) was derived from the hypothesis that an annular flow cannot exist, unless the vapor velocity in the vapor core is sufficient to lift the entrained droplets. When the vapor flow rate is insufficient, the droplets fall back, accumulate, form a bridge and a churn or slug flow takes place. The churn-to-annular flow transition criterion, Eq. (11), is almost identical to the empirical results for the flow reversal phenomena by Pushkina and Sorokin (1969), who determined the air velocity necessary to lift the liquid film for flooding experiments in tubes varying from 6 to 309 mm in diameter. They correlated the experimental results in terms of the Kutateladze number, except for the constant 3.1 of Eq. (11), which is replaced by the constant 3.2. In general, the flow reversal is defined as the change in flow direction of liquid initially in co-current upflow with a gas as the gas flow rate decreases sufficiently, while the flooding
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309
Fig. 8. Flow pattern transition criterion of Taitel et al. and the present CHF data: (a) mass flux vs. churn-to-annular flow pattern transition and (b) pressure vs. churn-to-annular flow pattern transition.
is defined as the stalling of a liquid downflow by a sufficient rate of gas upflow in counter-current flow conditions. As shown in Fig. 8, the CHF at a very low flow rate is closely related to the flow reversal phenomena or the churn-to-annular flow transition criterion, which is different with the CHF occurrence due to the flooding. Fig. 9 shows that the current CHF data also are correlated roughly by the complete evaporation criterion of the liquid for the dimensionless mass flux less than Eq. (12). Therefore, the present CHF data are well correlated with the churn-to-annular flow transition criterion of Taitel et al. and the complete evaporation of the liquid for very low mass flux conditions. This trend becomes clearer as the pressure increases. In general,
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Fig. 9. Complete evaporation of the liquid and the present CHF data: (a) mass flux vs. the complete evaporation criterion and (b) pressure vs. the complete evaporation criterion.
the churn-to-annular flow transition criterion underestimates slightly the CHF data while the complete evaporation criterion of the liquid overestimates slightly the CHF data. Thus, the present CHF data fall between the two criteria. 3.3. Comparison with conventional CHF correlations In order to investigate the applicability and prediction capability of the existing CHF correlations on the return-to-power CHF, four existing CHF correlations are used to predict the CHF data in return-to-power conditions. The four CHF correlations are the 1995 CHF look-up table (Groeneveld et al., 1996), EPRI
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309
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rod bundle correlation (Reddy and Fighetti, 1983), Macbeth correlation (1963), and the CHF correlations developed by the present authors (Moon et al., 2002). The CHF look-up table was developed by using extensive worldwide CHF data for round tubes, and is known to predict the CHF reasonably well for most of the conditions. However, it is known that the prediction capability becomes worse in the low flow and low pressure conditions because sufficient CHF data for those conditions are not used in the development of the table. The EPRI rod bundle correlation was developed based on a lot of rod bundle CHF data generated in HTRF at the Columbia University and, at present, it is the most reliable rod bundle CHF correlation which can be used for extensive experimental conditions. Since the applicable range of mass flux is 270–5560 kg/(m2 s), it is necessary to estimate the applicability of the EPRI correlation in return-to-power CHF conditions of very low mass flux conditions. The CHF correlation developed by the present authors uses the dimensionless parameters proposed by Mishima and Nishihara (1986) and predicted well the rod bundle CHF data generated by the present authors (Moon et al., 2002). The CHF correlation of the present authors is as follows: AH ∗ qC,avg,T Af C3 hi = C1 + C2 1 + G∗ + C4 G∗2 , (13) hfg
where C1 = 2.249, C2 = 0.72465, C3 = 0.91215 and C4 = −42.19535 × 10−4 . The local CHF values by the look-up table, EPRI and Macbeth correlations are calculated by assuming a total power applied to the heated section and using the local conditions at various axial locations. If the local heat flux at any axial location is equal to the local CHF value at that position predicted by the correlations, it is assumed that the CHF occurs at that axial location. Table 3 and Figs. 10–12 show the prediction results of the four correlations for the present total data and return-to-power CHF conditions. In general, the look-up table and KAERI correlation predict the av erage CHF, qC,avg,T , reasonably well for the present data including return-to-power conditions. Although the Macbeth correlation shows a large RMS error for the present total data, it predicts the average CHF well for the return-to-power conditions. As shown in Fig. 12, the Macbeth correlation overestimates highly the average CHF for mass fluxes greater than about 350 kg/(m2 s). The EPRI correlation overestimates the average CHF for low mass flux conditions smaller than about 250 kg/(m2 s). This is due to that the applicable range of the EPRI correlation is greater than about 270 kg/(m2 s) as mentioned above. However, the EPRI correlation predicts the average CHF within ±15% for mass fluxes greater than 250 kg/(m2 s). From this comparison, the following consequences are derived: the look-up table, KAERI and Macbeth
Table 3 CHF prediction results of the conventional CHF correlations Parameter
Correlation Look-up table Meana
KAERI
RMS error
Mean error
RMS error
Total database (no. of data = 299) qC,avg,T −0.035 0.128 −0.310 0.440 qC,loc QC,loc 0.045 0.136 ZC 0.157 0.184
0.087 −0.254 0.183 0.160
0.178 0.364 0.269 0.183
0.151 −0.225 0.255 0.164
0.291 0.368 0.390 0.188
0.017 – – –
0.114 – – –
Return-to-power conditions (no. of data = 93) qC,avg,T −0.090 0.124 qC,loc −0.286 0.396 QC,loc −0.031 0.087 0.130 0.160 ZC
0.183 −0.110 0.266 0.132
0.231 0.282 0.333 0.160
−0.052 −0.262 0.009 0.132
0.119 0.383 0.105 0.160
−0.004 – – –
0.114 – – –
a
1 N
N
RMS error
Macbeth
Mean error
Mean error =
error
EPRI
ε , RMS error = i=1 i
N 1 N
ε2 , i=1 i
N = no. of data.
Relative prediction error ε = (predicted value − measured value)/measured value.
Mean error
RMS error
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309
Fig. 10. Prediction results of the CHF correlations for the present average CHF: (a) total data and (b) return-to-power condition only.
correlations are recommended for the prediction of the average CHF for the return-to-power conditions except very low mass flux conditions. For very low mass flux of about 50 kg/(m2 s), the look-up table and Macbeth correlation underestimate slightly the average CHF while the KAERI correlation overestimates slightly the average CHF. In the viewpoint of the CHF analysis by system codes and subchannel codes, it is important to predict the local CHF value using local conditions parameters such as local quality. Since the look-up table, EPRI and Macbeth correlations are based on the local conditions, they can predict the CHF occurrence location and the local CHF value. On the other hand, the CHF correlation developed by the present authors is based on the inlet conditions, so it is not able to predict the CHF location but only the average CHF for the whole
2307
Fig. 11. Prediction errors for the present average CHF in the returnto-power condition: (a) mass flux and (b) inlet subcooling.
Fig. 12. Comparison of the CHF correlations with the present CHF data.
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test section. Table 3 shows the prediction results for the local CHF value, qC,loc , critical power up to the CHF location, QC,loc , and the CHF location, ZC , by the lookup table, EPRI and Macbeth correlations. In the present CHF experiment, an accurate first CHF location could not be obtained because the limited numbers of the wall thermocouples were welded to the heater rod surface and immovable. The predicted CHF locations by the look-up table and the two correlations are almost all at the end of the heated section. Thus, the local CHF values are highly underestimated. As examined above, the look-up table, Macbeth and KAERI correlations predict reliably the average CHF value for the return-to-power conditions. Thus, it is possible to use them for the analysis of the return-topower CHF in a steam line break accident. However, the Macbeth correlation is not recommended at high mass flux conditions due to the overestimation of the average CHF. If more accurate values of the total critical power and average CHF are required, the CHF correlation developed by the authors can be used with a further improvement at very low mass flux conditions. The prediction of the CHF location and the local CHF value by the look-up table, Macbeth and EPRI correlations was not satisfactory. Thus, we must draw attention when these correlations are used for the local CHF analysis using system codes and subchannel codes. More CHF data should be generated in low mass flux conditions less than about 100 kg/(m2 s) in order to improve the CHF prediction capabilities of the existing CHF correlation in the return-to-power CHF conditions.
(2)
(3)
(4)
(5)
As the mass flux decreases, the effects of the inlet subcooling and pressure on the CHF become small. The local CHF versus critical quality curve shows two distinct regions due to the change of the main governing process that are quite similar to the previous postulation or analysis result using liquid film dryout model. The low critical quality and high CHF region is characterized by a sharp slope while the high critical quality and low CHF region is characterized by a small slope or nearly constant local CHF with increasing critical quality. The CHF mechanism changes consecutively from the flooding, churn-to-annular flow transition, the onset of a droplet entrainment, and finally to a liquid film dryout in an annular flow as the mass flux increases. The CHF mechanism by the complete evaporation of the liquid (high quality CHF) is overlapped with the CHF occurrence by the churnto-annular flow transition criterion. For a dimensionless mass flux less than Eq. (12), the present CHF data are correlated well by the churn-to-annular flow transition criterion of Taitel et al. (1980). Thus, the CHF at a very low flow and high pressure conditions is closely related to the flow transition and flow reversal phenomena. Although look-up table, Macbeth and KAERI CHF correlations predict reasonably the average CHF in return-to-power conditions, the prediction capability becomes worse at a low mass flux less than about 100 kg/(m2 s). Therefore, it is necessary to improve the CHF correlations by using more CHF data generated in very low mass flux conditions.
4. Conclusions Using a 3 × 3 rod bundle, 3.673 m long, with a symmetric cosine axial heat flux distribution, a CHF experiment has been carried out for water flow under low mass flux and a wide range of pressure conditions. Also, the applicability and prediction capability of the existing CHF correlations for the return-to-power conditions were estimated. From these studies, the following conclusions were obtained: (1) The effects of the mass flux, inlet subcooling and pressure on the CHF are consistent with the general understanding. The effect of mass flux on the CHF is relatively large at low pressure conditions.
Acknowledgement The work presented in this paper was performed under the Long-Term Nuclear R&D Program sponsored by the Ministry of Science and Technology of Korea.
References ANSI/ASME PTC 19.1, 1985. Performance Test Codes, Supplement on Instruments and Apparatus, Part 1, Measurement Uncertainty. ASME, New York.
S.-K. Moon et al. / Nuclear Engineering and Design 235 (2005) 2295–2309 Biasi, L., Clerici, G.C., Garibba, S., Sala, R., Tozzi, A., 1967. Studies on burnout. Part 3—a new correlation for round ducts and uniform heating and its comparison with world data. Energia Nucl. 14, 530–537. Chun, S.Y., Chung, H.J., Moon, S.K., Yang, S.K., et al., 2001. Effect of pressure on critical heat flux in uniformly heated vertical annulus under low flow conditions. Nucl. Eng. Design 203, 159–174. Chun, S.Y., Chung, H.J., Hong, S.D., Yang, S.K., Chung, M.K., 2000. Critical heat flux in uniformly heated vertical annulus under a wide range of pressures 0.57 to 15.0 MPa. J. Korean Nucl. Soc. 32 (2), 128–141. Chun, S.Y., Moon, S.K., Baek, W.P., Chung, M.K., Aritomi, M., 2003. An experimental study of critical heat flux in nonuniformly heated vertical annulus under low flow conditions. KSME Int. J. 17 (8), 1171–1184. El-Genk, M.S., Haynes, S.J., Kim, S.H., 1988. Experimental studies of critical heat flux for low flow of water in vertical annuli at near atmospheric pressure. Int. J. Heat Mass Transfer 31 (11), 2291–2304. El-Genk, M.S., Rao, D., 1991. On the predictions of critical heat flux in rod bundles at low flow and low pressure conditions. Heat Transfer Eng. 12 (4), 48–57. Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng. 7, 46–62. Groeneveld, D.C., Leung, L.K.H., Kirillov, P.L., et al., 1996. The 1995 look-up table for critical heat flux in tubes. Nucl. Eng. Design 163, 1–23. Ishii, M., 1977. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various twophase flow regimes. ANL Report ANL-77-47. Katto, Y., 1984. Prediction of critical heat flux for annular flow in tubes taking into account the critical liquid film thickness concept. Int. J. Heat Mass Transfer 27 (6), 883–891. Kim, H.C., Baek, W.P., Chang, S.H., 2000. Critical heat flux of water in vertical round tubes at flow pressure and low flow conditions. Nucl. Eng. Design 199, 49–73. Lee, C.S., Kim, H.C., Kim, J.J., Baek, S.S., Lee, B.I., Chun, T.H., Lee, C.C., 1996. A Feasibility Study on the Extended Cycle From the
2309
Point of View of Non-LOCA Safety Analysis. KAERI Report, KAERI/TR-699/96. Levy, S., Healzer, J.M., Abdollahian, D., 1981. Prediction of critical heat flux in vertical pipe flow. Nucl. Eng. Design 65, 131–140. Macbeth, R.V., 1963. Burn-Out Analysis. Part-4. Application of a Local Condition Hypothesis to World Data for Uniformly Heated Round Tubes and Rectangular Channels. UKAEA Report, AEEW-R267, Winfrith. Mishima, K., Ishii, M., 1984. Flow regime transition criteria for upward two-phase flow in vertical tubes. Int. J. Heat Mass Transfer 27 (5), 723–737. Mishima, K., Nishihara, H., 1986. Critical heat flux at low velocity and pressure conditions. In: Proceedings of the 2nd International Topical Meeting on Nuclear Power Plant Thermal Hydraulics and Operations, April 1986, Tokyo, Japan. Moon, S.K., Chun, S.Y., Choi, K.Y., Park, J.K., Baek, W.P., 2002. Experimental study on the low flow CHF in vertical rod bundle with axial heat flux distribution. In: Proceedings of the Korean Nuclear Society Spring Meeting, May 2002. Park, J.W., Baek, W.P., Chang, S.H., 1997. Critical heat flux and flow pattern for water flow in annular geometry. Nucl. Eng. Design 172, 137–155. Pushkina, O.L., Sorokin, Y.L., 1969. Breakdown of liquid film motion in vertical tubes. Heat Transfer Sov. Res. 1 (5), 56– 64. Reddy, D.G., Fighetti, C.F., 1983. Parametric Study of CHF Data, vol. 2. A Generalized Subchannel CHF Correlation for PWR and BWR Fuel Assemblies. EPRI Report, NP-2609. Schoesse, T., Aritomi, M., Kataoka, Y., Lee, S.R., Yoshioka, Y., Chung, M.K., 1997. Critical heat flux in a vertical annulus under low upward flow and near atmospheric pressure. J. Nucl. Sci. Technol. 34 (6), 559–570. Taitel, Y., Bornea, D., Dukler, A.E., 1980. Modelling flow pattern transitions for steady upward gas–liquid flow in vertical tubes. AIChE J. 26 (3), 345–354. Wheeler, C.L. et al., 1976. COBRA-IV-I: An Interim Version of COBRA for Thermal Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements and Cores, BNWL-1962.