PFC/RR-81-26 DOE UC-20 C, D, E AN EVALUATION OF ACCIDENTAL WATER-REACTIONS WITH LITHIUM COMPOUNDS IN FUSION REACTOR BLANKETS P. J. Krane M. S. Kazimi July 1981 Plasma Fusion Center and the Department of Nuclear Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139 E.G. & G. Idaho, Inc. and The U.S. Department of Energy Idaho Operations Office under DOE Contract #DE-AP07-79ID00019 PUBLICATIONS UNDER CONTRACT #K-1702 ON FUSION SAFETY 1. M. S. Kazimi et al., "Aspects of Environmental Safety Analysis of Fusion Reactors," MITNE-212, Dept. of Nuclear Engineering, M.I.T., October 1977. 2. R. W. Sawdye, J. A. Sefcik, M. S. Kazimi, "Reliability Requirements for Admissible Radiological Hazards from Fusion Reactors," Trans. Am. Nucl. Soc. 27, 65-66, November 1977. 3. D. A. Dube, M. S. Kazimi and L. M. Lidsky, "Thermal Response of Fusion Reactor Containment to Lithium Fire," 3rd Top. Meeting in Fusion Reactor Technology, May 1978. 4. R. W. Sawdye and M. S. Kazimi, "Application of Probabilistic Consequence Analysis to the Assessment of Potential Radiological Hazards of Potential Hazards of Fusion Reactors," MITNE-220, Dept. of Nuclear Engineering, M.I.T., July 1978. 5. D. A. Dube and M. S. Kazimi, "Analysis of Design Strategies for Mitigating the Consequences of Lithium Fire within Containment of Controlled Thermonuclear Reactors," MITNE-219, Dept. of Nuclear Engineering, M.I.T., July 1978. 6. R. W. Sawdye and M. S. Kazimi, "Fusion Reactor Reliability Requirements Determined by Consideration of Radiological Hazards," Trans. Am. Nucl. Soc. 32, 66, June 1979. 7. R. W. Green and M. S. Kazimi, "Safety Considerations in the Design of Tokamak Toroidal Magnet Systems," Trans. ANS 32, 69, June 1979. 8. R. W. Green and M. S. Kazimi, "Aspects of Tokamak Toroidal Magnet Protection," PFC/TR-79-6, Plasma Fusion Center, M.I.T., July 1979. 9. S. J. Piet and M. S. Kazimi, "Uncertainties in Modeling of Consequences of Tritium Release from Fusion Reactors," PFC/TR-79-5, Center, M.I.T., July 1979. Plasma Fusion 10. M. J. Young and S. J. Piet, "Revisions to AIRDOS-II," PFC/TR-79-8, Contract #K-1702, Plasma Fusion Center, M.I.T., August 1979. 11. S. J. Piet and M. S. Kazimi, "Implications of Uncertainties in Modeling of Tritium Releases from Fusion Reactors," Proc. Tritium Technology in Fission, Fusion and Isotopic Applications, April 1980. 12. M. S. Tillack and M. S. Kazimi, "Development and Verification of the LITFIRE Code for Predicting the Effects of Lithium Spills in Fusion Reactor Containments," PFC/RR-80-ll, Plasma Fusion Center, M.I.T., July 1980. Publications Under Contract #K-1702 (continued) 13. M. S. Kazimi and R. W. Sawdye, "Radiological Aspects of Fusion Reactor Safety: Risk Constraints in Severe Accidents," J. of Fusion Energy, Vol. 1, No. 1, pp. 87-101, January 1981. 14. P. J. Krane and M. S. Kazimi, "An Evaluation of Accidental WaterReactions with Lithium Compounds in Fusion Reactor Blankets," PFC/RR-81-26, Plasma Fusion Center, M.I.T., July 1981. 15. D. R. Hanchar and M. S. Kazimi, "Tritium Permeation Modelling of a Conceptual Fusion Reactor Design," PFC/RR-81-27, Plasma Fusion Center, M.I.T., July 1981. AN EVALUATION OF ACCIDENTAL WATER-REACTIONS WITH LITHIUM COMPOUNDS IN FUSION REACTOR BLANKETS ABSTRACT Efforts to mitigate potential problems of lithium-based blankets for fusion reactors include the use of lithium compounds for breeding purposes. This report investigates the safety aspects of these alloys - relative to the use of pure lithium in a water-cooled blanket. Included in the study is a modification of the LITFIRE computer code to predict the thermal response of an internal blanket breeder-water interaction. For the problem analyzed, results indicate that some of the lithium-lead alloys may pose safety problems approximate to those associated with the use of liquid lithium. Li20 is shown to be significantly safer than liquid lithium, while results using LiAl are similar to those of the lithium-lead alloys. In addition, the study provides an overview of this safety question, signaling areas that require further development. -3- ACKNOWLEDGEMENTS Many people helped bring this effort to conclusion. In particular, Mark Tillack and Steve Piet, and Rachel Morton provided the needed hints to run LITFIRE and locate material properties. Gail Jacobson transformed the written notes into a typed manuscript. This report is based on a thesis submitted by the first author as part of the requirements for the degree of M.S. in Nuclear Engineering. -4- TABLE OF CONTENTS page Abstract ....................................................... 2 Acknowledgements ............................................... 3 List of Figures ................................................ 6 List of Tables ................................................. 7 CHAPTER 1. INTRODUCTION ....................................... CHAPTER 2. BLANKET DESIGN BASIS DESCRIPTION ................... 2.1 Introduction .................................. 2.2 Breeding Material ............................. 2.2.1 2.2.2 Lithium-Lead Alloys .................... Alternative Breeders ................ 2.3 Coolant ....................................... 2.4 NUWMAK Blanket Design ......................... 2.4.1 2.4.2 2.4.3 Structural Materials.................... Mechanical Design ...................... Summary of Important Parameters ........ CHAPTER 3. EQUILIBRIUM Tf CALCULATION ......................... 3.1 Introduction .................................. 3.2 Assumptions and Methodology ................... 3.3 Results and Discussion ........................ CHAPTER 4. DYNAMIC CALCULATIONS USING LITFIRE ................. 4.1 Introduction .................................. 4.2 LITFIRE Description ........................... 4.3 Internal Blanket Accident Option .............. 4.3.1 Assumptions and Structural Model ....... -5- Table of Contents (continued) 4.3.2 page Heat Transfer Mechanisms ................ A. Heat of Reaction .................... B. Sensible Heat Addition to Reactants . C. Forced Convective Cooling ........... D. Conduction .......................... E. Free Convection ..................... F. Radiation ........................... The Numerical Scheme .................... 49 Results and Discussion ........................ 56 CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS ..................... 67 4.3.3 4.4 References ..................................................... 49 51 52 53 53 54 55 69 Appendix A. Physical Properties Data ........................... 70 Appendix B. Complete Listing of LITFIRE ........................ 74 Appendix C. Sample Input to LITFIRE ............................ 115 Appendix D. Sample Output of LITFIRE ........................... 118 -6- LIST OF FIGURES page No. LITFIRE Predictions for Consequences of Lithium Spill in UWMAK III Containment ........................... 10 2.1 Cross-Sectional View of NUWMAK ........................... 13 2.2 Top View of NUWMAK ....................................... 14 2.3 Pb-Li Phase Diagram ...................................... 16 2.4 Effects of Lithium Concentration in a Lithium-Lead Breeder on Shielding Requirement and Tritium Breeding .... 18 Estimated Tritium Inventory in Alternative Breeder Blankets for 3000 MWth Reactor ........................... 19 1.1 2.5 2.6 Phase Diagram for LiAl System ............................ 23 2.7 Impact of Structural Material Content (316 Stainless Steel) on Tritium Breeding ............................... 27 2.8 Cross-sectional View of NUWMAK Blanket ................... 32 2.9 Schematic of the Blanket and Shield for NUWMAK ........... 34 3.1 Equilibrium Final Temperature Profiles for Various Breeders in Static Calculation ........................... 41 4.1 Internal Blanket Accident Option Heat Flow Diagram ....... 44 4.2 Internal Blanket Accident Option Node Structure .......... 48 4.3 Lithium Breeder Thermal Response to Water Interactions ... 57 4.4 Li7 Pb2 Breeder Thermal Response to Water Interactions .... 58 4.5 LiPb 4 Breeder-Thermal Response to Water Interactions ..... 59 4.6 LiAl Breeder Thermal Response to Water Interactions........60 4.7 Li2 O Breeder Thermal Response to Water Interactions ...... 61 4.8 Comparison of Reaction Zone Temperature Profiles of the Various Breeders .................................. 64 Comparison of First Breeder Element Temperature Profiles of the Various Breeders ......................... 66 4.9 -7- LIST OF TABLES No page 2.1 Reactions of Li-Pb Alloys and Lithium with Water ....... 20 2.2 Summary of Favorable and Unfavorable Features of Lithium-Lead Breeders .................................. 22 Summary of Favorable and Unfavorable Features of the Water-Cooled Blanket Concept ....................... 28 Summary of Structural Material Assessment for the Water-Cooled Blanket Concept ........................... 29 2.5 Physical Properties of Ti-6-4 .......................... 31 2.6 Major Features of NUWMAK Design ........................ 35 2.7 Summary of Important Blanket Parameters ................ 36 4.1 Breeder - Coolant Reactions of Interest ................ 50 2.3 2.4 -8- CHAPTER 1. INTRODUCTION Advancements in plasma physics research, together with a growing concern for the risks of energy production in the public sector, has led to an increasing number of detailed fusion safety studies. Topics, including routine and accidental releases of tritium, activation of structural material by neutron bombardment, and the consequences of lithium fires, are currently under various degrees of investigation. The findings of these studies are incorporated in subsequent fusion reactor designs, answering some questions and creating still more. This work is the product of a research program whose objective is to minimize the potential problems of a lithium-based blanket for fusion reactors. Such a blanket is practically forced upon us by the choice of The a D-T fuel mixture for first generation fusion power plants [1]. needed tritium is bred via the reactions: 6 Li (n,T) 4 He + 4.8 MeV 7Li (n,n'T) Initially, natural lithium (92.58% 4 He - 2.5 MeV. 7 Li, the rest 6Li), a liquid at operating blanket tenperatures, was the primary candidate for blanket breeder and/or coolant materials, due to its excellent breeding and heat transfer qualities, effectiveness in neutron moderation and relatively low pumping power need as compared to other liquid metals [2]. However, with time and study, serious disadvantages in the use of liquid lithium emerged. -9- Pure lithium is highly reactive with air, water and concrete; all materials that will be in abundant supply in the reactor environment. Experimentation at the Hanford Engineering Development Laboratory (HEDL) and computer modelling studies at MIT using the computer code LITFIRE (to be discussed in more detail later in this report) indicate that temperatures and pressures in the reactor containment area, in the event of a sizable lithium spill, can attain critically high values [3]. Figure 1.1 shows such a possibility. Such an event could provide a pathway for release of tritium or structural activation products, providing a hazard to plant personnel or the outside world. This problem and others, including corrosion, difficulties in tritium recovery, and magnetohydrodynamic instabilities [4], have led designers to consider alternative materials for fusion blankets. Among such considerations are lithium-lead alloys. This report will provide a preliminary analysis of lithium-lead alloys for use as breeding materials from the safety point of view. While it is thought that these materials provide less of a hazard than the use of liquid lithium, little has been demonstrated. Thus, there is the need to formulate some framework for a comparison. Before actual calculations can be made, a basis must be established. The NUWMAK reactor design by the University of Wisconsin (1978) was chosen for this purpose, due to its use of Li62 Pb38 eutectic as the tritium breeder. The primary hazard here involves interaction between the lithium- lead alloy breeder and the boiling water coolant, inside the blanket. Specifics of this design are further discussed in Chapter 2. -10- 1250- Pool 1000 750- CelI Gas 0750 Stee .e Li 250 0 2 4 6 TIME Figure 1 .1 8 10 (10 3 sec) LITFIRE predictions for consequences of lithium spill in UWOAK III containment (Reference 3) . 12 -11- Using this basis, two separate. studies are performed. a static calculation: The first is the breeder and coolant are allowed to interact immediately and the subsequent equilibrium final temperature of the blanket materials is determined. This is presented in Chapter 3. The second study is a dynamic calculation, using LITFIRE, of the temperature histories at various points in the blanket, if some accident allows breeder and coolant to come into contact. This is presented in Chapter 4. It should be stressed that in both studies, the values obtained are not sufficient evidence in themselves. Rather, these values must be compared with similar calculations employing the use of pure lithium. In this way, a measure of the relative hazards of the alternate breeders can be assessed. -12- CHAPTER 2. BLANKET DESIGN BASIS DESCRIPTION 2.1 Introduction NUWMAK, a conceptual thermonuclear reactor designed by the Fusion Engineering Program of the University of Wisconsin in March 1979, is one of a number of second generation studies aimed at maximizing the strengths of fusion while minimizing the weaknesses. This work builds upon the findings of a number of first generation designs aimed at identifying the important problems of fusion power. The design philosophy of this study was to search for an "end product that has the potential to be reliable, maintainable, environmentally acceptable, and reasonably economic [4]." To do this, a number of changes were made to the preceeding reactor concept, UWMAK III, including: an increase in the magnetic field to increase power density, a simplification of design to facilitate maintainence (as well as eliminate large cost items), the selection of structural materials to minimize resource requirements and costs, and a change in blanket breeder and coolant materials to reduce thermal fatigue and thereby increase reliability. The resulting structure is shown in Figures 2.1 and 2.2 The new elements in blanket breeder and coolant materials are of particular interest to those concerned with fusion safety studies. Utilized in NUWMAK are: (a) Li62 Pb38 eutectic for the breeding material, used because its melting point is very near the blanket operational temperature and thus, the latent heat of melting can provide energy storage, and (b) boiling water for the coolant, the "perfect choice," discarded previously with the presence of pure lithium as the breeder. -13- U, 0: I- _j L) CL 'T C .. U)IL a. L0 m0j ..... Ix 00J LUJ . <______ 0 cff. 5: -j z 2 0) 0 C-) z LL 0 U) 0 U) WWI \ -, V)' -Jq,-> MOM:Lj Zj -a~ CL < Figure 2.1 . ..~...~ .. . -.-. Cross-sectional View of NUWMAK (Reference 4). O i -14- TOP VIEW OF NUWMAK SUPERCONDUCTIVE OH COILS INNER BLANKET TUNGSTEN EDDY ZONE CURRENT SHIELD - NORMAL COPPER .TF TRIMMING COILS OUTER BLANKET CENTRAL STRUCTURAL CYLINDER - .RF CAVITY -L - -REFLECTOR / - GRAPHITE FIXED SHIELD VACUUM- REMOVABLE D SUPERCONDUCTIVE TF COILS Figure 2 (Reference 4 ) MOU- TABL CRYOGENIC SHIELD -15- A preliminary survey of the hazards of lithium-lead alloys indicates that interaction with water is by far the more severe problem, as these materials are relatively inert in air. NUWMAK, in addition to its use of Li62 Pb38 , provides an opportunity for the breeder and coolant to come into contact, specifically a breach in the cooling system inside the blanket. Thus, NUWMAK is the logical first choice for a basis for an investigation of the relative safety of the lithium-lead alloys. 2.2 Breeding Materials 2.2.1 Lithium-lead alloys The lithium compound selected as the tritium breeding material must satisfy many requirements. It must have desirable neutronic and irradia- tion characteristics, chemical stability at blanket operating temperatures, and be compatible with other blanket materials. More importantly, the compound must breed and release tritium at sufficient rates to fuel the reactor, yet limit the tritium inventory in the blanket to reasonable 1'vels. Lithium-lead compounds are interesting materials. the phase diagram of a Li-Pb two component mixture. Figure 2.3 shows However, beyond Li7 Pb2 ' considered the most attractive lithium-lead alloy for breeding purposes, little else on the subject of Li-Pb physical properties is certain.- -An accumulation of data relevant to this study through a literature search and "data synthesis" is presented in Appendix A. Two neutronic characteristics of the lithium-leads, breeding cabability and long-lived activation products, have been studied. In the latter only 205 Pb presents any problem in the long term unless significant amounts of impurities exist. This is not expected to be serious [4]. Breeding -16- 800 I I I i U Pb2 7260C IG 700 60c LiPb C.) 50C 48 2 CC 4 2 40C LLI I" 300 200 l00 177 0 C - - K -IF 0 20 Pb - Li 40 60 ATOM -% Li PHASE DIAGRAM Figure 2.3 (Reference 4) 80 100 -17- capability depends on the amount of lead present. Li7 Pb2 has been examined in detail and exhibits an excellent breeding property. multiplier. This is due to the presence of lead, which acts as a neutron Figure 2.4 shows the effect of lithium concentration in the lithium-lead breeder on the total breeding ratio. The total bulk shield thickness required to protect toroidal field coils is shown for reference. It is evident that a reduction of the lithium concentration will cause a substantial loss of fuel multiplication. However, the reduction of lithium also tends to enhance magnet protection by virtue of more effective nuclear radiation shielding by the added lead [5]. A diffusion study by Wiswall [6] shows that the soluability of tritium in Li-Pb is much lower than that in pure lithium, as the activity of lithium is very low due to the presence of lead. Thus, the tritium inventories can be much smaller, tritium diffusivities relatively higher, and tritium recovery much easier. Specifically, Fig. 2.5 shows that Li7 Pb2 has the lowest inventory of any of a number of proposed breeders. A problem here could be the fact that Li7 Pb2 becomes a "chunk" at high temperature. This would increase the diffusion path of tritium and make recovery difficult [4]. A more serious problem of the lithium-leads involves their compatibility with the blanket environment. All react to some extent with water. Table 2.1 shows the results of experimentation to investigate this at Argonne National Laboratory. It can be seen that Li-Pb alloys can react vigorously with water, more so at elevated temperatures. However, a significant result is that Li17 Pb83 exhibited only moderate reaction with water. Also, insufficient hydrogen was evolved by the alloy reactions to attain ignition conditions, unlike the case with liquid lithium. -18- S1M 13 I U 1 0 2 -- j) 090)6 '10) p 0i 05 103a ft 04 U 03 02 Of 0 0 Figure 2.4 10 20 30 60 so 40 L:ITMIU CONCENTIOATI0,. % 70 60 10 1O Effects of lithium concentration in a lithiumlead breeder on shielding requirement and tritium breeding (Reference 5). -19- 650 3.5 I 600 550 TEM. *C 450 500 1 .1 I 400 I I 300 I 3.01 0 0 2.5 F- 0 w z Li20 - 2.0 LI.Pb2 L.At CD 1.5 0 0 C 1.0 0.5 I.C ~~~~1 1.1 1.2 1.3 10 Figure 2.5 1.4 1.5 1.6 K/T Estimated tritium inventory in alternative breeder blankets for a 3000 1lth reactor (Reference 9). -20- TABLE 2.1 Reactions of Li-Pb Alloys and Lithium with Water Sample Water Case Composition State Temp/*K Ter-p/*K Reaction 1 Li 7 fpb2 s 773 298 Modest 2 Li7 Pb2 s 773 369 Vigorous 3 Li7 Pb2 s 873 368 Vigorous 4 Li7 Pb2 L 1103 36S Very Vigorous 5 Lio. 62 Pbo. 3 8 L 773 368 Vigorous 6 Li0 .17 Pb0 .8 3 z 773 368 Very modest 7 Li z 773 368 H 2 Detonation 8 Lia Z 773 368 Detonation a Injected under water (Reference 7) -21- In all reactions, LiOH (melting point at 470 'C) is formed. Liquid LiOH is an extremely corrosive substance and would degrade the integrity of the activated structural materials [7]. inert in air. Fortunately, Li-Pb is relatively It was reported [8] that "LiPb (50-50 mixture) resembles Pb in every respect except density. to the flame of a gas-air torch." LiPb would not ignite, even when exposed Therefore, though a Li-Pb - H20.reaction could be very serious, it is not expected to be as severe as an accident involving pure lithium. Table 2.2 provides a summary of the advantages and disadvantages of the lithium-lead alloys. 2.2.2 Alternative Breeders For completeness, LiAl and Li2 0, also candidates for the tritium breeding material, will be analyzed with regard to safety in this study. Other strong candidates, specifically Li2SiO 3 and LiAl0 2 , have been ignored in this study since they have no appreciable reaction with water. LiAl is in many ways akin to Li7 Pb2 , such as a similarity in reactivity with water. However, the latter material is preferred by designers due to a superior tritium breeding capability. This is because there is a lower lithium-atom density in LiAl and no neutron multiplier, with the absence of Pb. Tritium extraction characteristics are also poorer than that of Li7 Pb2 [9]. The primary activation product is problem than 205Pb. Physical properties of this breeder are also unexplored and are discussed in Appendix A. The 26 Al, more of a phase diagram is shown in Fig. 2.6. Li20 has a marked advantage over the lithium-lead alloys in the matter of reaction with water. Because it is in oxide form, this compound does not evolve hydrogen upon reaction and produces less heat [9]. It is -22- TABLE 2.2 Summary of Favorable and Unfavorable Features of Lithium-Lead Breeders Lithium-Lead Alloys Advantages 1. High breeding ratio attainable 2. Probably less reactive with water than liquid Li 3. Tritium recovery appears feasible with low-pressure helium Disadvantages 1. Poor technology base: high degree of uncertainty in properties 2. Reactive with water coolant 3. High blanket weight 4. Uncertain radiation damage effects 4. Lead helps shield magnets 5. Uncertain tritium release mechanism 6. Requires blanket changeout during reactor life 7. Activation product: 205Pb -23- S2} 8 456 2 WEIGHT PER CENT 1', 25 2A LITHIUU 40 5 30 0 7D BO 90 800 * REF 5 700 - o*Y. --- S * 600 601 0. or (At 7/ -So So t 400 300 I .17 1001____ 0 At. ___ _ .0 20 Figure 2.6 30 3D iC 40 H0 E5 PE 50 ATOMIC PER CENT 60 __:_ss_____s 70 SO LITHIUM Phase Diagram for LiAl System. (Reference 9) s 10D L. -24- therefore expected that the use of this breeder will not pose a major safety problem. However, Li20 has fallen into disfavor because it has a high lithium-atom density. This, combined with a poor diffusion rate, leads to excessive tritium inventories. Physical properties of this breeder are also discussed in Appendix A. 2.3 Coolant Many -factors affect the choice of coolant. Unique in power production to fusion is the interrupted burn cycle of the plasma. This produces the problem of thermal fatigue in the first wall and blanket, caused by the fluctuating temperature of these structures with the plasma burn cycle. The temperature change is a combination of three effects: 1. Coolant temperatures rise, Tcout-Tcin 2. Film temperature drop, Twall - Tc (=Q/h) 3. Temperature difference across the first wall, AT= Q X/k [4]. While the third effect depends on structural materials, the first two can be greatly reduced by choice of the proper coolant, one which has a small coolant temperature rise that simultaneously provides a large heat transfer coefficient. This describes a boiling liquid and the first logical choice is boiling water. A considerable technology has been developed through the years for the use of water as a coolant in energy production. advantages. There exist many Water is an excellent heat-transfer fluid, costs little and is readily available. It is easy to pump and is non-corrosive with conventional structural materials. -25- It is interesting to note, however, that up to this point, few designers have considered water for the primary coolant. There exist a number of concerns and questions including neutronics, tritium, and safety considerations. In addition, the use of a boiling water or steam coolant will require high pressure containment. The NUWMAK design calls for cooling water at 300 *C and 8.6 MPa (1250 psi). This poses additional design and safety problems. The safety concerns of a water-cooled blanket have been discussed. It should be noted that this problem effectively prohibited the use of water as a coolant until alternative breeders to lithium were suggested. Even so, current designs using water stress the use of strong cladding materials for coolant channels. High-integrity cladding is also the prescription to minimize tritium diffusion into the cooling water. Tritiated water is a safety hazard and recovery of the tritium is difficult and expensive. However, recent studies using permeation rates for stainless steel cooling tubes show tritium losses could be less and 1 Ci/day, assuming the formation of oxide films inside the tubes [9]. Irregardless, it is obvious that the coolant loop cannot be used for tritium recovery, necessitating some recirculation of the breeder. The necessity of avoiding contact between breeding materials and coolant tends inherently, to increase structural material content in the blanket. From a neutronics point of view, this increase tends to degrade the tritium breeding ability, due to increased parasitic neutron absorption. However, the strong neutron slowing-down power of water improves breeding performance by increasing the 6Li (n,T) 4He reaction rate for low energy neutrons. This decreases parasitic absorption by -26- the structural materials [5]. Therefore, proper design and choice of materials can leave the tritium breeding capability of a water-cooled blanket virtually unchanged. Figure 2.7 shows this phenomenon for various breeders, with 316 stainless steel used as structural material. It is important to note that the addition of water significantly improves the breeding ratio in the Li7 Pb2 , more so than the other breeders. This is due to reduced parasitic absorption in lead as well as the stainless steel. Table 2.3 summarizes the advantages and disadvantages of the water-cooled blanket concept. Chief among the assets is the use of available technology in its construction. The major liabilities appear to be the safety problem and limited choices in compatible breeding and structural materials. Further study in both areas is necessary before a final decision can be made. 2.4 NUWMAK Blanket Design 2.4.1 Structural Materials Many structural materials have been considered for a water-cooled blanket design, including: austenitic stainless steel, high nickel alloys and selected titanium, vanadium and niobium alloys [9]. Table 2.4 summarizes an assessment of these candidates with regard to properties associated with the blanket environment. One of the liabilities of the water-cooled design is apparent. The vanadium and niobium materials, which respond well to neutron bombardment, are eliminated due to water corrosion problems. Also noted is a general lack of data regarding the compatibility of these structural materials with the lithium-lead alloys. Since decomposition of these alloys is not -27- 1.8 1.7 LIP - WITHOUT W.TER 15 v/a Hs IN LI Pb2a ---- WITH WATER (10-15 v/o) 0-5 v/o He IN LiTpz IN 1.6 BREEDER BLANKz-T: 0.8 m 50 %SS+- 50 % SC SHIEL.D: 0.2 1.1 1. .0 LizO 0 Figure 2.7 15 to5 STAINLESS-STEEL VOLUME. Impact of Structural 20 % Material Content C316 SS) on Tritium Breeding (Reference 6). -28- TABLE 2.3 Summary of Favorable and Unfavorable Features of the Water-Cooled Blanket Concept Water Coolant Advantages Disadvantages 1. Excellent heat-transfer fluid 1. Highly reactive with candidate 2. Well-developed technology base 2. Reaction product (LiOH) is very corrosive 3. Low cost and readily available 3. Requires high-pressure containment 4. Relatively low temperature (-.320 *C) operation 4. Cannot be used for tritium recovery 5. Compatible with conventional structural materials 5. Expensive to remove tritium from H2 0 (safety) 6. Low pumping power need 6. Water tends to be a sink for tritium breeding materials 7. Enha'nces tritium production 8. Liquid at room temperature 7. Nb and V, candidate structure materials are incompatable I -29- TABLE 2.4 Summary of Structural Material Assessment for the Water-Cooled Blanket Concept Rat ing Property Requirement * Fe Ni Ti V Nb Bulk Radiation Effects 2 2 ? 1 1 Compatibility with H2 0 1 1 1 4 4 Compatibility with Liquid Li 3 5 3 1 1 Compatibility with Solid Li 2 0 and Li 7Pb 2 3 3 3 3 3 Compatibility with H(DT) Environment 1 1 3 -1 .1 Rating numbers defined as follows: 1. Compares favorably with other candidate structural materials. 2. Limits operating life but probably acceptable under certain conditions. - 3. Little data available but may be a libit4in 4. Probably not viable for conditions of interest. factor. -30- desirable, this question should be studied. The NUWMAK design utilizes Ti-6Al-4V alloy for the first wall and coolant tube material due to its high strength-to-weight-ratio, good fatigue resistance, fabricaility, low long term residual activity and well established industry [4]. shown in Table 2.5. Physical properties of this alloy are The NUWMAK shield is more conventional, primarily B4 C. 2.4.2 Mechanical Design The blanket of NUWMAK is shown in Fig. 2.8. The blanket structure is Ti-4A1-4V which operates at a temperature of approximately 350 *C. The coolant is boiling water at 300 *C.and 1250 psi. The breeder is Li62 Pb38 eutectic, operating at approximately 400 *C. The design life for each blanket module is two years. The blanket is divided into eight modules in the reactor. Each module is fed and discharged coolant and breeding materials separately. There are two blanket units- in each module; the inner blanket near the machine axis and the outer blanket, as seen in Fig. 2.8. These two units are completely separate from each other. The first wall consists of a continuous bank of tubes running in the vertical direction. Beyond this, the blanket is cooled with rows of vertical tubes on a triangular pitch. The spacing between rows of tubes is progressively increased towards the back of the blanket to account for the radially decreasing nuclear heating [4]. Radial struts are spaced at 20 cm intervals, reinforcing the first wall against the hydrostatic pressure of the breeding material, coolant tubes. which fills the space between the -31- TABLE 2.5 Physical Properties of Ti-6-4 Atomic Weight Melting Point Mass Density Yield Strength 45.9 1668 *C 4.4 g/cm3 Modulus of Elasticity 530 MPa 85 GPa Yield-to Weight Ratio 120 N-m/g Thermal Condcutivity Coefficient of Thermal Expansion Heat Capacity .12 W/cm-K 10 x 10- 6 /OC 668.8 J/kg-K i -32- COOLAN T INLET BREEDING MAl TERIAL INLET OUTER BLANKET NNER BLANKE T ,---FIRST WALL COOLING TUBES BREEDING MATERIAL OUTLET COOLANT OUTLET 0 Figure 2.8 Cross-Sectional Viewi of Blanket 2 (Reference 3 meters 4) . -33- At the blanket's edge is a thin graphite reflector. a shield to protect the cryogenic magnet coils. Beyond this is The shield is primarily B4GC, operating at approximately 150 *C. Figure 2.9 shows a schematic diagram of this system. 2.4.3 Summary of Important Parameters The major features of the NUWMAK design are given in Table 2.6. In addition, important blanket parameters pertinent to this study are given in Table 2.7. calculations. These values are used where appropriate in subsequent -34- SCHEMATIC AND OF THE BLANKET FOR NUWMAK SHIELD 6k- 41SHIELD -JBREEDG 2k D IG .A I I 2 1 13.75 HOT SHIELD BREEDING ZONE 1% 0.25% H20 Pb I% SHI ELD 3.5% 89.4% Pb Li 95.25% C 95.250% B4C H2 0 3.7% H20 1% Pb 1.2% 0.25% 93% W 2% GRAPHITE REFLECTOR 3.5%Ti.alloy 3.5%Ti alloy 4%Ti alloy 5.7%Ti alloy 95.25% B4C meters 10 7.95 6.4 6.9 2.9 3.35 3.95 COLD SHIELD 9 5 Pb Figure 2.9 (Reference 4) H2 0 Pb ri alloy 1% 0.25% Pb -35- TABLE 2.6 Major Features of NUWMAK Design Power Total Thermal Power Net Electric Power 2283 MWth 660 MWe Plasma Major Radius Minor Radius Plasma Height to Width Ratio (b/a) Plasma Current Toroidal Beta neTE q(a) 5.13 m 1.13 m 1.64 7.2 MA 6% 2 x 101 4 cm- 3-sec 2.64 Magnet On-Axis Toroidal Field Toroidal Field at NbTi Conductor Stabilizer Number of Toroidal Field Coils Number of Cu Trim Coils 6.05 Tesla 11.5 Tesla Al uminum 8 16 Blanket Structural Material Coolant Breeding Material Average Neutron Wall Loading Titanium Alloy Boiling Water Li6 2 Pb 38 4.34 MW/m 2 -36- TABLE 2.7 Summary of Important Blanket Parameters Plasma Burn Time Plasma Down Time 225 sec 20 sec Coolant Temperature Coolant Pressure Total Coolant Flow Rate Total Coolant Tube Surface Area Heat Transfer Coefficient of Boiling Water 300 *C 8.6 MPa 1500 kg/sec 4350 m2 20000 Btu/hr-ft 2 - OF 1.3 cm 1.0 cm Coolant Tube OD Coolant Tube ID N. Tubes in Outer Blanket Module Pitch Length 475 12 cm Space for Breeder in Outside Blanket Module Breeder Temperature Shield Temperature 17.72 m3 400 *C 150 *C -37- CHAPTER 3. EQUILIBRIUM Tf CALCULATION 3.1 Introduction Lithium-lead alloys are considered less of a safety hazard due to the presence of lead, which is thought to slow down the water reaction, decrease the heat of reaction and help absorb what heat is released. However, a number of physical properties are altered with the addition of lead. Since most of these properties have direct bearing on an interaction with water, the consequences of such an interaction are not directly predictable. For this reason, a preliminary analysis of the Li-Pb - H2 0 reaction is performed using a static calculation. In this case, the breeder inside one blanket module is allowed to interact completely with varying amounts of the water available to that module. Assuming the heat of reaction is contained within the blanket, the equilibrium temperature of the reaction products, unreacted breeder and blanket structural materials is then determined. Such a scenario is unrealistic, but this calculation is important for two reasons. First, it serves as a reference for further study. Second, with its assumptions, such a calculation may indicate the maximum attainable bianket temperature in a particular module in the case of an internal blanket water interaction. 3.2 Assumptions and Methodology The outer blanket section of an individual module is chosen for consideration. The inner blanket section contains only a nominal amount of breeder and the consequences of an accident in that section do not ---------- -38- appear as severe. Data from the NUWMAK design (Table 7.H.2) indicates that an outer blanket module contains 38.4 tonnes of titanium structural material, 106.0 tonnes of graphite and 17.7 m3 of space to contain the breeder. Therefore, the amount of breeder present can be determined with knowledge of the density. The initial temperature of breeder and graphite is 400 *C. The structural materials are at a temperature of 350 *C and the coolant is at 300 *C and 1250 psi. The reaction between breeder and coolant is assumed to be immediate and complete at 400 *C, the heat of reaction helping to raise the water temperature to that point. The heat of reaction can be determined using: AHr = AH 5 + ZAHprod - EAHreact, cal/g breeder (3.1) where AH2 5 is the standard heat of hydrolysis at 25 'C and AHprod and AHreact are the enthalpy changes of reaction products and reactants, respectively, as they are heated from 25 *C to 400 *C. The amount of coolant water available to the outer blanket module can be determined by analysis of NUWMAK's steam generating unit. In this respect, NUWMAK is very much like a fission boiling water reactor [4]. Examination of the Dresden BWR reveals that the total coolant volume in the 3411 MW th plant's cooling system is 11,695 ft3 [10]. Scaling this down to NUWMAK's 2283 MWth output and assuming the average density of water in the coolant loop to be 62.37 lb/ft 3 (an overestimate), it can be shown that approximately 15,260 pounds of water are available to interact with the breeder in one module. -39- It is assumed that a fixed percentage of this -cooling water interacts with the breeder. blanket. Thereafter, no loss of heat is allowed from the The resulting final equilibrium temperature can be calculated using the expression Tf= T0 + R (Ms~s + Mb'b + ZMRi (3.2) Ri Tf = final equilibrium blanket temperature where T = initial blanket temperature QR = reduced heat of reaction Ms = structural mass Mb = remaining breeder mass after reaction MR = reaction product mass after reaction C = mean specific heat for each component Reaction products include hydrogen gas, LiOH and the alloy element. A proper evaluation of the M C. terms in the above equation varies with each component. For example, LiOH is evaluated above its melting point as MLiOH where LiOH M LiOH [s(T mel t- To)+ AHmel t T T L(Tf-Tmelt) Cs = mean solid specific heat of LiOH CL = mean liquid specific heat of LiOH at 470 *C AHmelt = heat of melting for LiOH at 470 'C Tmelt = melting point of LiOH (470 *C) ( (3.3) -40- Similar expressions can be written for the other components. The reduced heat of reaction can be written as QR = xMc [ao AHR ~c (T where - T )] - MTi CTi (To - T i), (3.4) Mc = mass of total available- coolant M = mass of titanium structural material Cc = mean specific heat of coolant CTi mean specific heat of titanium structural material Tc = coolant temperature TTi = titanium structural material temperature x = fraction of available coolant reacting ao = reaction stoichiometric combination constant This is done to raise the coolant and titanium alloy structure to the initial blanket temperature of 400 *C. 3.3 Results and Discussion Figure 3.1 shows the resulting equilibrium blanket temperatures for the various breeders under consideration, plotted against the reacting percentage of available water. A number of interesting results are noted. First, as expected, the pure lithium breeding blanket reached the highest temperature upon reaction with water. The dotted line signifies that with a high percentage of available water reacting, some of the unreacted lithium will begin to vaporize at a temperature also close to the melting point of steel. This indicates a potential for further problems if a steel blanket liner is used. -41- ±1450 1300 Li T E 1±50 M P E R 1000 A LiAl Li Pb U R E C 700 -.- - Li2 - - 550 400 0.25 PERCENTAGE Figure 3.1 0.50 0.75 OF AVAILABLE Equilibrium Final 1.00 H20 .REACTING Temperature Profiles for Various Breeders in the Static Calculation. I-- I -42- Li7 Pb2 and LiAl are very much alike. Though lower equilibrium temperatures are exhibited than those of the pure lithium breeder, the difference is not very large to be significant. At low percentages of reacting available water, there is no difference. Li2 0 and LiPb 4 , on the other hand, appear to be significantly "cooler" than the pure lithium case. In the case of Li2 0, the key difference is a very low heat of reaction with water. LiPb 4 , with a relatively high density, is the only case in which there exists more available water than breeder. Thus, a limited heat of reaction and large residue of lead leads to reduced equilibrium temperatures. -43- CHAPTER 4. DYNAMIC CALCULATION USING LITFIRE 4.1 Introduction Though valuable as a reference, the calculations of Chapter 3 have little to do with a plausible internal blanket breeder-coolant interaction. It is incorrect to assume that these materials will react instantly at a constant temperature; it is imprudent to declare that the flow of cooling water will cease and that all heat will be retained within the blanket perimeter. Clearly, a dynamic formulation is needed. To this end, the LITFIRE computer code is modified to estimate the thermal response of the NUWMAK blanket to possible accidents. In this modification, called the internal blanket accident option, the breeder and water react in a zone located in the middle of the breeder mass. The leakage of water into this "reaction zone" is determined by the number of broken coolant tubes, set small enough to justify the assumption that this is the limiting effect on the reaction rate. The heat of reaction is transferred to the breeder mass by conduction and free convection, to the blanket liner and shield by further conduction, and out of the blanket via forced convective cooling by unbroken coolant tubes. Figure 4.1 shows the heat flow diagram for this system. It is hoped this model presents a truer picture of what will happen within the blanket in the event of a cooling system leak. Again, due to uncertainties concerning data and some assumptions, this study can only provide a measure of relativt safety, compared with the trials utilizing liquid lithium. -44- 7 Heat ve ;G4onvec Cooling REACTION ZONE of Reaction Conduction Free Convection FIRST BREEDER ELEMENT BREEDER ZONE Cooling Cooling Conduction SECOND BREEDER ELEMENT ) Convective Cooling C 4'Conduction FINAL BREEDER ELEMENT Convective Conduction LINER Conduction SHIELD Figure 4.1 Internal Blanket Accident Option Heat Flow Diagram. Cooling -45- 4.2 LITFIRE Description LITFIRE is a computer code developed at MIT [11] to predict the consequences of a hypothetical lithium spill in a fusion reactor containment. It was first written in 1977 as a mofidication of the Argonne National Laboratory code SPOOLFIRE, used to model the consequences of sodium fires. LITFIRE was later modified and improved in 1980 [3], utilizing the experimental results of small-scale lithium spill tests performed at the Hanford Engineering Development Laboratory. In this code, the flow of heat is traced from the lithium reaction zone source to reactor containment components, and eventually out to the ambient. This system is simulated by a nodal network in which each node has a heat capacity and temperature equal to that of its physical counterpart. Heat flows between nodes are calculated using standard heat transfer correlations. To provide the reactor containment thermal and pressure response, LITFIRE solves a set of coupled heat and mass transfer equations. This is done by using the method of finite differences for the spacial dimensions, and either Simpson's rule or a Runge-Kutta method in the time domain [3]. Properties are computed at each time step from the integral equation t Y(t) = Y(t0 ) + dt' dY/dt', where the rates of change dY/dt are given for each node by finite difference solution of the heat transfer relations. -46- 4.3 Internal Blanket Accident Option 4.3.1 Assumptions and Structural Model The internal blanket accident option models an accidental interaction of coolant water and lithium-based breeder in the center of an outside blanket module. This interaction is caused by a breach of several neighboring coolant tubes, while the reactor as a whole undergoes normal operation. It is assumed that this event is undetected, thus assuring continuance of the plasma burn and coolant recirculation. It is felt that the three monitored parameters relevant to an accident of this type, namely bulk breeding material temperature, coolant temperature, and coolant flow rate, will not change appreciably until later stages of the accident. The reaction rate is immediate and limited by the leakage of water into the breeding material. The leakage rate, dictated by the number of broken coolant tubes, is set very low, 0.6 kg/sec (three broken tubes), to make this assumption reasonable. Although there is a suspicion that the water reaction rate of the lithium-lead alloys is slow at low temperatures, no data exists. It is also assumed that the reaction zone pressure at high temperatures does not significantly retard the leakage rate of water into the zone. The reaction zone is very difficult to characterize. certain assumptions can be made. However, First, the zone can be considered spherical, as boiling water at 8.6 MPa will disperse equally in all directions upon tube rupture. The reaction zone must be large enough to accomodate the influx of breeder and coolant, thus the zone radius -47- should be large compared to the coolant tube pitch length. However, to accomodate the assumption that the water reiction is instantaneous, the reaction zone volume should be small, compared to that of the blanket module. The initial radius of the reaction zone for three ruptured coolant tubes is set at one foot. This is over six times the characteristic distance separating the three coolant tubes in question. of this zone is less than 2% of the total blanket volume. reasonable for the small leakage rate. The volume This seems Further research in this area would aid the accuracy of the model. The reaction products (LiOH and alloy element, if any) remain in the reaction zone, thus increasing the radius of this zone with time. The heat capacity of this expanded zone is calculated summing the products of the individual heat capacity of each component multiplied by the weight percent. The nodal structure of this system is shown in Figure 4.2. It can be seen that the reaction zone and breeder mass a.re broken into a number of sections. This is to more accurately account for heat transfer by conduction. The number of sections in each zone is selected so as to keep the element widths to approximately 6 inches. These elements increase and decrease in width with time in the reaction zone and breeder zone, respectively, as the reaction zone expands. The blanket elements are spherical, like the reaction zone, to facilitate computation. The outer element is therefore irregularly shaped to account for the NUWMAK geometry. create any difficulty, as it This is not expected to is doubtful that much heat will be -48- -a--. N "S N, *. *\ '.5' N' 'S \ REACTION ZONE L-' * a ,i .5 5. *\~) . . . I / i '~ 1 0 0 / 'S I -'p.. / I 5, 5/ 7, 5- / . SHIELD S / '5- / / / I 7/' ,LIN ER BREEDER ZONE Figure 4.2 Internal Blanket Accident Option Node Structure. -49- transferred to this region. For completeness, the steel liner and B4 C shield are also monitored in the code. The conduction of heat is assumed to stop at the far edge of the shield. The heat of reaction is distributed evenly throughout the reaction zone, heating the reactants and reaction products. Heat is removed by conduction and free convection to the breeder zone, and via forced convection by unbroken coolant tubes as shown in Fig. 4.1. The surface area of cooling tubes in each element is calculated as a volume percentage of the total. Finally, it should be noted that the densities and thermal conductivities of the lithium-lead alloys and other alternate breeders are held constant with temperature in this analysis. As discussed in the appendix, this data has only been determined at one temperature. Rather than increase uncertainties with various correlations, the values are unaltered. 4.3.2 Heat Transfer Mechanisms A. Heat of Reaction All of the alternate breeders considered in this study react to some extent with water. Table 4.1 shows the reactions of interest. Other reactions also take place, such as the production of Li202, but are discarded as they play a very minor role. For exampl.e, the peroxide is unstable above 250 'C [11] and is not produced above that temperature. Reaction occurs at the reaction zone temperature Tcz' The heat of reaction can be calculated using AHR H25 + AHrod - EAHreact ,e Btu/lb breeder (4.1) -50- TABLE 4.1 Breeder-Coolant Reactions of Interest AHhyd (kJ/g-atom of Li) Li + H2 0 - LiOH + 1/2 H2 205 1/7 Li7 Pb2 + H2 0 200 LiPb 4 + H2 0 + LiAl + H2 0 Li20 + H2 0 + LiOH+ 1/2 H2 + 2/7 Pb LiOH + 1/2 H2 + 4Pb LiOH +1/2 H2 + Al + 2LiOH 170 200 64 -51- where HO5 is the standard heat of hydrolysis at 25 C and AHprod and AHreact are the enthalpy changes of the reaction products and reactants, respectively, as they are heated from 25 *C to Tcz' Since the reaction is immediate, limited by the leakage of water into the reaction zone, the reaction rate is the leakage rate. This can be written as R = NT lb H2 0/sec (4.2) where m is the mass flow rate of water through one tube and NT is the number of ruptured tubes. Thus, the total heat generation rate inside the reaction zone can be given by Q = a0 AHR m NT where a BTU/sec (4.3) is the stoichiometric combination constant for the breeder and water in the given reaction. B. Sensible Heat Addition to Reactants in the Reaction Zone A portion of the heat of reaction is used to heat the inflowing coolant water and breeder to the reaction zone temperature. This can be written as Qs =NTi w cw (Tcz- Tc) + rb cb (Tcz- T ) where BTU/sec mw is the mass flow rate of water in a coolant tube cw is the mean specific heat of the coolant (4.4) -52- mb is the mass influx of breeder to the reaction zone Cb is the mean specific heat of the breeder Tc is the coolant temperature TL is the bulk breeder temperature. In this case. the influx of breeder into the reaction zone is considered equal to the leakage rate of the coolant into the zone, as reaction is immediate . This mass transfer is further discussed in the free convection section. C. Forced Convective Cooling Forced convection, due to the continued coolant recirculation through undamaged tubes, is an important heat transfer mechanism. Because only a small number of the 475 coolant tubes in an outside blanket module are damaged, cooling will take place in both the breeding and reaction zones. The cooling tube surface area in each element can be determined as a volume percentage of the blanket as a whole. For example, the initial reaction zone, approximately 2% of the blanket by volume, comes into contact with roughly 2% of the total cooling tube surface area. This total area can be determined using the information in Table 2.7. This total heat flow can be computed for each element using Qc where kTiAso + hA J (T - Tc) BTU/sec 6 is the coolant tube thickness kTi is the thermal conductivity of the titanium alloy (4.5) -53- As is the outer coolant tube surface area AsI is the inner coolant tube surface area h is the boiling water heat transfer coefficient T. is the bulk temperature of the element in question. D. Conduction Conduction plays a major role in the transfer of heat from the reaction zone to the breeder mass. The heat conduction term between two elements can be expressed'as Qcondij = Ai where (Ti - Tj)/d 1 j BTU/sec (4.6) A is the inner element surface area k is the inner element thermal conductivity k is the outer element thermal conductivity T is the inner element bulk temperature T is the outer element bulk temperature di. is the separation distance between the elements. The surface area assigned to each element is at its outer perimeter. In the above expression, it is assumed that the inner element is at a higFier temperature, as is the case at all times in the LITFIRE option. E. Free Convection A preliminary order of magnitude analysis indicates that the free convective enhancement to conduction is Pr Gr 1 /2, Gr are the Prandl and Grashof numbers. where Pr and For a 400 'C temperature -54- difference between the reaction and breeder zones in the lithium case, this enhancement is better than a factor of ten. Thus, free convection is an important mode of heat transfer in the model. As mentioned before, there will be mass transfer in the breeding zone due to the influx of this material into the reaction zone. It is this movement that allows convective cooling of the reaction zone by the first breeder zone element. Given the spherical shape of the reaction zone, the semi-empiracle relation Fi = 2.0 + 0.60 Gr1/4 Pr1/3 (4.7) is useful to find the average heat transfer coefficient for Grl/2 Prl/ 3 < 200. NIII is the average Nusselt number and is related to the average heat transfer coefficient him by Nu =h m L/k (4.8) where L, the characteristic distance, is in this case the reaction zone diameter. Thus, the heat flow due to free convection can be described by Q'c AczDkb (2.0 + 0.60 Gr1/4 PrT/3 )( D cz- T L sec 4.9) where Acz is the reaction zone surface area and kb is the bulk breeder thermal conductivity. Gr = D3 p2 gaAT and Pr 2 - C k are applicable to -55- the fluid breeders. F. Radiation Using an order of magnitude analysis, the radiative heat flow is related to the conductive heat flow by T3L Q grad (4.10) where a is the Stefan-Boltzmann constant. At 1500 OF, this radiative heat flow is a factor of ten less than that of conduction in a lithium breeder. Therefore, radiation is neglected in the model. 4.3.3 The Numerical Scheme The temperature of a thermal element may be found from the solution to mc t = q+ + q3 + ... , T = T0 at t = to, where mc is the element's heat capacity and ql, q2 ' q3 ... flows into the element, shown in Fig. 4.1. (4.11) are heat This may also be expressed as T ( +q 2 + q 3 + ... ) dt +T. (4.12) t 0 In LITFIRE, this is expressed as T = INTGRL (T , dt/dt). (4.13) -56- A set of sub-routines is used to perform the integrutions using either Simpson's Rule or a Runge-Kutta method. For example, heat flows into the reaction zone are the heat of reaction, sensible heat addition to the reactants, conduction, free convection and forced convective cooling. Therefore, the temperature of the reaction zone at time t can be determined in LITFIRE by using Eq. (4.13) and dT Q- lQQ dtQ Q1 (4.14) - Qs ~ QcR ~ condRL where the subscript R'denotes the reaction zone and Li denotes the first breeder element. Q, Qs' QcR' QcondRL1, and Q can be determined using Equations (4.3), (4.4), (4.5), (4.6), and (4.9), respectively. Similar equations can be written for each thermal element in the model. 4.4. Results and Discussion Figure 4.3 shows the thermal response of the reaction zone (TCZ), first breeder element (TLIl) and middle breeder element (TLI4) over the first 1000 seconds for a lithium breeder accident, as described earlier in this chapter. Similar graphs are plotted in Figures 4.4 through 4.7 for Li7 Pb2 , LiPb 4 , LiAl and Li2 0 breeders, respectively. A number of interesting points are noted. First, the general shapes of the curves in each case are similar, although different maximum temperatures are attained. step shows no appreciable difference. A change of time The reaction zone ri.ses rapidly, reaching a maximum value within the first two minutes of the coolant tube breaks. Thereafter, the temperature decreases monotonically, -57- aiee 1900 1700 T TCZ E M Isee P E R 1300 A T U 1.±00 R E 00 700 - T L I4 see 300 100 200 300 400 SO 6ee 7ee see goo e0e TIME (SECONDS) Figure 4.3 Lithium Breeder Thermal Interaction. Response to Water I -58- 19ee 1700 T 1500 E T CZ ~ M P 1300 E R A T 1100 U R E 900 F TTL14 L 11 700 500 300 100 200 300 400 500 600 700 800 900 1000 TIME (SECONDS) Figure 4.4 Breeder Thermal Li Pb Inter ction. Response to Hater -59- 1700 1500 TCZ T E 1300 M P E R 1100 A T U 900 R E '- TLIl - 700 TL14 see 300 100 200 300 400 500 600 700 800 90 TIME (SECONDS) Figure 4.5 LiPb 4 Breeder Thermal Interaction. Response to L'ater I 1000 -60- 1700 - - Ti'ee E M P 1300 TCZ E R 1100 U R E 90 TI TLIl ___ 700 - see -- L14 300 100 200 400 300 500 600 700 800 900 1000 TIME (SECONDS) Figure 4.6 Li,'.1 Breeder Thermal Interaction. Response to Vater -61- 1300 T. E 1100 M P E TCZ R A goo U R E 700 TL14 TLI4 - - 500 300 - I- I I I 100 200 300 400 I 500 I 600 700 I I 800 900 TIME (SECONDS) Figure 4.7 Li C Breeder Thermal Interaction. !esponse to Uater 1000 -62- more gradually as time progresses. The first blanket element exhibits similar behavior, but at lower temperatures and lagging over a minute behind. The middle blanket element is relatively unchanged, slowly increasing 50 OF in the lithium case and nearly constant in the alternate breeders. This behavior may be due to different characteristic times for the various heat transfer processes. The heat of reaction in the reaction zone is instantaneous and relatively large compared to the conductive and convective flows, thus a rapid initial rise. Eventually, as the temperature difference between the reaction zone and first breeder element increases, so do the conductive and convective flows and the temperature profile flattens and decreases. Thereafter, as this temperature difference decreases, the reaction zone temperature decreases more gradually. This continues until the breeder (or water, in the LiPb 4 case) is depleted, eliminating the heat of reaction. Thereafter, all zones are eventually recooled to 752 *F. The first 1000 seconds are shown as the entire process takes upwards to 11 hours (4 x 104 seconds). The relatively small volume of the reaction zone (less than 2% of the blanket module volume) may account for both the high temperatures attained in the reaction zone and the large temperature difference between this zone and the first breeder element (approximately 1000 *F in the lithium run). area. A small volume implies a small mass and surface The small mass is very sensitive to the heat of reaction and the small surface area impedes conductive and convective flows out. the reaction zone expands, this effect is diminished. As -63- The blanket liner, shield and other breeder elements were also monitored. All zones outside of the fourth breeder element showed no significant change. localized. Thus, the accident appears to be effectively The second and third breeder elements showed similar behavior as the first, with progressively shorter time lags. Figure 4.8 presents a comparison of the reaction zone temperature profiles for the various breeders. As expected, the liquid lithium breeder produces the highest temperatures. Also expected, using the results of Chapter 3 as reference, is that the Li20 breeder temperatures are significantly less. This breeder has a definite safety advantage compared to pure lithium. The same can not be said, however, of the lithium-lead breeders and LiAl. Though less, the resulting temperatures are well within the range of the lithium case, as close as 70 OF (Li 7 Pb 2 ) and not further apart than 250 OF (LiPb 4 ). These differences are insignificant at a base temperature of 1950 *F. This result was surprising in the case of LiPb 4 . Equation (4.14) indicates that the temperature rate of change in the reaction zone is inversely proportional to the reaction zone mass. Since the reaction zone volume is initially fixed and there is a factor of 20 increase in the density of LiPb 4 over that of Li (at 400 *C, the density of Li is 0.51 g/cm 3 ; the density of LiPb 4 is 9.9 g/cm 3), it was felt that the temperature rise would be proportionally decreased. However, a closer look at Eq. (4.14) indicates that the temperature rate of change is also inversely proportional to the reaction zone specific heat. In this case, the specific heat of LiPb 4 , approximately -64- 21ee iee Li T E 1700 Li -LiAl M Ph 2 P E Isee R A -. T I U 1300 R Li E F 0 1100 900 700 200 300 400 500 TIME (SECONDS) Figure 4.8 Comparison of Rleactor Zone Temperature Profiles of the Various Breeders -65- that of Pb, i-s nearly a factor of 20 less than that of pure lithium (at 400 *C, the specific heat of lithium is 1.01 cal/g- *F; that of LiPb 4 is 0.041 cal/g - 'F). Thus, the terms in the denominator of Eq. (4.14) effectively cancel each other out and the slightly different reaction zone temperature profiles of Li and LiPb 4 are simply a reflection of the slightly different heats of reaction of the two breeders with water. A comparison of the thermal responses of the first breeder elements for the various breeders, shown in Fig. 4.9, is also interesting. Again, the lithium case produces the highest temperatures and the Li2O case produces the lowest. again similar. The lithium-lead alloy and LiAl results are Here the Li7 Pb2 element is cooler overall due to a very low thermal conductivity, experienced in the lithium-lead system at a 20% lithium atom percentage [13]. However, in this comparison, the differences between these alloys and the lithium case are more pronounced. This indicates that the use of liquid lithium.will produce more widespread accidental consequences. -66- 1109 ieee T E M P E R A T U R E See F 800 Li 2 700 I 100 I 200 I 300 400 *I 500 I 600 I 700 800 s00 1000 TIME (SECONDS) Figure 4.9 Comparison of First Breeder Element Temperature Profiles of the '!arious Breeders. -67- CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS Results indicate that the lithium-lead alloys may not be significantly safer than pure lithium as a fusion reactor breeding material, utilizing the NUWMAK geometry. In both calculations, short term temperatures resulting from interaction of Li7 Pb2 and LiPb 4 with water, though lower, are within a few hundred degrees of those associated with the use of liquid lithium. However, a proper conclusion to this study is that a conclusion cannot yet be made. The calculations of Chapters 3 and 4 provide an overview of the safety question, raising some interesting observations and determining areas that need to be explored in more detail. First, the lithium-lead alloys and LiAl can pose safety problems approximate to those of liquid lithium, as noted above. This can be quite serious, as shown in Chapter 3, with temperatures reaching to the melting point of steel in a water-cooled blanket. For this reason alone, further study of these alternate breeders is required. Results of. Chapter 4 indicate that such an interaction could go undetected, as a continuance in coolant recirculation may keep the consequences localized. Measurable quantities, like bulk breeder temperature and coolant temperature and flow rate a're practically unperturbed. Thus, further design work might include features to mitigate this problem. Uncertainties in characterizing the reaction zone in the dynamic model render the resulting temperature profiles less meaningful. work in this area, perhaps experimental, would make the model more accurate. Further -68- Finally, better physical properties data on the alternate breeders is required. In particular, an understanding of the water reaction rates is central to the study of these materials. If it can be proved, as surmized, that these rates are significantly lower than those of liquid lithium, a significant reduction in safety hazards may be assured. -69- REFERENCES 1. A. J. Impink, Jr. and W. G. Homeyer, "Tritium Regeneration in Proposed Fusion Power Reactors," Transactions of the American Nuclear Society, S(l): 100, June 1962. 2. J. L. Ballif, et al., "Lithium Literature Review: Lithium's Properties and Interactions," HEDL report TC-1000, January, 1978. 3. Mark S. Tillack, "Development and Verification of the LITFIRE Model for Predicting the Effects of Lithium Spills in Fusion Reactor Containments," Master's Thesis, MIT, June 1980. 4. B. Badger, et al., "NUWMAK", University of Wisconsin, UWFDM-330, March 1979. 5. "Special Purpose Materials - Annual Progress Report," DOE/ET-0095, May 1979. 6. R. H. Wiswall and E. Wirsing, "Tritium Recovery from Fusion Blankets Using Solid Lithium Compounds," Radiation Effects and Tritium Technology for Fusion Reactors Conference, Gatlinburg, Tenn., 1975. 7. R. G. Clemmer, et al., "Assessment of Solid Breeding Blanket Ophons for Commercial Tokamak Reactors," ANL-CEN/205, 1980. 8. N. A. Frigerio and L. L. LaVoy, "The Preparation and Properties of LiPb, A Novel Material for Shields and Collimators," Nuclear Technology, 10, 322, 1971. 9. D. L. Smith, et al., "Fusion Reactor Blanket/Shield Design Study," ANL/FPP-79-1, July 1979. 10. "Dresden Nuclear Power Station Units 2 and 3, Safety Analysis Report," Commonwealth Edison Company, 1968. 11. D. A. Dube and M. S. Kazimi, "Analysis of Design Strategies for Mitigating the Consequences of Lithium Fire within Containment of Controlled Thermonuclear Reactors," MITNE-219, July 1978. 12. R. Bird, W. Stewart and E. Lightfoot, Transport Phenomenon, John Wiley & Sons, Inc., 1960. 13. Marie-Louis Sabourgi, et al., "Thermodynamic Properties of a Quasi-ionic Alloy from Electromotive Force Measurements: The Li-Pb System," The Journal of Chemical Physics, 68, 4, February 15, 1978. 14. John H. Perry, et al., Chemical Engineers' Handbook, McGraw-Hill Book Company, Inc., 1963. -70- APPENDIX A Physical Property Data -71- Table A.1 summarizes the important physical property data of the various alternate breeders analyzed in this report. Except as indicated, all of these values are gathered from the previously identified references. It is important to realize that, aside from the lithium and melting point data, all numbers are estimates at best. For reasons detailed earlier, only the physical properties of the lithium breeder are allowed to vary with temperature in calculations of Chapters 3 and 4. The correlations used are: p = 0.5368 - 1.0208 x 10~ 4 T (g/cm3 ) k = 10.48 + 4.98 x 10- 3 (T- 180.6) -0.58x10- 6 (T-180.6) 2 (cal/sec-m-*C) c Here, = 1.0037 - 0.01063x + 0.00564x 2 0.001279x 3 (cal/g *C) where x = .004938T - 6.20741 - p = density of lithium k = thermal conductivity of lithium cp = specific heat of lithium T = lithium temperature in *C The latent heats of melting for the alloy breeders are determined using the correlation Hmelt/Tmel t " 2.2 This is an average value for metallic alloys [14]. -72- The thermal conductivity of LiPb 4 is estimated with the correlation km = k1w1 + k2w2 - 0.72(k 2 - k1 )(w w2 ) This is appropriate for a binary liquid mixture. Here, the weight fraction w2 refers to the component having the larger value of k [14]. The specific heat data of the alloy breeders is determined using the relation C, Xi c Calloy where Li +XcA CLi + XA CPA XLi = weight fraction of lithium XA = weight fraction of the alloy element cpA = specific heat of the alloy element c =Li specific heat of lithium The specific heat values for the alloy elements, lead and aluminum, can be found in the literature. -73- TABLE A.1 Summary of Physical Properties of Candidate Breeding Materials at Standard Conditions Lithium Li7 Pb2 LiPb 4 LiAl Li2 0 973 2140 a 1970 Properties Melting Point, *K 453 999 508 AHmelt, cal/g mole 722.4 2200 a 1120a Density, g/cm 3 0.51 4.59 9.9 1.76 2.01 Li atom density, g/cm 3 0.51 0.49 0.08 0.37 0.93 Thermal conductivity w/m-k 50 30 1.73 Specific Heat cal/g OK 1.01 Heat of Reaction with Water \20 0.1 4 b ,'35a 0. 04 1 b 245 200 1 70 c 7 463 835 0 .44 b 200 0.35 64 g-atom Li Atomic weight a. correlation b. interpolated value c. ~estimated 34 30 -74- APPENDIX B Complete.Listing of LITFIRE -75- 00 w rim'Totot WOO'C'4M Nmqtntol woo 0 ow 1 N " NMvMwr-wMo 0 0 00 co 0 0 000000000 0 0000000000000000000 00000000000000000 0 00 0 0000000000000000000 0 0000000000000000 00 0 0 000000000 w It , f. 0 0 M LU -i U. 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J'0 C ,C O* C-0 l' I C'I00 *No 1 *-00 nOO11. *(1(( 3: 0 C1,U .0 C C,)1 0 0 uoau 1- , ,c I 0 0 . . .. 00 a .. o - -1,1-1 1 O LU V7 -0 Q U ll IA ., cc (DC-0 mv vv 00 0000000000 00000000000000000000 00 0*l"A 00. 0000 DC-0o0 000000 C-0d0(NI' 00000000 0000000000 00 000 000 0000000 000000000 I z - 1-0 x T 2 - -114- 01o 0 j- 1 1- 0 w *- * Is z-~ U. to 2l mh~ 0 z j. 0 00 0 0 0 0 -115- APPENDIX C Sample Input to LITFIRE 4 -1160 0 a 0 01 0 9 0 0 a 0 0 0 0 P4 zcc IL. 0 0 a In -J N II. 0 a a I- I LU U LU 0 4 -J 0 a. 0 0 0 O 0 o 0 .0 0 0 a N U U a 0 a O LU 0 4 -J II. Ou a CO x 4C 39 331 C; Uw 0 0 a 0 0 U a o -J a *a a 3 4 In 1 O0 a 0 a II. 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