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Buoyancy-Driven Two-Phase Flows of Liquid Metal Contributing to the Generation of Electricity from a Fusion Reactor by Magnetohydrodynamic Energy Conversion

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Buoyancy-Driven Two-Phase Flows of Liquid Metal Contributing to the Generation of Electricity from a Fusion Reactor by Magnetohydrodynamic Energy Conversion Buoyancy-Driven Two-Phase Flows of Liquid Metal contributing to the Generation of Electricity from a Fusion Reactor by Magnetohydrodynamic Energy Conversion A Thesis Submitted to the University of London for the Degree of Doctor of Philosophy by Charles Edwin Wood School of Engineering and Materials Science Queen Mary University of London Mile End E1 4NS October 2015 Declaration I, Charles Edwin Wood, confirm that the research included within this thesis is my own work or that where it has been carried out in collaboration with, or supported by others, that this is duly acknowledged below and my contribution indicated. I attest that I have exercised reasonable care to ensure that the work is original, and does not to the best of my knowledge break any UK law, infringe any third party’s copyright or other Intellectual Property Right, or contain any confidential material. I accept that the College has the right to use plagiarism detection software to check the electronic version of the thesis. I confirm that this thesis has not been previously submitted for the award of a degree by this or any other university. The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author. Signature: Charles E. Wood Date: October, 2015 2 Abstract Fusion is desirable for providing the world’s future base-load power capacity due to its lack of greenhouse gas emissions, low environmental and safety risk, and large, secure fuel reserves. Fusion power plants are not expected to deliver electricity commercially until 2050, when it is expected that most fossil-fuelled power plants will have been removed from the global electricity generating mix. However, for fusion power plants to remain competitive with other forms of primary energy sources, the unit cost of electricity should be kept as low as possible. The objective of this work has therefore been to examine and compare a range of conversion methods for the purpose of increasing overall fusion plant efficiency. Model C of the Power Plant Conceptual Study provided a benchmark against which a proposed power cycle could be compared. The power cycle associated with model C, using a thermal input of 3991 MWt and neglecting cycle pressure losses, delivers 1780 MWe with a cycle efficiency of 44.6%. Allowing for blanket gain, but after deducting plant power requirements, an overall plant efficiency of 45.9% is achieved. The proposed power cycle uses a primary Brayton cycle, which takes helium directly from the blanket, to deliver 1688 MWe. A topping cycle, which uses two-phase liquid metal magnetohydrodynamic energy conversion, delivers 22 MWe. Three water-based bottoming Rankine cycles are used to extract heat rejected by the Brayton cycle to deliver 409 MWe. Small-scale experimental work was undertaken to verify the performance of the topping cycle and observe the circulation of a dense liquid metal by using buoyancy, thereby removing the need to pump liquid metal through a blanket. The proposed power cycle, without cycle pressure losses, delivers a total of 2119 MWe with a combined cycle efficiency of 53.1%. An overall plant efficiency of 56 % is achieved, an improvement of 10.1% over PPCS model C. 3 Acknowledgements I would like to thank my primary supervisor Emeritus Professor Chris Lawn, Queen Mary University of London, for his support and patience. The feedback he has provided throughout my study has been invaluable in enabling this thesis to be completed. I would also like to thank Dr. Tom Barrett, Culham Centre for Fusion Energy, and Dr. Huasheng Wang, Queen Mary University of London, for their support. I would like to acknowledge Mr. Roger Nelson, Queen Mary University of London, for providing technical assistance during experimental testing. I would especially like to thank Mr. John Cowley, University College London, for his invaluable technical support, without which the experimental work could not have been undertaken. I would also like to acknowledge the following staff at Queen Mary University of London for their support: Jonathon Hills, Rajesh Chadha and Wei Zhang. This research was funded by a CASE Award from the Engineering and Physical Sciences Research Council (Grant No. EP/J502157/1) and a Russell Studentship from the Culham Science Centre of the UK Atomic Energy Authority (Contract No. 30000165044). Their support is gratefully acknowledged Finally, I would like to acknowledge the support of my family, to whom I dedicate this work. 4 Contents Declaration 2 Abstract 3 Acknowledgements 4 Contents 5 List of Figures 12 List of Tables 20 Nomenclature 24 1. Introduction 33 1.1 Conversion to Electrical Energy 33 1.2 Electricity Consumption 34 1.3 Primary Fuel Consumption 39 1.4 Primary Fuel Comparison 45 1.5 Summary 47 2 Nuclear Fusion 49 2.1 Fusion Fuel Cycles 50 2.2 Fusion Confinement 52 5 C. E. Wood, October 2015 Contents 2.2.1 Magnetic Confinement 53 2.3 Fusion Plant Models 58 2.3.1 Model A 58 2.3.2 Model B 60 2.3.3 Model AB 61 2.3.4 Model C 62 2.3.5 Model D 64 2.3.6 PPCS Summary 65 2.4 Fusion Constraints 67 2.5 Summary 69 3 Electrical Power Generation 71 3.1 Conventional Power Generation 71 3.1.1 Rankine Cycle 72 3.1.2 Brayton Cycle 79 3.1.2.1 Primary Brayton Cycles 80 3.1.2.2 Secondary Brayton Cycles 84 3.1.3 Binary Cycle 87 3.2 Alternative Energy Sources for Conversion 88 3.3 Direct Energy Conversion 90 3.3.1 Thermoelectric Energy Conversion 90 3.3.2 Thermionic Energy Conversion 97 6 C. E. Wood, October 2015 Contents 3.3.3 Electrohydrodynamic Energy Conversion 106 3.3.4 Magnetohydrodynamic Energy Conversion 114 3.3.4.1 Continuous Electrode Governing Equations 117 3.3.4.2 Segmented Electrode Governing Equations 119 3.3.4.3 Hall Generator Governing Equations 121 3.3.4.4 MHD Power Considerations 123 3.4 Summary 129 4 Two-Phase Liquid Metal MHD 132 4.1 Two-Phase Flow Models 132 4.1.1 Basic Parameter Definitions 133 4.2 Homogeneous Flow Model 134 4.3 Separated Flow Model 136 4.3.1 Gravitational Component 137 4.3.2 Frictional Component 140 4.3.3 Friedel Correlation for Friction 141 4.4 Two-Phase Liquid Metal MHD 142 4.4.1 Two-Phase Mixture Electrical Conductivity 143 4.4.2 Thermodynamics of MHD Section 145 4.5 Summary 147 5 Proposed Power Cycle 149 5.1 Introduction to Two-Phase Loop 150 7 C. E. Wood, October 2015 Contents 5.2 PPCS-C Power Cycle 151 5.3 Outline of Proposed Power Cycle 155 5.4 Governing Equations 158 5.4.1 Nozzle 159 5.4.2 Mixer 160 5.4.3 MHD Generator 162 5.4.4 Upcomer 163 5.4.5 Downcomer 163 5.4.6 Brayton Cycle 164 5.4.7 Rankine Cycle 170 5.4.8 Pb-17Li Physical Properties 174 5.5 Proposed Power Cycle Performance 175 5.6 Summary 194 6 Experiment Design Outline 196 6.1 Identifying the Objectives 196 6.1.1 First Tier Objectives 196 6.1.2 Second Tier Objectives 197 6.1.3 Third Tier Objectives 198 6.2 Liquid Metal 198 6.3 Experimental Apparatus 199 6.3.1 Materials 199 8 C. E. Wood, October 2015 Contents 6.3.2 Safety 201 6.3.3 Electric (Joule) Heating 203 6.3.4 Nozzle 204 6.3.5 Mixer 205 6.3.6 MHD Generator 205 6.3.7 Separator 206 6.3.8 Upcomer, Downcomer, and Cooling Section 207 6.3.9 Variable Flow Restriction/Drain 210 6.3.10 Thermocouples 210 6.3.11 Manometers 211 6.4 Viscosity Test 211 6.5 Surface Tension Test 213 6.6 Similitude 215 6.7 System Energy Balance 217 6.8 Summary 218 7 Experimental Results 219 7.1 Dynamic Viscosity 219 7.2 Surface Tension 222 7.3 Two-Phase Air/Water Mixture 229 7.4 Two-Phase Air/LM136 Mixture 239 7.5 Summary 245 9 C. E. Wood, October 2015 Contents 8 Discussion 247 8.1 Proposed Power Cycle 247 8.1.1 Brayton Cycle 247 8.1.2 Two-Phase MHD Topping Cycle 249 8.1.2.1 Experimentally Verifiable Assumptions 249 8.1.2.2 Non-Experimentally Verified Assumptions 252 8.1.2.3 Void Fraction Correlation 253 8.1.2.4 Liquid Metal Dynamic Pressure 257 8.1.3 Summary 259 8.2 Experimental Results 260 8.2.1 Air/Water 260 8.2.2 Air/LM136 263 8.2.3 Summary 265 8.3 Experimental Design Process 266 8.3.1 Liquid Metal 266 8.3.2 Measurement Devices 267 8.3.3 Electric Heating 267 8.3.4 Structural Materials and Experimental Scale 268 8.3.5 Other Considerations 270 10 C. E. Wood, October 2015 Contents 9 Conclusion 271 9.1 Specific Conclusions of this Research 272 9.2 Recommendations for Further Work 275 Appendices A LM136 Dynamic Viscosity Results 278 B LM136 Surface Tension Results 285 References 294 11 List of Figures Figure 1.1 Global electricity consumption between 1980 and 2012 showing contributions from grouped nations, reproduced using data [U.S. Energy Information Administration] 35 Figure 1.2 Averaged percentage of population by group with access to electricity, reproduced using data [The World Bank] 37 Figure 1.3 Population of grouped nations with sub-population that have access to electricity, reproduced using data [The World Bank] 38 Figure 1.4 Electricity consumption per capita in kWh, reproduced using data [The World Bank] 39 Figure 1.5 Electricity generation in 2010 reproduced using data from the World Energy Council [WEC, 2013] 40 Figure 1.6 Projected electricity generation in 2050 for Jazz scenario reproduced using data from the World Energy Council [WEC, 2013] 41 Figure 1.7 Projected electricity generation in 2050 for Symphony scenario reproduced using data from the World Energy Council [WEC, 2013] 41 Figure 2.1 Internal and external views of JET courtesy of EUROfusion 54 Figure 2.2 Tokamak magnetic confinement system, courtesy of EUROfusion 55 Figure 2.3 Cross-section showing tokamak zones, reproduced from Ricapito [2010] 56 12 C.
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