STUDY OF FUKUSHIMA DAIICHI NUCLEAR POWER STATION UNIT 4 SPENT-FUEL POOL

Transcription

1 STUDY OF FUKUSHIMA DAIICHI NUCLEAR POWER STATION UNIT 4 SPENT-FUEL POOL RADIOACTIVE WASTE MANAGEMENT AND DISPOSAL KEYWORDS: Fukushima Daiichi, spent-fuel pool, evaporation DEAN WANG,* IAN C. GAULD, GRAYDON L. YODER, LARRY J. OTT, GEORGE F. FLANAGAN, MATTHEW W. FRANCIS, EMILIAN L. POPOV, JUAN J. CARBAJO, PRASHANT K. JAIN, JOHN C. WAGNER, and JESS C. GEHIN Oak Ridge National Laboratory, 1 Bethel Valley Road #6167, Oak Ridge, Tennessee Received December 12, 2011 Accepted for Publication January 5, 2012 A study on the Fukushima Daiichi nuclear power station spent-fuel pool (SFP) at Unit 4 (SFP4) is presented in this paper. We discuss the design characteristics of SFP4 and its decay heat load in detail and provide a model that we developed to estimate the SFP evaporation rate based on the SFP temperature. The SFP level of SFP4 following the March 11, 2011, accident is predicted based on the fundamental conservation laws of mass and energy. Our predicted SFP level and temperatures are in good agreement with measured data and are consistent with Tokyo Electric Power Company evaluation results. I. INTRODUCTION The accident at the Fukushima Daiichi nuclear power station ~NPS! in Japan is one of the most serious accidents in commercial nuclear power plant operating history. Recently, a study on the spent-fuel pool ~SFP! of Fukushima Daiichi Unit 4 a ~SFP4! was performed at Oak Ridge National Laboratory ~ORNL!. This paper summarizes key findings and conclusions from this study and provides insight into conditions at SPF4 following the earthquake and tsunami of March 11, We present conclusions on such important issues as initial water level and fuel uncovery and heatup based on modeling and simulation results. II. CHRONOLOGY OF SFP4 The condition of SFP4 and the emergency responses taken after the earthquake and tsunami are described in a In this paper, all references to Unit 4 are to Fukushima Daiichi Unit 4. * wangda@ornl.gov reports prepared by the Japanese government for the International Atomic Energy Agency 1,2 ~IAEA!. Unit 4 was shut down and had been in a refueling outage since November 29, All of the fuel had been removed from the reactor and placed in the SFP to facilitate shroud work within the reactor. The reactor was disassembled with the head cover removed at the time of the earthquake. The cavity gates were installed, isolating the SFP from the upper pools. The SFP water temperature was ;278C. At 2:46 p.m. on March 11, 2011, the off-site power supply to the Fukushima Daiichi NPS was lost due to the Tohoku earthquake; however, alternating-current power was maintained since emergency diesel generators started and loaded properly with Unit 4 s diesel generator 4B ~DG4B! and Unit 4 s diesel generator 4H ~DG4H!. Unit 4 s diesel generator 4A ~DG4A! was in maintenance outage. At 3:38 p.m., the tsunami, generated by the Tohoku earthquake, struck the the Fukushima Daiichi NPS and flooded DG4H; the remaining DG4B became inoperable by flooding the seawater pump and associated electrical panel, which made the redundant SFP cooling unavailable. On March 15, a hydrogen explosion occurred in the Unit 4 reactor building. This was unexpected since there NUCLEAR TECHNOLOGY VOL. 180 NOV

2 was not enough decay heat in the SFP to result in overheating and the subsequent high-temperature interaction of zirconium and water to produce hydrogen gas. On March 16, a helicopter flew close to the operating floor of Unit 4, at which time the water surface of the SFP could be seen, but no exposed fuel was observed. On March 20, a water-spraying truck provided by the Japanese Self-Defense Force ~SDF! sprayed freshwater into the SFP. By March 21, ;250 tons of water had been sprayed into the SFP from the ground. On March 22, a concrete pump truck began spraying seawater into the SFP, and by June 14, ;5700 tons of water had been added to the SFP as a result ~freshwater spraying had resumed after March 30!. On June 16, water injection by a temporary SFP injection facility was started, and by July 31, ;280 tons of water had been injected by this facility. On June 19, water injection from the in-core-monitor piping to the reactor well and the dryer and separator ~DS! pit was performed to reduce the level of radiation coming from the in-core structure stored inside the DS pit. On June 31, SFP water cooling by the alternative cooling system was started. The water temperature was ;758C when the cooling was started and reached a steady condition on August 3, when the water temperature stabilized at 408C. The SFP water was sampled using the concrete pump truck on April 12, April 28, and May 7. Outflow water from the SFP to the skimmer surge tank was sampled on August 20, and nuclide analysis of the water was conducted. Analysis results indicated that most of the fuel in the SFP was in sound condition. III. ANALYSIS OF SFP4 III.A. SFP4 Design Characteristics, Fuel Inventory, and Decay Heat Unit 4 employs a Mark I containment, as shown in Fig. 1. The elevated SFP is located in the secondary containment. The Unit 4 reactor was shut down for core shroud replacement on November 29, A total of 548 reactor fuel assemblies was removed from the core and stored in the SFP after the shutdown. In addition to these recently discharged fuel assemblies, the SFP also contains 783 older spent fuel assemblies discharged from previous refuelings and 204 fresh assemblies. All of the fuel assemblies are stored vertically in the fuel storage racks sitting on the SFP floor. The total of 1535 fuel assemblies occupies ;95% of the total storage capacity of the SFP. A typical boiling water reactor ~BWR! SFP is rectangular in cross section and ;12 m ~40 ft! deep. The SFP walls are constructed of reinforced concrete typically having a thickness between 1.2 to 2.4 m ~4to8ft!. The SFPs contain a 6- to 13-mm ~ 1 4 _ -to 1 2 _ -in! thick stainless steel liner, which is attached to the inside walls with studs Fig. 1. Schematic of a typical Mark I containment. ~Courtesy of Wikispaces. 3! embedded in the concrete. The inside geometric dimensions of SFP4 are 12.2 m ~length! 9.9 m ~width! 11.8 m ~depth!. In SFP4, all of the fuel assemblies are stored vertically in 53 fuel storage racks, as shown in Fig. 2. The number in each numbered box denotes the cooling time in years for the stored fuel assembly. The red boxes are those fuel assemblies recently off-loaded from the core; the gray boxes are the fresh assemblies ~color online only!. The fuel storage racks are of a high-density design in a3 10 configuration. The rack dimensional data used in our analysis are based on the drawing of a spent-fuel storage rack, which is similar to the racks of SFP4. Each rack has 30 storage cells, each m square. The separation walls between cells are made of stainless steel. The total height of the racks is 4.44 m. The baseplate is 0.14 m in height and has holes on each side to allow SFP water circulation. The bottom of each cell has a m vertical hole, which houses the nose of the fuel assembly. All of the racks sit on floor pads. In this analysis, the rack floor pad is assumed to be m in height. SFP4 contains 204 fresh STEP-3B fuel assemblies, 548 recently discharged STEP3-B fuel assemblies, 188 older STEP3-B fuel assemblies, 560 older STEP2 fuel assemblies, 30 older 8x8BJ fuel assemblies, 4 older 8x8 fuel assemblies, and 1 older 7x7RD fuel provided by Tokyo Electric Power Company ~TEPCO!#. It is noted that typical General Electric design parameters ~rod diameter, rod pitch, etc.! for these assemblies are used in our analysis because specific design data for each fuel type is not available. Decay heat produced by spent fuel varies strongly with the time since the bundle was discharged from the core as well as the operating conditions and burnup. In 206 NUCLEAR TECHNOLOGY VOL. 180 NOV. 2012

3 Fig. 2. SFP4 fuel loading. SFP4, the decay times of interest range from 100 days to 30 yr. Because actual operating conditions for each fuel assembly are always difficult to obtain, some approximations have to be made to calculate the decay heat of spent fuel. In this study, the decay heat in SFP4 was calculated using ORIGEN. Table I summarizes the assembly design and the decay heat for each fuel type based on its cooling time. The calculated total decay heat on March 11, 2011, in SFP4 is ;2.28 MW, of which ;82% is produced by the 548 recently discharged fuel assemblies with 101 days of cooling. Figure 3 shows the predicted decay heat as a function of cooling time for all of the fuel of SFP4. The accuracy of the prediction should be within 62.4% of actual values. 4 It is noted that the TEPCO-calculated decay heat was 2.26 MW as of March 11 and 1.58 MW as of June 11 ~Ref. 2!. III.B. SFP Evaporation Model In a loss-of-pool-cooling event, the decay heat of the spent fuel will heat up the SFP. Heat will eventually leave the SFP by conduction through the side walls and the floor, SFP surface thermal radiation, air convection on the surface, and evaporation or boiling. For a typical BWR SFP, heat loss by wall conduction or convection from the SFP water surface is usually less than a few percent of the total decay heat load of the SFP; for NUCLEAR TECHNOLOGY VOL. 180 NOV

4 TABLE I SFP4 Fuel Inventory and Decay Heat Fuel Type Assembly Configuration Number of Fuel Assemblies Discharge Data Cooling Duration as of March 11, 2011 ~yr! Average Assembly Decay Heat as of March 11, 2011 ~W! 7 7RD September 26, September 2, BJ February 26, April 21, March 19, May 17, STEP March 19, May 17, October 2, September 16, June 25, October 2, February 11, March 28, STEP3-B October 2, March 28, September 29, November 30, STEP3-B Fresh Fuel In this paper, we derive an evaporation model for calculating the SFP evaporation rate based on an analogy between the heat transfer and mass transfer for the free convection at the SFP surface. For a typical BWR SFP, the Rayleigh number Ra L is.10 7 for the surface natural convection heat transfer; hence, the heat transfer Nu number for the SFP surface can be readily calculated by 5 Nu 0.15~Ra L! ~GrPr! 103 Fig. 3. Decay heat in SFP4. example, it is,5% of the total decay heat in SFP4. And, surface thermal radiation to the atmosphere is,3% of the total decay heat load for SFP4. When the SFP temperature increases above 708C, the evaporation on the SFP surface becomes significant in taking away heat and water from the SFP. Therefore, an accurate prediction of water evaporation plays a very important role in analyzing the energy and mass balance of the SFP, in particular, early heatup, and SFP temperature. ~10 7 Ra L 10 11!. ~1! So, in analogy to heat transfer, the Sherwood number Sh can be calculated as Sh k v l 0.15@~Gr Gr m!sc# 103 rd AB 0.15{ gl 3 b~t N 1 T 0! gl 3 z~v N A1 v A0! v 2 v 2 { v 103 D AB, ~2! 208 NUCLEAR TECHNOLOGY VOL. 180 NOV. 2012

5 where k v mass transfer coefficient or evaporation coefficient l SFP characteristic length r air density D AB vapor-air diffusivity Gr thermal Grashof number Gr m mass diffusional Grashof number Sc v Schmidt number D AB v air kinematic viscosity bn 1 ]r r ]T P zn r 1 ]r ]v A P, T Wang et al. v A1 vapor mass fraction in the saturated air at the same temperature as the SFP surface water temperature v A0 vapor mass fraction in the air at the atmospheric air temperature T 1 SFP surface water temperature T 0 atmospheric air temperature. Note that the thermal Grashof number in Eq. ~2! is replaced by the sum ~Gr Gr m! and that the Prandtl number Pr is replaced with the Schmidt number Sc. This simplification is widely used for the air-water system, where the small difference between the Sc and Pr numbers does not have a significant effect. 6 Hence, we have the mass transfer coefficient or the evaporation coefficient as k v rd AB Sh. ~3! l Normally, the diffusional Grashof number Gr m is much less than the thermal Grashof number Gr; therefore, we can often omit the second term in the brackets of Eq. ~2!. From Eq. ~2! we can see that the evaporation coefficient is dependent on temperature it increases as the water surface temperature increases because free convection flow is enhanced by the increased surface temperature. Finally, the evaporation rate can be calculated with the equation as W A0 k v A v A1 v A0 1 v A1, ~4! where W A0 water evaporation rate ~kg0s! A SFP surface area ~m 2!. However, it should be noted that there are uncertainties in any actual situation and the boundary layer model on which the evaporation model is essentially based. For example, the free convention flow could be disturbed by the wind. In addition, the uncertainty in the SFP surface heat transfer area caused by water ruffling should be studied further. It is worth mentioning that our evaporation model is in very good agreement with an engineering empirical model presented in Ref. 7. For air at 208C and 50% relative humidity, the water ~vapor! mass ratio in the air v A Using Eq. ~4!, the evaporation rates for various SFP temperatures for SFP4 with A m 2 are calculated and summarized in Table II. In addition, the heat supply for maintaining the SFP water temperature can be calculated based on the evaporation rate. These values are given in Table II for each SFP water temperature. It should be noted that the atmospheric air temperature at the Fukushima NPS was,58c in March 2011, and,208c in May The actual v A0 for SFP4 would be even smaller than As compared to the v A1 values in Table II, v A0 is so small that it can be omitted in calculating the evaporation rate. Figure 4 shows the evaporation rate and heat supply as a function of SFP temperature. From Fig. 4, the evaporation rate can be found for any SFP temperature. In addition, for any decay heat load of the SFP, one can find the equilibrium temperature the SFP may finally reach and the evaporation rate as well. The so-called equilibrium temperature is the maximum temperature that an SFP can reach with a certain decay heat load. Figure 4 can also be used for any other SFP with a different surface area. The evaporation rate is linearly proportional to the SFP surface area, so it can be estimated based on the ratio of the SFP surface area to m 2. It is interesting to make some simple calculations. For example, the SFP will daily lose 2 tons of water when the SFP temperature is at 408C. The water loss would increase to 86 tons when the SFP temperature reaches 87.58C, which means that such an evaporation rate would take away all the decay heat of SPF4 without reaching the boiling temperature. It should be pointed out that this analysis is very important to understand the SFP temperature data collected in SFP4. SFP4 would reach the equilibrium temperature within 2 days during the loss of SFP cooling with a total decay heat of 2.28 MW. We should not expect any observable changes in the SFP temperature over a short time ~days to months! during a loss-ofcooling event since the decay heat change is small. We will discuss this later in the paper. In addition, the evaporation rate at the equilibrium temperature can be calculated simply based on the energy balance between the evaporation rate and decay NUCLEAR TECHNOLOGY VOL. 180 NOV

6 TABLE II Calculated Evaporation Rates for SFP4 SFP Temperature ~8C! Saturated Vapor Pressure k v ~Pa! v A1 v A0 ~kg0m 2 {s! Evaporation Rate ~kg0s! Heat Supply to Maintain Temperature ~MW! ; Fig. 4. Evaporation rate and heat supply. heat, which means all decay heat is used to evaporate water: Evaporation Rate at the Equilibrium Temperature Decay Heat, ~5! h v h l where h v h l is the water latent heat between the water liquid and vapor phases. The water latent heat has a very weak dependence on temperature. III.C. SFP Level and Temperature Prediction At 3:38 p.m. on March 11, 2011, SFP4 lost its cooling and water supply, and the SFP started to heat up. Within 2 days, the SFP water temperature would reach the equilibrium point where the heat loss through evaporation was equivalent to the decay heat load of the SFP. Thereafter, the SFP level would drop continuously at an almost constant rate of 0.7 m0day before reaching the top of the fuel storage racks. 210 NUCLEAR TECHNOLOGY VOL. 180 NOV. 2012

7 When the SFP level is higher than the top of the racks, the SFP4 water level can be readily calculated based on the mass and heat balance of the SFP as h~t! M~0! M^ S ~t! M^ E ~t! r~t! A V Rack Region Wang et al. h TOR h~t! h TOR, ~6! where h~t! SFP water level at time t since March 11, 2011 h TOR m elevation of the top of the racks above the SFP floor M~0! SFP initial water inventory mass at 3:38 p.m. on March 11, 2011 ~kg! t M^ S ~t! m S ~t! dt cumulative mass of 0 sprayed water since March 11, 2011 ~kg! m_ S ~t! water spray rate ~kg0s! t M^ E ~t! m E ~t! dt cumulative mass of 0 evaporated water since March 11, 2011 ~kg! m_ E ~t! evaporation rate ~kg0s!. Before the SFP temperature reaches the equilibrium temperature, the evaporation rate can be computed based on the evaporation model, as discussed previously. Thereafter, the evaporation rate can be calculated with Eq. ~5! assuming no water addition to the SFP. V Rack Region m 3 water volumetric inventory in the bottom rack region A m 2 SFP cross-sectional area of the region above the racks. When the SFP water level drops below the top of the racks ~h m!, the level calculation becomes somewhat more complicated because of complex fuel design. The SFP natural-circulation flow will stop when the racks become uncovered. The SFP temperature will increase to the boiling temperature, and eventually, SFP bulk boiling will start. Before SFP boiling, the heat balance calculation includes both water heatup and SFP surface evaporation. For the evaporation calculation, the change in the SFP surface area should be considered when the water level drops below the top of the racks. After SFP bulk boiling occurs, one may assume that all decay heat is used to evaporate water. When the SFP water level drops below the top of active fuel ~TAF!, the level calculation becomes even more complicated since some heated region is uncovered. It is difficult to compute the level with a simple algebraic equation, so we have to calculate it numerically. The heat balance calculation needs to consider the change in the heated length and the variation of axial decay power. Based on the mass balance between the water spray and evaporation, the SFP level can be readily calculated for SFP4. Assumptions made in our analysis are given as follows: 1. The SFP initial water level was at m. It is indicated in the report of the Japanese government ~June 2011! that the fuel pool was fully filled with water at the cutting work of the shroud had been carried out at the reactor side The SFP initial water temperature was at 278C. 3. There was no SFP leakage. 4. Only 50% of the SDF spray in the first 2 days ~March 20 and March 21! went into the SFP. Thereafter, all concrete pump spray went into the SFP. 5. The sprayed water temperature was at 258C. 6. Heat conduction loss through the SFP walls and floor, radiation through the SFP surface, and heat convection loss through the SFP surface were not considered. The effect is actually negligible compared to the total decay heat load in the SFP. Our analysis results of SFP4 for the period of March 11 to May 20 are presented in Figs. 5, 6, and 7. Figure 5 shows the daily water spray amount and the calculated daily water evaporation amount. For the first two days, the daily evaporation rate was calculated based on the SFP water temperature using the evaporation model since the SFP temperature was still rising. When the water temperature reached the equilibrium temperature ~;908C for SFP4!, the daily evaporation rate was calculated using Eq. ~5!. When water spray started, the daily evaporation rate was adjusted by considering the energy needed for heating up sprayed cold water. Therefore, Fig. 5 shows that the daily evaporation rate becomes low when the daily spray is high, and vice versa. In general, the evaporation rate was decreasing slowly with time because of the slowly decreasing decay heat. The integrated amount of spray and evaporation is shown in Fig. 6, which is the basis for our analysis of the SFP level. The predicted SFP level is shown in Fig. 7. The measured data of the SFP level is also shown in Fig. 7 for comparison. In the first _ days into the accident, the SFP level started to increase due to thermal expansion. Evaporation increased as the SFP temperature increased, and eventually, the SFP level stopped increasing and started to drop when the evaporation became significant. Between March 13 and 20, the SFP level decreased at an NUCLEAR TECHNOLOGY VOL. 180 NOV

8 Fig. 5. Daily water spray and evaporation. Fig. 6. Cumulative mass of water spray and evaporation. almost constant rate of 0.7 m0day. From March 20 on, TEPCO started spraying water into the SFP on a daily basis. Thereafter, the SFP water level change was a balance of water evaporation and spray. Our analysis of the SFP level matches the measured data very well; the only exception was on April 12. On April 27, the predicted water level was higher than the initial water level, which indicated that some water might have flowed into the skimmer surge tank on that day. The measured water temperature in SFP4 rose to 848C on March 14, and on April 12, it was measured at 908C. Most measured temperatures were between 828C and 908C. Our evaporation model predicted that the SFP temperatures were slightly less than 908C for the decay heat load of SFP4. In addition, the temperatures predicted by our evaporation model for the Fukushima Daiichi Unit 2 SFP ~SFP2! agreed well with the measurements. It was noted that SFP2 has the same pool 212 NUCLEAR TECHNOLOGY VOL. 180 NOV. 2012

9 Fig. 7. Calculated SFP water level. area as SFP4. In SFP2, the decay heat was ;0.62 MW on March 11 and 0.52 MW on June 11, and the measured SFP temperatures were ;708C. Our evaporation model predicted that the temperatures were 708C and 728C for the decay heat at 0.52 and 0.62 MW, respectively. Comparisons of the predicted SFP temperatures with the measured temperatures for SFP2 and SFP4 are shown in Fig. 8. There is no credible temperature measurement data for the Fukushima Daiichi Unit 1 and Unit 3 SFPs. Fig. 8. SFP temperature comparisons. NUCLEAR TECHNOLOGY VOL. 180 NOV

10 III.D. Comparison with the TEPCO Evaluation In September 2011, the government of Japan released the second IAEA report on the Fukushima Daiichi accident. 2 The report presents results of Fukushima Daiichi SFP evaluations conducted by TEPCO. The results of SFP4 are shown in Fig. 9. The major assumptions in the TEPCO analysis are as follows: 1. The water level is presumed to have been reduced by 1.5 m ~;181 tons of water! as a result of sloshing by the earthquake and the explosion. 2. Inflow from the reactor well occurred beforeapril 22 ~see discussion that follows!. The water level was calculated by considering the water in the SFP and the water in the reactor well and DS pit collectively. After April 22, the SFP gate gap was closed, and no inflow from the reactor well was considered. Key differences between the TEPCO assumptions and our analysis were in the initial water level and the inflow from the reactor well. As discussed in the September report, 2 the reactor well and DS pit were full of water before the earthquake since the reactor was under regular maintenance. The spent-fuel storage SFP and the reactor well were separated by a SFP gate. TEPCO s assumption was that the watertightness of the SFP gate was lost because the gate was subjected to water pressure from the reactor well side when the SFP level became low. Then, the water flowed into the SFP through a small SFP-gate gap. Figure 6 plays a key role in understanding the SFP level change. It is interesting to see from Fig. 6 that the total amount of evaporated water and the total amount of sprayed water approached a balance on April 27. This implies that the total inflow from the reactor well side should be about the same as the total amount of sloshed water caused by the earthquake and explosion. Hence, we can estimate the diminished water level at the beginning of the accident from the total amount of inflow. On April 27, the measurement of the water level on the reactor well side was conducted, and the level was TAF 1.8 m. If we assume that the initial water level in the reactor well and DS pit is TAF 7.2 m, there would be ;150 to 300 tons of water that entered the SFP from the reactor well side. In other words, the diminished water level by the earthquake and explosion would be 1.2 to 2.4 m. The uncertainty of the estimation can be reduced when more information about the water inventory change in the reactor well and DS pit is available. Fig. 9. TEPCO evaluation results of SFP NUCLEAR TECHNOLOGY VOL. 180 NOV. 2012

11 IV. SUMMARY AND CONCLUSIONS Wang et al. In this paper, a detailed analysis was presented of SFP4 following the March 11 accident. First, we described in detail the design characteristics of SFP4 and its decay heat load. We developed an empirical model to calculate SFP surface evaporation based on SFP temperature. This evaporation model can be used to estimate the SFP evaporation rate during the early stage when the SFP water temperature was still rising. In addition, the SFP equilibrium temperature for any decay heat load can be estimated using the model. This equilibrium temperature is important for the energy balance analysis involving sprayed cold water. It has been verified that the temperatures predicted by the model for SFP2 and SFP4 agree well with the measured data. However, there is no credible temperature measurement data for the Fukushima Daiichi Unit 1 and Unit 3 SFPs. Finally, an extended analysis up to May 20 was conducted for SFP4. Our prediction of SFP level agrees very well with measured data. Our analysis was also compared with the TEPCO evaluation results. Based on our analysis, it is concluded that if there is inflow from the reactor well side, it should be about the same as the total assumed amount of water sloshed by the earthquake and0or falling rubble. In addition, it is reasonably concluded that there would have been no large leakage in the SFP and no occurrence of fuel uncovery at any time. ACKNOWLEDGMENTS This manuscript has been authored by UT-Battelle LLC under contract DE-AC05-00OR22725 with the U.S. Department of Energy. REFERENCES 1. Report of Japanese Government to the IAEA Ministerial Conference on Nuclear Safety The Accident at TEPCO s Fukushima Nuclear Power Stations, Government of Japan, Nuclear Emergency Response Headquarters ~June 2011!. 2. Additional Report of the Japanese Government to the IAEA The Accident at TEPCO s Fukushima Nuclear Power Stations ~Second Report!, Government of Japan, Nuclear Emergency Response Headquarters ~Sep. 2011!. 3. Wikispace Web Site: Fukushima 1 Reactor Details ~current as of June 5, 2012!. 4. G. ILAS and I. C. GAULD, Analysis of Decay Heat Measurements for BWR Fuel Assemblies, Trans. Am. Nucl. Soc., 94, 385 ~2006!. 5. F. P. INCROPERA et al., Fundamentals of Heat and Mass Transfer, 6th ed., Wiley ~2007!. 6. R. B. BIRD et al., Transport Phenomena, 2nd ed., Wiley ~2007!. 7. Evaporation from Water Surfaces, The Engineering Tool- Box; ~current as of Dec. 12, 2011!. NUCLEAR TECHNOLOGY VOL. 180 NOV