MIRTE PROGRAM FOUR WT.%-ENRICHED URANIUM-DIOXIDE FUEL-ROD ARRAYS IN WATER SEPARATED BY A CROSS-SHAPED SCREEN OF TITANIUM (5 MM AND 10 MM THICK)

Transcription

1 MIRTE PROGRAM FOUR WT.%-ENRICHED URANIUM-DIOXIDE FUEL-ROD ARRAYS IN WATER SEPARATED BY A CROSS-SHAPED SCREEN OF TITANIUM (5 MM AND 10 MM THICK) Evaluator Nicolas Leclaire Institut de Radioprotection et de Sûreté Nucléaire, IRSN Internal Reviewers Isabelle Duhamel François-Xavier Le Dauphin Institut de Radioprotection et de Sûreté Nucléaire, IRSN Independent Reviewer John D. Bess Idaho National Laboratory

2 MIRTE PROGRAM FOUR WT.%-ENRICHED URANIUM-DIOXIDE FUEL-ROD ARRAYS IN WATER SEPARATED BY A CROSS-SHAPED SCREEN OF TITANIUM (5 MM AND 10 MM THICK) IDENTIFICATION NUMBER: SPECTRA KEYWORDS: Acceptable, Apparatus B, critical approach, interacting configurations, light water, low enriched, MIRTE, reflector, screen, structural materials, thermal, titanium, UO 2 rod arrays 1.0 DETAILED DESCRIPTION 1.1 Overview of Experiments The MIRTE (Matériaux Interaction Réflexion Toutes Epaisseurs) a program (Reference 1) has been carried out from December 2008 to June 2010 at the CEA (Commissariat à l Energie Atomique et aux Energies Alternatives) Valduc Center on the Apparatus B assembly (see Figure 1). The purpose of the MIRTE program was to measure integral reactivity characteristics of various structural materials that are typically used in nuclear facilities. The intended use of the data is to validate computer codes and associated nuclear cross section data that are used for criticality safety and reactor physics applications. Figure 1: View of the Apparatus B facility. a The English translation is Materials, Interaction, Reflection, all Thicknesses. Revision: 0 Page 1 of 196

3 Phase 1 of the MIRTE program consisted of 43 sub-critical approaches extrapolated to critical conditions using the neutron amplification method. Three types of experimental setups have been built (see Figure 2): (1) Interacting configurations with large screens, which consisted of two arrays separated either by water or screens with a thickness varying from 5 cm to 30 cm composed of iron, nickel, zirconium, aluminum, lead, copper, concrete with varying water contents (3%, 6%, 9%), or an empty aluminum box, (2) Interacting configurations with thin plates, involving four arrays separated by water or cruciform plates with a thickness lower than 2 cm composed of copper, nickel, iron, titanium. (3) Reflected configurations, which consist of one array, reflected on all four lateral sides by water, aluminum or borated glass walls Figure 2: Schematic view of the experimental device. Revision: 0 Page 2 of 196

4 The 43 experiments, which involved wt.% enriched UO 2 rod arrays, included 19 experiments with tested screens, nine reference experiments in which the screens were replaced by water or an aluminum box filled with air, and 15 reproducibility experiments with or without material. Only eight experiments (comprised of four repeatability or reproducibility experiments three with titanium and one with only water) are documented in this report. Repeatability experiments were appropriately combined into a total of four experiments (two with titanium and two reference experiments). These four experiments were evaluated and determined to represent acceptable benchmark experiments. In order to easily identify the different experiments, they were named according to the number of arrays involved in the configurations (4A for titanium experiments), the material to be tested, and its thickness (in millimeters). A reference experiment was identified by adding an R at the beginning of the experiment identifier and, concerning reproducibility experiments, the kind of reproducibility was added at the end of the identifier as follows: (1) Rv for repeatability experiments, which consisted of a new sub-critical approach after water draining without any change in the configuration. This kind of experiment will give information about the uncertainties on the water height measurement and the extrapolation method. (2) Rb(S1) for reproducibility experiments S1 type, which consisted of a new sub-critical approach after water draining and removal of the experimental device (support pedestal and lattices) from the experimental tank without any change in the configuration, allowing the estimation of the uncertainty on the rods positioning due to the gap between grid holes and rods. (3) Rb(S2) for reproducibility experiments S2 type, which consisted of a new sub-critical approach after water draining, removal of the experimental device, moving and repositioning of lattices baskets, which highlights the uncertainty in lattice positioning. (4) Rb(S3) for reproducibility experiments S3 type, which consisted of a new sub-critical approach after water draining, removal of the experimental device (support pedestal and lattices), moving and repositioning of lattices baskets and use of a new rods sample (rods sample chosen among 1261 rods). The uncertainty in rod sampling is assessed. (5) Rb(S4) for reproducibility experiments S4 type, which consisted of a new sub-critical approach after a complete dismantling of the configuration, to evaluate the uncertainty in the screen positioning. Table 1 presents the five titanium experiments (plus three reference cases without titanium) with four arrays of UO 2 rods. A number of the critical assemblies performed in the Apparatus B facility at Valduc have been evaluated as ICSBEP benchmark experiments. Revision: 0 Page 3 of 196

5 Experiment Table 1: Experimental data for thin titanium screen experiments. Experiment Number Array Geometry (n x n y ) Last reached Sub-critical Height (cm) Average Critical Height (cm) (b) ± 2σ 4A-Ti ± A-Ti-005-Rv ± A-Ti-005-Rb(S2) ± A-Ti-005-Rb(S4) (a) ± R4A-Eau (c) ± R4A-Eau-005-Rb(S2) ± A-Ti ± R4A-Eau ± (a) This height is not included within the uncertainty margins of the 4A-Ti-005 reference critical height, which may be due to rod sampling and screen positioning effects. (b) This height is the average of the critical heights given by at least four of the six neutron detectors. (c) Eau means water in French. 1.2 Description of the Experimental Configuration The experimental configuration of Apparatus B was composed of four arrays of UO 2 fuel rods held by a basket, which were placed on a pedestal inside a right parallelepiped (or rectangular) tank. The tank was located on the floor in the middle (approximately) of a large room. Water, which was used as moderator and reflector, was introduced incrementally from the bottom of the tank. All configurations involved arrays with a 1.6-cm square lattice pitch. Titanium experiments differed from each other by the screen thickness, by the number of rods per array, and therefore by the water level Critical Approach and Results The experiments were based on the subcritical approach technique, with critical conditions estimated using extrapolation. The subcritical approach parameter was the water level. Two Am-Be neutron sources were used to drive the approach. Neutron counting rates were measured with six BF 3 counters, which provided a C counting rate (depending on the array height, H, that was immersed in water) and consequently the variation of the corresponding k eff of the assembly. At the end of the approach, all neutron counters were completely immersed in water. The water height was measured by a limnimeter (conductivity probe). The function 1/C = f(h) was extended by linear extrapolation to determine the critical height from water height measurements, as explained in Figure 3. In general, the level was raised very close to the critical one, such that the final k eff was approximately within -β/ from criticality. It should be noted that the critical water height given in Table 1 corresponds to the average critical water heights obtained using measurements from at least four neutron counters. Revision: 0 Page 4 of 196

6 Water height measurement, H Limnimeter K 1/C eff = F(H) Rod array UO 2 rod 0 When H 1/C 0 C = C /(1-k ) 0 eff H C H Fissile zone upper limit level Counting rate, C Neutron counters H C Fissile zone lower limit level Pedestal Water input and output 11-GA Figure 3: Principle of the experiments (screen not modeled). The critical water height is derived from the limnimeter measurement of water height, and the extrapolation to the criticality (inverse of the counting rate to zero). Consequently the uncertainty on critical water heights is evaluated through the uncertainty which results from the limnimeter measurement and the uncertainty on the average critical height. As the tolerance of limnimeters giving the water height is very low (less than 1/100 mm), the uncertainty on the average critical height can be assimilated into the uncertainty of the extrapolation to zero of the inverse count rate (methods uncertainty). The uncertainty on the extrapolated critical heights reported in Table 1 is given with a level of confidence of 95.45% (2σ). Revision: 0 Page 5 of 196

7 Five experiments with two cruciform thin titanium screens were performed. The characteristics (water height, array size) of titanium experiments are given in Table 1. Array geometry parameters n x and n y (number of lateral rods) are sketched in Figure 4. UO rods 2 n x Water n y Titanium screen Figure 4: Description sketch of 4A-Ti-005 and 4A-Ti-010 configurations Room The Apparatus B tank was approximately centered in a concrete cell named C172, in the radiological control zone, on the ground floor of Building 10 in the Valduc Nuclear Center. The cell was 12.1 m long, 8.8 m wide and 10.0 m high, with 1.45-m-thick concrete walls. The thickness of the concrete floor was 0.40 m. The thickness of the ceiling varied from 0.70 m (at the edges) to 1.10 m (in the middle). The concrete was covered with a decontaminable paint Experimental Tank The experimental tank had internal dimensions of cm cm horizontally and 140 cm vertically. It comprised 0.4-cm-thick walls and a 0.6-cm-thick bottom and was manufactured from stainless steel Z2CN The walls and bottom were reinforced with U-shaped girders. The tank was equipped with a limnimeter (needle of measurement) that followed the free upper level of water and provided the water height. The zero-level measurement of the limnimeter was the bottom of the fissile column. The limnimeter precision was ±0.01 mm. Because the arrays were centered in the tank, more than 20 cm of water surrounded the lateral sides of the fuel rod arrays. Revision: 0 Page 6 of 196

8 1.2.4 Support Structure The support pedestal (stainless steel Z2CN18-10), which enabled the experimental devices to be installed in the tank, was located at the bottom of the experimental tank (Figure 5). It was composed of the following parts: A support plate 186 cm 186 cm, 2.5 cm thick, which was reinforced with L-shaped girders; this plate was pierced with eight holes to allow the water rise (see Figure 8). Four legs. A tubular structure situated at the four pedestal corners, 9 cm in outer diameter and cm thick. These tubes were soldered to horizontal tubes, which had the same sections (the tubular structure is visible in Figure 5). The upper face of the pedestal was cm above the bottom of the pool tank. The support plate was equipped with rails which allowed positioning the baskets precisely in the middle of the pedestal. Figure 5: Pictures of the support structure with L-shaped reinforcements Setup Device The titanium experiments used the interacting configuration with the thin screens device (see Configuration 2 in Figure 2). It should be noted that the setup device slightly differed for reference configurations without screens: the setup device for configurations with screens is kept, and additional metallic parts were introduced to guarantee the water gap between the rod arrays. In particular, lower and upper wedges were positioned in contact between the grids of the two rod arrays. Their plans are provided in APPENDIX I. A cross-shaped titanium screen was placed between the four lattices of UO 2 rods. Figure 6 shows the experimental device, which comprised four movable aluminum baskets. The square grids were pierced by holes. A dedicated aluminum device was manufactured to maintain the screens Revision: 0 Page 7 of 196

9 positioning all along the height. A distance of half a pitch (0.8 cm) was imposed between the center of the outermost rods of the four arrays and the cruciform screens. Screen Frame Movable Baskets Leg of the Screen Frame Figure 6: Experimental device for titanium experiments without titanium screens. The four movable baskets (Figure 7) were made of the following parts (see Table 2): A bottom plate of the basket which could be approximately divided into a rectangular part and a triangular part. It was placed just below the array to support the fuel rods. Two grids vertically separated by 97.9 cm (center to center) with the following dimensions: 24 cm long, 24 cm wide, 0.4 cm thick, and 0.98 cm for diameter of holes. L-shaped angle brackets shown in Figure 8 (0.2 cm thick, 2.5 cm wide and cm high) that joined the end plate and the two grids. An aluminum frame composed of four legs (four vertical tubes) linked together by horizontal tubes that maintained the grids. The basket plans are given in APPENDIX H. Revision: 0 Page 8 of 196

10 Legs of the Movable Basket Lower Grid Large Horizontal Tube Bottom Plate Small Horizontal Tube Figure 7: Lateral view of the movable baskets. Revision: 0 Page 9 of 196

11 Structure Support Table 2: Characteristics of the movable basket parts. Element of structure Rectangular tube wall thickness (cm) Width (cm) Height (cm) Length (cm) Legs (vertical tubes) Large horizontal tube Small horizontal tube Grids Bottom plate Rectangular part With two sides equal to 24 cm and the last one equal to Triangular part 34 cm L-shaped Angle Brackets Aluminum Screen Frame Figure 8: Upper view of the grids with their L-shaped angle brackets during assembling of the configuration (the support plate holes that allow the water to rise are visible). It can be noted that the bottom of the fissile column was at the same level as the upper side of the bottom grid; the distance between the top of the basket bottom plate and the top of the lower grid was 1.8 cm. Axial position of the fissile column was checked visually. The screens were positioned on four vertical AG3 aluminum alloy plates that were 24 cm long, 1.2 cm thick, and 6.7 cm high. Figure 9 presents views of the frame that maintained the titanium screens. The frame dimensions are given in Table 3. Revision: 0 Page 10 of 196

12 Vertical Screen Guides Upper Grid of the Basket Horizontal Tubes Figure 9: Description of the screen frame. Revision: 0 Page 11 of 196

13 Table 3: Characteristics of the screen frame parts. Structure Screen frame Element of structure Rectangular tube wall thickness (cm) Width (cm) Height (cm) Length (cm) 4 legs (vertical tubes) horizontal tubes Vertical guides maintaining the screen for 4A-Ti for 4A-Ti Fuel rods In experiments performed at the Valduc Apparatus B facility before 1994, the fuel was clad with AGS. These rods were reclad in 1995 with Zircaloy-4 claddings. Measurements were performed on 100 rods (at the top, middle, and bottom of each rod) to determine the outer diameter of the clad. The average value and its associated standard deviation is: ± (1σ) cm. The outer clad diameter was measured with a micrometer (palmer) whose precision was ± cm. Measurements were also performed on fissile column height, fissile column weight, fissile pellet diameter, spring mass, and plug mass. Table 4 gives the measured values and the associated standard deviation (1σ) for the main parameters. The clad inner diameter is known only by the fabrication specification. Complete measurement of masses and dimensions are recorded for many of the 1261 fuel rods. However, the placement of a given rod in the assembly was not recorded. Measurement data for the fuel rods available at Valduc for use in these experiments are tabulated in APPENDIX J. The UO 2 fuel rods used for the experiments (Figure 10) contained uranium oxide fuel, enriched to wt.% 235 U. The fuel column was made of sintered oxide pellets, each ± cm long and ± cm in diameter (measurement values, from References 2 and 4). The pellet diameter was measured with a palmer (micrometer), whose precision was ± cm. The total rod length, including end plugs and retaining spring, was ± 0.04 cm (measurement value). Parameter Pellet Diameter (cm) from measurement statistics Table 4: Fuel rods characteristics (References 2 and 4). Mean Value Standard Deviation (1σ) Number of Measurements (a) (a) 53 Pellet Height (cm) Inner Clad Diameter (cm) (b) (b) 0 Outer Clad Diameter (cm) from measurement statistics (c) (c) 300 Fissile Column Height (cm) Fissile Column Mass (g) Rod Height (cm) (a) The diameter of 53 pellets has been measured using a micrometer (palmer); the uncertainty in the measured value does not include the accuracy of micrometer, which is cm. Revision: 0 Page 12 of 196

14 (b) Conversion to 1σ of the manufacturing tolerance dividing by 3 (c) The diameter of 300 claddings has been measured using a micrometer (palmer); the uncertainty in the measured value does not include the accuracy of micrometer, which is cm. Figure 10: Fuel rod (mean dimensions). Revision: 0 Page 13 of 196

15 The average height value of the fissile column was ± (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 5. Table 5: Characteristics of end plugs (Reference 4). Height (cm) Diameter (cm) Mass (g) Value Tolerance Value Tolerance Value Uncertainty Number of (σ) Measurements UO 2 Upper Plug Rods Lower Plug 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 had the following characteristics: Material: Stainless steel Z10CN18-09 Length: a cm Diameter: ± cm (measurements) Number of spirals: 30 Spring wire diameter: ± cm (manufacturing tolerance) Mass: ± g (measurements). Rods were arranged in arrays at a 1.6-cm square pitch. They were carefully placed and experimenters visually checked 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, and observed outside the tank. It was seen that the arrays were 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 were considered: (1) The hole position uncertainty due to error in adjustment of the hole-piercing device. For the grids employed in the experiments, no measurements of the pitch have been performed for these grids. From manufacturing tolerances in Reference 1 (0.01 cm), the 1σ uncertainty is then obtained dividing the manufacturing tolerance by 3 giving cm. (2) The rod positioning uncertainties due to the space between the rod s clad and the hole are the following: ± cm for the hole diameter 0.98 cm ( = ). This uncertainty is assumed to be random. It follows an equiprobable distribution; therefore, 1σ = / 3 = (3) The grid hole diameters were not measured. However, the tolerance on the hole diameter is reported to be 0.01 cm on the grids sketch. The uncertainty on the hole diameter is then obtained dividing the tolerance by 3 giving then cm. a Compressed length in the final produced rods. Revision: 0 Page 14 of 196

16 (4) The rod outer clad diameter uncertainty is measured to be ± cm (1σ); the systematic uncertainty (± cm) given by the palmer is used Titanium screens The titanium screens were cruciform plates made of two thin metallic plates grooved in their middle on a height of 500 mm. They were then assembled as a cruciform device to be installed between the four UO 2 arrays (see Figures 11 and 12). The design of the screens was optimized to ensure their positioning and minimize the experimental uncertainties. For that purpose, much effort was devoted to 3D measurements of the tested screens (Figures 13, 14, and 15) using different techniques. The dimensions, perpendicularity, and flatness of the different screens were investigated. A micrometer (palmer device) was used to measure the thickness of the screen (Figure 15) as well as the dimensions of the groove. The thicknesses were measured in the mesh shown in Figure 16. Measured dimensions of the screens from the analysis reports are given in Table 6. The reported values are provided in APPENDIX G. The screens dimensions were also measured (see Figures 13 and 14) using a laser tracker at different positions of a mesh similar to that shown in Figure 16. The laser tracker measures the thickness, the length, and the height with a precision of mm. The given thicknesses values and uncertainties are the means and the standards deviations of all the measurements. The given uncertainties for lengths and heights are the systematic uncertainties (see Table 6). The values given in Table 6 were obtained as follows: Only one series of thickness measurements were made for the two screens (2 measurements) used in experiment 4A-Ti-005 and those measurements were made using a micrometer. Laser tracker measurements were not possible for screens that are so thin. Values for height and width were obtained using the laser tracker. Two series of thickness measurements were made for the two screens (4 measurements) used in 4A-Ti-010. Those measurement were made with both the laser tracker and more traditional methods such as a micrometer (especially for the groove). Values for height and width were obtained using the laser tracker. During their assembly (see Figure 11), the titanium screens are slipped into guidance rails. The tolerance interval on the slit in which the screens are introduced is [+0.1 mm; +0.5 mm]. Moreover, the assembling of the two screens by means of the groove requires a perfect perpendicularity of the two assembled screens. Revision: 0 Page 15 of 196

17 Figure 11: Picture of the 5-mm titanium plates during the assembling of the configuration. Figure 12: Picture of the 5-mm titanium plates assembled for the experiment. Revision: 0 Page 16 of 196

18 Figure 13: Thin screen during measurement with laser tracker. Face 3 Z Laser ball Diameter Diameter 6 X Face 2 Screen Face 4 Y Z Face 6 X X 11 - G A Figure 14: Thin screen during measurement with laser tracker. Revision: 0 Page 17 of 196

19 Figure 15: Thin screen during measurement with micrometer device. Revision: 0 Page 18 of 196

20 Figure 16: Mesh for the metallic screen measurement. Revision: 0 Page 19 of 196

21 Material Titanium Configurations 4A-Ti-005 4A-Ti-010 Table 6: Measured dimensions of the titanium screens. Thickness (cm) ± mean standard deviation Height (cm) ± precision (Laser tracker) Length (cm) ± precision (Laser tracker) ± (a) ± ± ± (a) ± ± ± (a) ± (b) ± ± ± (a) ± (b) ± ± (a) Measurements with palmer device (precision of the palmer: mm). (b) Measurements with laser tracker device (precision of the laser tracker: mm) Neutron Counters and Sources Support Six BF 3 neutron counters were arranged around the core. Four of them were placed facing the four sides of the core at a distance of 6 cm laterally from the core boundary and 20 to 38 cm above the basket bottom. The two others were placed facing the sides of the core at a distance of 10 cm from the core boundary and 20 cm above the basket bottom. The neutron counters were located behind the rods array at a distance from the rods array boundary given in APPENDIX E. The two Am-Be neutron sources ( Bq) were located on two middle fuel rods, 25 cm above the bottom plate Command and control room The command and control room was adjacent to the experiment cell. Experimenters carried out the subcritical approach electronically and remotely, according to the information provided by the control panel, microcomputers, and video cameras. 1.3 Description of Material Data The UO 2 fuel rod comprised uranium oxide pellets clad with Zircaloy-4. Titanium screens were placed between arrays of the fuel rods with AG3 aluminum alloy and stainless steel Z2CN18-10 materials providing structural support for the entire assembly, which was reflected and moderated by light water at room temperature. Revision: 0 Page 20 of 196

22 1.3.1 Isotopic Content of Uranium The uranium of the UO 2 fuel was enriched to wt.% 235 U. The results of recent isotopic analyses on two pellet samples (1998) are provided in References 2 and 4 and are reported in Table 7. The uranium isotopic content was measured by thermal ionization mass spectrometry (TIMS), which gives very accurate results. Table 7: Results of TI/MS measurements in 1998 (2σ uncertainties). (a) Isotope (b) at.% (Sample 1) at.% (Sample 2) 234 U ± ± U ± ± U ± ± U ± ± (a) Measured by FBFC (Franco-Belge de Fabrication de Combustible). (b) 238 U atomic percentage is [100-( 234 U at.%+ 235 U at.%+ 236 U at.%)] Stoichiometry of Uranium Oxide Two values of the O/U stoichiometry derived from References 3 and 4 are reported in Table 8. Reference Table 8: Results of stoichiometry analysis for the UO 2 fuel. Experimental Study Relative to UO 2 Rods (Reference 4) FBFC Analysis Certificate (Reference 3) Date O/U ± (1σ) Density of Uranium Oxide Measurements were performed on 1261 rods during the production of new claddings by FBFC/Pierrelatte in The average values are the following: Average oxide weight: ± 2.82 g (1σ) Average fissile height: ± cm (1σ) Average linear density: ± g/cm (1σ, 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 ± cm (1σ) (see Reference 4). In References 2 and 4, it is stated that the nominal density is equal to ± 0.04 (3σ) g/cm Uranium Oxide Impurities The impurity content is reported in References 2 and 4. It was provided by FBFC (Franco-Belge de Fabrication de Combustible) measurements in Three elements were reported to be over the detection Revision: 0 Page 21 of 196

23 limit: aluminum, iron, and silicon. Other elements (referred to as undetected impurities) were under the detection limit. These data are reported in Table 9. Table 9: Uranium oxide impurity report provided by FBFC. Element Al Fe Si B Ca Cd Cr Mg Mo Ni Ti ppm (a) <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 UO 2 ; i.e., [(weight of element)/(weight of UO 2 ) 10 6 ] Zircaloy-4 Characteristics Plugs and clad were made of Zircaloy-4. Its composition was provided by the European manufacturer of zirconium, CEZUS. Three Zircaloy-4 analysis certificates were provided in the report on UO 2 rods (References 2 and 4) concerning, respectively, the cladding tubes, bottom end plugs, and top end plugs. The differences in the contents of the cladding and bottom and top plugs of element were 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 UO 2 fuel-rod cladding tubes, chemical composition. Element Zr (a) N O Sn Fe Cr Weight % Element C Si Al Hf H Weight % (a) The zirconium weight mass (%) is determined by difference. The density value of Zircaloy-4 (specification value) given in the references was ρ = 6.55 g/cm 3. The basic report also gives the contents of Zircaloy-4 impurities. Values were provided by the manufacturer for samples from three positions in the alloy ingot. a Detected impurities were included in the chemical composition ( Table 10). Other impurities are reported in Table 11. Table 11: Detection limits for the 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) 10 6 ] a The melted metal is 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. Revision: 0 Page 22 of 196

24 1.3.6 Spring Stainless Steel The spring was made of stainless steel Z10CN Its composition as reported in the analysis certificate in Reference 4 is given in Table 12. Table 12: Z10CN18-09 stainless steel chemical composition (ρ = 7.9 g/cm 3 ). Element N Fe (a) Cr C Si Cu Weight % Element Mn Ni P S Mo Co Weight % (a) The iron weight mass (%) is determined by difference Moderator and Reflecting Water Several chemical analyses of the water stored in tanks, which was used for the core reflection and moderation, were carried out after specific experiments in the frame of the MIRTE program. Results of the test measurement made before the experiment, which is consistent with all the other measurements, are reported in Table 13. Table 13: Impurities in water. Element Concentration (mg/l) Element Concentration (mg/l) Element Concentration (mg/l) Element Concentration (mg/l) Cl 10.1 S 3.1 Fe < Sn < Na 4.4 K 0.38 Ni < Gd < Mg 1.7 Ca 98.3 Cu Pb < Al < Ti < Zr < W < Si 2 Cr Nb < Sr P < 0.01 Mn < Mo < Titanium Screens During the fabrication process, the chemical analyses of most elements were performed in the U.S. by Evans Analytical Group (EAG). A mm pin was sectioned from each titanium sample, cleaned with HF and HNO 3 acid, and rinsed with deionized water and ethanol. Elements were individually scanned by a glow discharge ion source while the samples were sputtered. The glow discharge mass spectrometry (GDMS) system is well characterized with a Ta Quality Control sample and has an accuracy and precision of about 20 to 30%. Titanium reference material (TIM 573) was analyzed and used to correct measured data for B, Al, Si, P, S, V, Cr, Mn, Fe, Ni, Cu, Mo, and Sn. a The results of these analyses are reported in Table 14 and in Table 15. A complete description of the GDMS technique is given in APPENDIX F. a EAG Quantitate Analysis of Impurities for Idaho National Laboratory, Job# S08Q9239 for Titanium samples (A47A- C1 10-mm, A55C/C2 5-mm), December 9, Revision: 0 Page 23 of 196

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26 Table 14: Results of chemical analysis of both titanium screens performed in 2008 detected elements. Elements ppm/weight Titanium 5 mm Titanium 10 mm Fe Cr Ti Balance Balance Sn B Hf In Sb C N O 0.19 wt% 0.16 wt% Mg Al Si P S Cl V Mn Co Ni Cu Ga Ge As Zr Nb Mo Ru W Pb Th U Revision: 0 Page 25 of 196

27 Table 15: Results of chemical analysis of titanium screens performed in 2008 elements reported to be under the detection limit. Elements ppm/weight Elements ppm/weight Li <0.01 Cs <0.01 Cd <0.1 Ba <0.01 Be <0.005 La <0.005 Bi <0.05 Ce <0.005 F <0.5 Pr <0.005 Na <0.01 Nd <0.005 K <0.05 Sm <0.005 Ca <5 Eu <0.005 Sc <0.1 Gd <0.005 Zn <0.1 Tb <0.005 Se <0.05 Dy <0.005 Br <0.1 Ho <0.005 Rb <5 Er <0.005 Sr <3000 Tm <0.005 Y <200 Yb <0.005 Rh <0.1 Lu <0.005 Pd <0.05 Ta <16 Ag <0.1 Re <0.01 Te <0.05 Os <0.01 I <0.01 Ir <0.01 Pt <0.05 Au <0.1 Hg <0.1 Tl <0.01 At the end of 2010, new chemical analyses were performed by FILAB (France) using ICP-AES technique. The results are reported in Table 16 and in Table 17 for the 4A-Ti-005 and 4A-Ti-010, respectively. In addition, the material densities were measured using helium pycnometry. The 5-mm titanium screen density was evaluated to be ± g/cm 3. The 10-mm titanium screen density was evaluated to be ± g/cm 3. Revision: 0 Page 26 of 196

28 Table 16: New chemical analysis of titanium screen (5 mm thick) performed in December 2010, ρ = ± g/cm 3. Elements Fe Cr Ti B Li Cd Eu Weight % Balance <0.005 <0.005 <0.005 <0.005 Measurement Method ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES Element Gd Hf In Ir V Sn Zr Weight % <0.005 <0.005 <0.005 <0.005 <0.005 <0.005 <0.005 Measurement Method ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES ICP-AES Element Mo Dy Weight % <0.005 <0.005 Measurement Method ICP AES ICP AES Table 17: New chemical analysis of titanium screen (10 mm thick) performed in December 2010, ρ = ± g/cm 3. Elements Fe Cr Ti B Li Cd Eu Weight % Balance <0.005 <0.005 <0.005 <0.005 Measurement Method ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES Element Gd Hf In Ir V Sn Zr Weight % <0.005 <0.005 <0.005 <0.005 < <0.005 Measurement Method ICP AES ICP AES ICP AES ICP AES ICP AES ICP AES ICP-AES Element Mo Dy Weight % <0.005 <0.005 Measurement Method ICP AES ICP AES Revision: 0 Page 27 of 196

29 1.3.9 Characteristics of Other Structural Materials Compositions of other materials are given in Table 18 (Reference 2). The given values for AG3 aluminum alloy and stainless steel Z2CN18-10 correspond to specification values. It should also be noted that concrete walls were covered with a thin layer of paint, known as washable and decontaminable, with an unknown composition. Material AG3 Aluminum Alloy (a) (basket, grids, and plates) Stainless Steel (a) (support pedestal and experimental tank) Z2CN18-10 Table 18: Compositions of other materials. Density (g/cm 3 ) Nuclides Weight (%) Si 0.4 Fe 0.4 Cu 0.1 Mn 0.5 Mg Cr 0.3 Zn 0.2 Ti 0.15 Al Balance C <0.03 Cr 18 ± 1 Ni 10 ± 1 Fe Balance Mn 2 Si 1 S 0.03 P 0.04 Density Atom densities Material (g/cm 3 Nuclides ) (atom/barn-cm) H B O Concrete (c) Al (cell hall) Si Ca Fe Air (b) Not N mentioned O (a) Data comes from the AFNOR French standard. (b) A simplified air composition, calculated from the Handbook of Chemistry and Physics, 87 th edition, (c) Calculated from atoms/barn-cm data. 10 B content is an equivalent content, providing a neutron absorption equal to that of the total impurities in a thermal flux. Revision: 0 Page 28 of 196

30 1.4 Temperature Experiments were carried out at temperatures ranging from 18.6 C to 19.8 C. These temperatures were obtained by thermocouples in the room where the experiment was performed (Cell 172) and in the reflector. They are reported in Table 19. The diameter of these thermocouples was 3 mm, their length 550 mm and 1150 mm. The maximum error of the thermocouple temperature measurement was ±0.2 C. Information on calibration of thermocouples is not available. The thermocouples were located next to the tank walls, at a height of 968 mm and 368 mm from the bottom of the experimental tank and more than 200 mm from the arrays of rods. Experiment Number Configuration Table 19: Temperatures during and after the experiments. During the experiments Room (Cell 172) temperature ( C) Reflector temperature ( C) At the end of the experiments Room (Cell 172) temperature ( C) Reflector temperature ( C) A-Ti A-Ti-005-Rv A-Ti-005-Rb(S2) A-Ti-005-Rb(S4) A-Ti R4A-Eau R4A-Eau-005-Rb(S2) R4A-Eau Supplemental Experimental Measurements No additional measurements were performed. Revision: 0 Page 29 of 196

31 2.0 EVALUATION OF EXPERIMENTAL DATA Eight experiments are documented in this report, including four reproducabilty experiments (three with 5- mm-thick titanium sheets and one reference case) that were appropriately combined into four experiments. Those four experiments were evaluated and determined to represent acceptable benchmark experiments. In 1995, in the framework of the renovation of Apparatus B, measurements and chemical analyses were performed on the new fuel rods, which were reclad (1995 to 2000). 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). The MIRTE program used the same rods that were analyzed between 1995 and Furthermore, it can be noted that, for the MIRTE program, a dedicated effort was made to reduce the experimental uncertainties. Thus, measurements of the screens dimensions with laser trackers were performed, as well as chemical analyses for the screens composition. This came in addition to the stringent specification values. 2.1 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). Concerning the UO 2 rods, it should be noted that not all the rods used in the experiments were measured during their recladding process. The uncertainty attributed to the 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). Based on Formula 11 in Section C.12 of APPENDIX C of the ICSBEP Uncertainty Guide, it was shown by calculation that the sampling uncertainty associated with the rods involved in the experiment is negligible. As a consequence, the sampling uncertainty does not need 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 Manufacturing Tolerances In the case of manufacturing 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). Revision: 0 Page 30 of 196

32 2.1.3 Propagation of the Uncertainties in Terms of k eff Uncertainty in the Measurement Concerning the UO 2 rods and more specifically their positioning, caution should be used when propagating the uncertainties in terms of k eff. In fact, the approach of applying the standard deviation to the perturbed calculation and then dividing the obtained k eff 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 overestimate the result. As a consequence, whereas most parameters uncertainties are treated as systematic, the rod positioning uncertainty uses the square root of n factor. Calculations The uncertainties were propagated to k eff by performing either one APOLLO2-MORET 4 Monte Carlo calculation (CRISTAL V1 package using the JEF2.2 library) using the Correlated Sampling method (also named A2M4 CS or MORET 4 perturbation) or two multi-group APOLLO2-MORET 4 Direct Calculations (also named A2M4 DC using the JEF2.2 library). In the first case, the k eff variation is given without Monte Carlo uncertainty (a negligible uncertainty is obtained due to the method); in the second case, the k eff variation must take into account the associated Monte Carlo statistical standard deviation. When using a Monte Carlo code to calculate k eff of a perturbed case, the formula considered is: u 2 [( k k ) ] 2 2 i k = i + δxi δxi N δx. 4 i where (k +δxi - k -δxi ) represents the change in k eff induced by change +δx i - -δx i on parameter p i, u i is the standard uncertainty of the parameter ρ I, and N is the number of different parameters whose effects are included. In all Monte Carlo calculations run with a standard deviation of less than , a k eff of less than is considered as being negligible. Summaries of uncertainties and their reactivity effects are presented at the end of Section 2 in Table 35 and in Table 36. In addition, a comparison was made for propagated uncertainties between APOLLO2-MORET 4 (correlated sampling method), APOLLO2-MORET 4 (two direct calculations) and continuous energy MORET 5 (two direct calculations) with a low Monte Carlo standard deviation (=0.0001) for direct calculations. A general good agreement between calculations from the two codes was obtained. The results are reported in APPENDIX D. 2.2 Material Data and Chemical Uncertainties 1 The propagation in terms of k eff of all material and chemical uncertainties is summarized in Table 35 and Table 36. Revision: 0 Page 31 of 196

33 2.2.1 Isotopic Content of Uranium in UO 2 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, which is the mean of the two samples, is given in Table 20. In order to evaluate the reactivity effect of this uncertainty, MORET 4 perturbation calculations were performed. Table 20: Retained isotopic composition (1σ uncertainties). Element at.% wt.% 234 U ± ± U ± ± U ± ± U ± ± 0.02 The uranium 1σ uncertainties of the isotopic composition from Table 20 are assumed to be representative of the rod population encountered in the experiments. As can be seen, the uncertainty of 238 U is higher than the sum of uncertainties of other isotopes. Anyway, a variation of ±0.02% of 238 U isotopics, keeping other isotopes constant (including 235 U), is calculated to be negligible. The other isotopics are kept constant because their uncertainties are too low to counterbalance the 238 U uncertainty. Similarly, 234 U and 236 U isotopics are varied separately by ± As the uranium vector needs to be normalized to keep the total amount of uranium constant, 235 U is decreased or increased by the same variation. The uncertainties are also calculated to be negligible. 235 U isotopics is varied by its uncertainty range of ± U and 236 U isotopics remain constant. The total amount of uranium is kept constant by decreasing or increasing 238 U (see Table 36). Table 21: Perturbation calculation parameters: 4A-Ti-005 and 4A-Ti-010. Element at.% 234 U U / U U / The k eff results should be divided by 0.004/0.002 to scale to 1σ Stoichiometry The retained value for the O/U stoichiometry is the 1998 measurement by FBFC, i.e., ± (1σ). Revision: 0 Page 32 of 196

34 The value of was calculated on the basis of a 235 U enrichment of UO 2 fuel rods slightly differing from the wt.%; this value was found in old experimental reports. In fact, this value was reevaluated and consequently, the O/U was reviewed at the same time. The impact on reactivity worth of a ±0.01 variation is calculated using the perturbation method and is found to be negligible (< ) Oxide Density and Pellet Diameter Data regarding the measured masses and dimensions of fuel rods available for use in these experiments are given in APPENDIX J. However, the experimental procedure did not require that identification of the exact rod placement with the assemblies be recorded, and the measurements of fuel rod parameters is not 100% comprehensive for all 1261 fuel rods. Only smaller subsets of fuel rods were characterized with detail for some measurements. Therefore, the method described below was utilized to assess uncertainty in fuel rod dimensions and mass, and is considered to represent a bounding estimate Pellet diameter The 1σ uncertainty associated with the pellet diameter was assessed while keeping the fuel linear density constant. As a consequence, the density needed to be corrected accordingly. The following formula was applied: ρ = ρ 2 R R + R mass 1 where ρ =, ρ = ρ( R + R) ρ( R) 2 Length π R. The uncertainty of the measured pellet diameter is measured to be cm (1σ). However, the precision of the measuring device (palmer) being ±0.005 cm, this systematic uncertainty is calculated to be predominant. A MORET 4 perturbation calculation is performed for ±0.01 cm variation of the pellet diameter. The corresponding density variation is ± 0.26 g/cm 3. This result is then scaled to 1σ (systematic uncertainty: cm) by dividing by four Oxide Density In References 1, 2, and 4, it is stated that the density is equal to ± 0.04 (3σ) g/cm 3. This value was calculated using the 2010 Handbook a propagation uncertainty formula (APPENDIX B) on the basis of linear density and diameter uncertainties. A correlation between these two uncertainties was considered. In a new approach, the uranium oxide density uncertainty has been calculated considering that the linear density and diameter uncertainties are uncorrelated. 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. a NEA/NSC/DOC(95)03 International Handbook of Evaluated Criticality Safety Benchmark Evaluation Experiments September 2010 Edition Revision: 0 Page 33 of 196

35 Actually, the model considers the same density (10.38 g/cm 3 ) for all rods. This simplification is responsible for an uncertainty, which comprises two components: The uncertainty of the rod population (random), which is found to be ±0.073 g/cm 3 (1σ) A sampling uncertainty because only N rods were randomly drawn from a population of N 0 = 1261 available rods. Random component The average linear density has been obtained by measurements of mass and height of fissile columns made on 1261 rods during their fabrication process leading to ± g/cm (1σ). It has been checked that the distribution of measurements was close to Gaussian. It was seen in Section that the pellet diameter was measured and that the associated uncertainty was ± cm (1σ). The random component (see APPENDIX B) of the density uncertainty was derived from the linear density uncertainty and was calculated to be ±0.073 g/cm 3. A MORET 4 perturbation calculation, using the correlated sampling method, is performed to propagate the 1σ uncertainty in terms of k eff. A density variation of g/cm 3 and g/cm 3 was applied.the impact on reactivity worth of the variation on density is reported in Table 35 and in Table 36. The random component of the uncertainty is calculated to be negligible. Systematic component The systematic uncertainty of mass measurement is estimated to be ±0.5 g (mass reported without decimal places). The corresponding 1σ uncertainty is ±0.289 g since an equiprobable distribution is assumed. Similarly, the systematic uncertainty of critical height measurement is estimated to be ±0.001 cm (height reported with three decimal places). The corresponding 1σ uncertainty is ± cm since an equiprobable distribution is assumed. Moreover, the systematic component of the pellet diameter uncertainty is ±0.005 cm. The corresponding 1σ uncertainty is ± cm since an equiprobable distribution is assumed. These systematic uncertainties are propagated using formulas (1), (2), and (3) in order to obtain the density uncertainty: ρ ρ ρ σ m d H = σ σ + σ density +, (1) m d H m ρ =, (2) 2 π d H 4 ρ = m 1 2 π d 4, H ρ = d 2, 3 π d H 4 ρ = H 1 2 π d H 4 2, (3) with m being the mass of the fissile column, H, the height of the fissile column, and d the diameter of the fissile column. Revision: 0 Page 34 of 196

36 m = g, H = cm, d = cm This density uncertainty is assessed to be g/cm 3. To propagate the 1σ uncertainty in terms of k eff, the density of pellets was varied by g/cm 3, keeping their diameter constant. One APOLLO2-MORET 4 calculation using the correlated sampling method was performed with the reference density and the perturbed one in the APOLLO2 calculation. All the results are reported in Table 35 and in Table Oxide Impurities The fuel also contains impurities. In 2000, impurity analyses were performed on available pellets; the results are provided in Table 9. 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 impurity content (except aluminum, iron, and silicium) taken at the limit of detection include absorbing elements as boron, cadmium and gadolinium. The uncertainty on oxide impurities composition is assumed to be 100% of elements detection limits. The effect on k eff of the impurities below the detection limit 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 (100%). This uncertainty is considered to be a bounding Type-B uncertainty. The impact on reactivity worth of the undetected impurities is for 4A-Ti-005 and for 4A-Ti-010. This value is then divided by 3 to scale to 1σ. The impact on reactivity worth of the detected impurities (Al, Fe, and Si) was also studied. Two APOLLO2-MORET 4 direct Monte Carlo calculations with and without these three elements were performed Zircaloy-4 Density It is assumed that the last digit of the density value is significant. Thus, the corresponding uncertainty is ±0.005 g/cm 3, i.e. σ = g/cm 3, if the uniform-probability hypothesis is assumed. The effect of this uncertainty has been calculated with MORET 4 (using the correlated sampling method) on 4A-Ti-005 and 4A-Ti-010. A density variation of ±0.05 g/cm 3 is applied in the calculation. The obtained k eff is then scaled to 1σ Spring As the neutronic influence of the springs is quite low, no perturbation calculations have been made concerning the composition and dimensional uncertainties. Revision: 0 Page 35 of 196

37 2.2.7 Water Impurities The effect of water impurities has been assessed for 4A-Ti-005 experiment by the difference between a model using water without impurities and a model where the impurities are explicitly modeled (see Table 13). The calculated reactivity effect is lower than for all experiments. Consequently, water impurities were not considered further AG3 Aluminum Alloy Density The maximum contents of silicon, iron, copper, manganese, chromium, zinc, and titanium are retained. The magnesium content corresponds to the middle of the interval. Aluminum is calculated as the balance. No uncertainty value is provided for AG3 aluminum alloy density in the experimental reports. As a consequence, one-half of the last digit is retained (0.005 g/cm 3 ) as an uncertainty. The corresponding 1σ uncertainty is equal to g/cm 3. The effect on k eff is calculated to be negligible Stainless Steel Density (Z2CN18-10) The maximum contents of carbon, silicon, sulfur, and phosphorus are retained. The chromium and nickel contents correspond to the middle of the range. Half of the manganese content is retained and iron is calculated as the balance. Given the low worth on k eff of steel structures, the uncertainty of steel composition is assumed to have no impact on k eff. The stainless steel density is given as 7.9 g/cm 3. 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/cm 3 ) as an uncertainty. The 1σ uncertainty is equal to g/cm 3 since an equiprobable distribution is assumed Screens Densities At the end of 2010, the titanium screen density was measured by FILAB (France) with helium pycnometry. The uncertainty of the measurements is ± g/cm 3 (last significant digit). The results of measurements are reported in Table 22. Table 22: Titanium screens densities. 4A-Ti-005 4A-Ti-010 Density (g/cm 3 ) σ uncertainty Revision: 0 Page 36 of 196

38 The 1σ uncertainty shown in Table 22 reported by the experimentalists a is the standard deviation of measurements. It reflects the standard deviation of the measurements performed for each screen. To propagate the calculated screen density uncertainty in terms of k eff, MORET 4 perturbation calculation using the correlated sampling method were performed; the screen density is varied by ±0.05 g/cm 3. The k eff variation is then scaled to the 1σ uncertainty. The results are presented in Table 23. Experiment Table 23: Density uncertainty propagated in terms of k eff. Density variation in calculation (in g/cm 3 ) k eff 10 5 : k eff (+variation)- k eff (-variation) Uncertainty in density Scaling factor k eff A-Ti-005 ± A-Ti-010 ± Negligible Screen Composition Composition Two chemical analyses were performed to characterize the two titanium screens on 09/12/2008 in the US during the fabrication process and at the end of 2010 by FILAB company in France. The analyses are consistent for the main elements that are detected above the detection limits. The technique used in France was ICP-OES. The technique used in the U.S. to quantify the elements in the titanium was the Glow Discharge Mass Spectrometry (GDMS). The GDMS technique is more precise than ICP-OES, the detection limit of impurities being far lower. Consequently, the US analysis is retained. The impurities below the detection limit (referred to as undetected impurities) are not modeled as they can potentially be absent from the screen. However, their impact on k eff is calculated keeping 100% of the detection limit. These calculations are detailed in and Moreover, some detected impurities (B, Hf, In, Sb, Mg, S, Cl, V, Co, Cu, Ga, Ge, As, Zr, Nb, Mo, Ru, W, Pb, Th, U) whose concentration is very low (see Table 14) are not modeled. No bias is retained. The elements retained in the model are given in Table 24. Table 24: Retained elements in titanium screens. Elements Weight % Titanium 5 mm Titanium 10 mm Fe Cr a Oral communication Revision: 0 Page 37 of 196

39 Ti Sn C N O Al Si P Mn Ni Detected Elements The precision of the measurement of detected elements (by GDMS technique) is not reported in the U.S. analysis. Nevertheless the detected impurities are included in the model, and an uncertainty corresponding to the last digit of each impurity weight in percent (see Section 1.3.8) is taken into account. A variation of the last digit of impurities content is calculated with MORET 4 code using the correlated sampling method. This calculation allows knowing the worth of all impurities. The results of these calculations are reported in Table 25. The results are then scaled to 1σ (divided by 3 since all values are considered equiprobable in the range of the uncertainty). Experiment Table 25: Detected elements uncertainties propagated in terms of k eff. Parameter variation in calculation: (± Last digit of elements content) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in last digit of elements content Scaling factor k eff A-Ti-005 ± A-Ti-010 ± Undetected Impurities The impurities, reported to be below a detection limit, are not included in the model. The maximum content of detected impurities depends on the impurity for the American analysis. This content is reported in Table 26. Revision: 0 Page 38 of 196

40 Table 26: Detection limit of impurities in titanium experiments. Elements ppm/weight Elements ppm/weight Li <0.01 Cs <0.01 Cd <0.1 Ba <0.01 Be <0.005 La <0.005 Bi <0.05 Ce <0.005 F <0.5 Pr <0.005 Na <0.01 Nd <0.005 K <0.05 Sm <0.005 Ca <5 Eu <0.005 Sc <0.1 Gd <0.005 Zn <0.1 Tb <0.005 Se <0.05 Dy <0.005 Br <0.1 Ho <0.005 Rb <5 Er <0.005 Sr <3000 Tm <0.005 Y <200 Yb <0.005 Rh <0.1 Lu <0.005 Pd <0.05 Ta <16 Ag <0.1 Re <0.01 Te <0.05 Os <0.01 I <0.01 Ir <0.01 Pt <0.05 Au <0.1 Hg <0.1 Tl <0.01 The effect of all the undetected impurities presented in the chemical analysis in Section is calculated. An uncertainty of 100% of the detection limit is retained. The impact on reactivity worth of a 100% perturbation on undetected impurities is calculated using MORET 4 perturbation calculations with the correlated sampling method. The results are then scaled to 1σ (divided by 3 since all values are considered equiprobable in the range of the uncertainty). The uncertainty values are also presented in Table 27. Experiment 4A-Ti-005 4A-Ti-010 Table 27: Undetected impurity uncertainties propagated in terms of k eff. Parameter variation in calculation (+variation) 100% for all impurities 100% for all impurities k eff 10 5 k eff -k eff (+variation) Revision: 0 Page 39 of 196 Uncertainty in undetected impurities content Scaling factor k eff 10 5 Negligible 100% 3 Negligible Negligible 100% 3 Negligible

41 Stainless Steel Impurities The stainless steel specifications are given in Reference 1. Chromium and nickel contents are given with an uncertainty value. The uncertainty for manganese and silicon are assumed to be half of the retained value. A MORET 4 calculation using the correlated sampling method is performed to propagate these uncertainties in terms of k eff. The variations result in a k eff variation of ± for all cases, considered as being negligible. As a consequence, the 1σ uncertainty is considered as being negligible Temperature and water density Temperature The temperature uncertainty value was not reported in experimental reports. A value of ±2 C corresponding approximately to the range of variation of the temperature in the reflector is then retained. A ±2 C variation was applied, which, consequently,would modify the water density. The k eff corresponding to the total range of variation was then scaled to 1σ by dividing by Water Density Value The temperature of the experiments (for density of moderating and reflecting water) is considered to be 21 C. For this temperature, the corresponding water density from the Handbook of Chemistry and Physics a is g/cm 3. No water density uncertainty was reported. However, since a ±2 C uncertainty on temperature is assumed, a 0.05% uncertainty on water density is derived. The effect of a 0.1% variation of the water density is evaluated by performing a MORET 4 perturbation calculation that uses the correlated sampling method. The k eff variation is then scaled to the uncertainty (0.05%) and divided by 3 to scale the bounds, assuming uniform probability distribution, to one standard deviation. 2.3 Geometrical Uncertainties Water Height The experiments were sub-critical approaches extrapolated to criticality. In general, the level was raised very close to the critical one, such that the final k eff was approximately within -β/ from criticality. As a consequence, k eff was set equal to Table 1 gives the uncertainty for each experiment (Reference 1); these uncertainties are of statistical and methodological origin. a Handbook of Chemistry & Physics, 87 th edition, Revision: 0 Page 40 of 196

42 The effect on k eff of the uncertainty on critical height is calculated by the difference between two APOLLO2-MORET 4 calculations with a small standard deviation (σ calc <0.0001). The deviation applied on water height are lower than ±1 cm to stay within the linearity interval Rod Height A 1σ uncertainty of ±0.04 cm is retained in the fuel rod height. Two independent APOLLO2-MORET 4 direct calculations with a low Monte Carlo standard deviation were performed to assess the impact of a variation of ±2 cm of the rod height. The k eff variation was negligible for all cases Fissile Column Height A 1σ uncertainty of ±0.254 cm is retained. Two independent APOLLO2-MORET 4 direct calculations with a low Monte Carlo standard deviation were performed to assess the impact of a variation of ±1 cm of the fissile column height. The k eff variation was negligible for all cases Cladding Dimensions Table 4 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. Manufacturing tolerances give an uncertainty of ±0.005 cm. Variation calculations on each parameter have been carried out. The uncertainty of the outer clad diameter was measured to be cm (1σ), which is the same order as the precision of the measuring device (the palmer, the precision being ± cm). A MORET 4 perturbation calculation is performed using the correlated sampling method and varying the outer clad diameter by ± cm. The result was then scaled to 1σ (divided by 3 for the measuring device precision). Another MORET 4 perturbation calculation is performed using the correlated sampling method and varying the inner clad diameter by ±0.005 cm. The result was then scaled to 1σ (divided by 3 since a manufacturing tolerance is used) Rod Positioning The rod positioning 1σ uncertainty is dealt with in Section A MORET 4 pertubation calculation was performed to propagate the uncertainty on the gap between the rod and the grid hole. The dimension was modified in the MORET 4 calculations to take into account an increase and a decrease of the gap. The gap between the rod and the grid hole is assumed to vary from cm. Revision: 0 Page 41 of 196

43 Sensitivity analysis shows that the rod positioning uncertainty due to the space between the rod clad and the hole is the main contributor to the overall uncertainty originated from the pitch. Nevertheless, the contribution of the different components to the global uncertainty was assessed. The variation applied on the pitch is cm. Its impact on reactivity is calculated using a MORET 4 perturbation calculation. The effect on k eff of the variation is then scaled to 1σ (divided by 3 ) and divided by N (number of rods in the core: 400 for 4A-Ti-005 and 440 for 4A-Ti-010) contrary to what was done for other parameters. In fact, the external size of the array is limited by the position of grid external holes. As a consequence, all the rods cannot get further from one another of the value of the gap at the same time; the N can account for that. The same calculations are used to determine the impact of the hole positioning, grid hole diameter, and rod clad outer diameter uncertainties on both titanium experiments. All results are given in Table 35 and in Table Screen Dimensions Two different techniques were used to measure the screens: the laser tracker and the palmer device. The measurements are reported in Table 6. For a consistency purpose and given the low discrepancy between the two types of measurements, it is decided to keep, in the benchmark model, the average of thicknesses given by the palmer device for the two screens. The retained values are reported in Table 28. Material Titanium Table 28: Measured dimensions of the titanium screens. Thickness Height Length Configurations (cm) (cm) (cm) 4A-Ti A-Ti Concerning the laser tracker technique, the screens were measured at different positions of a mesh. The given values are the mean values of approximately 60 measurements. Consequently two types of uncertainty are taken into account: A precision of mm which is associated to each measurement. A random uncertainty which is the standard deviation of all the measurements. The standard deviations are tabulated in Table 6. Concerning the thicknesses measurements with the palmer, 60 measurements were also performed at different locations. No uncertainty associated with the technique itself is given. The retained uncertainty combines the dispersion of the measurements and a systematic uncertainty associated with the palmer device, which can be assumed to be equal to ±0.005 mm (half of the last digit). It is to be noted that the discrepancy between this set of measurements and the measurements made with the laser tracker is lower than the laser tracker precision. The applied deviation on thicknesses is ±0.12 mm for 4A-Ti-005 and for 4A-Ti-010. It is to be noted that the uncertainty on screen length and height is assumed to be negligible. The effect on k eff of the uncertainty in screen thicknesses is evaluated by the difference between two direct APOLLO2-MORET 4 calculations. The results of those calculations are reported in Table 29. Revision: 0 Page 42 of 196

44 These calculations are used to determine the impact of the random uncertainty, and the systematic uncertainty: Random uncertainty (1σ : ± cm for 4A-Ti-005, ± cm for 4A-Ti-010). Systematic uncertainty (1σ : ± cm for both titanium experiments). Experiment Table 29: Thicknesses uncertainties propagated in terms of k eff. Thickness variation in calculation (mm) k eff 10 5 k eff (+variation) - k eff (-variation) 4A-Ti-005 ± A-Ti-010 ± Uncertainty in Thickness (mm) Random uncertainty Systematic uncertainty Random uncertainty Systematic uncertainty Scaling factor Total k eff 10 5 uncertainty k eff x Positioning of Arrays and screens During their assembling, the titanium screens are slipped into guidance rails. The tolerance interval on the slit in which the screens are introduced is [+0.1 mm; +0.5 mm]. Moreover, the assembling of the two screens by means of the groove requires a perfect perpendicularity of the two assembled screens. The UO 2 rods baskets are positioned in order to have perfect contact between the grids and the titanium screens. Considering the maximum shift between the rod arrays and the screen, the arrays positioning uncertainty is estimated to be 0.4 mm. It corresponds to three sources of uncertainty: The uncertainty corresponding to how the array grids are stuck onto the screen (0.15 mm) The uncertainty due to the positioning of the first row of holes in the grid (0.15 mm) The uncertainty due to the flatness of the grid (0.1 mm). For each experiment two APOLLO2-MORET 4 calculations were performed: one without gap (in that case, the grid is in contact with the screen and the distance between the outermost row of rods and the screen is half a pitch) and another with a gap between screens and arrays (see Figure 17). The gap has to be sufficient so that k eff is higher than the Monte-Carlo standard deviation. The calculation gap retained is 1 mm for all the experiments. The effect of a asymetric postioning of baskets has also been investigated. Revision: 0 Page 43 of 196

45 Figure 17: Positioning of arrays for 4A-Ti-005 and 4A-Ti-010 experiments. The k eff variation is then scaled to the uncertainty (0.4 mm) and divided by values are considered equiprobable within the uncertainty range. 3 to be scaled to 1σ since all Table 30 presents the results of these calculations for both titanium experiments. Experiment Table 30: k eff uncertainties caused by the array positioning uncertainties. Gap between screen and array variation in calculation (+ variation) (mm) k eff 10 5 k eff (without variation)- k eff (+variation) Uncertainty in Gap (mm) Scaling factor k eff 10 5 Revision: 0 Page 44 of 196

46 4A-Ti A-Ti The impact of asymetry in the positioning of grids against the screen was also investigated. APOLLO2- MORET 4 calculations were performed moving separately the four arrays of UO 2 rods. The results are reported in Table 31. Table 31: Impact of Assymmetry on the positioning uncertainty. Shift of position of UO 2 arrays in cm k eff k eff Upper right Lower left Lower right Upper left k eff (reference) array shift array shift array shift array shift in pcm (reference) It is shown that the impact on reactivity is associated with the way the arrays are moved. However, the impact is close to maximum when the four arrays are moved the same distance together Repeatability and Reproducibility Experiments Preliminary sensitivity/uncertainty calculations were performed in order to evaluate the impact on k eff of specific uncertainties (such as the rod positioning and the screen positioning). These calculations lead to imposing strong constraints on the experimental device and proposing reproducibility experiments in order to reduce the experimental uncertainties. Reproducibility experiments can be divided as follows: Repeatability experiments (Rv), which consist of a new sub-critical approach after water draining without any change in the configuration. This kind of experiments will give information about the uncertainties on the water height measurement and the extrapolation method. Reproducibility experiments (Rb), which consist of a new sub-critical approach after: (S1) Water draining and removal of the experimental device (support pedestal and lattices) without any change in the configuration, allowing the estimation of the uncertainty in rod positioning due to the gap between grid holes and rods. (S2) Water draining, removal of the experimental device and moving lattice baskets, which highlights the uncertainty in lattice positioning. Revision: 0 Page 45 of 196

47 (S3) Water draining, removal of the experimental device (support pedestal and lattices) and change of rods in order to estimate the uncertainty in rod sampling; notice that the rods are issued from a completely different batch. (S4) Water draining, removal of the experimental device, the UO 2 rods and the tested screens to evaluate uncertainty in screen positioning. It should be mentioned that the batch of UO 2 rods is different from S2, S1, Rv, and reference experiments. The repeatability and reproductibility experiments give new critical water heights values. The k eff value of the repeatability or reproducibility experiment is calculated and then compared to the k eff value of the original experiment. Repeatability and reproducibility experiments Table 32: Reproducibility and repeatability experiments results (APOLLO2-MORET 4 and MORET 5, Monte Carlo uncertainty: 1σ = ± ). hc (cm) ±2σ h c (cm) (repeatabilityreference) APOLLO2-MORET 4 MORET 5 k eff k eff (hc Ti5 ) - k eff (hc repeatablility ) k eff k eff (hc Ti5 ) - k eff (hc repeatablility) 4A-Ti ± A-Ti-005(Rv) ± A-Ti-005-Rb(S2) ± A-Ti-005-Rb(S4) ± R4A-Eau ± R4A-Eau-005-Rb(S2) ± It can be noted that, except for 4A-Ti-005-Rb(S4) experiment, the discrepancies between repeatability/reproducibility experiments and the reference experiment are within the 2σ uncertainty on critical heights associated with the extrapolation method and the level measurement device. The results confirm that the uncertainty in rod positioning and critical water height are small or negligible, as confirmed with independent calculations in Sections and 2.3.1, respectively. However, a significant but small effect on rod sampling and/or screen positioning (S4 reproducibilities) can be highlighted. The effect of array positioning with respect to the screen is evaluated in Section The effective uncertainties due to variation in the properties of the fuel rods are summarized in Tables 32 and 33. The repeatability/reproducibility experiments are not unique benchmark experiment configurations in comparison with 4A-Ti-005, even if they constitute new critical configurations. For 4A-Ti-005, it is proposed to average the water heights of the reference experiment and the Rv and S2 experiments, and then average this water height with the S4 experiment. The aim of that treatment is to clearly make a distinction between the Rv and S2 experiments and the S4 experiment, for which the sample of UO 2 rods is different, which introduces an effect on reactivity. The obtained critical heights are reported in Table 33. The retained critical height uncertainty for the 4A-Ti-005 experiment is the highest amongst the reference, Rv, S2, and S4 experiments. Nevertheless, no additional uncertainty related to the dispersion of critical height amongst the experiments should be added since they are already summed up in other parameter uncertainties (positioning of baskets, rod sampling). The calculated values are consistent with the k eff effects of Table 32 corresponding to the h c. Revision: 0 Page 46 of 196

48 Similarly, for the R4A-Eau-005 and R4A-Eau-005-Rb(S2) experiments, it is proposed to average the critical heights for the same reasons (see Table 33). Table 33: Retained critical heights. Repeatability and reproducibility hc (cm) ±2σ experiments R4A-Eau ± R4A-Eau ± A-Ti ± A-Ti ± Reactivity Sensitivity Calculations Sensitivity calculations are carried out with either one APOLLO2-MORET 4 (correlated sampling method) or two independent APOLLO2-MORET 4 Monte Carlo calculations. The uncertainty effect on k eff is determined directly through a correlated sampling method or by the difference of two independent direct MORET 4 calculations (with a small Monte Carlo deviation). A comparison between continuous energy Monte Carlo MORET 5 (under validation ) code and APOLLO2- MORET 4 code was performed. The results are provided in APPENDIX D. A general good agreement is obtained between calculated results obtained using either MORET 5 or APOLLO2-MORET 4 codes. Table 34a and b summarizes the evaluation of experimental uncertainties for all the parameters discussed in Sections 2.2 and 2.3. The uncertainties in k eff corresponding to most parameters are presented in Table 35 for 4A-Ti-005, in Table 36 for 4A-Ti-010, in Table 37 for R4A-Eau-005, and in Table 38 for R4A-Eau-010. For reference experiments (R4A-Eau-005 and R4A-Eau-010), the uncertainties pertaining to the rods are not calculated. The uncertainties of the corresponding configuration with a screen are retained. However, for what is specific to the reference configuration (critical water height, distance between arrays), calculations are performed. The individually evaluated uncertainties were summed in quadrature to obtain the total uncertainty in each experiment. The most significant uncertainty is in the density of the UO 2 fuel. All four experiments were determined to represent acceptable benchmark experiments. Revision: 0 Page 47 of 196

49 Parameter Identification Mean Value Table 34a: Material uncertainties. 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.%): 234 U A 2 U U U UO 2 Density (g/cm 3 ) - random A / N UO 2 Density (g/cm 3 ) - systematic B UO 2 Detected Impurities 100% B 3 100%/ 3 UO 2 Undetected Impurities %(LD) B 3 100%/ 3 Water Density (g/cm 3 ) % B / 3 Screen Density and and and A Screen Undetected Impurities 0 100%(LD) B 3 100%/ 3 Screen Detected Elements (last digit of elements content in %) ±1 B 3 1/ 3 Water Impurities 0 100% B 3 100%/ 3 Stainless Steel Density (g/cm 3 ) B / 3 Stainless Steel Content (Cr) 18% 1% B 3 1%/ 3 Stainless Steel Content (Ni) 10% 1% B 3 1%/ 3 Stainless Steel Content (Si) 0.5% 0.5% B 3 0.5%/ 3 Stainless Steel Content (Mn) 1% 1% B 3 1%/ 3 Zircaloy Density (g/cm 3 ) B / 3 O/U Stoichiometry A Water Temperature ( C) 20 2 B 3 2/ 3 Revision: 0 Page 48 of 196

50 Parameter Identification Mean Value Table 34b: Geometrical uncertainties. 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) Fuel Pellet Diameter A measurement (cm) Fuel Pellet Diameter B / 3 systematic (cm) Fissile Column Height (cm) A Clad Outer Diameter measurement (cm) A Clad Outer Diameter systematic (cm) B / 3 Clad Inner Diameter (cm) B / 3 Rod Height (cm) B / 3 Critical Water Height (cm) Between From From to A None 2 70 and to Rod Location Gap rod/grid hole (cm) B / 3 N (a) Rod Location Grid hole diameter (cm) B / 3 N (a) Rod Location grid hole positioning (cm) B / 3 N (a) Rod Location rod diameter (cm) B / 3 N (a) Titanium Screen Thickness (mm) 5 and 10 Systematic uncertainty Random uncertainty to A to Position of Arrays (cm) 0.04 B / 3 (a) N is the number of rods in the rod arrays Revision: 0 Page 49 of 196

51 Table 35: Results of sensitivity calculations, titanium experiment (4A-Ti-005). Parameter Identification Uranium Isotopic Contents 235 U (at.%) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor k eff 10 5 ±0.004 A2M4 CS UO 2 Density (g/cm 3 ) random ±0.073 A2M4 CS 220 UO 2 Density (g/cm 3 ) systematic UO 2 detected Impurities ±100% A2M4 CS 5 100% 3 2 UO 2 undetected Impurities 100% A2M4 CS % 3 24 Water Density (g/cm 3 ) ±0.1% A2M4 CS % 3 7 Water impurities 100% A2M4 CS Negligible 100% 3 Negligible Fuel Pellet Diameter measurement (cm) ±0.01 A2M4 CS Fuel Pellet Diameter systematic (cm) ±0.01 A2M4 CS Clad Outer Diameter measurement (cm) ± A2M4 CS Clad Outer Diameter systematic (cm) ± A2M4 CS Clad Inner Diameter (cm) ±0.005 A2M4 CS Zircaloy Density (g/cm 3 ) ±0.05 A2M4 CS Negligible AG3 density (g/cm 3 ) ±0.005 A2M4 CS Negligible Negligible Stainless Steel density ±0.05 A2M4 CS Negligible Negligible Stainless Steel impurities 100% A2M4 CS Negligible 100% 3 Negligible O/U Stoichiometry ±0.01 A2M4 CS Negligible Negligible Rod height (cm) ±2 A2M4 DC Negligible Negligible Fissile Column Height (cm) ±1 A2M4 DC Negligible Negligible Critical Water Height (cm) ±0.6 A2M4 DC Rod Location Grid Hole Positioning (cm) Gap Grid/Rod Rod Location Grid Hole Positioning (cm) Hole Position ± A2M4 CS Rod Location Grid Hole Positioning (cm) Grid Diameter Rod location Grid Hole Positioning (cm) Rod Diameter Negligible Revision: 0 Page 50 of 196

52 Parameter Identification Table 35: Results of sensitivity calculations, titanium experiment (4A-Ti-005) (continued) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor Screen Thickness (cm) ±0.012 Random A2M4 DC uncertainty 210 Systematic A2M4 DC uncertainty Screen Density (g/cm 3 ) ±0.05 A2M4 CS Screen Detected Elements (last digit of elements content in %) ±1 A2M4 CS Screen Undetected Impurities 100% A2M4 CS Negligible 100% 3 Negligibl e Position of Rod arrays (cm) 0.1 A2M4 DC Temperature ( C) ±2 A2M4 CS OVERALL UNCERTAINTY 124 (a) A2M4 CS: APOLLO2-MORET 4 code using the correlated sampling method A2M4 DC: two APOLLO2-MORET 4 direct calculations (Monte Carlo standard deviation) k eff 10 5 Revision: 0 Page 51 of 196

53 Table 36: Results of sensitivity calculations, titanium experiment (4A-Ti-010). Parameter Identification Uranium Isotopic Contents 235 U (at.%) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor k eff 10 5 ±0.004 A2M4 CS UO 2 Density (g/cm 3 ) - random ±0.073 A2M4 CS 196 UO 2 Density (g/cm 3 ) - systematic UO 2 detected Impurities ±100% A2M4 CS 5 100% 3 2 UO 2 undetected Impurities 100% A2M4 CS % 3 24 Water Density (g/cm 3 ) ±0.1% A2M4 CS % 3 7 Water impurities 100% A2M4 CS Negligible 100% 1 Negligible Fuel Pellet Diameter measurement (cm) ±0.01 A2M4 CS Fuel Pellet Diameter systematic (cm) ±0.01 A2M4 CS Clad Outer Diameter measurement (cm) ± A2M4 CS Clad Outer Diameter systematic (cm) ± A2M4 CS Clad Inner Diameter (cm) ±0.005 A2M4 CS Zircaloy Density (g/cm 3 ) ±0.05 A2M4 CS Negligible AG3 density (g/cm 3 ) ±0.005 A2M4 CS Negligible Negligible Stainless Steel density ±0.05 A2M4 CS Negligible Negligible Stainless Steel impurities 100% A2M4 CS Negligible 100% 3 Negligible O/U Stoichiometry ±0.01 A2M4 CS Negligible Negligible Rod Height (cm) ±2 A2M4 DC Negligible Negligible Fissile Column Height (cm) ±1 A2M4 DC Negligible Negligible Critical Water Height (cm) /- 0.6 A2M4 DC Negligible Rod Location Grid Hole Positioning (cm) Gap Grid/Rod Rod Location Grid Hole Positioning (cm) Hole Position ± A2M4 CS Rod Location Grid Hole Positioning (cm) Grid Diameter Rod location Grid Hole Positioning (cm) Rod Diameter Negligible Revision: 0 Page 52 of 196

54 Parameter Identification Table 36: Results of sensitivity calculations, titanium experiment (4A-Ti-010) (continued) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor k eff 10 5 Screen Thickness (cm) ±0.012 Random A2M4 DC uncertainty 148 Systematic A2M4 DC uncertainty Screen Density (g/cm 3 ) ±0.05 A2M4 CS Negligible Screen Detected Elements (last digit of elements content in %) ±1 A2M4 CS Screen Undetected Impurities 100% A2M4 CS Negligible 100% 3 Negligible Position of Rod arrays (cm) 0.1 A2M4 DC Temperature ( C) ±2 A2M4 CS OVERALL UNCERTAINTY 110 (a) A2M4 CS: APOLLO2-MORET 4 code using the correlated sampling method A2M4 DC: two APOLLO2-MORET 4 direct calculations (Monte Carlo standard deviation) Revision: 0 Page 53 of 196

55 Table 37: Results of sensitivity calculations, reference experiment (R4A-Eau-005). Parameter Identification Uranium Isotopic Contents 235 U (at.%) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor k eff 10 5 ±0.004 A2M4 CS UO 2 Density (g/cm 3 ) - random ±0.073 A2M4 CS 220 UO 2 Density (g/cm 3 ) - systematic UO 2 detected Impurities ±100% A2M4 CS 5 100% 3 2 UO 2 undetected Impurities 100% A2M4 CS % 3 24 Water Density (g/cm 3 ) ±0.1% A2M4 CS % 3 7 Water impurities 100% A2M4 CS Negligible 100% 1 Negligible Fuel Pellet Diameter measurement (cm) ±0.01 A2M4 CS Fuel Pellet Diameter systematic (cm) ±0.01 A2M4 CS Clad Outer Diameter measurement (cm) ± A2M4 CS Clad Outer Diameter systematic (cm) ± A2M4 CS Clad Inner Diameter (cm) ±0.005 A2M4 CS Zircaloy Density (g/cm 3 ) ±0.05 A2M4 CS Negligible AG3 density (g/cm 3 ) ±0.005 A2M4 CS Negligible Negligible Stainless Steel density ±0.05 A2M4 CS Negligible Negligible Stainless Steel impurities 100% A2M4 CS Negligible 100% 3 Negligible O/U Stoichiometry ±0.01 A2M4 CS Negligible Negligible Rod height (cm) ±2 A2M4 DC Negligible Negligible Fissile Column Height (cm) ±1 A2M4 DC Negligible Negligible Critical Water Height (cm) ±0.6 A2M4 DC Rod Location Grid Hole Positioning (cm) Gap Grid/Rod Rod Location Grid Hole Positioning (cm) Hole Position ± A2M4 CS Rod Location Grid Hole Positioning (cm) Grid Diameter Rod location Grid Hole Positioning (cm) Rod Diameter Negligible Position of Rod arrays (cm) 0.1 A2M4 DC Temperature ( C) ±2 A2M4 CS OVERALL UNCERTAINTY 121 (a) A2M4 CS: APOLLO2-MORET 4 code using the correlated sampling method A2M4 DC: two APOLLO2-MORET 4 direct calculations (Monte Carlo standard deviation) Revision: 0 Page 54 of 196

56 Table 37: Results of sensitivity calculations, reference experiment (R4A-Eau-010). Parameter Identification Uranium Isotopic Contents 235 U (at.%) Parameter Variation in Calculation Type of Calculation (a) k eff 10 5 k eff (+variation) k eff (-variation) Uncertainty in Parameter Scaling factor k eff 10 5 ±0.004 A2M4 CS UO 2 Density (g/cm 3 ) - random UO 2 Density (g/cm 3 ) - ±0.073 A2M4 CS 196 systematic UO 2 detected Impurities ±100% A2M4 CS 5 100% 3 2 UO 2 undetected Impurities 100% A2M4 CS % 3 24 Water Density (g/cm 3 ) ±0.1% A2M4 CS % 3 7 Water impurities 100% A2M4 CS Negligible 100% 1 Negligible Fuel Pellet Diameter measurement (cm) ±0.01 A2M4 CS Fuel Pellet Diameter systematic (cm) ±0.01 A2M4 CS Clad Outer Diameter measurement (cm) ± A2M4 CS Clad Outer Diameter systematic (cm) ± A2M4 CS Clad Inner Diameter (cm) ±0.005 A2M4 CS Zircaloy Density (g/cm 3 ) ±0.05 A2M4 CS Negligible AG3 density (g/cm 3 ) ±0.005 A2M4 CS Negligible Negligible Stainless Steel density ±0.05 A2M4 CS Negligible Negligible Stainless Steel impurities 100% A2M4 CS Negligible 100% 3 Negligible O/U Stoichiometry ±0.01 A2M4 CS Negligible Negligible Rod Height (cm) ±2 A2M4 DC Negligible Negligible Fissile Column Height (cm) ±1 A2M4 DC Negligible Negligible Critical Water Height (cm) ±0.6 A2M4 DC Rod Location Grid Hole Positioning (cm) Gap Grid/Rod Rod Location Grid Hole Positioning (cm) Hole Position Rod Location Grid Hole ± A2M4 CS Positioning (cm) Grid Diameter Rod location Grid Hole Positioning (cm) Rod Negligible Diameter Position of Rod arrays (cm) 0.1 A2M4 DC Temperature ( C) ±2 A2M4 CS OVERALL UNCERTAINTY 109 (a) A2M4 CS: APOLLO2-MORET 4 code using the correlated sampling method A2M4 DC: two APOLLO2-MORET 4 direct calculations (Monte Carlo standard deviation) Revision: 0 Page 55 of 196

57 2.5 Reactivity worth of screens MIRTE experiments were designed in a such way that they present a sufficient reactivity worth of screens in the configuration. This condition is paramount when evaluating the bias of material screens. The reactivity worth of screens is calculated using either APOLLO2-MORET 4 or KENO-V.a codes and replacing the screen either by air or water. The Monte Carlo standard deviation of both calculations is The results are reported in Table 38. Table 38: Reactivity worth of screens. Experiment Code Screen replaced by Air Reactivity worth of screen (pcm) Screen replaced by Water Reactivity worth of screen (pcm) 4A-Ti-005 4A-Ti-010 KENO-V.a APOLLO2-MORET KENO-V.a APOLLO2-MORET Revision: 0 Page 56 of 196

58 3.0 BENCHMARK SPECIFICATIONS 3.1 Description of Model The benchmark-model geometry is shown in Figure 19 through 26. 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. The effective bias is assumed to be negligible. The baskets structure (tubes, feet, plates) and the frame of the screens are made of AG3 aluminum alloy; the tubes of the basket and frame structures are hollow and filled with water. The worth of each of these devices has been assessed for 4A-Ti-005 configuration (see Table 39). These devices are omitted from the model and a bias is applied on the benchmark model. It is calculated using APOLLO2-MORET 4 code; two calculations are performed: one with the detailed model and another with the simplified benchmark model. The standard deviation of the Monte Carlo calculation is ± The biases are reported in Table 41. Table 39: Simplification calculations (calculations performed for Case 1). Part omitted APOLLO2-MORET 4 (172-group, CEA93V6) k eff (a) (pcm) σ Monte-Carlo (pcm) Support pedestal tubes -18 Tank -11 Basket structure +6 Frame of screen -2 Base of array Reinforcement base +10 Part of the grid without holes +19 All omitted part -37 (b) (a) Difference between k eff with component and k eff without component. (b) Summation of the individual simplifications in the table is not equivalent to the effective bias calculated with the omission of all parts. There is a large Monte Carlo statistical uncertainty compared to the magnitude of many of these simplifications and possible correlation effects exist between individual omissions. Revision: 0 Page 57 of 196

59 Table 40: Biases for the bechmark models. Cases Bias ± uncertainty APOLLO2-MORET 4 (172-group, CEA93V6) (pcm) 1-37 ± ± ± ± 18 Given the relatively low worth of the biases, the related uncertainties are assumed to be ±30% of the bias value. The springs in the fuel rods are not included in the benchmark models; no bias was evaluated because they are not significant in terms of reactivity. 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 constant, and the top plug is replaced by a cm-high cylinder, both with a cm diameter (see APPENDIX C). The impact on reactivity of such simplifications is negligible. Only the three fuel impurities measured over the detection limit are included in the models. The impact on k eff of impurities below this detection limit is studied in Section The homogenization process is described in APPENDIX C. Because the effects of homogenization have not been thoroughly evaluated, and although it is known that this effect is negligible, the homogenized zones are not proposed in the benchmark model. The parts of the lower grid not occupied by UO 2 rods are not described exactly; an homogenization of the AG3 aluminum alloy of the grid and water is proposed for the lower grids and an homogenization of the AG3 aluminum alloy of the grid and air is proposed for the upper grid. Calculations demonstrated that the effect of homogenization is negligible. The AmBe source, liminimeter, and neutron counters (sufficiently far from the core) are not modeled. They are assumed to lead to a negligible bias. The fuel pellet diameter is rounded to cm, which led to a negligible bias. The outer clad diameter is rounded to cm, which led to a negligible bias. Concerning titanium screens, some detected impurities are not modeled. As explained in Section , this led to a negligible bias. No bias related to the non-modeling of thermocouples has been established. Revision: 0 Page 58 of 196

60 3.2 Dimensions The model comprises the following parts surrounding the baskets: The support pedestal, reduced to the Z2CN18-10 stainless steel support plate, 186 cm 186 cm and 2.5 cm thick. The water, cm thick beneath the support plate. The water inside and around the fuel arrays under the critical level (see Table 41). The air inside and around the fuel arrays over the critical level. The arrays of fuel rods described in Figure 20, 22, 24, and 26 (rods characteristics are given in Table 42 and Figure 18). The bottom of the fissile column is 1.18 cm above the bottom of fuels rods. The cruciform screen between the rods arrays (see Figure 20, 22, 24, and 26), when necessary (configurations with screens). Table 41: Benchmark data for titanium screen experiments and their references. Case Experiment Array Geometry (n x n y ) Critical Height, H c (cm) 1 4A-Ti A-Ti R4A-Eau R4A-Eau (a) Section summarizes how the final benchmark critical heights were obtained. The baskets comprise the lower and upper grids of AG3 aluminum alloy. The distance from the top surface of the lower grid to the bottom surface of the upper grid is 97.5 cm.the four square shaped grids measure cm and are 0.4 cm thick. The parts of the lower grids and the upper grids without rods are homogenized zones of AG3 aluminum alloy and water (for lower grids) or air (for upper grids) (see Table 45). The holes diameters are set equal to 0.98 cm. The bottom of the screens is 6.7 cm above the support plate of the pedestal. As the bottom plugs have been cylindrized, the bottom of the fuel rods array is 7.32 cm above the support plate. The fuel rods dimensions are given in Table 42. The water critical heights (H c ) and the array dimensions are given in Table 41. A description of the rods is given in Figure 18. It is to be noted that the bottom of the fissile column coincides exactly with the top of the bottom grid in Figures 19, 21, 23, and 25. Revision: 0 Page 59 of 196

61 Table 42: Geometrical data for fuel rods. Fuel Diameter Clad Inner Diameter Clad Outer Diameter Fissile Column Height Bottom Plug Height (a) Top Plug Height (a) cm cm cm cm 1.18 cm cm Spring Zone Height cm Total Rod Height (a) (Fissile Column Height + Spring Zone cm Height + Top and Bottom Plug Heights) Lattice Pitch 1.6 cm Distance between Surface of the Screens and the Centers of the Adjacent Fuel Rods 0.8 cm (Half Pitch) (a) Plugs are replaced by cylinder-shaped plugs (see the first paragraph of APPENDIX C). Revision: 0 Page 60 of 196

62 Diameter = Upper plug (Zircaloy 4) Air Clad (Zircaloy 4) ~ Air H C ~ ~ Fuel pellets Water Clad (Zircaloy 4) Pellet diameter = Lower plug (Zircaloy 4) Dimensions in cm not to scale Figure 18: UO 2 rod. The screen dimensions reported in Table 43 are derived from Table 6 (see discussion in Section and Figure 16). Table 43: Experiment screen dimensions. Case Experiment Thickness, e (cm) Length, L (cm) Height, H (cm) 1 4A-Ti A-Ti Revision: 0 Page 61 of 196

63 A general schematic of the benchmark configurations is shown in Figure 19 to Figure 27. The critical water height, H C, and the array size, n x and n y, are taken from Table 41. The screen thickness or distance between the arrays (for reference experiments), e; height, H; and length, L; are taken from Table Titanium screen U O 2 rod Air e Top grid AG3 24 x 24 x 0.4 e: thickness of the screen H: height of the screen H : water critical height c H c Fuel column height H Detail A Bottom grid 0.98 Pedestal Bottom grid AG3 24 x 24 x 0.4 Water 6.7 Steel plate (186 x 186 x 2.5) Detail A Distance from top of bottom grid to bottom of top grid Drawing not to scale Dimensions in cm 11-GA Figure 19: Benchmark model - Case 1 (lateral view). Revision: 0 Page 62 of 196

64 Water or air L e: thickness of the screen: cm L: length of the screen Array size: 10 x 10 Total number of fuel rods: 400 e Titanium screen Drawing not to scale Dimensions in cm 11-GA Figure 20: Benchmark model Case 1 (top view). Revision: 0 Page 63 of 196

65 189.7 Titanium screen U O 2 rod Air e Top grid AG3 24 x 24 x 0.4 e: thickness of the screen H: height of the screen H : water critical height c H c Fuel column height H Detail A Bottom grid 0.98 Pedestal Bottom grid AG3 24 x 24 x 0.4 Water 6.7 Steel plate (186 x 186 x 2.5) Detail A Distance from top of bottom grid to bottom of top grid Drawing not to scale Dimensions in cm 11-GA Figure 21: Benchmark model - Case 2 (lateral view). Revision: 0 Page 64 of 196

66 Water or air L e: thickness of the screen: cm L: length of the screen Array size: 11 x 10 Total number of fuel rods: 440 e Titanium screen Drawing not to scale Dimensions in cm 11-GA Figure 22: Benchmark model - Case 2 (top view). Revision: 0 Page 65 of 196

67 U O 2 rod Air e Top grid AG3 24 x 24 x 0.4 e: separation between arrays H: height of the screen H : water critical height c H c Fuel column height Detail A Bottom grid 0.98 Pedestal Bottom grid AG3 24 x 24 x 0.4 Water Steel plate (186 x 186 x 2.5) Detail A Distance from top of bottom grid to bottom of top grid Figure 23: Benchmark model - Case 3 (lateral view). Drawing not to scale Dimensions in cm 11-GA Revision: 0 Page 66 of 196

68 Water or air e e: separation between arrays: 0.5 cm Array size: 9 x 8 Total number of fuel rods: 288 Drawing not to scale Dimensions in cm 11-GA Figure 24: Benchmark model - Case3 (top view). Revision: 0 Page 67 of 196

69 U O 2 rod Air e Top grid AG3 24 x 24 x 0.4 e: separation between arrays H: height of the screen H : water critical height c H c Fuel column height Detail A Bottom grid 0.98 Pedestal Bottom grid AG3 24 x 24 x 0.4 Water Detail A Distance from top of bottom grid to bottom of top grid Steel plate (186 x 186 x 2.5) Drawing not to scale Dimensions in cm 11-GA Figure 25: Benchmark model - Case 4 (lateral view). Revision: 0 Page 68 of 196

70 Water or air e e: separation between arrays: 1 cm Array size: 9 x 8 Total number of fuel rods: 288 Drawing not to scale Dimensions in cm 11-GA Figure 26: Benchmark model - Case 4 (top view). Revision: 0 Page 69 of 196

71 D 0.98 Pitch 1.6 Pitch 1.6 Dimensions in cm 11-GA Figure 27: Upper and lower grids. Please note: Grid regions not occupied by fuel rods that are outside the four arrays are represented as homogeneous regions of aluminum and water for the lower grid and aluminum and air for the upper grid (see Table 45 for homogeneous compositions). Revision: 0 Page 70 of 196

72 3.3 Material Data Fuel Rod Materials Fuel rod material data are derived from Table 7 through Table 12. Atom densities for these materials are given in Table 44. Table 44: Atom densities for fuel rod materials. Material UO 2 Elements and Isotopes Atom densities (atom/barn-cm) O E-02 Fe E-06 Si E-05 Al E U E U E U E U E-02 Zircaloy-4 (Fuel-rod Clad, End Plugs) N O Sn Fe Cr C Si Al Zr Hf H E E E E E E E E E E E Structural Materials Structural materials data are derived from Table 13 and Table 18. They are reported in Table 45. Revision: 0 Page 71 of 196

73 Material Table 45: Atom densities for structural materials. Elements and Isotopes Atom densities (atom/barn-cm) Si E-04 Fe E-04 Cu E-05 Mn E-04 Mg E-03 Cr E-05 Zn E-05 Ti E-05 Al E-02 Cr E-02 Ni E-03 Mn E-04 Si E-03 P E-05 S E-05 C E-04 Fe E-02 O E-02 Water H E-02 N E-05 Air (a) O E-05 AG3 Aluminum Alloy (Grids, Top and Bottom Plate of Baskets) Stainless Steel Z2CN18-10 (Steel Plate of Pedestal) Compound AG3 Aluminum Alloy + Water or Air (Lower Grids and Upper Grids without rods) Elements Atom densities Atom densities Elements (atom/barn-cm) (atom/barn-cm) Si E-04 Si E-04 Fe E-05 Fe E-05 Cu E-05 Cu E-05 Mn E-04 Mn E-04 Mg E-03 Grid Mg E-03 Grid + Water Cr E-05 + Cr E-05 Zn E-05 Air Zn E-05 Ti E-05 Ti E-05 Al E-02 Al E-02 H E-02 N E-05 O E-03 O E-06 Revision: 0 Page 72 of 196

74 3.3.3 Titanium Screens The screen composition is provided in Table Temperature Data Table 46: The atom densities for titanium screens. Atom densities Element (atom/barn-cm) 4A-Ti-005 4A-Ti-010 Case 1 Case 2 Fe E E-05 Cr E E-05 Ti E E-02 Sn E E-07 C E E-05 N E E-06 O E E-04 Al E E-06 Si E E-05 P E E-06 Mn E E-06 Ni E E-06 The temperature of the benchmark models is 21ºC. 3.5 Experimental and Benchmark-Model k eff The critical heights reported in Table 1 are the results of measurements extrapolated to criticality. The critical heights reported are intended to correspond to an experimental k eff of No significant bias or additional bias uncertainty due to the simplication of the experimental device has been determined. An analysis of experimental uncertainties was performed in Section 2.2. The benchmark k eff s for both benchmark configurations is given in Table 47. Experiment ID Case Table 47: Benchmark k eff and 1σ uncertainty. Experiment k eff Benchmark k eff Bias (pcm) Bias uncertainty (pcm) 1σ uncertainty Revision: 0 Page 73 of 196

75 4.0 RESULTS OF SAMPLE CALCULATIONS Table 48 and Table 49 give the calculated k eff s obtained with: The APOLLO2-MORET 4 codes with CEA group library based on JEF2.2 evaluation; APOLLO2 calculates with the Pij method homogenized, self shielded macroscopic cross sections. These cross sections are then used in a MORET 4 3D Monte Carlo calculation. The continuous energy MORET 5 code (under validation) with JEF2.2 evaluation cross section. The continuous energy MCNPX2.6 Monte Carlo code with ENDF/B-VII.0 cross section library. The multi-group KENO-V.a code, using the 238-group ENDF/B-VI.7 cross section library. Some zones comprising several materials have a low impact on reactivity; as a consequence, their materials could be homogenized. These zones are the followings: Bottom plug in water Grid, bottom plug, and water Clad in air corresponding to the spring zone Grid, clad in air (for the spring zone) Top plug in air Grids, water Grids, air. A typical input listing is provided for the 4A-Ti-005 experiment (Case 1) for each code in APPENDIX A. Table 48: Calculation results of benchmark model with codes using pointwise cross sections. Case Experiment MCNPX2.6 ENDF/B-VII k eff ± 1σ MORET 5 JEF2.2 k eff ± 1σ 1 4A-Ti ± ± A-Ti ± ± R4A-Eau ± ± R4A-Eau ± ± Table 49: Calculation results of benchmark model with multi-group codes. APOLLO2-MORET 4 KENO-V.a Case Experiment JEF2.2 ENDF/B-VI.7 k eff ± 1σ k eff ± 1σ 172 group 238 group 1 4A-Ti ± ± A-Ti ± ± R4A-Eau ± ± R4A-Eau ± ± Revision: 0 Page 74 of 196

76 Calculations with APOLLO2-MORET 4 have a tendency to overestimate k eff a significantly for both configurations with and without titanium. This may be explained by the physical models (pij calculation and self-shielding options) of the calculational scheme. For configurations with titanium, an additional overestimation is observed and comes from the multi-group treatment of nuclear data. Calculations with KENO-V.a have a tendency to underestimate k eff significantly for both configurations without titanium. This is observed for all thermal configurations with low enriched uranium. It can be attributed to ENDF/B-VI.7 uranium cross sections. This underestimation no longer exists for experiments with titanium. Calculations with MCNPX2.6 and MORET 5 show a quite good agreement with the benchmark k eff. a N. Leclaire, I. Duhamel, Y.K. Lee, C. Venard, Experimental validation of the French CRISTAL V1.0 package, NCSD 2005, Knoxville, Tennessee, September 19 22, Revision: 0 Page 75 of 196

77 5.0 REFERENCES 1. J. Piot Appareillage B Rapport définitif d expériences Programme Matériaux Interaction Réflexion Toutes Epaisseurs MIRTE Phase 1 - MIRTE 1 program. 2. 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/ Revision B du 22/03/ 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%)O 2 et Synthese des Etudes» - Rapport SRNC [Translation: «PWR U(4,738%)O 2 Fuel Rods Characteristics and Synthesis of Studies»] SRNC Report. Revision: 0 Page 76 of 196

78 APPENDIX A: TYPICAL INPUT LISTINGS A.1 APOLLO2-MORET 4 Input Listing The calculation is run in two steps using the CRISTAL package (Version 1.2). APOLLO2 (release 2.5.5) is a 1-D multi-group cell code. It is used to determine material buckling B m 2, k infinite, and homogenized self shielded cross sections; it uses the CEA93.V6, 172-group library (derived from JEF2.2). MORET 4 is a 3-D multi-group Monte Carlo code. It uses self-shielded macroscopic cross sections coming from APOLLO2. The cross section library is derived from JEF2.2 evaluation batches and 8000 neutrons per batch are simulated. The first 200 batches are skipped. A third code (or graphical user interface) called CIGALES is also used to generate the APOLLO input data. It also calculates atomic densities from chemical data. The benchmark models for 4A-Ti-005 configuration are presented in this appendix. A.1.1 APOLLO2-MORET 4 input listing for thin thickness configuration (4A-Ti-005). IRSN / SEC APOLLO2 / MORET 4 LEU-COMP-THERM-MIRTE MIRTE 1 Programme revision 0 experiment Interacting configuration with thin screens 4 Arrays of UO2 rods (4.738 %) 10x10 pitch 1.6cm Critical Height : cm Titanium 5 mm keff(exp)± 1 s = ± Writer N. LECLAIRE Reviewer F.X. LEDAUPHIN DEBUT_APOLLO2 =+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ CIGALES version 3.2 en date du 12/09/2007 Creation du Fichier le 13/12/ :12:20 =+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+ -=- INITIALISATION - CALCUL 1 -=- TOPT = TABLE: ; TRES = TABLE: ; TSTR = TABLE: ; TOPT.'CALCUL_CRISTAL' = 1 ; REPPROC = OUVRIR: 22 'VARIABLE' 'ADRESSE' 'aprocristal' ; CHARGE_APROCRISTAL = LIRE: REPPROC 'APROC' 'CHARGE_APROCRISTAL' ; FERMER: REPPROC ; EXECUTER CHARGE_APROCRISTAL ; Revision: 0 Page 77 of 196

79 TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; -=- OPTIONS -=- TOPT.'STCRI'.'NGROUP_FINAL' = 172 ; 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 ' = E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-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 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 ============================================================== STEEL TITRE: ' STEEL ' ; CALCUL_AP2 = 2 ; WRITE: TOPT.'RESU' 'STEEL CAS 2 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; STEEL nom_calc = 'MILHOM2' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'STEEL' ; TOPT.'STMIL'.nom_mil = TABLE: ; Revision: 0 Page 78 of 196

80 TOPT.'STMIL'.nom_mil.'CRNAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'NINAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'P31 ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-04 ; 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 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 ============================================================== WATER TITRE: ' WATER ' ; CALCUL_AP2 = 3 ; WRITE: TOPT.'RESU' 'WATER CAS 3 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; WATER nom_calc = 'MILHOM3' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'WATER' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'H2O ' = E-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 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 ; Revision: 0 Page 79 of 196

81 -=- Creation de la Macrolib pour le milieu MILHOM3 -=- APOTRIM: &EDIT 1 TSTR.nom_calc.'MAC' ANISO &NOMA &FICH 47 &NOMMIL TSTR.'MILREF'.nom_mil nom_mil ; DETRUIRE: TSTR.'APOLIB' ; ============================================================== APOLLO PIJ CALCUL 4 ============================================================== AG3 TITRE: ' AG3 ' ; CALCUL_AP2 = 4 ; WRITE: TOPT.'RESU' 'AG3 CAS 4 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; AG3 nom_calc = 'MILHOM4' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'AG3' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-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 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 ============================================================== AG3 + HOLES (air) TITRE: ' AG3 + HOLES (air) ' ; CALCUL_AP2 = 5 ; WRITE: TOPT.'RESU' 'AG3 + HOLES (air) CAS 5 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; AG3 + HOLES (air) nom_calc = 'MILHOM5' ; Revision: 0 Page 80 of 196

82 TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'AG3 + HOLES (air)' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-02 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-06 ; 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 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 ============================================================== Titanium TITRE: ' Titanium ' ; CALCUL_AP2 = 6 ; WRITE: TOPT.'RESU' 'Titanium CAS 6 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; Titanium nom_calc = 'MILHOM6' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'Titanium' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-07 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-06 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-04 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'P31 ' = E-07 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-06 ; Revision: 0 Page 81 of 196

83 TOPT.'STMIL'.nom_mil.'NINAT ' = E-06 ; 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 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 ============================================================== AP TITRE: ' AP ' ; CALCUL_AP2 = 7 ; WRITE: TOPT.'RESU' 'AP CAS 7 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; AP nom_calc = 'MILHOM7' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'AP' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-04 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-07 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-07 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-06 ; 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 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' Revision: 0 Page 82 of 196

84 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 8 ============================================================== AC TITRE: ' AC ' ; CALCUL_AP2 = 8 ; WRITE: TOPT.'RESU' 'AC CAS 8 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; milieu_23 nom_calc = 'MILHOM8' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'milieu_23' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-07 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-08 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-07 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-07 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-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 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 9 ============================================================== TITRE: ' ' ; CALCUL_AP2 = 9 ; WRITE: TOPT.'RESU' '( CAS 9 ' ; Revision: 0 Page 83 of 196

85 -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; milieu_24 nom_calc = 'MILHOM9' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'milieu_24' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-02 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-07 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-08 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-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 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 10 ============================================================== Array in air CAS 10 TITRE: 'Array in air CAS 10 ' ; CALCUL_AP2 = 10 ; WRITE: TOPT.'RESU' 'UO2 poudre ' ' CAS 10' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; 'CELLUL10 NZ=4 C1= C2=.418 C3= C4= ' ' ' ; nom_calc = 'CELLUL10' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; Revision: 0 Page 84 of 196

86 UO2 poudre nom_mil = 'FISSIL1_ 1' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'U234 ' = E-06 ; TOPT.'STMIL'.nom_mil.'U235 ' = E-03 ; TOPT.'STMIL'.nom_mil.'U236 ' = E-05 ; TOPT.'STMIL'.nom_mil.'U238 ' = E-02 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-02 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-06 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-05 ; 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 nom_mil = 'STRUCT1 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; ZR4_1_87 nom_mil = 'STRUCT2 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = E-04 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-06 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-06 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; AIR nom_mil = 'STRUCT3 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-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 &EQD &EQD &EQD &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 10 ; -=- Creation de la bibliotheque interne -=- TSTR.'APOLIB' = BIBINT: &EDIT 1 TSTR.'IDB' TSTR.nom_calc.'GEO' &SFIN &TP ( TEXTE TOPT.'REPBIB' ) ; -=- Autoprotection -=- Revision: 0 Page 85 of 196

87 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 CELLUL10 -=- 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 11 ============================================================== Array in water CAS 11 TITRE: 'Array in water CAS 11 ' ; CALCUL_AP2 = 11 ; WRITE: TOPT.'RESU' 'UO2 poudre ' ' CAS 11' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; 'CELLUL11 NZ=4 C1= C2=.418 C3= C4= ' ' ' ; nom_calc = 'CELLUL11' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; UO2 poudre nom_mil = 'FISSIL1_ 1' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'U234 ' = E-06 ; TOPT.'STMIL'.nom_mil.'U235 ' = E-03 ; TOPT.'STMIL'.nom_mil.'U236 ' = E-05 ; TOPT.'STMIL'.nom_mil.'U238 ' = E-02 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-02 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-06 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-05 ; 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 nom_mil = 'STRUCT1 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; Revision: 0 Page 86 of 196

88 TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; ZR4_1_87 nom_mil = 'STRUCT2 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'O16 ' = E-04 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-06 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-06 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TEMPERATURE' = 21. ; EAU a 21 degres nom_mil = 'STRUCT3 ' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'H2O ' = E-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 &EQD &EQD &EQD &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 10 ; -=- 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' ; Revision: 0 Page 87 of 196

89 -=- 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 CELLUL11 -=- 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 12 ============================================================== WP TITRE: ' WP ' ; CALCUL_AP2 = 12 ; WRITE: TOPT.'RESU' 'WP CAS 12 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; WP nom_calc = 'MILHOM10' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'WP' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'H2O ' = E-02 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-07 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-06 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-06 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-07 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-06 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-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 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 Revision: 0 Page 88 of 196

90 ============================================================== WPG TITRE: ' WPG ' ; CALCUL_AP2 = 13 ; WRITE: TOPT.'RESU' 'WPG CAS 13 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; WPG nom_calc = 'MILHOM11' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'WPG' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-02 ; TOPT.'STMIL'.nom_mil.'N14 ' = E-06 ; TOPT.'STMIL'.nom_mil.'O16 ' = E-05 ; TOPT.'STMIL'.nom_mil.'SNNAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'CNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZRNAT ' = E-02 ; TOPT.'STMIL'.nom_mil.'HFNAT ' = E-07 ; TOPT.'STMIL'.nom_mil.'H1 ' = E-06 ; TOPT.'STMIL'.nom_mil.'H2O ' = E-04 ; 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 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' ; ============================================================== APOLLO PIJ CALCUL 14 ============================================================== AG3 + HOLES (water) TITRE: ' AG3 + HOLES (water) ' ; CALCUL_AP2 = 14 ; WRITE: TOPT.'RESU' 'AG3 + HOLES (water) CAS 14 ' ; -=- Description des milieux -=- TRES TSTR TOPT = INITIALISER_CRISTAL 1 TSTR TOPT TRES ; AG3 + HOLES (water) Revision: 0 Page 89 of 196

91 nom_calc = 'MILHOM12' ; TOPT.'STCRI'.'CALCUL_INITIAL' = nom_calc ; TOPT.'STCRI'.'CALCULS_INITIAUX'.nom_calc = TABLE: ; TSTR.nom_calc = TABLE: ; nom_mil = 'AG3 + HOLES (water)' ; TOPT.'STMIL'.nom_mil = TABLE: ; TOPT.'STMIL'.nom_mil.'SINAT ' = E-04 ; TOPT.'STMIL'.nom_mil.'FENAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'CUNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'MN55 ' = E-04 ; TOPT.'STMIL'.nom_mil.'MGNAT ' = E-03 ; TOPT.'STMIL'.nom_mil.'CRNAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'ZN64 ' = E-05 ; TOPT.'STMIL'.nom_mil.'TINAT ' = E-05 ; TOPT.'STMIL'.nom_mil.'AL27 ' = E-02 ; TOPT.'STMIL'.nom_mil.'H2O ' = E-03 ; 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 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 MILHOM12 -=- 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 IRSN / SEC APOLLO2 / MORET 4 LEU-COMP-THERM-MIRTE MIRTE 1 Programme revision 0 experiment Interacting configuration with thin screens 4 Arrays of UO2 rods (4.738 %) 10x10 pitch 1.6cm Critical Height : cm Titanium 5 mm keff(exp)± 1 s = ± Writer N. LECLAIRE Reviewer F.X. LEDAUPHIN ==================================== CIGALES version 3.1 en date du 06/04/2006 ==================================== Revision: 0 Page 90 of 196

92 ( AIR AIR Milieu 1 macroscopique AIR 1 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE AIR TEMP 21 MACRO 1 1 AIR E+00 FINC SECTION TOUT FIN ( STEEL STEEL Milieu 1 CONC. ATOMIQUES- %volumique 100 CRNAT E-02 NINAT E-03 MN E-04 SINAT E-03 P E-05 S E-05 CNAT E-04 FENAT E-02 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE STEEL TEMP 21 MICRO 1 8 CRNAT NINAT MN55 SINAT P31 S32 CNAT FENAT CONC E E E E E E E E-02 FINC SECTION TOUT FIN ( WATER WATER Milieu 1 macroscopique EAU 1 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE WATER TEMP 21 MACRO 1 1 EAU E+00 FINC SECTION TOUT FIN ( AG3 AG3 Milieu 1 %-prop MASSIQUES- Dens= %volumique 100 SINAT FENAT CUNAT MN MGNAT CRNAT ZN TINAT AL Revision: 0 Page 91 of 196

93 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE AG3 TEMP 21 MICRO 1 9 SINAT FENAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT AL27 CONC E E E E E E E E E-02 FINC SECTION TOUT FIN ( AG3 + HOLES (air) AG3 + HOLES (air) Milieu 1 %-prop MASSIQUES- Dens= %volumique 70.5 SINAT FENAT CUNAT MN MGNAT CRNAT ZN TINAT AL Milieu 2 CONC. ATOMIQUES- %volumique 29.5 N E-05 O E-05 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE AG3 + HOLES (air) TEMP 21 MICRO 1 11 SINAT FENAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT AL27 N14 O16 CONC E E E E E E E E E E E-06 FINC SECTION TOUT FIN ( Titanium Titanium Milieu 1 CONC. ATOMIQUES- %volumique 10 FENAT E-05 CRNAT E-05 TINAT E-02 SNNAT E-07 CNAT E-05 N E-06 O E-04 AL E-06 SINAT E-05 P E-07 MN E-06 NINAT E-06 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE Titanium TEMP 21 MICRO 1 12 FENAT CRNAT TINAT SNNAT CNAT N14 O16 AL27 SINAT P31 MN55 NINAT CONC E E E E E E E E E E E E-06 Revision: 0 Page 92 of 196

94 FINC SECTION TOUT FIN ( AP AP Milieu 1 CONC. ATOMIQUES- %volumique 72 N E-05 O E-05 Milieu 2 CONC. ATOMIQUES- %volumique 28 N E-06 O E-04 SNNAT E-04 FENAT E-04 CRNAT E-05 CNAT E-05 SINAT E-05 ZRNAT E-02 AL E-06 HFNAT E-06 H E-05 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE AP TEMP 21 MICRO 1 11 N14 O16 SNNAT FENAT CRNAT CNAT SINAT ZRNAT AL27 HFNAT H1 CONC E E E E E E E E E E E-06 FINC SECTION TOUT FIN ( AC AC Milieu 1 CONC. ATOMIQUES- %volumique CRNAT E-05 H E-05 HFNAT E-06 O E-04 SINAT E-05 FENAT E-04 N E-06 CNAT E-05 ZRNAT AL E-06 SNNAT E-04 Milieu 2 CONC. ATOMIQUES- %volumique N E-05 O E-05 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE milieu_23 TEMP 21 MICRO 1 11 CRNAT H1 HFNAT O16 SINAT FENAT N14 CNAT ZRNAT AL27 SNNAT CONC E E E E E E E E E E E-05 FINC SECTION TOUT FIN ( Revision: 0 Page 93 of 196

95 ( ACG ACG Milieu 1 CONC. ATOMIQUES- %volumique SINAT E-04 FENAT E-04 CUNAT E-05 MN E-04 MGNAT E-03 CRNAT E-05 ZN E-05 TINAT E-05 AL Milieu 2 CONC. ATOMIQUES- %volumique N E-05 O E-05 Milieu 3 CONC. ATOMIQUES- %volumique CRNAT E-05 H E-05 HFNAT E-06 O E-04 SINAT E-05 FENAT E-04 N E-06 CNAT E-05 ZRNAT AL E-06 SNNAT E-04 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE milieu_24 TEMP 21 MICRO 1 16 SINAT FENAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT AL27 N14 O16 H1 HFNAT CNAT ZRNAT SNNAT CONC E E E E E E E E E E E E E E E E-05 FINC SECTION TOUT FIN RAPPEL DONNEES MORET Pij ======================================================================= BIBLIO CEA93.V6 172 groupes ANISOTROPIE P5 <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL GEOMETRIE du MILIEU FISSILE HETEROGENE Array in air GEOMETRIE CYLINDRIQUE ZONES NB POINTS ABSCISSES CHIMIE FISS AIR AUTRE AIR MILIEU FISSILE 1: <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL MILIEU AUTRE UO2 poudre Milieu 1 CONC. ATOMIQUES- %volumique U E-06 U E-03 Revision: 0 Page 94 of 196

96 U E-05 U O AL E-06 FENAT E-06 SINAT E-05 <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL MILIEU AUTRE ZR4_1_87 Milieu 1 CONC. ATOMIQUES- %volumique 100 N E-06 O E-04 SNNAT E-04 FENAT E-04 CRNAT E-05 CNAT E-05 SINAT E-05 ZRNAT AL E-06 HFNAT E-06 H E-05 ( Array in air CAS 10 UO2 poudre CAS 10 UO2 poudre SORTIE SECTIONS TOUTE LA CELLULE ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOMETRIE CYLINDRE AUTO 1 1 CHIMIE UO2 poudre TEMP 21 MICRO 1 8 U234 U235 U236 U238 O16 AL27 FENAT SINAT CONC E E E E E E E E-05 AIR TEMP 21 MACRO 1 1 AIR 1 ZR4_1_87 TEMP 21 MICRO 1 11 N14 O16 SNNAT FENAT CRNAT CNAT SINAT ZRNAT AL27 HFNAT CONC H E E E E E E E E E E E-05 AIR TEMP 21 MACRO 1 1 AIR 1 FINC SECTION TOUT FIN RAPPEL DONNEES MORET Pij ======================================================================= BIBLIO CEA93.V6 172 groupes ANISOTROPIE P5 <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL GEOMETRIE du MILIEU FISSILE HETEROGENE Array in water GEOMETRIE CYLINDRIQUE Revision: 0 Page 95 of 196

97 ZONES NB POINTS ABSCISSES CHIMIE FISS AIR AUTRE EAU MILIEU FISSILE 1: <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL MILIEU AUTRE UO2 poudre Milieu 1 CONC. ATOMIQUES- %volumique U E-06 U E-03 U E-05 U O AL E-06 FENAT E-06 SINAT E-05 <><><><><><><><><<><><><><><<><><><><><><><><><> RAPPEL MILIEU AUTRE ZR4_1_87 Milieu 1 CONC. ATOMIQUES- %volumique 100 N E-06 O E-04 SNNAT E-04 FENAT E-04 CRNAT E-05 CNAT E-05 SINAT E-05 ZRNAT AL E-06 HFNAT E-06 H E-05 ( Array in water CAS 11 UO2 poudre CAS 11 UO2 poudre SORTIE SECTIONS TOUTE LA CELLULE ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOMETRIE CYLINDRE AUTO 1 1 CHIMIE UO2 poudre TEMP 21 MICRO 1 8 U234 U235 U236 U238 O16 AL27 FENAT SINAT CONC E E E E E E E E-05 AIR TEMP 21 MACRO 1 1 AIR 1 ZR4_1_87 TEMP 21 MICRO 1 11 N14 O16 SNNAT FENAT CRNAT CNAT SINAT ZRNAT AL27 HFNAT H1 CONC E E E E E E E E E E-06 Revision: 0 Page 96 of 196

98 E-05 EAU a 21 degres TEMP 21 MICRO 1 1 H2O CONC FINC SECTION TOUT FIN ( WP WP Milieu 1 CONC. ATOMIQUES- %volumique 72 H2O Milieu 2 CONC. ATOMIQUES- %volumique 28 O E-04 AL E-06 FENAT E-04 SINAT E-05 N E-06 SNNAT E-04 CRNAT E-05 CNAT E-05 HFNAT E-06 H E-05 ZRNAT ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE WP TEMP 21 MICRO 1 12 H2O O16 AL27 FENAT SINAT N14 SNNAT CRNAT CNAT HFNAT CONC H1 ZRNAT E E E E E E E E E E E E-02 FINC SECTION TOUT FIN ( WPG WPG Milieu 1 %-prop MASSIQUES- Dens= %volumique 70.5 SINAT FENAT CUNAT MN MGNAT CRNAT ZN TINAT AL Milieu 2 CONC. ATOMIQUES- %volumique 29.5 N E-06 O E-04 SNNAT E-04 FENAT E-04 CRNAT E-05 CNAT E-05 SINAT E-05 ZRNAT AL E-06 HFNAT E-06 H E-05 H2O E-03 ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE WPG TEMP 21 Revision: 0 Page 97 of 196

99 MICRO 1 17 SINAT FENAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT AL27 N14 O16 SNNAT CNAT ZRNAT HFNAT CONC H1 H2O E E E E E E E E E E E E E E E E E-04 FINC SECTION TOUT FIN ( AG3 + HOLES (water) AG3 + HOLES (water) Milieu 1 %-prop MASSIQUES- Dens= %volumique 70.5 SINAT FENAT CUNAT MN MGNAT CRNAT ZN TINAT AL Milieu 2 CONC. ATOMIQUES- %volumique 29.5 H2O ) OPTION V6 GROUP 172 P5 TEMPER 21 FINOPTION MORET GEOM HOMO CHIMIE AG3 + HOLES (water) TEMP 21 MICRO 1 10 SINAT FENAT CUNAT MN55 MGNAT CRNAT ZN64 TINAT AL27 H2O CONC E E E E E E E E E E-03 FINC SECTION TOUT FIND DEBUT_MORET4 LEU-COMP-THERM-STRUCTURE Materials 1 - Air 2 - Steel Z2CN18-10 (AFNOR) 3 - Water 4 - AG3M (alluminium alloy) 5 - AG3M + hole (air) 6 - Titanium 7 - AP (air+plug) 9 - AC (air+clad+spring) 10 - ACG (air+grid) 11 - Array in air 12 - Array in water 13 - WP (water+plug) 14 - WPG (water+plug+grid) 15 - AG3M + hole (water) MINI 500 SIGM GEOM MODU 0 plate TYPE 8 BOIT VOLU tank Revision: 0 Page 98 of 196

100 air TYPE 20 BOIT VOLU water (value to modifie the water level) TYPE 21 PLAZ INFE VOLU ETSU TYPE 23 BOIT VOLU ECRA TYPE 24 BOIT TROU ECRA FINM MODU 1 universe TYPE 1 BOIT VOLU grid 1st plate (right) TYPE 10 BOIT OBLI 45 VOLU VOLU nd plate (left) TYPE 14 BOIT OBLI 45 VOLU VOLU rd plate (lower) TYPE 18 BOIT OBLI 45 VOLU VOLU th plate (upper) TYPE 22 BOIT OBLI 45 VOLU VOLU material to test 1st part of the cross TYPE 59 BOIT OBLI 45 VOLU ECRA nd part of the cross TYPE 60 BOIT OBLI -45 VOLU ECRA 1 88 Fissile media Array in air TYPE 80 BOIT OBLI 45 VOLU ECRA left VOLU ECRA right VOLU ECRA lower VOLU ECRA upper AP (air+plug) TYPE 81 BOIT OBLI 45 VOLU VOLU VOLU VOLU Revision: 0 Page 99 of 196

101 ACS (air+clad+spring) TYPE 83 BOIT OBLI 45 VOLU VOLU VOLU VOLU AG (air+grid) TYPE 84 BOIT OBLI 45 VOLU VOLU VOLU VOLU Array in water (value to modifie the water level) TYPE 85 BOIT OBLI 45 VOLU VOLU VOLU VOLU WP (water+plug) TYPE 86 BOIT OBLI 45 VOLU VOLU VOLU VOLU WPG (water+plug+grid) TYPE 87 BOIT OBLI 45 VOLU VOLU VOLU VOLU Water tank (value to modifie the water level) TYPE 88 PLAZ INFE VOLU ETSU 1 1 FINM FING CHIMIE SEALINK 15 APO FINCHIMIE SORT CARA REDUIT ICSBEP ETENDU FCARA POST TAUX 1000 FPOS FSOR SOURCES UNIF 1000 MODU 1 FUNI FINSOURCES SIMU DEBU 200 FSIM Revision: 0 Page 100 of 196

102 FIND FIN_MORET4 Revision: 0 Page 101 of 196

103 A.2 KENO-V.a - Input Listings Comparisons calculations are performed with the KENO-V.a from the SCALE5.1 code systems using 238-group ENDF/B-VI.7 cross-sections data batches and 5000 neutrons per batch are simulated. The first 100 batches are skipped from the simulation. A.2.1 KENOV.A input listing for thin thickness configuration(4a-ti-005). =csas25 Programme materiaux, ecran en titane cm, HcE = cm v6-238 read composition 'Fissile pellets u E end u E end u E end u E end o E end al E end fe E end fe E end fe E end fe E end si E end si E end si E end ' Fuel Clad zr E end zr E end zr E end zr E end zr E end fe E end fe E end fe E end fe E end cr E end cr E end cr E end cr E end o E end hf E end hf E end hf E end hf E end hf E end hf E end h E end si E end si E end si E end c E end al E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end Revision: 0 Page 102 of 196

104 n E end ' Water h E end o E end 'Fissile pellets u E end u E end u E end u E end o E end al E end fe E end fe E end fe E end fe E end si E end si E end si E end ' Fuel Clad zr E end zr E end zr E end zr E end zr E end fe E end fe E end fe E end fe E end cr E end cr E end cr E end cr E end o E end hf E end hf E end hf E end hf E end hf E end hf E end h E end si E end si E end si E end c E end al E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end sn E end n E end ' Air n o E end E end 'AG3 si-28 si-29 si-30 Fe-54 Fe-56 Fe-57 Fe E end E end E end E end E end E end E end Revision: 0 Page 103 of 196

105 cu-63 cu-65 mn mg 'mg-24 'mg-25 'mg-26 cr-50 cr-52 cr-53 cr-54 'zn-64 ti 'ti-46 'ti-47 'ti-48 'ti-49 'ti-50 al E end E end E end E end E end E end E end E end E end E end E end E end E end E end E end E end E end E end E end ' STEEL cr E end cr E end cr E end cr E end Ni E end Ni E end Ni E end Ni E end Ni E end Mn E end Si E end Si E end Si E end P E end S E end 'S E end 'S E end 'S E end 'S E end C E end FE E end FE E end FE E end FE E end ' Water h E end o E end 'titanium FE E end FE E end FE E end FE E end CR E end CR E end CR E end CR E end TI E end SN E end SN E end SN E end SN E end SN E end SN E end SN E end SN E end SN E end Revision: 0 Page 104 of 196

106 SN E end C E end n E end o E end al E end si E end P E end mn E end NI E end NI E end NI E end NI E end NI E end 'air 2 n E end o E end end composition read celldata infhommedium 7 end infhommedium 8 end infhommedium 9 end infhommedium 10 end infhommedium 61 end latticecell squarepitch fuelr= gapr= cladr= hpitch=0.8 3 end centrm data demin=0.2 end centrm latticecell squarepitch fuelr= gapr= cladr= hpitch=0.8 6 end centrm data demin=0.2 end centrm end celldata read parameters gen=3100 nsk=100 npg=5000 ' run=no plt=no flx=yes sig= ' tsunami parameter block ' agn=10000 ' apg=30000 ' asg= ' tfm=no ' nqd=0 ' pnm=2 ' mfx=yes ' msh=10 end parameters read geometry unit 1 com='plug in water' zcylinder cuboid unit 2 com='plug in grid' zcylinder zcylinder cuboid unit 3 com='uo2 rod up to surface i.e. critical height' zcylinder zcylinder zcylinder cuboid Revision: 0 Page 105 of 196

107 unit 4 com='uo2 rod, above surface' zcylinder zcylinder zcylinder cuboid unit 5 com='clad+spring+air above fissile below grid' zcylinder zcylinder cuboid unit 6 com='clad+spring+grid' zcylinder zcylinder zcylinder cuboid unit 7 com='clad+spring+air abode fissile above grid' zcylinder zcylinder cuboid unit 8 com='plug in air' zcylinder cuboid unit 70 'reconstruction des combustibles sous eau array unit 80 'reconstruction des combustibles sous air array unit 94 com='plaque en acier sous l ensemble' cuboid cuboid unit 72 ' reseau sous eau + ecran' cuboid cuboid hole hole hole hole hole hole unit 721 '10x10 reseau eau' array cuboid unit 722 ' ecran gauche sous eau cuboid unit 723 ' ecran droit sous eau cuboid unit 82 ' reseau sous air' cuboid Revision: 0 Page 106 of 196

108 cuboid hole hole hole hole hole hole unit 821 com='10x10 reseau air' array cuboid unit 822 cuboid unit 823 cuboid global unit 100 com='whole parts' array end geometry read array 'Array 1 ara=1 nux=1 nuy=1 nuz=3 com='uo2 fuel rod' fill end fill 'Array 3 ara=3 nux=1 nuy=1 nuz=5 com='uo2 fuel rod air' fill end fill 'Array 5 ara=5 nux=10 nuy=10 nuz=1 com='reseau sous eau' fill F70 end fill 'Array 15 ara=15 nux=10 nuy=10 nuz=1 com='reseau sous eau' fill F80 end fill 'Array 10 com='ensemble des parties' ara=10 nux=1 nuy=1 nuz=3 fill end fill end array read bnds +xb=vacuum -xb=vacuum +yb=vacuum -yb=vacuum +zb=vacuum -zb=vacuum end bnds read plot ttl=' y=100' xul=0 yul=100 zul=141 xlr=190 ylr=100 zlr=0 nax=2000 uax=1 wdn=-1 lpi=10 Revision: 0 Page 107 of 196

109 end plt1 ttl='x=100' xul=100 yul=0 zul=141 xlr=100 ylr=190 zlr=0 nax=2000 vax=1 wdn=-1 lpi=10 end plt2 ttl=' XY slice eau ' xul=0. yul=190 zul=45 xlr=190 ylr=0. zlr=45. uax=+1 vdn=-1 nax=2000 lpi=10 end plt3 ttl=' XY slice air' xul=0. yul=190 zul=111 xlr=190 ylr=0. zlr=111. uax=+1 vdn=-1 nax=2000 lpi=10 end plt4 ttl=' XY slice eau' xul=60. yul=130 zul=80 xlr=130 ylr=60. zlr=80 uax=+1 vdn=-1 nax=2000 lpi=10 end plt5 ttl=' XY slice eau' xul=80. yul=110 zul=130 xlr=110 ylr=80. zlr=130 uax=+1 vdn=-1 nax=2000 lpi=10 end plt6 ttl='x=84' xul=84 yul=0 zul=141 xlr=84 ylr=190 zlr=0 nax=2000 vax=1 wdn=-1 lpi=10 end plt7 end plot end data 'read sams ' nomix ' prtimp 'end sams end Revision: 0 Page 108 of 196

110 A.3 MCNPX - Input Listings Comparisons calculations are also performed with the MCNPX2.6 code using continuous energy ENDF/B- VII.0 cross-sections data batches and 4000 neutrons per batch are simulated. The first 50 batches are skipped from the simulation. A.3.1 MCNPX input listing for thin thickness configuration (4A-Ti-005) MESSAGE: xsdir=/home/leclaire/xsdir70 file name=4a-ti-005 c reseau avec tous les materiaux sauf Zn64 et Pt nb atomes mcnp c four 1010 reseau c critical water level c lattice pitch 1.6(cm); c c cellcards c e imp:n=1 u=1 $ cylindre fissile E #1 imp:n=1 u=1 $ cylindre air E #1 #2 imp:n=1 u=1 $ cylindre gaine E #1 #2 #3 imp:n=1 u=1 $ eau bas entre plaque et crayon E #1 #2 #3 imp:n=1 u=1 $ air haut entre plaque et crayon E #1 #2 #3 #4 imp:n=1 u=1 $ grille bas E #1 #2 #3 #5 imp:n=1 u=1 $ grille haut E #1 #2 #3 #4 #5 #6 #7 imp:n=1 u=1 $ eau du reseau E #4 #5 #6 #7 imp:n=1 u=1 $ air du reseau imp:n=1 u=2 lat=1 fill=0:9 0:9 0:0 1 99r imp:n=1 fill=2 12 like 11 but trcl ( ) 13 like 11 but trcl ( ) 14 like 11 but trcl ( ) E-02 ( ):( ) & imp:n=1 $ ecran E imp:n=1 $ plaque en steel E #11 #12 #13 #14 imp:n=1 $ grille haut E #11 #12 #13 #14 imp:n=1 $ grille haut E #11 #12 #13 #14 imp:n=1 $ grille haut E #11 #12 #13 #14 imp:n=1 & $grille haut E #11 #12 #13 #14 imp:n=1 & $grille bas E #11 #12 #13 #14 imp:n=1 & $grille bas E #11 #12 #13 #14 imp:n=1 & $grille bas E #11 #12 #13 #14 imp:n=1 & $grille bas E #11 #12 #13 #14 #20 #30 #31 #32 #33 #34 & #35 #36 #37 #38 imp:n=1 $ eau en dehors du reseau E #11 #12 #13 #14 #20 #30 #31 #32 #33 #34 & #35 #36 #37 #38 imp:n=1 $ air en dehors du reseau :2:-3:-4:-5:6 imp:n=0 $ exterieur c surface cards c parallelpiped outer world 1 p p p p pz 0 6 pz 140 c c plaque steel 10 p p p p Revision: 0 Page 109 of 196

111 14 pz pz c c water critical water level 16 pz c c grille coordonnées x y 20 px px py py C c material to test 120 px px px px py py py py pz pz c c 140 px px py py c pas reseau 145 px py c c c c CRAYONS 30 C/Z $cyl fissile 31 C/Z $cyl air 32 C/Z $cyl gaine en zr 33 C/Z $cyl d'eau ou d'air entre plaque et crayon 34 pz $z bas du crayon 35 pz $z bas grille du bas 36 pz $z haut grille du bas de 0,4 cm (bas du combu) 37 pz $z haut du comustible 38 pz $z haut du cyl d'air (debut du cyl de zr) 39 pz $z haut du cyl de zr 40 pz $z bas de la grille du haut 41 pz $z haut de la grille du haut c data cards c mode n $ transfort neutrons only c c material cards c c c air m c E-05 $N c E-05 $O16 c c steel m c E-04 $cr c E-02 $cr c E-03 $cr c E-04 $cr c E-03 $Ni c E-03 $Ni c E-05 $Ni c E-04 $Ni c E-05 $Ni c E-04 $Mn c E-03 $Si c E-05 $Si29 Revision: 0 Page 110 of 196

112 c E-05 $Si c E-05 $P c E-05 $S c E-07 $S c E-06 $S c E-09 $S c E-04 $C c E-03 $FE c E-02 $FE c E-03 $FE c E-04 $FE58 c c water(300k) m c E-02 $H_H2O c E-02 $O16 mt3 lwtr01.70t $H eau legère à 300 K (01 indique la temp) c c AG3M m c E-04 $SI c E-05 $SI c E-06 $SI c E-06 $FE c E-04 $FE c E-06 $FE c E-07 $FE c E-05 $CU c E-06 $CU c E-04 $MN c E-03 $MG c E-04 $MG c E-04 $MG c E-06 $CR c E-05 $CR c E-06 $CR c E-06 $CR c E-05 $ zn c E-06 $TI c E-06 $TI c E-05 $TI c E-06 $TI c E-06 $TI c E-02 $AL27 c c ecran en Ti m c E-06 $FE c E-05 $FE c E-06 $FE c E-07 $FE c E-07 $CR c E-05 $CR c E-06 $CR c E-07 $CR c E-03 $TI c E-03 $TI c E-02 $TI c E-03 $TI c E-03 $TI c E-09 $SN c E-09 $SN c E-09 $SN c E-08 $SN c E-08 $SN c E-08 $SN c E-08 $SN c E-07 $SN c E-08 $SN c E-08 $SN c E-05 $C c E-06 $N c E-04 $O c E-06 $Al c E-06 $si c E-07 $si29 Revision: 0 Page 111 of 196

113 c E-07 $si c E-07 $P c E-06 $Mn c E-06 $Ni c E-06 $Ni c E-08 $Ni c E-07 $Ni c E-08 $Ni64 c c fissile m c E-06 $U c E-03 $U c E-05 $U c E-02 $U c E-02 $O c E-06 $AL c E-07 $FE c E-06 $FE c E-07 $FE c E-08 $FE c E-05 $SI c E-06 $SI c E-07 $SI 30 c c zircaloy m c E-06 $N c E-04 $O c E-06 $SN c E-06 $SN c E-06 $SN c E-05 $SN c E-05 $SN c E-04 $SN c E-05 $SN c E-04 $SN c E-05 $SN c E-05 $SN c E-06 $FE c E-04 $FE c E-06 $FE c E-07 $FE c E-06 $CR c E-05 $CR c E-06 $CR c E-06 $CR c E-05 $C c E-05 $SI c E-07 $SI c E-07 $SI c E-02 $ZR c E-03 $ZR c E-03 $ZR c E-03 $ZR c E-03 $ZR c E-06 $AL c E-09 $HF c E-08 $HF c E-07 $HF c E-07 $HF c E-07 $HF c E-07 $HF c E-05 $H1 c c AG3M+HOLES(W) grille avec trous eau bas m c E-04 $SI c E-06 $SI c E-06 $SI c E-06 $FE c E-05 $FE c E-06 $FE c E-07 $FE c E-05 $CU c E-06 $CU 65 Revision: 0 Page 112 of 196

114 c E-04 $MN c E-03 $MG c E-04 $MG c E-04 $MG c E-06 $CR c E-05 $CR c E-06 $CR c E-06 $CR c E-05 $ZN c E-06 $TI c E-06 $TI c E-05 $TI c E-06 $TI c E-06 $TI c E-02 $AL c E-02 $H_H2O c E-03 $O16 mt9 lwtr01.70t $H eau legère à 300 K (01 indique la temp) c c c c AG3M+HOLES(A) grille avec trous air haut m c E-04 $SI c E-06 $SI c E-06 $SI c E-06 $FE c E-05 $FE c E-06 $FE c E-07 $FE c E-05 $CU c E-06 $CU c E-04 $MN c E-03 $MG c E-04 $MG c E-04 $MG c E-06 $CR c E-05 $CR c E-06 $CR c E-06 $CR c E-05 $ZN c E-06 $TI c E-06 $TI c E-05 $TI c E-06 $TI c E-06 $TI c E-02 $AL c E-05 $N c E-06 $O16 c c criticality cards c KCODE c nb de sources par cycle, keff estimé, nb cycle non pris en compte, c nb total de cycles c 1 source est placée en x y au centre de chaque crayon combustible c la cote z de la chaque est source est tirée aléatoirement entre c et c combu bas gauche KSRC PRINT -40 Revision: 0 Page 113 of 196

115 A.4 MORET 5 - input listing Comparisons calculations are also performed with the MORET 5 (under validation at IRSN) code using continuous energy JEF2.2 cross-sections data. The cross section library is based on JEF2.2 evaluation batches and 8000 neutrons per batch are simulated. The first 200 batches are skipped. A.4.1 MORET 5 input listing for thin thickness configuration (4A-Ti-005) DEBUT_MORET Materials 1 - Air 2 - Steel Z2CN18-10 (AFNOR) 3 - Water 4 - AG3M (alluminium alloy) 5 - AG3M + hole (air) 6 - Cu 7 - AP (air+plug) 9 - AC (air+clad+spring) 10 - ACG (air+grid) 11 - Array in air 12 - Array in water 13 - WP (water+plug) 14 - WPG (water+plug+grid) 15 - AG3M + hole (water) ARREt ETAPes ACTIves 500 KEFF SIGMa FARRet CONNECTION APIJ NUMBER TO CHEMICAL MEDIUM NUMBER CHIMie SEALink 20 APO _0 10_1 10_2 10_3 11_0 11_1 11_2 11_ FINChimie NEW CHEMICAL MEDIUMS DEFINING CHIMie PONCtuel BIBLiotheque jef22.xml Revision: 0 Page 114 of 196

116 TEMP 293 FOR THIS APPOLO CALCULATION Calcul number : 1 - Calcul name : MILHOM1 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature AIR CHEMICAL MEDIUM DEFINING : COMP MILHOM1 CONCentration 2 N E-05 O E-05 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 2 - Calcul name : MILHOM2 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STEEL CHEMICAL MEDIUM DEFINING : COMP MILHOM2 CONCentration 22 C E-04 CR E-04 CR E-02 CR E-03 CR E-04 FE E-03 FE E-02 FE E-03 FE E-04 MN E-04 NI E-03 NI E-03 NI E-05 NI E-04 NI E-05 P E-05 S E-05 SI E-03 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 3 - Calcul name : MILHOM3 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature WATER CHEMICAL MEDIUM DEFINING : Revision: 0 Page 115 of 196

117 COMP MILHOM3 CONCentration 2 H1-H2O E-02 O E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 4 - Calcul name : MILHOM4 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature AG CHEMICAL MEDIUM DEFINING : COMP MILHOM4 CONCentration 15 AL E-02 CR E-06 CR E-05 CR E-06 CR E-06 CU E-05 FE E-06 FE E-04 FE E-06 FE E-07 MG E-03 MN E-04 SI E-04 TI E-05 ZN E-05 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 5 - Calcul name : MILHOM5 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature AG3 + HOLES (air) CHEMICAL MEDIUM DEFINING : COMP MILHOM5 CONCentration 17 AL E-02 CR E-06 CR E-05 CR E-06 CR E-06 CU E-05 FE E-06 FE E-05 FE E-06 FE E-07 MG E-03 MN E-04 N E-05 O E-06 SI E-04 TI E-05 ZN E-05 ENDComp Revision: 0 Page 116 of 196

118 FOR THIS APPOLO CALCULATION Calcul number : 6 - Calcul name : MILHOM6 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature CU CHEMICAL MEDIUM DEFINING : COMP MILHOM6 CONCentration 12 FE E-06 FE E-05 FE E-06 FE E-07 CR E-07 CR E-05 CR E-06 CR E-07 TI E-02 SN E-09 SN E-09 SN E-09 SN E-08 SN E-08 SN E-08 SN E-08 SN E-07 SN E-08 SN E-08 C E-05 N E-06 O E-04 AL E-06 SI E-05 P E-07 MN E-06 NI E-06 NI E-06 NI E-08 NI E-07 NI E-08 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 7 - Calcul name : MILHOM7 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature AP CHEMICAL MEDIUM DEFINING : COMP MILHOM7 CONCentration 31 AL27 C CR50 CR52 CR53 CR54 FE54 FE E E E E E E E E-05 Revision: 0 Page 117 of 196

119 FE E-07 FE E-07 H E-06 HF E-10 HF E-08 HF E-08 HF E-08 HF E-08 HF E-07 N E-05 O E-04 SI E-06 SN E-06 SN E-07 SN E-07 SN E-05 SN E-06 SN E-05 SN E-05 SN E-05 SN E-06 SN E-06 ZR E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 8 - Calcul name : MILHOM8 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature milieu_ CHEMICAL MEDIUM DEFINING : COMP MILHOM8 CONCentration 31 AL E-07 C E-06 CR E-07 CR E-06 CR E-07 CR E-07 FE E-07 FE E-06 FE E-07 FE E-08 H E-07 HF E-10 HF E-09 HF E-08 HF E-08 HF E-08 HF E-08 N E-05 O E-05 SI E-07 SN E-07 SN E-07 SN E-07 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 ZR E-03 ENDComp Revision: 0 Page 118 of 196

120 FOR THIS APPOLO CALCULATION Calcul number : 9 - Calcul name : MILHOM9 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature milieu_ CHEMICAL MEDIUM DEFINING : COMP MILHOM9 CONCentration 36 AL E-02 C E-06 CR E-06 CR E-05 CR E-06 CR E-06 CU E-05 FE E-06 FE E-05 FE E-06 FE E-07 H E-07 HF E-10 HF E-09 HF E-08 HF E-08 HF E-08 HF E-08 MG E-03 MN E-04 N E-05 O E-05 SI E-04 SN E-07 SN E-07 SN E-07 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 SN E-06 TI E-05 ZN E-05 ZR E-03 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 10 - Calcul name : CELLUL10 - Zone number : 0 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature FISSIL1_ FISSIL1_ FISSIL1_ FISSIL1_ CHEMICAL MEDIUM DEFINING : Revision: 0 Page 119 of 196

121 COMP CELLUL10_0 CONCentration 11 AL E-06 FE E-07 FE E-06 FE E-07 FE E-08 O E-02 SI E-05 U E-06 U E-03 U E-05 U E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 10 - Calcul name : CELLUL10 - Zone number : 1 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL10_1 CONCentration 2 N E-05 O E-05 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 10 - Calcul name : CELLUL10 - Zone number : 2 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL10_2 CONCentration 31 AL E-06 C E-05 CR E-06 CR E-05 CR E-06 CR E-06 FE E-06 FE E-04 FE E-06 FE E-07 H E-05 HF E-09 HF E-08 HF E-07 HF E-07 HF E-07 HF E-07 N E-06 O E-04 SI E-05 SN E-06 SN E-06 SN E-06 Revision: 0 Page 120 of 196

122 SN E-05 SN E-05 SN E-04 SN E-05 SN E-04 SN E-05 SN E-05 ZR E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 10 - Calcul name : CELLUL10 - Zone number : 3 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STRUCT STRUCT STRUCT STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL10_3 CONCentration 2 N E-05 O E-05 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 11 - Calcul name : CELLUL11 - Zone number : 0 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature FISSIL1_ FISSIL1_ FISSIL1_ FISSIL1_ CHEMICAL MEDIUM DEFINING : COMP CELLUL11_0 CONCentration 11 AL E-06 FE E-07 FE E-06 FE E-07 FE E-08 O E-02 SI E-05 U E-06 U E-03 U E-05 U E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 11 - Calcul name : CELLUL11 - Zone number : 1 - Geometry type : CYLINDRE Revision: 0 Page 121 of 196

123 No Ext. radius Name of medium Temperature STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL11_1 CONCentration 2 N E-05 O E-05 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 11 - Calcul name : CELLUL11 - Zone number : 2 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL11_2 CONCentration 31 AL E-06 C E-05 CR E-06 CR E-05 CR E-06 CR E-06 FE E-06 FE E-04 FE E-06 FE E-07 H E-05 HF E-09 HF E-08 HF E-07 HF E-07 HF E-07 HF E-07 N E-06 O E-04 SI E-05 SN E-06 SN E-06 SN E-06 SN E-05 SN E-05 SN E-04 SN E-05 SN E-04 SN E-05 SN E-05 ZR E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 11 - Calcul name : CELLUL11 - Zone number : 3 - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature STRUCT3 21. Revision: 0 Page 122 of 196

124 STRUCT STRUCT STRUCT CHEMICAL MEDIUM DEFINING : COMP CELLUL11_3 CONCentration 2 H1-H2O E-02 O E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 12 - Calcul name : MILHOM10 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature WP CHEMICAL MEDIUM DEFINING : COMP MILHOM10 CONCentration 32 AL E-07 C E-05 CR E-06 CR E-05 CR E-06 CR E-07 FE E-06 FE E-05 FE E-07 FE E-07 H E-06 H1-H2O E-02 HF E-10 HF E-08 HF E-08 HF E-08 HF E-08 HF E-07 N E-06 O E-02 SI E-06 SN E-06 SN E-07 SN E-07 SN E-05 SN E-06 SN E-05 SN E-05 SN E-05 SN E-06 SN E-06 ZR E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 13 - Calcul name : MILHOM11 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature WPG 21. Revision: 0 Page 123 of 196

125 CHEMICAL MEDIUM DEFINING : COMP MILHOM11 CONCentration 37 AL E-02 C E-05 CR E-06 CR E-05 CR E-06 CR E-06 CU E-05 FE E-06 FE E-04 FE E-06 FE E-07 H E-06 H1-H2O E-03 HF E-10 HF E-08 HF E-08 HF E-08 HF E-08 HF E-07 MG E-03 MN E-04 N E-06 O E-04 SI E-04 SN E-06 SN E-07 SN E-07 SN E-05 SN E-06 SN E-05 SN E-05 SN E-05 SN E-06 SN E-06 TI E-05 ZN E-05 ZR E-02 ENDComp FOR THIS APPOLO CALCULATION Calcul number : 14 - Calcul name : MILHOM12 - Zone number : None - Geometry type : CYLINDRE No Ext. radius Name of medium Temperature AG3 + HOLES (water) CHEMICAL MEDIUM DEFINING : COMP MILHOM12 CONCentration 17 AL E-02 CR E-06 CR E-05 CR E-06 CR E-06 CU E-05 FE E-06 FE E-05 FE E-06 FE E-07 H1-H2O E-02 MG E-03 MN E-04 O E-03 Revision: 0 Page 124 of 196

126 SI E-04 TI E-05 ZN E-05 ENDComp FINChimie GEOM MODU 0 plate TYPE 8 BOIT OBLI -45 VOLU tank air TYPE 20 BOIT OBLI -45 VOLU water (value to modifie the water level) TYPE 21 PLAZ INFE VOLU ETSU TYPE 23 BOIT OBLI -45 VOLU TYPE 24 BOIT OBLI -45 TROU ECRA FINM MODU 1 universe TYPE 1 BOIT OBLI -45 VOLU grid 1st plate (right) TYPE 10 BOIT VOLU VOLU nd plate (left) TYPE 14 BOIT VOLU VOLU rd plate (lower) TYPE 18 BOIT VOLU VOLU th plate (upper) TYPE 22 BOIT VOLU VOLU material to test 1st part of the cross TYPE 59 BOIT VOLU ECRA nd part of the cross TYPE 60 BOIT VOLU ECRA 1 88 Fissile media Array in air TYPE 80 BOIT left TYPE 801 BOIT TROU ECRA 1 88 right TYPE 802 BOIT TROU ECRA 1 88 lower TYPE 803 BOIT TROU ECRA 1 88 upper TYPE 804 BOIT TROU ECRA 1 88 AP (air+plug) TYPE 81 BOIT TYPE 811 BOIT VOLU Revision: 0 Page 125 of 196

127 TYPE 812 BOIT VOLU TYPE 813 BOIT VOLU TYPE 814 BOIT VOLU ACS (air+clad+spring) TYPE 83 BOIT TYPE 831 BOIT VOLU ECRA TYPE 832 BOIT VOLU ECRA TYPE 833 BOIT VOLU ECRA TYPE 834 BOIT VOLU ECRA AG (air+grid) TYPE 84 BOIT VOLU VOLU VOLU VOLU Array in water (value to modifie the water level) TYPE 85 BOIT TYPE 851 BOIT TROU TYPE 852 BOIT TROU TYPE 853 BOIT TROU TYPE 854 BOIT TROU WP (water+plug) TYPE 86 BOIT TYPE 861 BOIT VOLU ECRA TYPE 862 BOIT VOLU ECRA TYPE 863 BOIT VOLU ECRA TYPE 864 BOIT VOLU ECRA WPG (water+plug+grid) TYPE 87 BOIT VOLU VOLU VOLU VOLU Water tank (value to modifie the water level) TYPE 88 PLAZ INFE VOLU ETSU 1 1 FINM MODU 2 External lattice's Volume TYPE 851 BOIT VOLUME Lattice's principal mesh Volume TYPE 8511 BOITe VOLUME Revision: 0 Page 126 of 196

128 Rods and sheaths in the principal mesh TYPE 8512 CYLZ VOLUME TYPE 8513 CYLZ VOLUME TYPE 8514 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8511 DIMR INDP FINR FINM MODU 3 External lattice's Volume TYPE 852 BOIT VOLUME Lattice's principal mesh Volume TYPE 8521 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8522 CYLZ VOLUME TYPE 8523 CYLZ VOLUME TYPE 8524 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8521 DIMR INDP FINR FINM Revision: 0 Page 127 of 196

129 MODU 4 External lattice's Volume TYPE 853 BOIT VOLUME Lattice's principal mesh Volume TYPE 8531 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8532 CYLZ VOLUME TYPE 8533 CYLZ VOLUME TYPE 8534 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8531 DIMR INDP FINR FINM MODU 5 External lattice's Volume TYPE 854 BOIT VOLUME Lattice's principal mesh Volume TYPE 8541 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8542 CYLZ VOLUME TYPE 8543 CYLZ VOLUME TYPE 8544 CYLZ VOLUME LATTICE's Parameters Revision: 0 Page 128 of 196

130 RESC MPRI 8541 DIMR INDP FINR FINM MODU 6 External lattice's Volume TYPE 801 BOIT VOLUME Lattice's principal mesh Volume TYPE 8011 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8012 CYLZ VOLUME TYPE 8013 CYLZ VOLUME TYPE 8014 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8011 DIMR INDP FINR FINM MODU 7 External lattice's Volume TYPE 802 BOIT VOLUME Lattice's principal mesh Volume TYPE 8021 BOITe VOLUME Revision: 0 Page 129 of 196

131 Rods and sheaths in the principal mesh TYPE 8022 CYLZ VOLUME TYPE 8023 CYLZ VOLUME TYPE 8024 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8021 DIMR INDP FINR FINM MODU 8 External lattice's Volume TYPE 803 BOIT VOLUME Lattice's principal mesh Volume TYPE 8031 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8032 CYLZ VOLUME TYPE 8033 CYLZ VOLUME TYPE 8034 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8031 DIMR INDP FINR FINM Revision: 0 Page 130 of 196

132 MODU 9 External lattice's Volume TYPE 804 BOIT VOLUME Lattice's principal mesh Volume TYPE 8041 BOITe VOLUME Rods and sheaths in the principal mesh TYPE 8042 CYLZ VOLUME TYPE 8043 CYLZ VOLUME TYPE 8044 CYLZ VOLUME LATTICE's Parameters RESC MPRI 8041 DIMR INDP FINR FINM FING SORTies SCORes ANNUle EXCEpt 3 CARA_REDUIT CARA_ETENDU CARA_ICSBEP FSCOres FSORties SOURces UNIF 1 MODU 3 FINU UNIF 1 MODU 2 FINU UNIF 1 MODU 5 FINU UNIF 1 MODU 4 FINU UNIF 1 MODU 7 FINU UNIF 1 MODU 6 FINU UNIF 1 MODU 9 FINU UNIF 1 MODU 8 FINU FINSOURces SIMU DEBU 200 Revision: 0 Page 131 of 196

133 FSIM FIND FIN_MORET Revision: 0 Page 132 of 196

134 APPENDIX B: UO 2 FUEL RODS: CALCULATIONS OF THE DENSITY AND ITS ASSOCIATED UNCERTAINTY The mean fuel density is obtained by considering: The mean linear mass density calculated on 1261 rods, ML = Linear Mass density: ± (1σ) g/cm The mean pellet diameter calculated on 53 pellets; D = diameter: ± (1σ) cm. ML ρ = = g/cm 3. 2 πd / 4 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) Z 2 Z 2 Z Z σ Z = σ x + σ y + 2 cov( x, y). x y x y The correlation coefficient is r = cov(x,y)/σ x σ y, r is equal to 0, because the linear mass density and the diameter were measured independently, therefore: ML 2 σ ρ = σ + σ 2 ML. 3 D πd πd Hence, σ ρ = 0.073, that is to say 3σ ρ = g/cm 3. Revision: 0 Page 133 of 196

135 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 modelled into cylinders using two different methods for the two plugs: The lower plug is cylindrized, keeping the total mass constant (total mass = plug mass + clad mass in the zone); the equivalent plug height is derived from the following formula: H Plug mass + Clad mass = π φ plug ρ Zr 4 = plug 2 The simplification does not have a significant impact on reactivity since the total mass is kept constant. The upper plug is cylindrized, keeping the total length constant and the density constant. This does not have a significant impact on reactivity since the upper plug does not contribute significantly to total reactivity. cm. Therefore the rod length becomes = cm. Table C-1: Characteristics of the true plugs. Height (cm) Diameter (cm) Weight (g) Value Value Value Rods Upper Plug Lower Plug Clad (Lower Plug) 0.8 cm Revision: 0 Page 134 of 196

136 Figure C-1: Sketch of the plugs (lower and upper, respectively). Revision: 0 Page 135 of 196

137 Homogenization of Materials The modelling process for cross sections in APOLLO2-MORET 4 requires homogenized materials. The homogenized materials are water (W), Zircaloy-4, or Zr4, for fuel cladding [Plug (P), Clad (C)], AG3 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 (cm) Array Pitch p 1.6 Fuel Clad Internal Diameter ø int clad Fuel Clad External Diameter ø ext clad AG3 Grid Holes Diameter ø holes 0.98 Plug Diameter ø plug_cyl The springs were not proposed in the benchmark definition (Section 3). Therefore, they are not retained in APOLLO2-MORET 4 homogenization calculations. The spring impact on reactivity worth is negligible. Lower zones in water There are two zones under water: the water-plug (WP) mixture and the water-plug-grid (WPG) mixture. Water Plug (WP Mixture : Bottom Plug) This zone is located between levels cm and -0.4 cm, relative to the bottom of the UO 2 V = p 2. cell h WP φ π h. WP 4 2 plug _ cyl V = Zr 4 V water = V V. cell Zr 4 The results of calculation are reported in Table C-3 Revision: 0 Page 136 of 196

138 Table C-3: Volume fractions in WP mixture. Element Volume Fractions % Zr4 (Plug) Water Water-Plug-Grid (WPG Mixture : Lower Grid) The grid is 0.4 cm thick with holes of 0.98 cm diameter. This zone is located between the levels -0.4 cm and 0 cm. V cell = p 2 h WPG. φ π h. WPG 4 2 plug _ cyl V = Zr 4 V V AG3M water = p 2 cell h WPG φ π 4 2 holes = V V V. AG3M Zr 4 h WPG. The results of calculation are reported in Table C-4. Table C-4: Volume fractions in WPG mixture. Element Volume Fractions % Zr4 (Plug) AG3 (Grid) Water 1.82 Intermediate Zones : Fissile Column This zone is located between the levels 0 cm and cm. There are two different zones: fissile rods in water (0 cm to critical height) and fissile rods in air (critical height to cm). Upper Zones in Air There are three zones in air: air-clad (AC) mixture, air-grid-clad (AGC) mixture, air-plug (AP) mixture. Air-Clad (AC Mixture) This zone is located between the heights cm and cm (height = cm). It includes clad and air without spring. The clad is homogenized with air. Revision: 0 Page 137 of 196

139 V = p 2. V V cell h ACS Zr 4 air φ φ 2 2 ext _ clad int_ clad = V = π h. clad ACS = V V. cell Zr 4 4 The results of calculation are reported in Table C-5. Table C-5: Volume fractions in AC mixture. Element Volume Fractions Zr4 (Clad) 6.20% Air 93.80% Air-Grid-Clad (AGC Mixture) The grid is 0.4 cm thick with holes of 0.98 cm of diameter. This zone is located between the heights 97.5 cm and 97.9 cm for large and thin screen configurations and is located between 97.3 cm and 97.7 cm for reflexion screen configuration. 2 V cell p V V V Zr AG 3 air 4 = h. φ AGCS 2 2 ext _ clad int_ clad = π h. AGCS φ holes = p h π h. M AGCS AGCS 4 = V V V. cell AG 3 Zr 4 The results of calculation are reported in Table C-6. φ Table C-6: Volume fractions in AGCS mixture. Element Volume Fractions % Zr4 (Clad) 6.20 AG3 (Grid) Air Revision: 0 Page 138 of 196

140 Air-Plug (AP Mixture Top Plug) This zone is located between the heights cm and cm (height = cm). It includes the cylindrized top plug. V cell = p 2 h AP. 2 φplug _ cyl V = π h. Zr 4 AP 4 V = V V. air cell The results of the calculation are reported in Table C-7. Zr 4 Table C-7: Volume fractions in AP mixture. Element Volume Fractions % Zr4 (Plug) Air Lower and upper grids without rods. The grids are 0.4 cm thick with holes of 0.98-cm diameter. V = p 2. Cell h Grid 2 φhole _ cyl V Hole = π hgrid. 4 V = V V. Grid Cell Hole The results of the calculation are reported in Table C-8. Table C-8: Volume fractions in AP mixture. Element Volume Fractions % AG3 (Grid) Air or Water (Holes) Revision: 0 Page 139 of 196

141 Five zones of small reactivity worth could be described with homogenized materials according to percentages given in Table C-3 to C-9. The corresponding atom densities are given in Table C-10, Table C-11, and Table C-12. Table C-9: Volume percentages of homogenized zones. Zones Volume Percentages (%) Bottom Plug Plug (Zircaloy-4) Water Lower Grid With rods Without rods Plug (Zircaloy-4) Grid (AG3 ) Water 1.82 Grid (AG3) Water Top Plug Plug (Zircaloy-4) Air Clad (Zircaloy-4) 6.20 Upper Grid With rods Without rods Spring Zone Grid (AG3 ) Air Grid (AG3) Water Clad (Zircaloy-4) 6.20 Air Revision: 0 Page 140 of 196

142 Table C-10: Atom densities for homogenized zones (atom/barn-cm). ZONE Bottom Plug (Plug + Water) Lower Grid (Plug + Water +Grid) Top Plug (Plug + Air) Element H O Al Fe Si N Sn Cr C Hf H Zr Si Fe Cu Mn Mg Cr Zn Ti Al N O Sn C Zr Hf H H 2 O N O Sn Fe Cr C Si Zr Al Hf H Atom Densities (atom/barn-cm) E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 Revision: 0 Page 141 of 196

143 Table C-11: Atom densities for homogenized zones (atom/barn-cm). ZONE Upper Grid (Grid + Clad + Air) Spring Zone (Clad + Air) Element Si Fe Cu Mn Mg Cr Zn Ti Al N O H Hf C Zr Sn Cr H Hf O Si Fe N C Zr Al Sn Atom Densities (atom/barn-cm) E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 Revision: 0 Page 142 of 196

144 Table C-12: Atom densities for homogenized zones (atom/barn-cm) ZONE Lower Grids without holes (AG3 + H 2 O) Upper Grids without holes (AG3 + Air) Element Si Fe Cu Mn Mg Cr Zn Ti Al H O Si Fe Cu Mn Mg Cr Zn Ti Al N O Atom Densities (atom/barn-cm) E E E E E E E E E E E E E E E E E E E E E E-06 Revision: 0 Page 143 of 196

145 APPENDIX D: COMPARISON WITH MORET 5 CODE (UNDER VALIDATION AT IRSN) MONTE CARLO CONTINUOUS ENERGY CODE The APOLLO2-MORET 4 calculations using the correlated sampling method were compared to two APOLLO2-MORET 4 direct calculations with a low Monte Carlo standard deviation; the purpose was to validate the correlated sampling method. In a second step, the APOLLO2-MORET 4 calculations were compared to MORET 5 calculations to validate the cell calculations and the different physical assumptions and models in APOLLO2 code. The results in Table D-1 show that a general good agreement is obtained between codes. Parameter Identification Parameter Variation in Calculation Table D-1: 4A-Ti-005 Case 1. APOLLO2-MORET energy groups Correlated sampling k eff 10 5 JEF2.2 library APOLLO2-MORET energy groups Direct calculations (σ = ) k eff 10 5 JEF2.2 library MORET 5 continuous energy Direct calculations (σ = ) k eff 10 5 JEF2.2 library Density (g/cm 3 ) ± Water Density (g/cm 3 ) ±0.1% Fuel Pellet Diameter (mm) ± Clad Outer Diameter systematic (mm) ± Critical water height (mm) ± Sructural material thickness (mm) ± Screen density (g/cm 3 ) ± Position of rod arrays (mm) Subtotal Revision: 0 Page 144 of 196

146 APPENDIX E: NEUTRON COUNTERS POSITION AND NEUTRON SOURCES The neutron counters and neutron sources positions are presented in this appendix. The data come from the logbooks. H is the distance between the bottom of the fissile column and the level of the neutron counters. D is the distance between the core periphery and the neutron counters. Figure E-1: 4A-Ti-005. Revision: 0 Page 145 of 196

147 Figure E-2: 4A-Ti-010. Revision: 0 Page 146 of 196

148 APPENDIX F: GLOW DISCHARGE MASS SPECTROMETRY TECHNIQUE (GDMS) A description a the GDMS technique, as well as trhe results of titanium screens measurements are provided below. Revision: 0 Page 147 of 196

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152 APPENDIX G: MEASUREMENT OF TITANIUM SCREENS WITH A MICROMETER In this appendix, the measurements performed with the micrometer device are provided for the 4A-Ti-005 and 4A-Ti-010 experiments. The points positions are shown in Figure 16. Measurement of the groove Measurement of the thickness Revision: 0 Page 151 of 196

153 Measurement of the groove Measurement of the thickness Revision: 0 Page 152 of 196

154 Measurement of the groove Measurement of the thickness Revision: 0 Page 153 of 196

155 Measurement of the groove Measurement of the thickness Revision: 0 Page 154 of 196