MODELING AND ANALYSIS OF THERMAL-HYDRAULIC RESPONSE OF URANIUM-AL- REACTOR FUEL PLATES

UNDER TRANSIENT HEATUP CONDITIONS*

S . Navarro-Valenti S. H. Kim

V. Georgevich R. P. Taleyarkhan

Oak Ridge National Laboratory P.O. Box 2009

Oak Ridge, Tennessee 3783 1-821 8

T. Fuketa K. Soyama K. Ishijima T. Kodaira

Japan Atomaic Energy Research Institute Tokai, Japan

For presentation at the 7th International Meeting on

Nuclear Reactor Thermal-Hydraulics

Saratoga Springs, New York September 10-15, 1995

(NURETH-7)

'The submitted manuscript has been authored by a contractor of the US. Government under con&act DE-ACO5-84OR21400. According&, the US. Government retains a nonexclusive,

royalp3ee license to publish or reproduce the published form of this contribution, or allow others to do so,

for US. Government purposes. I'

*Research sponsored by the Office of Energy Research, U. S. Department of Energy, under contract DE-ACO5-84OR21400 with Martin Marietta Energy Systems, Inc.

c

Modeling and Analysis of Thermal-Hydraulic Response of Uranium-Aluminum Reactor Fuel Plates Under Transient Heatup Conditions

S. Navarro-Valenti, S.H. Kim, V. Georgevich, R.P. Taleyarkhan, Oak Ridge National Laboratory, Oak Ridge, TN.

T. Fuketa, K. Soyama, K. Ishijima and T. Kodaira Japan Atomic Energy Research Institute, Tokai, Japan.

A three-dimensional model to predict the thermal behavior of fuel miniplates has been developed. The possibility of explosive boiling was considered, and it was concluded that the heating rates are not large enough for explosive boiling to occur. However, transient boiling effects were pronounced. Because of the complexity of transient pool boiling and the unavailability of experimental data for the situations studied, an approximation was made that predicted the data very well within the uncertainties present. If pool boiling from the miniplates had been assumed to be steady during the heating pulse, the experimental data would have been greatly overestimated. This fact demonstrates the importance of considering the transient nature of heat transfer in the analysis of reactivity excursion accidents. An additional contribution of the present work is that it provided data on highly subcooled steady nucleate boiling from the cooling portion of the thermocouple traces.

INTRODUCTION

The Advanced Neutron Source ( A N S ) is a user facility currently in the design stage at the Oak Ridge National Laboratory (ORNL). ANS is planned to be a 330-MW research reactor using uranium-silicide cermet fuel in a plate-type configuration. A defense-in-depth philosophy has been adopted for the facility. In response to this commitment, A N S Project management initiated severe accident analysis and related technology development early in the design phase. This was done to aid in designing a robust containment for retention and controlled release of radionuclides in the event of a severe accident. It also provides a means for satisfying on- and off-site regulatory requirements, accident-related dose exposures, and containment response and source-term best estimate analyses for the level-2 and -3 probabilistic risk analyses that will be produced.

As part of the safety evaluation of ANS from the standpoint of damage initiation and propagation, it is necessary to understand the behavior of fuel plates under transient heatup conditions. Effects to be studied are the onset of blistering, bowing, cracking, melting, chemical interactions, and material dispersion leading to steam explosions. For beyond design-basis accidents, damaging transient heatup conditions for ANS-type research reactors may occur due to rapid energy deposition during reactivity insertion accidents from flow blockage accidents.

For the past several years, the Japan Atomic Energy Research Institute (JAERI) has been developing a data base of information related to uranium silicide-fueled plate performance under rapid power deposition conditions. Data have been obtained for fuel plate performance subjected to rapid neutron power bursts in JAERI's Nuclear Safety Research Reactor (NSRR). Tests are conducted with a single fuel plate in a relatively large pool of water, and also with a plate-cluster geometry (wherein narrow gap spacing effects are simulated). The range of temperatures cover heatup to melting and superheating past the phase change boundaries.

The purpose of this paper is to present the model developed to analyze the thermal behavior of the fuel miniplates under pulse irradiation experiments.

1

DESCRIPTION OF THE EXPERIMENT

The NSRR is a modified TFUGA annular core-pulsed reactor with large pulsing capability and a 0.22-m-dim dry irradiation space located at the center of the reactor core to accommodate the test specimens. The pulsing operation is performed by withdrawal of the transient rods from the core. The maximum pulse of 4.7$ (3.41% Ak) produces a peak reactor power of 21,000 MW and a core energy release of 1 17 MJ with a minimum reactor period of 1.13 ms. Details on the reactor configuration and on the experimental data taken for Japanese Material Test Reactor (JMTR) fuel miniplates are given by Yanagisawa et. at. [ 11.

The ANS fuel miniplates consist of a uranium silicide-aluminum mixture located in the center (70 mm long, 25 mm wide and .77 mm thick), surrounded by an aluminum 6061 cladding. The miniplates are 130 mm long, 35 mm wide, and 1.27 mm thick. The instrumentation available consists of five P e t - R h 13% intrinsic thermocouples spot-welded to the surface of the cladding and one thermocouple to measure the temperature of the coolant. The location of the thermocouples is shown in Figure 2.

Typical thermocouple traces obtained for ANS fuel miniplates are shown in Fig. 1. The reactor power and the cumulative reactor energy as functions of time are also shown. As shown in the figure, the reactor power increases monotonically to a peak and then decreases monotonically. The thermocouple traces have a similar behavior, but the peak is reached with some time lag related to the time that it takes the thermal wave to travel from the fuel to the surface of the cladding. At later times, during the cooling period of the plates, the reactor power remains almost constant and at a very low level, and the cumulative reactor energy increases very slowly.

The total energy deposited in the plates was determined by performing gamma scans of the plates at selected times after they were irradiated. These values were confirmed with neutronic calculations. It should be noted that the prompt energy deposited in the plate causes the rapid increase in temperature. This energy was estimated by JAERI's researchers using a point kinetics code and experimentally [2].

Five tests have been performed with single plate configurations. For four of them temperature measurements were obtained. Table 1 contains a description of each of these tests. It includes the homogeneity status (i.e., distribution of fuel particles in plate), the energy deposited in the plates during the pulse, the maximum cladding temperature, and a description of the plate after the test.

-

Table 1 Description of Experimental Tests

Test No. Fuel Energy Peak 0 bservation homogeneity deposited temperature -

c"cj - (a)

518-1 Inadequate 3.3 410 Cracking 518-2 Inadeauate 5.2 700 Me1 tin e 518-3 Adequate 3.5 N/A No failure 518-4 Adequate 2.5 210 No failure 518-5 Adeuuate 5.66 600 Me1 tin E

2

DESCRIPTION OF THE MODEL

A detailed three-dimensional heat conduction model for the ANS fuel miniplates was developed. For this purpose, the heat conduction code HEATING 7 [3] was used. A transient heat source was introduced to simulate the heating process. The temporal dependence of the heat source is the same as the reactor power temporal behavior.

The fuel miniplate was divided into 4 nodes in the thickness direction, 18 nodes in the length direction, and 16 nodes in the direction of the width. A schematic diagram of the fuel plate nodalization is shown in Fig. 2. The fuel was assumed to be homogeneously distributed. The properties of the materials were modeled as functions of temperature and included in HEATING 7 in the form of tables. The melting of pure aluminum in the fuel section was modeled (as occurring at a fixed temperature), and the melting of the alloyed aluminum cladding (Al6061) was approximated by dividing the solidus-liquidus region into 4 equal, discrete phase changes.

To model the boundary conditions, it is necessary to determine the heat transfer coefficient as a function of the wall and coolant temperatures for a very broad range of wall temperatures. Since the water is at room temperature (approximately 2OoC), we are dealing with highly subcooled pool boiling (80°C subcooling).

During the pulse irradiation period, given the very rapid heating of the plate (-1W0C/s), the possibility of explosive boiling of the coolant was considered. Explosive boiling occurs when the fluid reaches the homogeneous nucleation temperature before the surface is completely covered by bubbles (i.e., the presence of active nucleation sites on the surface does not prevent the increase of the temperature to the homogenous nucleation point).

We can estimate the criteria for the occurrence of explosive boiling as follows. It will be assumed that the liquid is saturated initially and that the rate of heating of the liquid adjacent to the surface of the plate is the same as that of the plate itself. Thus, the instantaneous liquid temperature asuming a constant heating rate, will be given by:

T, - T,, = Tit

The fraction of the surface that is covered by bubbles for a given bubble number density (number of bubbles per unit area) is given by:

f = ~ R ~ N

The growth of bubbles early in the boiling process is predicted by the Rayleigh equation [4]. Thus, the radius will be:

For explosive boiling to occur, the liquid must reach the spontaneous nucleation temperature (T?J before the surface is covered with vapor (i.e., before f=l). Thus, the criterion for explosive boiling would be given as:

3

1

From the data obtained by Gaertner and Westwater [5] and Sultan and Judd[6] for a surface heat flux of the order of lo6 W/mz we know that N is at least equal to 106 sitedmz. Blander et. a1.[7] measured the spontaneous nucleation temperature of water of 25OOC. Substituting these values in Eq. (4), we will conclude that explosive boiling can only occur if the rate at which temperature increases is greater than 1.35 x 1070C/s. Even if we assume that explosive boiling occurs at only 13OoC, the temperature rise required would be 5.7 x loS°C/s. The change in temperature as a function of time in the NSRR is of the order of lo"'%, which is clearly smaller than the criterion for explosive boiling to occur.

Thus, we can conclude that the heat transfer phenomena occurring in the tests is not explosive in nature. However, the heating rates are high enough that the boundary layer does not have enough time to respond to the heating rates of the surface. Such a transient pool boiling phenomenon needs to be considered to be able to model the thermal behavior of the fuel plates.

We can divide the overall heatup transient into three different regions:

Region I. Transient heating of the plate before the onset of nucleate boiling Region 11. Transient boiling during the heatup period of the plate (including nucleate and film boiling) Region 111. Transient cooling of the plate after the power level has become small and constant (including nucleate and film boiling)

Analysis of Region I

Since no boiling occurs in this region, the transient heat transfer problem can be addressed by solving simultaneously the transient energy equation of the coolant and the plate. Because the heating periods of the transients are very small, the increasing rate of the surface temperature is loo rapid for natural convection to contribute appreciably to the heat transfer before boiling commences. Goldstein and Briggs [SI developed a model to predict the time necessary for natural convection to develop over a vertical surface. This time is given by:

If we apply this equation to the conditions of the NSRR tests, the time necessary to develop natural convection would be of the order of 1 s, which is clearly much greater than the transient heating time period of the NSRR tests.

Thus, in this region, water can be treated like an infinite solid. The heat conduction equation in the coolant was solved using HEATING 7. This solution was utilized up to the onset of nucleate boiling.

Incipience of boiling in transient pool boiling was studied by Sakurai and Shiotsu [9]. Their experimental results indicate that the incipience of boiling depends on the heating period and the water subcooling. For a subcooling of 75OC and a period of 12 ms, the incipience will occur at 121OC; for a period of 8 ms, at 125OC; and for 5 ms, at 130OC. These data were used in the model to determine the onset of nucleate boiling. Sakurai and Shioutsu [9] also observed that the

4

incipience of boiling occurs near the intersection between the solution of the transient conduction equation in the water and the steady boiling curve.

11 CaSe Period (ms) 9 DNBtr qt'DNB b W D * s t 2 518-1 12 21 3.4 5 18-2 8.3 18 4.0

Analysis of Region II

- .-

5 18-4 I 6.0 5 18-5 5.4

It has been observed in the past by Kawamura et. al. [lo] that for very rapid heating transients, there is not enough time for the boundary layer to respond to the heating rate of the surface. Thus, the boiling phenomena that occur are different from a steady situation. Hall and Harrison (1 11 observed transient heat transfer fluxes that exceeded by a factor of up to ten the maximum heat fluxes for steady pool boiling. It has also been observed that the heat transfer coefficient depends on the period of heating, the peak heating rate, the wall superheat, and the coolant subcooling.

~-

26 I 418 29 5.4

Kawamura et. al. [ 101 reported pool boiling curves for a subcooling of 4OoC, a square secant heating pulse shape, and eight different peak powers. For nucleate boiling, the heat flux increased with increasing surface temperature superheat and reached a maximum value. This is called the transient Departure from Nucleate Boiling (DNB) point. The heat flux maintains a fairly high level even after the DNB point. In addition, the boiling curves depend on the peak power. In the NSRR experiments, each test has a different period and peak power. Thus, to model the heat transfer coefficient accurately, we would need to know the boiling curve for each pair of values of period and power peak for an 80°C subcooling. Given that this information is not available in the literature and that the scope of this work is not to develop a heat transfer correlation for transient boiling, aq approximation to the heat transfer rate has been developed.

The maximum heat transfer rate for transient nucleate boiling at different subcoolings and average periods was reported by Kawamura et. al. [lo], who defined the average period for a given pulse shape as:

This period is constant for an exponential pulse. The average periods for each of the NSRR tests were obtained using this definition and are given in Table 2. For these periods and a subcooling of 8OoC, the DNB heat transfer rate can be obtained by extrapolating Kawamura's data [lo]. Table 2 contains the DNB heat transfer rate for each of the A N S tests.

Table 2 Average Period, Transient DNB Heat Flux and Multiplier for NSRR Tests

The heat transfer rate for transient boiling (excluding film boiling) in the tests was approximated by multiplying the steady heat transfer coefficient by the ratio of the DNF3 transient heat transfer rate to the maximum steady heat transfer rate. This means that the shape of the transient pool

5

boiling curve (for nucleate and transition boiling) has been approximated to the shape of the steady pool boiling curve. Even though we expect the transient pool boiling curve to be different from the steady pool boiling curve, and to be dependent on the peak power, the approximation performed here is good enough to produce reasonable predictions of the experimental data obtained at JAERI.

As shown in Table 2, the average periods for NSRR tests are in the range of 12 to 5.4 ms with a corresponding ratio of transient to steady DNB heat transfer rate varying from 3.8 to 5.4. Thus, the transient nucleate heat transfer rate was approximated as 3.8 to 5.4 times the steady heat transfer rate for these tests.

It has been reported [ 121 that the behavior of heat transfer during transient film boiling follows the same behavior as for steady film boiling. Thus, film boiling was modeled using the steady state values that will be discussed in the description of modeling of region 111 (in the next section).

Analysis of Region III

After the reactor power pulse, the reactor power becomes small and remains approximately constant during the cooling period of the plate. Thus, the question arises as to the time that it takes for a quasi-steady heat transfer rate to develop.

Sakurai et. al. [12] observed that the transient cooling process follows the steady-state nucleate boiling curve. However, the time frame of their transient was one order of magnitude larger than the one present in the NSRR tests.

To obtain information on the heat transfer rates present in Region III, the cooling portion of the curve was used to determine the steady heat transfer coefficient. If we model the plate as one node (i.e., utilize a lumped parameter approach), the energy equation for Region 111 will be given by:

-= dTm q"'V - hA(Tm - T,) mmCpIll dt

Thus, the heat transfer coefficient will be given by:

where cpm is the mass averaged specific heat, given as:

(7)

The heat transfer rate from the surface of the miniplate to the coolant is given as:

4'' = h(T, - T,) (10)

6

The results obtained using Eq. (10) are compared with the steady, highly subcooled heat transfer rate data available in the literature in Fig. 3. As shown in this figure, the heat transfer rates obtained are in the range of values of the steady state heat transfer coefficients. As mentioned in the description of the model for Region 11, transient boiling heat transfer rates for the period and subcooling ranges in NSRR experiments are several times larger than steady boiling heat transfer rates. Thus, these results for Region I11 demonstrate that the heat transfer rates will follow a quasi-steady pool boiling curve.

The results obtained from the NSRR data agree very well with the results obtained by Ohnishi et. al. [ 131. Their data were obtained using fuel rods; thus, geometry does not seem to have great effect on the heat transfer rate in this case. Ohnishi et. al. [13] did not obtain data for the region of nucleate boiling, but only for transition and film boiling. The data obtained in the NSRR tests with ANS plates include only heat transfer rates for temperatures lower than the solidus temperature of A1 606 1.

Thus, for temperatures lower than the melting point of the aluminum, the heat transfer coefficient obtained from the data will be used. For larger temperatures, the data of Ohnishi et. al. [I31 will be utilized.

As demonstrated by Bradfield [ 141, for steady-state heat transfer, the coolant subcooling has great influence on the heat transfer coefficient and on the critical heat flux. Several authors have studied highly subcooled steady pool boiling [13,14,15,16]. However, to the knowledge of the authors, there are no data available for a vertical plate geometry. Thus, one contribution of the present work is to provide data for highly subcooled steady nucleate and transition pool boiling from a vertical plate.

RESULTS

From the results obtained using the three-dimensional model it can be noted that, the temperature difference between the center of the fueled region and the surface of the cladding (in the direction of the thickness) is of the order of 10%. The temperature at the interface between the Xueled and unfueled regions (in the direction of the length and width) was noted to be generally about 20% smaller than the temperature at the thermocouple 5 (TC5) location. In addition, the temperature difference between the different locations of the thermocouples is less than 1% (since we assumed homogenously distributed fuel). Considering the above, and for the sake of clarity, the location of TC5 (at center of thermocouple cluster) has been chosen to display predicted results and to compare them with the experimental data in the discussion that follows.

To illustrate the, importance of recognizing the transient nature of pool boiling in Region 11, case 518-4 was modeled using a steady state heat transfer coefficient for Region 11. The results that are obtained are shown in Fig. 4. As presented, the temperature traces are overpredicted by -100% if the fact that transient boiling is occurring during the heatup period is not recognized.

The error due to the fin effect of the thermocouples was estimated using a three dimensional model of the thermocouple spot welded to a portion of the fuel miniplate. The results obtained indicate that an error of the order of 10% can be expected because of this effect.

The results obtained for case 518-4 using the approximation for the heat transfer coefficient in Region I1 and the model described in the preceding section are shown in Fig. 5. As presented in the figure, the predictions obtained for Region I1 using the approximation for the heat transfer coefficient produces results that only slightly overpredict (+12%) the experimental data for the peak temperature. However, this variation is well within the overall uncertainties of the measurements. In addition, the cooling portion of the curve is predicted very well within the

7

uncertainty of the data. This means that the steady heat transfer coefficient values that are being used in Region I11 of the experiment correctly represent the data.

Figure 6 contains the predictions for test 518-1. In this case, the predictions are in very good agreement with the experimental data. The variation between the thermocouple readings for this test is greater than in test 518-4. This is caused by the inhomogeneities present in fuel miniplates used for tests 5 18- 1 and 5 18-2.

The predictions obtained for test 518-2 are presented in Fig. 7. Melting of the aluminum is predicted, and the predictions are within the range of experimental values. In this case, the analysis of the plates after the test indicated that the center region of the plate had completely melted (corresponding to TC 5). As observed in Fig. 7, there are strong variations in the thermocouple readings for this test. This is partly due to inhomogeneities present in the first two miniplates. In addition, after melting occurs, the possibility exists that the thermocouples will relocate or penetrate deeper into the thickness of the miniplate. Thus, thermocouple 5 could be measuring the temperature of the fuel instead of the cladding after melting has occurred. This aspect was c o n f m e d via destructive examination of the A N S miniplates.

The results for test 518-5 are shown in Fig. 8. In this case, more melting than in case 518-2 was predicted and experimentally observed. The results obtained are in the range of variation of the experimental data. However, it seems that one of the thermocouples malfunctioned after melting occurred.

SUMMARY AND CONCLUSIONS

To understand the structural behavior subsequent to transient heating of ANS fuel miniplates, it is necessary to model the thermal behavior. A three-dimensional model of the fuel miniplates has been developed. This model includes the heat transfer analysis of highly subcooled nucleate and film boiling. Given the large heating rates present in these tests, the possibility of the occurrence of explosive boiling was considered. It was concluded that no explosive boiling will occur under the heating rates existent in the NSRR tests.

The heat deposition rates in NSRR do cause transient pool boiling to occur during the time frame of the reactor pulse. Thus, the transient was divided into three temporal regions:

Region I. Heating of the plate before the onset of nucleate boiling Region 11. Heating of the plate with transient nucleate and film pool boiling Region III. Cooling of the plate after power has become small and fairly constant

It was determined that for the time frame of the transients occumng in NSRR tests, no natural convection would develop. Thus, the coolant was treated as an infinite solid for temperatures lower than the onset of nucleate boiling during the heating of the plate (Region I).

Due to the complex behavior of transient boiling and to the unavailability of experimental data in the literature for our specific situation, an approximation to the transient heat transfer coefficient in Region I1 was performed. The results obtained using this approximation predicted the experimental data very well, within the uncertainties of the data. If a steady state heat transfer coefficient in this region is used, the experimental data are greatly overpredicted. Thus, the importance of considering the transient nature of heat transfer in Region II was demonstrated.

By determining the heat transfer rates to the coolant from the cooling portion of the tests (after the reactor power has tapered off), and comparing it to the steady heat transfer rates for highly subcooled pool boiling, it was concluded that the heat transfer rate occurring in Region I11

8

follows the steady pool boiling curve. The exact time at which transient heat flux becomes quasi- steady is not known. Thus, the transition was assumed to occur at the moment the power tapers off.

To the knowledge of the authors, there are no data available in the literature for nucleate boiling in the conditions present in these tests. Thus, an additional contribution of this work consists on providing data for highly subcooled nucleate and transition boiling from a vertical plate.

Acknowledgements

The authors acknowledge the consulting advice provided by M. Epstein of Fauske & Associates, Inc., Chicago, IL, dealing with explosive boiling and steady state highly subcooled boiling.

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recorn- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

9

LIST OF SYMBOLS

A

? g h k L m N P 9

R T t V

q"'

Cross sectional area (0.07 m x 0.025 m) [m2] Specific heat [J/kgK] Fraction of surface covered by bubbles Gravity acceleration [m/s2] Heat transfer coefficient [W/Km2] Thermal conductivity [WKm] Length of heated section of plate (0.07 m) [m] Mass of fuel plate [kg] Number density of bubbles [ l/m2] Pressure [Pa] Heat flux to coolant [W/m2] Volumetric heat generation in plate [w/m3] Radius of bubble [m] Temperature [ "C] Time [SI Volume [m3]

Greek symbols

a P P Density [kg/m3] z 6 Dummy variable

Thermal diffusivity of coolant [m2/s] Coefficient of thermal expansion [ l/K]

Average period of pulse defined by Eq. (6) [SI

lndexes

NC DNB

f 1 m sat sn

C

St tr W

Nucleate boiling onset Departure from nucleate boiling Cladding Fuel Liquid coolant Miniplate considered as one node Saturated Spontaneous nucleation Steady Transient Surface of the cladding

10

REFERENCES

[ 11 Yanagisawa,K , Fujishiro, T., Kazuhiko, S., Ichikawa, H. and Kodaira, T., "Dimensional Stability of JAW Enriched Uranium Silicide Plate-Type Fuel for Research Reactors at Transient Conditions", J. Nucl. Sc i. Tech. 39., 233-243 (1992).

[2] Ohnishi, N. and Inabe, T., "Evaluation of Effective Energy Deposition in Test Fuel During Power Burst Experiment in NSRR" J. Nucl. Sci. Tech.. 19,528-542 (1982).

[3] Childs, K.W., "Heating 7.2b Multidimensional, Finite-Difference Heat Conduction Analysis", RSIC Peripheral Shielding Routine Collection. ORNUTM- 12262 (1993).

[4] Hsu, Y-Y, Graham, R. W., "Transport Processes in Boiling and Two-Phase Systems", Mc. Graw-Hill, p. 18 (1976).

[5] Gaertner, R. F. and Westwater, J. W., "Population of Active Sites in Nucleate Boiling Heat Transfer", Chem. EnFr. Prog. Sv mD. - Se ries 56 , 39-48 (1960).

[6] Sultan, M., and Judd, R. L., "Spatial Distribution of Active Sites and Bubble Flux Density", J. Heat Transfer, JQQ, 56-62 (1978).

[7] Blander, M., Hengstenberg, D., and Katz, J. L., "Bubble Nucleation in n-Pentane, n -Hexane,

[8] Goldstein, J. and Briggs, D. G. "Natural Convection from Vertical Surfaces", Trans. ASME, J. Heat Transfer 86, No. 4 (1964).

n-Pentane +Hexadecane Mixtures and Water", J. Phvsical Che mistrv 75 , 3613-3619 (1971).

[9] Sakurai, A. and Shiotsu, M., "Transient Pool Boiling Heat Transfer", Trans. ASME, J. Heat Transfer 99, 554-560 (1964).

€101 Kawamura, H., Fujio, T., Akiyama, M., "Heat Transfer and DNB Heat Flux in Transient Boiling". 4th. Intl. Heat Transfer Conference, Versailles (1970).

[ 113 Hall, W.B., Harrison, W.C., "Transient Boiling of Water at Atmospheric Pressure", 3rd. Intl. Heat Transfer Conference, Chicago, vol. 3 (1966).

[ 121 Sakurai, A., Shiotsu, M., Hata, K., "Transient Boiling Caused by Vapor Film Collapse at Minimum Heat Flux in Film Boiling", Nucl. Enprp Des. 99, 167-175 (1987).

[ 131 Ohnishi, N.,Ishijima, K., Tanzawa, S., "A Study of Subcooled Film-Boiling Heat Transfer Under Reactivity-Initiated Accident Conditions in Ligth Water Reactors", 33 1-341 (1984).

[ 141 Bradfield, W.S., "On the Effect of Subcooling on Wall Superheat in Pool Boiling", J. Heat Transfer 89, 269-270 (1967).

[ 151 Siviour, J.B., Ede, A.J., "Heat Transfer in Subcooled Pool Film Boiling", 4th Intl. Heat Transfer Conference, Versailles (1970).

[ 161 Lauer, H. and Hufschmidt, W., "Heat Tranfer and Surface Rewet During Quenching", Two- Phase Flows and Heat Transfer, Proc. NATO Advanced Study Institute, Vol. 2, 1310, Hemisphere Publishing Corp. (1977).

11

TC1

Tc2 I.................

0.28 0.35

t [SI

Fig. 1 Typical Data Obtained from NSRR for Each Test.

12

Coolant

0.77 - TCI

\ h --,*

Coolant

0 b

TC3 /

- 1.27

All dimensions are in mm.

35 - 25

11.25

17.5 e-----, 23.75

Fig. 2 Schematic Diagram of Fuel Plate Nodalization.

13

q" [MWlmZ] 3

0 0

._c)_I q" Data

q" Ohnishi -....+.....

250 5 0 0 7 5 0

Tw ["C]

1000 1250

Fig. 3 Comparison of Heat Transfer Coefficient from Cooling Region of Data with Steady Heat Transfer Coefficients by Other Authors.

14

400

300

200

100

TCalcuiated

0.3 0.325 0.35 0.375 0.4

t [SI

Fig. 4 Predictions and Experimental Data for Case 518-4 Assuming Steady Pool Boiling in Region II.

15

400

TC1

TC2 I-............

TC4

TC5 -------

0 . 3 0.325 0.35 0.375 0.4

t [SI

Fig. 5 Predictions and Experimental Data for Case 518-4.

16

600

500

400

T [“CI

300

200

100

0 0.3 0.35

Fig. 6 Predictions and Experimental Data for Case 5 18- 1.

0.4

17

800

600

Tc1

TC2

Tc3

Tc4

Tc5

T calculated

0.5 1

Figure 7. Predictions and Experimental Data for Case 5 18-2.

1.5

18

600

400 T S'CI

200

0

518-5

I TC 1

x 2

TC3

TC4

TC5

T calculated

, 0.4 0.6 0.8 1 1.2

tis1

Fig. 8 Predictions and Experimental Data for Case 5 18-5.

19