PNC-TN--9410-96-187 JP9703019 PNC TN9410 96-187
JP9703019
Effect of 0.3eV Resonance Cross Section for Plutonium on Coolant Void Reactivity in Heavy Water Lattice
May, 1996
00 2 3 89 8® OARAI ENGINEERING CENTER POWER REACTOR AND NUCLEAR FUEL DEVELOPMENT CORPORATION
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Copyright © 1 9 9 6 Power Reactor and Nuclear Fuel Development Corporation PNC TN9410 96-187
PNCTN9410 96-187 M a y , 1 9 9 6
Effect of 0.3eV Resonance Cross Section for Plutonium on Coolant Void Reactivity in Heavy Water Lattice
Yasuki Kowata*1 and Nobuo Fukumura*2
Abstract
Plutonium fuel could be utilizedin the entire core of heavy water moderated, boiling light water cooled pressure-tube-type reactor (HWR). The void reactivity, however, depends on the various parameters of the lattice. It is especially significant to clarify the influence of plutonium nuclides on the void reactivity. The void reactivitiesin the in finite HWR lattices have been parametricallyanalyzed to clarify the influences of changes in the latticeparameterson the void reactivity using the WIMS-D4code with the JENDL-3.1 nuclear data. In this latdcecalculation, it has been known that the behavior of the void reactivity can be made clear by separating the components for fuel nuclides, neutron cross sections, energy group and regions in lattice cell from the void reactivity using the important reaction rates. If the macroscopic 2200m/s neutron absoiption cross section of fuel is identical each other, it has been shown that the void reactivity of the HWR latticeshifts further to the negative side in the narrower pitch lattice, and in the plutonium latticethan in the uranium lattice. The effect reducing the void reactivity to the negative by plutonium is caused mainly by the presence of the resonance cross section at around 0.3eV ofz'9Pu. Because the higher the content of^Pu is, the less the recovery effect of neutron density within the resonance energy due to decrease in the thermal neutron scattering of hydrogen is with increase in coolant void fraction, so that the decreased resonance fission rate for^Pu contributes to the more negative side for the void reactivity.
1 Advanced Technology Division, Frontier Technology 2 Fugen Nuclear Power Station PNC TN9410 96-187
CONTENTS
I. INTRODUCTION 1
II. ANALYTICAL METHODS 2
II.A. Approaching Process 2
II.B. Derivation of Components for Void Reactivity 5
II.C. Verification of Lattice Calculation Code 7
III. RESULTS AND DISCUSSION • 10
III.A. Characteristics for Coolant Void Reactivity in HWR Lattices : 10
IILB. Component of the Coolant Region 11
III.C. Component of the Fuel Region 13
IV. CONCLUSION 17
ACKNOWLEDGMENTS 18
REFERENCES • 18 PNC TN9410 96-187
LIST OF ALL TABLE AND FIGURE TITLES
TABLE I Nuclide Composition in Fuel for Void Reactivity Analyses
Fig.1. Cross-sectional view of 28-rod fuel assembly. Dimensions are given in millimetres.
Fig.2. Comparison between calculated and experimental values for q^ of
0.87wt%(R)PuO2-UO2 duster.
Fig.3. Intra-cell thermal neutron flux distribution in 25.0cm pitch 0.87wt%(R)PuO2-UO2 lattice.
Fig.4. Components in fuel and coolant regions of void reactivity in 22.5cm pitch UOX and MOX lattices.
Fig.5. Components in fuel and coolant regions of void reactivity in 25.0cm pitch UOX and MOX lattices.
Fig.6. Absorption components of hydrogen in H2O coolant to void reactivity in 25.0cm pitch lattice.
Fig.7. Intra-cell thermal neutron flux distribution in 25.0cm pitch MOX(S) fuel lattice.
Fig.8. Contribution of fission and fuel absorption components to void reactivity in
22.5cm pitch MOX(S) fuel lattice.
Fig.9. Contribution in 5th and 6th energy groups of fission component for each fissile nuclide to void reactivity.
1 Fig.10. Thermal neutron spectrum in inner layer fuel rod of MOX(S) ('I a0=0.35cm" ) lattice.
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I. INTRODUCTION
The high burnup of fuels and utilization of plutonium tend to increase in the thermal reactor. Actually the thermal reactor which is able to utilize plutonium most effectively is the pressure-tube-type, boiling light water cooled heavy water reactor(HWR). In Japan the utilization characteristics of plutonium in the HWR have been studied with the experiments using Deuterium Critical Assembly
(DCA)1'2 and through the operational experience of the prototype reactor
Fugen3. The HWR has the advantage in burnup of plutonium compared with the light water reactor(LWR), because the thermal neutron spectrum is more softened than that in LWR and the neutron economy is comparatively excellent. On the viewpoint of evaluation for reactor safety, using plutonium in the HWR has desirable characteristics for shifting the coolant void reactivity more to negative side compared with using uranium. It is revealed from the previous studies that the presence of resonance cross section at around 0.3eV of ~'i9Pu is much contributed to the reduction of the void reactivity in plutonium fuel lattice.
However, the mechanism of contribution of the resonance for reducing the void reactivity is not always clarified sufficiently based on the theoretical consideration.
Isotopes of plutonium in the fuel are mixed to cause the complicated compositions of fissile and fertile nuclides due to fuel burnup. Each isotope of plutonium has the resonance in the low energy region. The resonances influence
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to the thermal neutron spectrum in the fuel due to increase in void fraction so that the resonance reaction rate of each plutonium changes delicately. Here, from the viewpoint of grasp of reactor physics characteristics and verification of nuclear data for widely utilizing of plutonium to the thermal reactor, the mechanism of the negative contribution to the void reactivity by plutonium in HWR lattice has been clarified by the parametric analyses with the lattice calculation code based on the collision probability method.
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II. ANALYTICAL METHODS
II.A. Approaching Process
It has been clarified from our experiments1'2 that change in the effects of the
kind of fuel nuclides and change in plutonium isotopic composition in the MOX
fuel on the coolant void reactivity result in the presence of the resonance cross
section at around 0.3eV of 239Pu. In order to confirm sufficiently the conclusion
obtained from the experimental results, it is inevitable to analyze the dependence
of the coolant void reactivity on key parameter for the fuel enrichment by
changing widely fissile nuclide enrichment and the plutonium isotopic composition
(for example, the macroscopic absorption cross section of fuel corresponding to
the thermal neutron is adopted as the parameter indicated the fuel absorptivity).
For this purpose, the components of the void reactivity for fuel nuclide,
neutron cross section, energy groups and space regions in a lattice cell have to be
determined from the lattice calculation using the nuclear calculation code with a
confirmed accuracy. The validity for the conclusion obtained from the critical experiments and the effect of the 0.3eV resonance of 2'9Pu have to be evaluated quantitatively by the present analyses. As it is necessary to extract the effect of the 0.3eV resonance on the void reactivity, the calculation with use of the HWR lattice calculation code WIMS-D4 is carried out by considering the following items.
1) The JENDL-3.14 data library which is compiled recently is used to assess exactly the effect of the resonance cross section of plutonium.
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2) Mesh-dividing is done in detail by considering the cluster-type fuel lattice with
strong heterogeneity, and the components of the fuel and the coolant regions are
derived from the void reactivity.
3) The basic library of the WIMS-D4 code has been compiled with 69 energy groups and the grouping at around 0.3eV is set up so as to be able to focus the component in the energy region including the 0.3eV resonance of 239Pu.
Then, the following total six energy groups were applied: ©1st group is the region for the " U fast fission threshold energy and over (10MeV~~0.82MeV), (2)
2nd the region for slowing down (0.82MeV"-5.53keV), d)3rd the region for resonance absorption (5.53keV~0.625eV), ©4th the region for 1/E spectrum of the epithermal neutron above the cadmium cutoff energy (0.625eV ~ 0.4eV), ©
5th the region including the 0.3eV thermal resonance of 239Pu and 24lPu(0.4eV ~
0.2eV), and ©6th the Maxwellian spectrum region(0.2eV~0.0eV).
The MOX fuel assemblies supplied to the critical experiments using DCA are the 28-rod clusters of plutonium composition which has two kinds of isotopic ratio : One is called standard grade (S) plutonium =F92 wt% fissile and another is reactor grade (R) plutonium#74 wt% fissile. Then, so the MOX fuel selected in the present analyses is conformed to that with the same plutonium composition as used in the experiments. The cross sectional view of the fuel assembly (cluster type fuel) used in the experiments is shown in Fig. 1.
In the present study, the macroscopic absorption cross section (2a0) for the fuel with the neutron velocity(2200 m/s) corresponding to the most probable
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value for the Maxwellian distribution of the neutron energy spectrum is adopted as the key parameter showing an absorptivity of fuel. The value of 2a0 for fuel enrichment considered in the analyses ranges from 0.2 corresponding to approximately natural uranium to 0.5 the uranium enrichment of about 30GWd/t for the attainable burnup. The some range of £a0 corresponding to plutonium enrichment was also applied in the MOX fuel lattice. Ingredient of nuclides in each fuel corresponding to variety of Sa0 is shown in Table I.
II.B. Derivation of Components for Void Reactivity
The analyzed system for the void reactivity in present study is limited in the infinite HWR lattice, because the leakage component of the reactivity in the finite lattice can be regarded as only an additional absorption5. Here, the coolant void reactivity pv can be obtained from change in the infinite multiplication factor due to increase in the coolant void fraction from 0%(H2O) to 100%(Air) in all pressure-tubes. According to the definition of the reactivity perturbation in the noncritical system, the pv is expressed as
Pv k° where
ki,kl= infinite multiplication factors of 0% and 100% voided lattices,
respectively.
Then, the important components can be derived from the eq.(l) for the void
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reactivity. The change in the reaction rate on the i-type cross section between unvoided and 100% voided lattices is defined as follows
(5(Z.(r,E)
< > = inner product for energy and space
<(>(r,E) = neutron flux of energy E at position r in the lattice.
The following condition is adopted in the lattice calculation.
<2l • <|»0 + s S[, Z a = macroscopic absoiption cross section of the fuel and the other structural regions, respectively. Suffix s represents the entire regions in the lattice for H2O coolant and lattice structural materials including D2O moderator and zirconium alloy cladding, etc.. Accordingly, ki and kl are shown as follows ki = Thus, the coolant void reactivity can be rewritten as follows by introducing eqs. (2) and (3) to eq.(l), < 8(vSf• In the equation (5), each term of the right hand side represents the following components of the void reactivity ; -6- PNC TN9410 96-187 + f + Pv = pfis Pabs Pabs • (6) f The first term p fis is the component based on the fission yield cross section in the f fuel region, the second term p abs the absorption cross section in the fuel region, s and the third term p abs the absorption cross sections in the coolant and the structural material regions. II.C. Verification of Lattice Calculation Code It needs to be evaluated the calculational accuracy by WIMS-D4 code incorporated with the JENDL-3.1 library in order to clarify how the resonance absorption of 239Pu at around 0.3eV contributes to the void reactivity. The neutron spectrum index7 (q§ ) indicating the plutonium resonance fission ratio at around 0.3eV and the thermal neutron flux distribution in the unit lattice cell are suitable to the present evaluation. They are obtained for the 22.5cm and 25.0cm pitch lattices as parameters of the plutonium enrichment, plutonium isotopic composition and coolant void fraction in the experiments. The qf5 obtained from the experiment is defined as • v , -y ,dE 49_Jo dE ' ^f) where 239 235 O?(E),O?(E) = microscopic fission cross sections for Pu and U in energy -7- PNC TN9410 96-187 E, respectively. In the range of the fuel concentration on the present study, it is confirmed by experiments and analyses that the cadmium ratio1 for 239Pu-fission ranges from 10 to 20(the cadmium cutoff energy ranges from 0.4eV to 0.5eV). The integral range for neutron energy in Eq.(7) is almost up to the cadmium cutoff energy so that the Eq.(7) represents the index showing remarkably the neutron behavior at around 0.3eV. Here, the thermal neutron flux distribution in the pressure-tube is obtained from the cadmium ratios distribution of dysprosium reaction rates8. The comparison between the experimental and calculated values using the WIMS-D4 code for qf5 of the 0.87wt% MOX(R) fuel is' shown in Fig.2 as parameters of coolant void fraction and lattice pitch. From the results of this figure, the calculational value of cell averaged qg is estimated about an accuracy ± 2.2% and is within experimental error ±4.0%. It is understood that the qg increases toward the outer fuel pin from the inner fuel one in the 100% voided lattice and decreases, however, in the unvoided lattice. The reason is that the depression of neutron flux at around 0.3eV recovers by thermal neutron scattering effect of H2O coolant in the unvoided lattice, while the depression is more promoted toward the inner fuel pin due to the absence of the H2O coolant in the 100% voided lattice. The thermal neutron flux distribution in the unit lattice cell is shown in Fig.3 with the comparison of the experiment and the calculation. The experimental values for the thermal neutron flux are obtained in the right angle and diagonal -8- PNC TN9410 96-187 directions of square lattice, but the calculated values becomes identical in the circumferential direction because of considering the equivalent cylindrical lattice. The calculational accuracy for the thermal neutron flux distribution is estimated about ±2.5% as a fuel rod average, that is almost equal to the experimental error ±2.0%. In the HWR lattice, the thermal neutron flux falls greatly toward the cluster center from the heavy water moderator and the falling becomes remarkable with increase in the fuel enrichment. The thermal neutron flux distribution in the pressure-tube becomes flattened in the 100% void lattice compared with that of the unvoided lattice, because of an absence of thermal neutron scattering effect by the H2O coolant. In the larger pitch lattice with excess moderation, the distribution is inclined to be fallen more than that in the narrower pitch lattice with under moderation, because of an increased thermal neutron absorption effect of the H,0 coolant with the softened thermal neutron spectrum. -9- PNC TN9410 96-187 III. RESULTS AND DISCUSSION Most of composed materials in the HWR lattice are the heavy water and the zirconium which have the small thermal neutron absorption cross sections. According to the present analyses, the third term of right hand side in the eq.(6) represents almost the component of H2O coolant itself. III.A. Characteristics for Coolant Void Reactivity in HWR Lattices The analytical results using the WIMS-D4 code for the dependence of the coolant void reactivity pv in the infinite HWR lattices on the £a0 are shown in Fig.4 (22.5 cm pitch lattice) and Fig.5 (25.0 cm pitch lattice) for the parameters of the f c kinds of fuel (UOX, MOX(S), MOX(R)). The two components(p v and p v) of the void reactivity in the fuel and in the coolant regions separated from the Eq.(5), are also shown in these figures. The following characteristics of the void reactivity are clarified from the results shown in Figs.4 and 5. (1) Results of pv CD The pv tends to exponentially shift toward the negative side with increase in the 2a0 , and it tends to shift toward the more negative side for the narrower pitch lattice. (D If the value of £a0 is identical for each lattice, the pv shifts toward the more negative side in the MOX lattice than in the UOX lattice. (2) Results of p' CD The p' shifts toward the more negative side with increase in the 2a0, and has -10- PNC TN9410 96-187 the positive contribution for any of the £a0. The pv does not depend on the lattice pitch. (2) If the value of £a0 is identical, the Pv has always the negative contribution for the MOX lattice rather than for the UOX lattice and has the more negative contribution for the MOX(S) lattice which has the higher concentration of fissile plutonium. f (3) Results of pv (D The p[. shifts slightly toward the negative side with increase in the £a0, but has the negative contribution for any fuel composition and any of the £a0 (it tends to be saturated at around Eao=O.4cm"'). (D The pi with the narrower lattice pitch has the negative contribution for the MOX lattice rather than for the UOX lattice. (3) The Pv with the larger lattice pitch shifts toward the positive side and it depends a little on fuel nuclide. III.B. Component of the Coolant Region The component of coolant, pv for the void reactivity is the direct one and the other component is the indirect one because the void generated in the coolant causes the void reactivity. The analytical results of the dependence of the pv on the neutron energy for each fuel lattice are shown in Fig.6 as the parameter of £ao- Thermal neutron absorption of oxygen is negligibly small. Thus, the pv is the positive component due to the change of the thermal neutron absorption effect of -11- PNC TN9410 96-187 hydrogen by the change in void fraction. The thermal neutron absorption cross section of hydrogen in the coolant is nearly 1/v type, then the Pv represents the positive effect of thermal neutron absorption by hydrogen in the sixth energy group. From the result of Fig.6, the component of coolant region is the positive contribution for any lattice, and the larger the content of 239Pu in the MOX fuel lattice is, the more it contributes to the negative side of the void reactivity. Figure 7 shows an example of the analyzed thermal neutron flux distribution (below 0.5eV) in the lattice cell normalized at the value of the outer surface of the pressure-tube. With increase in the concentration(2a0) of fuel nuclides and in the lattice pitch, the falling toward the cluster center of the distribution increases. The latter reason is because the thermal neutron spectrum in the coolant region is so softened more for the larger pitch lattice that the thermal neutron shielding effect by the coolant becomes more remarkable. This effect causes the negative contribution to the coolant void reactivity because of resulting in the decrease of the thermal neutron flux. As the thermal neutron shielding effect by coolant increases with increase of lattice pitch, the larger pitch lattice tends to cause the negative contribution to the void reactivity. On the other hand, softening of thermal neutron spectrum with increase of lattice pitch means the increase of the effective thermal neutron absorption cross section. It results in causing the positive contribution. The latter positive contribution offsets the former less positive contribution, then the p' is almost the same in both 22.5cm and 25.0cm pitch lattices. -12- PNC TN9410 96-187 III.C. Component of the Fuel Region The use of plutonium fuel and the increase of the fuel concentration shift the coolant void reactivity toward the more negative side especially in the narrower f pitch lattice as shown in Fig.4. The components (p ns, pabs) of both the fission yield and absorption cross sections for each energy region are shown in Fig.8 as parameters of fuel nuclide (235U, 238U, 239Pu) for MOX(S) lattices with 22.5cm f f pitch. As evident from the figure, both components of p abs and p fis due to changes in 2 a and v 2 f have opposite signs and are different in absolute values each other. The reason why both components have the different values is due to the differences of a-value(= ojo() and the energy dependence among the fuel nuclides or the fuel isotopes. The cc-value for the fissile material ranges from 0.2 to 0.5 •- and Of is greater than oc in the Maxwellian region below 0.2eV of neutron f f ; energy. As the results, the p fis is predominant rather than the p[bs,and the p, becomes negative due to the effect of p'fis especially in the sixth energy group. It is found from the above discussions that changes of the p,is within the energy range from 1/E region to Maxwellian region should be considered especially as the study on the behavior of the void reactivity components in the HWR lattices. f 23D 2 I9 24I • In Fig.9, fission components (p fis) of representative nuclides ( U, " PU, PU) are \ shown for the fifth and the sixth energy groups as the parameters of lattice pitch [ and IaC. In Fig. 10, the calculated thermal neutron spectrums in the inner fuel pin t | for the MOX(S) lattice with £a0=0.35cm"' are shown as parameters of the coolant ( I void fraction and the lattice pitch. It is evident from Fig. 10 that the thermal PNC TN9410 96-187 neutron spectrum hardens due to increase in void fraction and that the relative neutron flux increases except the 0.3eV resonance energy width. The degree of the spectrum hardening due to increase in coolant void fraction is more remarkable with the narrower pitch lattice in the Maxwellian region below 0.2eV. On the contrary, the thermal neutron flux increase conspicuously with the larger pitch lattice. Then, in the 22.5cm pitch lattice, components for " U, ' Pu, and 241 Pu become negative in 6th group by decreasing of fission reaction rate due to the hardening of the thermal neutron spectrum as shown in Figs.8 and 9. In the larger pitch lattice, however, the p[ shifts toward the positive side f because the p fls of every fissile nuclide becomes zero or shifts toward the positive side as shown in Fig.9 due to increase of the thermal neutron flux in the Maxwellian region(see Fig5). The increase of the thermal neutron flux due to increasing of coolant void fraction means the increase of slowing down density in the heavy water moderator with the larger pitch lattice. In the 0% voided lattice, the difference of the thermal neutron spectrum between 22.5cm and 25.0cm pitch lattices is small due to the large slowing down ratio of light water as shown in Fig. 10. Therefore, the p' shifts toward the positive side for the larger pitch lattice. Because the positive contribution by increasing of fission reaction rate due to the increase of the thermal neutron flux tends to be superior to the negative contribution by hardening of the thermal neutron spectrum. f 239 The p fls of Pu in the 5th group for the MOX fuel lattice shifts toward the more negative side with the increase of 239Pu concentration because of existing the -14- PNC TN9410 96-187 large resonance absorption cross section at around 0.3eV. The deep depression of the neutron flux at the resonance energy width is easy to recover in the 0% voided lattice due to a large thermal neutron scattering effect by hydrogen of H2O coolant as clearly shown from the thermal neutron spectrum in Fig. 10. This depression is promoted more deeply with increases in void fraction so that the resonance fission reaction rate which is the product of the resonance neutron flux and the resonance absorption cross section decreases. f 239 The component of p fis of Pu in the 5th group including of 0.3eV resonance becomes slightly negative with the larger pitch lattice differing from that in the 6th group. This effect is comparatively small. This is because the flux depression at around 0.3eV becomes relatively larger by the thermal neutron spectrum softening due to the increase of slowing down density in the moderator with the larger pitch lattice for the 100% voided lattice. For the narrower pitch lattice, the component of 2"i9Pu in the 0.3eV resonance energy adding to the component of 239Pu in the 6th group contributes the shifting to the more negative side of the void reactivity. f 24l As for the component p fis of Pu, the negative contribution in the 5th group is negligible small compared with that of 2j9Pu because the resonance cross section at around 0.3eV is smaller than that of 239Pu. However, the component of f 24l p ns of Pu in the 6th group for MOX(R) lattice shifts toward the more negative side with the narrower pitch lattice, because of relatively large content of 24IPu. Then, the influence of the difference in plutonium isotopic ratio between the two -15- PNC TN9410 96-187 MOX fuels on the void reactivity is small in the entire region of the 5th and 6th groups. f 238 The component p fis of U becomes positive by the spectrum hardening due to increase in the void fraction, because 238U has only the fast fission cross section in the 1st group as shown in Fig.8. The negative contribution of 2"'9Pu with 0.3eV resonance is the final reason why the void reactivity in the MOX lattice shifts toward the more negative side compared with that in the UOX lattice. This negative effect is more remarkable for the MOX(S) lattice with higher content of 2?9Pu than for the MOX(R) lattice. -16- PNC TN9410 96-187 IV. CONCLUSION The void reactivities in the infinite HWR lattices have been analyzed to clarify the influences of changes in key parameters of fuel enrichment, plutonium isotopic compositions and lattice pitch on the coolant void reactivity using lattice calculation code WIMS-D4. In the present calculation, it is known that the behavior of the void reactivity can be made clear by separating the components for fuel nuclide, neutron cross sections, energy group and regions in the lattice cell from the void reactivity by considering some types of the reaction rates. The nuclear library data for the WIMS-D4 code has been replaced with the JENDL-3.1 which is evaluated in Japan, from the original UKAEA. The calculational accuracies for the neutron spectrum indexes and the thermal neutron flux distributions in the lattices have been improved with the new library. From the present study in the HWR lattices with the same macroscopic 2200 m/s neutron absorption cross section of fuel, it has been shown that the void reactivity shifts farther to the negative side with narrower pitch lattice, and in the plutonium lattice than in the uranium lattice. The effect reducing the void reactivity to the negative by plutonium originates mainly in the presence of the resonance cross section at around 0.3eV of 2i9Pu. Because the higher the content of 239Pu is, the less the recovery effect of neutron density within the resonance energy width due to decrease in thermal neutron scattering by hydrogen is with increase in coolant void fraction, so that the -17- PNC TN9410 96-187 decreased resonance fission reaction rate for 239Pu contributes to the more negative side for the void reactivity. ACKNOWLEDGMENTS The authors are deeply indebted to Professor M.Narita of Hokkaido University for their valuable comments and fruitful discussion. We are also indebted to S.Iwasaki of Nuclear Energy System Inc. for data analyses. We wish to thank T.Ihara(Current belonging is Electric Power Development Co., LTD) and M.Takami of CRC Research Institute, Inc., who gave' support through this study and the analyses. REFERENCES 1. N.FUKUMURA,"Measurement of Local Power Peaking Factors in Heavy-Water Moderated Plutonium Lattice," J. Nucl. Sci. &Technol, 18[4](1981). 2. Y.KOWATA and N.FUKUMURA, Nucl. Sci. Eng.,99,299 (1988). 3. H.KATO, "FUGEN plant dynamic test," Proc. 25th ANS Winter Meeting, San Francisco, Trans. Am. Nucl Soc. 33,761(1979) . 4. K.SHIBATA.et al, "Japanese Evaluated Nuclear Data Library, Version-3 -JENDL-3-," JEAR/1319(1990). 5. Y.KOWATA and N.FUKUMURA, Nucl. Sci. Eng., 108, 308(1991). 6. J.J. DUDERSTADTandL.J. HAMILTON, "Nuclear Reactor Analysis'^ 1975). -18- PNC TN9410 96-187 7. S.SAWAI.T.WAKABAYASHI and N.FUKUMURA," Characteristics of Plutonium Utilization in the Heavy-Water-Moderated, Boiling-Light-Water-Cooled Reactor ATR," Nucl. Engineering and Design 125,251-257(1991). 8. T.WAKABAYASHI and Y.HACHIYA, Nucl. Sci. Eng., 63,292 (1977). -19- z o TABLE I Nuclide Composition in Fuel for Void Reactivity Analyses H z 23SU+Pufiss Ingredient (wt%) FUEL 1 (wt%) 235 238 2?9 240 241 242 CD (cm" ) U U Pu Pu Pli Pu en 1 ! I 0.20 0.88 0.7690 87.08 1 00 0.25 1.19 1.047 86.80 0.30 1.51 1.325 86.53 UO2 (UOX) 0.35 1.82 1.603 86.25 — 0.40 . 2.12 1.881 86.97 0.45 2.46 2.159 85.69 0.50 2.77 2.437 85.41 1 0.20 0.82 0.6239 87.13 8.205E-02 2.751E-02 1.196E-02 3.804E-03 to 0.25 1.01 0.6223 86.90 2.300E-01 7.712E-02 3.351E-02 1.066E-02 o 0.30 1.20 0.6207 86.67 3.779E-01 1.267E-01 5.507E-02 1.752E-02 PuO2-UO2 (MOX(R)) 0.35 1.39 0.6190 86.45 5.258E-01 1.763E-01 7.662E-02 2.438E-02 0.40 1.58 0.6174 86.22 6.737E-01 2.259E-01 9.818E-02 3.124E-02 0.45 1.77 0.6158 85.99 8.217E-01 2.755E-01 1.197E-01 3.810E-02 0.50 1.96 0.6141 85.76 9.696E-01 3.251E-01 1.413E-01 4.496E-02 0.20 0.83 0.6240 87.14 L081E-01 1.034E-02 1.095E-03 7.700E-05 0.25 1.05 0.6225 86.93 2.940E-01 2.811E-02 2.980E-03 2.080E-04 0.30 1.26 0.621 1 86.73 4.798E-01 4.588E-02 4.860E-03 3.400E-04 PuO2-UO2 (MOX(S)) 0.35 1.47 0.6196 86.52 6.657E-01 6.365E-02 6.740E-03 4.700E-04 0.40 1.68 0.6181 86.32 8.516E-01 8.142E-02 8.620E-03 6.000E-04 0.45 1.89 0.6167 86.12 1.037E+00 9.920E-02 1.051E-02 7.000E-04 0.50 2.11 0.6152 85.91 1.223E+00 1.170E-01 1.239E-02 8.700E-04 PNC TN9410 96-187 Moderator (D2O) Calandria Tube (Aluminum) Air Gap Pressure Tube (Aluminum) Cladding (Zircaloy-2 for PuO2 -UO2, Aluminum for UO2) Fuel Pellet Coolant (H2O or Air) 26.25 60.00 95.15 120.80 136.50 Fig. 1. Cross-sectional view of 28-rod fuel assembly. Dimensions are given in millimetres. -21- •u C.\J C.\J i i i i 0%Voided 100%Voided 0%Voided 100%Voided o H CD 1.9 - - 1.9 - O CD t 00 -si r 1.8 \ 1.8 - i < i 1.7 1.7 WX P—»-^ O) IO en in S •••A •* CM cr CX to to 1.6 - - 1.6 - t 1.5 - - 1.5 - • 1.4 1.4 I I i i i i i i 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd Fuel Rod Layer Fuel Rod Layer (1) Lattice Pitch = 22.5 cm (2) Lattice Pitch = 25.0 cm -•- : Calculation Fig. 2. Comparison between calculated and experimental values : Experiment for q^ of 0.87wt%(R) PuO2-UO2 cluster. PNC TN9410 96-187 t . 1 1 ( 2.5 • • i • • • • i ' • • ' Pressure Tube 5 S Calandria Tube 2.0 - (0 „ B H • • • : 45 T3 ^j*-*—"^ ° : CO 0) 1.0 - 2^ - t Calculation 0.5 - f Experiment 0.0 i 5 10 15 20 Distance from Cluster Center (cm) (1)0%Voided lattice ' • i Pressure Tube «» - Calandria Tube a o 9 D • D 45 o • 2.0 B B | H 0° - o $ ar—• : cc 1.5 - io n -J • ;ac t ,r - °c 1.0 r >% a 0 5 f J | Calculation | Experiment ' 0.0 " .... . 5 10 15 20 Distance from Cluster Center (cm) (2) 100%Voided lattice Fig. 3. Intra-cell thermal neutron flux distribution in 25.0cm pitch 0.87wt%(R)PuO2-UO2 lattice. -23- PNC TN9410 96-187 Total: pv Fuel: p ' Coolant: p 0.5 1 Za0 (cm" ) Fig. 4. Components in fuel and coolant regions of void reactivity in 22.5cm pitch UOX and MOX fuel lattices. -24- PNC TN9410 96-187 f Total: pu Fuel: pv Coolant: p Fig. 5. Components in fuel and coolant regions of void reactivity in 25.0cm pitch UOX and MOX fuel lattices. -25- o -\ z CO 4 - 4 - 4 - CO CD (30 3 - 3 - < 5? 2 2 - I 2 u > o > (J > Q. a. Q. to 1 - 1 - 0 0 0 -1 -1 -1 12 3 4 5 12 3 4 5 12 3 4 5 6 Energy Group 6 Energy Group 6 Energy Group -1 Ea0=0.35 cm Fig. 6. Absorption components of hydrogen in H2O coolant 1 to void reactivity in 25.0 cm pitch lattice. —o-— Sa0=0.50 crrf PNC TN9410 96-187 2.0 Pressure Tube • • Calandria Tube Fuel Rod Position 1.5 x CD I gi.o 03 E 0.5 - 0.35cm"1 - •- 0.50cm'1 0%Voided 0.0 0 10 15 2.0 Pressure Tube -Calandria Tube.. Fuel Rod Position 1.5 X O I 1.0 f TO E •a0 sz 0.35cm"1 0.5 0.50CITT1 ...r' 100%Voided 0.0 0 5 10 15 Distance from Cluster Center (cm) Fig. 7. Intra-cell thermal neutron flux distribution in 25.0cm pitch MOX(S) fuel lattice. -27- PNC TN9410 96-187 Component on 2. Component on v I. r i i r i i i 0.35cm"1-. -1 o in c C o o -3 -4 2 I 1 I I T 0.50cm"1 _ -1 I o. E o -3 -4 j i I l I j I I I I 12 3 4 5 6 Total 1 2 3 4 5 6 Total Energy Gourp Energy Gourp 235U Fig. 8. Contribution of fission and fuel absorption 238 components to void reactivity in 22.5cm pitch u MOX(S) fuel lattice. 239pu -28- PNC TN9410 96-187 Energy Group=5th Energy Group=6th -0.05 0.20 0.35 . 0.50 1 ZaQ (cm" ) Lattice Pitch ..__ UOX __^___ MOX(R) __.»__ MOX(S) 22.5cm 25.0cm Fig. 9. Contribution in 5th and 6th energy groups of fission component for each fissile nuclide to void reactivity. -29- PNC TN9410 96-187 -1 10 ' ' ' ' ' ' ' ' I ; 25.0cm Pitch - 10,-2 r- CD a J^\ , • -, i ! CD 1... | 5 10,-3 - - 0%void 100%void i i 10-4 ; 22.5cm Pitch 10"-^2 r 03 "1 "j 10"-3J r — \ i 0%void 100%void \ -4 i , . i 10- 10"2 10'1 10° 3x10o Neutron Energy (eV) Fig. 10. Thermal neutron spectrum in inner layer fuel 1 rod of MOX(S) (Ia0=0.35cnr ) lattice. -30-