A Brief Summary of Analysis of FK-1 and FK-2 by RANNS

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1 A Brief Summary of Analysis of FK- and by RANNS Motoe Suzuki, JAEA. Introduction For the purpose of benchmarking the RANS code, FK- and experiments conducted at NSRR were analyzed. Emphasis was placed on the predictability of rod temperature and deformation in a very fast transient. The present calculations are different to some extent from those presented at the meeting in Pisa in May 2, because a few modifications have been done in the model and calculation conditions. 2. FK- and experiments at NSRR Design specifications of the mother rods for FK- and are listed in Table, and simplified power history in base irradiation is shown in Fig.. Fuel type Cladding type Cladding diameter Cladding thickness, Diameter (with chamfer, without dish) Length Fuel density, 235U enrichment, Fill gas, Local burnup, GWd/tU Oxide thickness, m Hydrogen absorption, ppm Cladding radial creep down ( m) FK- xbj (Step I) Zr-lined Zry-2 recrystallized 2.27 mm.6 mm (including Zr liner:.9mm).3mm.3mm 95 % theoretical density 3.4 wt%? 3.9 a wt% He:.3 MPa av ~2.5max 45..6av ~24.max 45 to 59 (radial displacement) vs.2(initial gap) Fission gas release, % EOL gas pressure, MPa Peak linear heat rate, W/cm Span number from bottom/total Irradiation period in BWR Fast fluence.5x 25 n/m /7 94 to 99 (5 cycles) in TEPCO Fukushima 3. Models and assumptions of the RANNS code The thermal model and mechanical model are the same as those in FEMAXI-7. That is, -dimensional calculation is carried out in a cylindrical geometry. In FK- and, the neutron flux is uniform along the axial length, so that basic calculations were done with one segment approximation. Also, three-segment calculation using the measured cladding surface temperatures was performed. The cladding surface heat transfer model is a steady model, i.e. RELAP model. This is not a transient model, so that the calculated cladding temperatures have a considerable

2 uncertainty. Also, in the three-segment calculation, the measured cladding temperatures seem to have a marked fluctuation due to fin effect or turbulent flow of coolant with natural convection. In the calculation, a power generation density profile is given as a function of burnup by the result of a burning analysis code. For Zr-liner cladding of BWR fuel, ten ring elements are set. 2 LHR (W/cm) Time (day) Fig. Base irradiation power history 4. NSRR Experiments 4. Experimental condition The details have been described in : T.Nakamura, M.Yoshinaga, M.Takahashi, K.Okonogi, and K.Ishijima, Boiling Water Reactor Fuel Behavior under Reactivity-Initiated-Accident Conditions at Burnup of 4 to 45 GWd/tonneU, Nuclear Technology, Vol.29, pp.4 (2). 4.2 Results of experiments Main results of the two experiments analyzed in the present study are listed in Table 2. The pulse power generated in the experiments and input to the calculations are shown in Fig.2. Table 2 FK- Peak fuel enthalpy, cal/g (J/g) 3 (544) 7 (293) Cladding surface temperature, o C 36 (6) - Pellet stack elongation, %.4.7 Cladding strain (%), [residual] % by PCMI axial. [.3].3 [] hoop - [.5-.3] - [] Rod internal pressure, (initial) MPa.9 (.3).2 (.3) FGR, (base irradiation) %.2 (.5) 3. (.5) Cladding Failure No No 2

3 Linear heat rate (MW/m) Fig.2 FK Pulse power generated in the NSRR experiments. 5. Results of Analysis 5. One segment geometry calculation 5.. FK- ) Cladding temperature Measured and calculated temperatures of cladding are shown in Fig.3. of Fig.3. Fig.4 is a zoomed view Cladding temperature (C) TF2 TF3 Surface TF Fig.3 Measured and calculated cladding temperatures. Cladding temperature (C) TF2 Surface FK- TF TF Fig.4 Zoomed view of measured and calculated cladding temperatures. 2) Cladding stress The mechanical analysis was performed with two extreme conditions. One is assuming that the rod has a strong friction, or bonding between pellet stack and cladding (Fig.5), and the other is assuming that that the rod has a very weak friction, or sliding between pellet stack and cladding (Fig.6). The element is Zr-liner, and element is the outermost element of cladding, and the elements 3, 5, are those between the elements and. 3

4 Cladding stress (MPa) 2 Hoop FK- Axial Fig.5 Calculated cladding stress in bonding condition. Cladding stress (MPa) FK Fig.6 Calculated cladding stress in sliding condition. Hoop Axial 3) Axial elongations The axial elongations of pellet stack and cladding are shown in Fig.7. Fig is a zoomed view of Fig.7. In these figures, measured data and calculated curves in both the bonding condition and sliding condition are compared. A marked difference in elongation rate is clearly found between calculated results and measured data. Axial elongation (mm) Pellet: Sliding Calc. Pellet: Measured Clad: Sliding Calc. FK- Clad: Bonding Calc. Clad: Measured Pellet: Bonding Calc Fig.7 Measured and calculated axial elongations of pellet stack and cladding. Axial elongation (mm) FK- Pellet: Sliding Calc. Pellet: Measured Pellet: Bonding Calc. Clad: Bonding Calc. Clad: Sliding Calc. Clad: Measured Fig. Zoomed view of measured and calculated axial elongations. 4) Cladding strain Calculated strains of cladding are shown in Figs.9 to 2. Total hoop strain in element and, plastic and creep strains in element of cladding in bonding condition are shown in Fig.9. Similarly, the hoop strains in sliding condition are shown in Fig.. Total axial strain, and plastic and creep strains in element of cladding in bonding condition are shown in Fig.. Similarly, the axial strains in sliding condition are shown in Fig.2. 4

5 Cladding hoop strain (%) Fig Calculated hoop strains of cladding in bonding condition. Cladding hoop strain (%) Sliding Fig. Calculated hoop strains of cladding in sliding condition. Cladding axial strain (%) Fig Calculated axial strains of cladding in bonding condition. Cladding axial strain (%) Sliding Fig.2 Calculated axial strains of cladding in sliding condition. 5) Cladding diameter profile Measured and calculated rod (cladding) diameter profiles are shown in Fig.3. The calculated post-pulse diameter PD is determined by the following equation: PD = [initial diameter 2.27mm] x [. + plastic strain of ring element #] + [average oxide thickness] x2. In the experiment, the upper part of cladding is more expanded than the lower part. This suggests that the temperature of upper part of cladding rose by coolant convection and as a result the mechanical strength of cladding fell and plastic strain increased. 5

6 On the other hand, the calculated results indicate that the hatched zone made by the two cases, i.e. bonding condition and sliding condition covers the upper part of the measured diameter only. Here, during. -.s, the calculation indicates a gap closure due to PCMI, as shown in Fig.4.This period is well included by the period.2-2.5s during which PCMI is taken place. However, the pre-pulse gap size depends on the analytical results of base-irradiation. 6) Internal pressure The measured internal pressures are shown in Fig.5. These pressure histories were input to the calculations. They are less than one-tenth of the PCMI contact pressure, so that their effect on cladding deformation is negligible. Cladding diameter (mm) Diameter gap size ( m) Internal pressure (MPa) Top Fig bonding Post-pulse profile Pre-pulse profile Bottom Rod axial position (mm) High temperature period of cladding FK- sliding Fig Rod diameter profiles Calculated P-C diameter gap size. FK Fig.5 Measured internal pressures. 6

7 5..2 ) Cladding temperature Measured and calculated temperatures of cladding are shown in Fig.6. view of Fig.3. Fig.7 is a zoomed Cladding temperature (C) Surface Fig.6 Calculated cladding temperatures. Cladding temperature (C) Fig Surface Zoomed view of calculated cladding temperatures. 2) Cladding stress The mechanical analysis was performed with two extreme conditions. One is assuming that the rod has a strong friction, or bonding between pellet stack and cladding (Fig.), and the other is assuming that that the rod has a very weak friction, or sliding between pellet stack and cladding (Fig.9). The element is Zr-liner, and element is the outermost element of cladding, and the elements 3, 5, are those between the elements and. Cladding stress (MPa) Hoop Axial Fig. Calculated cladding stresses in bonding condition Cladding stress (MPa) Fig.9 Calculated cladding stresses in sliding condition 7

8 3) Axial elongations The axial elongations of pellet stack and cladding are shown in Fig.2. Fig2 is a zoomed view of Fig.2. In these figures, measured data and calculated curves in both the bonding condition and sliding condition are compared. Axial elongation (mm) Axial elongation (mm) Pellet Bonding Clad Sliding Pellet Sliding Clad Bonding Clad Sliding Pellet Bonding 4) Cladding strain Calculated strains of cladding are shown in Figs.22 to 24. Total hoop strain in element and, plastic and creep strains in element of cladding in bonding condition are shown in Fig.22. Similarly, the hoop strains in sliding condition are shown in Fig.23. Total axial strain, and plastic and creep strains in element of cladding in bonding condition are shown in Fig.24. Similarly, the axial strains in sliding condition are shown in Fig.25. Pellet Stack Cladding Fig.2 Measured and calculated axial elongations of pellet stack and cladding. Pellet Sliding Clad Bonding Pellet Stack Cladding Fig.2 Zoomed view of measured and calculated axial elongations of pellet stack and cladding.

9 Cladding hoop strain (%) Fig.22 Calculated hoop strains of cladding in bonding condition. Cladding axial strain (%) Fig.24 Calculated axial strains of cladding in bonding condition. Cladding hoop strain (%) Cladding axial strain (%) Fig.23 Calculated hoop strains of cladding in sliding condition Fig.25 Calculated axial strains of cladding in sliding condition. 5) Cladding diameter profile Measured and calculated rod diameter profiles are shown in Fig.26. The calculated post-pulse diameter PD, which is overestimated in the bonding condition (plastic strain=.9%), is determined by the following equation: PD= [initial diameter 2.27mm] x [. + plastic strain of ring element #] + [average oxide thickness] x2. In the sliding condition, plastic strain is.%. Cladding diameter (mm) 2.2mm=.9x % Fig.26 Comparison of measured diameter change and calculated diameter change. 9

10 5.2 Calculated results of FK- with three segments geometry In the FK- experiment, cladding surface temperature was measured at three axial locations. These measured data were modified to some extent and used as input to pre-determine the cladding surface temperatures at three segments, lower, middle and upper segments in the calculation. In this calculation, the rod was divided into axial lengths of 37mm, 32mm, and 37mm. The friction between pellet stack and cladding was assumed as intermediate of the bonding condition and sliding condition, i.e. frictional coefficient was set 4.. The input cladding surface temperatures are shown in Fig.27. Fig.2 is a zoomed view of Fig.27. Clad temperature (C) Fig.27 Middle segment 2 Lower segment Upper segment 3 Input cladding surface temperatures derived from measured data. Clad temperature (C) Fig.2 Middle seg.2 Upper seg.3 Lower Seg. Zoomed view of input cladding surface temperatures derived from measured data. The calculated PCMI contact pressures at the pellet-clad interface and induced stresses in cladding outermost element are shown in Fig.29 and Fig.3, respectively. PCMI contact pressure (MPa) Fig.29 Upper seg.3 Lower Seg. Middle seg Calculated PCMI contact pressures. Cladding stress (MPa) Fig.3 Upper seg.3 Lower Seg. Middle seg.2 Hoop stress Axial stress Calculated cladding hoop and axial stresses in element. The calculated diameter gap size and hoop plastic strains in cladding outermost element are shown in Fig.3 and Fig.32, respectively. The creep strains have no changes during the transient irradiation. The plastic strains of cladding, which give rise to the diameter increase, are generated

11 during the most severe PCMI period, i.e. stress peaking period, and after that the plastic strains remain as they are. Diameter gap size ( m) Middle seg.2 Lower Seg. Upper seg Fig.3 Calculated P-C diameter gap Fig.32 Calculated hoop plastic strains size. of cladding element. Measured and calculated rod diameter profiles are shown in Fig.33. The calculated post-pulse diameter PD is determined in each axial segment. The calculated results indicate that the lower segment has the largest increase of diameter, and the upper segment has the smallest increase of diameter. This is contrary to the measured profile. In the calculation, the plastic strain is generated in the very early period of transient only in which the measured cladding temperature is highest in the lower segment and lowest in the upper segment, so that the calculated amount of plastic strain corresponds to the temperature level of cladding segments. Cladding diameter (mm) Top bonding Fig.33 Comparison of cladding diameter profiles: one-segment calculations in bonding and sliding conditions, three-segment calculations using measured cladding temperatures, and measured profiles in FK-. 6. Summary There are significant differences between the measured data and calculated results both in FK- and. These differences are attributable to the uncertainty of measured data, particularly the measured cladding surface temperature, and to some inadequacy of models, particularly PCMI calculation model. These problems are further investigated to have a better prediction of such very fast transient as the NSRR experiments. Cladding hoop plastic strain (%) Using measured temperatures Post-pulse profile Pre-pulse profile Lower Seg. Upper seg Bottom Rod axial position (mm) Middle seg sliding