Investigation of Spent Nuclear Fuel Pool Coolability447049/FULLTEXT01.pdf · spent nuclear fuel pool in a worst case scenario. Air, as with any gas, has too low density and a speciﬁc

Master Thesis

Investigation of Spent Nuclear Fuel Pool Coolability

Fredrik Nimander

Supervisor:Henryk Anglart

Division of Nuclear Reactor TechnologyRoyal Institute of Technology

Stockholm, Sweden, August 2011

TRITA-FYS 2011:51 ISSN 0280-316X ISRN KTH/FYS/–11:51–SE

ii

ABSTRACT

The natural catastrophe at Fukushima Dai-ichi 2011 enlightened the nuclear community. This master thesisreveals the non-negligible risks regarding the short term storage of spent nuclear fuel. The thesis has alsoinvestigated the possibility of using natural circulation of air in a passive safety system to cool the spentnuclear fuel pools. The results where conclusive: The temperature difference between the heated air andambient air is far too low for natural circulation of air to remove any significant amount of heat from thespent nuclear fuel pool in a worst case scenario. Air, as with any gas, has too low density and a specificheat too low to be able to remove the heat generated by spent nuclear fuel shortly after it has been removedfrom the reactor core. The author does not deny the possibility of slightly prolonging the boiling with otherdesigns. The author does however suggest other possibilities to prolong cooling with the conclusion thatlarge enough spent fuel pools would constitute the simplest solution.

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iv Abstract

ACKNOWLEDGEMENTS

The author would like to thank Henryk Anglart for his help and supervision of the master thesis. He allowedthe author to complete the master thesis during the summer of 2011 even though it is standard to write athesis during a normal semester.

The author also wants to thank PHD-student Roman Thiele for his help with OpenFoam. This softwarepackage is extremely useful and valuable, but it has a rather steep learning curve when getting started sincethe documentation is very general rather than detailed. Without the help of Roman there might not havebeen enough time to learn how to use this software package as a tool for the work that needed to be done.

A special thanks goes to Nils-Gunnar Ohlson, teacher at KTH, for his help with finding the appropriateinformation on how to calculate the structural integrity of the copper wall designed for the passive safetysystem that was investigated for this thesis.

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vi Acknowledgements

NOMENCLATURE

Symbol Dimensions DescriptionLatin Symbols

Cp Jkg−1K−1 Specific heatE J EnergyEsat J Energy required to saturate poolEvap J Energy reguired to evaporate waterGr - Grashof numberh Wm−2K−1 Heat transfer coefficientk Wm−1K−1 Thermal conductivityNu - Nusselt numberPr - Prandtl numberq′′ Wm −2 Heat fluxQ Js−1 HeatQ0 Js−1 Thermal Power of reactor during operationRa - Rayleigh numbers Pa Stresstop s Continuous perational time of fuel in reactorts s Time since reactor shutdowntsat s Time until spent fuel pool becomes saturatedT K TemperatureTi K Initial temperatureTsat K Saturation temperatureT∞ K Bulk temperatureV m3 VolumeVaf m3 Volume of water above fuel assemblies

Greek Symbolsα m2s−1 Thermal diffusivityβ - Dimensionless structure coefficientλ Wm−1 Thermal conductivityµ cm2g−1 Gamma attenuation coefficientν m2s−1 kinematic viscosityρ kgm−3 Density

Subscriptsaf Above fueli Initialop Operationsat Saturationvap Vaporization

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viii Acknowledgements

CONTENTS

Abstract iii

Acknowledgements v

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 March 2011 events at Fukushima Dai-ichi 3

2.1 The Natural Disaster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Event sequence at Fukushima Dai-ichi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Spent nuclear fuel pools, spent fuel and Decay heat 7

3.1 Spent Nuclear Fuel Pools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 Spent Nuclear Fuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2.1 Radiotoxicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Boil off times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3.1 Boiling off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3.2 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.4.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4.3 Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 The possibility of air cooled passive safety systems 15

4.1 Design requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Design Suggestion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2.1 Copper wall design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.2 Wall strength and thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Theory of heat transfer and governing equations . . . . . . . . . . . . . . . . . . . . . . . . . 18

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x CONTENTS

4.3.1 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.3.2 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3.3 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3.4 Air duct mass flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4 Results and feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4.1 Structual Integrity of the wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4.2 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.4.3 Verification with OpenFoam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Alternative design suggestions and emergency prepardness 25

5.1 Closed System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2 Prolonging Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2.1 Larger pools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2.2 Implementing other types of existing passive cooling systems . . . . . . . . . . . . . . 25

5.2.3 Enclosed pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2.4 Multiple pool heat sink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2.5 Lessons from Fukushima Dai-ichi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Discussion and Conclusion 27

Appendix A Verification with openFOAM 31

A.1 OpenFoam framewrok . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

A.2 CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

A.2.1 Boussinesq approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.2.2 Newtonian Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.2.3 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

A.2.5 Accuracy of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

A.3 Post processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Appendix B Heat loss calculations 35

Appendix C Boil off times 37

Appendix D Passive safety system calculations 39

Appendix E OpenFoam Mesh 41

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LIST OF FIGURES

2.1 Picture showing the epicenter location of Japan March 2011 earthquake. . . . . . . . . . . . . 3

2.2 Picture showing units 1,2,3, and 4 starting from the right. . . . . . . . . . . . . . . . . . . . . 4

3.1 Total radiotoxic inventory in spent nuclear fuel as a funciton of time[13]. . . . . . . . . . . . 9

3.2 The time dependency of decay heat along with some of the largest contributing isotopes[13]. . 9

3.3 Thermal power after shut down for different burnup times top. . . . . . . . . . . . . . . . . . 10

4.1 Passive safety system that was investigated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Passive safety system that was investigated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Copper wall design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.4 Stress distribution in copper wall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.5 Temperature distribution through copper wall [3] . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.6 Pressure distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.7 Temperature distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.8 Flow velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.1 Alternative safety system design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

A.1 The data for the physical properties were extracted form the red line at the top of the duct. . 34

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xii List of Figures

LIST OF TABLES

3.1 Relative power of fuel for different burnup times given in %. . . . . . . . . . . . . . . . . . . . 10

3.2 Variables used for boil-off calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Case 1 results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.4 Case 2 results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.5 Case 3 results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.6 Case 3 corrected results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 Temperature distribution for a full core unloading, case 1. . . . . . . . . . . . . . . . . . . . . 21

A.1 OpenFoam bondary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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xiv List of Tables

CHAPTER 1INTRODUCTION

1.1 Background

The events that occurred in Japan in March of 2011 showed us that there might be parts of the nuclearindustry that has a lack of proper safety margins. The nuclear reactors that managed to withstand such apowerful earthquake and an unprecedented tsunami belongs to the second generation of reactors that werebuilt in the 1970’s. This freak of nature catastrophe had a very low probability of occurring but came veryclose to having disastrous consequences. Even though the design of these reactors belong to the historybooks there are still some similarities in the design between the oldest generation of reactors and the modernreactors that are being built and designed today, generation three and generation three plus.

The Three Mile Island(TMI) accident in 1979 was a milestone withinin the nuclear industry that will notbe forgotten. It showed us the importance of safety systems and control systems in a nuclear power plant.Maybe most importantly it showed us that the human factor can play a vital role in safety. Attention wasgiven both to the possible direct actions of a single human being but also the behavior of an organization.Modern reactors incorporate safety systems that can even counter faulty human behavior. Even though TMIdid not cause any dangerous release of radiotoxic material, it suffered a severe meltdown from a to that dayunpredicted sequence of events. The mindset at that time was that large break LOCAs would constitutethe worst-case scenario and therefore no studies had been made on the behaviour of a reactor during smallbreak LOCAs. This changed the way we think about safety and it gave rise to deterministic and probabilisticsafety calculations.

In 1986, when Chernobyl suffered a massive power surge leading to an enormous release of radiotoxic materialsit became clear that we had not yet learned enough. The Chernobyl accident was caused by faulty operationin a forbidden operational zone. The control rods also had a design flaw that largely contributed to theaccident. After Chernobyl computers became part of the world. Thanks to them we can make almost anytype of calculation, making it possible for us to run simulations that could calculate even some of the mostunpredictable chains of events. From the Chernobyl accident we did learn how important it is to protectevery power plant from design base accidents and ensuring passive and redundant safety systems.

25 years after the Chernobyl accident Mother Nature gave Japan all her wrath with an enormous earthquakethat even slowed down the earths rotation and a following tsunami of mythological proportions. The nuclearpower plants at Fukushima Dai-ichi came disturbingly close to a second nuclear catastrophe (only countingChernobyl as a catastrophe) that could even have become worse than Chernobyl. Due to these events designflaws have come in to light once again, showing us that some of our predictions might underestimate theprobability of certain chains of events. Risk is defined as the probability times the consequence and it istherefore of the uttermost importance that we learn from these events in order to ensure that this was thelast accident within the nuclear industry.

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2 Introduction

1.2 Thesis objectives

This MSc.Thesis recognizes that spent fuel pools used at some power plants today might have design flaws.These pools are today dependent on electricity to ensure cooling and the circulation of water with the use ofpumps. Accident scenarios where power is lost can be postulated with far less serious initiating events than agroundbreaking earthquake or a mythologically sized tsunami. This thesis will investigate not only how longthese pools remain safe without a power supply but will also investigate a simple design for a passive coolingsystem that does not require electricity. The thesis uses conservative calculations as well Computation FluidDynamics in order to try and verify the calculations made.

The initial plan was to investigate the possible accident scenarios for all of the Swedish reactors but unfortu-nately only Ringhals 1 data were made available to this author during the course of this work and this powerplant will therefore serve as a real life example. The scenarios investigated are however generall and couldbe applied to all spent nuclear fuel pools with some modifications. Calculations made throughout this thesisuses conservative simple correlations for heat and mass transfer. The reader should therfore be familiar withwith heat transfer and how a nuclear power plant is designed.

Chapter 2 describes the events that occured in Japan 2011. In Chapter 3 the spent nuclear fuel is investigatedand the decay heat which it generates. The problem of storing it in spent nuclear pool with active safetysystems is brought into light as well as a possible worst case accident scenario. Chapter 4 investigates thepossbility och passive cooling using air as the heat transport medium. In the first appendix the Authordescribes the OpenFoam software that as been used to validate the results in Chapter 4. In Chapter 5 theauthor suggest possible systems that might investigated for the purpose of passive safety.

CHAPTER 2MARCH 2011 EVENTS AT FUKUSHIMA DAI-ICHI

The events that occurred in Japan March 2011 serves as the background for the work done in this thesis.The author therefore wanted to describe what happened at the Fukushima Dai-ichi nuclear power plants.

2.1 The Natural Disaster

Figure 2.1: Picture showing the epicenter location of Japan March 2011 earthquake.

Earthquakes are not something unusual in Japan. History has taught the Japanese not to underestimate theforces of nature but on 11 March 2011 it became painfully clear that nature can and will be underestimated.An earthquake of magnitude 9 occurred in the ocean east of Japan. Nuclear power plants and other utilitiesthat handle radioactive material are highly protected against earthquakes and they are supposed to auto-matically shut down whenever the ground acceleration reaches certain magnitudes. However, the earthquakewas extremely powerful and a tsunami shortly followed the earthquake. This tsunami reached as high as 38.9meters in some coastal areas and around 14 meters at the Fukushima Daiichi power plant. Except for theconsequences at the Fukushima Dai-ichi nuclear power plant 15391 people lost their lives and 8171 people

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4 March 2011 events at Fukushima Dai-ichi

are unaccounted for. It must be mentioned than none has yet died from the effects of exposure to radiation.Towns where washed away and much of the east coast infrastructure was destroyed. In other words the 11March 2011 was a tragedy in itself but it could have become much worse [1].

2.2 Event sequence at Fukushima Dai-ichi

The power plants at Fukushima Dai-ichi were successfully shutdown after the earthquake as with many otherpower plants. The external power was lost but all back up diesel generators were put in to use and everythingseemed under control. The ground acceleration did not exceed the standard design basis at units 1,4 and6. Thereby showing that the risk of earthquakes had been accounted for. But, this earthquake was largeenough to exceed the design basis at units 2,3 and 5. However, 46 minutes after the accident a tsunamistruck the power plants reaching a maximum height of 14 meters. The tsunami exceeded the design basis atall plants thereby reaching deep into the facilities. All backup power was lost except for one diesel generatorand outside help was at this point very far away. Units 5 and 6 shared the working diesel generator power.This was in a sense unlucky since the fuel hade been removed from the reactor cores at unit 4,5 and 6 andpower was urgently needed at the other units. All instrumentation and control systems were therefore lost atunits 1,2,3 and 4. Communications systems were also affected. The personnel at all units were temporarilyevacuated due to aftershocks and further tsunami warnings. When they returned they had to secure allnuclear facilities along with fuel storage facilities without any instrumentation and reduced communicationpossibilities. Reactors 5 and 6 remained in cold shutdown, which is a safe condition. Cooling was howeverlost in units 1, 2 and 3 and coolability of the spent fuel pools was lost at unit 4 [1].

Figure 2.2: Picture showing units 1,2,3, and 4 starting from the right.

As is known and will be shown in the next chapter the loss of coolability can in some facilities quite rapidlybecome a problem. The residual decay heat within the reactors and the spent fuel pools, which can be in theorder of MW, caused the water to start boiling within the reactor cores. Indications have shown that the wateralso started boiling in the spent fuel pools at unit 4. When the fuel became hot enough hydrogen productionstarted as a chemical reaction between the fuel cladding and the cooling water. After the earthquake somecooling was available. For example a gravity driven isolation condenser (IC) was available for some timeat unit 1 and in units 2 and 3 a reactor core isolation cooling system (RCIC) was available. The RCICuses produced steam to drive a pump that could inject water in the core. The RCIC in unit three failedapproximately 19.5 hours after the accident and a high-pressure injection system (HPCI) was available foranother 14 hours. When the IC failed in unit 1 and the RCIC in unit 2 and 3 as well as the HPCI in unit3 failed other modes of cooling had to be established. Fire trucks and low pressure pumps were thereforeused[1].

In the afternoon on 12 March 2011 the first of three hydrogen explosions occurred at unit 1. When ventingof the hydrogen was later confirmed workers established means to inject borated seawater into the core. On25 March 2011 this this was discontinued as they managed to establish means to insert fresh water thatcontinues to this day.

At units 2 and 3 fire trucks were used to try and supply the cores with borated seawater. However, steamwas produced which was bleeding into the suppression pools through safety relief valves. This meant that

Event sequence at Fukushima Dai-ichi 5

the temperature increased in the suppression pools and pressure rose in the containments making it difficultto refill the system with low-pressure pumps. Pressure had to be lowered.

At unit 2 workers managed to open relief valves that operated on pressurized air on 13 March 2011. A secondhydrogen explosion that occurred at unit 3 would render these valves inoperable. The safety relief valves ofthe containment that remained needed both DC power and pressurized nitrogen to be realigned. This wasnot possible at unit 2 since the nitrogen pressure was to low. The second hydrogen explosion occurred on 14March 2011 in unit 3 further damaging the plant and the valves using pressurized air. The nitrogen pressureat unit three was high enough and DC power was established with car batteries after the explosions. Oncethe pressure was reduced injection of seawater was possible. Fresh water injection was established at unit 3shortly after unit 2 on 25 March 2011 [1].

On 15 March 2011 the third hydrogen explosion occurred in unit 4. Indications hade shown that the fuelwas never uncovered prior to the explosion leading to the theory that hydrogen had leaked from unit 3 intounit 4 since they share venting lines leading to the exhaust stack. The core melt down sequences has not yetbeen confirmed but Tepco have been running simulations showing that damage to the unit 1 core startedonly 4 hours after the shutdown. Damage and partial meltdowns to units 1, 2 and 3 has been confirmed. Allreactors remain shutdown to this day. This is the case for many other power plants in Japan since safetyrequirements have been heightened and public support has been lowered[1].

6 March 2011 events at Fukushima Dai-ichi

CHAPTER 3SPENT NUCLEAR FUEL POOLS, SPENT FUEL AND DECAY HEAT

Nuclear power constitutes a great alternative for electricity production. Its effective, relatively cheap andgreat for the environment compared with fossil fuels such as coal, gas and oil. Simplified one can say thatthere are only two drawbacks to nuclear power. The first one is the safety related to the operation of thenuclear power plant, even during normal operation, but especially during unforeseeable chains of events. Thesecond drawback is of course the radiotoxic waste that is produced, which can be very harmful to humansfor a very long time after it’s been used. There is an ongoing debate on the long-term safety and handlingof nuclear waste but this thesis will only concern itself with the short-term safety issues that are related tothe storage of spent nuclear fuel in the reactor buildings. These issues are clearly worth investigating in theaftermath of the events in Japan 2011.

3.1 Spent Nuclear Fuel Pools

Spent nuclear fuel pools serve as short-term fuel storage before the fuel is shipped away for intermediatestorage or reprocessing. That is at least the original purpose for them. In some countries there is no planfor the handling of the nuclear waste and spent fuel has therefore been accumulating in the reactor pools.In Sweden the fuel is shipped off to an intermediate storage (CLAB). The spent nuclear pools are designedto safely cool the fuel as well as protect the workers from the radiation. There are also regulations fordealing with the criticality issue of the fuel, but that was not a topic for the work done in this thesis. Forradiation safety reasons minimum water coverage of three meters is required to be present at all times inthe pools. Most pools like the ones at Ringhals 1 has a water coverage of approximately ten meters duringnormal operation to increase the safety margins[12]. A design flaw today is that the piping is installed onlythree meters above the fuel in order to ensure that even with a leak the radiation protection level of wateris kept at three meters. But as will be shown this can gravely diminish the safety margins during certainpostulated events. There might be other designs present elsewhere where the pipes are elevated. The CLABintermediate storage facility in Sweden has this type of design and the author therefore assume that thismight be a safety standard at least for Swedish nuclear facilities.

The safety issue that this thesis concerns itself with is what would happen if the possibility to refill and coolthe spent fuel pools were lost. The decay heat may then at some points in time be sufficiently large enoughto evaporate or even too boil off all of the protective water. If this were to happen radioactive nuclides mightbe released into the reactor building and to the environment. When the fuel pins get hot enough hydrogenproduction starts due to a thermochemical reaction between the Zircaloy cladding that encapsulates the fueland the water surrounding it. This build up of hydrogen could lead to a hydrogen explosion that couldfurther damage the power plant leading to even more dangerous accidents[16]. At Fukushima Dai-ichi unit1,3 and 4 three such hydrogen explosions occurred. These hydrogen build-ups were however caused by theheating of the rods within the reactor core rather than the rods in the spent fuel pools[4].

There are a number of scenarios that can be postulated under which the backup electricity supply to anuclear power plant might be lost. As will be shown there are few high probability scenarios where the timeto boil off is short enough to cause any real concern. But suppose that the entire core has been unloadedinto the spent fuel pools as was the situation at Fukushima Dai-ichi unit 4 and suppose that a leak in the

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8 Spent nuclear fuel pools, spent fuel and Decay heat

piping occurs so that the water level is not 10 m above the fuel but rather the minimum 3 m. In this typeof scenario there might be cause for concern.

3.2 Spent Nuclear Fuel

The most common reactors today are light water reactors. And the nuclear fuel that is most commonconsists of natural or enriched Uranium. This fuel is practically entirely safe before it has been irradiated inthe reactor core. Within the reactor core highly radioactive nuclides are created through the fission processof heavy nuclides as well as through the neutron capture process in many nuclides.

The spent nuclear fuel is transferred to the spent nuclear fuel pools after it’s been irradiated in the reactorcore. This fuel is therefore highly radioactive. But radio toxicity is not the only problem with the spentnuclear fuel. Heat generation is the natural consequence of radioactive decay. This decay heat constitutesalmost 7% of the total heat generation within a operating reactor core. The half lives of some isotopes isvery short and therefore the decay heat decreases quite rapidly as soon as the reactor has been shut down.There are however longer lived fission products like 137Cs that has a half life of 30 years along with actinidesthat can be as long lived as 105 years. Radiotoxicity and decay heat will therefore be a concern even forintermediate and long term storage as well as for the short term storage[16].

3.2.1 Radiotoxicity

When heavy metal nuclear fuels are irradiated by neutrons in a reactor core there are several processes oc-curring. The main process that occurs is the fission process that generates the bulk heat within a reactor.The fission products that are produced are often radioactive and decay by means of β and γ decay. Duringnormal operation these decays constitutes a non-negligible amount of the total heat. Neutron capture is an-other process where particles may absorb an extra neutron. This process gives us several different radioactiveisotopes that can decay by the same means as the fission product but some of the heavy metal isotopes mightalso decay by the emission of α particles. These two processes are the main processes that occur along withelastic and non-elastic scattering that might excite nuclei to higher energy states that most often decay bythe emission of γ radiation. There is also a mode of decayed competing with β decay called electron capture.

When the reactor is shut down this radioactive decay continues. All generated radioactive isotopes havedifferent half lives, spanning from very short almost unmeasurable times to very long geological time-spans.The radiotoxicity of spent nuclear fuels is therefore strongly coupled to the composition of the fuel after ithas been irradiated. The typical radiotoxic profile of spent light water reactor fuel can be seen in figure 3.1.The issue with radiotoxicity is important for safety reason, were the water to boil off, but it is also importantto make sure that the design of a spent fuel pool safely protects the workers during normal conditions. Thiswill play an important part in the suggested passive safety system design in Chapter 4.

The storage of nuclear fuel within the power plant should be limited to a maximum of a few years and duringthis period of time it’s the fission products that will generate the bulk of the decay heat. The first decadesof decay heat are dominated by decay of 90Sr and 137Cs. In the first year however we need to accountfor all fission products[13]. Since the decay heat is in effect a result of the beta and accompanied gammadecay it will decrease in proportion to the half lives of the different isotopes. It is therefore ensured thatthe maximum decay heat will be generated directly after shutdown of the reactor and that we will have aquite rapid decrease within the first 100 days after shutdown[13]. For this thesis a worst case scenario willbe investigated for the decay heat and boil off times. The decay heat is therefore investigates during a shortperiod of time after operation. The typical total heat production per metric ton heavy metal (MTHM) canbe seen in figure 3.2.

The decay heat that is being generated by the fuel assemblies from one core can be related to their initialpower Q0 by equation (3.1) where ts[s] is the time since shutdown of the reactor and top[s] is the operationaltime of the fuel in the reactor[5].This equation as been determined for 4.5% enrichment of 235U in the fuel.The amount of fission products goes up with enrichment and can therefore safely be used for Swedish reactorsthat usually utilizes a lower enrichment. Since the amount of fission products would saturate when the burnuptime of the fuel goes towards infinity we could assume a long burnup for the calculations in order to ensurea worst-case scenario. Within the first minute, delayed neutrons does play a role in the heat generation butwe can assume that no one removes the fuel assemblies within a minute of shutdown, nor within the firsthours or even days. According to [11], an assumption that fuel is placed in the spent fuel after 7 days is avalid assumption.

Spent Nuclear Fuel 9

Figure 3.1: Total radiotoxic inventory in spent nuclear fuel as a funciton of time[13].

Figure 3.2: The time dependency of decay heat along with some of the largest contributing isotopes[13].

Q(ts)Q0

= 0.065[t−0.2s − (ts + top)−0.2] (3.1)

Figure 3.3 has been generated in Matlab using equation 3.1 and it shows the relative decay heat generationin fuel as function of the total burnup time. Starting from the bottom the first three lines corresponds to1, 2 and respectively 3 years of burnup and the fourth line corresponds to the solution for 1000 Years ofburnup. Due to this saturation behavior of the burnup we can use say 5 years of continuous burnup and


be quite confident the that the amount of heat production represents a realistic value for any thermal lightwater reactor with an enrichment of 4.5% 235U or less.

Figure 3.3: Thermal power after shut down for different burnup times top.

In table 3.1 we can see the fraction of heat generation in the fuel relative to the operational power at differentpoints in time after shutdown for different operational times(burnup times).

Table 3.1: Relative power of fuel for different burnup times given in %.

ts top = 1y top = 10y1 week 0.25 0.321 month 0.14 0.213 months 0.075 0.14

Equation 3.1 is generated for a fuel enrichment of 4.5% 235U . This means that the Swedish reactors will havea decay heat generation lower than the prediction of this equation which will ensure a worst-case scenarioprediction. In the data received from Ringhals they postulate a worst-case scenario where the entire core isunloaded giving a thermal load of 7.245MW one week after shutdown. Equation (3.1) with a burnup of 5years predicts a thermal load of 7.614 MW[12].

3.3 Boil off times

3.3.1 Boiling off

Throughout this chapter it’s assumed that the spent fuel pool will boil at some points. These calculations aremade conservative assuming that radiation and evaporation heat loss is negligible for the short term storage.This will not be the case for lower thermal loads nor for large enough pools [17]. Some simple calculationscan be made using the equations in example 14.13 in [3]. The calculations shows that for a temperaturedifference of 80 degrees celsius between the pool water and the air the total heat loss for radiation, convectionand evaporation adds up to 55.3 kW. Comparing this to the heat loads of the spent fuel which is in the orderof a couple MW certainly validates that a worst case scenario calculation can neglect these heat loss effects.The Matlab code can be found in appendix B.

Results 11

3.3.2 Governing equations

To calculate the time it will take until the fuel assemblies are uncovered the process is divided into two steps.The first step is the process when the pool water saturates. Until the water has been saturated vapor willcondense soon after its been created before it reaches the surface of the pool and therefore no mass willbe lost from the so called subcooled pool boiling[3]. The second step is when the pool has been saturated.When the pool is already saturated we can assume that all heat generated from the radioactive decay goesundivided to the phase change process to ensure a worst-case scenario. In a best-estimate calculation onewould have to account for heat losses to the surrounding enviroment.

Step 1: Pool saturation

This first step is very simple since we know how much energy we transfer from the fuel to the water each secondthanks to equation (3.1). If we know the volume of the pool, the density of the water, initial temperature ofthe pool, the saturation temperature and the amount of energy required to increase the temperature of thewater by one degree(specific heat Cp) we can easily find out how much time it takes to saturate the entirepool. Equation (3.2) gives us the total amount of energy required to saturate the pool. The volume occupiedby the fuel assemblies has not been accounted for.

Esat = ρV Cp(Tsat − Ti) (3.2)

Equation (3.3) then gives us the time until the pool has become saturated. The fuel decay heat is given inW [Js−1].

tsat = EsatQfuel

(3.3)

Step 2: Boil off

When the pool is saturated it can be assumed that all decay heat goes too the phase change of the waterin order to keep the calculations conservative. Some heat will be lost to the the surroundings and even asmall fraction will be lost through heat radiation. Since these energy losses are small and very extensive toevaluate they have been ignored for the insurance of the worst case scenario. The amount of energy requiredto boil off all the water above the fuel is then given by equation (3.4).

EBoil = ρVafEvap (3.4)

The critical time when enough energy has been produced to boil off the water above the can be found byintegrating equation (3.1) from the time where cooling is lost tstart to the the critical time tc that we arelooking for. This gives us equation (3.5) which can easily be solved in Mathematica with the numerical solverNSolve() where we set E to EBoil and Q0 is the initial thermal power of the reactor.

E =∫ tc

tstart

0.065Q0[t−0.2s − (ts + top)−0.2]dts (3.5)

3.4 Results

At Fukushima Dai-ichi unit 4 the entire core had been unloaded in november and therefore this is assumedas a certainly plausible scenario. A full core unloading correspond to an initial thermal power 2500MWfor Ringhals 1. Since the thesis is trying to evaluate a worst-case scenario three different cases have beenpostulated. In case 1 the normal case of unloading a third of the core with a full pool is investigated. In thesecond case a scenario close to the events at Fukushima Dai-ichi unit 4 where a full core has been unloadedis investigated. And in the third case a worst case scenario is investigated. In all three cases geometriesand thermal power corresponds to Ringhals 1 since this is the plant for which the actual geometry data wasavailable. In table 3.2 the variables used for the three different cases can be seen. For all three cases the boiloff times have been calculated for three individual scenarios where the cooling is lost after respectively 7, 30and 100 days. The code used for these calculations can be found in Appendix C.


Table 3.2: Variables used for boil-off calculations.

Const Case 1 Case 2 Case 3Vsat[m3] 995.5 995.5 511.875Vaf [m3] 648.375 648.375 204.75Tsat[K] 373.15 373.15 373.15Tin[K] 313.15 313.15 313.15Cp(Tin)[kJkg−1K−1] 4.205 4.205 4.205ρ(Tin)[kgm−3] 992.2 992.2 992.2Q0[MWs−1] 833.333 2500 2500

3.4.1 Case 1

This is the normal case when the pool is filled, cooled to 313.15 K and only a third of the core has beenunloaded. This should constitute the normal circumstance when refueling a reactor core. The results of thesecalculations can be seen in table 3.3.

Table 3.3: Case 1 results.

Days after shutdown 7 30 100Days until uncovered fuel 8.77 13.07 20.38

3.4.2 Case 2

This case does not constitute the worst case scenario, rather a quite possible scenario. Had disaster struckFukushima Daiich shortly after the entire core had been unloaded the scenario would look close to whatssimulated in case 2. In table 3.4 the time until the fuel would be uncovered after loss of cooling has beencalculated.



3.4.3 Case 3

In this scenario a leak has occurred prior to the loss of cooling and the water level is only the minimum 3 mabove the fuel. In addition an entire core has been unloaded. Table 3.5 shows the boil off times for case 3.



3.5 Conclusions

For normal circumstances where only a third of the core is unloaded to a filled spent fuel pools there is noreason for concern. However if procedure requires or does not prohibit the removal of an entire core, severesituations might occur. It is quite clear that routines for unloading the fuel at plant with spent fuel poolswith the current design must guarantee that this type of situation does not occur. If there are situationswhere the entire core must be unloaded, procedures or design has to be changed to accommodate the heatload. Extra back up systems might be installed in existing reactor while passive safety system might be a

Conclusions 13

requirement for the next generation of nuclear reactors. The author recognizes that the data for Ringhals 1might not constitute a standard for which all nuclear power plants can be measured against.

Situations for loss of cooling in a power plant spent fuel pool has prior been investigated at least for normalcircumstances. One such investigation for the Ignalina NPP showed that the time until the fuel becameuncovered would be 12.5 days for a total thermal load of 4.253MW and a water volume more than five timeslarger (5070 m3) then the one at Ringhals (995 m3)[9]. The thermal load used corresponds the thermal loadafter 41 days for Ringhals 1. Using the model used in this thesis for the same thermal load and water volumesas the article results in 11.4 days for the top fuel assemblies (complicated geometry of Ignalina spent fuelpool). In the article a Relap 5 best estimate code was used rather than a worst-case scenario approximation.The difference in the results are probably due to the fact that the Relap code is a best estimate code anddoes account for the thermal losses through the concrete walls as well as to the building surrounding thepools. The difference due to these effects can then be estimated to 8.77% assuming this effect is close tolinear. Then the a best estimate for case three can be seen in table 3.6. When the values have been correctedwith an increase of 8.77% one would still draw the same conclusions.

Table 3.6: Case 3 corrected results.

Days after shutdown 7 30 100Days until uncovered fuel worst case 0.9 1.42 2.27Days until uncovered fuel best estimate 0.98 1.54 2.47


CHAPTER 4THE POSSIBILITY OF AIR COOLED PASSIVE SAFETY SYSTEMS

A passive safety system could be one that either prolongs the boling process or one that makes sure boilingnever occurs. The first type of system that comes to mind is the one that prolongs the time for boiling sothat the worst case scenario will have the same safety margins as the existing systems has today for a normalscenario. Such a system might be quite complicated since it might have to account for boiling, vapor andrising pressures. Therefore the author decided to investigate the possibility of a system that ensure thatboiling never occurs. Other design suggestion are brought up in Chapter 5.

4.1 Design requirements

As was shown in Chapter 3 a realistic situation might occur where the fuel might be uncovered rapidly. Theprobability for such a series of events is not necessarily negligible. Whether or not the the probability ofsuch a chain of events is higher than the regulations allow is not under investigation in this thesis. Since thesystem only has to lower the probability of boil off, a system should be designed that will weigh in the safetyissues but also the economical aspects as with all engineering problems. For this thesis it was investigatedwhether an open passive cooling system could be built using air as the heat transfer medium. The feasibilityof such a system is investigated in this chapter.

The author investigated a passive safety system that would remove enough energy to ensure that boiling neveroccurs. In other words a system that would keep the pool temperature below the saturation temperatureTsat. Due to the temperature difference of the pool and the surrounding air, evaporation of the water wouldstill occur [3]. To counteract the loss of water through this mechanism a system is suggested that enclosesthe spent fuel pool and retains the water. The type of machinery that would enclose the pool when notbeing filled or emptied is not part of this thesis. It is however possible to imagine that such a system neednot be very complicated since it would not have to handle pressures above normal. A simple hydraulic thinfolding lid with a seal could be one solution. If the pool is enclosed and if the temperature is kept belowthe boiling point any vapor would then condense and return to the pool. In this way the water level can bekept nearly constant except for the height increase due to the change in density when the water heats up.Whether or not the height would remain nearly constant could be investigated in a small scale lab where onecould compare the water height in a enclosed aquarium with a heat source with the water heights in such anaquarium where one of the walls is replaced by a heat exchanging metal wall.

4.2 Design Suggestion

In figure 4.1 and 4.2 a graphic interpretation of the suggested system can be seen. The dark grey area isthe concrete fuel pool. The red part will be any type of doors that can seal the pool whenever fuel is notbeing inserted or removed from the pool. A lid that can be moved would allow for the use of the same typeof storage system that are used today to move the fuel in and out of the pools under water. The light greyrepresents the air ducts that will transport air from the bottom of the reactor building into the building andup via a heat exchanging copper wall to a stack. The air duct bottom part would probably be a concrete

15

16 The possibility of air cooled passive safety systems

design feature of the power plant while the top would be made out of metal. The air duct has two inlets forthe purpose of redundant safety were anything to happen to the outer walls on one side of the building. Theorange shows the upper part of the pool wall that will be replaced by a copper wall. As can be seen in figure4.2 the pool has thick concrete walls that serves as radiation protection surrounding the pool and air duct.Most spent fuel pools today are lined with stainless steel and so would this one be except for the copper wall.

The initial idea of this design is a simple heat exchanger where heat is transported through the wall by meansof convection and conduction. Since both of these heat transport phenomena are strongly dependent on thethermal conductivity of the wall material used the necessity for a metal is quite obvious. Copper was chosensince the author believes that it has the highest thermal conductivity of the metals that can realistically beused for this type of application.

Figure 4.1: Passive safety system that was investigated.

4.2.1 Copper wall design

Initially a plane wall was designed. The feasibility of this type of heat exchanger is strongly dependent onthe outdoor temperature since it’s a passive system and initial results showed it might not be efficient enoughduring the hottest summers in Sweden. Also the initial wall design was tall and narrow but since the heightof the wall defines the characteristic length of the wall for convection a broader but shallower design might bepreferred. And finally the wall side have been designed with triangular teeth shown in figure 4.3. If designedwith many short teeth(1 cm or shorter) the conduction conditions could be considered nearly unchangedwhile the area for heat convection may be doubled using in the shape of equilateral triangles.

4.2.2 Wall strength and thickness

The feasibility of such a design would first of all depend on the structural strength of the copper wall. Thedesign of the system would also have to ensure radiation protection work workers in the plant.

Design Suggestion 17

Figure 4.2: Passive safety system that was investigated.

Figure 4.3: Copper wall design.

Radioactive Particles

Radioactive particles will give the minimum thickness of the copper wall. α, β and γ particles are all createdin the decay of radioactive particles and can be harmful to health and cannot be allowed out of the powerplant nor be allowed to cause any harm to the workers. 3 meters of water is enough to contain these particlesbut how about copper? Decay particles such as α and β are easily stopped but γ photons are what we wouldneed to concern ourselves with. Energy from radiation is measured in the unit Grey [Gy] and is calculatedinto Sievert through a radiation weighting factor that takes into the the damage of the particle in question.For gamma rays the weighting factor is equal to one for all energies. Equation 4.1 can be used to calculatethe attenuation in a material as a function of distance where µ is the attenuation coefficient that is dependenton the absorption coefficient of the material. Since the duct is surrounded by the same amount of concreteas the pool the radial distribution from the pool can be considered safe. Depending on the final design, theupper part of the duct has to be investigated. If this part of the duct were to be designed with concreteas well the problem might easily be solved. However, concrete structures constitutes the largest cost in anuclear power plant and cost saving designs should be investigated if the passive design turned out to befeasible.


I

I0= e−µx (4.1)

Structural strength

The copper wall could be built very thick from the structural integrity and the radiation protection perspec-tive. There are however two limiting factors, the cost and the heat transfer. As can be seen in equation 4.12a thinner wall will give a higher heat flux through the wall [3]. The second limiting factor of cost is alwayspresent since the largest costs of nuclear power are the construction costs of the nuclear power plant itself.According to [8] the maximum stress for a flat plate with three supported edges (here: bottom and sides)and with a third free edge(here: top) can be calculated with equation (4.2) where w is the hydrostatic stressat the bottom of the wall where its the highest, t is the thickness of the wall, b is the wall height and βis determined by tables in [8] A standard norm for the allowed maximum stress is given by equation (4.3)which gives a large margin to plastic deformation of the wall.

smax = βωb2

t2(4.2)

smax = σs1.5 (4.3)

Combining these equations we get equation (4.4) that gives us the minimum allowed thickness of the wall.

t =

√β

1.5ωb2

σs(4.4)

4.3 Theory of heat transfer and governing equations

Heat transfer is defined as the natural redistribution of thermal energy due to a temperature gradient ina medium. Since there will be a temperature difference between the spent fuel pool water and the air inthe air duct thermal energy will travel from the pool to the wall by natural convection, trough the wall bythermal conduction and then to the air in the duct by natural convection [7]. Because the air will be heatedthe density will be lowered and the air will rise through the duct due to the buoyancy effect caused by adensity difference. The duct must therefore be designed to allow for enough air to travel through the ductby itself to cool the wall enough to cause a heat gradient large enough to keep the pool below it’s saturationtemperature Tsat. If enough buoyancy can be achieved an entirely passive safer system could be designed.

4.3.1 Convection

Convection is a transport phenomena caused by the bulk motion of the medium particles. The heat fluxedis defined according to Newtons law of cooling (4.5) where h is the heat transfer coefficient which is stronglydependent on the surface and the flow conditions [3]. The heat transfer coefficient can be calculated withequation (4.6) where Nu is the Nusselt number, λ is the thermal conductivity of the solid material and L isthe characteristic length of the surface.

q′′ = h(Ts − T∞) (4.5)

h = Nuλ

L(4.6)

The Nusselt number is the dimensionless heat gradient at the surface and varies with the type of mediumand the flow conditions. It will therefore differ on the water-metal side of the heat exchanger from theair-metal side. The Nusselt number is dependent on the Prandtl number (equation 4.7) and the Grashofnumber(equation (4.8)) which have the same definition for both the air and water side. The differencebetween the two convection conditions is how the Nusselt number is related to the Grashof number and thePrandtl number [2, 7]. This dependency is often determined empirically.

Theory of heat transfer and governing equations 19

Pr = ν

α(4.7)

Gr = gβ(Ts − T∞)L3

ν2 (4.8)

Nusselt on water-metal side

On the water side of the heat exchanger we have water and we have free convection driven by the boyancyforces of the water caused by a temperature difference due to the heating of the water from the fuel assemblies.The recommended equation for external natural convection is given by equation (4.9) [2, 7] for externallaminar natural convection for a vertical wall. Ra is the Rayleigh number which substitutes for the Reynoldsnumber for natural convection it is defined in equation (4.10) [2, 7].

Nu = 0.68 + 0.67Ra 14

(1 + ( 0.492Pr

916 )) 4

9

(4.9)

Ra = PrGr (4.10)

Nusselt on air-metal side

On the air side of the metal we also have free convection due too buoyancy forces acting on the air in theduct. On this side however we have air but we also have a duct, not an infinite heat sink. In a duct we cannot threat the convection boundary conditions as free convection on a vertical plate since the enclosed fluidwill behave differently from a an infinite heat sink that we could threat the pool as. Instead we have to usea correlation for an internal free heat convection in a rectangular vertical tall duct given in equation (4.11)[2].

Nu = 0.364 LHRa

14 (4.11)

4.3.2 Conduction

Conduction is a heat transport phenomena that can be conceived as an effect of particle movement. Energyis transported from the more energetic particles to the lesser energetic ones through interactions betweenthese particles. The rate of heat transfer in one dimension is determined by Fourier’s law given in equation(4.12) where k is the coefficient known as the thermal conductivity of a material [7]. Equation (4.12) givesthe heat flux and equation (4.13) gives the total heat rate through a wall of thicknes x.

q′′x = −kdTdx

(4.12)

Q = kA∆T∆x (4.13)

4.3.3 Heat transfer

The total heat transfer can be calculated with equation (4.14) by adding all thermal resistances from theconduction and convection boundaries. For a vertical plate the areas would be the same but due to my designthe area for conduction is twice the area of conduction due to the equilateral triangle design of the copperwall teeth.

∆T = Q( 1h1A1

+ ∆xkA2

+ 1h2A1

) (4.14)


4.3.4 Air duct mass flow

The air duct must be designed to allow for an air mass flow large enough to get a heat transfer coefficient hthat is large enough to remove all the heat generated by the spent nuclear fuel. The buoyancy forces causeby the temperature difference of the ambient air and the air in the duct can be calculated using equation(4.15). The pressure losses in the air duct can be calculated using equation (4.16) where ξ is the friction losscoefficient and Dh is the hydraulic diameter of the duct.

Pb = gHρairβ∆T (4.15)

∆Pch = ξHρairv

2

2Dh(4.16)

To achieve buoyancy the forces must counteract the pressure losses. Setting these two equation equal to oneanother we can calculate the flow velocity in the duct (equation (4.17)). With the velocity and temperaturedifference known we can calculate the heat removed by the air in the duct using equation (4.18). Thefriction loss coefficient is calculated using a handbook[6]. In this engineering handbook loss coefficents canbe looked up for flows in the particualr geometries used along with coefficents for flow area changes. Theseloss coefficients can the be added up and used in equation (4.17).

v =

√2PbDh

ξHρair(4.17)

Qremoved = WCpair∆T (4.18)

4.4 Results and feasibility

4.4.1 Structual Integrity of the wall

Most non-alloyed coppers have a tensile strength between 200-400 MPa. Pure copper properties are usedthroughout this thesis. The water pressure and the added atmospheric pressure adds up to about 290kPa ata depth of 9 m. Inserting the values along with the dimensions of the copper wall into equation (4.4) resultsin a minimum thickness of 14.68 cm and therefore the wall design would have to be 15 cm thick.

Teacher Nils-Gunnar Ohlson at the solid-mechanics department was kind enough to input the values into aprogram called EMRC by NISA which solves this problem by the Finite Element Method. The model didnot account for the walls own weight nor the stresses caused by the edge-walls but these should be negligiblefor this case since the wall is vertical and the walls that its attached to are 1-1.5 m thick concrete walls.Figure 4.4 shows the stresses in the wall if it is 15 cm thick. The highest stress found is 76.75 MPa andaccording to equation (4.3) the maximum allowed stress is 133 MPa, in other words a good margin to plasticdeformation. Teacher Nils-Gunnar also did the calculations for a wall 10 cm thick and the maximum stressfor that case was 170 MPa which is above the allowed value confirming the calculations used by the author.

4.4.2 Heat transfer

The author investigated the the maximum allowed temperature of the air in the duct that would allow for ansafety system that would passively remove all heat generated by the spent fuel. Since we know the saturationtemperature of water we can say that the maximum allowed temperature of the spent fuel pool water is 95degrees celsius. And since we know how much heat is produced we also know how much heat that must betransferred to the air in the duct. We can there for calculate the temperature required fore each part of thesystem each step by step starting with the convection from the water to the wall. In appendix D the Matlabcode used for these calculations can be seen. The entire heat transfer could have been calculated by equation(4.14) but had the heat transfer coefficients been know. The author set the maximum temperature for thepool, and since the amount of heat produced was known the temperature distribution could be calculated

Results and feasibility 21

Figure 4.4: Stress distribution in copper wall.

Figure 4.5: Temperature distribution through copper wall [3]

step by step finally finding out the maximum allowed temperature of the outdoors temperature allowing forfull passive safety. The temperature distribution is illustrated in figure 4.5.

Calculations were made for what would constitute the worst case scenario corresponding to an accidentoccurring seven days after a full core unloading. The author calculated the temperature distribution basedon the requirement that the spent fuel pool temperature, T∞1 in figure 4.5, must remain at 368.15 K. Resultsfor these calculations can be seen in table 4.1.

Table 4.1: Temperature distribution for a full core unloading, case 1.

Temperature Celsius

Bulk Water 95Wall Water Side 94.41Wall Air Side 63.8Bulk Air 37.9

If the bulk air leaving the duct would have an average temperature of 37.9 degrees celsius and the ambientoutdoors temperature would bearound 20 degrees celsius the velocity of the the air over the plate would be0.7996 m

s and would remove only about 7.91kW of heat(out of 6.7 MW ). This means that temperature ofthe wall and air boundary layer in the duct would reach close to the saturation temperature of the water inthe spent fuel pool but would still only remove a fraction of the heat needed. With an average temperature


of 37.9 degrees celsius in the duct the air would reach a flow velocity of 0.8 ms .

4.4.3 Verification with OpenFoam

The author has used openFoam as a verification tool. In Appendix A the software package openFoam ispresented and explained. Simulations were run to investigate the flow velocities and temperatures within theair duct. The author set the hot wall temperature in OpenFoam to 100 degrees celcius since it was knownthat only a small amount of heat would be removed and the temperature of the wall would rise to or nearthe boiling temperature of the pool. These simulations verifies the calculated results. In figure 4.6,4.7 and4.8 the pressure, temperature and flow velocities caluclated are shown. The author spent a lot of time tryingto contruct a three dimensional case but the mesh grew too big and therefore a two dimensionall case waschosen. The author also tried constructing a two dimensional duct representating the air duct but did notmanage to apply the correct boundary conditions and the solution became non-physical. The correct resulthave been obtained for a closed natural circualtion system such as the ones used in [2] when explaining abuoyance driven system with a heat source and a heat sink.

Figure 4.6: Pressure distribution.

The author believs the obtained results represents a physical system since the pressure distribution showsa higher density in the bottom of the system and the lower density air in the top. The author also believsthat the system used has a heat sink large enough since the temperature distribution is quite small. Thevelocities behaves as expected, the air rises in the duct and circulates down i the large ”enviroment”.

The average velocity in the top of the duct is 0.4012ms−1 and the average temperature is 310.5492K. Forthe suggested design this means that the system would remove 3.15kW compared with 7.9 kW that wascaclulated by the author.

4.5 Conclusions

The suggested design is not effective enough to remove enough heat in a worst case scenario. The pool wouldstill boil and the reduction in saturation and boil off time would be negligible. At the point of boiling thewater level would decrease uncovering the copper wall with time and thereby further decrease its effective-ness. Another problem with the correlations used by the author shown with the OpenFoam calculations isthe fact the only a thin layer close to the heated copper wall will reach the ”bulk air temperatures” calcu-lated. Therefore the mass flow would be even lower and the amount of heat removed will be even less thancalculations used for internal natural convection. As is seen by these calculations even a perfect heat transferto air at atmospheric pressure would require an enormous heat gradient in order to achieve the buoyancy

Conclusions 23

Figure 4.7: Temperature distribution.

Figure 4.8: Flow velocities.

needed to remove enough heat from the spent fuel pool wall. The author has therefore concluded that an aircooled passive safety system can’t feasibily be designed and applied to a spent nuclear fuel pool within anynuclear power plant.


CHAPTER 5ALTERNATIVE DESIGN SUGGESTIONS AND EMERGENCY

PREPARDNESS

5.1 Closed System

The first type of passive air-cooled safety system isn’t efficient enough. A different possibility might be closedsystems with a heat transfer medium different from air. A quick check through reference tables makes itobvious that the heat capacity along with the low densities of gases at atmospheric pressures is too low.The density for water is however a thousand times higher and the specific heat is four times larger than thespecific heat for air. A closed system with a pressurizer ensuring the correct water level might be a possiblesolution. The water-cooled closed system would work if the system is designed with the outdoors temperatureas a heat sink. A large enough heat exchanger must be design to keep the water at a constant temperaturebut with flow resistance low enough to ensure stable natural buoyancy driven flow. The problem with watermight be that the low heat gradient won’t be enough for a stable flow.

5.2 Prolonging Designs

5.2.1 Larger pools

The simplest solution to the problem of spent fuel pool boil off is of course to design the pools large enoughso that the boil off times for a worst case scenario are within an acceptable limit. On could reason the waterfrom the other pools could be used to enlarge the total amount of water but since we are investigating aworst-case scenario we can presume that the other pools are emptied for some maintenance right after thecore has been refueled. Presuming that there is a fixed limit to the shortest allowed time for possible boil offdetermined by the authorities, and then the pool would have to be built to uphold these conditions.

5.2.2 Implementing other types of existing passive cooling systems

There are several system used today to prevent pressure build-ups and ensure cooling in current and futurereactor designs. One such system is the gravity driven passive cooling system utilizing the pressure head ofan elevated reserve pool to inject water in the spent fuel pool could be a simple solution that might savespace. This can be designed with passive pressure valve so that injection of water starts when the water levelof the spent fuel pool reaches a certain level. Another benefit to this system is that the water in the reservepool could be saturated with boron to further ensure any criticality issues that might occur during accidentscenario such as those at Fukushima Dai-ichi. This could also be combined with a system that condense asrecycles the water that evaporates from the spent fuel pool.

25

26 Alternative design suggestions and emergency prepardness

5.2.3 Enclosed pool

Having some type of sealing or lid made from a highly conductive material such as aluminum that couldclose off the pool would prolong the time until boil off since the water would remain in the pool as Vaporand vapor would condense and return to the pool. And due to the high thermal conduction of aluminum orcopper some heat would be transferred to the reactor hall. This type of system might lack in efficiency dueto the same reasons, as the design in Chapter 2, the convective properties of air during free circulation israther ineffective. The pool could however be built to withstand large vapor pressures.

5.2.4 Multiple pool heat sink

As was mentioned in Chapter 2 passive systems that prolongs the evaporation and boil off times could beinvestigated. One such system might utilize the rest of the water in the reactor hall without a connectedpassaged way. Figure 5.1 represents this design. Here as in the design suggested in Chapter 2 one of theconcrete walls would replaced by a copper wall that in turn could be coupled with rerouted water from theother pools in the reactor hall. The orange wall is the wall that would exchange heat with the rest of thewater in the reactor hall thereby prolonging the time until boil off. The green circle only symbolizes the poolthat is on top of the reactor lid. This type design is rather easy to implement.

Figure 5.1: Alternative safety system design

5.2.5 Lessons from Fukushima Dai-ichi

In the event that any severe accident occurs external action might be vital to ensure the safety of the powerplant. At Fukushima Dai-ichi fire trucks and make up fire trucks with low pressure pumps where used topump water into the reactor buildings [1]. Ensuring that trucks fitted with water and pumps are close enoughfor a quick response but at such a safe distance from the power plant to not be affected by the same externalevents as the power plant might be a recommendation for some utilities since it increases the redundancyof possible safety actions that can be taken. Mobile power, compressed air and water supply that is safelylocated is the second and third lesson learned in IAEAs expert fact finding report made after the events inJapan[1]. NISA has required that all Japanese power plants implement these lessons without delay.

CHAPTER 6DISCUSSION AND CONCLUSION

Since the author was limited to the data from Ringhals 1 the assumptions made in Chapter 2 might not berelevant for other nuclear power plants. It might also be the case that routines at Ringhals are such that theevent scenarios suggested within this thesis are not valid. With that said the author believes that there mightbe some need for evaluation of the probabilities for possible chains of events that might lead to a worst-casescenario. The case might be such that the probability for a pipe leak that would lead to ”case 3”-scenario isfar to low for any real concern. If such investigations would show non-negligible risk there might be a needfor revisions.

One conclusion can be drawn from the work and research done for the possibility of an air-cooled passivesafety system. A passive safety system that mitigates the consequences of a worst-case scenario is not feasiblewith gases at atmospheric pressures. The efficiency would be so low that the size and implementation of sucha system would not be feasible. Several soccer fields of wall area would be needed to remove all the heat oreven prolong the boil off times using natural circulation.

There are prolonging systems that might and should implemented if the conditions are such that there areaccident event sequences that might lead to same conditions as in Case 3 in Chapter 2. The author mentionsseveral times that other nuclear power plants might have larger spent nuclear fuel pools and therefore largersafety margins. But there might also be nuclear power plants where the spent nuclear fuel pools containseven smaller quantities of water and therefore inhabiting smaller safety margins.

The possibility of using personnel during accident scenario should not be underestimated since the prepared-ness of the personnel can severely affect the outcome of a severe accident. For examples if valves are realigneddirectly when external power is lost to prepare for external refilling of water crucial time can be saved in theevent that small incidents becomes accidents.

Today internal events are very well understood and power plants are inherently safe. External events suchas natural disasters and possible human threats are however hard to predict. This area has to be wellunderstood and governments and utilities should take this into account when building, revising and updatingsecurity measurements. With that said the author still believes in the inherent safety of modern nuclearpower plants. Nuclear power will have to be part of the future at least as a intermittent solution to theenvironment issues the world is facing today. The author believes that limiting the nuclear industry is a riskgreater than expanding it since a larger industry gives more funding and incentives for safety research andimprovements.

27

28 Discussion and Conclusion

BIBLIOGRAPHY

[1] International Atomic Energy Agency. Iaea international fact finding expert mission of the fukushimadaiichi npp accident following the great east japan earthquake and tsunami, 2011. Published onwww.IAEA.org.

[2] Adrian Bejan. Convection heat transfer (John Wiley and Sons New York, Incorporated, 1995, 2. ed).ISBN 0471579726.

[3] Yunus. A. Cengel. Heat Transfer a Practical Approach ed. 2 (McGraw-Hill Education, 2002). ISBN9780070634534.

[4] Biello David. Partial meltdowns led to hydrogen explosions at fukushima nuclear powerplant. http://www.scientificamerican.com/article.cfm?id=partial-meltdowns-hydrogen-explosions-at-fukushima-nuclear-power-plant, 2011. Scientific American article.

[5] Samuel Glasstone. Nuclear Reactor Engineering (Van Nostrand Reinhold New York, Incorporated, 1981,3. ed). ISBN 0442200579.

[6] I. E. Idelchik. Flow resistance, a design guide for engineers (Hemisphere Publishing Incorporated, 1989).ISBN 0891164359.

[7] Frank P. Incropera. Fundamentals of heat and mass transfer (John Wiley and Sons New York, Incor-porated, 2002, 5. ed). ISBN 0471386502.

[8] Raymond J.Roark. Formulas for stress and strain (McGraw Hill, 1965, 4th:ed).

[9] A. Kaliatka, V. Ognerubova, and V. Vileiniskisa. Analysis of the processes in spent fuel pools of ignalinanpp in case of loss of heat removal. Nuclear Engineering and Design, 240, 2010. doi:10.1016/j.nucengdes.2009.12.026.

[10] Roman Thiele PHD KTH. Interview, based on openfoam course.

[11] Nilsson Markus. Okg, 2011. Email with Oskarshamn employee.

[12] Henrik Nylen. Vattenfall, 2011. Spentfuelstorage.doc regarding Ringhals 1, consider as quote.

[13] Massachusetts Institute of Technology. The Future of Nuclear Power an interdisciplinariy MIT study(2003). ISBN 0615124208.

[14] OpenFoam. Openfoam users guide. Http://www.openfoam.com/docs/user/.

[15] OpenFoam. Openfoam users guide tutorials. Http://www.openfoam.com/docs/user/cavity.php.

[16] Bengt Pershagen. Light Water Reactor Safety 2.ed (KTH, 1996).

[17] M.E. Weech and Y.J. Lee. Heat transfer in spent fuel storage. Nuclear Engineering and Design, 67,1982. doi:10.1016/0029-5493(82)90066-8.

[18] David C. Wilcox. Turbulence Modeling for CFD (2006). ISBN 9781928729082.

29

30 Bibliography

APPENDIX AVERIFICATION WITH OPENFOAM

The feasibility of the suggested passive safety system is largely dependent on the the conditions in the airduct. The velocity and distribution largely effects the convective heat transfer. An experimental verificationof the results is of course out of the question but a numerical verification of the results using a computationalfluid dynamics(CFD) code is possible. In the effort to support the results of the previous chapters openFOAMhas been used.

A.1 OpenFoam framewrok

OpenFoam is an open source computational fluid dynamics(CFD) software package. CFD codes such asOpenFoam has been developed for the purpose of theoretical verification of dynamical fluid systems sinceexperimental validation is very complicated and expensive. Researchers can now first do the veificationon their computer and since the OpenFoam code is open source it can be changed and improved upon bythe user. OpenFoam accounts for all physical properties and can therefore compute anything from fluidflows, chemical reactions, turbulence, heat transfer and even electromagnetics by the addition of Maxwell’sequations. OpenFoam contains many standard solvers that are used for different purposes. This thesis hasused the‘‘buoyantBoussinesqSimpleFoam’’ and the ‘‘buoyantBoussinesqPimpleFoam’’ solver that isused for buoyant turbulent flow with for a incompressible fluid. The next section will motivate the choice ofsolver [14].

A.2 CFD

Air flowing through a duct is constituted by real particles moving around individually with respect to eachother but they also have collective flow properties. A macroscopic system would be rather impossible todescribe by describing each one of these particles with computers used today. The fluid is therefore modeledas continuum that tries to approximate the fluid structure. This continuum is based on the fundamentalprinciples conserving mass, momentum and energy. In CFD the momentum equation(Newtons second law ofmotion) is replace by the Navier-Stokes equation that relates the stresses applied to the surface of the fluidto the viscous properties of the fluid. The Navier-Stokes equation can be seen in equation (A.1).

δuδt

+ u · ∇u = g

ρ− ∇P

ρ+ ν∇2u (A.1)

A computation fluid dynamics software such as OpenFoam solves the mass, momentum and energy equa-tions through an iterative process. These equation are however very difficult or impossible to solve for morecomplex problems since the introduction of the convective acceleration(second term on LHS of equationA.1makes it a non-linear equation. The convective acceleration is the change in velocity related to the positionof the fluid.The non-linearity arises from the turbulence within the fluid and its impact on the stresses act-

31

32 Verification with openFOAM

ing on the fluid. A model for the turbulence is therefore needed to solve the problem for turbulent conditions.

Any property of a turbulent fluid can be described as an average value with a fluctuating part, in otherwords as a stochastic variable. These stochastic variables are averaged over a time interval representing thetime of fluctuation. Applying this time averaged variable results in the Reynolds Averaged Navier-Stokesequation, equation (A.2) [18], for the momentum equation. This makes it possible to solve the non-averagedNavies-Stokes equations for turbulent fluids. However, expressing the momentum equation for an incom-pressible fluid means that the velocity of the fluidis described by introducing its fluctuating velocity. Thenon vanishing fluctuating part, last term on RHS of equation (A.2), of the velocity means that we have morevariables than equations and we need to add another equation relating the fluctuating part of the velocity tothe viscous properties in order to solve the system of equations.

ρδuiδt

+ ρujδuiδxj

= − δPδxi

+ δ

δxj

(2µSji − u′iu′j

)(A.2)

The Boussinesq assumption, equation (A.3) says that the effective viscosity can be calculated by the sumof the laminar viscosity with the turbulence viscosity. The Menter k-ω-SST model relates the turbulentviscosity with the kinematic turbulence energy k and the specific dissipation ω with equations (A.4). k andω are related to the turbulent velocities by a two equation system. The system of equations is then closed,making them solvable by replacing the non-linear term with equation (A.5).

νeff = ν + νt (A.3)

νt = k

ω(A.4)

−u′iu′j = νt

(δuiδxj

+ δujδxi

)− 2

3

(k + νt

δukδxk

)δij (A.5)

A.2.1 Boussinesq approximation

The Boussinesq assumption used in the previous section is not the Boussinesq approximation that isreferenced to in the solver name “buoyantBoussinesqSimpleFoam/PimpleFoam”. The Boussinesq approxima-tion is used for heat transfer solvers where the temperature change of the fluid is rather small. The densityin the approximation can then be approximated from a reference temperature and the thermal expansioncoefficient, see equation (A.6).

ρ(T ) = ρ(Tref )(1 + β(Tref )∆T ) (A.6)

A.2.2 Newtonian Fluid

The definition of a newtonian fluid is a fluid which has a linear dependence between the stress and the strain.This is the case for fluids such as water and air. The proportionality constant that defines this dependenceis the viscosity µ. Therefore, a Newtonian fluid description of the air flowing the duct was used.

A.2.3 Mesh

When using OpenFoam one would first define the geometry which in itself can be difficult when you do nothave any experience. The mesh must have cells small enough so allowing for the solution to converge if infactyour simulation will end in a steady state solution. The mesh can however not be to small, partly becauseof the runtime of the simulation that you want as short as possible and because the k- and ω-wallfunctionsare not accurate enough for all cell sizes. The k-ω model was chosen since it is less sensitive to the wall cellsize than the k-ε model. With some experience a best guess could be used for approximating the amountof cells needed. However for someone that is unexperienced with the code such as the author, an iterative

CFD 33

method was used to determine the amount of cells needed. After a lot of trial and error the mesh defined inappendix E was used.

A.2.4 Boundary conditions

In order to to run OpenFoam calculations the user must define a set of initial and boundary conditions in the‘‘0"-file. Different models require different sets of initial conditions. The boundary conditions used in thesimulations run by the author can be seen in Table A.1. First the initial temperatures and initial velocitiesare set accordingly. The pressure initial conditions are set in two seperate files. The ‘‘p’’ file contains theintitial pressure conditions which are calculated in this case since we use the Boussinesq approximation. Inthe ‘‘p rgh’’-file the pressure is set to ‘‘calculated’’ as ρ times g time h.

For the ‘‘omega’’ (specific turbulence kinetic energy dissipation rate), ‘‘nut’’ (turbulent viscosity), ‘‘kappat’’(turbulent conductance energy) and ‘‘k’’(turbulence kinetic energy)-files wall functions are set. The ref-erence are set to standard values since the values are later calculated. The wall functions are used to keepa high resolution in the wall area to avoid inaccurate predictions in the velocity profile. The problem thatthe models have is the predictions made by ‘the law of the wall”. The law of the wall has been determinedempirically and gives a logaritmic velocity distribution close to the wall. The omega model is the only modelthat gives acceptable values to these predictions without the addition of dampening factors. This is whatgives the k-ω model an advantage in a large model with large cells over the k-ε model. Initial values aregiven for the wall funcitons but these are used only for the post processing tool ‘ParaView” [18].

Table A.1: OpenFoam bondary conditions

Properties Value UnitHot Wall Temperature 373.15 KWall Temperatures 293.15 KInitial velocities 0 m s−1

Pressure “calculated” PaPrgh ‘buoyantPressure” PaOmega “omegaWallFunction” s−1

Nut “nutkWallFunction” m2s−1

kappat “kappatJayatillekeWallFunction” m2s−1

k “kqRWallFunction” m2s−2

A.2.5 Accuracy of the results

When a suitable model has been chosen an iterative method solves the governing equations. For each step aresidual can be calculated, a measure of how much the solution has changed from one step to another. Theoptimal criterion would be if this residual reached zero but this will not happen in practice. A ”small enough”residual could be criterion enough to establish that the solution is converging, but how small depends on eachindividual problem. A normalized residual is therefore calculated by OpenFOAM removing the individualityof the problem. A general criterion of a residual which is of the order of 10−6 is therefore an acceptable con-vergence criterion for any simulations. This is established due to the fact that the computer is only accurateto the power 10−8. The author first tried to solve the problem using buoyantBoussinesqSimpleFoam but thetime needed for convergence with the computer available would be enormous[10].

The solver was then changed to buoyantBoussinesqPimpleFoam which is a non-steady state solver. ThePimpleFoam gives the solution over a time interval. When running a non-stead-state solver using openFoamconvergence of the result canon be controlled in the same manner as for stead state solvers. In order to preventinherent errors propagating in the solution the Courant number is introduced. This can be interpreted ashow far each ”particle” moves in the mesh with each iteration. To ensure non-propagating errors the Courantnumber limit it must be set to be lower than 1 in the control dict file. This basically means that each timestep is kept short enough so that the fluid does not travel further than on cell during one time step [15].

34 Verification with openFOAM

A.3 Post processing

There are several methods that can be used to interpret the results of the computations. Graphically,paraFoam can be used to see the distributions of the physical properties. Data can also be exported in filesthat can be used with Matlab for example. To calculate the average physical properties for Chapter 4 a linewas defined at the upper boundary of the duct for which all needed physical properties where extracted fromthe output files using the command sample. The line from which the data was extracted can be seen in figureA.1

Figure A.1: The data for the physical properties were extracted form the red line at the top of the duct.

APPENDIX BHEAT LOSS CALCULATIONS

1 %Fredrik Nimander KTH thesis2 %Radiation, convection and evaporation heat loss form hot bath3 %Exampel 14−13 Cengel Heat transfer 2:ed4

5

6 % Radiation7

8 epsilon = 0.95; %Emissivity9 As = 10.5*6.5; %Surface area

10 sigma = 5.67*10ˆ−8; %StefanBoltzman constant11 Ts = 373; %Saturation Temperature12 T = 298; %Ambient Temperature13

14 Qrad = epsilon*As*sigma*(Tsˆ4 −Tˆ4); %Stefan−Boltzma radiation law15

16

17 %Convection18

19 Pv = 1.65*10ˆ3; %Vapour pressure20 rhos = 0.942*323/373; %Suuface air vapor mixture density21 rhoinf = 1.0684; %Ambient air vapor mixture density22 rhoave = (rhos + rhoinf)/2; %Average density23 Lc = As / (2 *(10.5 +6.5)); %Characteristic lenght24 nu = 1.848 *10ˆ5; %kinetic viscosity25 k = 0.02644; %Water heat conductivity26

27 Gr = 9.81 *(rhoinf − rhos) *Lcˆ3 / rhoave/ nuˆ2; %Grashof number28 Pr = 0.7261; %Prandtl number29

30 Nu = 0.15 * (Gr*Pr)ˆ(1/3); %Nusselt Number31

32 hc = Nu *k /Lc; %Heat transfer coefficient33

34 Qcon = hc * As * (Ts − T); %Convective heat35

36 % Evaporation37 hfg = 2383*10ˆ3; %Latent heat38 Dab = 3*10ˆ−5; %Diffusion coefficient39 Sc = 0.616; %Schmidt number40 sh = 76.2 %Sherwood Number41 hm = sh *Dab/Lc; %Mass transfer coefficient42 rhovs = 0.0828; %Vapor surface density43 rhovinf = 0.012; %Vapor ambient density44

45 mv = hm *As *(rhovs −rhovinf); %Evaporation rate46

47 Qev = mv *hfg; %Evaporation Heat48

49 %Qtot50

51 Qtot = Qrad + Qcon + Qev %Total heat

35

36 Heat loss calculations

APPENDIX CBOIL OFF TIMES

Fredrik NimanderKTH M.Sc thesisBoil off timesGeometry and power data for RinghalsPhysical properties found in Wolfram Alpha

Clear[“Global*”]Clear[“Global*”]Clear[“Global*”]

Cp = 4.205 ∗ 10∧3; (*WolframAlphaforTi = 313.15K*)Cp = 4.205 ∗ 10∧3; (*WolframAlphaforTi = 313.15K*)Cp = 4.205 ∗ 10∧3; (*WolframAlphaforTi = 313.15K*)

Tsat = 373.15; (*Wolfram Alpha Boiling Temperature*)Tsat = 373.15; (*Wolfram Alpha Boiling Temperature*)Tsat = 373.15; (*Wolfram Alpha Boiling Temperature*)

Ti = 313.15; (*Should be below 333.15 but assuming more realistic 40*)Ti = 313.15; (*Should be below 333.15 but assuming more realistic 40*)Ti = 313.15; (*Should be below 333.15 but assuming more realistic 40*)

h = 9.5; (*WaterHeightabovecore, 9.5m = max forRinghals*)h = 9.5; (*WaterHeightabovecore, 9.5m = max forRinghals*)h = 9.5; (*WaterHeightabovecore, 9.5m = max forRinghals*)

V1 = 5 ∗ 10.5 ∗ 6.5 ∗ (h+ 4.5); (*Entire water volume*)V1 = 5 ∗ 10.5 ∗ 6.5 ∗ (h+ 4.5); (*Entire water volume*)V1 = 5 ∗ 10.5 ∗ 6.5 ∗ (h+ 4.5); (*Entire water volume*)

ρ = 992.2; (*Water density at 313.15K*)ρ = 992.2; (*Water density at 313.15K*)ρ = 992.2; (*Water density at 313.15K*)

m = V1 ∗ ρ;m = V1 ∗ ρ;m = V1 ∗ ρ;

Esat = m ∗ Cp ∗ (Tsat− Ti); (*Amount of energy required to saturate pool*)Esat = m ∗ Cp ∗ (Tsat− Ti); (*Amount of energy required to saturate pool*)Esat = m ∗ Cp ∗ (Tsat− Ti); (*Amount of energy required to saturate pool*)

q0 = 2500 ∗ 10∧6; (*Thermal energy of Ringhals reactor*)q0 = 2500 ∗ 10∧6; (*Thermal energy of Ringhals reactor*)q0 = 2500 ∗ 10∧6; (*Thermal energy of Ringhals reactor*)

top = 3600 ∗ 24 ∗ 365 ∗ 5; (*Operationaltime[s]*)top = 3600 ∗ 24 ∗ 365 ∗ 5; (*Operationaltime[s]*)top = 3600 ∗ 24 ∗ 365 ∗ 5; (*Operationaltime[s]*)

ta = 41 ∗ 24 ∗ 3600; (*Timesinceshutdown[[[sss]]]*)ta = 41 ∗ 24 ∗ 3600; (*Timesinceshutdown[[[sss]]]*)ta = 41 ∗ 24 ∗ 3600; (*Timesinceshutdown[[[sss]]]*)

(*Saturation Time*)(*Saturation Time*)(*Saturation Time*)

q[t ]:=q0 ∗ 0.065 ∗ (t∧ − 0.2− (t+ top)∧ − 0.2);q[t ]:=q0 ∗ 0.065 ∗ (t∧ − 0.2− (t+ top)∧ − 0.2);q[t ]:=q0 ∗ 0.065 ∗ (t∧ − 0.2− (t+ top)∧ − 0.2);

Eq[tc ] = Integrate[q[t], {t, ta, tc}];Eq[tc ] = Integrate[q[t], {t, ta, tc}];Eq[tc ] = Integrate[q[t], {t, ta, tc}];

T = NSolve[Esat==Eq[tc], tc,Reals];T = NSolve[Esat==Eq[tc], tc,Reals];T = NSolve[Esat==Eq[tc], tc,Reals];

Tc = tc/.T [[[[1][1][1]]]];;;Tc = tc/.T [[[[1][1][1]]]];;;Tc = tc/.T [[[[1][1][1]]]];;;

SSStringForm[“Power at failure [%]”];SSStringForm[“Power at failure [%]”];SSStringForm[“Power at failure [%]”];

q[ta]q[ta]q[ta]/q0;q[ta]q[ta]q[ta]/q0;q[ta]q[ta]q[ta]/q0;

StringForm[“Saturation Time[d]”];StringForm[“Saturation Time[d]”];StringForm[“Saturation Time[d]”];

37

38 Boil off times

Tc2Tc2Tc2 === ((((tc/.T [[[[1][1][1]]]])))−−− tatata)))///360036003600///242424;;;Tc2Tc2Tc2 === ((((tc/.T [[[[1][1][1]]]])))−−− tatata)))///360036003600///242424;;;Tc2Tc2Tc2 === ((((tc/.T [[[[1][1][1]]]])))−−− tatata)))///360036003600///242424;;;

(*Time to boil*)(*Time to boil*)(*Time to boil*)

V2V2V2 === 10.510.510.5 ∗ 6.5 ∗ h;V2V2V2 === 10.510.510.5 ∗ 6.5 ∗ h;V2V2V2 === 10.510.510.5 ∗ 6.5 ∗ h;

m2m2m2 === ρρρ ∗V2;m2m2m2 === ρρρ ∗V2;m2m2m2 === ρρρ ∗V2;

EEEEEE === 2.2302.2302.230 ∗ 10∧6 ∗m2; (*Totalvaporizationenergy(WolframAlpha)*)EEEEEE === 2.2302.2302.230 ∗ 10∧6 ∗m2; (*Totalvaporizationenergy(WolframAlpha)*)EEEEEE === 2.2302.2302.230 ∗ 10∧6 ∗m2; (*Totalvaporizationenergy(WolframAlpha)*)

Eq2[te ] = Integrate[q[t], {t,Tc, te}]]];;; (*Evaluatedfromtimesinceshutdown + staurationtime*)Eq2[te ] = Integrate[q[t], {t,Tc, te}]]];;; (*Evaluatedfromtimesinceshutdown + staurationtime*)Eq2[te ] = Integrate[q[t], {t,Tc, te}]]];;; (*Evaluatedfromtimesinceshutdown + staurationtime*)

T2 = NSolve[EE==Eq2[te], te,Reals];T2 = NSolve[EE==Eq2[te], te,Reals];T2 = NSolve[EE==Eq2[te], te,Reals];

TeTeTe === tetete/.T2[[1]];TeTeTe === tetete/.T2[[1]];TeTeTe === tetete/.T2[[1]];

StringForm[“Evaporation time[d]”];StringForm[“Evaporation time[d]”];StringForm[“Evaporation time[d]”];

Te2Te2Te2 === ((((((tetete/.T2[[1]])− (Tc))/3600/24;Te2Te2Te2 === ((((((tetete/.T2[[1]])− (Tc))/3600/24;Te2Te2Te2 === ((((((tetete/.T2[[1]])− (Tc))/3600/24;

StringForm[“Total boil-off time including saturation time[d]”]StringForm[“Total boil-off time including saturation time[d]”]StringForm[“Total boil-off time including saturation time[d]”]

Tc2 + Te2 (* Prints the total time until Boil off*)Tc2 + Te2 (* Prints the total time until Boil off*)Tc2 + Te2 (* Prints the total time until Boil off*)

APPENDIX DPASSIVE SAFETY SYSTEM CALCULATIONS

1 % NaturalCirculation heat removal (case 1)2 % Fredrik Nimander KTH master thesis3 % Copper wall with equilateral triangle teeth4 % Removing all decay heat from spent nuclea fuel5 % Material properties taken from Wolfram Alpha6

7 clear global8 clear all9 clc

10

11 % Design Height = 9m w1 = 10.5 => w2 =2112

13 Q = DHP (2500,5,7) %Use the function DHP to get the decay heat seven days after unloading14 A = 9*21; %Convection area, height 9 m, width 2*10.5 m15 Acond = 9*10.5; %Conduction are height 9m, width 10.5 m16 g = 9.81; %Gravity constant17 Thickneswall = 0.15; %Copper Wall thickness18

19 %Convection water−metal20 kCuw = 394.9; %Copper Heat conductivity21 Betaw = 7.236*10ˆ−4; %Thermal expansion coefficient22 Tinfw = 95 + 273.15; %Pool water bulk temperature23 Tsgw = 367.5624; %Wall surface temperature (manually itterated).24 CL = 9; %Characteristic Lenght water side = vertical height of wall = 9m.25 rhow = 962.3; %Density Water26 nu = 2.99*10ˆ−4; %Dynamic viscosity27 vw = nu/rhow; %Kinetic viscosity water28 cp = 4.205*10ˆ3; %Specific heat water29 k = 0.677; %Thermal conductivity water30 Prw = nu*cp/k; %Wolfram Alpha31 Grw = −g*Betaw*(Tsgw−Tinfw)*CLˆ3/vwˆ2; %Grashof number water32 Raw = Grw*Prw; %Rayleigh number water33

34 Nuw = 0.68 +0.670*Rawˆ(1/4)/(1 +(0.492/Prw)ˆ(9/16))ˆ(4/9); % Nusselt number, Incropera, Bejan reference35 hwm = Nuw*kCuw/CL % Heat transfer coefficient water side36 %Q1 = hwm*A*(Tinfw−Tsgw); % Heat rate convection water side37 TW = Tinfw − Q/hwm/A38

39 dt=Q/kCuw/Acond*Thickneswall %Temperautre difference needed over Copper. to receive heat rate = Q40

41 % Convection Air−Metal42 CLa = 4*10.5*0.5 / (2*(11));43 kCuwa = 397.3; %Thermal conductivity copper air outer temperature44 Betaa = 3.3*10ˆ−3; %Thermal expansion coefficient45 Tinfa = 311.9709 %Bulk air temperature, iterated manually46 Tsga = TW − dt %Duct copper surface temperature47 Toutw= Tsga − 273.15; %Outer wall temperature for printing48 rhoa = 1.053; %Air density49 nua = 2.02*10ˆ−5; %Dynamic viscosity air50 va = nua/ rhoa; %Kinematic viscosity air51 cpa = 1008; %Isobaric specific heat air

39

40 Passive safety system calculations

52 k = 0.0289; %Thermal conductivity air53 Pra = nua *cpa /k; %Prandtl number air54 Gra = g*Betaa*(Tsga−Tinfa)*CLaˆ3/vaˆ2; %Grashof number air55 Raa = Pra*Gra; %Rayleigh number56

57 Nua = 0.364*0.5*Raaˆ(1/4)/9; %Nusselt number from Bejan58

59 ham = Nua*kCuwa/CLa; %Heat transfer coefficient air side60 TWO = Tsga − Q/ham/A; %Bulk Air temperature61

62 % Temperature difference over entire structure63 % This is to check64 r = Thickneswall;65 DeltaT = Q*(1/ham/A + r/Acond/kCuwa + 1/hwm/A)66 DeltaTcalc = Tinfw − Tinfa67 Tinfr = Tinfw −DeltaT −273.1568

69 % Channel Conditions70 Th = Tinfa ; %Assuming linear heating we can calculate max inlet temperature71 Text = 293.1572 Aduct = 10.5*0.5; %Tube Area73 H = 9; %Total chimney height74 Hc = 30;75 f = 1.8195; %Loss coefficient76 rhoah = 0.993; %hot air density77 Betaah = 3.3*10ˆ−3;78

79 Ph =g*H*rhoah*Betaah*(Th−Text); %Buoyancy Pressure head80 velocity =(Ph*2*CLa/(f*H*rhoah))ˆ(1/2) %Flow velocity81 W = velocity*rhoah*Aduct;82 Q4 = W*cpa*(Th−Text) %heat removed

APPENDIX EOPENFOAM MESH

1 /*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*− C++ −*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*\2 | ========= | |3 | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |4 | \\ / O peration | Version: 2.0.0 |5 | \\ / A nd | Web: www.OpenFOAM.com |6 | \\/ M anipulation | |7 \*−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−*/8 FoamFile9 {

10 version 2.0;11 format ascii;12 class dictionary;13 object blockMeshDict;14 }15 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //16

17 convertToMeters 1;18

19 vertices // here alla the corners of the blocks are defined.20 (21 (−5 0 0) //0 block122 (0 0 0)23 (0 11 0)24 (−5 11 0)25 (−5 0 0.01)26 (0 0 0.01)27 (0 11 0.01)28 (−5 11 0.01)//7 block 129 (0.5 0 0)30 (0.5 1 0)31 (0 1 0)32 (0.5 0 0.01)33 (0.5 1 0.01)34 (0 1 0.01)// 13 block 235 (0.5 10 0)36 (0 10 0)37 (0.5 10 0.01)38 (0 10 0.01)// 17 block 339 (0.5 11 0)40 (0.5 11 0.01)// 19 block 441 (−5 1 0)42 (−5 1 0.01)43 (−5 10 0)44 (−5 10 0.01)// 2345 (−0.01 10 0)46 (−0.01 11 0)47 (−0.01 10 0.01)48 (−0.01 11 0.01)//2749 (−0.01 1 0)50 (−0.01 1 0.01)51 (−0.01 0 0)

41

42 OpenFoam Mesh

52 (−0.01 0 0.01)53

54 );55

56 blocks //The model is made up of cells with only one cell on the z−axis for 2D case. Here the amount of cells is defined.57 (58 //level 159 hex (0 30 28 20 4 31 29 21) (800 30 1) simpleGrading (0.25 0.25 1)60 hex (20 28 24 22 21 29 26 23) (800 180 1) simpleGrading (0.25 1 1)61 hex (22 24 25 3 23 26 27 7) (800 30 1) simpleGrading (0.25 4 1)62

63 //level 264 hex (1 8 9 10 5 11 12 13) (250 30 1) simpleGrading (1 0.25 1)65

66 //level 367 hex (10 9 14 15 13 12 16 17) (250 180 1) simpleGrading (1 1 1)68

69 //level 470 hex (15 14 18 2 17 16 19 6) (250 30 1) simpleGrading (1 4 1)71 //extra72 hex (24 15 2 25 26 17 6 27) (3 30 1) simpleGrading (1 4 1)73 hex (30 1 10 28 31 5 13 29) (3 30 1) simpleGrading (1 0.25 1)74 );75

76 edges77 (78 );79

80 boundary81 (82 hotWall // The heated wall83 {84 type wall;85 faces86 (87 (9 12 16 14)88

89 );90 }91 Walls // Walls with normals in x,y−direction92 {93 type wall;94 faces95 (96 (0 4 21 20)97 (20 21 23 22)98 (22 23 7 3)99 (28 29 26 24)

100 (10 13 17 15)101 (0 4 31 30)102 (30 31 5 1)103 (1 5 11 8)104 (8 11 12 9)105 (14 16 19 18)106 (2 6 19 18)107 (25 27 6 2)108 (3 7 27 25)109 (28 29 13 10)110 (24 26 17 15)111 );112 }113

114

115 emptyWalls // Walls with normals in the z−direction, "empty" for 2D case116 {117 type empty;118 faces119 (120 (0 30 28 20)121 (20 28 24 22)122 (22 24 25 3)123 (4 31 29 21)124 (21 29 26 23)125 (23 26 27 7)126 (1 8 9 10)127 (10 9 14 15)

43

128 (15 14 18 2)129 (5 11 12 13)130 (13 12 16 17)131 (17 16 19 6)132 (24 15 2 25)133 (30 1 10 28)134 (31 5 13 29)135 (26 17 6 27)136

137 );138 }139

140 );141

142 mergePatchPairs143 (144 );145

146 // ************************************************************************* //

44 OpenFoam Mesh

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