use of sensitivity and uncertainty analysis in reactor design verification part ii: flux measurement...

Annals of Nuclear Energy 60 (2013) 448–458

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Annals of Nuclear Energy

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Use of sensitivity and uncertainty analysis in reactor designverification Part II: Flux measurement analysis

0306-4549/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.anucene.2013.03.011

⇑ Corresponding author. Tel.: +1 905 823 9060.E-mail address: [email protected] (D. Kastanya).

1 ACR-1000 is a registered trademark of Atomic Energy of Canada Limited, usedunder exclusive license by Candu Energy Inc.

Doddy Kastanya ⇑, Mohamed DahmaniReactor Physics Department, Candu Energy Inc., 2285 Speakman Drive, Mississauga, Ontario, Canada L5K 1B1

a r t i c l e i n f o a b s t r a c t

Article history:Available online 3 April 2013

Keywords:ACR-1000FUGENTSUNAMICANDUDesign verification

As for any new reactor design, the ACR-1000� design has to go through a comprehensive design verifica-tion process. One of the activities for supporting the ACR physics design calculations using the ACR phys-ics code toolset, namely WIMS-AECL/DRAGON/RFSP, is to compare the flux distributions resulting fromthe calculation using this toolset at various power calibration monitor (PCM) detector locations againstthe flux measurement data from the Japanese Advanced Thermal Reactor (ATR) FUGEN. The discussionof this particular design verification exercise will be presented in a two-part paper. The usage of datafrom the FUGEN reactor qualifies this exercise as design verification by alternate analysis. In order to havemeaningful results at the end of the design verification process, the similarity between the ACR-1000 andFUGEN reactors has to be demonstrated. It is accomplished through the sensitivity and uncertainty anal-ysis using the TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation)methodology. The results from the similarity comparison have been presented in Part I of the paper. InPart II, results from flux distribution comparison will be presented. Favourable results from this designverification exercise give a high level of confidence that using the same physics toolset in calculatingthe flux distribution for ACR-1000 reactor will produce results with acceptable fidelity. In addition, theresults will also give an indication of expected margins in the design calculations, not only at the loca-tions of the PCM detectors but also at the derived bundle and channel powers obtained through the fluxmapping calculation.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction the physics design verification of the ACR-1000. For each operating

As for any new reactor design, the ACR-1000�1 has to go througha comprehensive design verification process. One of the activities forsupporting the verification of the ACR physics design calculationsusing the ACR physics code toolset (WIMS-AECL (Irish and Douglas,2002)/DRAGON (Roy et al., 1994)/RFSP (Rouben, 2002)) is to com-pare the flux distributions resulting from the calculation using thistoolset against the flux measurement data from the Japanese Ad-vanced Thermal Reactor (ATR) FUGEN (Ohtani et al., 2003). For theverification process reported in this paper, the predictions of fluxdistribution in various power calibration monitor (PCM) locationsthroughout the FUGEN core, as calculated by the ACR physics codetoolset, are compared against the measurement data from FUGEN.These comparisons with the measured data will also allow the veri-fication of the margins used in the design calculations of bundle andchannel powers.

Flux measurement data from the 1st, 2nd, 3rd, 27th, and 28thoperating cycles of FUGEN reactor have been used as a part of

cycle, the flux measurements were performed on a monthly basis.The measurement is performed during normal operation of thecore where the power level is close to the 100% full power condi-tion (i.e., 557 MW thermal). There are 14, 4, 5, 6, and 7 monthly cal-culations in the 1st, 2nd, 3rd, 27th, and 28th operating cycles,respectively. The ACR-1000 physics design toolsets are used to cre-ate the FUGEN reactor models for these monthly calculations. Thecalculated flux distributions at various PCM locations are thencompared against the measurement data. The results from suchcomparisons are reported herein.

Part II of this paper is structured as follows. Section 2 provides abrief description on how the flux measurement is performed at FU-GEN and the methodology used for comparing the flux distribu-tions. Some discussions on the results are presented in Section 3.Section 4 concludes the paper with some closing remarks.

2. Methodology

2.1. Flux distribution measurement at FUGEN

The neutron flux measurement is done using moveable-typepower calibration monitor (PCM). There are 15 strings of PCM in

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Fig. 1. PCM location.

Fig. 2. Axial nodes and PCM detector locations.

D. Kastanya, M. Dahmani / Annals of Nuclear Energy 60 (2013) 448–458 449

the FUGEN core and they are shown in Fig. 1. The strings of PCMare grouped into PCM Channel A, PCM Channel B, and a CommonString. There are eight strings in the PCM Channel A, namely theones at these locations (as indicated in Fig. 1): 10–80, 10–72, 18–72, 10–64, 18–64, 10–56, 18–56, and 26–56. There are eight stringsin the PCM Channel B, namely the ones at these locations: 18–80,26–80, 34–80, 18–72, 26–72, 34–72, 26–64, and 34–64. The detec-tor located at 18–72 is a common string.

During the measurement, the detector reading is obtained at 18axial locations from the bottom to the top of the core. Then, thedata from these 18 locations are converted into the values corre-sponding to the 16 axial locations used in the computational model(i.e., the centres of 16 axial nodes in POLESTAR2 or RFSP – see Fig. 2).In the next step, the detector readings from PCM Channel A at loca-tion 18–72 and PCM Channel B at location 18–72, which is the com-mon location, are used to calculate the relative compensation factor,which is calculated using this formula:

RCF ¼P16

i¼1A18�72iP16

i¼1B18�72i

ð1Þ

where X18�72i represents the detector reading from PCM channel X at

axial location i and X can be either A or B. The RCF is then used toscale or ‘‘compensate’’ the readings from PCM channel B. The com-pensated reading of PCM channel B is determined by multiplyingthe RCF to the original detector reading. Finally, the detector read-ings (both from Channel A and Channel B) are normalized to givean average of 1.0. These normalized detector readings are subse-quently compared to the results from the WIMS-AECL/DRAGON/RFSP calculations3. For the RFSP calculation, the detector readings

2 The POLESTAR code (Ohtani et al., 2003) is a two-energy group, threedimensional, coupled neutronic and thermal-hydraulic code developed for FUGENanalyses. This code employs the coarse-mesh finite difference method as well asanalytic nodal method.

3 It should be noted that WIMS-AECL code is used to generate the burnupdependent, two-group cross sections information, the DRAGON code is used togenerate the incremental cross sections to account for the presence of devices in thecore, and the RFSP code is used to perform the full-core, two-group, threedimensional neutronic calculations.

-

-

are first determined at each detector location (16 locations per PCM– giving a total of 240 detector readings). These detector readings arethen normalized to give an average of 1.0.

An example of calculations performed to derive the normalizeddetector readings is illustrated in Tables 1–6. Tables 1 and 2 showthe ‘‘raw’’ detector readings for Channel A and Channel B, respec-tively. Tables 3 and 4 show the processed detector readings wherethe 18 detector readings have been converted into 16 detectorreadings for the two PCM channels. Table 5 shows the compen-sated detector readings for PCM Channel B. Finally, Table 6 pre-sents the normalized detector readings.

Table 1PCM reading for Channel A.

Axial location PCM location

18–80 26–80 26–72 26–64 34–80 34–72 34–64 18–72

18 26.00 19.90 31.30 27.90 8.50 14.80 12.60 31.2017 41.60 33.10 49.60 43.80 14.40 23.70 20.20 48.7016 54.30 44.50 63.80 57.00 19.30 31.70 27.10 62.4015 63.20 53.00 73.20 66.70 22.50 37.80 32.20 71.0014 68.70 59.60 78.80 73.40 24.70 41.80 35.70 75.8013 72.00 64.30 81.80 77.80 25.80 44.20 37.90 78.3012 73.30 66.70 82.90 79.60 26.30 45.10 39.10 79.1011 71.90 66.00 81.00 78.00 25.10 43.70 38.00 77.3010 60.00 54.60 67.70 65.80 21.40 36.70 31.30 64.509 72.80 66.80 81.30 79.20 25.00 44.20 37.80 77.608 76.80 70.80 85.50 83.90 26.40 46.40 40.20 81.107 78.20 72.00 86.60 85.20 26.40 46.50 40.40 81.806 78.10 71.50 85.90 84.80 25.90 45.60 39.60 81.005 76.10 69.10 83.20 82.60 24.70 43.60 37.80 78.504 70.80 64.10 77.50 77.10 22.70 40.20 34.60 73.003 61.50 55.40 67.50 66.90 19.50 34.50 29.60 63.502 46.50 41.20 50.90 50.80 14.90 25.70 22.00 48.101 26.40 22.70 28.30 28.80 8.90 14.70 13.00 27.90

Table 2PCM reading for Channel B.


10–80 10–72 10–64 10–56 18–72 18–64 18–56 26–56

18 12.70 24.50 18.40 8.50 29.30 30.30 14.00 11.4017 21.90 41.70 31.90 14.40 49.10 51.70 23.90 19.8016 29.50 55.20 42.90 19.30 63.50 66.40 32.50 26.5015 35.80 63.80 51.20 22.60 71.70 75.00 39.20 31.2014 41.30 69.30 57.80 24.70 76.20 80.40 43.70 34.1013 45.80 72.60 62.30 25.80 78.60 83.40 46.40 35.9012 48.40 74.00 64.50 26.30 79.20 84.40 47.50 36.7011 48.10 72.60 63.10 25.10 76.80 81.70 46.00 35.7010 39.50 61.10 53.50 21.30 65.60 69.60 38.90 29.509 48.20 73.20 64.50 25.10 77.50 83.80 46.70 35.608 51.10 77.20 67.90 26.60 81.10 87.50 49.50 37.607 51.30 78.30 68.60 26.40 81.80 88.70 50.00 37.806 50.30 77.60 67.90 25.80 80.90 88.40 49.10 37.205 47.90 75.00 65.30 24.60 78.50 86.00 46.90 35.504 43.90 69.50 60.20 22.50 73.20 80.60 42.90 32.403 37.60 60.30 51.40 19.40 63.80 70.70 36.40 27.702 28.10 44.90 38.20 14.70 48.00 53.50 26.90 20.701 15.80 25.70 22.10 8.80 27.60 29.90 15.50 12.20

450 D. Kastanya, M. Dahmani / Annals of Nuclear Energy 60 (2013) 448–458

2.2. Challenges in modelling the FUGEN reactor

The FUGEN reactor is a boiling water reactor loaded with a sig-nificant number of MOX fuel assemblies. There are challenges re-lated to this fact such as:

a. Higher concentration of 242Pu in the fuel.b. Significant axial variation of neutron energy spectrum due to

coolant density changes within the fuel channel.c. Compositions of the MOX assemblies.d. Tracing of 241Am (which is a strong neutron absorber) due to

the decay of 241Pu during the down times between cycles.

Each of these added modelling complexities is addressed byapplying some appropriate assumptions and approximations insetting up the WIMS-AECL, DRAGON, and RFSP models.

2.3. RFSP model for flux measurement

2.3.1. �SIMULATE module methodologyThe �SIMULATE runs in RFSP are performed using two-group

cross sections. The core conditions (i.e., power level, fuel tempera-

tures, coolant density, coolant temperature, and control rod posi-tions) are input into the RFSP model. The positions of the controlrods involved in the monthly calculations evaluated here areshown in Fig. 3. Note that most of the time, except for the first 8monthly calculations for Cycle 1, only control rod bank C and reg-ulating rod bank E are present in the core during the five cycles ofinterest. In the first 8 monthly calculations, control rod bank L isalso inserted. The control rod positions (in terms of % withdrawn)for each monthly calculation of the first three cycles of operationare presented in Table 7.

2.3.2. �INTREP moduleThe detector readings are determined using the �INTREP mod-

ule of RFSP. The detector names and locations are defined withinthis module. It should be noted that the actual detectors are notmodelled in the RFSP. The resulting detector readings (which rep-resent the thermal flux values at the corresponding detector loca-tion) are reported as an output file. The calculated detectorreadings from the 15 PCM locations are normalized to give an aver-age of 1.0. The numbering of these PCMs is presented in Fig. 4. Theresulting calculated detector readings are subsequently comparedagainst the results from measurement.

Table 3Processed PCM reading for Channel A – 16 axial locations.


18–80 26–80 26–72 26–64 34–80 34–72 34–64 18–72

16 33.80 26.50 40.45 35.85 11.45 19.25 16.40 39.9515 47.95 38.80 56.70 50.40 16.85 27.70 23.65 55.5514 58.75 48.75 68.50 61.85 20.90 34.75 29.65 66.7013 65.95 56.30 76.00 70.05 23.60 39.80 33.95 73.4012 70.35 61.95 80.30 75.60 25.25 43.00 36.80 77.0511 72.65 65.50 82.35 78.70 26.05 44.65 38.50 78.7010 72.60 66.35 81.95 78.80 25.70 44.40 38.55 78.209 66.17 60.50 74.42 72.20 23.22 40.32 34.60 70.978 74.80 68.80 83.40 81.55 25.70 45.30 39.00 79.357 77.50 71.40 86.05 84.55 26.40 46.45 40.30 81.456 78.15 71.75 86.25 85.00 26.15 46.05 40.00 81.405 77.10 70.30 84.55 83.70 25.30 44.60 38.70 79.754 73.45 66.60 80.35 79.85 23.70 41.90 36.20 75.753 66.15 59.75 72.50 72.00 21.10 37.35 32.10 68.252 54.00 48.30 59.20 58.85 17.20 30.10 25.80 55.801 36.45 31.95 39.60 39.80 11.90 20.20 17.50 38.00

Table 4Processed PCM reading for Channel B – 16 axial locations.


10–80 10–72 10–64 10–56 18–72 18–64 18–56 26–56

16 17.30 33.10 25.15 11.45 39.20 41.00 18.95 15.6015 25.70 48.45 37.40 16.85 56.30 59.05 28.20 23.1514 32.65 59.50 47.05 20.95 67.60 70.70 35.85 28.8513 38.55 66.55 54.50 23.65 73.95 77.70 41.45 32.6512 43.55 70.95 60.05 25.25 77.40 81.90 45.05 35.0011 47.10 73.30 63.40 26.05 78.90 83.90 46.95 36.3010 48.25 73.30 63.80 25.70 78.00 83.05 46.75 36.209 43.82 67.00 58.65 23.20 71.38 76.17 42.62 32.578 49.65 75.20 66.20 25.85 79.30 85.65 48.10 36.607 51.20 77.75 68.25 26.50 81.45 88.10 49.75 37.706 50.80 77.95 68.25 26.10 81.35 88.55 49.55 37.505 49.10 76.30 66.60 25.20 79.70 87.20 48.00 36.354 45.90 72.25 62.75 23.55 75.85 83.30 44.90 33.953 40.75 64.90 55.80 20.95 68.50 75.65 39.65 30.052 32.85 52.60 44.80 17.05 55.90 62.10 31.65 24.201 21.95 35.30 30.15 11.75 37.80 41.70 21.20 16.45

Table 5Compensated PCM reading for Channel B.


10–80 10–72 10–64 10–56 18–72 18–64 18–56 26–56

16 17.26 33.03 25.10 11.43 Use PCM Channel A detector reading 40.91 18.91 15.5715 25.65 48.35 37.32 16.81 58.93 28.14 23.1014 32.58 59.38 46.95 20.91 70.55 35.78 28.7913 38.47 66.41 54.39 23.60 77.54 41.36 32.5812 43.46 70.80 59.92 25.20 81.73 44.96 34.9311 47.00 73.15 63.27 26.00 83.72 46.85 36.2210 48.15 73.15 63.67 25.65 82.88 46.65 36.129 43.73 66.86 58.53 23.15 76.02 42.54 32.518 49.55 75.04 66.06 25.80 85.47 48.00 36.527 51.09 77.59 68.11 26.44 87.92 49.65 37.626 50.69 77.79 68.11 26.05 88.37 49.45 37.425 49.00 76.14 66.46 25.15 87.02 47.90 36.274 45.80 72.10 62.62 23.50 83.13 44.81 33.883 40.66 64.76 55.68 20.91 75.49 39.57 29.992 32.78 52.49 44.71 17.01 61.97 31.58 24.151 21.90 35.23 30.09 11.73 41.61 21.16 16.42


3. Results and discussions

There are 36 monthly calculations performed using the RFSPcode for the five cycles of interest. The results of these calculationsare compared against the measured data from FUGEN reactor. An

example of a summary of comparisons between these data is pre-sented in Fig. 5. The x-axis represents the PCM numbering and they-axis represents the average relative difference (expressed in%)between RFSP results and either POLESTAR (a code used in Japanfor FUGEN analysis) or measurement. The averaging process is

Table 6Normalized detector readings.


18–72 18–64 10–72 18–56 26–72 26–64 26–80 34–64

16 0.80 0.82 0.66 0.38 0.81 0.72 0.53 0.3315 1.11 1.18 0.97 0.56 1.14 1.01 0.78 0.4714 1.34 1.41 1.19 0.72 1.37 1.24 0.98 0.5913 1.47 1.55 1.33 0.83 1.52 1.40 1.13 0.6812 1.54 1.64 1.42 0.90 1.61 1.52 1.24 0.7411 1.58 1.68 1.47 0.94 1.65 1.58 1.31 0.7710 1.57 1.66 1.47 0.94 1.64 1.58 1.33 0.779 1.42 1.52 1.34 0.85 1.49 1.45 1.21 0.698 1.59 1.71 1.50 0.96 1.67 1.63 1.38 0.787 1.63 1.76 1.56 1.00 1.73 1.70 1.43 0.816 1.63 1.77 1.56 0.99 1.73 1.70 1.44 0.805 1.60 1.74 1.53 0.96 1.70 1.68 1.41 0.784 1.52 1.67 1.45 0.90 1.61 1.60 1.34 0.733 1.37 1.51 1.30 0.79 1.45 1.44 1.20 0.642 1.12 1.24 1.05 0.63 1.19 1.18 0.97 0.521 0.76 0.83 0.71 0.42 0.79 0.80 0.64 0.35


18–80 10–64 10–80 10–56 34–72 26–56 34–80

16 0.68 0.50 0.35 0.23 0.39 0.31 0.2315 0.96 0.75 0.51 0.34 0.56 0.46 0.3414 1.18 0.94 0.65 0.42 0.70 0.58 0.4213 1.32 1.09 0.77 0.47 0.80 0.65 0.4712 1.41 1.20 0.87 0.51 0.86 0.70 0.5111 1.46 1.27 0.94 0.52 0.90 0.73 0.5210 1.46 1.28 0.97 0.51 0.89 0.72 0.529 1.33 1.17 0.88 0.46 0.81 0.65 0.478 1.50 1.32 0.99 0.52 0.91 0.73 0.527 1.55 1.37 1.02 0.53 0.93 0.75 0.536 1.57 1.37 1.02 0.52 0.92 0.75 0.525 1.55 1.33 0.98 0.50 0.89 0.73 0.514 1.47 1.26 0.92 0.47 0.84 0.68 0.483 1.33 1.12 0.82 0.42 0.75 0.60 0.422 1.08 0.90 0.66 0.34 0.60 0.48 0.341 0.73 0.60 0.44 0.24 0.40 0.33 0.24

Fig. 3. Locations of control rod banks C, E, and L.


done per PCM location (i.e., over 16 detector locations). The blue-diamonds are used to show the difference between the RFSP and

POLESTAR (PS) results and the red-squares are used to show thedifferences between the RFSP results and measured data. The cor-

Table 7Control rod positions for monthly flux measurements for Cycle 1 through Cycle 3.

Cycle Monthly calculation Control Rod Position (% withdrawn)

L 1E 2E 3E 4E 1C 2C 3C 4C

1 1 15.0 20.0 20.0 20.0 20.0 73.3 73.5 73.0 73.32 15.0 20.0 20.0 20.0 20.0 72.8 73.1 71.7 73.63 15.0 25.0 25.0 24.9 25.1 64.5 64.2 64.3 65.14 15.0 25.0 25.0 25.0 25.0 74.9 75.7 74.9 75.65 14.9 24.9 25.0 25.0 25.0 76.3 76.5 75.8 76.86 15.0 27.1 24.6 25.8 27.1 73.0 65.8 67.5 74.87 15.2 26.6 24.6 24.3 24.1 74.9 75.0 74.9 75.58 15.2 25.0 25.0 25.1 25.0 72.8 73.0 72.8 73.49 100.0 69.9 70.0 70.0 70.0 70.5 70.3 70.9 71.010 100.0 67.9 66.0 65.6 65.6 75.3 75.8 74.7 76.011 100.0 69.4 68.9 66.3 67.9 69.8 70.3 68.8 70.012 100.0 65.0 65.0 65.0 65.0 74.9 75.3 74.5 74.813 100.0 65.0 65.0 65.0 65.0 74.6 74.6 74.4 74.614 100.0 65.0 65.0 65.0 65.0 74.6 74.6 74.4 74.6

2 1 100.0 70.0 69.9 70.1 70.1 66.9 67.1 67.3 67.62 100.0 70.1 69.8 70.1 70.1 72.8 73.0 73.2 73.93 100.0 70.1 69.8 70.1 69.6 69.1 70.8 69.5 71.14 100.0 70.1 69.8 70.1 69.6 69.1 70.8 69.5 71.1

3 1 100.0 65.0 65.0 65.0 65.0 71.4 71.7 71.1 71.52 100.0 66.4 66.2 63.3 66.6 70.0 70.1 71.0 71.53 100.0 64.6 65.5 64.5 63.3 67.9 68.5 67.8 69.34 100.0 65.5 68.2 62.9 66.8 68.2 68.9 67.9 69.65 100.0 66.2 68.1 63.7 66.6 68.0 67.6 67.7 69.4

Fig. 4. Power calibration monitor (PCM) numbering.


responding ‘‘error bars’’ represent the spread of relative differencesat each PCM location. It should be noted that the relative differenceis defined as:

D ¼ RFSP� ðPS or MeasuredÞPS or Measured

� 100% ð2Þ

The results presented in Fig. 5 (which are taken from one of the36 monthly calculations) are representative of the results observedin all 36 monthly calculations. The largest average relative differ-ences are observed at PCM#12 and PCM#15. These PCMs are lo-cated at the fuel-reflector interface (as indicated in the smallermaps). The absolute magnitude of the detector readings at loca-tions near the reflector region is relatively smaller than toward

the centre of the core. This artificially boosts the relative differenceat this location. Within each PCM, a similar observation can also bemade. In this figure, the axial relative difference for PCM#6 isshown in the smaller sub-plot. In this sub-plot, it can be observedthat the relative difference is higher toward the reflector regions aswell.

The comparison can also be presented in a slightly differentmanner. Instead of using PCM number, the relative difference canbe plotted against the distance between the location of a particularPCM and the centre of the core. An example of this approach is pre-sented in Fig. 6. In this figure, the x-axis is the distance from theradial centre of the core (in terms of lattice pitch (LP) where 1 LPis 24 cm) and the y-axis is the absolute of the relative difference.

Fig. 5. Summary of flux distribution comparison.

Fig. 6. Summary of flux distribution comparison – alternate approach.


From this figure, it can be seen that the average relative error in-creases as the location of the PCM moves further away from thecentre of the core. Again, similar trends are observed throughoutthe 36 monthly calculations.

The results from these comparisons are succinctly summarizedin Figs. 7–11 for the five cycles of interest. In each of these figures,

the x-axis represents the distance between the location of the PCMassembly to the radial centre of the core (expressed in the unit ofLP) and the y-axis represents the average relative difference(in%). For these figures, each square dot represents the averageover monthly calculations for a particular PCM location (I). Mathe-matically it can be written as:

Fig. 7. Summary of relative differences for Cycle 1.



DPCMI ¼PM

m¼1DPCMmI

Mð3Þ

where DPCMMI is calculated as follows:

DPCMMI ¼

P16n¼1;n2I

/RFSPn �/PS

n

/PSn� 100%

n o16

ð4Þ

The corresponding ‘‘error bars’’ coming out from each dot repre-sent the spread of relative differences at each PCM location for all

monthly calculations perform during this particular cycle. Lastly,the cycle-dependent overall root-mean-squared or RMS reportedin the figures can be calculated as follows:

RMS ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP15i¼1ðDPCMIÞ2

15

sð5Þ

Fig. 7 shows that the average relative difference for each PCMlocation based on 14 monthly calculations performed in Cycle 1




of FUGEN operation ranges from �4.23% to +5.61%, with an overallRMS of 2.77% (as calculation using Eq. (5)). Fig. 8 shows that theaverage relative difference for each PCM location based on the fourmonthly calculations performed in Cycle 2 of FUGEN operationranges from �2.33% to +3.27%, with an overall RMS of 1.77%.Fig. 9 shows that the average relative difference for each PCM loca-tion based on the five monthly calculations performed in Cycle 3ranges from �3.97% to +4.97%, with an overall RMS of 2.62%.Figs. 10 and 11 show that the overall RMS values for Cycle 27and Cycle 28 are 3.67% and 3.54%, respectively. As mentioned be-fore, these figures also show that the differences are higher towardthe periphery of the core. Since the difference is presented as a

relative quantity, the fact that the absolute flux (or detector read-ing) in the periphery is lower than the values toward the centre ofthe core will artificially increase the relative difference for thedetectors located toward the edge of the core.

From these results, one can see that the overall RMS values forthe first three cycles of FUGEN are smaller than the ones for Cycles27 and 28. This behaviour can be related to the approximationintroduced, at the lattice level, when modelling multiple cycles.In Cycles 27 and 28, the fuel assemblies loaded into these cyclescome from previous seven cycles while for the first three cyclesthe fuel assemblies come from at most two previous cycles. Theapproximation used to account for the down times between


Fig. 12. Summary of differences for all PCM locations.


consecutive cycles apparently has a bigger impact as more andmore cycles are involved.

Finally, from these results, one can also derive an expected mar-gin for flux distribution calculations using the ACR-1000 physics

design. Fig. 12 summarizes the average relative difference for allPCM locations and for all monthly calculations. The presentationof the sub-plots is related to the location of the PCM in the core,as illustrated in Fig. 13 (along with the location of control rods

Table 8Summary of Expected Margin in Flux Measurement Calculations.

PCM involved Average(%)

Standard deviation(r) (%)

All +0.16 3.25All, except PCM#12 and PCM#15 �0.68 2.42Centre core (PCM# 1, 2, 3, 5, 6, 7, 9, 10,

and 11)�1.42 2.20

Fig. 13. PCM and control rod locations.


which are marked by red4, yellow, and green circles). In each sub-plot, the x-axis represents the monthly calculation and the y-axisrepresents the relative difference (in%). The five different regionsin each sub-plot marked by different colours indicate the cycle ofinterests (i.e., Cycles 1, 2, 3, 27, and 28). The same scale of y-axis isused for all 15 sub-plots (i.e., from �10.0% to +10.0%) so that the var-iation in the relative differences can be easily compared for all PCMlocations. Table 8 succinctly summarizes the variations in the rela-tive differences from the data depicted in Fig. 12. When all PCM loca-tions are considered, the average relative difference is +0.16% with astandard deviation of 3.25%. When PCM#12 and PCM#15 which arelocated on the fuel-reflector boundary are excluded, the average rel-ative difference is �0.68% with a standard deviation of 2.42%. Lastly,if only PCMs located toward the centre of the core are considered,the average relative difference and the corresponding standard devi-ation are �1.42% and 2.20%, respectively. From these results, it canbe concluded that on average the flux distribution can be predictedwithin 1.50% with a standard deviation less than 2.50%. This is a rea-sonable estimate of the expected margin in the design calculationsusing the ACR-1000 physics design toolset.

4 For interpretation of colour in Fig. 13, the reader is referred to the web version ofthis article.

4. Closing remarks

As a part of physics design verification of the ACR-1000, calcu-lations of the flux distribution for five cycles of the FUGEN reactorusing the ACR physics toolsets have been performed. The overallagreement between the results obtained using ACR physics toolsetand FUGEN data (as calculated by the POLESTAR code), in terms ofthe cycle-dependent overall RMS of the differences, are 2.77%,1.77%, 2.62%, 3.67%, and 3.54% for Cycles 1, 2, 3, 27, and 28, respec-tively. These results indicate that the physics behaviour of the FU-GEN reactor, particularly related to the flux distribution, has beenpredicted quite accurately. The calculations also indicate that theexpected margin in the flux distribution calculations using thesetoolsets is within 1.50% with a standard deviation less than2.50%. Based on these results, it may be expected that the ACRphysics toolsets should be able to adequately predict the behaviourof the flux distributions of the ACR-1000.

References

Irish, D., Douglas, S.R., 2002. Validation of WIMS-IST. In: Proceeding of 23rd AnnualConference of the Canadian Nuclear Society, Toronto, Ontario, Canada, June 2–5.2002.

Ohtani, T., Iijima, T., Shiratori, Y., 2003. Analysis of mixed oxide fuel loaded cores inthe heavy water reactor FUGEN. Journal of Nuclear Science and Technology 40(11), 959–969.

Rouben, B., 2002. RFSP-IST, the Industry Standard Tool Computer Program forCANDU Reactor Core Design and Analysis. In: Proceeding of 13th Pacific BasinNuclear Conference, Shenzhen, China, October 2002.

Roy, R., Marleau, G., Tajmouati, J., Rozon, D., 1994. Modeling of CANDU reactivitycontrol devices with the lattice code DRAGON. Annals of Nuclear Energy 21,115–132.

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