Effects of Neutron Flux Distribution and Control Rod Shadowing on Control Rod Calibrations in the Oregon State TRIGA^® Reactor

Round 1

Reviewer 1 Report

I recommend adding more references and improving the quality of some plots (Letters and subtitles are too small) . Please also add a reference dimension to the Fig. 2. Also please consider adding information about Xe135 effects. Is it important in OSTR MC modelling? In some cases, not uniform Xe135 concentration can introduce numerical power shift (and thus flux) anomalies in MC modelling, which can influence other parameters. The worth-citing paper was published recently in  MDPI  Sustainability and may be added to references (https://doi.org/10.3390/su15043373).

From a scientific point of view, the paper is very good, well done.

Author Response

Please see attachment. 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper addresses the interesting feature of control rod worth measurements in reactors and attempts to explain the reasons for the differences between measurements and calculations.

The solution of the transport equation can be expanded in terms of the eigenfunctions. For a small reactor like TRIGA the dominance ratio of the eigenvalues suggests that the higher mode eigenfunctions would decay rather quickly and hence the (normalized) neutron flux distribution would be stable soon after the perturbation (i.e. the rod-pull). This justifies the use of the steady-state Monte Carlo analysis for the simulation. However, in the example discussed in the paper the reactor period was as low as 6 seconds. A rough guess is that this is sufficient for the flux distribution to stabilize, but with such a short period the time for the power to rise from 10 W to 200 W is of the order of 30 seconds (in the extreme case). In transients with short periods the higher terms take longer to die away and could affect reactivity measurements based on reactor period. If the trace of the measured flux signal has been recorded, it would be useful to check and report its linearity in the log-log scale, since this could affect the reactivity measured via the Inhour equation.

As the authors state, the results of control rod worth measurement by the rod-pull method are not unique, since they depend on the position of the other control rods, which change after every pull to compensate the reactivity. The authors performed an extensive computational simulation of the experiment, where they proved that the detectors at different locations respond differently. This is due to flux redistribution after the perturbation by the control rods. However, as soon as the higher spatial eigenfunctions die away and the asymptotic flux rise is achieved, they should all measure the same reactivity. Unfortunately this cannot be verified, since only one fission chamber was available for the measurements. The authors mention that this could be verified by the time-dependent Monte Carlo calculation, but this would be very demanding in terms of the computational effort.

The authors report very small biases in their calculated reactivities using MCNP and the ENDF/B-VII.1 data library. However, the reported bias in the ICSBEP Handbook for a similar reactor "IEU-COMP-THERM-003" is bigger. Also, the estimated uncertainty due to the benchmark specifications and the nuclear data is fairly large, indicating that the uncertainties in the calculations are likely to be significant. The largest discrepancies between measured and calculated control rod worths are expected for configurations where the control rods lie close to the radial direction from the core centre to the detector.

Although some effect of the time-dependent detector response after the initial transient following the rod pull is possible, in my opinion the most likely source of the discrepancies between measurements and calculations are computational uncertainties due to nuclear data. In the ICSBEP Handbook there are several benchmark cases containing zirconium hydride and they show rather large discrepancies between the calculations and the reference benchmark values.

Overall, the paper is clearly written and highlights the problem of the interpretation of control rod worth measurements. The paper is worth publishing as it is, but perhaps the authors would consider adding a stronger statement about the possible impact on the discrepancies due to nuclear data. If the flux traces from the measurements are available, a log-log plot would be useful to prove the linearity.

Specific comment:

It is not obvious if orientation of figure 2 implies north at the top. Perhaps some mark could be placed on the figure to mark the position of the actual detector.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is well written, the problem and the physical origin is clearly explained. Unfortunatly no solution is proposed to the detected problem, that will be probably the focus of following work. The time-dependent problem is mentioned as perspective, but it is not explained how it may help. Some suggestions are provided to improve the quality and clarity of the work and its presentation. 

Abstract, line 13: "chamber and shifts" -> "and" to be removed

Figure 1 is not readable : please increase the text font and quality of the picture

Equation 1: please define the variable present in this equation. ALso please precise where those values come from, for instance references for nuclear data, or if it is a value that was calculated, or experimentally measured.

page 4, line 132: "uses Evaluated Nuclear Data File 7 (ENDF/B-VII.1)" -> replace by "uses ENDF/B-VII.1 Nuclear Data library"

line 148: the author mention "each critical control rod configuration", can the authors specify if those configurations were determined to be critical by experiment or by simulation ?

line 179: I was confused reading lines 179-184. The authors mention a "little uncertainty" of the reactivity measurements, while the conclusion of the paper is that the calibration was not valid meaning that calibration uncertainty was apprently underestimated. So, it is disturbing to read a mention of a "little experimental uncertainty", please reformulate and be more specific of which component of the uncertainty you refer to, and which you did not taken into account.

line 245-249:  I think I understand the physics behind, but I'm not sure the link between the ideas is clearly shown here. 

line 385: "1.15and" -> "1.15 and"

line 407-411: the authors refers only to the time term in the inhour equation, why not the power ?

line 407: can the authors please precise what they mean by "time dependent method", adding some reference or phenomenon  they want to capture with this method. It is not clear. 

lien 418: method This" -> "method. This" 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Applying a time-dependent Monte Carlo analysis might show some differences in the results, but to demonstrate the magnitude of this effect compared to the uncertainties due to nuclear data would be a subject for another paper.

Overall, it is good work worthy of publishing.

Author Response

Thank you for the kind feedback. We agree, and this is work that is in progress by one of the authors. 

Reviewer 3 Report

Congratulations for this work. Your corrections answers the majority of my comments.

Only a minor comment: I think you do not cite the reference [13], please correct. 

Author Response

Thank you for the kind feedback. This has been corrected in the revised manuscript.