A High-Fidelity Model of the Peach Bottom 2 Turbine-Trip Benchmark Using VERA^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is well-written and shows impressive results obtained by the VERA modeling tool.

Some minor details should be fixed to improve the paper and publish it.

End of Section 1. Please include additional references on other simulation efforts for the PBTT benchmark.

Figure 2 and 3. Please comment on the evolution of the burnup. It seems that in this work there is a sistematic underprediction, while the other participants obtain a (similar in magnitude) overprediction. Do you have any explanation or hypothesis about this behavior?

Figure 6. The pictures show a quarter of the reactor. Is the simulation done on the quarter domain, or is it done on the whole core? No information about this is present in the text.

Section 4.2. Please explain better what information can be gathered using the approach described in the paper compared to other approaches.

End of Section 4.2. Please add a paragraph detailing the computational costs associated with this type of simulation and, if possible, a comparison with computational costs incurred by other participants or, in general, using "traditional" simulation techniques.

Author Response

Thank you for your comments. Here is my response to each one numbered:

1. The linked benchmark documents showcase all of the initial simulation efforts for the benchmark. I have also added two recent efforts from this decade to illustrate that it is still in use.
2. For figure 2 and 3, there is no comparison to participants since they did not simulate the depletion of Peach Bottom 2 through cycles 1 and 2, rather they simply used computed cross sections in the benchmark provided by the NEA/OECD from their own depletion simulations. The eigenvalue results of that depletion are not shared by the benchmark committee. I have specified though in section 3.2 what the maximum and minimum participant keff values were (using the provided XS) so that it is clear that we fall within the range of benchmark participant values reported and that some difference is expected due to difference in means of specifying initial conditions for the turbine trip.
3. The peach bottom 2 core has quarter-core symmetry and the PBTT benchmark introduces no asymmetry. Therefore, modeling the core as full-core, half-symmetric, or quarter-symmetric is appropriate. We utilized quarter-symmetric modeling for VERA. I have made a note of it on the paper near the plots.
4. I have added specifying that the high fidelity of the VERA results provides pin-wise values that can be used in fuel and cladding analysis for limiting calculations.
5. I have added a note at the end of section 4.2 on the computational costs of this simulation. Benchmark participant costs are not provided and therefore not compared to, though they surely would be significantly less as these were done using coarser fidelity methods typically designed for running on laptops or desktops.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents an effort of using VERA to simulate PBTT benchmark with good agreement, showing the ability of VERA on modeling complex multi-physics. Even though concise, the reviewer finds this paper well-written, with a clear and logical structure that guides the reader through the key arguments and findings. The validation result also indicates a promising use of VERA for further transient study. The reviewer thus is in favor of publishing in its present form. 

Author Response

Thank you for your comments.

Reviewer 3 Report

Comments and Suggestions for Authors

1. The results shown in Figure 2 indicate that k_eff fluctuates within the range of approximately 0.985 to 1.005, corresponding to around 2000 pcm, not 1500 pcm as previously stated. A similar discrepancy is observed in Figure 3, where k_eff ranges from 0.996 to 1.001, corresponding to around 500 pcm, not 400 pcm. These estimates should be more precise, as an uncertainty of 100 pcm in k_eff calculations is significant and not negligible.

2. In Figure 5, the absolute power values should be compared, rather than the relative values, to provide a more accurate assessment of the system behavior.

3. In Figure 9, after 1.9 seconds, it can be observed that the fuel temperature is lower than at t = 0.3 s. However, the cladding temperature at t = 1.9 s remains higher than that at t = 0.3 s. Please provide a sufficient explanation for this behavior. Additionally, why does a ~50°C increase in fuel temperature only result in about a 5°C increase in cladding temperature?

4. The author states that no dryout was detected. However, in a commercial water-cooled reactor, an increase in cladding temperature is typically accompanied by a rise in coolant temperature, which can increase the void fraction in the coolant. The results presented in Figure 10, however, appear to contradict this expectation. Please explain this inconsistency.

Author Response

Thank you for your comments. Here is my response to each one numbered:

1. “The results shown in Figure 2 indicate that k_eff fluctuates within the range of approximately 0.985 to 1.005, corresponding to around 2000 pcm, not 1500 pcm as previously stated. A similar discrepancy is observed in Figure 3, where k_eff ranges from 0.996 to 1.001, corresponding to around 500 pcm, not 400 pcm. These estimates should be more precise, as an uncertainty of 100 pcm in k_eff calculations is significant and not negligible.”
   
   The paper does not state that the fluctuations are within 1500 pcm of each other, rather the paper say that the results stay within 1500 pcm of critical (and critical is the desired result since this is a simulation of approximate operating conditions for the two cycles and operation happens at an approximately critical state). Similarly for the 400 pcm in cycle 2. Yes, the fluctuations have a range of around 500 pcm, but they stay within 400 pcm of critical. The authors are not certain what the reviewer means by “precise” or “uncertainty” here since these are not Monte Carlo simulations but rather deterministic calculations (and uncertainty quantification is not a subject of this paper). The authors will assume that the reviewer means accuracy compared to the expected result when they say “precise” and error compared to the expected result when they say “uncertainty” here. The authors disagree that these estimates should be more accurate. 100 pcm agreement is a good measure for k_eff when comparing single-physics steady state simulations with very precisely defined materials and conditions, but that is not what these simulations are. These are multiphysics depletion simulations of approximate reactor operating conditions recorded in the 1970s when the operators had difficulty maintaining a consistent power level (as mentioned in the paper regarding the variance in power over the cycles). As such, agreement within a few hundred pcm of critical would be considered generally good accuracy if the operating conditions were recorded with complete accuracy (which they are not in this case). Indeed, these results are consistent with previously published simulations of the PB2 cycle 1 and 2 depletion, as stated in the paper. The authors never state that the differences are “negligible” in the paper, and indeed state that the large errors in cycle 1 are likely due to imprecise recording of operating conditions for a reactor experiencing more fluctuation than is common in modern reactor operations.
2. “In Figure 5, the absolute power values should be compared, rather than the relative values, to provide a more accurate assessment of the system behavior.”
   
   The authors disagree that absolute power should be compared instead of relative here for two reasons. The first is that a comparison of absolute power would simply be the given plot just scaled up by the MW/cm value of the core, but the shape of the plot and comparison would remain identical. The second reason is that the benchmark participant results are presented in terms of relative axial power levels in the benchmark reports, not absolute axial power levels. Since the purpose of this plot is to demonstrate our agreement with benchmark participants, altering their results to a different scale would be inappropriate. Instead, relative axial power provides the same comparison and does not require scaling benchmark participant results.
3. “In Figure 9, after 1.9 seconds, it can be observed that the fuel temperature is lower than at t = 0.3 s. However, the cladding temperature at t = 1.9 s remains higher than that at t = 0.3 s. Please provide a sufficient explanation for this behavior. Additionally, why does a ~50°C increase in fuel temperature only result in about a 5°C increase in cladding temperature?”
   
   In a fuel pin, the heat source is produced by fission and is internal to the fuel. The heat sink is the water flowing past and occurs on the outside of the cylinder. The reason that the fuel temperature goes below the initial value before the clad temperature does over this time is because the scram initiated at 0.75 seconds reduces the power rapidly (see Figure 7). Because the power is rapidly reduced, the heat source is removed quickly at this point while the heat sink of water flowing around the fuel cladding does not change as rapidly during this period. Because of this, the fuel, which is where fission happens and therefore responds first to changes in fission induced power, will experience a temperature change much more rapidly than the fuel cladding in this situation since the change in heat source will take time to propagate out to the surface of the cladding which is still experiencing a similar heat sink. Additionally, the significantly lower heat source interior the cylinder will push the cylinder to a spatially flatter temperature profile, so since the maximum fuel temperature is at the center of the cylinder and the clad surface temperature is on the outside, one would expect that they would get more similar as the temperature profile flattens. As far as why a 50 C increase in fuel temperature only results in a 5 C increase in cladding temperature, this is because this is a cylindrical head conduction problem with an interior source and an exterior sink. For a cylindrical conduction problem with such sources and sinks, the temperature and heat capacity will be nonlinear with respect to radius (notice there is more mass per radius cm as you go outward). As such, an increase of 50 C in the center of the fuel pin should translate to a lower increase at the exterior of the cladding (in this case 5 C). The authors are not including these explanations in the paper because this is assumed knowledge for a reader of this journal and would therefore constitute bloat.
4. “The author states that no dryout was detected. However, in a commercial water-cooled reactor, an increase in cladding temperature is typically accompanied by a rise in coolant temperature, which can increase the void fraction in the coolant. The results presented in Figure 10, however, appear to contradict this expectation. Please explain this inconsistency.”
   
   I am not sure what dryout has to do with the rest of this comment (no dryout was detected in our simulation, neither was it in the original benchmark, nor should it be since safety margins prohibited dryout), so the authors will address the rest of the comment. Yes, an increase in cladding temperature can result in an increase in coolant temperature and therefore an increase in void fraction, if all else is equal (i.e. at steady state). But this is a transient, so not all else is equal. In fact, this is a turbine trip, which is a type of transient where the reactivity insertion is caused by void collapse (as stated in the paper) due to an increase in incoming pressure and flow rate driven by decreased head loss in the turbine. As such, the very cause of the power excursion is driven by the void fraction decrease shown in figure 10. If the temperature change were enough to offset the increased pressure and flow rate to keep the void fraction the same (or even increase it) then there would be no significant reactivity insertion, and no power excursion would occur. The temperatures go up because the power goes up because the void decreases because the flow rate and pressure in the incoming flow increases. If the void didn’t decrease, the temperatures wouldn’t go up. That’s why you can see comparing Figures 9 and 10, that the void decrease begins just prior to the temperature increase.

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

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