Optimisation of the Nuclear Reactor Neutron Spectrum for the Transmutation of Am 241 and Np 237

Transcription

1 Optimisation of the Nuclear Reactor Neutron Spectrum for the Transmutation of Am 241 and Np 237 Sarah M. Don under the direction of Professor Michael J. Driscoll and Bo Feng Nuclear Science and Engineering Department Massachusetts Institute of Technology Research Science Institute July 29, 2008

2 Abstract Nuclear energy is increasing in popularity, and so the amount of nuclear waste in temporary storage is also increasing. One way to reduce the amount of nuclear waste is to recycle it. The objective of this investigation was to identify the optimal coolant/moderator density in a PWR in order to destroy the greatest amount of Am 241 and Np 237 in a modified MOX fuel assembly. Recycling by adding 12.8% transuranics to a MOX fuel assembly in a core containing 100% coolant/moderator density transmuted a greater amount of Am 241 and Np 237 than a lesser amount of moderator. By transmuting more Am 241 in the fuel assembly, less Np 237 is formed from the decay of Am 241 after the fuel is removed from the core. This method of recycling transuranics in MOX fuel reduces the radiotoxicity of the final waste and permits more storage options.

3 Contents 1 Introduction Nuclear Waste Constituants Recycling Fast vs. Thermal Reactors Pressurised Light-Water Reactors CASMO MCNP Method Standard UO 2 Case Modified MOX Composition Matching Burnup Relative Percent Burnup of Am 241 and Np Neutron Spectra at Varying Coolant/Moderator Densities Results Amount of Transuranics Required to Achieve Burnup at 40 MWd/kg Destruction of Am 241 and Np Neutron Spectra Analysis Adjustments to the Amount of Transuranics in MOX Fuel Destruction of Am 241 and Np Neutron Spectra Comparison Destruction of Am 241 and Np 237 by Extended Irradiation

4 5 Waste Disposal Options for Radiotoxic Nuclides 15 6 Conclusion 15 7 Acknowledgements 16 A Definition of k 18 B CASMO Input - 100% Coolant 12.8% Transuranics 19 C Number Densities of Burnable Nuclides 21 D Wt% of Nuclides 22 E Change in k over 60 MWd/kg 23 F MCNP Input 24 2

5 1 Introduction Nuclear power is becoming more prevalent in many countries around the world as the price of fossil fuels continues to rise. However, nuclear power s many benefits are often overshadowed by the complications of nuclear waste disposal. In this theoretical investigation, the transmutation 1 of nuclides in a MOX (see Section 1.2) fuel assembly over the course of 60 MWd/kg 2 burnup 3 in a pressurised water reactor was simulated using CASMO (see Section 1.5) with each case, the coolant/moderator density was varied in order to find the optimum neutron spectrum for destroying Am Nuclear Waste Constituants Uranium, neptunium, plutonium, curium, californium, and americium are the most prevalent actinides produced by nuclear fission. These elements are problematic because of their radioactivity and extremely long half-lives. Am 241, in particular, decays to Np 237 (as shown in Figure 1), which has a half-life of years[3], and thus determines the long-term radiotoxicity of the nuclear waste. If the amount of Am 241 in the spent fuel is reduced, then the part of the spent fuel that cannot be recycled can be more easily stored. 1.2 Recycling One approach to reducing the long-term radiotoxicity of spent nuclear fuel involves recycling some of the more radiotoxic nuclides by adding them to a MOX (heavy metal oxide) fuel assembly. MOX fuel consists of the Pu vector from spent LWR (light water reactor) fuel added to depleated or natural uranium. MOX assemblies that can be used in LWR cores which normally run on uranium oxide (UO 2 or UOX ) fuel. As these minor actinides are 1 the process of an atom decaying or capturing neutrons, causing it to become another isotope or element 2 mega watt days per kilogram - SI units for burnup 3 length of time a fuel assembly spends inside the core of the reactor while nuclear fission occurs 3

6 Figure 1: Decay of Am 241 into Np 237 exposed to the neutron thermal flux of LWRs, they capture neutrons or undergo fission, becoming less radiotoxic isotopes. This in turn makes disposal of the spent fuel much easier. In this investigation, the transuranics in the waste from a uranium oxdide fuel assembly were added to a MOX fuel assembly. This process is shown in Figure Fast vs. Thermal Reactors A thermal reactor uses moderators such as light (H 2 O) or heavy water (D 2 O), with which fast neutrons from fisson collide. This way the efficiency of the neutron captures is higher. Typically, thermal reactors burn fuel for MWd/kg, staggered between three fuel batches inside the core. Fast reactors avoid moderation. This increases the ratio of fission to capture and also facilitates the breeding of new Pu 239 from U 238. This allows extended burnup to 140 MWd/kg. 1.4 Pressurised Light-Water Reactors In pressurised light water reactors (PWRs, as shown in Figure 3), light water is typically pressurised to g/cm 3 in the core of the reactor. As the amount of water between 4

7 Figure 2: Composition of fuel assembly at different stages throughout the nuclear fuel cycle that were analysed in this investigation fuel rods decreases, the neutrons that are produced as a result of nuclear fission are able to maintain a higher amount of energy since there are fewer water molecules to slow them down. This causes the relative quantities of the different actinides in the waste to be altered since the actinides ability to capture neutrons varies with neutron energies. Thus, by modelling burnup with different coolant/moderator densities inside the core of the reactor, an optimal coolant/moderator density, that produced the least Am 241, was identified. 1.5 CASMO The CASMO code is a commercial program written in Fortran, which is designed to perform calculations specifically for PWRs. As the conditions inside the reactor core are varied in the input, CASMO calculates the subsequent changes in the spent fuel composition. In this investigation, CASMO was used to run simulations of the fuel burnup as the amount of water in the core was reduced by factors of up to 10, in order to identify the optimal coolant/moderator density for the destruction of Am 241 and Np

8 Figure 3: Pressurised light-water reactor design [16] 1.6 MCNP The Monte-Carlo N-Particle code (MCNP) is specifically used for modelling particle transport inside the core of a reactor. It was primarily useful in generating the neutron spectra required for the analysis of the core neutron energy under different core conditions. 2 Method All the calculations in this investigation were made using CASMO or MCNP in order to reach theoretical conclusions about the changes in spent fuel composition as the amount of coolant/moderator is changed. A standard UOX fuel assembly, with U 235 enriched to 4.5%, was run through CASMO as a control, and a modified MOX fuel assembly was used for all subsequent cases. 6

9 2.1 Standard UO 2 Case The first case that was run through CASMO was that of a standard fuel assembly with U 235 enriched to 4.5%. The coolant/moderator density was kept at CASMO s default of 100% (0.705 g/cm 3 ), and the fuel was burnt for 60 MWd/kg. As in Figure 4, which was generated from the output of the standard uranium oxide case, the reactor became subcritical 4 at 40 MWd/kg. CASMO was then used to simulate five years cooling of the spent uranium fuel. Figure 4: The standard U 235 fuel assembly, enriched to 4.5%, reaches its batch burnup limit at 40 MWd/kg, when k =1 2.2 Modified MOX Composition After the standard UOX cooling simulation was run, the transuranic composition of the spent fuel was taken and adjusted so that it made up 13% of a MOX fuel core. When the coolant density was at 100%, it was estimated that 13% transuranics composition in the MOX fuel would achieve a burnup when k =1 at 40 MWd/kg. The burnup for five different coolant/moderator densities (100%, 75%, 50%, 25% and 10%) with 13% transuranics 4 a reactor is subcritical when k <1 (see Appendix A) 7

10 was calculated using CASMO (an input example can be found in Appendix B). The U 235 enrichment was adjusted to 0.2% for all trials. 2.3 Matching Burnup As the coolant density was reduced, the point at which the core passed the point of criticality occurred earlier. The only exception to this trend was in the case in which the coolant/moderator density was reduced to 10%, for which the core did not reach the point of being critical within 60 MWd/kg. This was most likely because the spectrum was hardened due to the low density of coolant/moderator, causing the PWR to behavelike a steam-cooled fast reactor(see Section 4.3). By keeping the burnup the same for all 5 cases, the net burnup of Am 241 could be compared relative to each case. In order to make all five different coolant/moderator density cases have the same burnup, the percent composition of transuranics in the fuel was iterated until all five cases reached the state of being critical at 40 MWd/kg. 2.4 Relative Percent Burnup of Am 241 and Np 237 For the standard UOX case and each of the five different coolant/moderator density cases, the relative amounts of Am 241 and Np 237 before and after 60 MWd/kg of burnup were extracted from the output files from each CASMO run. The case in which the highest weight percent of Am 241 and Np 237 was transmuted into other elements was identified as having the optimal coolant/moderator density inside the core. 2.5 Neutron Spectra at Varying Coolant/Moderator Densities For the 100%, 50% and 10% coolant/moderator density cases, as well as the standard UOX case, the percent compositions of transuranics, used in order to reach the same burnup as 8

11 the standard UOX case, were inserted into MCNP input files (see example in Appendix F) along with their respective coolant density (in g/cm 3 ). From the output of the MCNP code, the neutron spectrum experienced by Am 241, under the conditions previously mentioned, was generated. The softer the spectrum, the more Am 241 is burnt, making the spent fuel from a reactor with these optimal conditions less radiotoxic. 3 Results 3.1 Amount of Transuranics Required to Achieve Burnup at 40 MWd/kg Figure 5: Iterating the amount of transuranics required to achieve the same burnup as the standard UOX case (see Appendix E for the exact k values for the 100% coolant/moderator case) As coolant/moderator was removed from the core, the amount of transuranics in the MOX fuel cell had to be adjusted (see Figure 5) in order to achieve the same burnup at 40 9

12 Coolant/Moderator Density (g/cm 3 ) Wt% Transuranics Table 1: Weight percent transuranics of the total MOX fuel assembly required to match burnup at 40 MWd/kg MWd/kg (see Table 1 for exact figures). 3.2 Destruction of Am 241 and Np 237 Figure 6: As the coolant density increases, the percentage of Am 241 remaining increases As the coolant/moderator density approached 100%, the amount of Am 241 that was destroyed by transmutation also increased by a factor of 5 (see Figure 6). Np 237 was not directly affected by the change in coolant/moderator density. However, the destruction of Am 241 has a more significant impact on the long-term radiotoxicity of the nuclear waste. 10

13 3.3 Neutron Spectra Figure 7: Neutron spectrum for the modified MOX fuel assembly for the 100% coolant/moderator case The neutron spectrum for the reactor when moderation was at 100% (see Figure 7) is relatively soft 5 compared to that of a fast reactor, which means that a larger portion of neutrons travelling in the core have lower energy than they would in a faster or harder spectrum/ 4 Analysis 4.1 Adjustments to the Amount of Transuranics in MOX Fuel There are several reasons why changing the coolant/moderator density and the weight percent of transuranics causes the burnup to occur earlier or later, as well as gradually or suddenly. As moderation decreases, fewer neutrons are absorbed, so more neutrons with 5 more neutrons have lower energy 11

14 higher energy are present inside the core. Because these have higher energy, the relative cross section of nearby atoms decreases, fewer neutrons are captured, and less Am 241 is transmuted into other isotopes. So, to compensate, more transuranics were added. As a higher composition of transuranics is added to the MOX fuel assembly, it acts as a poison 6, and reduces the overall energy of the neutrons inside the core. However, as the coolant/moderator density nears 10%, the neutron spectrum hardens (see Section 4.3), causing the reactor to behave like a fast reactor. Figure 8: Percent transuranics of total fuel required to achieve burnup at 40 MWd/kg at varying coolant/moderator densities 4.2 Destruction of Am 241 and Np 237 The destruction of Am 241 when the coolant/moderator density was at 100%, was higher than when there was less water in the core. This is most likely because as the neutrons energy is decreased by the increase in moderation, they can be more easily absorbed by atoms such as Am 241, causing the Am 241 atoms to transmute into other isotopes (see Appendices C and D for CASMO output segments of the number density and weight percent of transuranics in 6 a poison is a substance that absorbs neutrons and effectively poisons the nuclear fuel inside the core of the reactor by decreasing the rate at which the fuel itself fissions 12

15 the spent fuel for the 100% coolant/moderator case). It is unclear why Np 237 was unaffected by the change in the amount of moderation. However, reducing the amount of Am 241 in the spent fuel has more impact on the amount of Np 237 in the long-run. 4.3 Neutron Spectra Comparison Figure 9: Comparison of neutron spectra in a core with 100%, 50% and 10% coolant/moderator as well as the neutron spectrum of a standard uranium core As shown in Figure 9, as coolant/moderator was removed from the core of the reactor, the neutron spectrum became harder 7. This means that as the amount of moderation in the core decreased, the neutrons were able to sustain higher energy for a longer period of time. This caused the neutron flux to increase towards higher energy levels. On the other hand, 7 causes the graph to become steeper towards the higher energy end of the spectrum 13

16 as the amount of moderation increased, more neutrons were absorbed, and so the neutron flux became more evenly spread across the spectrum of energy levels. The thermal bump at the low energy end of the UOX fuel assembly neutron spectrum is absent in the neutron spectra for the MOX fuel assemblies in different coolant/moderator densities (see Figure 9). The absense of this thermal bump is most likely due to the fact that the nuclides added to the MOX fuel assembly acted as a poison, absorbing more neutrons than if the core were entirely composed of uranium isotopes. 4.4 Destruction of Am 241 and Np 237 by Extended Irradiation Figure 10: Comparison of methods of destruction of Am 241 and Np 237 by extended irradiation To further investigate the behaviour of neutrons under different conditions, a graph was generated from the output of CASMO that showed the number density 8 of Am 241 and Np 237 as burnup progressed to 140 MWd/kg. The number densities of Am 241 and Np 237 in 100% and 10% coolant/moderator continue to decrease as burnup progresses. This means that the longer these isotopes are irradiated, the more they transmute and thus reduce in quantity. 8 number density is the number of nuclei per unit volume b cm (1barn=10 24 cm 2 ) 14

17 5 Waste Disposal Options for Radiotoxic Nuclides The data shows that the current design of nuclear reactors is already optimal for Am 241 destruction. To further reduce the amount of Am 241 in the nuclear waste, other recycling options must be considered. A possible method of reducing the amount of Am 241 in the nuclear fuel cycle is to extend the time for which the transuranics are irradiated inside a reactor. This could be achieved by concentrating the transuranics into discrete fuel rods that sit amongst the MOX rods inside the fuel assembly of a PWR or fast reactor. This way, the MOX part of the fuel assembly can be removed after burnup, while the transuranic rods remain inside the reactor for several burnup cycles so that remaining Am 241 can continue to transmute into other isotopes for as long as economically feasible. Another alternative way to reduce the amount of Am 241 in the waste may be to include moderated Am 241 in the blanket 9 of a fast reactor. This would work in the same way as placing discrete transuranic rods amongst the fuel rods in a PWR. The Am 241 and Np 237 would continue to be irradiated until they transmute into other isotopes or elements, reducing the longterm radiotoxicity of the nuclear waste. 6 Conclusion In order to destroy the highest net amount of Am 241 and Np 237, the optimal coolant/moderator density is 100% (0.705g/cm 3 ). As water is removed from the core, the reactor begins to behave like a BWR, and as the 10% coolant/moderator mark is approached, the reactor begins to behave like a fast reactor. As there are over 100 PWRs currently in operation in the U.S., not needing to change any structural part of the PWR design in order to achieve this favourable effect is economically beneficial. For reactors currently using UOX cores, to use a 9 excess row of assemblies that sit inside the core of a fast reactor 15

18 MOX core would certainly help to reduce the amount of Am 241 in circulation in the nuclear fuel cycle. 7 Acknowledgements I would like to thank Professor Driscoll for guiding my research, and Sara Ferry and Bo Feng for their resourcefulness throughout the project. Many thanks to Zach Wissner-Gross for editing this paper and to Rafic Itani for sharing his results with me, making my research much more efficient. Thank you also to the Centre for Excellence in Education (CEE) for running the Research Science Institute (RSI) for giving me the opportunity to conduct research, and the Massachusetts Institute of Technology (MIT) and the Nuclear Science and Engineering department for allowing me to work in their labs and use the CASMO and MCNP codes. 16

19 References [1] Ahn et al., Effects of Accelerator-Driven System on Radiotoxicity of HLW, Nuclear Technology, 158, 418 (2007). [2] E.M. Baum et al., Nuclides and Isotopes, Lockheed Martin (2002). [3] V. Berthou, C. Degueldre, and J. Magill, Transmutation Characteristics in Thermal and Fast Neutron Spectra: Applications to Americium, Journal of Nuclear Materials, 320, (2003). [4] D. Bittermann, T. Schulengurg, Status of Supercritical Water Reactor Design, Fuels and Materials for Supercritical Water-Cooled Reactors (SCWR), (2006). [5] T.E. Booth et al. MCNP5 Manual, University of California, Los Alamos National Laboratory (2005). [6] J.A. Dahlheimer et al., The Westinghouse Pressurized Water Reactor Nuclear Power Plant, Westinghouse (2006). [7] M.J. Driscoll, T.J. Downar, E.E. Pilat, The Linear Reactivity Model for Nuclear Fuel Management, American Nuclear Society (1990). [8] M.J. Driscoll, personal communication (2008). [9] B. Feng, personal communication (2008). [10] Y. Fukaya et al., Investigation on spent fuel characteristics of reduced-moderation water reactor (RMWR), 238, (2008). [11] M. Gaines, Radiation and Risk, New Scientist - Inside Science, 129, 1-4 (2000). [12] GE Nuclear Energy, The ABWR Plant General Description, GE Nuclear Energy (1999). [13] P. Grimm et al., Seiler, Experimental validation of the reactivity loss of highly-burnt PWR fuel, PSI Scientific Report, (2007). [14] W. Haeck et al., Assessment of americium and curium transmutation in magnesia based targets in different spectral zones of an experimental accelerator driven system, Journal of Nuclear Materials, 352, (2006). [15] E. Malte et al. CASMO-4 User s Manual, Studsvik, [16] Hughes, Rachel.: Nuclear Radiation and Human Health, University of Arizon (2007). [17] D. Sang, Atoms Unleashed, New Scientist - Inside Science, 157, 1-4 (2003). 17

20 A Definition of k The k value of a nuclear reactor core is the ratio of neutrons produced to neutrons consumed in an infinite medium, as shown in Equation 1 below. k = neutrons produced neutrons consumed (1) As shown in Table 2, when k >1, the reactor is supercritical, which means that there is positive reactivity inside the reactor and more neutrons are being produced than consumed. When k =1, the reactor is critical, at which point it is considered that the fuel assembly has reached burnup. When k <1, the reactor is subcritical, where less neutrons are being produced than consumed. In a PWR, the fuel is typically burnt until k 0.8, which occurs at approximately 55 MWd/kg. k Subcritical <1 Critical =1 Supercritical >1 Table 2: k value and criticality [8] CASMO is able to calculate the k value at intervals over the course of burnup in a PWR. Thus the output from CASMO provides the data required to generate a burnup graph such as in Figure 4 (Section 2.1). 18

21 B CASMO Input - 100% Coolant 12.8% Transuranics * * * * FUEL SEGMENT: TRU12.8\% COO100\% * TTL * STANDARD WESTINGHOUSE PWR ASSEMBLY, 17X17 LATTICE ***** STATE POINT PARAMETERS ***** TFU=900.0 TMO=583.1 BOR=0.0 VOI=0.0 COO= ***** OPERATING PARAMETERS ***** PRE * CORE PRESSURE, bars PDE KWL * POWER DENSITY, kw/liter ***** MATERIAL COMPOSITIONS ***** FUE / =3.6396E =5.8982E =2.7208E =1.3861E =9.2022E =3.8129E =5.6731E =7.7504E =5.8651E =1.9200E =4.3429E =8.6740E =2.0740E =3.6361E =1.3661E =7.3588E =8.4618E =6.6670E =9.1740E =1.2462E =9.9159E =2.0735E-19 ***** GEOMETRY SPECIFICATION ***** PWR PIN / 1 AIR CAN PIN / COO BOX * INSTRUMENT TUBE PIN / COO BOX * GUIDE TUBES LPI

22 DEP -60 STA END 20

23 C Number Densities of Burnable Nuclides NUCLIDE NO. DENSITY NUCLIDE NO. DENSITY NUCLIDE NO. DENSITY U E+18 Cm E+17 Cs E+19 U E+19 Cm E+19 Ba E+17 U E+18 Cm E+19 La E+17 U E+17 Cm E+18 Nd E+19 U E+22 Cm E+16 Nd E+19 U E+16 Cm E+15 Pm E+18 Np E+15 Cm E+10 Pm E+16 Np E+19 Bk E+14 Pm E+16 Np E+17 Bk E+10 Sm E+18 Np E+18 Cf E+13 Sm E+17 Pu E+20 Cf E+13 Sm E+19 Pu E+20 Cf E+13 Sm E+18 Pu E+20 Cf E+13 Sm E+18 Pu E+20 Kr E+18 Eu E+19 Pu E+20 Rh E+19 Eu E+18 Pu E+16 Rh E+17 Eu E+17 Am E+19 Ag E+19 Eu E+17 Am E+16 I E+16 Gd155F E+16 Am E+19 Xe E+19 LFP E+21 Am E+16 Xe E+16 LFP E+20 Am242m E+18 Cs E+19 Cm E+19 Cs E+19 Table 3: Average number densities of burnable nuclides present in the spent modified MOX fuel which initially contained 12.8% transuranics and was burned in a PWR containing 100% coolant/moderator 21

24 D Wt% of Nuclides NUCLIDE WT(%) CAPTURE FISSION INT CAPT INT FISS MWD/KG U E E E E U E E E E U E E E E U E E E E Pu E E E E Pu E E E E Pu E E E E Pu E E E E Pu E E E E Am E E E E TOT U E E E E TOT PU E E E E FISSILE E E E E FERTILE E E E E Table 4: Wt% of more prevalent nuclides present in the spent modified MOX fuel which initially contained 12.8% transuranics and was burned in a PWR containing 100% coolant/moderator 22

25 E Change in k over 60 MWd/kg BURNUP (MWD/KG) K-INF K-INF M2 PIN U-235 (WT %) FISS PU (WT%) TOT PU (WT%) Table 5: k =1 at 40 MWd/kg when the modified MOX fuel, containing 12.8% transuranics, is burned in a PWR containing 100% coolant/moderator 23

26 F MCNP Input 1/8th Full Assembly model of PWR solid fuel c 17x17 Lattice with 12.8\% TRUs c c Bo Feng July 1st, 2008 c c c c cell specification c c no. mt density surf orient. geometry vol= u=1 imp:n=1 \$ fuel pellet e u=1 imp:n=1 \$ air gap e u=1 imp:n=1 \$ clad u=1 imp:n=1 \$ water u=2 imp:n=1 \$ water/control rod e u=2 imp:n=1 \$ guide tube u=2 imp:n=1 \$ water u=3 imp:n=1 \$ water rod e u=3 imp:n=1 \$ guide tube u=3 imp:n=1 \$ water imp:n=1 u=5 lat=1 fill=-8:8-8:8 0: u=10 fill=5 imp:n=1 \$ assembly :-42:43:-44 u=10 imp:n=1 \$ interassembly coolant u=11 lat=1 fill=10 imp:n=1 \$ assembly fill=11 imp:n=1 \$ 1/8 slice :-62:-63:64:65 imp:n=0 \$ outside c end of cell specification LEAVE BLANK c surface specification c c no. shape parameter 24

27 11 cz \$ fuel radius 12 cz \$ clad inner radius 13 cz \$ clad outer radius 21 cz \$ guide tube inner radius 22 cz \$ guide tube outer radius 31 px 0.63 \$ pin pitch / 2 32 px \$ -pin pitch / 2 33 py 0.63 \$ pin pitch / 2 34 py \$ pin pitch / 2 41 px \$ assembly width / 2 42 px \$ assembly width / 2 43 py \$ assembly width / 2 44 py \$ assembly width / 2 51 px \$ assembly pitch/ 2 52 px \$ assembly pitch / 2 53 py \$ assembly pitch / 2 54 py \$ assembly pitch / 2 *61 p \$ reflective diagonal *62 py 0 \$ reflective x-axis *63 pz -5 \$ reflective bottom *64 pz 5 \$ reflective top *65 px \$ reflective x-value c end of surface specification LEAVE BLANK c data specification c Tally cards c fc64 Flux spectrum - constant lethargy (u=0.1) Paul Romano e E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-04 25

28 3.04E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+01 T f64:n 1 T c c material specification c c LEAVE at least 5 spaces before material ID c (10.4 g/cc) m c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E c E-07 c c AIR (gap) 26

29 m c E-05 c c Zircaloy-4 (6.550g/cc) m c e c e c e c e c e-4 c c H2O (15.5MPa at 583.1K) (0.705g/cc) m c e c e-2 c c initial source ksrc c c mode n kcode prdmp print 27