under-moderated 4.738-wt.%-enriched uranium dioxide … · 2010. 1. 26. · nea/nsc/doc/(95)03/iv...

NEA/NSC/DOC/(95)03/IV Volume IV

LEU-COMP-THERM-072

UNDER-MODERATED 4.738-WT.%-ENRICHED URANIUM DIOXIDE FUEL ROD ARRAYS REFLECTED BY WATER OR POLYETHYLENE

Evaluator

Nicolas Leclaire Institut de Radioprotection et de Sûreté Nucléaire, IRSN

Internal Reviewer

Pascal Grivot Commissariat à l’Energie Atomique, CEA

Independent Reviewer

Reza Gouw Bechtel Bettis, Inc


LEU-COMP-THERM-072

Revision: 0 Page 1 of 117 Date: September 30, 2008

UNDER-MODERATED 4.738-WT.%-ENRICHED URANIUM DIOXIDE FUEL ROD ARRAYS REFLECTED BY WATER OR POLYETHYLENE

IDENTIFICATION NUMBER: LEU-COMP-THERM-072 SPECTRA KEY WORDS: acceptable, array, cladding, critical experiment, fuel rods, low-enriched, under-

moderated, pool, small pitches, water-moderated, water-reflected, uranium dioxide, polyethylene

1.0 DETAILED DESCRIPTION 1.1 Overview of Experiment Low-enriched and low-water-moderated arrays composed of UO2 (4.738 wt.% 235U) fuel rods at a 1.6-cm square pitch (reflected or not by polyethylene, and by water) or at a 1.075-cm or 1.1-cm square pitch (reflected by polyethylene and water) were studied in this experimental program. These experiments were subcritical approaches extrapolated to critical, with the multiplication factor reached being very close to 1.000 (within 0.1%). The subcritical approach parameter was the water level. These experiments were carried out in the testing equipment called “Apparatus B” in the experimental criticality facility at the CEA center at Valduc in 1998. The fuel in the rods is identical to the fuel used in LEU-COMP-THERM-071, and the configurations involve the same polyethylene reflector blocks as in the MARACAS program (LEU-COMP-THERM-049). However, the pitch between rods was chosen variable to test the polyethylene reflector over a wider energy spectrum (undermoderated for 1.075- and 1.1-cm pitches corresponding to MARACAS or at the moderation optimum for 1.6-cm pitch). LEU-COMP-THERM-071 experiments were used as reference experiments (without polyethylene) for the configurations with small pitches (1.075 or 1.1 cm). These experiments with tight pitches might also be used to validate calculation methods for such pitches in support of nuclear manufacturer needs for storing higher quantities of fuel assemblies in a limited amount of area. All nine experiments in this evaluation are considered acceptable for use as benchmarks. 1.2 Description of Experimental Configuration The experimental program is described in the basic report (Reference 1), but other reports were consulted in order to have the whole set of data (References 2 through 5). The experimental configuration tank of Apparatus B (Figures 1 through 7) was comprised of an array of UO2 fuel rods held by a basket and surrounded with a polyethylene (CH2) reflector, which was placed on a pedestal inside a parallelepiped tank. The tank was located on the floor in the middle (approximately) of a large room. Water, which was used as the moderator and the reflector (with polyethylene), was introduced step by step from the bottom of the tank. The water level was the subcritical approach parameter. Photos of the experimental device outside the tank were taken for this program. They are given in Figures 1.a through 1.c. Figure 1.a shows the array of UO2 rods, the polyethylene reflector partly installed


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and the basket. Figure 1.b is a top view of the array of UO2 rods with their polyethylene reflector, basket, and upper grid. Figure 1.c is another top view of the array of UO2 rods.

Figure 1.a. Front View of Array of UO2 Rods with their Polyethylene Reflector and Basket.

Figure 1.b. Top View of the Array of UO2 Rods with their Polyethylene Reflector, Basket, and Upper Grid.


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Figure 1.c. Top View of the Array of UO2 Rods with their Polyethylene Reflector, Basket, and Upper Grid.

1.2.1 Critical Approach and Results

The experiment is based on the subcritical approach technique, with critical conditions obtained using extrapolation. The subcritical approach parameter is the water level. Two Am-Be neutron sources were used to drive the approach. Neutron counting rates were measured with 6 BF3 counters, which provided a “C” counting rate (depending on the array height, H, that was immersed in water) and consequently the corresponding keff of the assembly. The function 1/C = f(H) was extended by linear extrapolation to determine the critical height from water height measurements, as explained in Figure 2. In general, the level was raised very close to the critical one, such that the final keff was approximately within -β/10 ≈ -65 × 10-5 from criticality. The water height was measured by a needle of measurement (conductivity probe).


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08-GA50017-175-1

C = C /(1-k )0 eff

When H HC1/C 0

H0

1/CeffK = F(H)

H

HC

Water height measurement system

Rod array

UO2 rod

Fissile zone upper limit level

Pedestal

Water input and output

Neutron counters

Counting rate, C

Fissile zone lower limit level

Needle of measurement

Figure 2. Principle of the Experiments.

Usually, the experiment was performed so that the fissile zone height in water was the highest possible. This was done by adding or removing fuel rods symmetrically on two or four external rows of the initial square array. A sketch of the basic experimental configuration is given in Figure 3.


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08-GA50017-175-2

Tank

Support pedestal(Stainless Steel Z2CN18 10)

Additional plate

Basket

Top grid

Anglebracket

Bottom grid

Top plate

Tubular structure(Stainless Steel)

Bottom plate

1.02.5

17.5

0.6

0.3

1.8

1.2 Thickness = 0.4

Wedge

Dimensions in cm

1.2

1.2

Figure 3. Sketch of an Experimental Configuration.

Nine experiments were performed with various pitches:

• A 17 × 17 rod array with a square pitch of 1.6 cm, without polyethylene reflector • A 16 × 16 rod array with a square pitch of 1.6 cm, without polyethylene reflector • A 16 × 17 rod array with a square pitch of 1.6 cm, without polyethylene reflector • A 17 × 17 rod array with a square pitch of 1.6 cm, with polyethylene reflector • A 16 × 16 rod array with a square pitch of 1.6 cm, with polyethylene reflector • A 16 × 17 rod array with a square pitch of 1.6 cm, with polyethylene reflector • A 33 × 33 rod array with a square pitch of 1.1 cm, with polyethylene reflector • A 32 × 32 rod array with a square pitch of 1.1 cm, with polyethylene reflector • A 35 × 35 rod array with a square pitch of 1.075 cm, with polyethylene reflector.


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Experimental results are given in Tables 1 to 4 and in Figures 4.a to 4.c. The “zero level” for the critical height is the bottom of the rod fissile column.

Table 1. Arrays with a Square Pitch of 1.6 cm without CH2 Reflector.

Case Number

Experiment Number (Valduc)

Array Size(rods)

Number of Rods

Temperature (°C)

Critical Water Height ± 2σ (cm) (a)

1 2789 17 × 17 289 19 60.479 ± 0.022 2 2790 16 × 16 256 17 91.523(b) ± 0.030 3 2791 16 × 17 272 17 71.836 ± 0.020

(a) The given uncertainties correspond to 2σ. (b) The fissile column is completely under water.

Table 2. Arrays with a Square Pitch of 1.6 cm with CH2 Reflector.

Case Number


Array Size(rods)

Number of Rods

Temperature (°C)


4 2792 17 × 17 289 19 56.293 ± 0.038 5 2793 16 × 16 256 19 81.616 ± 0.055 6 2794 16 × 17 272 19 65.765 ± 0.029

(a) The given uncertainties correspond to 2σ.

Table 3. Arrays with a Square Pitch of 1.1 cm with CH2 Reflector.

Case Number


Array Size(rods)

Number of Rods

Temperature (°C)


7 2795 33 × 33 1089 19 69.431 ± 0.030 8 2796 32 × 32 1024 20 81.854 ± 0.038

(a) The given uncertainties correspond to 2σ.

Table 4. Array with a Square Pitch of 1.075 cm with CH2 Reflector.

Case Number


Array Size(rods)

Number of Rods

Temperature (°C)


9 2797 35 × 35 1225 20 82.227 ± 0.028 (a) The given uncertainties correspond to 2σ.


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Experiment number: 2789Array 17 × 17: 289 rodsSquare pitch: 1.6 cmCritical height: 60.479 cm


UO fuel rod2

UO fuel rod with Am-Be neutron source2


08-GA50017-176-1

Figure 4.a. Rod Arrays for 1.6-cm Square Pitch without CH2.


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Polyethylene

UO fuel rod2


08-GA50017-176-2

Figure 4.b. Rod Arrays for 1.6 cm Square Pitches with CH2 Reflectors.


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Polyethylene

UO fuel rod2


08-GA50017-176-3

Figure 4.c. Rod Arrays for 1.1-cm and 1.075-cm Square Pitches with CH2 Reflectors.


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1.2.2 The Room Apparatus B was approximately centered in a concrete cell (C 172), in the radiological control zone, on the ground floor of Building 10 in the Valduc Nuclear Centre. The concrete was covered with a decontaminatible paint.

The cell was 12.1 × 8.8 × 10 m high, with 1.45-m-thick concrete walls. The thickness of the concrete floor was 40 cm. The thickness of the ceiling varied from 70 cm (at the edges) to 110 cm (in the middle).

1.2.3 Experimental Tank

The experimental tank had internal dimensions of 189.7 cm × 189.7 cm horizontally and 140 cm vertically (Figures 3). It was comprised of 0.3-cm-thick walls and a 0.6-cm-thick bottom and was manufactured of stainless steel Z2CN18 10. The walls and bottom were reinforced with U-shaped girders. Consequently, the inside face of the experimental tank bottom was at the elevation of 23.7 cm above the concrete floor. The tank was equipped with a needle of measurement that followed the free upper level of water and provided the water height. The zero-level measurement of the needle was the bottom of the fuel. Because the array was centered in the tank, more than 40 cm of water surrounded the sides of the fuel rod array.

1.2.4 Fuel Rods

The UO2 fuel rods used for the experiments (Figure 5) contained uranium oxide fuel, enriched to 4.738 wt.% 235U, and clad with Zircaloy-4. The fuel column was made of sintered oxide pellets, each 1.4954 ± 0.0068 cm long and 0.78919 ± 0.00176 cm in diameter (measurement values, from References 4 and 5). The pellet diameter was measured with a palmer (micrometer) whose precision was +/- 0.005 cm. The total rod length, including end plugs and retaining spring, was 102.082 ± 0.04 cm (measurement value). In previous experiments in the low-moderated-fuel-rod-array experimental program, the fuel was clad with AGS. These rods were reclad in 1995 for a fission-product experimental program. After the rod recladding, measurements were performed on 100 rods (at the top, middle, and bottom of each rod) to determine the outer diameter of the clad. A statistical method gave the average value and its associated standard deviation: 0.949245 ± 0.000439 (1σ). The outer clad diameter was measured with a palmer whose precision was +/- 0.0005 cm. Measurements were also performed on fissile column height, fissile column weight, fissile pellet diameter, spring mass, and plug mass. Table 2 gives the measured values plus the standard deviation (1σ) for the main parameters. The clad inner diameter is known only by the fabrication specification.


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Table 5. Uncertainties of Fuel Rods Characteristics (References 4 and 5).

Parameter Mean Value Standard Deviation Number of Measurements

Pellet Diameter (cm) from measurement statistics 0.78919 0.00176 53

Pellet Diameter (cm) from accuracy of micrometer 0.78919 0.005 0

Pellet Height (cm) 1.4954 0.0068 53

Inner Clad Diameter (cm) 0.836 (a) 0.00289(a) 0

Outer Clad Diameter (cm) from measurement statistics 0.949245 0.000439 300

Outer Clad Diameter (cm) from accuracy of micrometer 0.949245 0.0005 0

Fissile Column Height (cm) 89.765 0.254 1261

Fissile Column Mass (g) 455.78 2.82 1261

Rod Height (cm) 102.082 0.04 1261

(a) Derived from manufacturing tolerance (= 0.005).

The average height value of the fissile column was 89.765 ± 0.254 (1σ) cm, which is in agreement with the original specification value of 90 cm ± 1 cm. The average density and average oxide mass are given in Section 1.3. Plugs of rod ends are also made of Zircaloy-4. Both plugs have a cylindrical form with a truncated end simplifying the attachment. Their characteristics are given in Table 6.

Table 6. Characteristics of End Plugs (Reference 4).

Height (cm) Diameter (cm) Mass (g)

Value Tolerance Value Tolerance Value Uncertainty Number of Measurements

Upper Plug 1.468 0.024 0.95 0.005 3.4675 σ = 0.0047 15 UO2 Rods Lower Plug 1.8 0.005 0.95 0.005 4.6321 σ = 0.0138 10


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Above the fuel, between the end of the fissile zone and the bottom of the top end plug, a stainless steel spring retains and compresses oxide pellets inside the clad, ensuring contact between them. The spring has the following characteristics for UO2-type fuel rods:

• Material: Stainless steel Z10CN18-09 • Lengtha: 9.049 cm • Diameter: 0.78919 ± 0.015 cm (production tolerance) • Number of turns: 30 • Spring wire diameter: 0.1445 ± 0.0025 cm (production tolerance) • Mass: 8.09583 ± 0.00895 g.

a compressed length in the final produced rod


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1.468

0.9492

Top plug (Zr4)

Steel spring (Z10CN18-09)0.789 cm outside diameter,

0.1445 cm wire diameter30 spirals,

UO pellet (4.738 wt.%)

0.789 cm diameter, 1.495 cm height2

Clad (Zr4)0.949 cm outside diameter0.836 cm inside diameter

Bottom plug (Zr4)

9.049

89.765

102.082

1.8

08-GA50017-177-1

Dimensions in cm

Figure 5. Fuel Rod (Mean Dimensions).


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1.2.5 Basket and Grids Fuel rods were held in an aluminium (AG3M) basket. It was composed of the following:

• Two end plates (top and bottom, 95 cm × 95 cm),a 1.2 cm thick, 107 cm apart. • Two intermediate grids, 96.5 cm apart, with holes for the rods to be installed in a square array (17 ×

17 holes at a 1.6-cm square pitch for Cases 1 to 6, 36 × 36 holes at a 1.1-cm square pitch for Cases 7 and 8, and 36 × 36 holes at a 1.075-cm square pitch for Case 9). The hole diameter is 0.99 cm. The grid dimensions are the following:

– 30.6 cm × 30.6 cm lower grid, 0.4 cm thick, for Cases 1 through 6; 43.5 cm × 43.5 cma lower grid, 0.4 cm thick, for Cases 7 and 8; and 42.625 cm × 42.625 cm lower grid, 0.4 cm thick, for Case 9 (Figure 6.a). Simplified shapes are shown in Figures 7.a, 7.b, and 7.c.

– approximately 95 cm × 95 cma upper grid, 0.6 cm thick, for all cases; This upper grid had a complex shape with area without material, as shown in Figure 6.b; simplified shapes are shown in Figures 7.a, 7.b, and 7.c.

• Four L-shaped angle brackets (109.4 cm long, 10 cm wide, and 0.4 cm thick) that join the end plates and the two intermediate grids.

Figure 6.a. Part of the 1.1-cm-pitch Bottom Grid.

a These data are derived from private conversations with Pascal Grivot, on April 25, 2007 and Emmanuel Girault, an experimenter for these experiments. They differ from those provided in Reference 1, which gave 50 cm × 50 cm for the top and bottom end plates’ dimensions and 50 cm × 50 cm for the top and lower grids’ dimensions, with a thickness of 0.4 cm for the upper grid. Based on the photos in Figures 1 and 6, the dimensions given in the experimental report seem to be erroneous.


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Figure 6.b. Photograph of the 1.1-cm-pitch Upper Grid.


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HoleD 0.99

1.6-cm pitchDimensions in centimeters08-GA50017-178-1

0.6

95 95

30.630.6

96.5

1.6-cm pitch

17 x 17 holes

Upper gridCases 1-6

Lower gridCases 1-6

0.4

Figure 7.a. Sketch of the 1.6-cm-pitch Bottom Grid and Simplified Top Grid, Cases 1 - 6.

(See Figures 6.a and 6.b for the exact shapes.)


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HoleD 0.99

1.1-cm pitchDimensions in centimeters

0.6

95 95

43.543.5

96.5

1.1-cm pitch

36 x 36 holes

Upper gridCases 7-8

Lower gridCases 7-8

0.4

08-GA50017-178-2

Figure 7.b. Sketch of the 1.1-cm-pitch Bottom Grid and Simplified Top Grid.



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0.6

95 95

96.5

36 x 36 holes

Upper gridCase 9

Dimensions in centimeters

42.62542.625

Lower gridCase 9

0.4 HoleD 0.99

1.075-cm pitch 1.075-cm pitch08-GA50017-178-3

Figure 7.c. Sketch of the 1.075-cm-pitch Bottom Grid and Simplified Top Grid.



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1.2.6 Support Pedestal

The support pedestal (stainless steel Z2CN 18/10), which enables the basket to be installed in the tank, was located on the bottom of the experimental tank (Figures 1.b and 3). It is composed of the following:

• A support plate 186 cm × 186 cm, 2.5 cm thick. • Four legs, 17.5 cm high. • An additional plate 150 cm × 150 cm, 1 cm thick. • A tubular structure situated at the four pedestal corners, 9 cm in diameter and 0.549 cm thick. These

tubes were soldered to horizontal tubes, which have the same sections (vertical tubes are visible in Figure 1.b).

Centering pins allowed positioning of the basket in the middle of the pedestal and in the middle of the pool tank. The upper face of the pedestal is 21 cm above the bottom of the pool tank. 1.2.7 Polyethylene Shield (Reflector Blocks)

The reflector (CH2) was situated against the four lateral sides of parallelepiped array (Figures 1.a to 1.c). Each reflector was composed of blocks. These blocks were held in an AG3M aluminium structure by screws and put on wedges, which are shown in Figure 3. The shield characteristics were as follows:

• Width: 58.8 cm • Aluminium structure height: 94.9 cm • Polyethylene reflector height: 91.0 cm (+0/-0.5 mm) • Thickness: 19.6 cm (+0.1/-0.1 mm) • Polyethylene density: 0.96 (specification).

The reflectors were arranged next to the arrays as shown in Figures 4.b and 4.c. According to the pitches, the CH2 reflectors were always at the same distance from the lateral faces of the array of rods. This distance was conditioned by the position of the wedges. The nominal values (from Reference 1) are 0.305 cm for Cases 4, 5, and 6 and 0.2 cm for Cases 7, 8, and 9. Consequently, the shields were moved when the array size changed. The same polyethylene blocks were used for the MARACAS experiments (LEU-COMP-THERM-049). 1.2.8 Neutron Counters and Sources Support

Six BF3 neutron counters were arranged around the core. Four of them were placed facing the four array sides at a distance between 10 cm and 12 cm, 28 cm above the basket bottom. The two others were located below the core bottom. The two Am-Be neutron sources were located on two middle fuel rods (Figures 4.a to 4.c), 25 cm above the bottom plate. 1.2.9 Command and Control Room

The command and control room (cells F102a and F102b) was adjacent to the experiment hall. Experimenters carried out the subcritical approach electronically and remotely, according to the information provided by the control panel, microcomputers, and video cameras.


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1.3 Description of Material Data The UO2 fuel rod comprises uranium oxide pellets inside tubes of Zircaloy-4. Isotopic Content of Uranium (References 4 and 5) The uranium of the UO2 fuel was enriched to 4.738 wt.% 235U. The results of recent isotopic analyses on two pellet samples (1998) are provided in References 4 and 5 and are reported in Table 7. The uranium isotopic content was measured by thermal ionization mass spectrometry (TI/MS), which gives very accurate results.

Table 7. Results of TI/MS Measurements in1998 (2σ uncertainties).(a)

Element at.% (Sample 1) at.% (Sample 2) 234U 0.0308 ± 0.001 0.0306 ± 0.001 235U 4.7956 ± 0.004 4.7949 ± 0.004 236U 0.1375 ± 0.001 0.1371 ± 0.001 238U 95.0361 ± 0.020 95.0374 ± 0.020

(a) measured by FBFC (Franco-Belge de Fabrication de Combustible).

Stoichiometry of Uranium Oxide (Reference 3) Two values of the O/U stoichiometry derived from References 1 and 3 are reported in Table 8.

Table 8. Results of Stoichiometry Analysis for the UO2 Fuel.

Reference Experimental Study Relative to UO2 Rods

FBFC Analysis Certificate Reference 3

Date Reference 1 1998 O/U 2.0035 2.000 ± 0.001 (1σ)

Density of Uranium Oxide (References 4 and 5)

Measurements were performed on 1261 rods during the production of new claddings by FBFC/Pierrelatte in 1995. The average values are the following:

• Average oxide weight: 455.78 ± 2.82 g (1σ) • Average fissile height: 89.765 ± 0.254 cm (1σ) • Average linear density: 5.0778 ± 0.0282 g/cm (The average linear density was obtained by

averaging the linear densities of each rod.) • Later, in 2000, the diameter of 53 oxide pellets was measured. The average diameter was 0.78919 ±

0.00176 cm (1σ). In References 1, 4, and 5, it is stated that the density is equal to 10.38 ± 0.04 (3σ) g/cm3. This density is the the nominal one. Oxide Impurities

The impurity content is reported in References 4 and 5. It was provided by FBFC measurements in 2000. Three elements were detected (over the detection limit): aluminum, iron, and silicon. Other elements were under the detection limit. These data are reported in Table 9.


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Table 9. Uranium Oxide Impurity Report Provided by FBFC.

Element Al Fe Si B Ca Cd Cr Mg Mo Ni Ti ppm(a) 18 85 101 <0.35 <20 <0.53 <15 <6 <20 <20 <10

Element Th Zn C Cl F N Dy Eu Gd Sm ppm(a) <2 <10 <4 <5 <2 <7.5 <0.05 <0.05 <0.1 <0.15

(a) parts per million by weight relative to UO2; i.e., (weight of element)/(weight of UO2) × 106 Zircaloy-4 Characteristics

Plugs and clad are made of Zircaloy-4. Its composition is provided by the European manufacturer of zirconium, CEZUS. Three Zircaloy-4 analysis certificates are provided in the report on UO2 rods (References 4 and 5) concerning, respectively, the cladding tubes, bottom end plug, and top end plug. The discrepancy of isotope contents between the cladding and bottom and top plugs was within one standard deviation of measurement precision. The composition given in Table 10 corresponds to the cladding analysis.

Table 10. Selected Zircaloy-4 Analysis for UO2 Fuel-Rod Cladding Tubes, Chemical Composition (Reference 4, page 72).

Element Zr N O Sn Fe Cr Weight % 98.12347 0.0031 0.1368 1.366 0.222 0.118 Element C Si Al Hf H

Weight % 0.01286 0.0099 0.00194 0.00556 0.00037 The density value of Zircaloy-4 (specification value) given in the references is ρ = 6.55 g/cm3.

The basic report (Reference 1) also gives the contents of Zircaloy-4 impurities. Values are provided by the manufacturer for samples from three positions in the alloy ingot.a Detected impurities are included in the chemical composition (Table 10). Other impurities are reported in Table 11.

Table 11. Undetected Impurities in Fuel-Rod Zircaloy-4 Cladding.

Element B Ca Cd Cl Co Cu Mg Mn Mo ppm(a) <0.4 <10 <0.4 <10 <10 <10 <10 <10 <10

Element Nb Ni Pb Ta Ti U V W ppm(a) <50 <40 <20 <100 <10 <0.5 <20 <30

(a) parts per million by weight relative to Zircaloy-4; i.e., (weight of element)/(weight of Zircaloy-4) × 106

Spring Stainless Steel

The spring is made of stainless steel Z10CN18.09. Its composition as reported in the analysis certificate in Reference 4 is given in Table 12.

a The melted metal is then transformed into an ingot, which is used to produce the Zircaloy-4 bars used to produce the cladding. Compositions are measured in three positions: on top, in the middle and at the bottom of the ingot.


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Table 12. Z10CN18.09 Stainless Steel Chemical Composition.

Element N Fe Cr C Si Cu Weight % 0.046 70.3674 18.51 0.08 0.7 0.36 Element Mn Ni P S Mo Co

Weight % 0.92 8.79 0.02 0.0026 0.15 0.054

Moderator and Reflecting Water A relatively recent analysis of water, which is used for array reflection and moderation, was carried out (February 18, 1999). Results are provided in Reference 1 and are reported in Table 13.

Table 13. Composition of Impurities in Moderating and Reflecting Water.

Element Concentration (μg/l) Element Concentration

(μg/l) Element Concentration (μg/l) Element Concentration

(μg/l) U 0.52 Cr < 25 Al 70 Zn 20

Hg < 1 Cu < 25 Sr 90 Ba 20 Cd < 3 Mg 2450 Pb < 25 As < 25 Ni < 25

NO3 21000 CO3 54000 SO4 14000 Cl 11000

Elements with content lower than 20 μg/l Li – B – Sc – V – Mn – Fe – Ni – As – Zn – Ge – Zr – Ru – Pd – In – Sb – Cs – La – Pr – Sm – Gd – Dy – Er –

Yb – Hf – W – Re – Au – Tl – U – Hg – Be – Ti – Cr – Co – Cu – Ga – Rb – Y – Nb – Mo – Rh – Ag – Cd – Sn – Te – Ce – Nd – Eu – Tb – Ho – Tm – Lu – Ta – Os – Pt – Th – Bi

Experiments were carried out at temperatures of 17 °C and 20 °C (Table 1). These temperatures were the mean values of measurements at different locations in the reflector. Other Structural Materials Characteristics Compositions of other materials are given in Tables 14 (Reference 1). Values for AG3M were measured values. For stainless steel Z2 CN18-10, only tolerance values were available.


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Table 14. Compositions of Other Materials.

Material Density (g/cm3)

Nuclides Weight % or Atomic Densities (1024/cm3)

Sn 0.01125 Fe 0.375 Cr 0.025 Si 0.31 Al 95.98125 Cu 0.045 Pb 0.01 Mn 0.23 Mg 2.92 Ni 0.01 Ti 0.035 Bi 0.0025

AG3M (basket grids and plates)

(Reference 1 pages 47, 48) 2.65

Zn 0.045 C < 0.03 Cr 18±1 Ni 10±1 Fe balance Mn ≤ 2 Si ≤ 1 S ≤ 0.03

Stainless Steel(a) (support pedestal and

experimental tank) Z2 CN18-10

(Reference 1, Table 2)

7.9

P ≤ 0.04

Concrete (cell hall)

(Reference 1, Table 1) 2.4013(c)

H 10B O Al Si Ca Fe

1.035 × 10-2 1.602 × 10-6 4.347 × 10-2 1.563 × 10-3 1.417 × 10-2 6.424 × 10-3 7.621 × 10-4

Air(b) Not mentioned

N O

4.1985 × 10-5 1.1263 × 10-5

C 4.16448 × 10-2 Polyethylene 0.97 H 8.32896 × 10-2

(a) Data comes from the AFNOR French standard. (b) A simplified air composition, calculated from the Handbook of Chemistry and Physics, 74th Ed.,

1993/1994, p. 14–12. (c) Calculated from atoms/barn-cm data. 10B content is an equivalent content, providing a neutron

absorption equal to that of the total of impurities in a same thermal flux (personal communication from P. Grivot).

It should also be noted that concrete walls are covered with a thin layer of paint, known as “washable and decontaminable,” with an unknown composition (possibly hydrogenated, vinyl, acrylic, heavy and/or any neutron-absorbing elements that might modify the boron equivalent composition).


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Polyethylene Blocks Polyethylene blocks used as a reflector in some experiments were fabricated in Germany. The density of these blocks was measured by the supplier and was announced as being 0.955 g/cm3 with an uncertainty of ± 0.05%. Since then, additional measurements were performed by Valduca to improve the precision of the measurement. These measurements led to a density value of 0.970 ± 0.002 g/cm3. No data related to impurities was provided. Analyses conducted on similar polyethylene showed that the boron content was less than 50 ppm (detection limit) and the chlorine content equal to 50 ppm. After a discussion with the experimentalists in which it was said that the fabrication process was such that boron and cadmium could not be present in significant quantities in the polyethylene blocks, it was assumed that the content of boron or cadmium was negligible. The H/C ratio in polyethylene was not measured but was not supposed to differ significantly from 2.000. 1.4 Supplemental Experimental Measurements No additional measurements were performed.

a Data communicated in a telecopy by L. Chiri and L. Le Manach (INB010QIN-X6602CR) on April, 21st 1999.


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2.0 EVALUATION OF EXPERIMENTAL DATA

The tight-packed lattice program involves 4.738 wt.% 235U-enriched UO2 rods. Before 1995, the fuel cladding of these rods was AGS (aluminium alloy). In 1995, the cladding was replaced by Zircaloy-4, with the prospect of the fission-products experimental program on Apparatus B at Valduc. Thus, measurements and chemical analyses on the fuel rods were performed (1995 to 2000).

Until 1995, the dimensions and uncertainties were mainly derived from the manufacturing process tolerances. As measurements are now available for numerous parameters, the corresponding data now take these measurements into account.

Moreover, the treatment of impurities of the different materials has also been reviewed. Impurities are modeled when they satisfy two conditions:

• They are detected

• Their effect on keff is not negligible.

Neither the model nor the uncertainty evaluation takes into account the detected impurities that have no effect on keff. Given their low reactivity worth, undetected impurities are assumed to be accounted for in the global uncertainty.

The pellet surplus was used for chemical analysis in Valduc and in the FBFC (Franco-Belge de Fabrication de Combustible) control laboratory in Romans (France).

Statistical Approach

The impact on reactivity of different uncertainties is evaluated through a statistical approach. Depending on the available data (measurements or fabrication tolerance), two different methodologies are used.

Evaluating the Uncertainty on Measurements

The uncertainty on a measured value is the (quadratic) sum of the experimental standard deviation (measurement dispersion) and the measurement accuracy (measurement device calibration).


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It should be noted that not all the rods used in the experiments were measured. During their recladding process, only a few were measured for some characteristics. According to the ICSBEP Uncertainty Guide, the uncertainty attributed to the experiment rods should be divided into three components:

• The uncertainty of the measurement sample.

• The sampling of rods used for the experiment. (The rods used for the experiment were randomly chosen from the 1261 inventory.)

• The sampling of measured rods (around 100).

Section C.12 in Appendix C of the ICSBEP Uncertainty Guide (attached to the 2007 Handbook) shows that for the first six cases the sampling uncertainty associated with the rods involved in the experiment is negligible. Nevertheless, this uncertainty is not negligible for Cases 7 to 9 (smaller pitch and fewer rods).

As a consequence, the sampling uncertainty needs to be considered.

Moreover, given that the number of measured values is almost sufficient to determine that the distribution is close to normal, it was decided to attribute the uncertainty of the measured population to the entire population of rods.

Evaluating the Uncertainty on Fabrication Tolerances

In the case of fabrication tolerances, the available data are a nominal value and bounds. A uniform law should be applied to model this tolerance (division by 2√3 to scale the bounds to one standard deviation).

Propagation of the Uncertainties in Terms of Δkeff

Uncertainty on Measurement Caution should be used when propagating the uncertainties in terms of Δkeff. In fact, the approach of applying the standard deviation to the perturbated calculation and then dividing the obtained Δkeff by the square root of n (number of rods in the array) to account for independent random variation of the parameter (according to its Gaussian distribution), could underestimate the result. It should be noted that a stochastic method could improve the knowledge on the reactivity weight of such uncertainty.

Calculations

The uncertainties were propagated to Δkeff by performing either APOLLO2 (CRISTAL V1 package) calculations, using the deterministic Sn method based on a simplified model (cylindrical array omitting some low-worth materials), or APOLLO2-MORET 4 Monte Carlo calculations (CRISTAL V1 package) using the correlated sampling method (MORET 4 perturbation) based on the benchmark model. When possible, a comparison was made between the two types of results. A good agreement was obtained. Summaries of uncertainties and their reactivity effects are presented at the end of Section 2 in Tables 19 through 25. It should be noted that this model was not retained as a benchmark model. In order to perform Sn calculations, the model was made cylindrical and simplified, the rod array being replaced by a homogeneous mixture, equivalent in terms of neutronic treatment. An APOLLO2 cell calculation was performed. The radius of the equivalent cylinder is given by the following formula:

R = pitch × N ¹ (N = number of rods in the array) It should be noted that this simplified model totally differs from the simplified model proposed in Section 3.


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The radii for all cases are reported in Table 15.

Table 15. Fuel Zone Diameter for Simplified Model.

Case Number

Fuel Zone Diameter (cm)

(Simplified Model)

Critical Height (cm)

1 15.346 60.479 2 14.443 91.523 3 14.888 71.836 4 15.346 56.293 5 14.443 81.616 6 14.888 65.765 7 20.480 69.431 8 19.859 81.854 9 21.228 82.227

Because of their low reactivity effect, we omitted zones above fissile columns, including:

• The spring zone • The top plugs • The upper grid • The basket top plate.

A bias is associated with the former simplified model. This bias is evaluated by running the benchmark model and the simplified model with APOLLO2-MORET 4 Monte Carlo code (Table 16) and determining the keff difference between these two calculations. On average (of the nine cases), the bias is assessed to be -0.014%. The bias is mainly due to the cylindrization. Given that the bias is quite low and because this bias does not affect the keff variation, most variation calculations are performed using the APOLLO2-Sn deterministic code based on the simplified model.

Table 16. Bias between Benchmark Model and Simplified Model Used for Uncertainty-Effect Calculations.

Code (Cross Section Set)→

Case Number↓

Benchmark Model APOLLO2-MORET 4 (172-group, CEA93V6)

keff ± 1σ JEF2.2

Simplified Model APOLLO2-MORET 4

(172-group, CEA93V6)

keff ± 1σ JEF2.2

Bias (pcm)

1 1.00219 ± 0.00030 1.00295 ± 0.00030 76 ± 42 2 1.00223 ± 0.00030 1.00165 ± 0.00030 -58 ± 42 3 1.00263 ± 0.00030 1.00280 ± 0.00030 17 ± 42 4 1.00398 ± 0.00030 1.00385 ± 0.00030 -13 ± 42 5 1.00251 ± 0.00030 1.00258 ± 0.00030 7 ± 42 6 1.00365 ± 0.00030 1.00248 ± 0.00030 -117 ± 42 7 0.99592 ± 0.00030 0.99604 ± 0.00030 12 ± 42 8 0.99660 ± 0.00030 0.99603± 0.00030 -57 ± 42 9 0.99516 ± 0.00030 0.99519 ± 0.00030 3 ± 42


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2.1 Material Data and Chemical Uncertainties

Isotopic Content of Uranium in UO2 Rods

Different reports provide the results of measurements performed over a period of 20 years (1978 to 1998). The latest measurement results are provided by FBFC (Franco-Belge de Fabrication de Combustible) and reported in Table 7. The retained isotopic composition is the mean of the two samples and is given in Table 17.

In order to evaluate the reactivity effect of this uncertainty, Monte-Carlo (MORET 4) perturbation calculations (using the correlated sampling method) were run with the fuels described in Table 18.

Table 17. Retained Isotopic Composition (1σ Uncertainties).

Element at.% wt.% 234U 0.03070 ± 0.0005 0.03020 ± 0.0005 235U 4.79525 ± 0.002 4.73760 ± 0.002 236U 0.13730 ± 0.0005 0.13620 ± 0.0005 238U 95.03675 ± 0.01 95.0959 ± 0.01

The uranium 1σ uncertainties of the isotopics from Table 17 are assumed to be representative of the rod population encountered in the experiments. As can be seen, the uncertainty of 238U is higher than the sum of uncertainties of other isotopes. No reason for that is given, but it seems reasonable to assume that 238U is overestimated. Either way, the impact of 238U isotopics’ uncertainty is negligible. A variation of ± 0.01% of 238U isotopics, keeping other isotopes constant, is calculated to be negligible.

Similarly, 234U and 236U isotopics are varied separately, keeping other isotopes constant. The uncertainties are also calculated to be negligible.

Then, 235U isotopics is varied in its uncertainty range. 234U and 236U isotopics remain constant. As the uranium vector needs to be normalized to keep the total amount of uranium constant, 238U variation is decreased by the same variation.

Table 18. Perturbations Calculation Parameters and Results.

Element Case 1 at.%

(%235U+variation)

Case 4 at.%

(%235U+variation)

Case 7 at.%

(%235U+variation)

Case 9 at.%

(%235U+variation) 234U 0.03070 0.03070 0.03070 0.03070 235U 4.79525 ± 0.01 4.79525 ± 0.01 4.79525 ± 0.01 4.79525 ± 0.01 236U 0.13730 0.13730 0.13730 0.13730 238U 95.03675 m 0.01 95.03675 m 0.01 95.03675 m 0.01 95.03675 m 0.01 Δkeff ± 0.046% ± 0.046% ± 0.033% ± 0.033%

The reactivity worth of the variation is ± 0.046% for Cases 1 and 4 and ± 0.033% for Cases 7 and 9. The variation results should be divided by 0.01/0.002. As a consequence, the retained 1σ uncertainty is ±0.009% for Cases 1 and 4 and ±0.007% for Cases 7 and 9.


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Stoichiometry

The retained value for the O/U stoichiometry is the 1998 measurement by FBFC, i.e., 2.000 ± 0.001 (1σ). The impact on reactivity worth of the uncertainty (± 0.001), calculated using the perturbation method, is negligible (<1pcm). As a consequence, the 1σ uncertainty is determined to be negligible. Oxide Density and Pellet Diameter In References 1, 4, and 5, it is stated that the density is equal to 10.38 ± 0.04 (3σ) g/cm3. A new value of uncertainty of uranium oxide density has been calculated in Appendix D and is ± 0.073 g/cm3 (1σ). It should be noted that the uncertainty is, in fact, the density dispersion obtained on 1261 rods. It includes the pellet heterogeneity and diameter dispersion of the fissile column, which varies from one rod to another. Actually, the model considers the same density (10.38 g/cm3) for all rods. This simplification is responsible for an uncertainty, which comprises two components:

• The uncertainty of the rod population, which is found to be ± 0.073 g/cm3 (1σ) and is assumed to be systematic.

• A sampling uncertainty because only N rods were randomly drawn from a population of N0 = 1261 available rods.

To propagate the 1σ uncertainty in terms of Δkeff, the density was varied by 0.204 g/cm3. The impact on reactivity worth of the variation on density is ± 0.283% for Case 1, ± 0.284% for Case 4, ± 0.092% for Case 7, and ± 0.067% for Case 9. The result is scaled to 1σ, yielding a 1σ uncertainty of ± 0.102% for Cases 1 and 4 and ± 0.033% for Case 7 and 0.024% for Case 9. A sampling uncertainty needs to be added to account for the fact that only some of the rods were used in the experiments. Following formula 12 given in Appendix C.12 of the Uncertainty Guide, this results in an additional uncertainty equal to σmean

2 = σ2 (N0-N)/N(N0-1) with N0 = 1261 and N = 289, 1089, or 1225. When propagated in terms of Δkeff, it leads to a 1σ uncertainty of 0.005% for Cases 1 and 4 and 0.001% for Cases 7 and 9. The 1σ uncertainty associated with the pellet diameter was assessed while keeping the fuel linear mass constant. As a consequence, the density needed to be corrected accordingly. The following formula was applied:

12

−⎟⎠⎞

⎜⎝⎛

Δ+=Δ

RRR

ρρ

The uncertainty of the measured pellet diameter is measured to be 0.00176 cm (1σ). However, the precision of the measuring device (palmer) being +/-0.0005 cm, this systematic uncertainty is calculated to be predominant. A MORET 4 perturbation calculation is performed for 0.004 cm variation of the pellet diameter. The corresponding density variation is ± 0.104 g/cm3. The Δkeff result is 0.034% for Cases 1, 4, 7 and 9. This result is then scaled to 1σ. As a consequence, the impact of 1σ uncertainty in terms of reactivity is found to be equal to 0.085%. Two sampling uncertainties need to be added to account for the fact that only some of the rods were used in the experiments and that only some of the pellet diameters were measured.


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Following formula 12 given in Appendix C.12 of the Uncertainty Guide, this results in the following:

• An additional uncertainty equal to σmean2 = σ2 (N0-N)/N(N0-1) with N0 = 1261 and N = 289, 1089 or

1225 for the sampling of rods • An additional uncertainty equal to σmean

2 = σ2 (N0-N)/N(N0-1) with N0 = 1261 and N = 53 for the sampling of measurements.

When propagated in terms of Δkeff, it leads to a global 1σ uncertainty of 0.086% for Cases 1 to 9.

Oxide Impurities

The fuel also contains impurities. In 2000, impurity analyses were performed on available pellets; the results are provided in Appendix E. Except for three impurities of specifically measured content (Al = 18 ppm, Fe = 85 ppm, and Si = 101 ppm, ppm being the ratio of impurity weight to oxide weight in units of 10-6), the given values correspond to the measurement limit of the apparatus. The total impurity content (except Al, Fe, and Si) taken at the limit of detection is equivalent to 1.21 × 10-6 g of Bnat/g of oxide. Multiplying this value by the density (10.38 g/cm3) gives 12.56 ×10-6 g/cm3 equivalent boron. Because this value corresponds to the maximum, half is retained in the UO2 and half is considered as an uncertainty with an equiprobable distribution (σ√3). It is to be noted that the detected impurities are included in the model, and no uncertainty is associated with their concentration.

The effect on keff by the undetected impurities is evaluated through a sensitivity calculation with MORET 4 perturbation module based on the correlated sampling method. The calculation is made with all the undetected impurities at their detection limit. This uncertainty is considered to be a bounding Type-B uncertainty. The impurity content is assumed to vary with a uniform parameter distribution. Therefore, the uncertainty is divided by √3 to scale the bounds to one standard deviation. The impact on reactivity worth of the undetected impurities is 0.029%. As a consequence, the 1σ uncertainty is found to be 0.017%.

Zircaloy-4 Density and Impurities

According to experimenters, the last digit of density value is significant. Thus, the corresponding uncertainty is ± 0.005 g/cm3, i.e., σ = 0.0029 g/cm3, if the uniform-probability hypothesis is assumed. The effect on keff

of the variation of ± 0.005 g/cm3 leads to a keff variation of ± 0.002% for Cases 1, 4, 7, and 9, respectively. The 1σ uncertainty is calculated to be negligible (1·10-5) for all cases.

The impact on reactivity worth of the perturbation on undetected impurities is 0.012% for Cases 1 and 4 and 0.018% for Cases 7 and 9. The result should be divided by √3 (they are considered as tolerance values). As a consequence, the retained 1σ uncertainty is ± 0.007% for Cases 1 and 4 and ± 0.010% for Cases 7 and 9.

Spring

As the neutron influence of the springs is quite low, no perturbation calculations have been made concerning the composition and dimension uncertainties.


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Water Impurities

The effect of water impurities has been assessed for Cases 1 through 9 by the difference between a model without impurity and a model where the impurity concentrations are 1,000 times higher than the concentrations provided in the basic report (Reference 1). The calculated reactivity effect is lower than 0.001% for Cases 1 through 9. Consequently, water impurities were not considered further.

Water Density Value The temperature of the experiments (for density of moderating and reflecting water) is assumed to be 20°C. For this temperature, the corresponding water density from the Handbook of Chemistry and Physics is 0.99820 g/cm3.

No water density uncertainty was reported; thus, a maximum measurement uncertainty of 0.1% (corresponding to ± 5°C) was assumed. The effect of a 1% variation of the water density is evaluated by performing a MORET 4 perturbation calculation that uses the correlated sampling method. The variation (± 1%) results in a keff variation of 0.349% for Case 1, 0.310% for Case 4, 0.344% for Case 7, and 0.338% for Case 9. The uncertainty is a bounding Type-B uncertainty. The variation is then scaled to the total uncertainty and divided by √3 to scale the bounds to one standard deviation. The corresponding Δkeff value is 0.020% for Case 1, 0.018% for Case 4, and 0.020% for Cases 7 and 9. AG3M Density No uncertainty value is provided for AG3M density in the experimental reports. As a consequence, one half of the last digit is retained (0.005 g/cm3).

The effect of the variation of 0.005 g/cm3 on the AG3M density is evaluated by performing a MORET 4 perturbation calculation that uses the correlated sampling method. The variation (± 0.005 g/cm3) results in a keff variation of 0.0002% for Case 1, 0.0003% for Case 4, and 0.0001% for Cases 7 and 9. The variation is a bounding Type-B uncertainty. The variation is then divided by √3 to scale the bounds to one standard deviation. The retained 1σ uncertainty value of keff is 0.0001% for Cases 1 through 9 and is considered as negligible. Stainless Steel Density (Z2 CN18/10)

The stainless steel density is given as 7.9 g/cm3. No uncertainty value is provided for stainless steel in the experimental reports. As a consequence, one half of the last digit is retained (0.05 g/cm3).

The effect of the variation of 0.05 g/cm3 on the stainless steel density is evaluated by performing a MORET 4 perturbation calculation that uses the correlated sampling method. The variation (± 0.05 g/cm3) results in a keff variation of ± 0.002% for Cases 1 and 4 and ± 0.001% for Cases 7 and 9. It is a bounding Type-B uncertainty. The result is then scaled to 1σ and divided by √3. The retained 1σ keff uncertainty value is 0.001% for Cases 1 and 4 and is considered negligible for Cases 7 and 9.


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Stainless Steel Impurities The stainless steel specifications are given in Reference 1. Chromium, nickel, manganese, and silicon contents are given with an uncertainty value. A MORET 4 calculation using the correlated sampling method is performed to propagate these uncertainties in terms of Δkeff. The variations result in a keff variation of ± 0.001% for Cases 1, 4, 7, and 9. The uncertainty is a bounding Type-B uncertainty. The result is then scaled to 1σ and divided by √3. As a consequence, the 1σ uncertainty is ± 0.001%. Polyethylene Blocks Polyethylene block density is given as 0.970 g/cm3. Half the last significant digit is taken as an uncertainty. The effect of the variation of 0.005 g/cm3 on the polyethylene density is evaluated by performing a MORET 4 perturbation calculation that uses the correlated sampling method. The variation (± 0.005 g/cm3) results in a keff variation of ± 0.008% for all cases with a CH2 reflector. It is a bounding Type-B uncertainty. The result is then scaled to 1σ and divided by √3, which leads to a 1σ uncertainty of ± 0.005%. A 0.01 uncertainty (1σ) in the H/C ratio in polyethylene was retained. It led to a 0.001% Δkeff. Analyses conducted on different polyethylene showed that the boron content was less than 50 ppm (value under the detection limit), the chlorine content was equal to 35 ppm, and the fluorine content was equal to 10 ppm. The experimentalists indicated that the polyethylene used in the experiments should not contain any boron (content less than 1 ppm). Further analyses are scheduled for 2009. Given that the impurities in the polyethylene blocks used in the experiments were not measured but impurities for similar blocks were reported (fluorine, chlorine), they were not retained in the model but are accounted in the uncertainties. Their effect on reactivity was calculated to be less than 0.005%. 2.2 Physical Uncertainties Water Height

The uncertainty on the measured critical water heights is said to include the following:

• Statistic uncertainty: accuracy of the height-measuring equipment and the counting equipment

• Experimental uncertainty: basket position in the tank and deformation due to the fuel weight (repeatability measurements were performed for experiments with a polyethylene reflector; the polyethylene reflector was removed and then repositioned)

• Method uncertainty: accuracy of the extrapolation to zero of the inverse count rate.

The uncertainty on the measured critical heights reported in Tables 1 to 4 is given with a level of confidence of 95.45% (2σ).

Tables 1 to 4 give the uncertainty for each experiment, and they are also provided in the experimental report (Reference 1); these uncertainties are of statistical and methodological origin.

The effect on keff of the uncertainty on critical height is evaluated by the difference between two APOLLO2-MORET 4 calculations with a small standard deviation (σcalc < 0.005%).

Several calculations highlighted that the reactivity effect depends on the critical height itself, with a decreasing trend with increasing critical height.


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The impact on the reactivity worth of the variation (± 0.5 cm) on critical heights is 0.073% for Case 1, 0.082% for Case 4, 0.056% for Case 7, and 0.031% for Case 9. The result should be scaled to 1σ. As a consequence, the retained 1σ uncertainty is ± 0.002% for Case 1, ± 0.003% for Case 4, ± 0.002% for Case 7, and ± 0.001% for Case 9. Temperature

The temperature uncertainty value was not reported in experimental reports. A value of ± 2°C is then retained. A ± 5°C variation was applied, which, consequently, modified the water density. The impact on keff of this variation was ± 0.041% for Case 1, ± 0.031% for Case 4, ± 0.033% for Case 7, and ± 0.039% for Case 9.

The result was then scaled to 1σ dividing by 5 ⋅ 32

. The retained 1σ uncertainty is 0.009% for Case 1,

0.007% for Case 4, 0.008% for Case 7, and 0.009% for Case 9. Fissile Column Height A 1σ uncertainty of ± 0.254 cm is retained. Two independent APOLLO2-MORET 4 calculations with a low standard deviation were performed to assess the impact of a variation of ± 0.508 cm of the fissile column height. The Δkeff variation was negligible for Cases 1 and 4 and equal to 0.016% for Cases 7 and 9. The result is scaled to 1σ and divided by N (N = 289, 1089, or 1225); the retained 1σ uncertainty is negligible.

Cladding Dimensions Table 2 gives the measured values plus the standard deviation (1σ) for all parameters except for the clad inner diameter, for which only the specification value is given. Perturbation calculations on each parameter have been carried out. A variation of 0.002 cm on the clad inner diameter was applied to Cases 1, 4, 7, and 9. The uncertainty is considered to be a bounding Type-B uncertainty with a uniform distribution. The impact on keff of this variation was ± 0.008% for Cases 1 and 4 and ± 0.011% for Cases 7 and 9. The result was then scaled to 1σ and divided by √3. The retained 1σ uncertainty is 0.011% for Cases 1 and 4 and 0.016% for Cases 7 and 9. The uncertainty of the outer clad diameter is measured to be 0.000439 cm (1σ), which is the same order as the precision of the measuring device (the palmer, the precision being +/-0.0005 cm); this systematic uncertainty is calculated to be predominant. MORET 4 perturbation calculations were run, varying the outer clad diameter by 0.004 cm. The Δkeff value obtained was ± 0.084% for Case 1, ± 0.080% for Case 4, ± 0.370% for Case 7, and ± 0.406% for Case 9. The result was then scaled to 1σ. The retained 1σ uncertainty value is 0.011% for Cases 1 and 4 and 0.046% for Case 7 and 0.051% for Case 9.


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Two sampling uncertainties need to be added to account for the fact that only some of the rods were used in the experiments and that only some of the rods diameters were measured. Following formula 12 given in Appendix C.12 of the Uncertainty Guide results in the following:

• An additional uncertainty equal to σmean2 = σ2 (N0-N)/N(N0-1) with N0 = 1261 and N = 289, 1089, or

1225 for the sampling of rods, σ being the value obtained on 300 measurements assumed valid for the whole set of rods

• An additional uncertainty equal to σmean2 = σ2 (N0-N)/N(N0-1) with N0 = 1261 and N = 300 for the

sampling of measurements.

When propagated in terms of Δkeff, it leads to a global 1σ uncertainty of 0.0111% for Cases 1 and 4, 0.046% for Case 7 and 0.051% for Case 9. Rod Positioning

Rods are carefully placed and experimenters visually check their alignment in the two horizontal, perpendicular directions. It was also checked that the rods were perfectly straight. The rods were installed into the grid, employed for the tight packed lattice program, and observed outside the tank. It was seen that the array was aligned in such a way that light should pass through the rows. There were no visible rod deviations.

Four sources of uncertainty associated with rod positioning are considered:

(1) The hole position uncertainty due to error in adjustment of the hole-piercing device. For the grids employed in the experiments, the holes were drilled with numeric command. No measurements of the pitch have been performed for these grids. From a conversation with the experimentalists, the uncertainty was set equal to 0.001 cm.

(2) The rod positioning uncertainties due to the space between the rod’s clad and the hole are the following: ±0.0407 cm for the hole diameter 0.99 cm (0.99-0.949245 =0.0407). This uncertainty is assumed to be random. It follows an equiprobable distribution; therefore, 1σ = 0.0407/√3 = 0.0235.

(3) It is adopted that the uncertainty on the hole diameter is less than 1×10-2 cm. No measurements were performed for the tight packed lattice grids. But some diameters were measured for another grid in 2000 that was made in the same years but used for another programme. It is a grid of 19 × 19 holes with a 2.1-cm pitch. Fifty measurements of diameter and pitch were performed with a cathetometer in 2000. The result of the measurement was as follows: 1.0105+/-0.0085 (1σ) cm.

(4) The rod outer clad diameter uncertainty is ± 0.000878 cm (1σ).

Sensitivity analysis shows that the rod positioning uncertainty due to the space between the rod clad and the hole (item 2) is the main contributor to the overall uncertainty originated from the pitch. The other three components are recognized as negligible. It is also shown in LEU-COMP-THERM-027. The uncertainty associated with it is a bounding Type-B uncertainty. The gap must be divided by √3 to obtain the 1σ uncertainty (equiprobable distribution). The 1σ uncertainty is calculated to be (0.99-0.949245)/√3 = 0.0235 cm for Cases 1 and 4. As a consequence, the retained uncertainty on the pitch is 0.0235 cm at the 1σ level. The variation applied on the pitch is 0.04 cm (Cases 1 and 4) and 0.004 cm (Cases 7 and 9) and is calculated through two Monte-Carlo APOLLO2-MORET 4 calculations. The result of the variation is 0.177% for Case 1, 0.192% for Case 4, 0.329% for Case 7, and 0.375% for Case 9. The effect on keff on the variation is


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then scaled to 1σ and divided by √N (number of rods in the array: 289, 1089, or 1225). The retained uncertainty is 0.006% for Cases 1 and 4, 0.057% for Case 7, and 0.062% for Case 9. Positioning of Polyethylene Shields

The uncertainty of the polyethylene block positioning is not known. However, the uncertainty of polyethylene shield placement can be accounted for as an uncertainty on the critical height. Nine repeated experiments were performed with this particular aim (the polyethylene blocks and rods were removed and then reassembled). It was shown that this resulted in an uncertainty of ±0.43 cm on the critical height.

As a consequence, two APOLLO2-MORET 4 calculations were performed varying the water level by 0.5 cm. They resulted in a Δkeff of 0.082% for Case 4, 0.056% for Case 7, and 0.031% for Case 9. The result needs to be scaled to 1σ. As a consequence, the retained uncertainty is 0.071% for Case 4, 0.048% for Case 7, and 0.029% for Case 9. With regard to sensitivity of keff to shield positioning in centimeters, Cases 7 and 9 were calculated, by increasing the distance between the array and the four CH2 blocks by +0.1 cm, and then decreasing it by -0.1 cm. For both cases, the calculated Δkeff’s of the 0.2-cm variation were less than the Monte Carlo statistical uncertainty of the calculation, 0.00020. Therefore a ±0.1-cm uncertainty results in a negligible Δkeff.


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Table 19. Material Uncertainties.

Parameter Identification Mean Value

Reported Uncertainties in

Parameter

Type of Uncertainty

(A or B)

ν Number of Degrees of Freedom

Number of Standard Deviations Associated

with the Uncertainty

Standard Deviation

(1σ)

Uranium Isotopic Contents (at.%):

234U 235U 236U 238U

0.0307 4.79525 0.1373

95.03675

0.001 0.004 0.001 0.02

A ∞ 2

0.0005 0.002 0.0005 0.01

Density (g/cm3) 10.38 0.04 A ∞ 1 0.073 UO2 Undetected Impurities (eq.

boron in g/cm3) 6.28.10-6 100% B ∞ √3(a) 100/√3

Water Density (g/cm3) 0.998 0.1% B ∞ √3(a) 0.1/√3 Water Impurities 0 100% B ∞ √3(a) 100/√3

Stainless Steel Density (g/cm3) 7.9 0.05 B ∞ √3(a) 0.05/√3 Stainless Steel Content (Cr) 18% 1% B ∞ √3(a) 1/√3 Stainless Steel Content (Ni) 10% 1% B ∞ √3(a) 1/√3 Stainless Steel Content (Si) 0.5% 0.5% B ∞ √3(a) 0.5/√3

Stainless Steel Content (Mn) 1% 1% B ∞ √3(a) 1/√3 AG3M Density (g/cm3) 2.65 0.005 B ∞ √3(a) 0.005/√3

Zircaloy-4 Density (g/cm3) 6.55 0.005 B ∞ √3(a) 0.005/√3 Zircaloy-4 Impurities 0 100% B ∞ √3(a) 100/√3

O/U Ratio 2.000 0.001 A ∞ 1 0.001 Polyethylene Density (g/cm3) 0.97 0.005 A ∞ 1 0.005

Polyethylene H/C content 2 0.01 A ∞ 1 0.01 Polyethylene impurities (ppm) 35 35 B ∞ √3(a) 35/√3

Water Temperature (°C) 20 2 B ∞ √3(a) 2/√3 (a) The number of standard deviations associated with the uncertainty was not reported; thus, a uniform

distribution is assumed.


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Table 20. Physical Uncertainties.

Parameter Identification (cm)

Mean Measured

value

Reported Uncertainties in Parameter

Type of Uncertainty

(A or B)

ν Number of Degrees of Freedom

Number of Standard Deviations Associated

with the Uncertainty

Standard Uncertainty

Fuel Pellet Diameter - measurement 0.78919 0.00176 A 52 1 0.00176

Fuel Pellet Diameter - systematic 0.78919 0.005 A ∞ 1 0.005

Fissile Column Height 89.765 0.254 A 1260 1 0.254 Clad Outer Diameter - measurement 0.949245 0.000439 A 299 1 0.000439

Clad Outer Diameter - systematic 0.949245 0.0005 A ∞ 1 0.0005

Clad Inner Diameter 0.836 0.005 B ∞ √3(a) 0.005/√3 Rod Height 102.082 0.04 A ∞ 1 0.04 Critical Water Height: • Array 17 × 17 pitch 1.1 • Array 16 × 16 pitch 1.1 • Array 16 × 17pitch 1.1 • Array 17 × 17 pitch 1.1 • Array 16 × 16 pitch 1.1 • Array 16 × 17pitch 1.1 • Array 33 × 33 pitch 1.075 • Array 32 × 32 pitch 1.075 • Array 35 × 35 pitch 1.075

60.479 91.523 71.836 56.293 81.616 65.765 69.431 81.854 82.227

0.022 0.030 0.020 0.038 0.055 0.029 0.030 0.038 0.028

A None 2

0.011 0.015 0.010 0.019 0.027 0.014 0.015 0.019 0.014

Rod location 1.6, 1.1 or 1.075 0.023 A N-1 1 0.023

Polyethylene Shield Positioning 0.43 A None 1 0.43

(a) The number of standard deviations associated with the uncertainty was not reported; thus, a uniform distribution is assumed.

2.3 Reactivity Sensitivity Calculations Sensitivity calculations are carried out with either APOLLO2-MORET 4 (correlated sampling method) or APOLLO2 (a multigroup cell code) by using the Sn-2D method. The uncertainty effect on keff is determined directly through a correlated sampling method or by comparing the difference of two APOLLO2 Sn-2D calculations of an equivalent cylindrical model of the experiment, the array being replaced by a neutronic-equivalent homogeneous mixture calculated with APOLLO2.


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Table 21. Results of Sensitivity Calculations, Case 1.

Case Pitch (cm) Parameter Identification

Parameter Variation in Calculation

Δkeff × 105

Reported Uncertainty

in Parameter

Standard Deviation of

Experimental Parameter

Δkeff × 105

235U Enrichment (At.%) 0.01 46 0.004 0.002 15 Undetected Impurities in UO2 (%) 100 29 100 100/√3 17 Water Impurities (%) 100 0 100 100/√3 negligible Fuel Density (g/cm3) with a Constant Fuel Pellet Diameter - systematic 0.204 283 0.073 0.073 102

Fuel Pellet Diameter (cm) with a Constant Linear Mass - systematic 0.004 34 0.005 0.005 43

Clad Outer Diameter (cm) - systematic 0.004 84 0.0005 0.0005 11

Clad Inner Diameter (cm) 0.002 8 0.005 0.005/√3 11 Rod location (cm) 0.04 177 0.023 0.023/√289 6 Critical Water Height (cm) 0.5 73 0.022 0.011 2 Temperature (°C) 2 41 5 2/√3 9 Fissile Column Height (cm) 0.508 0 0.508 0.254 negligible ρwater (g/cm3) 1% 349 0.1% 0.1/√3 20 ρag3m (g/cm3) 0.05 2 0.005 0.005/√3 negligible ρZr (g/cm3) 0.05 2 0.005 0.005/√3 negligible Zr Impurity (%) 100 12 100 100/√3 7 Steel Cr Content (%) 1 1 1 1/√3 negligible Steel Ni Content (%) 1 1 1 1/√3 negligible Steel Si Content (%) 0.5 1 0.5 0.5/√3 negligible Steel Mn Content (%) 1 1 1 1/√3 negligible ρsteel (g/cm3) 0.05 2 0.05 0.05/√3 1

1 1.6

O/U Ratio 0.001 0 0.001 0.001 negligible


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Parameter Variation in Calculation

Δkeff × 105


in Parameter

Standard Deviation of Experimental

Parameter Δkeff × 105




Clad Inner Diameter (cm) 0.002 8 0.005 0.005/√3 11 Rod location (cm) 0.04 192 0.023 0.023/√289 6 Critical Water Height (cm) 0.5 82 0.038 0.019 3 Temperature (°C) 2 31 2 2/√3 7 Fissile Column Height (cm) 0.508 0 0.508 0.254 negligible ρwater (g/cm3) 1% 310 0.1% 0.1/√3 18 ρag3m (g/cm3) 0.05 3 0.005 0.005/√3 negligible ρZr (g/cm3) 0.05 3 0.005 0.005/√3 negligible Zr impurity (%) 100 12 100 100/√3 7 Steel Cr Content (%) 1 1 1 1/√3 negligible Steel Ni Content (%) 1 1 1 1/√3 negligible Steel Si Content (%) 0.5 1 0.5 0.5/√3 negligible Steel Mn Content (%) 1 1 1 1/√3 negligible ρsteel (g/cm3) 0.05 2 0.05 0.05/√3 negligible ρCH2 (g/cm3) 0.005 8 0.005 0.005/√3 5 Polyethylene impurities (ppm) 35 5 35 35/√3 3 Polyethylene H/C ratio 0.1 107 0.01 0.01 11 O/U ratio 0.001 0 0.001 0.001 negligible

4 1.6

Shield positioning 0.5 82 0.43 0.43 71


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Parameter Variation in Calculation Δkeff × 105


in Parameter






Clad Inner Diameter (cm) 0.002 11 0.005 0.005/√3 16 Rod location (cm) 0.004 329 0.023 0.023/√1089 57 Critical Water Height (cm) 0.5 56 0.030 0.015 2 Temperature (°C) 2 33 2 2/√3 8 Fissile Column Height (cm) 0.508 16 0.508 0.254 negligible ρwater (g/cm3) 1% 344 0.1% 0.1/√3 20 ρag3m (g/cm3) 0.05 1 0.005 0.005/√3 negligible ρZr (g/cm3) 0.05 2 0.005 0.005/√3 negligible Zr impurity (%) 100 18 100 100/√3 10 Steel Cr Content (%) 1 1 1 1/√3 negligible Steel Ni Content (%) 1 1 1 1/√3 negligible Steel Si Content (%) 0.5 1 0.5 0.5/√3 negligible Steel Mn Content (%) 1 2 1 1/√3 negligible ρsteel (g/cm3) 0.05 1 0.05 0.05/√3 negligible ρCH2 (g/cm3) 0.005 8 0.005 0.005/√3 5 Polyethylene impurities (ppm) 35 5 35 35/√3 3 Polyethylene H/C ratio 0.1 107 0.01 0.01 11 O/U ratio 0.001 0 0.001 0.001 negligible

7 1.1



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Parameter Variation in Calculation Δkeff × 105


in Parameter






Clad Inner Diameter (cm) 0.002 11 0.005 0.005/√3 16 Rod location (cm) 0.004 375 0.023 0.023/√1225 62 Critical Water Height (cm) 0.5 31 0.028 0.014 1 Temperature (°C) 2 39 2 2/√3 9 Fissile Column Height (cm) 0.508 16 0.508 0.254/√1225 negligible ρwater (g/cm3) 1% 338 0.1% 0.1/√3 20 ρag3m (g/cm3) 0.05 1 0.005 0.005/√3 negligible ρZr (g/cm3) 0.05 2 0.005 0.005/√3 negligible Zr impurity (%) 100 18 100 100/√3 10 Steel Cr Content (%) 1 1 1 1/√3 negligible Steel Ni Content (%) 1 1 1 1/√3 negligible Steel Si Content (%) 0.5 1 0.5 0.5/√3 negligible Steel Mn Content (%) 1 2 1 1/√3 negligible ρsteel (g/cm3) 0.05 1 0.05 0.05/√3 negligible ρCH2 (g/cm3) 0.005 8 0.005 0.005/√3 5 Polyethylene impurities (ppm) 35 5 35 35/√3 3 Polyethylene H/C ratio 0.1 107 0.01 0.01 11 O/U ratio 0.001 0 0.001 0.001 negligible

9 1.075


Table 25. Quadratic Total: Δkeff × 105.

Case Quadratic Total (1σ) Quadratic Total (3σ) 1 117 351 4 137 411 7 110 330 9 104 312

The quoted uncertainties for Case 1 were applied to Cases 2 and 3 because the array square pitches were the same. The uncertainties for Case 4 were applied to Cases 5 and 6 and the uncertainties for Case 7 were applied to Case 8. Note that the critical water height did not have an important effect on the global uncertainty.


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3.0 BENCHMARK SPECIFICATIONS 3.1 Description of Model The benchmark-model geometry is shown in Figures 8 and 9. Model simplifications are described below. Due to the large amount of water around the core and the small reactivity effect of the rods above the water, the concrete room and the steel tank walls are omitted. Moreover, for the benchmark model, the fuel-rod springs are not considered because they are not significant in terms of reactivity. The dimensions of the lower grid are 30.6 cm × 30.6 cm with a thickness of 0.4 cm for Cases 1 to 6, 43.5 cm × 43.5 cm with a thickness of 0.4 cm for Cases 7 and 8, and 42.625 cm × 42.625 cm with a thickness of 0.4 cm for Case 9. The dimensions of the upper grid are 50 cm × 50 cm (instead of 95 cm × 95 cm) with a thickness of 0.6 cm for all cases. The bottom and top basket plate dimensions are 95 cm × 95 cm with a thickness of 1.2 cm. Rod plugs can also be replaced by cylinder-shaped plugs for calculation: the bottom plug is replaced by a 1.18-cm-high cylinder by keeping the mass, and the top plug is replaced by a 1.468-cm-high cylinder, both with 0.949-cm diameter. The impact on reactivity of such simplifications is negligible. The description of polyethylene blocks has been intentionally simplified. In particular, the structure and wedges supporting these blocks are made of AG3M and filling completely the space between the basket bottom plate and polyethylene block. The impact of this assumption in terms of reactivity is negligible. It should be noted that some impurities in uranium oxide rods are indicated under the detection limit of the measuring device. A calculation was run to assess their reactivity worth. A Δkeff of 0.058% was found. As recommended in the ICSBEP Uncertainty Guide, half of these impurities was modeled. The other half was accounted for in the global uncertainty. Some zones comprising several materials have a low impact on reactivity; as a consequence, their materials can be homogenized. These materials are described in Appendix C. They are the following:

• Bottom plug in water • Grid, bottom plug, and water • Clad in air corresponding to the spring zone • Grid, clad, spring in air • Top plug in air.

The homogenization process is described in Appendix C. Because the effects of homogenization have not been thoroughly evaluated, the models with homogenized zones are not benchmark models.


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3.2 Dimensions The model comprises the following:

• The support pedestal, reduced to the Z2 CN18-10 stainless steel support plate, 150 cm × 150 cm and 3.5 cm thick

• The water inside and around the fuel array up to the critical level • The water 17.5 cm thick beneath the support plate • The bottom and top basket plates, 95 cm × 95 cm, 1.2 cm thick, of AG3M aluminium alloy, 107 cm

apart • The array of fuel rods, whose characteristics are given in Table 26 and in Figures 8, 9, and 12 • The lower and upper grids of AG3M aluminium alloy, 96.5 cm apart. Holes in the bottom grid (one

for each fuel rod) have diameter 0.99 cm. Holes in the upper grid are the same diameter as the fuel rod.

• The air • The polyethylene reflector, 19.6 cm thick and 91 cm high, in its 94.9-cm-high AG3M structure.

The bottom piece of the AG3M structure of the reflector block rests on the AG3M bottom plate of the basket. The bottom of the polyethylene is aligned with the top of the lower grid plate. The horizontal dimensions of the top and bottom pieces of the AG3M structure are the same as that of the polyethylene reflector (58.8 x 19.6 cm). The 4 reflector blocks (CH2 + metal structure) are each 58.8 cm wide, 94.9 cm high, and 19.6 cm thick. The polyethylene parts of the blocks are 58.8 cm wide, 91.0 cm high, and 19.6 cm thick. The blocks are arranged as shown in Figure 10 and described in Table 27. Two external pieces of the AG3M structure (5 cm wide and 1 cm thick) are located on the larger sides of each reflector block, in contact with the water reflector, as shown in Figures 10 and 11. AG3M internal pieces (5 cm wide and 1 cm thick) are located on the smaller sides and centered.a The dimensions retained for the model are given in Figures 8 to 11 and in Tables 26 and 27. Water critical heights (Hc) and other dimensions are given in Table 27. The fuel-rod dimensions are in Table 26 and in Figures 8 and 9.

a When internal AG3M pieces were replaced by polyethylene and external pieces were replaced by air, the calculated effect was only -0.00010. Nevertheless, the AG3M internal and external pieces are retained in the benchmark model.


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Table 26. Geometrical Data of Fuel Rods.

Fuel Diameter 0.789 cm

Clad Inner Diameter 0.836 cm

Clad Outer Diameter 0.949 cm

Fissile Column Height 89.765 cm

Rod Height(a) 102.082 cm

Bottom Plug Height(a) 1.18 cm

Top Plug Height(a) 1.468 cm

Spring Zone Height 9.049 cm (a) Plugs have been replaced by cylinder-shaped plugs.

Table 27. Pitch, Array Size, Distance between Array and CH2, Bottom Grid Dimensions, and Critical Heights for Benchmark Model.

Case Number

Pitch (cm)

Rods Along Edge

Number of Rods

Bottom Grid Horizontal Dimensions

(cm)

Distance between array

and CH2 (cm)(a)

Water Critical Height (cm)(b)

1 1.6 17 × 17 289 30.6 x 30.6 - 60.479 2 1.6 16 × 16 256 30.6 x 30.6 - 91.523 3 1.6 16 × 17 272 30.6 x 30.6 - 71.836 4 1.6 17 × 17 289 27.2 x 27.2 0.8 56.293 5 1.6 16 × 16 256 25.6 x 25.6 0.8 81.616 6 1.6 16 × 17 272 25.6 x 27.2 0.8 65.765 7 1.1 33 × 33 1089 36.59 x 36.59 0.695 69.431 8 1.1 32 × 32 1024 35.49 x 35.49 0.695 81.854 9 1.075 35 × 35 1225 37.94 x 37.94 0.695 82.227

(a) Distance between internal face of polyethylene shield and grid hole center of the first rod row. For Cases 4 – 6, the value is 0.305 + ½Ф, where Ф is the diameter of the holes in the bottom grid (0.99 cm). For Cases 7 – 9, the value is 0.2 + ½Ф.

(b) Measured from the bottom of the fissile column.


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Bottom grid

Bottom plate (AG3M)

Pedestal (Steel plate)3.5

1.2

0.4

Hc

Bottom plate AG3M (95 x 95 x 1.2)

Steel plate (150 x 150 x 3.5)

Top plate AG3M (95 x 95 x 1.2)

Top grid AG3M (50 x 50 x 0.6)

Air

Water

150

17.595 cm

Bottom grid AG3M (30.6 x 30.6 x 0.4)

14096.5

1.8

109.4

Detail A

89.765

Top plug (Zr4)

Bottom plug (Zr4)

Void

Fuel (UO )2

Clad (Zr4)

1.18

Dimensions in cm

9.049

1.468

1.18

08-GA50017-179-1

Detail A

Figure 8. Benchmark Description, Elevation View, Cases 1 to 3.


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Bottom plate AG3M (95 x 95 x 1.2)

Steel plate (150 x 150 x 3.5)

Top plate AG3M (95 x 95 x 1.2)

Top grid AG3M (50 x 50 x 0.6)

Air

150

17.5

95

Metallic structure AG3M (58.8 x 19.6 x 2.1)

140

109.4

Detail A

Water

19.6

Bottom grid AG3M (thickness = 0.4)*

08-GA50017-179-2

89.765

Top plug (Zr4)

Bottom plug (Zr4)

Void

Fuel (UO 4.738 wt. %)2

Clad (Zr4)

9.049

1.468

1.18

Bottom grid

Bottom plate

Pedestal3.5

1.2

0.41.181.8

Metallic structure AG3M (58.8 x 19.6 x 1.8)

Hc

96.5

Polyethylene reflector (58.8 x 19.6 X 91)

Dimensions in cm

Detail A* See Table 27 for horizontal dimensions

Figure 9. Benchmark Description, Elevation View, Cases 4 to 9.


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5119.6 CH block2

AG3M

58.8

19.6Dimensions in cm08-GA50017-180-1

Figure 10. Polyethylene Reflector Blocks, Horizontal Section View.


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55

19.6

CH block2

AG3M

Dimensions in cm08-GA50017-180-2

AG3M

94.9

2.1

1.8

AG3M

91

Figure 11. Polyethylene Reflector Block, Elevation View.


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Array 16 × 16: 256 rodsSquare pitch: 1.6 cm

Case 1:

Array 17 × 17: 289 rods

Square pitch: 1.6 cm

Case 2:

Critical height: 60.479 cm

Array 16 × 17: 272 rods



Case 3:

08-GA50017-181-1


Figure 12.a. Section View of Configurations.


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Case 5:

Array 16 × 16: 256 rods



Case 6:

Array 16 × 17: 272 rods


Critical height: 65.765 cm 08-GA50017-181-2


Case 4:

Array 17 × 17: 289 rods


Figure 12.b. Section View of Configurations.


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Case 7:

Array 33 × 33: 1089 rods



Case 8:

Array 32× 32: 1024 rods



Case 9:

Array 35 × 35: 1225 rods


Critical height: 82.227 cm 08-GA50017-181-3

Figure 12.c. Section View of Configurations.


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3.3 Material Data Material data are derived from Tables 7 through 14. Atom densities are given in Table 28.

Table 28. Atom Densities for Basic Materials (atom/barn-cm).

Material Isotope Wt.% Atom Densities 1024 at/cm3

O 4.6311E-2

Fe 9.5140E-6

Si 2.2479E-5

Al 4.1701E-6 10B 6.9037E-8 11B 2.7788E-7

234U 7.1087E-6 235U 1.1104E-3 236U 3.1792E-5

UO2

238U

2.2006E-2 N 0.00310 8.7300E-6

O 0.13680 3.3727E-4

Sn 1.36600 4.5389E-4

Fe 0.22200 1.5680E-4

Cr 0.11800 8.9516E-5

C 0.01286 4.2233E-5

Si 0.00990 1.3904E-5

Al 0.00194 2.8361E-6 Zr 98.12347 4.2428E-2 Hf 0.00556 1.2287E-6

Zircaloy-4 (Fuel-rod Clad, End Plugs)

H 0.00037 1.4480E-5


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Table 28 (cont’d). Atom Densities for Basic Materials (atom/barn-cm).

Compound Isotope Wt.% Atom Densities, 1024 at/cm3

Fe 0.3557 1.0716E-4 Si 0.2086 1.7615E-4 Cu 0.0557 1.1301E-5 Mn 0.2600 6.6811E-5 Mg 2.8886 1.9173E-3 Cr 0.0300 7.6730E-6 Zn 0.0786 1.0982E-5 Ti 0.0250 1.1666E-5 Pb 0.0054 7.7020E-7 Ni 0.0086 2.7190E-6 Sn 0.0021 1.5124E-6 Al 96.0796 5.6769E-2

AG3M (Grids, Top and Bottom

Plate of Basket, Structure of Reflector Blocks)

Bi 0.0021 1.9091E-7

Cr 17.9997 1.6469E-2 Ni 9.9995 8.1056E-3 Mn 1.0000 8.6597E-4 Si 1.0000 1.6939E-3 P 0.0400 6.1439E-5 S 0.0300 4.4509E-5 C 0.0300 1.1883E-4

Stainless Steel Z2CN18-10

(Steel Plate of Pedestal)

Fe 69.9007 5.9546E-2

O 3.3368E-2 Water

H

6.6736E-2

N 4.1985E-5 Air(a)

O

1.1263E-5

C 4.16448E-2 Polyethylene

H 100

8.32896E-2 (a) Air composition calculated from Handbook of Chemistry and Physics, 74th Edition (Edition 1993 –

1994, page 1412).


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3.4 Temperature Data The experiments were performed near room temperature (Table 1). The temperature used in the model is 20°C. 3.5 Experimental and Benchmark-Model keff The critical heights reported in Table 1 are the results of measurements extrapolated to criticality. Thus, they are intended to correspond to keff = 1.0000.

The estimated uncertainty arising from uncertainty on the experimental parameters leads to the following benchmark-model keff values:

• Cases 1 through 3: 1.0000 ± 0.0012 (1σ) • Cases 4 through 6: 1.0000 ± 0.0014 (1σ) • Cases 7 through 8: 1.0000 ± 0.0011 (1σ) • Case 9: 1.0000 ± 0.0010 (1σ).


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4.0 RESULTS OF SAMPLE CALCULATIONS In the standard APOLLO2-MORET 4 array calculations, plugs and grids (above or below the fissile column) are homogenized with water and air. (See Appendix C.) This assumption has very small impact on keff (less than the calculation standard deviation).

Table 29 gives the calculated keff for all cases obtained with the system of codes APOLLO2 (CEA93 172-group library based on JEF2.2 evaluation) and MORET 4 using 172-group cross sections CEA93.V6. A typical input listing is given in Appendix A. Other calculations were performed with the same code system but with the JEFF3.1 and ENDF/B-VI.4 evaluations.

Table 29. Sample Calculation Results (France).


Case Number↓

APOLLO2-MORET 4 (172-group, CEA93V6)

keff ± 1σ JEF2.2

APOLLO2-MORET 4 (172-group, CEA2003)

keff ± 1σ JEFF3.1

APOLLO2-MORET 4 (172-group, CEA2003)

keff ± 1σ ENDF/B-VI.4

1 1.0022 ± 0.0003 1.0032 ± 0.0003 0.9992 ± 0.0003 2 1.0022 ± 0.0003 1.0034 ± 0.0003 0.9994 ± 0.0003 3 1.0026 ± 0.0003 1.0035 ± 0.0003 0.9992 ± 0.0003 4 1.0040 ± 0.0003 1.0046 ± 0.0003 1.0005 ± 0.0003 5 1.0025 ± 0.0003 1.0036 ± 0.0003 1.0002 ± 0.0003 6 1.0037 ± 0.0003 1.0036 ± 0.0003 1.0001 ± 0.0003 7 0.9959 ± 0.0003 0.9964 ± 0.0003 0.9887 ± 0.0003 8 0.9966 ± 0.0003 0.9959 ± 0.0003 0.9891 ± 0.0003 9 0.9952 ± 0.0003 0.9953 ± 0.0003 0.9878 ± 0.0003

Table 30.a gives the calculated keff obtained with TRIPOLI4 (point-wise code with JEF2.2 and ENDF/B-VI.4 library).

Table 30.a Sample Calculation Results (France).


Case Number↓

TRIPOLI4 (continuous energy)

keff ± 1σ JEF2.2

TRIPOLI4 (continuous energy)

keff ± 1σ ENDF/B-VI.4

1 0.9982 ± 0.0005 0.9960 ± 0.0005 2 0.9977 ± 0.0005 0.9948 ± 0.0005 3 0.9980 ± 0.0005 0.9950 ± 0.0005 4 0.9995 ± 0.0005 0.9972 ± 0.0005 5 0.9982 ± 0.0005 0.9960 ± 0.0005 6 0.9985 ± 0.0005 0.9964 ± 0.0005 7 0.9982 ± 0.0005 0.9914 ± 0.0005 8 0.9979 ± 0.0005 0.9912 ± 0.0005 9 0.9990 ± 0.0005 0.9905 ± 0.0005

Table 30.b gives the calculated keff obtained with MONK9A (point-wise code with JEF2.2, ENDF/B-VI.3 and JENDL3.2 libraries)


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Table 30.b. Sample Calculation Results (United Kingdom).(a)

Code (Cross Section Set) → Case ↓

MONK9A (JEF2.2)

MONK9A (ENDF/B-VI.3)

MONK9A (JENDL3.2)

1 0.9976±0.0005 0.9922±0.0005 0.9994±0.0005 2 0.9959±0.0005 0.9911±0.0005 0.9994±0.0005 3 0.9970±0.0005 0.9922±0.0005 0.9990±0.0005 4 0.9983±0.0005 0.9939±0.0005 1.0010±0.0005 5 0.9966±0.0005 0.9924±0.0005 0.9987±0.0005 6 0.9983±0.0005 0.9945±0.0005 0.9998±0.0005 7 0.9981±0.0005 0.9907±0.0005 0.9987±0.0005 8 0.9983±0.0005 0.9908±0.0005 0.9970±0.0005 9 0.9986±0.0005 0.9890±0.0005 0.9971±0.0005

(a) Results provided by D. Hanlon, SERCO. The first trends of this evaluation point out a relatively good agreement for 1.6-cm pitch between the point-wise and the multi-group methods (Figure 13), allowing for the conclusion that the approximations used in the standard method (APOLLO2-MORET 4) are relevant for these kinds of configurations. Regarding the calculation vs. experiment comparison, a small under-prediction (less than 0.5%) has been highlighted for under-moderated lattices (corresponding to pitches ranging from 1.075 to 1.1 cm) with the APOLLO2-MORET 4 multi-group code. As the pointwise TRIPOLI4 code using JEF2.2 nuclear data does not show the same trend, this tendency can be attributed to the calculation schemes (homogenization, self-shielding, etc.). No significant discrepancy is obtained between JEF2.2 and JEFF3.1 evaluations.


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A trend to underprediction can be identified for the ENDF/VI.4 evaluation for low-moderated cases. This trend can be attributed to uranium cross sections (238U capture and 235U fission). This trend can also be observed for 1.6-cm pitch but to a smaller extent.

0.9820.9840.9860.9880.9900.9920.9940.9960.9981.0001.0021.0041.0061.008

1 2 3 4 5 6 7 8 9

case

Kef

f

APOLLO2-MORET 4 - JEF2.2 APOLLO2-MORET 4 JEFF3.1TRIPOLI 4 - JEF2.2 TRIPOLI 4 ENDF/B-VI.4APOLLO2-MORET 4 ENDF/B-VI.4

Figure 13. keff Dependency on Code and Cross Section Evaluation.


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5.0 REFERENCES 1. E. Girault, P. Fouillaud – Appareillage B - « Programme « Qualification du Polyéthylène » – Rapport

d’expériences » [Translation: « « Polyethylene Qualification » Program – Report of Experimentations »] Rapport IPSN/SRSC 00-230.

2. G. Poullot, P. Grivot « Laboratoire de Criticité de Valduc – Programmes 1977-1994 – Crayons de Type

REP U(4.738)O2 gainés AGS – Compléments d’informations » [Translation: « Critical Laboratory of Valduc – 1977-1994 Programs – UO2 Rods (4.738 wt.% 235U) with an AGS Clad - Additional Information »] Note Technique IPSN/SEC/T/98.424 - IPSN/SRSC/98.03.

3. H. Lecoq « Analyses Physico-chimiques des Pastilles REP et Poudre MARACAS » [Translation:

« Physicochemical Analysis of REP Pellets and MARACAS Powder »] Note IPSN/SRSC/00.177/CA ML.

4. E. Girault « Appareillage B - Caracteristiques des Crayons Combustibles de Type "REP" U(4,738%)O2 et

Synthese des Etudes » - Rapport SRNC 03-238 [Translation: « PWR U(4,738%)O2 Fuel Rods Characteristics and Synthesis of Studies »] SRNC 03-238 Report.

5. J. Bonnet, D. Doutriaux, P. Grivot, G. Poullot “Laboratoire de Criticité de Valduc – Programme

1977/1994 – Crayons de Type REP U(4.738)O2 Gainés AGS - Compléments d’informations - Note IPSN/SRSC/98.03 et note IPSN/SEC/T/ 98.424.- Revision B du 22/03/2002.


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APPENDIX A: TYPICAL INPUT LISTINGS A.1 MORET 4 - APOLLO2 Input Listing The calculation is run in two steps using the CRISTAL system of codes.

APOLLO2 (release 2.5.5) is a 1-D multi-group cell code. It is used to determine material buckling B2m,

kinfinite, and homogeneous macroscopic-medium cross sections; it uses the CEA93.V6, 172-group library (coming from JEF2.2).

MORET4 is a 3-D multi-group Monte Carlo code. It uses macroscopic cross sections coming from APOLLO2. Each calculation employed 1,000 neutron histories per stage and was run to achieve a precision 0.00030 (about 8,400,000 neutrons).

A third code (or graphical user interface) called CIGALES is also used to make the APOLLO input data. It also calculates atomic densities from chemical data. The benchmark model of Case 1 is presented in this appendix.

MORET 4 - APOLLO2 Input Listing for Case 6 of Table 29. DEBUT_APOLLO2 ******************************************************** * C.E.A./I.R.S.N CRISTAL system codes * * CRISTAL : APOLLO2 MORET4 (CEA93 library) 172 groups* ******************************************************** * LEU-COMP-THERM-072 * * ICSBEP Volume IV * * CASE6 * * revision 0 * ******************************************************** * BENCHMARK VALDUC - Tight lattice pitch experiments * * CAS 6 N 2794 * * UO2 array moderated and reflected by water * * Polyethylene Reflector * * UO2 enriched at 4.738 % - zircaloy clad * ******************************************************** * array 16 * 17 - Pitch = 1.6 cm * * Hc = 65.765 cm * * T = 20 C * ******************************************************** * Keff(exp) +/- 1s =1.0000 +/-0.00137 * ******************************************************** * writer: N. LECLAIRE reviewer : I. DUHAMEL * ******************************************************** *=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ * CIGALES version 3.2 en date du 12/09/2007 * Creation du Fichier le 20/06/2008 16:29:50 *=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ * -=- INITIALISATION - CALCUL 1 -=- TOPT = TABLE: ; TRES = TABLE: ; TSTR = TABLE: ; TOPT.'CALCUL_CRISTAL' = 1 ; REPPROC = OUVRIR: 22 'VARIABLE' 1024 10000 'ADRESSE' 'aprocristal' ; CHARGE_APROCRISTAL = LIRE: REPPROC 'APROC' 'CHARGE_APROCRISTAL' ; FERMER: REPPROC ; EXECUTER CHARGE_APROCRISTAL ; TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; * -=- OPTIONS -=- * TOPT.'STCRI'.'NGROUP_FINAL' = 172 ;


LEU-COMP-THERM-072


TOPT.'STCRI'.'ANISOTROPIE' = 'P5' ; * *============================================================== * APOLLO PIJ CALCUL 1 * ANISO = CONCAT: '&' TOPT.'STCRI'.'ANISOTROPIE' ; *============================================================== * * Air TITRE: ' Air ' ; CALCUL_AP2 = 1 ; WRITE: TOPT.'RESU' '*Air CAS 1 ' ; * * -=- Description des milieux -=- *Air nom_calc = 'MILHOM1' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Air' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 4.19850E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 1.12630E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM1 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 2 *============================================================== * * eau densite=0.998206 TITRE: ' eau densite=0.998206 ' ; CALCUL_AP2 = 2 ; WRITE: TOPT.'RESU' '*eau densite=0.998206 CAS 2 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *eau densite=0.998206 nom_calc = 'MILHOM2' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'eau densite=0,998206' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'H2O ' = 3.33679E-02 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ;


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* * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM2 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 3 *============================================================== * * acier inox Z2CN18-10 TITRE: ' acier inox Z2CN18-10 ' ; CALCUL_AP2 = 3 ; WRITE: TOPT.'RESU' 'acier inox Z2CN18-10 CAS 3 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *acier inox Z2CN18-10 nom_calc = 'MILHOM3' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'acier inox Z2CN18-10' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 1.64694E-02 ; TOPT.'STMIL'.nom_mil.'NINAT ' = 8.10561E-03 ; TOPT.'STMIL'.nom_mil.'MN55 ' = 8.65968E-04 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.69392E-03 ; TOPT.'STMIL'.nom_mil.'P31 ' = 6.14386E-05 ; TOPT.'STMIL'.nom_mil.'S32 ' = 4.45094E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.18828E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 5.95460E-02 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM3 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA


LEU-COMP-THERM-072


&FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 4 *============================================================== * * AG3M TITRE: ' AG3M ' ; CALCUL_AP2 = 4 ; WRITE: TOPT.'RESU' '*AG3M CAS 4 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *AG3M nom_calc = 'MILHOM4' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'AG3M' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'FENAT ' = 1.07158E-04 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.76146E-04 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = 1.13010E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = 6.68111E-05 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = 1.91726E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 7.67296E-06 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = 1.09823E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = 1.16656E-05 ; TOPT.'STMIL'.nom_mil.'PBNAT ' = 7.70201E-07 ; TOPT.'STMIL'.nom_mil.'NINAT ' = 2.71897E-06 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 1.51237E-06 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 5.67693E-02 ; TOPT.'STMIL'.nom_mil.'BI209 ' = 1.90910E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM4 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 5 *============================================================== * * Lower Plug + Water TITRE: ' Lower Plug + Water ' ; CALCUL_AP2 = 5 ; WRITE: TOPT.'RESU' '*Lower Plug + Water CAS 5 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *Lower Plug + Water


LEU-COMP-THERM-072


nom_calc = 'MILHOM5' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Lower Plug + Water' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 1.17290E-02 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 1.25476E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 4.33460E-05 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 2.47461E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 9.32348E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = 2.41335E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 3.84369E-06 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 7.84027E-07 ; TOPT.'STMIL'.nom_mil.'H2O ' = 2.41436E-02 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.16750E-05 ; TOPT.'STMIL'.nom_mil.'H1 ' = 4.00279E-06 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 3.39670E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM5 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 6 *============================================================== * * Grid + Lower Plug + Clad + Water TITRE: ' Grid + Lower Plug + Clad + Water ' ; CALCUL_AP2 = 6 ; WRITE: TOPT.'RESU' '*Grid + Lower Plug + Clad + Water CAS 6 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *Grid + Lower Plug + Clad + Water nom_calc = 'MILHOM6' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Grid + Lower Plug + Cl' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 1.17290E-02 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 1.26533E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 1.18283E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 3.01119E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 9.32348E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = 2.41335E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.27024E-04 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = 7.90291E-06 ; TOPT.'STMIL'.nom_mil.'MN55 ' = 4.67216E-05 ;


LEU-COMP-THERM-072


TOPT.'STMIL'.nom_mil.'MGNAT ' = 1.34076E-03 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = 7.68005E-06 ; TOPT.'STMIL'.nom_mil.'TINAT ' = 8.15787E-06 ; TOPT.'STMIL'.nom_mil.'PBNAT ' = 5.38609E-07 ; TOPT.'STMIL'.nom_mil.'NINAT ' = 1.90140E-06 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 3.97001E-02 ; TOPT.'STMIL'.nom_mil.'H2O ' = 8.09082E-04 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.16750E-05 ; TOPT.'STMIL'.nom_mil.'BI209 ' = 1.33505E-07 ; TOPT.'STMIL'.nom_mil.'H1 ' = 4.00279E-06 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 3.39670E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM6 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 7 *============================================================== * *Crayon CAS 13 TITRE: 'Crayon CAS 13' ; CALCUL_AP2 = 7 ; WRITE: TOPT.'RESU' 'OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. ' ' CAS 12' ; * * -=- Description des milieux -=- ********************************************************************** TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; 'CELLUL7 NZ=4 C1=.3945 C2=.418 C3=.4745 C4=.902702 ' ' ' ; nom_calc = 'CELLUL7' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * *OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 nom_mil = 'FISSIL1_ 1' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = 4.63110E-02 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 9.51400E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 2.24790E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 4.17010E-06 ; TOPT.'STMIL'.nom_mil.'U234 ' = 7.10870E-06 ; TOPT.'STMIL'.nom_mil.'U235 ' = 1.11040E-03 ; TOPT.'STMIL'.nom_mil.'U236 ' = 3.17920E-05 ; TOPT.'STMIL'.nom_mil.'U238 ' = 2.20060E-02 ; TOPT.'STMIL'.nom_mil.'B10 ' = 6.90370E-08 ; TOPT.'STMIL'.nom_mil.'B11 ' = 2.77880E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * TOPT.'STMIL'.'FISSIL1_ 2' = TOPT.'STMIL'.'FISSIL1_ 1' ; TOPT.'STMIL'.'FISSIL1_ 3' = TOPT.'STMIL'.'FISSIL1_ 1' ;


LEU-COMP-THERM-072


TOPT.'STMIL'.'FISSIL1_ 4' = TOPT.'STMIL'.'FISSIL1_ 1' ; * Air_reference nom_mil = 'STRUCT1 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 4.19850E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 1.12630E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * * Zr4_reference nom_mil = 'STRUCT2 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 8.73002E-06 ; TOPT.'STMIL'.nom_mil.'O16 ' = 3.37265E-04 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 4.53892E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 1.56799E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 8.95160E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 4.22329E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.39041E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 2.83612E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 4.24280E-02 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 1.22871E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = 1.44796E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * * Water_reference nom_mil = 'STRUCT3 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'H2O ' = 3.33679E-02 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 4 .278954 .352852 .384511 .3945 1 &EQD .418 1 &EQD .4745 3 &EQD .902702 &MILI TSTR.'MILREF'.'FISSIL1_ 1' 1 TSTR.'MILREF'.'FISSIL1_ 2' 2 TSTR.'MILREF'.'FISSIL1_ 3' 3 TSTR.'MILREF'.'FISSIL1_ 4' 4 TSTR.'MILREF'.'STRUCT1 ' 5 TSTR.'MILREF'.'STRUCT2 ' 6 TSTR.'MILREF'.'STRUCT3 ' 7 &A 9 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * * -=- Autoprotection -=- * TSTR.'GEOAU' = TSTR.nom_calc.'GEO' ; TRES TSTR TOPT = AUTOPROTECTION_CRI_S 1 TSTR TOPT TRES ; * * -=- Flux a B2 nul -=- * TOPT.'TYPE_B2' = 'NUL' ; TOPT.'STPIJ' = TABLE: ; TOPT.'STPIJ'.'UP' = 'LINEAIRE' ; TRES TSTR TOPT = CALFLUX_PIJ_CRI_S 1 TSTR TOPT TRES ; * * -=- Flux a B2 critique -=- * SI ( TRES.'KINF' GT 1. ) ; TOPT.'TYPE_B2' = 'CRITIQUE' ; TRES TSTR TOPT = CALFLUX_PIJ_CRI_S 1 TSTR TOPT TRES ;


LEU-COMP-THERM-072


FINSI ; * TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc.'B2' = TRES.'B2' ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc.'KINF' = TRES.'KINF' ; * * -=- Sorties CARA Etendues -=- * TRES TSTR TOPT = SORTIE_FCARA_S 1 TSTR TOPT TRES ; * * -=- Condensation homogeneisation -=- * TRES TSTR TOPT = HOMOGE_COND_S 1 TSTR TOPT TRES ; * * -=- Creation de la Macrolib pour CELLUL7 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' TOPT.'STCRI'.'ANISOTROPIE' &NOMA &FICH 47 &NOMMIL TSTR.nom_calc.'MILEQ' nom_calc ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 8 *============================================================== * *Crayon CAS 12 TITRE: 'Crayon CAS 12' ; CALCUL_AP2 = 8 ; WRITE: TOPT.'RESU' 'OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. ' ' CAS 12' ; * * -=- Description des milieux -=- ********************************************************************** TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; 'CELLUL8 NZ=4 C1=.3945 C2=.418 C3=.4745 C4=.902702 ' ' ' ; nom_calc = 'CELLUL8' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * *OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 nom_mil = 'FISSIL1_ 1' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = 4.63110E-02 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 9.51400E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 2.24790E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 4.17010E-06 ; TOPT.'STMIL'.nom_mil.'U234 ' = 7.10870E-06 ; TOPT.'STMIL'.nom_mil.'U235 ' = 1.11040E-03 ; TOPT.'STMIL'.nom_mil.'U236 ' = 3.17920E-05 ; TOPT.'STMIL'.nom_mil.'U238 ' = 2.20060E-02 ; TOPT.'STMIL'.nom_mil.'B10 ' = 6.90370E-08 ; TOPT.'STMIL'.nom_mil.'B11 ' = 2.77880E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * TOPT.'STMIL'.'FISSIL1_ 2' = TOPT.'STMIL'.'FISSIL1_ 1' ; TOPT.'STMIL'.'FISSIL1_ 3' = TOPT.'STMIL'.'FISSIL1_ 1' ; TOPT.'STMIL'.'FISSIL1_ 4' = TOPT.'STMIL'.'FISSIL1_ 1' ; * Air_reference nom_mil = 'STRUCT1 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 4.19850E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 1.12630E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * * Zr4_reference nom_mil = 'STRUCT2 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 8.73002E-06 ; TOPT.'STMIL'.nom_mil.'O16 ' = 3.37265E-04 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 4.53892E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 1.56799E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 8.95160E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 4.22329E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.39041E-05 ;


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TOPT.'STMIL'.nom_mil.'AL27 ' = 2.83612E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 4.24280E-02 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 1.22871E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = 1.44796E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * * Air_reference nom_mil = 'STRUCT3 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = 4.19850E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 1.12630E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 4 .278954 .352852 .384511 .3945 1 &EQD .418 1 &EQD .4745 3 &EQD .902702 &MILI TSTR.'MILREF'.'FISSIL1_ 1' 1 TSTR.'MILREF'.'FISSIL1_ 2' 2 TSTR.'MILREF'.'FISSIL1_ 3' 3 TSTR.'MILREF'.'FISSIL1_ 4' 4 TSTR.'MILREF'.'STRUCT1 ' 5 TSTR.'MILREF'.'STRUCT2 ' 6 TSTR.'MILREF'.'STRUCT3 ' 7 &A 9 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * * -=- Autoprotection -=- * TSTR.'GEOAU' = TSTR.nom_calc.'GEO' ; TRES TSTR TOPT = AUTOPROTECTION_CRI_S 1 TSTR TOPT TRES ; * * -=- Flux a B2 nul -=- * TOPT.'TYPE_B2' = 'NUL' ; TOPT.'STPIJ' = TABLE: ; TOPT.'STPIJ'.'UP' = 'LINEAIRE' ; TRES TSTR TOPT = CALFLUX_PIJ_CRI_S 1 TSTR TOPT TRES ; * * -=- Flux a B2 critique -=- * SI ( TRES.'KINF' GT 1. ) ; TOPT.'TYPE_B2' = 'CRITIQUE' ; TRES TSTR TOPT = CALFLUX_PIJ_CRI_S 1 TSTR TOPT TRES ; FINSI ; * TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc.'B2' = TRES.'B2' ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc.'KINF' = TRES.'KINF' ; * * -=- Sorties CARA Etendues -=- * TRES TSTR TOPT = SORTIE_FCARA_S 1 TSTR TOPT TRES ; * * -=- Condensation homogeneisation -=- * TRES TSTR TOPT = HOMOGE_COND_S 1 TSTR TOPT TRES ; * * -=- Creation de la Macrolib pour CELLUL8 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' TOPT.'STCRI'.'ANISOTROPIE' &NOMA &FICH 47 &NOMMIL TSTR.nom_calc.'MILEQ' nom_calc ;


LEU-COMP-THERM-072


DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 9 *============================================================== * * Clad + air (spring area) TITRE: ' Clad + air (spring area) ' ; CALCUL_AP2 = 9 ; WRITE: TOPT.'RESU' '*Clad + air (spring area) CAS 9 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; * Clad + air (spring area) nom_calc = 'MILHOM7' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Clad + air (spring ar' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 2.63160E-03 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 2.81527E-05 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 3.07233E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 8.70828E-04 ; TOPT.'STMIL'.nom_mil.'O16 ' = 3.09079E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = 4.57598E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 6.14432E-05 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = 1.37700E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = 4.07037E-05 ; TOPT.'STMIL'.nom_mil.'NINAT ' = 3.64014E-04 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 1.75910E-07 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.88089E-05 ; TOPT.'STMIL'.nom_mil.'SNAT ' = 1.97082E-07 ; TOPT.'STMIL'.nom_mil.'MONAT ' = 3.80024E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = 8.98097E-07 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 7.62109E-08 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM7 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 10 *============================================================== * * Clad + air + Grid TITRE: ' Clad + air + Grid ' ; CALCUL_AP2 = 10 ; WRITE: TOPT.'RESU' '*Clad + air + Grid CAS 10 ' ; * * -=- Description des milieux -=- ************************************************************


LEU-COMP-THERM-072


TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *Clad + air + Grid nom_calc = 'MILHOM8' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Clad + air + Grid' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 2.63160E-03 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 2.92103E-05 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 3.14726E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 8.76194E-04 ; TOPT.'STMIL'.nom_mil.'O16 ' = 2.30315E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = 1.63993E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 1.84624E-04 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = 2.16729E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = 8.74253E-05 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = 1.34076E-03 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = 7.68005E-06 ; TOPT.'STMIL'.nom_mil.'TINAT ' = 8.15787E-06 ; TOPT.'STMIL'.nom_mil.'PBNAT ' = 5.38609E-07 ; TOPT.'STMIL'.nom_mil.'NINAT ' = 3.65916E-04 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 3.96995E-02 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.88089E-05 ; TOPT.'STMIL'.nom_mil.'SNAT ' = 1.97082E-07 ; TOPT.'STMIL'.nom_mil.'MONAT ' = 3.80024E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = 8.98097E-07 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 7.62109E-08 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM8 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 11 *============================================================== * * Upper Plug + air TITRE: ' Upper Plug + air ' ; CALCUL_AP2 = 11 ; WRITE: TOPT.'RESU' '*Upper Plug + air CAS 11 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; *Upper Plug + air nom_calc = 'MILHOM9' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Upper Plug + air' ;


LEU-COMP-THERM-072


TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 1.17290E-02 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 1.25476E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 4.33460E-05 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 2.47461E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 1.01384E-04 ; TOPT.'STMIL'.nom_mil.'N14 ' = 3.27919E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 3.84369E-06 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 7.84027E-07 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.16750E-05 ; TOPT.'STMIL'.nom_mil.'H1 ' = 4.00279E-06 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 3.39670E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM9 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 12 *============================================================== * * Air + Plug + Clad TITRE: ' Air + Plug + Clad ' ; CALCUL_AP2 = 12 ; WRITE: TOPT.'RESU' '* Air + Plug + Clad CAS 12 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; * Air + Plug + Clad nom_calc = 'MILHOM10' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Air + Plug + Clad' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = 1.02158E-02 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = 1.09287E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = 3.77537E-05 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = 2.15535E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = 8.97573E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = 3.39779E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = 3.34780E-06 ; TOPT.'STMIL'.nom_mil.'AL27 ' = 6.82876E-07 ; TOPT.'STMIL'.nom_mil.'CNAT ' = 1.01688E-05 ; TOPT.'STMIL'.nom_mil.'H1 ' = 3.48637E-06 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = 2.95847E-07 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=-


LEU-COMP-THERM-072


* TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM10 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; *============================================================== * APOLLO PIJ CALCUL 13 *============================================================== * * Polyethylene TITRE: ' Polyethylene ' ; CALCUL_AP2 = 13 ; WRITE: TOPT.'RESU' '* Polyethylene CAS 13 ' ; * * -=- Description des milieux -=- ************************************************************ TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; * Polyethylene nom_calc = 'MILHOM11' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; * nom_mil = 'Polyethylene' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'CH2 ' = 4.16448E-02 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 20. ; * TRES TSTR TOPT = GENERE_MILIEUX_S 2 TSTR TOPT TRES ; * * -=- Creation de la geometrie -=- * TSTR.nom_calc.'GEO' = GEOM: &CYLI &MAIL 1 &EQD 1. &MILI TSTR.'MILREF'.nom_mil 1 ; * * -=- Creation de la bibliotheque interne -=- * TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; * TSTR.nom_calc.'MAC' = MACROLIB: &EDIT TOPT.'STIMP'.'MACROLIB' TSTR.'MILREF'.nom_mil &TOTA &SELF &ABSO &ENER &FISS &ENER &SNNN &TRAC &P0 &DIFF ANISO &TRAN ANISO ; * * -=- Creation de la Macrolib pour le milieu MILHOM11 -=- * APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; * EDTIME: ; ARRET: ; FIN_APOLLO2 ******************************************************** * C.E.A./I.R.S.N CRISTAL system codes * * CRISTAL : APOLLO2 MORET4 (CEA93 library) 172 groups*


LEU-COMP-THERM-072


******************************************************** * LEU-COMP-THERM-072 * * ICSBEP Volume IV * * CASE6 * * revision 0 * ******************************************************** * BENCHMARK VALDUC - Tight lattice pitch experiments * * CAS 6 N 2794 * * UO2 array moderated and reflected by water * * Polyethylene Reflector * * UO2 enriched at 4.738 % - zircaloy clad * ******************************************************** * array 16 * 17 - Pitch = 1.6 cm * * Hc = 65.765 cm * * T = 20 C * ******************************************************** * Keff(exp) +/- 1s =1.0000 +/-0.00137 * ******************************************************** * writer: N. LECLAIRE reviewer : I. DUHAMEL * ******************************************************** *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* * CIGALES version modifiée pour CRISTAL V1 en date du 06/01/2000 *=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=* ( Air *Air *------- Données milieu de structure------- * --- Milieu 1 CONC. ATOMIQUES- %volumique 100 * N14 4.1985E-5 * O16 1.1263E-5 ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *Air MICRO 1 2 N14 O16 CONC 4.1985E-05 1.1263E-05 FINC SECTION TOUT FIN ( eau densite=0.998206 *eau densite=0.998206 *------- Données milieu de structure------- * --- Milieu 1 %-prop MASSIQUES- Dens= 0.998206- %volumique 100 * H2O 1 ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *eau densite=0.998206 MICRO 1 1 H2O CONC 3.33679E-02 FINC SECTION TOUT FIN ( acier inox Z2CN18-10 ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *acier inox Z2CN18-10 MICRO 1 8 CRNAT NINAT MN55 SINAT P31 S32 CNAT FENAT CONC 1.64694E-02 8.10561E-03 8.65968E-04 1.69392E-03 6.14386E-05 4.45094E-05 1.18828E-04 .0595460 FINC


LEU-COMP-THERM-072


SECTION TOUT FIN ( AG3M *AG3M ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *AG3M MICRO 1 13 FENAT SINAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT PBNAT NINAT SNNAT AL27 BI209 CONC 1.07158E-04 1.76146E-04 1.13010E-05 6.68111E-05 1.91726E-03 7.67296E-06 1.09823E-05 1.16656E-05 7.70201E-07 2.71897E-06 1.51237E-06 5.67693E-02 1.90910E-07 FINC SECTION TOUT FIN ( Lower Plug + Water *Lower Plug + Water ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *Lower Plug + Water MICRO 1 22 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT MONAT BI209 H1 HFNAT CONC 1.17290E-02 1.25476E-04 4.33460E-05 2.47461E-05 9.32348E-05 2.41335E-06 3.84369E-06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 7.84027E-07 2.41436E-02 1.16750E-05 0.00000E+00 0.00000E+00 0.00000E+00 4.00279E-06 3.39670E-07 FINC SECTION TOUT FIN ( Grid + Lower Plug + Clad + Water *Grid + Lower Plug + Clad + Water ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *Grid + Lower Plug + Clad + Water MICRO 1 22 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT MONAT BI209 H1 HFNAT CONC 1.17290E-02 1.26533E-04 1.18283E-04 3.01119E-05 9.32348E-05 2.41335E-06 1.27024E-04 7.90291E-06 4.67216E-05 1.34076E-03 7.68005E-06 8.15787E-06 5.38609E-07 1.90140E-06 3.97001E-02 8.09082E-04 1.16750E-05 0.00000E+00 0.00000E+00 1.33505E-07 4.00279E-06 3.39670E-07 FINC SECTION TOUT FIN ( Crayon CAS 13 OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. § CAS 12 *OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 SORTIE SECTIONS TOUTE LA CELLULE ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOMETRIE CYLINDRE 1. 4 4 1 0.3945 1 2 0.418 1 3 0.4745 3 4 0.9027022 AUTO 1 1 CHIMIE


LEU-COMP-THERM-072


*OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 TEMP 21 MICRO 1 46 N14 O16 SNNAT FENAT CRNAT CNAT SINAT AL27 CUNAT PBNAT MN55 MGNAT NINAT TINAT ZN64 MONAT CO59 BNAT VNAT CANAT CDNAT TH232 CLNAT F19 DYNAT EUNAT SM144 SM147 SM148 SM149 SM150 SM152 SM154 GDNAT U234 U235 U236 U238 PU238 PU239 PU240 PU241 PU242 AM241 B10 B11 CONC 0.00000E+00 4.63110E-02 0.00000E+00 9.51400E-06 0.00000E+00 0.00000E+00 2.24790E-05 4.17010E-06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 7.10870E-06 1.11040E-03 3.17920E-05 2.20060E-02 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 6.90370E-08 2.77880E-07 * Air_reference TEMP 21 MICRO 1 2 N14 O16 CONC 4.19850E-05 1.12630E-05 * Zr4_reference TEMP 21 MICRO 1 11 N14 O16 SNNAT FENAT CRNAT CNAT SINAT ZRNAT AL27 HFNAT H1 CONC 8.73002E-06 3.37265E-04 4.53892E-04 1.56799E-04 8.95160E-05 4.22329E-05 1.39041E-05 4.24280E-02 2.83612E-06 1.22871E-06 1.44796E-05 * Water_reference TEMP 21 MICRO 1 1 H2O CONC 3.33679E-02 FINC SECTION TOUT FIN ( Crayon CAS 12 OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. § CAS 12 *OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 SORTIE SECTIONS TOUTE LA CELLULE ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOMETRIE CYLINDRE 1. 4 4 1 0.3945 1 2 0.418 1 3 0.4745 3 4 0.9027022 AUTO 1 1 CHIMIE *OX MIX ANAL Dens=10.38 Pu/(U+Pu)=. Jours=0 TEMP 21 MICRO 1 46 N14 O16 SNNAT FENAT CRNAT CNAT SINAT AL27 CUNAT PBNAT MN55 MGNAT NINAT TINAT ZN64 MONAT CO59 BNAT VNAT CANAT CDNAT TH232 CLNAT F19 DYNAT EUNAT SM144 SM147 SM148 SM149 SM150 SM152 SM154 GDNAT U234 U235 U236 U238 PU238 PU239 PU240 PU241 PU242 AM241 B10 B11 CONC 0.00000E+00 4.63110E-02 0.00000E+00 9.51400E-06 0.00000E+00 0.00000E+00 2.24790E-05 4.17010E-06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 7.10870E-06


LEU-COMP-THERM-072


1.11040E-03 3.17920E-05 2.20060E-02 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 6.90370E-08 2.77880E-07 * Air_reference TEMP 21 MICRO 1 2 N14 O16 CONC 4.19850E-05 1.12630E-05 * Zr4_reference TEMP 21 MICRO 1 11 N14 O16 SNNAT FENAT CRNAT CNAT SINAT ZRNAT AL27 HFNAT H1 CONC 8.73002E-06 3.37265E-04 4.53892E-04 1.56799E-04 8.95160E-05 4.22329E-05 1.39041E-05 4.24280E-02 2.83612E-06 1.22871E-06 1.44796E-05 * Air_reference TEMP 21 MICRO 1 2 N14 O16 CONC 4.19850E-05 1.12630E-05 FINC SECTION TOUT FIN ( Clad + air (spring area) *Clad + air (spring area) *------- Données milieu de structure------- ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE * Clad + air (spring area) MICRO 1 21 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT MONAT H1 HFNAT CONC 2.63160E-03 2.81527E-05 3.07233E-03 8.70828E-04 3.09079E-05 4.57598E-05 6.14432E-05 1.37700E-05 4.07037E-05 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 3.64014E-04 1.75910E-07 0.00000E+00 1.88089E-05 1.97082E-07 3.80024E-06 8.98097E-07 7.62109E-08 FINC SECTION TOUT FIN ( Clad + air + Grid *Clad + air + Grid ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *Clad + air + Grid MICRO 1 21 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT MONAT H1 HFNAT CONC 2.63160E-03 2.92103E-05 3.14726E-03 8.76194E-04 2.30315E-05 1.63993E-05 1.84624E-04 2.16729E-05 8.74253E-05 1.34076E-03 7.68005E-06 8.15787E-06 5.38609E-07 3.65916E-04 3.96995E-02 0.00000E+00 1.88089E-05 1.97082E-07 3.80024E-06 8.98097E-07 7.62109E-08 FINC SECTION TOUT FIN ( Upper Plug + air *Upper Plug + air ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE *Upper Plug + air MICRO 1 22 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT


LEU-COMP-THERM-072


MONAT BI209 H1 HFNAT CONC 1.17290E-02 1.25476E-04 4.33460E-05 2.47461E-05 1.01384E-04 3.27919E-05 3.84369E-06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 7.84027E-07 0.00000E+00 1.16750E-05 0.00000E+00 0.00000E+00 0.00000E+00 4.00279E-06 3.39670E-07 FINC SECTION TOUT FIN ( Air + Plug + Clad * Air + Plug + Clad ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE * Air + Plug + Clad MICRO 1 21 ZRNAT SNNAT FENAT CRNAT O16 N14 SINAT CUNAT MN55 MGNAT ZN64 TINAT PBNAT NINAT AL27 H2O CNAT SNAT MONAT H1 HFNAT CONC 1.02158E-02 1.09287E-04 3.77537E-05 2.15535E-05 8.97573E-05 3.39779E-05 3.34780E-06 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 6.82876E-07 0.00000E+00 1.01688E-05 0.00000E+00 0.00000E+00 3.48637E-06 2.95847E-07 FINC SECTION TOUT FIN ( Polyethylene * Polyethylene ) OPTION V4 GROUP 172 P5 TEMPER 20 FINOPTION MORET GEOM HOMO CHIMIE * Polyethylene MICRO 1 1 CH2 CONC 4.16448E-02 FINC SECTION TOUT FIND DEBUT_MORET4 Experience reseau serre * HC = 65.765 Pas 1.6 reseau 16 * 17 * *Precision MINI 150 SIGI 0.0003 SIGE 0.0003 NOBIL PAS 20 * ************************************************ * * 1 ==> Air * 2 ==> Water * 3 ==> Stainless steel Z2CN18/10 * 4 ==> AG3M * 5 ==> Lower Plug + Water * 6 ==> WPG * 7 ==> Rods + Water * 8 ==> Rods + Air *9 ==> ACS (spring area) *10 ==> AGCS *11 ==> AP *12 ==> APC *13 ==> Polyethylene * ************************************************* *CHIMIE CHIM SEALINK 13 APO2 13 1 2 3 4 5 6 7 8 9 10 11 12 13 FINCHIM


LEU-COMP-THERM-072


* GEOMETRIE MODU 0 * * Air external volume TYPE 1 BOITE 75 75 70 VOLUME 1 0 1 1 0 0 70 * * Water (Hc + 24)/2 TYPE 2 BOITE 75 75 44.8825 VOLUME 2 1 2 2 0 0 44.8825 * * Support pedestal Z2CN18-10 TYPE 3 BOITE 75 75 1.75 VOLUME 3 2 3 3 0 0 19.25 * BasketAG3M TYPE 4 BOITE 47.5 47.5 0.6 VOLUME 4 2 4 4 0 0 21.6 * * Reflector CH2 + AG3 TYPE 5 BOITE 32.4 33.2 47.45 VOLUME 5 1 5 4 0 0 69.65 ECRASE 1 2 TYPE 6 BOITE 32.4 33.2 45.5 VOLUME 6 5 6 13 0 0 69.5 * * Aray of rods TYPE 7 BOITE 12.8 13.6 51.041 VOLUME 7 1 7 1 0 0 73.241 ECRASE 4 2 5 6 21 * * rods array assembly *--------------------- TYPE 10 BOITE 12.8 13.6 51.041 VOLUME 10 7 10 1 0 0 73.241 * *****Lower part of assembly * Lower grid TYPE 20 BOITE 15.3 15.3 0.2 VOLUME 20 5 20 4 0 0 23.8 ECRASE 2 7 10 * Water + plug TYPE 11 BOITE 12.8 13.6 0.59 VOLUME 11 10 11 5 0 0 23.41 ECRASE 1 20 * Grid + Plug + water TYPE 12 BOITE 12.8 13.6 0.2 VOLUME 12 11 12 6 0 0 23.8 * *****Rods * Rods in air TYPE 13 BOITE 12.8 13.6 44.8825 VOLUME 13 10 13 8 0 0 68.8825 * Rods in water TYPE 14 BOITE 12.8 13.6 32.8825 VOLUME 14 13 14 7 0 0 56.8825 * *****Upper part of the assembly * Upper grid TYPE 21 BOITE 25 25 0.3 VOLUME 21 1 21 4 0 0 120.8 * Clad + air TYPE 15 BOITE 12.8 13.6 4.5245 VOLUME 15 10 15 9 0 0 118.2895 * Grid + Clad + air TYPE 16 BOITE 12.8 13.6 0.3 VOLUME 16 15 16 10 0 0 120.8 * Upper plug + air TYPE 17 BOITE 12.8 13.6 0.734 VOLUME 17 10 17 12 0 0 123.548 * * Upper slab AG3M VOLUME 18 1 4 4 0 0 129.8


LEU-COMP-THERM-072


* * CH2 angles TYPE 30 BOITE 6.8 9.8 47.45 TYPE 31 BOITE 6.8 9.8 45.5 VOLUME 30 1 30 4 39.2 23.4 69.65 ECRASE 1 2 VOLUME 31 30 31 13 39.2 23.4 69.5 VOLUME 32 1 30 4 -39.2 -23.4 69.65 ECRASE 1 2 VOLUME 33 32 31 13 -39.2 -23.4 69.5 * TYPE 34 BOITE 9.8 6 47.45 TYPE 35 BOITE 9.8 6 45.5 VOLUME 34 1 34 4 22.6 -39.2 69.65 ECRASE 1 2 VOLUME 35 34 35 13 22.6 -39.2 69.5 VOLUME 36 1 34 4 -22.6 39.2 69.65 ECRASE 1 2 VOLUME 37 36 35 13 -22.6 39.2 69.5 * * montant rectangulaire 1x5x91 des blocs de CH2 (interne) TYPE 40 BOITE 0.5 2.5 45.5 TYPE 41 BOITE 2.5 0.5 45.5 VOLUME 40 31 40 4 45.5 23.4 69.5 VOLUME 401 6 40 4 -12.3 23.4 69.5 VOLUME 41 6 41 4 22.6 13.1 69.5 VOLUME 411 35 41 4 22.6 -44.7 69.5 VOLUME 42 6 40 4 12.3 -23.4 69.5 VOLUME 420 33 40 4 -45.5 -23.4 69.5 VOLUME 43 6 41 4 -22.6 -13.1 69.5 VOLUME 430 37 41 4 -22.6 44.7 69.5 * * montant 1x5x91 des CH2 (en dehors des blocs, face externe) VOLUME 50 1 41 4 6.8 33.7 69.5 ECRASE 1 2 VOLUME 501 1 41 4 26.4 33.7 69.5 ECRASE 1 2 VOLUME 51 1 40 4 32.9 -6 69.5 ECRASE 1 2 VOLUME 511 1 40 4 32.9 -25.6 69.5 ECRASE 1 2 VOLUME 52 1 41 4 -6.8 -33.7 69.5 ECRASE 1 2 VOLUME 521 1 41 4 -26.4 -33.7 69.5 ECRASE 1 2 VOLUME 53 1 40 4 -32.9 6 69.5 ECRASE 1 2 VOLUME 531 1 40 4 -32.9 25.6 69.5 ECRASE 1 2 FINM FINGEOMETRIE * SOUR POINT 900 MODU 0 VOLU 14 0.0 0.0 61.0 FPOINT POINT 900 MODU 0 VOLU 14 0.0 0.0 46.0 FPOINT POINT 900 MODU 0 VOLU 14 0.0 0.0 76.0 FPOINT * FINSOURCES * * GRAPH Z 30 FGRAPH GRAPH Y 0 FGRAPH SORT CARA REDUIT ETENDU ICSBEP FCARA FSOR FIND FIN_MORET4


LEU-COMP-THERM-072


A.2 MONK9A Input Listings Each MONK9A calculation, using either its standard JEF2.2-based, ENDF/B-VI.3-based or JENDL3.2-based cross section library, employed 2500 superhistories per stage and was run to achieve a precision of 0.0005. MONK9A Input Listing for Case 1 of Table 30.b. COLUMNS 1 132 * LEU-COMP-THERM-072 Working Group Review Document Model * Case 1 <parms Label SD_0_0005 @Pitch=1.6 @Crit_Ht=60.479 @Grid=30.6 @Grid_HD=0.99 ! Hole Diameter in Grid BEGIN MATERIAL SPECIFICATION NUMDEN MATERIAL Fuel O 4.6311E-2 Fe 9.5140E-6 Si 2.2479E-5 Al 4.1701E-6 B10 6.9037E-8 B11 2.7788E-7 U234 7.1087E-6 U235 1.1104E-3 U236 3.1792E-5 U238 2.2006E-2 MATERIAL Clad N 8.7300E-6 O 3.3727E-4 Sn 4.5389E-4 Fe 1.5680E-4 Cr 8.9516E-5 C 4.2233E-5 Si 1.3904E-5 Al 2.8361E-6 Zr 4.2428E-2 Hf 1.2287E-6 H1 1.4480E-5 MATERIAL Plugs SAME Clad MATERIAL Grids Fe 1.0716E-4 Si 1.7615E-4 Cu 1.1301E-5 Mn 6.6811E-5 Mg 1.9173E-3 Cr 7.6730E-6 Zn 1.0982E-5 Ti 1.1666E-5 Pb 7.7020E-7 Ni 2.7190E-6 Sn 1.5124E-6 Al 5.6769E-2 Bi 1.9091E-7 MATERIAL Basket SAME Grids MATERIAL Pedestal Cr 1.6469E-2 Ni 8.1056E-3 Mn 8.6597E-4


LEU-COMP-THERM-072


Si 1.6939E-3 P 6.1439E-5 S 4.4509E-5 C 1.1883E-4 Fe 5.9546E-2 MATERIAL Water O 3.3368E-2 H1 6.6736E-2 MATERIAL Air N 4.1985E-5 O 1.1263E-5 MATERIAL Polyethylene C 4.16448E-2 H1INCH2 [4.16448E-2*2] END BEGIN MATERIAL GEOMETRY PART 1 NEST ZROD M Fuel 3*0.0 [0.789/2] 89.765 ZROD M Air 3*0.0 [0.836/2] [89.765+9.049] ZROD M Clad 2*0.0 -1.18 [0.949/2] 101.462 ZROD GH Water 2*0.0 -1.18 [@Grid_HD/2] 101.462 BOX GH Grids [-@Pitch/2] [-@Pitch/2] -1.18 @Pitch @Pitch 101.462 PART FuelArray ARRAY 17 17 1 289*1 PART Complete BOX 1 [-150.0/2] [-150.0/2] [-1.8-1.2-3.5-17.5] 150.0 150.0 140.0 BOX 2 [-(17*@Pitch)/2] [-(17*@Pitch)/2] -1.18 [17*@Pitch] [17*@Pitch] 101.462 ZONES GH Grids +1 -2 P FuelArray +2 END BEGIN HOLE GEOMETRY HOLE Water PLATE 0 0 1 1 @Crit_Ht M Air M Water HOLE Grids XYZMESH 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 11 [-1.8-1.2-3.5-17.5] [-1.8-1.2-3.5] [-1.8-1.2] -1.8 -0.4 0.0 @Crit_Ht 96.5 [96.5+0.6] [109.4-1.2-1.8-1.2] [109.4-1.2-1.8] [140.0-1.8-1.2-3.5-17.5] 25*{M Water} 25*{M Pedestal} 5*{M Water} 3*{M Water M Basket M Basket M Basket M Water} 5*{M Water} 25*{M Water} 10*{M Water} 1*{M Water M Water M Grids M Water M Water} 10*{M Water} 25*{M Water} 25*{M Air} 10*{M Air} 1*{M Air M Air M Grids M Air M Air} 10*{M Air} 25*{M Air} 5*{M Air} 3*{M Air M Basket M Basket M Basket M Air} 5*{M Air} 25*{M Air} M Water END


LEU-COMP-THERM-072


BEGIN CONTROL DATA STAGES [1-@NUMSET] @NUMSTG @NUMNEUT STDV @STDV END BEGIN SOURCE GEOMETRY ZONEMAT ALL / MATERIAL Fuel END


LEU-COMP-THERM-072


MONK9A Input Listing for Case 2 of Table 30.b. COLUMNS 1 132 * LEU-COMP-THERM-072 Working Group Review Document Model * Case 2 <parms Label SD_0_0005 @Pitch=1.6 @Crit_Ht=91.523 @Grid=30.6 @Grid_HD=0.99 ! Hole Diameter in Grid BEGIN MATERIAL SPECIFICATION NUMDEN MATERIAL Fuel O 4.6311E-2 Fe 9.5140E-6 Si 2.2479E-5 Al 4.1701E-6 B10 6.9037E-8 B11 2.7788E-7 U234 7.1087E-6 U235 1.1104E-3 U236 3.1792E-5 U238 2.2006E-2 MATERIAL Clad N 8.7300E-6 O 3.3727E-4 Sn 4.5389E-4 Fe 1.5680E-4 Cr 8.9516E-5 C 4.2233E-5 Si 1.3904E-5 Al 2.8361E-6 Zr 4.2428E-2 Hf 1.2287E-6 H1 1.4480E-5 MATERIAL Plugs SAME Clad MATERIAL Grids Fe 1.0716E-4 Si 1.7615E-4 Cu 1.1301E-5 Mn 6.6811E-5 Mg 1.9173E-3 Cr 7.6730E-6 Zn 1.0982E-5 Ti 1.1666E-5 Pb 7.7020E-7 Ni 2.7190E-6 Sn 1.5124E-6 Al 5.6769E-2 Bi 1.9091E-7 MATERIAL Basket SAME Grids MATERIAL Pedestal Cr 1.6469E-2 Ni 8.1056E-3 Mn 8.6597E-4 Si 1.6939E-3 P 6.1439E-5 S 4.4509E-5 C 1.1883E-4 Fe 5.9546E-2 MATERIAL Water O 3.3368E-2


LEU-COMP-THERM-072


H1 6.6736E-2 MATERIAL Air N 4.1985E-5 O 1.1263E-5 MATERIAL Polyethylene C 4.16448E-2 H1INCH2 [4.16448E-2*2] END BEGIN MATERIAL GEOMETRY PART 1 NEST ZROD M Fuel 3*0.0 [0.789/2] 89.765 ZROD M Air 3*0.0 [0.836/2] [89.765+9.049] ZROD M Clad 2*0.0 -1.18 [0.949/2] 101.462 ZROD GH Water 2*0.0 -1.18 [@Grid_HD/2] 101.462 BOX GH Grids [-@Pitch/2] [-@Pitch/2] -1.18 @Pitch @Pitch 101.462 PART FuelArray ARRAY 16 16 1 256*1 PART Complete BOX 1 [-150.0/2] [-150.0/2] [-1.8-1.2-3.5-17.5] 150.0 150.0 140.0 BOX 2 [-(16*@Pitch)/2] [-(16*@Pitch)/2] -1.18 [16*@Pitch] [16*@Pitch] 101.462 ZONES GH Grids +1 -2 P FuelArray +2 END BEGIN HOLE GEOMETRY HOLE Water PLATE 0 0 1 1 @Crit_Ht M Air M Water HOLE Grids XYZMESH 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 11 [-1.8-1.2-3.5-17.5] [-1.8-1.2-3.5] [-1.8-1.2] -1.8 -0.4 0.0 @Crit_Ht 96.5 [96.5+0.6] [109.4-1.2-1.8-1.2] [109.4-1.2-1.8] [140.0-1.8-1.2-3.5-17.5] 25*{M Water} 25*{M Pedestal} 5*{M Water} 3*{M Water M Basket M Basket M Basket M Water} 5*{M Water} 25*{M Water} 10*{M Water} 1*{M Water M Water M Grids M Water M Water} 10*{M Water} 25*{M Water} 25*{M Air} 10*{M Air} 1*{M Air M Air M Grids M Air M Air} 10*{M Air} 25*{M Air} 5*{M Air} 3*{M Air M Basket M Basket M Basket M Air} 5*{M Air} 25*{M Air} M Water END BEGIN CONTROL DATA STAGES [1-@NUMSET] @NUMSTG @NUMNEUT STDV @STDV END BEGIN SOURCE GEOMETRY ZONEMAT


LEU-COMP-THERM-072


ALL / MATERIAL Fuel END


LEU-COMP-THERM-072


MONK9A Input Listing for Case 3 of Table 30.b. COLUMNS 1 132 * LEU-COMP-THERM-072 Working Group Review Document Model * Case 3 <parms Label SD_0_0005 @Pitch=1.6 @Crit_Ht=71.836 @Grid=30.6 @Grid_HD=0.99 ! Hole Diameter in Grid BEGIN MATERIAL SPECIFICATION NUMDEN MATERIAL Fuel O 4.6311E-2 Fe 9.5140E-6 Si 2.2479E-5 Al 4.1701E-6 B10 6.9037E-8 B11 2.7788E-7 U234 7.1087E-6 U235 1.1104E-3 U236 3.1792E-5 U238 2.2006E-2 MATERIAL Clad N 8.7300E-6 O 3.3727E-4 Sn 4.5389E-4 Fe 1.5680E-4 Cr 8.9516E-5 C 4.2233E-5 Si 1.3904E-5 Al 2.8361E-6 Zr 4.2428E-2 Hf 1.2287E-6 H1 1.4480E-5 MATERIAL Plugs SAME Clad MATERIAL Grids Fe 1.0716E-4 Si 1.7615E-4 Cu 1.1301E-5 Mn 6.6811E-5 Mg 1.9173E-3 Cr 7.6730E-6 Zn 1.0982E-5 Ti 1.1666E-5 Pb 7.7020E-7 Ni 2.7190E-6 Sn 1.5124E-6 Al 5.6769E-2 Bi 1.9091E-7 MATERIAL Basket SAME Grids MATERIAL Pedestal Cr 1.6469E-2 Ni 8.1056E-3 Mn 8.6597E-4 Si 1.6939E-3 P 6.1439E-5 S 4.4509E-5 C 1.1883E-4 Fe 5.9546E-2 MATERIAL Water O 3.3368E-2


LEU-COMP-THERM-072


H1 6.6736E-2 MATERIAL Air N 4.1985E-5 O 1.1263E-5 MATERIAL Polyethylene C 4.16448E-2 H1INCH2 [4.16448E-2*2] END BEGIN MATERIAL GEOMETRY PART 1 NEST ZROD M Fuel 3*0.0 [0.789/2] 89.765 ZROD M Air 3*0.0 [0.836/2] [89.765+9.049] ZROD M Clad 2*0.0 -1.18 [0.949/2] 101.462 ZROD GH Water 2*0.0 -1.18 [@Grid_HD/2] 101.462 BOX GH Grids [-@Pitch/2] [-@Pitch/2] -1.18 @Pitch @Pitch 101.462 PART FuelArray ARRAY 17 16 1 272*1 PART Complete BOX 1 [-150.0/2] [-150.0/2] [-1.8-1.2-3.5-17.5] 150.0 150.0 140.0 BOX 2 [-(17*@Pitch)/2] [-(16*@Pitch)/2] -1.18 [17*@Pitch] [16*@Pitch] 101.462 ZONES GH Grids +1 -2 P FuelArray +2 END BEGIN HOLE GEOMETRY HOLE Water PLATE 0 0 1 1 @Crit_Ht M Air M Water HOLE Grids XYZMESH 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 11 [-1.8-1.2-3.5-17.5] [-1.8-1.2-3.5] [-1.8-1.2] -1.8 -0.4 0.0 @Crit_Ht 96.5 [96.5+0.6] [109.4-1.2-1.8-1.2] [109.4-1.2-1.8] [140.0-1.8-1.2-3.5-17.5] 25*{M Water} 25*{M Pedestal} 5*{M Water} 3*{M Water M Basket M Basket M Basket M Water} 5*{M Water} 25*{M Water} 10*{M Water} 1*{M Water M Water M Grids M Water M Water} 10*{M Water} 25*{M Water} 25*{M Air} 10*{M Air} 1*{M Air M Air M Grids M Air M Air} 10*{M Air} 25*{M Air} 5*{M Air} 3*{M Air M Basket M Basket M Basket M Air} 5*{M Air} 25*{M Air} M Water END BEGIN CONTROL DATA STAGES [1-@NUMSET] @NUMSTG @NUMNEUT STDV @STDV END BEGIN SOURCE GEOMETRY ZONEMAT


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ALL / MATERIAL Fuel END


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MONK9A Input Listing for Case 4 of Table 30.b. COLUMNS 1 132 * LEU-COMP-THERM-072 Working Group Review Document Model * Case 4 <parms Label SD_0_0005 @Pitch=1.6 @Crit_Ht=56.293 @Grid=30.6 @Grid_HD=0.99 ! Hole Diameter in Grid @Sep=[0.305+(@Grid_HD/2)] BEGIN MATERIAL SPECIFICATION NUMDEN MATERIAL Fuel O 4.6311E-2 Fe 9.5140E-6 Si 2.2479E-5 Al 4.1701E-6 B10 6.9037E-8 B11 2.7788E-7 U234 7.1087E-6 U235 1.1104E-3 U236 3.1792E-5 U238 2.2006E-2 MATERIAL Clad N 8.7300E-6 O 3.3727E-4 Sn 4.5389E-4 Fe 1.5680E-4 Cr 8.9516E-5 C 4.2233E-5 Si 1.3904E-5 Al 2.8361E-6 Zr 4.2428E-2 Hf 1.2287E-6 H1 1.4480E-5 MATERIAL Plugs SAME Clad MATERIAL Grids Fe 1.0716E-4 Si 1.7615E-4 Cu 1.1301E-5 Mn 6.6811E-5 Mg 1.9173E-3 Cr 7.6730E-6 Zn 1.0982E-5 Ti 1.1666E-5 Pb 7.7020E-7 Ni 2.7190E-6 Sn 1.5124E-6 Al 5.6769E-2 Bi 1.9091E-7 MATERIAL Basket SAME Grids MATERIAL Pedestal Cr 1.6469E-2 Ni 8.1056E-3 Mn 8.6597E-4 Si 1.6939E-3 P 6.1439E-5 S 4.4509E-5 C 1.1883E-4 Fe 5.9546E-2


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MATERIAL Water O 3.3368E-2 H1 6.6736E-2 MATERIAL Air N 4.1985E-5 O 1.1263E-5 MATERIAL Polyethylene C 4.16448E-2 H1INCH2 [4.16448E-2*2] MATERIAL Legs SAME Grids END BEGIN MATERIAL GEOMETRY PART 1 NEST ZROD M Fuel 3*0.0 [0.789/2] 89.765 ZROD M Air 3*0.0 [0.836/2] [89.765+9.049] ZROD M Clad 2*0.0 -1.18 [0.949/2] 101.462 ZROD GH Water 2*0.0 -1.18 [@Grid_HD/2] 101.462 BOX GH Grids [-@Pitch/2] [-@Pitch/2] -1.18 @Pitch @Pitch 101.462 PART FuelArray ARRAY 17 17 1 289*1 PART PolyShield BOX 1 0.0 0.0 0.0 58.8 20.6 94.9 ! Container Body BOX 2 0.0 1.0 0.0 58.8 19.6 94.9 ! AG3M Top and Bottom BOX 3 0.0 1.0 1.8 58.8 19.6 [94.9-1.8-2.1] ! Poly Body BOX 4 0.0 [1.0+((19.6-5.0)/2)] 0.0 1.0 5.0 94.9 ! AG3M Internal Leg BOX 5 [(58.8/2)-(19.6/2)-(5.0/2)] 0.0 0.0 5.0 1.0 94.9 ! AG3M External Leg 1 BOX 6 [(58.8/2)+(19.6/2)-(5.0/2)] 0.0 0.0 5.0 1.0 94.9 ! AG3M External Leg 2 ZONES GH Grids +1 -2 -5 -6 M Legs +2 -3 -4 M Polyethylene +3 -4 M Legs +4 M Legs +5 M Legs +6 PART Complete BOX 1 [-150.0/2] [-150.0/2] [-1.8-1.2-3.5-17.5] 150.0 150.0 140.0 BOX 2 [-(17*@Pitch)/2] [-(17*@Pitch)/2] -1.18 [17*@Pitch] [17*@Pitch] 101.462 BOX 3 [((16*@Pitch)/2)[email protected]] [-((16*@Pitch)/2)-20.6-@Sep] -1.8 58.8 20.6 94.9 BOX 4 [-((16*@Pitch)/2)-20.6-@Sep] [-((16*@Pitch)/2)-@Sep+58.8] -1.8 58.8 20.6 94.9 ZROT 90.0 BOX 5 [-((16*@Pitch)/2)-@Sep+58.8] [((16*@Pitch)/2)+@Sep+20.6] -1.8 58.8 20.6 94.9 ZROT 180.0 BOX 6 [((16*@Pitch)/2)+@Sep+20.6] [((16*@Pitch)/2)[email protected]] -1.8 58.8 20.6 94.9 ZROT 270.0 ZONES GH Grids +1 -2 -3 -4 -5 -6 P FuelArray +2 P PolyShield +3 P PolyShield +4 P PolyShield +5 P PolyShield +6 END BEGIN HOLE GEOMETRY HOLE Water PLATE 0 0 1 1 @Crit_Ht M Air M Water HOLE Grids


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XYZMESH 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 11 [-1.8-1.2-3.5-17.5] [-1.8-1.2-3.5] [-1.8-1.2] -1.8 -0.4 0.0 @Crit_Ht 96.5 [96.5+0.6] [109.4-1.2-1.8-1.2] [109.4-1.2-1.8] [140.0-1.8-1.2-3.5-17.5] 25*{M Water} 25*{M Pedestal} 5*{M Water} 3*{M Water M Basket M Basket M Basket M Water} 5*{M Water} 25*{M Water} 10*{M Water} 1*{M Water M Water M Grids M Water M Water} 10*{M Water} 25*{M Water} 25*{M Air} 10*{M Air} 1*{M Air M Air M Grids M Air M Air} 10*{M Air} 25*{M Air} 5*{M Air} 3*{M Air M Basket M Basket M Basket M Air} 5*{M Air} 25*{M Air} M Water END BEGIN CONTROL DATA STAGES [1-@NUMSET] @NUMSTG @NUMNEUT STDV @STDV END BEGIN SOURCE GEOMETRY ZONEMAT ALL / MATERIAL Fuel END


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MATERIAL Water O 3.3368E-2 H1 6.6736E-2 MATERIAL Air N 4.1985E-5 O 1.1263E-5 MATERIAL Polyethylene C 4.16448E-2 H1INCH2 [4.16448E-2*2] MATERIAL Legs SAME Grids END BEGIN MATERIAL GEOMETRY PART 1 NEST ZROD M Fuel 3*0.0 [0.789/2] 89.765 ZROD M Air 3*0.0 [0.836/2] [89.765+9.049] ZROD M Clad 2*0.0 -1.18 [0.949/2] 101.462 ZROD GH Water 2*0.0 -1.18 [@Grid_HD/2] 101.462 BOX GH Grids [-@Pitch/2] [-@Pitch/2] -1.18 @Pitch @Pitch 101.462 PART FuelArray ARRAY 35 35 1 1225*1 PART PolyShield BOX 1 0.0 0.0 0.0 58.8 20.6 94.9 ! Container Body BOX 2 0.0 1.0 0.0 58.8 19.6 94.9 ! AG3M Top and Bottom BOX 3 0.0 1.0 1.8 58.8 19.6 [94.9-1.8-2.1] ! Poly Body BOX 4 0.0 [1.0+((19.6-5.0)/2)] 0.0 1.0 5.0 94.9 ! AG3M Internal Leg BOX 5 [(58.8/2)-(19.6/2)-(5.0/2)] 0.0 0.0 5.0 1.0 94.9 ! AG3M External Leg 1 BOX 6 [(58.8/2)+(19.6/2)-(5.0/2)] 0.0 0.0 5.0 1.0 94.9 ! AG3M External Leg 2 ZONES GH Grids +1 -2 -5 -6 M Legs +2 -3 -4 M Polyethylene +3 -4 M Legs +4 M Legs +5 M Legs +6 PART Complete BOX 1 [-150.0/2] [-150.0/2] [-1.8-1.2-3.5-17.5] 150.0 150.0 140.0 BOX 2 [-(35*@Pitch)/2] [-(35*@Pitch)/2] -1.18 [35*@Pitch] [35*@Pitch] 101.462 BOX 3 [((34*@Pitch)/2)[email protected]] [-((34*@Pitch)/2)-20.6-@Sep] -1.8 58.8 20.6 94.9 BOX 4 [-((34*@Pitch)/2)-20.6-@Sep] [-((34*@Pitch)/2)-@Sep+58.8] -1.8 58.8 20.6 94.9 ZROT 90.0 BOX 5 [-((34*@Pitch)/2)-@Sep+58.8] [((34*@Pitch)/2)+@Sep+20.6] -1.8 58.8 20.6 94.9 ZROT 180.0 BOX 6 [((34*@Pitch)/2)+@Sep+20.6] [((34*@Pitch)/2)[email protected]] -1.8 58.8 20.6 94.9 ZROT 270.0 ZONES GH Grids +1 -2 -3 -4 -5 -6 P FuelArray +2 P PolyShield +3 P PolyShield +4 P PolyShield +5 P PolyShield +6 END BEGIN HOLE GEOMETRY HOLE Water PLATE 0 0 1 1 @Crit_Ht M Air M Water HOLE Grids XYZMESH


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5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 5 [-150.0/2] [-95.0/2] [-@Grid/2] [@Grid/2] [95.0/2] [150.0/2] 11 [-1.8-1.2-3.5-17.5] [-1.8-1.2-3.5] [-1.8-1.2] -1.8 -0.4 0.0 @Crit_Ht 96.5 [96.5+0.6] [109.4-1.2-1.8-1.2] [109.4-1.2-1.8] [140.0-1.8-1.2-3.5-17.5] 25*{M Water} 25*{M Pedestal} 5*{M Water} 3*{M Water M Basket M Basket M Basket M Water} 5*{M Water} 25*{M Water} 10*{M Water} 1*{M Water M Water M Grids M Water M Water} 10*{M Water} 25*{M Water} 25*{M Air} 10*{M Air} 1*{M Air M Air M Grids M Air M Air} 10*{M Air} 25*{M Air} 5*{M Air} 3*{M Air M Basket M Basket M Basket M Air} 5*{M Air} 25*{M Air} M Water END BEGIN CONTROL DATA STAGES [1-@NUMSET] @NUMSTG @NUMNEUT STDV @STDV END BEGIN SOURCE GEOMETRY ZONEMAT ALL / MATERIAL Fuel END Parameter List File PARMS read into each input at runtime. <UP SD_0_0005 @STDV=0.0005 @NUMSET=20 @NUMSTG=1000 @NUMNEUT=2500 <UP


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APPENDIX B: DERIVATION OF ATOM DENSITIES OF UO2 FUEL PINS The values of the isotopic composition of uranium were measured in the summer of 1998, and the isotope atom percentages are given in Table B.1, in which the following formulas apply:

Average uranium atomic mass A = ∑ ×100

ii Aa,

Isotopic content weight (%) wi = A

Aa ii ×.

Table B.1. Uranium Isotopic Content (Sample 1 + Sample 2).

Isotope i Isotopic Content

atom (%) ai

Atomic Weight Ai

Atom (%) × 0.01 × Ai Isotopic Content

Weight (%) wi

234U 0.03070 234.0409 0.07185056 0.0302 235U 4.79525 235.0439 11.2709426 4.7376 236U 0.13730 236.0456 0.32409061 0.1362 238U 95.03675 238.0508 226.235744 95.0959

Average uranium atomic mass A 237.9026


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Because the atomic ratio O/U is 2.0000 and the fuel density is 10.38 g/cm3, the total number of UO2 atoms in atom/ barn-cm is

32 /37872103.10)( cmgUO =ρ

0.023157230000.29994.159026134.237

60221.037872103.10)2

( =×+

×=UON .

The uranium isotope atom densities (atoms/barn-cm) Ni are equal to N(UO2) × ai. 234U = 0.02315723 × 0.000307 = 7.1087 × 10-6 235U = 0.02315723 × 0.0479525 = 1.1104 × 10-3

236U = 0.02315723 × 0.001373 = 3.1792 × 10-5 238U = 0.02315723 × 0.9503675 = 2.2006 × 10-2 16O = 0.02315723 × 2.0000 = 4.6311 × 10-2

Fe = 9.5140 × 10-6

Si = 2.2479 × 10-5

Al = 4.1701 × 10-6

10B = 6.9037 × 10-8

11B = 2.7788 × 10-7


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APPENDIX C: CYLINDRIZATION OF THE PLUGS AND HOMOGENIZATION OF MATERIALS Cylindrization of the Plugs As can be seen in Figure C.1 below, the shape of fuel-rod end plugs is quite complex. As a consequence, the lower and upper plugs have been simplified for the convenience of the benchmark-model users. The rods have been made into cylinders using two different methods for the two plugs:

The lower plug was cylindrized keeping the total mass constant (total mass = plug mass + clad mass); the equivalent plug height is derived from the following formula:

cmmassCladmassPlug

Hplug

181

4

2 .=×

+=

φπ

The simplification does not have a significant impact on reactivity since the total mass is kept constant.

The upper plug was cylindrized keeping the total length constant, which does not have a significant impact on reactivity since the upper plug does not contribute significantly to total reactivity.

Table C.1. Characteristics of Plugs.

Height (cm) Diameter (cm) Weight (g) Value Value Value

Upper Plug 1.468 0.9492 3.4675 Rods Lower Plug 1.8 0.9492 4.6321

Clad (Lower Plug) 0.8 cm 0.9492 – 0.836 0.8317

Figure C.1. Sketch of the Plugs (Lower and Upper).


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Homogenization of Materials The modeling process for cross sections in APOLLO2-MORET 4 requires homogenized materials. Materials to be homogenized are water (W), Zircaloy-4, or Zr4, for fuel cladding [Plug (P), Clad (C)], AG3M Grid (G), and air (A). Mixture zones are identified by the combination of these initials. The major geometrical values used in the homogenizations are in Table C.2.

Table C.2. Major Geometrical Values Used in Homogenizations.

Geometrical Dimension Notation Nominal Value Array Pitch p 1.6, 1.1 or 1.075 cm

Fuel Clad Internal Diameter øint clad 0.836 cm Fuel Clad External Diameter øext clad 0.949245 cm AG3M Grid Holes Diameter øholes 0.99 cm

Plug Diameter Øplug_cyl 0.949245 cm Spring Mass mspring 9.35 g

Spring Length Lspring 9.049 cm Spring Density ρspring 7.9 g/cm3

Lower Zones in Water

There are two zones under water: Water-Plug (WP) mixture and Water-Plug-Grid (WPG) mixture.

Water Plug (WP Mixture: Bottom Plug)

This zone is located between levels -1.18 cm and -0.4 cm, relative to the bottom of the UO2.

WPcell hpV ×= 2

WP

cylplug

Zr hV ×=4

2

4

_φπ

4Zrcellwater VVV −=

The results of calculation are reported in Table C.3.

Table C.3. Volume Fractions in WP Mixture.

Pitch 1.1 cm 1.075 cm 1.6 cm

Zr4 (Plug) 58.49% 61.24% 27.64% Water 41.51% 38.76% 72.36%


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Water-Plug-Grid (WPG Mixture: Lower Grid)

The grid is 0.4 cm thick with holes of 0.99 cm diameter. This zone is located between the levels -0.4 cm and 0 cm.

WPGcell hpV ×= 2

WPG

cylplug

Zr hV ×=4

2

4

_φπ

WPGholes

WPGMAG hhpV4

22

3φπ−×=

43 ZrMAGcellwater VVVV −−=


Table C.4. Volume Fractions in WPG Mixture.

Pitch 1.1 cm 1.075 cm 1.6 cm

Zr4 (Plug) 58.49% 61.24% 27.64% AG3M (Grid) 36.38% 33.39% 69.93%

Water 5.13% 5.37% 2.43%

Intermediate Zones: Fissile Column

This zone is located between the levels 0 cm and 89.765 cm. There are two different zones: fissile rods in water (0 cm to critical height) and fissile rods in air (critical height to 89.765 cm).

Upper Zones in Air

There are three zones in air: Air-Clad-spring (ACS) mixture, Air-Grid-Clad-Spring (AGCS) mixture, Air-Plug (AP) mixture.

Air-Clad-Spring (ACS Mixture: Spring Zone)

This zone is located between the levels 89.765 cm and 98.814 cm (height=9.049 cm). It includes clad and spring. The spring is assumed to have a constant linear mass all along its length. The spring is homogenized with air around and inside the clad.

ACScell hpV ×= 2

ACS

cladcladext

cladZr hVV4

22

4int__ φφ

π−

==

ACS

springspring

spring

spring hL

mV

×=

ρ

springZrcellair VVVV −−= 4



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Table C.5. Volume Fractions in ACS Mixture.

Pitch 1.1 cm 1.075 cm 1.6 cm

Zr4 (Clad) 13.12% 13.74% 6.20% Air 76.07% 74.94% 88.69%

Z10CN18.09 (Spring) 10.81% 11.32% 5.11%

Air-Grid-Clad-Spring (AGCS Mixture)

The grid is 0.4 cm thick with holes of 0.99 cm in diameter. This zone is located between the levels 96.5 cm and 96.9 cm.

AGCScell hpV ×= 2

AGCS

springspring

spring

spring hL

mV ×

×=

ρ

AGCS

cladcladext

Zr hV4

22

4int__ φφ

π−

=

AGCSholes

AGCSMAG hhpV4

22

3

φπ−×=

springZrMAGcellair VVVVV −−−= 43


Table C.6. Volume Fractions in AGCS Mixture.

Pitch 1.1 cm 1.075 cm 1.6 cm

Zr4 (Clad) 13.12% 13.74% 6.20%

AG3M (Grid) 36.38% 33.39% 69.93% Air 39.69% 41.55% 18.76%

Z10CN18.09 (Spring) 10.81% 11.32% 5.11%

Air-Plug (AP Mixture – Top Plug)

This zone is located between the levels 98.814 cm and 100.282 cm (height=1.468 cm). It includes the conical part of the top plug and 0.094 cm of the cylinder part.

APcell hpV ×= 2

AP

cylplug

Zr hV ×=4

2

4

_φπ

4Zrcellair VVV −=


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The results of the calculation are reported in Table C.7.

Table C.7. Volume Fractions in AP Mixture.

Pitch 1.1 cm 1.075 cm 1.6 cm

Zr4 (Plug) 58.49% 61.24% 27.64% Air 41.51% 38.76% 72.36%

Five zones of small reactivity worth (Figure 8) could be described with homogenized materials according to percentages given in Table C.8. The corresponding atom densities are given in Table C.9.

• The outside upper structure zones: top plug + air, clad + upper grid + spring + air, clad + spring + air.

• The immersed structure zones: bottom plug + water, bottom plug + clad + lower grid + water + air.

Table C.8. Volume Percentages of Homogenized Zones.

Pitch (cm)

1.1 cm

(Case 7, 8) 1.075 cm (Case 9)

1.6 cm (Case 1 to 6)

Bottom Plug Plug-Clad (Zircaloy-4)

Water 58.49% 41.51%

61.24% 38.76%

27.64% 72.36%

Lower Grid Plug-Clad (Zircaloy-4)

Grid (AG3M) Water

58.49% 36.38% 5.13%

61.24% 33.39% 5.37%

27.64% 69.93% 2.43%

Top Plug Plug-Clad (Zircaloy-4)

Air 58.49% 41.51%

61.24% 38.76%

27.64% 72.36%

Upper Grid

Plug-Clad (Zircaloy-4) Grid (AG3M)

Air Spring

13.12% 36.38% 39.69% 10.81%

13.74% 33.39% 41.55% 11.32%

6.20% 69.93% 18.76% 5.11%

Spring Zone Clad (Zircaloy-4)

Air Spring

13.12% 76.07% 10.81%

13.74% 74.94% 11.32%

6.20% 88.69% 5.11%


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Table C.9. Atom Densities for Homogenized Zones (atom/barn-cm).

Pitch (cm)

1.1 cm

(Case 7, 8) 1.075 cm (Case 9)

1.6 cm (Cases 1 to 6)

Bottom Plug (plug + water)

Zr Sn Fe Cr O N Si Al C H Hf

2.4815E-02 2.6547E-04 9.1707E-05 5.2355E-05 1.4049E-02 5.1059E-06 8.1321E-06 1.6588E-06 2.4701E-05 2.7712E-02 7.1864E-07

2.5983E-02 2.7796E-04 9.6022E-05 5.4819E-05 1.3140E-02 5.3462E-06 8.5147E-06 1.7368E-06 2.5863E-05 2.5876E-02 7.5245E-07

1.1729E-02 1.2548E-04 4.3346E-05 2.4746E-05 2.4237E-02 2.4134E-06 3.8437E-06 7.8403E-07 1.1675E-05 4.8291E-02 3.3967E-07

Lower Grid (plug + clad + grid +

water + air)

Zr Sn Fe Cr O N Si Cu Mn Mg Zn Ti Pb Ni Al C Bi H Hf

2.4815E-02 2.6602E-04 1.3069E-04 5.5147E-05 1.9090E-03 5.1059E-06 7.2219E-05 4.1116E-06 2.4308E-05 6.9755E-04 3.9957E-06 4.2443E-06 2.8022E-07 9.8924E-07 2.0656E-02 2.4701E-05 6.9458E-08 3.4320E-03 7.1864E-07



Top Plug (plug + air)

Zr Sn Fe Cr O N Si Al C H Hf

2.4815E-02 2.6547E-04 9.1707E-05 5.2355E-05 2.0193E-04 2.2535E-05 8.1321E-06 1.6588E-06 2.4701E-05 8.4687E-06 7.1864E-07

2.5983E-02 2.7796E-04 9.6022E-05 5.4819E-05 2.1090E-04 2.1620E-05 8.5147E-06 1.7368E-06 2.5863E-05 8.8672E-06 7.5245E-07

1.1729E-02 1.2548E-04 4.3346E-05 2.4746E-05 1.0138E-04 3.2792E-05 3.8437E-06 7.8403E-07 1.1675E-05 4.0028E-06 3.3967E-07


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Table C.9 (cont’d). Atom Densities for Homogenized Zones (atom/barn-cm).

Pitch (cm)

1.1 cm

(Case 7, 8) 1.075 cm (Case 9)

1.6 cm (Cases 1 to 6)

Upper Grid (clad +spring + grid

+ air)

Zr Sn Fe Cr O N Si Cu Mn Mg Zn Ti Pb Ni Al C S

Mo Bi H Hf

5.5677E-3 6.0113E-5 6.5391E-3 1.8452E-3 4.8728E-5 3.4696E-5 1.9408E-4 3.3245E-5 1.1043E-4 6.9755E-4 3.9957E-6 4.2443E-6 2.8022E-7 7.7114E-4 2.0655E-2 3.9794E-5 4.1697E-7 8.0402E-6 6.9458E-8 1.9001E-6 1.6124E-7



Spring Zone (clad + spring + air)

Zr Sn Fe Cr O N Si Cu Mn Ni Al C S

Mo H Hf

5.5677E-3 5.9563E-5 6.5001E-3 1.8424E-3 5.2826E-5 4.9971E-5 1.3000E-4 2.9133E-5 8.6117E-5 7.7015E-4 3.7217E-7 3.9794E-5 4.1697E-7 8.0402E-6 1.9001E-6 1.6124E-7




LEU-COMP-THERM-072


APPENDIX D: UO2 FUEL RODS: CALCULATION OF THE DENSITY AND ITS ASSOCIATED UNCERTAINTY

D.1 Calculation of the Density The mean fuel density is obtained by considering:

• The mean linear mass density calculated on 1261 rods, ML = Linear Mass density: 5.0778 ± 0.0282 (1σ) g/cm

• The mean pellet diameter calculated on 53 pellets; D = diameter: 0.78919 ± 0.00176 (1σ) cm.

4/2DML

πρ = = 10.38 g/cm3

The standard density uncertainty is obtained by combining the standard uncertainties of two measurements, x and y, the first one being ML and the second D:

Z = f(x,y)

( )yxyZ

xZ

yZ

xZ

yxZ ,cov222

22

2

∂∂×

∂∂+⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂+⎟

⎠⎞

⎜⎝⎛

∂∂= σσσ

The correlation coefficient is r = cov(x,y)/σxσy, r is equal to 0, because the linear mass density and the diameter were measured independently, therefore:

2

2

3

2

2

2

2 84DML D

MLD

σπ

σπ

σ ρ ⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛=

Hence, σρ = 0.073, that is to say 3σρ = 0.219 ≈ 0.22 g/cm3.


LEU-COMP-THERM-072


APPENDIX E: IMPURITIES IN FUEL Since 1977, fuel pellets of U(4.738 wt.% 235U)O2 have been available in the Valduc facility. In 1995, the firm FBFC (compagnie Franco Belge de Fabrication de Combustible) replaced the cladding on 1299 fuel rods. They changed the clad material from AGS (aluminium magnesium alloy) to Zircaloy-4. During this operation, chipped pellets were removed and not introduced into the new cladding. In 2000, the same firm was ordered to measure impurity content; results are given in Table E.1.

Table E.1. Natural-Boron Equivalence of Impurities in ppm (isotope weight/weight UO2 × 106).

Element C(impurity), 10-6 g/gUO2 FBFC Coefficient(a) Equivalent Boron Al =18 1.27 0.002286 Fe =85 6 0.051 Si =101 0.82 0.008282

Bnat < 0.35 10000 0.35 Ca < 20 2 0.004 Cd < 0.53 3172 0.168116 Cr < 15 8 0.012 Mg < 6 0.41 0.000246 Mo < 20 4 0.008 Ni < 20 11 0.022 Ti < 10 18 0.018 Th < 2 4.67 0.000934 Zn < 10 2 0.002 C < 4 0.04 0.000016 Cl < 5 132 0.066 F < 2 0.072 0.0000144 N < 7.5 19 0.01425

Dy < 0.05 818 0.00409 Eu < 0.05 4250 0.02125 Gd < 0.1 43991 0.43991 Sm <0.15 5336 0.08004

Σ(impurities) 1.27 (a) The FBFC coefficients are boron equivalent coefficients of impurities times 10000.

The boron equivalent for all elements under the detection limit at their maximum values is 1.209 × 10-6 g/g UO2. The boron equivalence is calculated in the thermal spectrum by the following relationship: {Mass(I)/Aw,I}σth

I = {Mass(Bnat)/Aw,Bnat}σthBnat


LEU-COMP-THERM-072


Therefore: Mass(Bnat) equivalent = {Mass(I) × AW,Bnat}σth

I /{AW,I × σthBnat}

or Mass(Bnat) equivalent = Mass(I) × coef(I) with AW,I = impurity atomic mass Aw,Bnat = boron atomic mass = 10.811 σth

I , σthBnat = thermal microscopic cross section of impurity and boron

coef(I) = equivalence coefficient of impurity For example, gadolinium: σth

Gd= 49000 barns σth

Bnat= 759 barns coef(Gd) = 10.811×49000/(157.25×759) = 4.438; multiplied by 10,000, one obtains 44,380, a value close to 43,991, given in the table.

under-moderated 4.738-wt.%-enriched uranium dioxide … · 2010. 1. 26. · nea/nsc/doc/(95)03/iv...

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