ML24061A036
| ML24061A036 | |
| Person / Time | |
|---|---|
| Issue date: | 03/12/2024 |
| From: | Patrick Raynaud NRC/RES/DE |
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| Shared Package | |
| ML24065A104 | List: |
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| TLR-RES/DE/REB-2024-01 | |
| Download: ML24061A036 (1) | |
Text
Technical Letter Report
[TLR-RES/DE/REB-2024-01]
Confirmatory Calculation: Influence of Cladding Modeling Assumptions for NuScale Pressure - Temperature Limits Date:
February 2024 Prepared in response to Informal Assistance Request from NRR/DNRL/NVIB to RES/DE/REB, by:
Patrick A.C. Raynaud Senior Materials Engineer Reactor Engineering Branch U.S. Nuclear Regulatory Commission Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001
ii DISCLAIMER This report was prepared as an account of work sponsored by an agency of the U.S. Government.
Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party's use, or the results of such use, of any information, apparatus, product, or process disclosed in this publication, or represents that its use by such third party complies with applicable law.
iii This report does not contain or imply legally binding requirements. Nor does this report establish or modify any regulatory guidance or positions of the U.S. Nuclear Regulatory Commission and is not binding on the Commission.
iv Execuve Summary In support of NRRs review of NuScales Standard Design Approval Applicaon, RES/DE/REB performed independent con"rmatory calculaons with the FAVPRO code. The goal of the analyses was to study the in"uence of several dierent modeling assumpons on Pressure Temperature limits for the NuScale vessel.
RES studied four dierent modeling assumpons for the vessel inner diameter cladding, all based on a plant cooldown transient at 100°F per hour (37.8°C per hour). The analysis of me histories and through-wall pro"les of the temperatures, stresses, and stress intensity factors for relevant 1/4 thickness cracks at mes of interest showed that the in"uence of the dierent modeling assumpons on the resulng pressure temperature limit curves would be small.
In conclusion, the author of this report determined that the assumpons chosen by NuScale in the PT limit calculaon are acceptable, and that these conclusions would remain the same even for more realisc transients.
v Table of Contents Execuve Summary...................................................................................................................................... iv 1
Background........................................................................................................................................... 1 2
Modeling Assumpons......................................................................................................................... 2 2.1 Geometry...................................................................................................................................... 2 2.2 Transient........................................................................................................................................ 3 3
Results................................................................................................................................................... 5 3.1 Time Histories............................................................................................................................... 5 3.2 Through-Wall Pro"les.................................................................................................................... 8 4
Summary and Conclusions.................................................................................................................. 14 5
References........................................................................................................................................... 15
1
1 Background
As part of the NuScale Standard Design Approval Applicaon (SDAA) Pressure Temperature Limit Report (PTLR) review, it became necessary to invesgate clad modeling assumpons used for calculang the stress intensity factors (SIF) needed to derive their Pressure temperature (PT) limits.
Clad modeling assumpons have an impact on the through-wall stress pro"les, and thus on the SIF calculated at the crack p for the purpose of deriving a PT limit.
This calculaon using the FAVPRO v0.1.19 code models a cooldown at a rate of 100°F/hour following the cooldown PT limit proposed by NuScale (Table 5.3-2 in [1]). 4 dierent geometries were invesgated to understand the impact of dierent cladding modeling assumpons on the calculated SIF for a relevant "aw.
2 2 Modeling Assumpons 2.1 Geometry The dimensions of the NuScale vessel are listed in Table 5.3-1 of [1]. For a PT limit calculaon, a 1/4 thickness "aw on the ID of the vessel is assumed, with a "aw aspect rao equal to 6.
The NuScale vessel has cladding on the ID and OD surfaces. Removal of the cladding thus changes the thickness of the vessel being modeled. 4 dierent geometries were considered, as shown in Figure 2-1:
Case 1: Full thickness vessel including cladding on the ID (note that the NuScale vessel also has cladding on the OD, but this cannot be modeled with FAVPRO, as a result, the OD cladding thickness was added to the base metal thickness), with a 1/4 thickness surface "aw that goes through the enre cladding and into the base metal.
Case 2: Full thickness vessel where the ID cladding thickness is assumed to be part of the base metal (i.e. no cladding but full wall thickness as if the cladding was there), with a 1/4 thickness surface "aw that goes into the base metal.
Case 3: Cladding thickness removed on both ID and OD, thus reducing the vessel wall thickness, and with the crack depth also being reduced by the ID cladding thickness. This results in a normalized crack depth of 22.2% (instead of 25% for a 1/4 thickness "aw). This case is what would occur if the crack depth was calculated and modeled using the full vessel model, and then the cladding elements were simply removed from the model.
Case 4: Cladding thickness removed on both ID and OD, thus reducing the vessel wall thickness, with a crack size equal to 25% of the reduced vessel thickness (a 1/4 thickness "aw using the reduced wall thickness).
It is unclear which case NuScales model incorporated, consequently all are compared below.
3 Figure 2-1: Geometries studied 2.2 Transient The transient modeled is a cooldown at 100°F/hour along the PT limit curve, starng at 600°F (the upper temperature limit of the PT limit) and at the 2000 psi operang pressure of the NuScale power module (from Table 1.2-1 in [2]). The resulng transient history is shown in Figure 2-2, and Figure 2-3 shows the corresponding PT limit curve provided by NuScale. This case was modeled for this comparison and is not a realisc NuScale transient or one used by NuScale in their PTLR methodology.
4 Figure 2-2: Transient history Figure 2-3: Cooldown PT limit curve
5 3 Results 3.1 Time Histories For the 4 geometry and "aw combinaons studied, the stress intensity factor, crack p stress, and crack p temperature histories were calculated. In addion, for each of these 3 quanes, the instantaneous normalized standard deviaon between the 4 cases (i.e. standard deviaon divided by average) was also calculated, as shown in Figure 3-1, Figure 3-2, and Figure 3-3, respecvely.
Figure 3-1 shows that the SIF varied by a maximum of 2 ksiin between all 4 cases studied, corresponding to a normalized standard deviaon of less than 3.5% over the course of the transient. It should be noted that Case 3 is slightly non-conservave compared to the other 3 cases. It is unclear whether the NuScale analysis is most closely represented by Case 3 (least conservave) or by Case 4 (most conservave), but the dierences are overall small, thus the impact on the PT limits should also be small.
Figure 3-1: Crack tip stress intensity factor history
6 Figure 3-2 shows that the stress varied by a maximum of 2 ksi between all 4 cases studied, corresponding to a normalized standard deviaon of less than 7% over the course of the transient. Pernently the normalized standard deviaon was lowest when the overall stress was lowest.
Figure 3-2: Crack tip stress history
7 Figure 3-3 shows that the temperature varied by a maximum of 3°F between all 4 cases studied, corresponding to a normalized standard deviaon of less than 2% over the course of the transient.
Figure 3-3: Crack tip temperature history
8 3.2 Through-Wall Pro"les To beter understand the eects of clad modeling assumpons on the resulng stresses and SIFs, through-wall pro"les of the stress and SIF were extracted at transient mes of 50 minute and 350 minutes.
At t=50 minutes, the temperature gradient across the vessel wall is relavely high (see Figure 3-4), and the pressure is sll holding at the operang pressure, resulng in a near-maximum total stress (see Figure 3-2).
Figure 3-4: Through-wall temperature pro"le at transient time t=50 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
9 At t=50 minutes, when modeled, the cladding is in relave compression due to the thermal expansion mismatch between the cladding and the base metal (blue line in Figure 3-5): the stress in the cladding is
~60% of that in the base metal at the clad to metal interface. Further comparison of the Thick wall with clad and thick wall no clad lines in Figure 3-5 indicates that once in the base metal, the presence or absence of the cladding has very litle in"uence on the overall stress. In comparison, the wall thickness has a larger in"uence than the presence of cladding on the through-wall stress, as indicated by the fact that the stress dierence resulng from a thin wall (cases 3 and 4 in secon 2.1) is larger than that resulng from the absence of cladding.
Figure 3-5: Through-wall stress pro"le at transient time t=50 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
Cladding in compression relave to base metal
10 Figure 3-6 shows that the impact of the cladding on the SIF is large for shallow cracks near the clad to metal interface, but that this eect quickly decreases as a funcon of crack depth, such that the eect is negligible for cracks deeper than ~0.5 inches (~11% through-wall). The eect of the higher stress in a thinner walled vessel without cladding is larger than the eect of the cladding for a 1/4 thickness crack, as seen in the purple box in Figure 3-6, and this eect is conservave relave to a thicker vessel with cladding.
Figure 3-6: SIF as a function of crack depth at transient time t=50 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
11 In contrast from the condions at t=50 minutes, at t=350 minutes, the stress is low, temperature is near constant at 65.0-65.5°F across the enre vessel wall (see Figure 3-7), and pressure has been reduced by 75% from the operang pressure, resulng a near-minimum stress (see Figure 3-2).
Figure 3-7: Through-wall temperature pro"le at transient time t=350 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
12 At t=350 minutes, the cladding is in tension because of the low temperature and the thermal expansion mismatch between the cladding and the base metal (thick wall with clad line in Figure 3-8): the stress in the cladding is ~440% of that in the base metal at the clad to metal interface. Because of the larger stress dierence between the cladding and the base metal, as well as low overall stress, the relave in"uence of the cladding of the through-wall stress pro"le is greater than it was at t=50 minutes, but remains small (~1ksi). As expected, the stress in the thin wall no clad case is higher than that in the thick wall cases, but the eect is even smaller than that of the impact of the cladding.
Figure 3-8: Through-wall stress pro"le at transient time t=350 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
Cladding in tension relave to base metal
13 As was the case for t=50 minutes, Figure 3-9 shows that the impact of the cladding at t=350 minutes Is very large for shallow cracks, and diminishes as the crack depth increases. For the 1/4 thickness cracks of interest in this study, the eect of modeling the cladding is similar to the eect of not modeling it and using a thinner wall in the model, and both are conservave relave to the thick wall no clad model (see purple box in Figure 3-9).
Figure 3-9: SIF as a function of crack depth at transient time t=350 min. The purple box indicates the range of crack depths studied in the 4 geometry cases presented in section 2.1.
14 4 Summary and Conclusions This study presents the results of FAVPRO analyses to invesgate the in"uence of 4 dierent modeling assumpons related to representaon (or lack thereof) of an ID cladding layer in the NuScale upper reactor pressure vessel. The modeling assumpons are discussed in secon 2, including geometry and transient consideraons.
Analysis of me histories and through-wall pro"les of the temperatures, stresses, and SIFs for relevant 1/4 thickness cracks show that the impact of the cladding modeling assumpons that were studied are overall small and do not signi"cantly change the overall SIFs that would be used to calculate PT limits. As a result, the assumpons chosen by NuScale in the PT limit calculaon are deemed acceptable by the author of this report.
Based on the nature of the subject studies, it is expected that these results would remain largely the same for other potenal transients (e.g. normalized uncertaines would vary linearly with the mean stress state of other postulated transients). Consequently, more realisc transients would not substanvely aect the results of this analysis.
15 5 References
[1] NuScale Power, LLC, "NuScale US460 Plant Standard Design Approval Applicaon, Chapter 5: Reactor Coolant System and Connecng Systems, Revision 0 (NRC ADAMS ML22365A016)," NuScale, Corvallis, OR, USA, 2023.
[2] NuScale Power, LLC, "NuScale US460 Plant Standard Design Approval Applicaon, Chapter One:
Introducon and General Descripon of the Plant (NRC ADAMS ML22365A002)," NuScale, Corvallis, OR, USA, 2022.