wims-aecl course notes57 10. validation of wims-ist for standard candu wims-ist is defined to be...

WIMS-AECL Course Notes

J.D. Irish, D.V. Altiparmakov, R.S. Davis

Reactor and Radiation Physics Branch Atomic Energy of Canada Limited

Chalk River Laboratories Chalk River, Ontario K0J 1J0

Canada

Presented at Sheridan Park 2004 April 19

PROTECTED – Proprietary ii

Table of contents SECTION PAGE

PROTECTED – Proprietary iii

TABLES

FIGURES

PROTECTED – Proprietary iv

FLOWCHARTS

BLOCK DIAGRAMS

PROTECTED – Proprietary 1

1. INTRODUCTION


2. CHRONICLE OF A WIMS-AECL CALCULATION


3. NEUTRON TRANSPORT MATHEMATICS IN WIMS-AECL


3.1 Steady state criticality equation


3.1.1 Assumptions in the derivation of the transport equation

3.1.2 Simplification of the neutron multiplication operator


3.1.3 Isotropic neutron scattering

3.1.4 Boundary conditions


3.2 Multigroup approximation


3.3 Within-group transport equation

3.4 Integral transport equation


3.5 Collision probability method


3.6 Reciprocity and conservation relations


3.7 Albedo boundary condition


4 MULTIGROUP CROSS SECTIONS

4.1 Multigroup data libraries

4.2 Multigroup constants


4.3 Resonance treatment in WIMS-AECL release 2-5d


4.3.1 Homogeneous geometry


4.3.2 Heterogeneous geometry


4.3.3 Winfrith treatment of heterogeneity


4.3.4 AECL treatment of heterogeneity


4.4 Resonance treatment in WIMS-AECL release 2-6a


4.5 Resonance treatment in WIMS-AECL version 3.0


5 ‘SPECTROX’ FINE FLUX SPECTRA

5.1 Collision probability equations


5.2 ‘Spectrox’ flux approximation in the moderator region


5.3 Derivation of collision-probability-like equations


5.4 Calculation of collision probabilities


5.5 Computation of fine flux spectra


6 MAIN TRANSPORT SOLUTION

6.1 Calculation of matrix coefficients


6.2 Annular geometry


6.3 Ray tracing


6.4 Solution of multigroup equations


7 LEAKAGE AND BUCKLING CALCULATIONS

7.1 Diffusion coefficients


7.2 Buckling calculations


8 BURNUP CALCULATIONS


8.1 Construction of burnup equations


8.2 Solution of burnup equations


9 OUTPUT

9.1 Printed output file

9.2 Tape16 interface file

9.3 TAPE50 restart file

9.4 TAPE7 material composition file

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10. VALIDATION OF WIMS-IST FOR STANDARD CANDU

WIMS-IST is defined to be WIMS-AECL Release 2-5d, used with the ENDF/B-VI-based NDAS library Version 1a and the guidelines for preparing input decks for standard CANDU lattices. WIMS-IST was validated for standard CANDU applications using the following five-step phenomena-based methodology:

a. Review of postulated accidents in the design basis and their associated physical phenomena,

b. Assembly of validation matrices that relate postulated accidents to physical phenomena and phenomena to data sets,

c. Preparation of a validation plan, d. Performance of the validation exercises, and e. Preparation of validation reports that document the results of the validation exercises.

The validation matrices identify 16 reactor physics phenomena of interest. WIMS-IST calculates 11 of these phenomena. Thus, WIMS-IST has been validated against experimental measurements for the following 11 phenomena:

a. coolant-density-change induced reactivity, b. coolant-temperature-change induced reactivity, c. moderator-density-change induced reactivity, d. moderator-temperature-change induced reactivity, e. moderator-poison-concentration-change induced reactivity, f. moderator-purity-change induced reactivity, g. fuel-temperature-change induced reactivity, h. fuel-isotopic-composition change, i. flux and power distribution, j. lattice-geometry-distortion reactivity effects, and k. coolant-purity-change induced reactivity.

The validation was accomplished by comparing the results of WIMS-IST calculations with experimental data.

10.1 Experimental data and method of comparison Nine of the eleven phenomena involve reactivity changes. Data to validate WIMS-IST for these phenomena came from critical experiments performed in ZED-2, a zero-power reactor located at AECL Chalk River Laboratories. The appropriate calculated quantity to compare with experimental measurement is the reactivity coefficient associated with the phenomenon.

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The reactivity coefficient can be quoted in either reactivity units or buckling units. It can be expressed as a change in reactivity or critical buckling associated with a given change of the relevant parameter, divided by the change in the relevant parameter. For instance, the fuel-temperature reactivity coefficient is the rate of change of reactivity as the fuel temperature is varied. The measured reactivity coefficient must be obtained from a series of tests, each performed at a specific value of the parameter of interest. In each test the critical buckling is measured in a critical reactor. Here, the series of tests used to define a single reactivity coefficient for a given fuel type is referred to as an experiment. There are two ways in which the results of the calculations can be compared with the experimental data. The two methods are actually equivalent, but provide a different outlook on the comparison. For the first method, the measured critical bucklings are input to WIMS-IST for each test, and the WIMS-IST-predicted k-eff is obtained for each test. If both the code and the experiment are able to simulate the reactivity coefficient exactly, then the resulting calculated k-eff values will be constant as a function of the parameter of interest. Any deviation from a constant value is a measure of the bias and uncertainty between calculation and measurement. For the second method, the experimental reactivity coefficient in buckling units can be determined from the measured critical bucklings. Then, WIMS-IST is used to calculate the critical buckling for each test. This calculation does not involve the use of any information from the experimental measurement. The calculated reactivity coefficient in buckling units can then be determined. The difference between the two determinations is the bias between calculation and measurement. The individual uncertainties in the individual buckling measurements can be propagated through the determination of the measured reactivity coefficient, in order to provide an estimate of the uncertainty. Although the two methods are equivalent, both of the above methods were generally used to determine the bias and uncertainty to be associated with calculations for each phenomenon with WIMS-IST; however, here, usually only one of the methods is discussed for each phenomenon. Even though only one method is discussed per phenomenon, the quoted biases and uncertainties often come from consideration of the results of both methods. Values for critical buckling had been determined previously in ZED-2 experiments using two different methods. The most direct method is by flux mapping, where the flux shape is measured (and fit to cosine and Bessel functions to extract axial and radial bucklings) either in a full core or in a large region of a core containing the test fuel. The other method is the substitution method. A substitution experiment involves a reference lattice, usually a regular, hexagonal array of vertical channels with a pitch of 31 cm. Usually, the reference lattice consists of 55 driver rods, each containing a string of five 28-element natural

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UO2 fuel bundles. Sometimes, booster channels of another fuel type (depending on the particular experiment) surround these driver channels and help ensure criticality. A substitution experiment replaces the driver fuel bundles in 1, 3, 5, and then 7 of the centrally located channels with a given set of test fuel bundles. Criticality is achieved by varying the moderator height. The basic premise of this method is that the critical buckling for a full core of the test fuel can be obtained by extrapolating the results from the 1-, 3-, 5-, and 7-rod substitutions. The substitution method is less direct than the flux mapping method, and depends on an elaborate analysis of the experimental measurements; however, it can provide critical buckling values when there is insufficient test fuel to provide bucklings from flux mapping. Two of the phenomena do not involve reactivity coefficients. For the fuel-isotopic-composition change phenomenon, the appropriate calculated quantities to compare with experimental measurement are the concentrations of various isotopes in the fuel after a given period of irradiation in a power reactor and are determined by isotopic analysis during post-irradiation examinations. For the flux and power distribution phenomenon, the appropriate calculated quantities to compare with experimental measurement are the fluxes or reaction rates in various foil materials located in the fuel elements during experiments performed in ZED-2.

10.2 WIMS-IST input model The accuracy of the results generated by WIMS-IST is dependent upon the input description used and the options selected in the code. If a very detailed input description is used, then the results are more accurate. However, the greater the detail in the input model and the more sophisticated the options chosen, the greater are the resources (mainly computer time) needed to run WIMS-IST. Thus, for normal design and fuel management calculations a standard input model is chosen, which is a compromise between accuracy and required resources. The present validation is performed with this standard input model. This model calls for a combination of one- and two-dimensional collision probability methods to solve the neutron transport equation and employs 33 energy groups, shielded Zr cross-sections, end regions, and a reasonable spatial mesh.

10.3 Results of comparison Coolant-Density-Change Induced Reactivity This phenomenon is probably the most important phenomenon in the reactor physics validation matrix, as far as safety analysis is concerned. In a standard CANDU, loss of coolant will cause a significant positive reactivity insertion. Fairly small inaccuracies in the void reactivity coefficient can cause significant uncertainties in the magnitude of the power pulse following a loss-of-coolant accident. This phenomenon was studied by comparing the difference in k-eff values calculated by WIMS-IST using bucklings measured for a voided and a cooled critical core. If the experiment had no error and the calculation was able to model the phenomenon exactly, then there would be no

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difference between the two k-effectives. Thus, any difference is a measure of the bias and uncertainty in the void reactivity coefficient. Because of the importance of the void effect in reactor safety, the effect has been studied extensively in ZED-2 over many years. Only a sampling of the available data will be discussed here, even though a larger set of experimental data was used in the actual validation. Table 1 shows the void reactivity discrepancy (k-effvoided - k-effcooled) for the most recent fuel designs. In the table, “FNU” refers to fresh natural uranium fuel, and “MOX” refers to mixed-oxide fuel. The MOX fuel was made to simulate mid-burnup CANDU fuel. The “AECL calibration” and “OPG method” refer to different methods of determining the critical buckling from substitution measurements. The AECL calibration applies a correction, which calibrates the critical bucklings measured by substitution to those measured by flux mapping. The OPG method uses a statistical model to consider all of the flux mapping and substitution data to obtain a maximum likelihood estimate of the critical bucklings and their uncertainties. For the fuel types presented in Table 1, WIMS-IST overpredicts the void effect. For 37-element FNU fuel this overestimate amounts to 1.9 mk, and for 37-element MOX fuel the overestimate amounts to 1.3 to 1.7 mk, depending on whether the OPG method or AECL calibration is used. The uncertainty for MOX fuel determined by the OPG method is ±0.78 mk. This error, rounded up to ±0.8 mk, was taken as a conservative estimate of the uncertainty for the calculated void reactivity for all fuel types.

Table 1. Overestimate of Void Reactivity by WIMS-IST using the Standard Input Model

Fuel 22 °°°°C, 99.75 wt% Heavy Water, 31-cm Hexagonal Pitch

Void Reactivity Discrepancy (mk)

28-element FNU (flux mapped) 0.57 ± 0.4 28-element FNU (AECL calibration) 0.78

28-element FNU (OPG method) 0.73 37-element FNU (AECL calibration) 1.89 ± 0.64

37-element FNU (OPG method) 1.90 ±0.45 37-element MOX (AECL calibration) 1.68 ± 0.75

37-element MOX (OPG method) 1.29 ±0.78 43-element CANFLEX FNU (AECL calibration) 1.83

Coolant-Temperature-Change Induced Reactivity From a neutronics viewpoint, a change in coolant temperature has several effects. An increase in coolant temperature will increase upscattering of neutrons into the adjacent fuel. In general, thermal neutrons of higher than average speeds are less likely to be absorbed by any fuel material, although the situation is subtle because of the existence of thermal neutron resonances in plutonium isotopes. An increase in coolant temperature will be accompanied by a decrease in coolant density, thus reducing the number of neutron scattering targets in the coolant, and thereby enhancing neutron leakage and decreasing parasitic resonance absorption in 238U.

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It is not possible in a measurement to separate the phenomenon of changing coolant temperature from that of changing coolant density. Also, because the fuel is contained within the coolant, the fuel temperature will change with the coolant temperature. In this validation, the coolant temperature coefficient encompasses three effects: changing coolant temperature; the associated change in coolant density; and the accompanying change in fuel temperature. Experiments have been performed in the ZED-2 reactor, in which one to seven of the central channels were heated from 300 K to 600 K. When coolant water is present, this temperature range corresponds essentially to that for coolant found in CANDU reactors. Since only the central channels can be heated while the remainder of the reactor remains at room temperature, the critical bucklings for the heated channels must be obtained using the substitution method. For the majority of the measurements, the full 1-, 3-, 5-, and 7-rod substitutions were only performed at room temperature. For higher temperatures, only a 7-rod substitution was performed, and the extrapolation to a full core of test fuel at that temperature was based on the extrapolation determined at room temperature. However, for one experiment, involving MOX fuel, the full 1-, 3-, 5-, and 7-rod substitutions were performed at each temperature. This experiment was analysed to extract critical bucklings both by using the room temperature extrapolation at each temperature and also by using the appropriate measured temperature-dependent extrapolation at each temperature. ZED-2 substitution experiments with the following test fuels were performed for the coolant temperature coefficient:

• 37-element FNU fuel bundles • no boosters, room temperature extrapolation at all temperatures.

• 37-element simulated mid-burnup MOX fuel bundles containing dysprosium to mimic fission product absorption

• 19-element boosters, room temperature extrapolation at all temperatures. • 19-element boosters, measured temperature-dependant extrapolation at all

temperatures. • ZEEP rod boosters, room temperature extrapolation at all temperatures.

• 43-element CANFLEX� natural UO2 fuel bundles • no boosters, room temperature extrapolation at all temperatures.

Figure 1 shows the k-eff values obtained with WIMS-IST when the measured critical bucklings are used as input. As expected the lines are almost horizontal. If a straight line is drawn through the points for any specific fuel type measurement, then the slope of the line gives the bias in the coolant-temperature reactivity coefficient, and the uncertainty in the slope is the uncertainty in the coefficient.

� CANFLEX is a registered trademark of AECL and the Korea Atomic Energy Research Institute (KAERI).

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Accuracy of WIMS-AECL Coolant Temperature Coefficient

0.9920.9930.9940.9950.9960.9970.9980.999

1

0 100 200 300

Coolant Temperature ( C )

k-ef

fect

ive

Figure 1. Accuracy of WIMS-IST Coolant-Temperature Reactivity Coefficient

Legend: square=FNU; diamond=CANFLEX; black+gray triangles=MOX(U19); white triangle=MOX(ZEEP) Consideration of all the data lead to an assignment of zero bias to the coolant-temperature reactivity coefficient calculated by WIMS-IST, with an uncertainty of ±4%. Moderator-Density- and Moderator-Temperature-Change Induced Reactivity Although moderator-density-change induced reactivity and moderator-temperature-change induced reactivity were identified as separate phenomena, it is not possible to separate the two phenomena in zero-power reactor experiments, because a change in temperature will lead to a corresponding change in density. A reduced moderator density offers fewer scattering targets to neutrons, and an increased temperature alters the scattering characteristics for neutrons, such as the likelihood of upscattering. The neutron spectrum therefore changes, resulting in a change in the reactivity of the reactor. This phenomenon is commonly called the moderator-temperature reactivity coefficient. Data for the validation came from the following three flux mapping experiments: an experiment with 19-element UO2 fuel performed in the ZEEP reactor covering the temperature range from 20 to 65 C; an experiment with 19-element UO2 fuel performed in the ZED-2 reactor covering the temperature range from 11 to 82 C, and an experiment with 28-element UO2 fuel performed in the ZED-2 reactor covering the temperature range from 20 to 40 C. In all cases the fuel was unirradiated natural uranium. For all cases the reactor was uniformly chilled or heated. Therefore, part of the observed effect is due to the temperature change of the fuel and coolant; this was estimated to be about 25% of the total effect. By comparing calculated and measured buckling, it was determined that WIMS-IST accurately calculates the moderator-temperature reactivity coefficient with an uncertainty of ±2.6%.

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Moderator-Poison-Concentration-Change Induced Reactivity Neutron poison can be dissolved in the moderator of a CANDU reactor to compensate for excess reactivity or to provide emergency shutdown. Either gadolinium or boron may be used. While there are CANDU-specific experiments with boron in the moderator, none have been identified with gadolinium in the moderator. Data from the following three experiments in ZED-2 were used in the validation: a flux mapping experiment performed with 28-element air-cooled bundles; a substitution experiment with 37-element FNU bundles that were both D2O- and air-cooled; and a substitution experiment with 37-element MOX bundles that were both D2O- and air-cooled. These latter bundles were meant to simulate mid-burnup CANDU fuel. The experiments covered a poison concentration range of 0 to 3.5 ppm by weight of natural boron in the moderator. Table 2 shows the relative difference between WIMS-IST calculations and measurement for the moderator-poison buckling coefficients corresponding to the different experiments.

Table 2. Difference between Moderator-Poison (Boron) Buckling Coefficients from WIMS-IST Calculations and ZED-2 Experiments

Experiment Bundle Fuel Type Coolant Relative Difference in Coefficient

28-element air-cooled 28-element Fresh natural

UO2 Air -1.3%

37-element natural UO2 37-element Fresh natural UO2

Air 1.7%

D2O 0.0% 37-element simulated mid-

burnup 37-element Simulated

mid-burnup Air -2.6%

D2O -3.0%

The uncertainty in the measured moderator-poison buckling coefficients ranges from 2 to 4%. The differences between calculation and experimental measurement in the last column of Table 2 are not significant compared to the experimental uncertainty. Thus, WIMS-IST has no bias in its calculation of the poison reactivity coefficient and an uncertainty of ±2%. Moderator-Purity-Change Induced Reactivity The neutron absorption cross-section of hydrogen is orders of magnitude greater than that of deuterium; thus, moderator purity (i.e., the fraction of moderator water that is D2O) has a large impact on reactivity. The validation exercise used data from 19 separate measurements with 28-element UO2 fuel bundles that were arranged on a 31-cm hexagonal pitch. The experiments were performed over the period 1965 to 1999 and covered a range of moderator purity from 99.15 to 99.86 % by weight. These measurements were not made specifically to study the effect of moderator purity.

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They were made as part of the operational requirements for the ZED-2 reactor and as part of the characterization of reference lattices used in substitution measurements. For each of these measurements the coolant purity was the same as the moderator purity, and there were small variations in temperature from measurement to measurement. These effects were taken into account when doing the validation. Figure 2 shows the k-eff values calculated by WIMS-IST when the experimentally measured bucklings were used as input. The line is a “least squares” fit to the data. It can be seen that the line deviates from the horizontal. It was found that the moderator-purity reactivity coefficient was overestimated by 8% with an uncertainty of ±3%.

0.9985

0.9990

0.9995

1.0000

1.0005

1.0010

1.0015

1.0020

1.0025

99.1 99.2 99.3 99.4 99.5 99.6 99.7 99.8 99.9

Purity (w t%)

Cal

cula

ted

k-ef

fect

ive

Figure 2. Calculated k-effective versus Moderator Purity

Since the experiments were performed over 35 years and were not performed specifically to measure the moderator purity coefficient, there is the possibility that minor changes in experimental conditions have gone unnoticed over this period. These changes could introduce a bias into the experimental measurements. Because of this, confidence in the measured coefficient is not sufficiently high to prove that there is a bias in WIMS-IST-calculated moderator purity coefficients. Fuel-Temperature-Change Induced Reactivity The reactivity induced by a fuel temperature change (also known as the fuel temperature coefficient) is the first line of defence for an unexpected power excursion in any nuclear reactor.

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The reason is obvious—increased fission power heats the fuel material first. In most reactors the power coefficient and the fuel temperature coefficient are negative for the whole reactor core. The main physical processes that affect the fuel temperature coefficient include Doppler broadening of resonance absorber nuclides within the fuel. In CANDU reactors this broadening primarily involves the 238U isotope, along with lesser contributions from various plutonium nuclides. The rates of neutron absorption in plutonium nuclides and in the 235U isotope are also affected by neutron upscattering from oxygen in the fuel as the fuel temperature changes. Experiments were performed in the ZED-2 reactor, in which one to seven of the central channels were heated with hot CO2 from 300 K to 600 K. This caused only the fuel to be heated and resulted in a uniform fuel temperature distribution. The experiments suffered from a deficiency, in that an average fuel temperature of 600 K is neither a typical operating temperature nor an accident temperature for CANDU fuel. Centreline temperatures within each fuel element in a power reactor are much higher. There is also a distribution of average fuel temperatures across a bundle with different temperatures in each fuel ring. As a result, the overall validation of the lattice code WIMS-IST for the fuel temperature coefficient occurs in two parts. In the first part, discussed here, calculations made with WIMS-IST are compared with measurements in ZED-2. The second part, known informally as scale-up, uses code-to-code comparisons and other investigations to extend the conclusions on the accuracy of WIMS-IST calculations of fuel temperature coefficient to conditions of interest in operating CANDU reactors. This is not discussed here. Experiments were performed in the ZED-2 reactor, in which one to seven of the central channels have been heated from 300 K to 600 K. Since only the central channels can be heated while the remainder of the reactor remains at room temperature, the critical bucklings for the heated channels must be obtained using the substitution method. As outlined in the section on coolant-temperature-change induced reactivity, some of the critical bucklings were obtained using an extrapolation based on room temperature measurements, while some were based on a temperature-dependent extrapolation. ZED-2 substitution experiments with the following test fuels were performed for the fuel temperature coefficient:

• 37-element FNU fuel bundles • no boosters, room temperature extrapolation at all temperatures.

• 37-element simulated mid-burnup MOX fuel bundles containing dysprosium to mimic fission product absorption

• 19-element boosters, room temperature extrapolation at all temperatures. • 19-element boosters, measured temperature-dependent extrapolation at all

temperatures. • ZEEP rod boosters, room temperature extrapolation at all temperatures.

• 43-element CANFLEX natural UO2 fuel bundles • no boosters, room temperature extrapolation at all temperatures.

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Figure 3 shows the k-eff values obtained when the measured critical bucklings are used as input. As expected the lines are almost horizontal. If a straight line is drawn through the points for any one fuel type measurement, then the slope of the line gives the bias in the fuel-temperature reactivity coefficient and the uncertainty in the slope is the uncertainty in the coefficient.

Accuracy of WIMS-AECL Fuel Temperature Coefficient

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1

0 100 200 300

Fuel Temperature ( C )

k-ef

fect

ive

Figure 3. Accuracy of WIMS-IST Fuel Temperature Coefficient

Caption: square=FNU; diamond=CANFLEX; black+gray triangles=MOX(U19); white triangle=MOX(ZEEP) For the temperature range from 25–300 C of the ZED-2 substitution experiments, it was found that WIMS-IST calculates the fuel temperature coefficient to lie within the 95% confidence interval of the MOX measurements. The FNU and CANFLEX comparisons are slightly better. In percentage terms, WIMS-IST calculates the fuel temperature coefficient over the measured range to within about 10%. WIMS-IST overpredicts the fuel temperature coefficient for unirradiated natural UO2 fuel, but underpredicts the coefficient for simulated mid-burnup fuel. In a reactor core, there would be a range of fuel burnups. Thus, within this temperature range, there would be the potential for a cancellation of some error for the full-core fuel temperature coefficient. Fuel-Isotopic-Composition Change The phenomenon studied here is fuel-isotopic-composition change; however, fuel-isotopic-composition-change induced reactivity was the phenomenon that was listed in the validation

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matrix. This latter phenomenon must be calculated from a full reactor calculation, in which WIMS-IST generated data are used. Thus, it is not possible to validate WIMS-IST by itself for this phenomenon. However, it is possible to validate the WIMS-IST calculation of fuel-isotopic-composition change, which is an important component of this phenomenon. As fuel material is irradiated in a CANDU reactor, it undergoes changes in isotopic composition. The most important of these changes involve the depletion of 235U, the production of Pu isotopes and the production of fission products, some of which have high absorption cross-sections and act as neutron poisons. These changes in isotopic composition affect reactivity. Data for this validation exercise came from isotopic compositions that were measured in three bundles from CANDU power reactors. One bundle was irradiated in NPD, one in Pickering-A, and one in Bruce-A. The 19-element NPD bundle was irradiated for 621 full-power days, followed by 182 days of decay. The Pu/U, 235U/238U and Pu isotopic ratios were measured for each fuel ring of the fuel bundle. The 28-element Pickering-A bundle was irradiated to an outer element burnup of about 9208 MWd/MgU. Measurements of fissile isotope compositions and the activities of a few fission products were made on an outer element of the bundle. The 37-element Bruce-A bundle was irradiated to a burnup of about 7800 MWd/MgU, and was then allowed to cool for 1162 days. Fuel assays were performed on 9 elements of the outer ring, 6 elements of the middle ring, and 3 elements of the inner ring. The results were averaged to give isotopic ratios for the inner, middle and outer rings of the fuel bundle. Table 3 shows the ratio of calculated to measured (C/M) isotopic ratios for fissile isotopes. Before calculating the C/M ratio, each nuclide isotopic ratio was averaged over all of the fuel elements from all the bundles for which that particular isotopic ratio was measured. In general the agreement is very good—within 2%, except for 236U and 241Pu. 236U has little neutronic importance and 241Pu undergoes radioactive decay; therefore, its concentration is much more dependent on the detailed power history and the length of cooling time after the fuel is removed from the reactor. In general there is no bias or only a small bias in the calculated actinide concentrations, and there is an uncertainty of ±2%.

Table 3. Bias and Uncertainty using Element Data (All Bundles)

Atom Ratio Average C/M Standard Deviation C/M

Bias Uncertainty

235U/U 1.005 0.016 0.5% ±2% 236U/U 0.961 0.040 -4% ±4% 238U/U 1.000 0.000 0 0

239Pu/Pu 0.996 0.004 -0.4% ±0.4% 240Pu/Pu 1.006 0.008 0.6% ±0.8% 241Pu/Pu 1.037 0.023 4% ±2%

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242Pu/Pu 1.001 0.024 0.1% ±2% Pu/U 1.017 0.021 2% ±2%

Table 4 shows the C/M ratios for fission-product and transuranic activities for the outer element of the Pickering-A bundle. Except for the ratios for 99Tc and 154Eu, all of the ratios are within one experimental standard deviation from 1. The agreement for the 99Tc and 154Eu ratios is significantly worse. It is not expected that this would have a significant effect on reactivity calculations, since the WIMS-IST library also includes two pseudo-fission products, which account for omitted fission products. The pseudo-fission products are determined by comparing the total absorptions in the fission products specifically represented in WIMS-IST with the total absorptions predicted in all fission products in a computer code that represents all fission products. This procedure would also compensate for inaccuracies in the represented fission products. Table 4. Fission-Product and Transuranic Activities for Outer Element of Pickering-A Bundle

Nuclide Measured (Bq/kgU)

Calculated (Bq/kgU)

Calculated/Measured

237Np 9.99x105 ± 20% 8.60x105 0.86 241Am 1.86x1010 ± 20% 1.86x1010 1.00

99Tc 1.08x108 ± 10% 1.46x108 1.36 129I 2.44x105 † 3.47x105 1.42

134Cs 4.16x109 ± 7% 4.00x109 0.96 154Eu 8.14x109 ± 5% 9.19x109 1.13 155Eu 3.35x109 ± 8% 3.30x109 0.99

† Uncertainty not quantified but expected to be large due to difficulty of collecting gas.

Flux and Power Distribution The calculation of flux and power distributions within a CANDU reactor requires the use of the entire reactor physics code suite, WIMS-IST/DRAGON-IST/RFSP-IST. WIMS-IST has been validated for one of its contributions to this phenomenon—the ability of WIMS-IST to calculate flux and power distributions within a lattice cell, and in particular, the radial flux and power distribution across a CANDU bundle. The validation was carried out by comparing reaction rates measured by activation foils placed within demountable bundles in the ZED-2 reactor, with the reaction rates of these activated foils calculated by WIMS-IST. Calculated and measured foil activities and foil activity ratios were compared. The uncertainty in the calculated flux-power distribution in each fuel element was derived under the assumption that a bundle-average flux-power level is already known.

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The data used in the validation came from eight experiments, in which foil materials, activation wires or activation wafers were irradiated in the elements of different fuel bundle types. The six experiments in which foil materials were used are

��43-element natural UO2 fuel in a CANFLEX bundle measured during a substitution experiment at a 31-cm hexagonal lattice pitch, cooled with heavy water at room temperature and then with the coolant removed.

��37-element natural UO2 fuel bundle measured in a full core at a 28.575-cm-square lattice pitch, cooled with heavy water at room temperature and then with the coolant removed.

��36-element natural UO2 fuel during a substitution experiment at a 31-cm hexagonal lattice pitch, cooled with light water and heavy water at room temperature and at elevated coolant temperatures and then with the coolant removed.

��37-element simulated mid-burnup MOX fuel bundle measured during a substitution experiment at a 31-cm hexagonal lattice pitch, cooled with heavy water at room temperature and at elevated coolant temperatures and then with the coolant removed.

��31-element UO2 and (Pu,U)O2 Savannah River Laboratories fuel measured during experiments at a 23.7-cm hexagonal pitch, cooled with light water and heavy water at room temperature and then with the coolant removed.

��36-element Italian (Pu,U)O2 fuel measured during experiments at 24.5-cm and 31-cm hexagonal pitches, cooled with heavy water at room temperature and an elevated temperature and then with the coolant removed.

The other two experiments were performed in the early 1960s using 28-element fuel. In one of the experiments, copper and manganese wires were inserted in small holes that had been drilled in some of the fuel pellets. In another related experiment on the same 28-element fuel, uranium wafers were inserted. Some of the foil materials used in the experiments were 63Cu, 55Mn, 115In, 176Lu, 197Au, 164Dy, 235U, 238U and 239Pu. In a typical experiment with a 37-element bundle, reactions in specific foil materials were measured in the central pin, in two of the six pins of the inner ring of fuel, in two of the twelve pins of the middle ring, in two of the eighteen pins of the outer ring, and often along the outer surface of the calandria tube. A small correction to compensate for foil self-shielding was applied to the experimental activation data. Measured activities have unknown normalizations; hence, to make a comparison, the calculations were normalized to agree with the measured pin-weighted average over all of the fuel pins of a bundle. The accuracy of WIMS-IST for calculating the effect of the total (primarily thermal) neutron flux and power distribution through a CANDU fuel bundle has been established by comparing calculated foil activities with the foil spatial fine structure, as measured in ZED-2. Though the number of ZED-2 experiments is small, the range of geometry, coolant material, coolant temperature and fuel composition is quite varied. The standard input model for WIMS-IST does remarkably well in calculating the flux-power distribution through the CANDU bundles. Overall, the flux-power depression through a CANDU bundle is calculated by WIMS-IST to an accuracy of about 1%. No systematic bias is detected. Lattice-Geometry-Distortion Reactivity Effects

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Lattice-geometry-distortion effects include pressure tube diametral creep, channel sag and channel elongation caused by irradiation. Of these effects, only a component of the reactivity effect of channel sag can be modelled by WIMS-IST. Channel sag leads to a deviation of the spacing between adjacent channels from that given by the design pitch. This change in spacing between channels is equivalent to variations in lattice pitch. Thus, WIMS-IST was validated for the reactivity effect due to changes in lattice pitch. The data for this validation come from the following two flux mapped experiments performed in ZED-2: an experiment with D2O-cooled 19-element UO2 fuel covering hexagonal lattice pitches from 18 to 36 cm, and an experiment with D2O-cooled 28-element UO2 fuel covering hexagonal lattice pitches from 24 to 40 cm. Measured and calculated reactivity spacing coefficients were compared. For the experiments with 19-element fuel, the mean difference between the calculated and measured reactivity spacing coefficients is 0.379 mk/(cm change in spacing) and the standard deviation about this mean is 0.757 mk/(cm change in spacing). For the experiments with 28-element fuel, the mean difference between the calculated and measured reactivity spacing coefficients is 0.085 mk/(cm change in spacing) and the standard deviation about this mean is 0.661 mk/(cm change in spacing). In both cases the differences are small, and less than the standard deviations, and are therefore not significant. Coolant-Purity-Change Induced Reactivity Coolant purity can be downgraded either by degradation of the coolant during normal operation or by the addition of light water from the emergency core cooling system during an accident. Light water in the coolant increases the absorption of neutrons, and degraded coolant is slightly more effective at slowing down neutrons than pure heavy water. An increase in the amount of light water will also affect the void coefficient. The data used in the validation come from the following two substitution experiments performed in ZED-2: an experiment using 37-element FNU bundles, and an experiment using 37-element MOX bundles, which simulate mid-burnup CANDU fuel. Both experiments were performed with a 31-cm hexagonal lattice pitch and with three different coolant purities ranging from 99.76 to 95.1 wt% D2O. The relative uncertainty in two individual buckling measurements at different coolant purities was taken to be equal to the uncertainty in the buckling change on voiding for the same fuel type determined from ZED-2 substitution measurements. Measured and calculated coolant purity buckling coefficients were compared. For the experiments with FNU fuel, the difference between the calculated and measured coolant purity buckling coefficients was 8%, with an estimated uncertainty of ±11%. For the experiments with MOX fuel, the difference between the calculated and measured coolant purity buckling coefficients was -10%, with an estimated uncertainty of ±8%. WIMS-IST overpredicts the coolant-purity coefficient for unirradiated natural UO2 fuel, but underpredicts the coefficient for simulated mid-burnup fuel. For both fuel types, calculation is within 1.5 times the uncertainty

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derived from the estimated uncertainties in the measured bucklings. Therefore, a bias of zero with an uncertainty of ±12% was assigned for the coolant purity reactivity coefficient.

10.4 Summary of WIMS-IST validation The bias and uncertainties associated with WIMS-IST predictions for the various phenomena are summarised in Table 5. It was found that WIMS-IST overpredicted the reactivity change on voiding for CANDU fuel bundle types. For fresh 37-element fuel the overprediction was 1.9±0.8 mk. The overprediction of the reactivity change on coolant voiding would lead to an overprediction of both the rate of rise of power and the peak power in the fuel during a loss-of-coolant-accident transient. The moderator-purity reactivity coefficient was overpredicted by 8±3%. For the other phenomena studied, the results of the code show little or no bias and are within the uncertainty of the experimental measurements.

Table 5. Summary of Bias and Uncertainty for Each Phenomenon

Description of Phenomenon Bias Uncertainty Coolant void reactivity Overestimate

+1.9 mk (37-element FNU †) ±0.8 mk

Coolant-temperature coefficient

No bias ±4%

Moderator-density and moderator-temperature

coefficient

No bias ±3%

Moderator-poison coefficient No bias ±2% Moderator-purity coefficient Overestimate

+8% ±3%

Fuel-temperature coefficient Overestimate for FNU Underestimate for simulated

mid-burnup fuel

±10%

Fuel isotopic change No or small bias for actinides ±2% Flux-power distributions No bias in bundle flux shape ±1% in bundle flux shape

Lattice distortion reactivity No bias in lattice cell with varying pitch

______

Coolant-purity coefficient No bias ±12% † FNU fuel

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11. CREATING A MACROLIB FOR DRAGON

11.1 The Need for a Macrolib

T16MAC is a computer program used to process WIMS-AECL Tape16 to produce a library of cross sections (called a Macrolib) for DRAGON to use when calculating cross-section data to represent reactivity devices in RFSP.

RFSP represents the reactor as being divided into an exhaustive, disjoint set of cells, and the neutrons as being in two energy groups. It represents each cell by means of a set of macroscopic cross sections, here denoted CΣ , which are calculated by WIMS-AECL for each cell. These cells must be exhaustive, so that WIMS-AECL represents the correct amount of moderator per length of fuel channel, and therefore derives the correct neutron energy spectra in them. Therefore, it is not possible to define additional cells in the reactor in which to represent reactivity devices. However, WIMS-AECL operates in two dimensions, and therefore is unable to represent the reactivity devices of CANDU power reactors, which have axes oriented perpendicularly to those of fuel channels. Thus, any set of macroscopic cross sections CΣ that it calculates can only represent a cell with no reactivity device.

Wherever a cell contains a reactivity device, RFSP-IST represents it as having a cross section DeviceTube-GuideC ∆Σα+∆Σ+Σ . (1)

in which α is the degree to which the reactivity device is inserted into the cell. ( 10 ≤α≤ .) The terms in this expression are the following:

CΣ represents the device-free cell as explained above.

Tube-GuideC ∆Σ+Σ represents a cell with a guide tube unoccupied by the moveable absorber that is part of the reactivity device.

DeviceTube-GuideC ∆Σ+∆Σ+Σ represents a cell with a reactivity device fully inserted into that cell (although it may not be fully inserted into the reactor).

The fundamental purpose of DRAGON is to calculate those “incremental” cross sections, Tube-Guide∆Σ and Device∆Σ .

Figure 7 shows the configuration modeled by DRAGON for the purpose. This figure is not to scale, and it does not show the boundaries of the supercell that DRAGON models. Its purpose is to show the materials that DRAGON represents in its model, because they are defined by T16MAC. Each material is represented, for the purposes of DRAGON, by a set of macroscopic cross sections for neutron reactions.

In three-dimensional geometry with cylindrical structures, such as fuel channels, DRAGON cannot represent “cluster” geometry, that is, the set of fuel pins in a fuel bundle within a fuel

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channel. Instead, the model represents a homogeneous material in the lumen of the fuel channel, shown as material number 1 in Figure 7. For the model to be valid, the macroscopic cross sections of that material must be derived by homogenization of a cluster calculation. That cluster calculation can be performed in two dimensions.

In this three-dimensional representation, the fuel channel is customarily represented as a single material obtained by homogenizing the pressure tube, gap and calandria tube. The fuel channel is labeled material number 2 in Figure 7. Although DRAGON could represent the fuel channel in more detail, such detail would not be worth-while when the lumen must be homogenized.

Figure 8 shows diagrammatically how DRAGON calculates Tube-Guide∆Σ and Device∆Σ . It calculates a set of homogenized macroscopic cross sections for the indicated subset of the supercell with the following sets of materials, numbered per Figure 7:

Material Number in Figure 7 Quantity Calculated

4 5 6

NoΣ Moderator Moderator Moderator

OutΣ Guide-Tube Material

Moderator Moderator

InΣ Guide-Tube Material

Absorber Sheath Material

Absorber Material

(An actual reactivity device might use more or fewer materials. The above list is only to illustrate the sorts of materials T16MAC must define.) From these, DRAGON calculates the incremental macroscopic cross sections.

The specifications for the materials listed in the above table, the specifications for the homogenized materials, number 1 and 2 in Figure 7, and the specifications for the moderator that fills the remaining space all come from T16MAC

11.2 The Purpose of T16MAC

The homogenizations over different materials, materials 1 and 2 in Figure 7, require macroscopic cross sections of all the materials in a detailed description of the lattice, and also fluxes to calculate the weights of those detailed macroscopic cross sections in the homogenized macroscopic cross sections. WIMS-AECL forms the macroscopic cross sections of materials in the detailed representation, and it performs the two-dimensional cluster-geometry calculation that yields the necessary fluxes.

Although DRAGON could also perform the cluster calculation in two dimensions, this use of WIMS-AECL has the advantage that full quality assurance, including source-code verification, is only necessary on those parts of DRAGON that are used in the above-described supercell calculation. Since DRAGON has been written in a clear, modular style, the relevant parts have been identified and have undergone full quality assurance.

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Thus, DRAGON draws macroscopic cross sections for all the materials from an outside source based on calculations by WIMS-AECL. That source is labeled “Macrolib” in Figure 8. This name denotes the format that DRAGON uses for a data file that is intended to convey a set of macroscopic cross sections. Sections 11.3 and 11.4 describe how to obtain an accurate macrolib for the present purpose.

Although Figure 8 shows only one macrolib, it is possible for DRAGON to use properties from more than one macrolib in its representation. This would be useful, for example, if both the fuel channel and the reactivity device contain cluster geometry.

11.3 Input Data for WIMS-AECL to Prepare a Macrolib

Ultimately, the macroscopic cross sections in the macrolib are derived from an analysis by WIMS-AECL. Therefore, a case must be set up for WIMS-AECL that can yield macroscopic cross sections for all the materials shown in Figure 7.

A WIMS-AECL case that is used to calculate CΣ would provide the necessary information for materials 1, 2, and 3. This is represented diagrammatically in Figure 9. The lines in the areas marked “Material 1” and “Material 2”, in the upper part, represent the normal detail in such a calculation. However, to obtain the information that is needed about the reactivity-device materials, a few changes are necessary to the input data that would be used to calculate CΣ .

One change is in the neutron-energy-group structure used in the transport calculation in WIMS-AECL. Since the cluster-geometry calculation cannot precisely represent the neutron energy spectrum in reactivity-device materials, the results of the calculation by WIMS-AECL cannot be used to derive macroscopic cross sections in a condensed group structure. Therefore, the cross sections in the macrolib must be in the same energy-group structure as the library of microscopic cross sections that WIMS-AECL uses. That way, the macroscopic cross sections that are derived for materials in the reactivity device do not depend on the fluxes that are used in the derivation. Even though the macroscopic cross sections are calculated as reaction rates divided by fluxes, the resulting values are the same as if the macroscopic cross sections were obtained directly by multiplication of microscopic cross sections by number densities. This energy-group provision has the same effect on the moderator’s derived macroscopic cross sections, since it is also a homogeneous material.

To obtain this energy-group structure, the FEWGroups data in the input file must contain a full list of the energy-group numbers in the microscopic nuclear data library; that is, a list of consecutive integers from 1 up to the number of energy groups.

Another change is of course the addition of materials that are in the reactivity devices. They must be represented with the same compositions, including the same densities, as in the reactivity devices. These materials are placed in regions defined in the input data to WIMS-AECL for that purpose. Because of the above condition on energy groups, the derived properties of these materials do not depend on where their regions are in the WIMS-AECL model. The simplest place to put them is in annuli at the periphery of the circular, two-dimensional cell that WIMS-AECL represents. The regions in Figure 9 marked “Material 4, 5, and 6” represent those annuli.

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The volumes of those regions make no difference to the derived macroscopic cross sections, because of the use of all energy groups. However, those volumes make a difference to the results for materials 1 and 2, by perturbing the calculated fluxes in their regions. Perturbation is due to neutron reactions in the device materials and to displacement of some moderator. With appropriate sizes of annuli of peripheral reactivity-device materials, those perturbations would approximately reproduce the actual effects of reactivity devices on nearby fuel channels. However, there is no good way to estimate the appropriate sizes. Instead, in current practice, a thickness, for each annulus, of 10-4 centimetres is used. This thickness is designed to have negligible effect on the neutron energy spectrum, yet not incur roundoff error. The regions in Figure 9 marked “Material 4, 5, and 6” are not to scale. In proper scale, they would be invisible.

T16MAC draws its data from the Tape16 file from WIMS-AECL. To provide the necessary data on that file, the main section of the data input to WIMS-AECL must include the instructions MTRFlux and MATSig.

With these exceptions, the input file to WIMS-AECL for preparation of a macrolib is identical to that for calculation of CΣ . Therefore, a complete sample input file is not reproduced here. However, an excerpt is shown in Figure 11 to help explain input to T16MAC. It shows the above-mentioned annuli that contain reactivity-device materials.

11.4 Input Data for T16MAC to Prepare a Macrolib

T16MAC is written according to the same conventions as DRAGON. It similarly uses CLE-2000, and it uses the same style of input. It may be thought of as a version of DRAGON, but one that has only one module, which is known as T16MAC:, plus the usual utilities found in DRAGON. Some of the explanation here is also true for DRAGON.

As in the documentation of DRAGON, any data here shown in italics are to be replaced by users’ specifications. Any data shown in brackets are optional, and the brackets are not part of the data. A pipe symbol delimits options of which one must be selected.

Any file name given to T16MAC may refer either to a desired file directly or to a shortcut file (in Windows) or symbolic-link file (in UNIX) that points to a desired file. This is important in the files named in the ASCII input, because their filenames are limited to twelve characters. They are interpreted in relation to the current working directory. A shortcut/symbolic link in the current working directory is necessary to refer to a longer filename, or a file located in a remote directory.

The command to run T16MAC is T16MAC [< Input file name] [> Output file name]

in which the italicized items are to be replaced by file names for the indicated purposes. The input file referred to above is the ASCII input file to be prepared by the user and discussed in this section. The default is direct input from the console keyboard, which is unlikely to be useful. The output file is the ASCII output addressed to the user. The default is output to the console monitor, which may be useful during interactive debugging. The names of other files involved in the operation are given in the ASCII input file as described below.

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T16MAC prepares a macrolib with the energy-group structure specified by the FEWGroups data in the input file to WIMS-AECL. With the above provisions, this means that the macrolib has the same energy groups as the microscopic nuclear data library that WIMS-AECL used.

A sample input file to T16MAC is shown in Figure 10.

A line beginning with an asterisk is considered to be a comment.

A record of input is terminated by a semicolon, and not by an end of line. The semicolon must be separated by at least one space from other data.

In the sample in Figure 10, after the comments, the data structures to be used are declared. Any data structure must be declared before it is mentioned in a command. In T16MAC, the only data structures that will be useful are files. In the example, the one resulting macrolib is output to two files of different types. Only one macrolib file is necessary for input to DRAGON, but each of the two formats has an advantage, so the user may choose either or (as here) both. In the example in Figure 10, MacroXSs is given the format XSM_FILE. This is the most efficient format for input to DRAGON, being a binary, direct-access file. MacroXSs.txt is given the format SEQ_ASCII which, as the name suggests, is a sequential ASCII file. This has the advantage that it can be read by a human, and this format has therefore proven useful for quality assurance. It also has the advantage that T16MAC and DRAGON can run on different systems that use incompatible binary-file formats.

The Tape16 file from WIMS-AECL is a sequential binary file, and accordingly it must be specified as SEQ_BINARY in the input to T16MAC. The sample name in Figure 10, Tape16, is the name that WIMS-AECL gives the file. The use of any other name will require renaming and/or use of a shortcut/symbolic link.

A MODULE statement must declare any module before a command refers to it. A run of T16MAC will always use the two modules T16MAC: and END:.

The line MacroXSs := T16MAC: Tape16 ::

follows the usual format of DRAGON commands. It states that T16MAC: is to use Tape16 as input and MacroXSs as output. The double colon introduces other parameters that the module T16MAC: is to use, which continue to the next semicolon.

The following are the parameters that T16MAC: uses. Many of them are optional, as indicated by enclosure in brackets. Their defaults are indicated. They are shown in two groups. Any parameter in the first group must precede any parameter in the second group. Otherwise, their sequence is immaterial. The keywords are case-sensitive, but they may have additional characters appended to make them more readable; for example: NZONES, NMIXtures. First group: [EDIT nedit] NMIX nmixture [NZON nzone]

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The meanings of these data are: EDIT Keyword used to specify data written to standard output. nedit ≤ 0: No output.

≥ 1: Scalar quantities in the standard input, the Tape16 input, and the macrolib output are echoed in the standard output file. ≥ 2: Vector quantities are similarly echoed. These include macroscopic cross sections other than scattering, radii of regions on Tape16, and echoes of vector inputs in the data structure second group of data, shown below. ≥ 3: Matrix quantities are similarly echoed. These are transfer cross sections. If this quantity is not specified, it defaults to 1.

NMIX Keyword used to set the number of mixtures to be placed in the macrolib. This keyword has the same function as in the MAC: module of DRAGON-IST.

nmixture The number of mixtures to be placed in the macrolib. NZON Keyword used to specify the number of distinct zones in the Tape16 data

from WIMS-IST. This datum is necessary only if non-consecutive zones in the Tape16 data are to be merged into one mixture for DRAGON-IST.

nzone The number of zones, i.e. distinct sets of regions in the Tape16 data from WIMS-IST. If this quantity is not specified, it defaults to nmixture.

Second group: RADI (radius (i), i = 1, {nzone|nzone - 1}) [IMIX (imixture (i), i = 1, nzone)] The meanings of these data are: RADI Keyword used to specify a set of radii by which to identify the regions that are to

be included in each zone. Each zone may include several of the regions into which WIMS-IST has partitioned the cell. Each specification is the maximum outside radius of any region to be included in a zone.

radius T16MAC compares each radius with the values of “region” radii on Tape16 in the "REGION ", "DESCRIPTON" record. If a region, on Tape16, has a radius less than or equal to the specified radius for some zone, then T16MAC includes that region in that zone, unless that region is already included in an inner zone. The radii in this input must be in increasing order. They must be in the same units as the radii on Tape16, centimetres. If a specified radius is exactly that of a region it is to include, it may be misinterpreted, because of roundoff error. A larger specified radius, less than the radius of the next region outward, is reliable. Radius number nzone need not be specified. T16MAC does not use it, but instead assumes that the last zone includes all of the regions not included in other zones. This means that every region is in a zone.

IMIX Keyword used to specify which zones are to be homogenized together to form each mixture. These data are necessary only if consecutive mixtures are not formed by the homogenization of the regions in consecutive zones (one mixture per zone, numbers increasing outward).

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imixture imixture (izone) specifies that the homogenization over zone number izone is to be included in the definition of mixture number imixture. If these data are absent, they default to consecutive integers starting from 1, so that successive mixtures are formed by the homogenization of the regions in successive zones, one mixture per zone.

In the example, EDIT is 1, which is redundant since that is the default. It means that just a few data are requested, to confirm what happened. NMIX is 6, because there are 6 materials needed for the three-dimensional calculation in this example. NZON and IMIX are not specified, because in the recommended configuration consecutive materials are derived from consecutive regions, working outward radially.

The RADI specification has a bit of subtlety, as is suggested by the lengthy explanation above. The sample input to WIMS-AECL is not shown here, because it differs so little from usual. Figure 11 shows the annuli, for comparison with the RADI specification. The latter radii are somewhat bigger than those of the annuli to which they refer. This is important, because a specification of the exact same number might be incorrectly interpreted because of roundoff error. (No two real numbers can be guaranteed to be equal unless both have been explicitly set to the same integer.) When a RADI specification is not exactly equal to an annulus radius in Tape16, T16MAC takes it to refer to the next radius down.

With this interpretation, the first RADI specification defines zone number 1 to be the fuel channel’s lumen, zone number 2 to be the channel’s structure, and so on, in accordance with Figure 11. Since there is no IMIX specification, these zones correspond one-to-one with the materials as indicated.

A semicolon terminates the record that gives instructions to the module T16MAC:. After that, the optional line MacroXSs.txt := MacroXSs ;

will cause the binary information in MacroXSs to be copied to the ASCII file MacroXSs.txt, which has the possible uses described above. The line END: ;

ends the T16MAC run. This operation is treated as an invocation of a module.

11.5 Input Data to DRAGON to Use a Macrolib

When DRAGON uses a macrolib derived as above, it must start by declaring the file in the same manner as it was declared in the input to T16MAC. In the above example, the declaration would be either of the lines

XSM_FILE MacroXSs ; SEQ_ASCII MacroXSs.txt ;

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(not both). DRAGON could also refer to the file not directly, as shown, but rather through a shortcut (Windows) or symbolic link (UNIX). Such a reference may be useful if several DRAGON runs are to be performed to analyze different reactivity devices, because the input to WIMS-AECL and T16MAC can give a shopping list of many reactivity-device materials, not limited to materials for one type of reactivity device


Table 1: A comparison of the WIMS-AECL microscopic data libraries


Table 2: List of WIMS-AECL input keywords indicating their impact on particular parts of calculation


Table 2 (continued)


Table 2 (concluded)


Table 3: Fission products in the “ENDF/B-VI” library of WIMS-AECL code


Table 3 (concluded)


Figure 1: Capture cross section of 238U as an illustration of the resonance behaviour of cross section


Figure 2: Graphical representation of the numerical integration in two-dimensional geometry


Figure 3: A graphical illustration of the ray tracing technique in two-dimensional geometry


Figure 4: Graphical representation of the numerical integration of collision probabilities in annular geometry


Figure 5: Decay chains of fission products as used in the WIMS-AECL “ENDF/B-VI” library


Figure 6: Actinide decay chains in the WIMS-AECL “ENDF/B-VI” library

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Figure 7: Supercell represented by DRAGON

FuelChannels

2. Fuel Channel Structure

ReactivityDevice

3. Moderator (ambient)

1. Fuel Channel Lumen Contents

4.5.6.

ReactivityDeviceComponents

93

Figure 8: Calculation of incremental cross sections by DRAGON

1. 3-D Supercell

2. Homogenize

3. Subtract

∆ΣGuide Tube

ΣNo

∆ΣDevice

ΣInΣOut

Macrolib

94

Figure 9: Homogenization performed by T16MAC

Microscopic Nuclear Data Library

1. 2-Dimensional, Cluster

2. Homogenize

Macrolib

Material 1 Material 2Material 3

Material 4, 5,and 6

95

Figure 10: Sample input to T16MAC

* * * * * * * * * * * * * * * ** ** Input to T16MAC for ** Hypothetical Control Rod ** in ** Hypothetical Reactor ** ** * * * * * * * * * * * * * * *

* Input file was prepared by Ron Davis, 2004-01-28.

XSM_FILE MacroXSs ;SEQ_ASCII MacroXSs.txt ;SEQ_BINARY Tape16 ;MODULE T16MAC: END: ;

MacroXSs := T16MAC: Tape16 ::EDIT 1NMIXtures 6RADIi 5.18095 6.58755

16.12146 16.12156 16.12166 ;MacroXSs.txt := MacroXSs ;END: ;


Figure 11: Annuli in input to WIMS-AECL


Flowchart 1: General scheme of WIMS-AECL calculations


Flowchart 2: Schematic representation of the resonance calculations - Chain #3


Flowchart 3: Schematic representation of the ‘Spectrox’ calculation - Chain #4


Flowchart 4: Schematic representation of the collision probability calculations - Chains #7 and #8


Flowchart 5: Schematic representation of the leakage and buckling calculations - Chain #14


Flowchart 6: Schematic representation of the burnup calculations - Chain #16


Block Diagram 1: Calling hierarchy in the macroscopic cross-section calculations - Chain #2


Block Diagram 2: Calling hierarchy in the resonance self-shielding calculations - Chain #3


Block Diagram 3: Calling hierarchy in the ‘Spectrox’ calculation - Chain #4


Block Diagram 4: Calling hierarchy in the collision probability calculations - Chain #7


Block Diagram 5: Calling hierarchy in the ray tracing procedure - a part of Chain #8


Block Diagram 6: Calling hierarchy in the leakage and buckling calculations - Chain #14


Block Diagram 7: Calling hierarchy in the burnup calculations - Chain #16

wims-aecl course notes57 10. validation of wims-ist for standard candu wims-ist is defined to be...

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