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Specifications and User Guide for NAP : module in DRAGON

1. rep900cluster x2m Original Split CAR3D 331 FIGURE 8 Automatic geometries IGE 345 43234 04440 PLANE 3 SAME 2 PLANE 4 SAME 1 MESHX lt lt mx1 gt gt lt lt mx2 gt gt lt lt mx3 gt gt lt lt mx4 gt gt lt lt mx5 gt gt lt lt mx6 gt gt MESHY lt lt mx1 gt gt lt lt mx2 gt gt lt lt mx3 gt gt lt lt mx4 gt gt lt lt mx5 gt gt lt lt mx6 gt gt MESHZ O 10 110 210 220 SPLITX 2 1 1 1 SPLITY 2 1 1 1 SPLITZ 2 1 1 2 2 2 Build geometry for heterogeneous assembly GeoH NAP Geol CpoU EDIT 10 DIRGEO lt lt DirHet gt gt MIXASS 3 1 23 SPLITX ASS 1 2 1 SPLITY ASS 1 2 1 leads to Original mesh corresponding to assemblies X direction AXD 1 NXD 0 1 1 1 0 Y direction AYD 1 NYD 0 1 1 1 0 Splitting within assemblies SXP 1 2 1 SYP 1 2 1 New mixtures plane 1 0 4 4 4 4 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 0 plane 2 0 4 4 4 4 4 4 4 4 4 0 4 13 12 13 10 9 10 13 12 13 4 4 12 11 12 9 8 9 12 11 12 4 4 13 12 13 10 9 10 13 12 13 4 4 10 9 10 7 6 7 10 9 10 4 4 9 8 9 6 5 6 9 8 9 4 4
2. 15 4 3 1 Mesh splitting and tracking polynomial order 15 4 3 2 Homogenization geometry cs pr es o oto koe Roy Roh e n 15 4 3 3 Homogenization SPH option osse or m 17 5 Modules and data structures rms 21 5 1 DONTON PP A a Ges E HOR amp AT 21 5 2 DRAGON 4 2 RR K som RE EEE Lee e a we due s 21 5 3 TRIVAC uu don ox DE x e e Red ae A qa 21 5 4 au CL SE pe Re aa sudiste bas 21 6 Conclusions and recommandations 22 A Detailed alporti a Li ss E R 63 su 432x899 eed He lee x ER SX 23 A1 Detailed algorithm and input file description 23 A 1 BIBD dE IS a RRAEIoLasqqeRCre xs 23 A 2 e MMC C 24 A 3 NN de 25 A 2 Automatic geometry generation a 26 AS VELLA 3x xo mem Eus R e a a ok a E Oe A 29 A l Verification part l sas des bb a de 4 4 eS Dia 29 A 2 VenBeauou DAVE 2 us e val same Es RR m RARER AA 30 A 3 VOnuca von DANE 3 62 Ju Jus ela as ae el ee ee ee E o ee ER 30 B Description of input files used as examples and validation tests 36 Bl Dael Seb o LUE Pa RG Pee AR E Ge ee be aed b LES 36 B 2 rapOUUbst queo x esa ga REUS a RON AUR RE Ip m S PR E 36 B rep900EnrichCOMPOxPM sa s sr dee da amd peus n y EU x A 3T BA testNAPGHO SOM 25 456 2055 9 9 9 Pee pa ba da E o e s 37 B 5 PepO0UcbusbbE ada ge Lu de A Ue C S mg Rok Eo Gu DER 38 B6 t
3. 4 68 2 90 1 23 7 58 4 68 3 28 1 03 7 96 8 47 7 38 1 39 15 84 CA DUAL 2 3 1 28 1 81 0 99 3 09 1 32 1 85 0 99 3 18 1 70 1 92 1 03 3 62 2 76 3 88 1 18 6 65 DUAL 33 1 32 1 86 0 99 3 17 1 62 2 03 1 02 3 66 2 76 3 88 1 18 6 64 C5 DUAL 23 1 06 2 82 0 67 3 88 2 41 6 24 0 91 8 65 2 43 7 00 0 85 9 43 4 18 14 77 1 15 18 94 DUAL 33 2 45 6 38 0 93 8 83 2 39 7 18 0 83 9 57 4 21 14 80 1 19 19 01 C6 DUAL 23 5 12 1 72 1 74 6 85 5 63 1 93 2 00 7 56 5 90 3 13 1 81 9 03 8 51 3 29 1 92 11 80 DUAL 3 3 5 61 1 95 2 00 7 56 5 16 1 92 1 79 7 08 8 60 3 26 1 95 11 87 DUAL 2 3 1 98 2 05 0 75 4 03 5 77 3 67 0 98 9 44 6 45 4 79 1 16 11 24 1127 10 58 1 63 21 85 en DUAL 33 5 87 3 76 0 97 9 63 6 49 4 91 0 98 11 40 sas 10 59 1 63 21 94 C8 DUAL23 2 63 3 18 1 74 5 81 4 07 3 36 2 11 7 43 3 98 4 89 1 88 8 87 6 63 8 68 2 24 15 31 DUAL 3 3 4 12 3 47 2 13 7 59 3 97 3 84 1 90 7 81 6 67 8 66 2 31 15 33 C9 DUAL 23 0 14 0 15 0 05 0 29 0 10 0 11 0 04 0 22 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 DUAL 33 0 11 0 12 0 04 0 22 0 11 0 12 0 04 0 22 0 10 0 12 0 04 0 22 C10 DUAL 2 3 2 01 1 41 0 92 3 42 2 26 1 50 0 96 3 77 2 25 1 59 0 92 3 84 2 03 1 45 0 92 3 49 DUAL 3 3 2 14 1 48 0 96 3 62 2 07 1 57 0 93 3 64 2 04 1 51 0 93 3 55 cu DUAL 23 2 07 3 19 1 73 5 26 2 99 6 70 1 97 9 69 2 36 7 00 1 78 9 36 4 06 14 60 1 95 18 66 DUAL 33 3 03 6 87 1 98 9
4. Reference transport pin power distribution a as S 45 2 o o 2 4 2 4 2 homog 4x4 homog 8x8 HFdiff 5 hl sl t2 HFdiff 5 hl s2 t2 s 4 2 E h 8x8 1 heter 4x4 eter 8x 1 heterl mixtures are used FIGURE 12 Relative difference between transport reference and diffusion pin power distribution of the cluster case 5 IGE 345 36 B Description of input files used as examples and validation tests Several input files have been generated for the different steps of calculations Step 1 rep900het mco x2m set Step 2 rep900EnrichCOMPO x2m set Step 3 two sets of files testNAPGEO z2m and rep900cluster x2m Validation rep900cluster mco z2m and rep900cluster z2m sets for transport and diffusion cal culations respectively Most of these input files have been launched many times for the different fuel heterogeneity level in the assembly homogenization diffusion mesh splitting Raviart Tomas order interpolation or not To make thing easier faster and most importantly to reduce the chance of error in all these parameter consistency most of the computation inputs have been automatically generated and launched using bash scripts notification that a bash script was used will be provided in the description of each input file when applicable B 1 bash scripts All the bash scripts used to generate the input files and to launch the calculations are stored at
5. baad Lo ratio reference macro average flux ratio reference macro side flux Using this definition and Eq 2 5 the averaged SPH factor fi is equal to Pret out PT This normalization corresponds to the SELE MWG option in the SPH module of DRAGON Note that in the case of an homogeneous assembly the Selengut macro calculation water gap norma lization is equivalent to the classical Selengut normalization since the diffusion flux is constant over the assembly BHT dmc mec 2 3 Pin Power Reconstruction 2 3 1 Definition As mention previously the pin power reconstruction methodology can be seen as a de homogenization technique for core calculations performed with arbitrarily homogenized fuel assembly geometries The general idea is to look at the the detailed flux distribution get in the core as the product of two contri butions the macro flux provided by the macro calculations which represents the general shape at the core level Ome the local flux provided by the transport calculations which represents the ripple shape at the assembly level de IGE 345 6 In order to keep consistency the local flux is normalized and is referred as the shape factor The reaction rate for each pin is then given by the following equation E gt xu b TEE Dores X dip 33 X IN V withl lt i lt M and1 lt p lt P 2 14 NS Rae shape factor lt 1 lt Pp ref ari dp x EM 2 15 pref pl Apo Ei p
6. rable to those obtained with the classical Selengut sometime better sometime worst depending on the configuration TABLE 4 Relative error between reconstruction and transport calculations coarse mesh SELE_FD SELE M WG STD 4x4 4x4 4x4 min max rms 0 min max rms min max rms C1 DUAL 2 3 2 46 3 93 1 35 6 39 3 64 6 75 1 68 10 39 5 39 13 69 2 27 19 08 DUAL 3 3 2 55 3 49 1 31 6 04 2 02 6 32 1 38 8 34 4 88 17 76 1 90 22 64 C2 DUAL 2 3 2 54 3 42 1 53 5 96 2 76 6 21 1 67 8 97 4 33 11 82 2 18 16 15 DUAL 3 3 2 42 3 31 1 50 5 73 2 21 6 13 1 47 8 34 4 50 15 92 1 95 20 41 C3 DUAL 23 3 01 2 51 1 27 5 52 2 92 3 66 1 83 6 58 6 34 5 70 2 07 12 04 DUAL 3 3 3 04 2 52 1 21 5 56 3 08 3 51 1 57 6 58 8 75 7 63 1 57 16 38 CA DUAL 2 3 1 58 2 01 1 01 3 59 1 44 2 19 0 90 3 63 2 60 3 60 1 20 6 20 DUAL 3 3 1 50 1 62 0 99 3 13 1 27 1 44 0 83 2 71 2 78 3 92 1 18 6 70 C5 DUAL 2 3 2 45 3 75 0 94 6 19 2 91 5 59 1 32 8 49 3 89 11 16 1 62 15 06 DUAL 3 3 2 24 3 70 0 90 5 94 1 36 5 41 1 16 6 77 4 29 15 22 1 33 19 51 C6 DUAL 2 3 6 42 2 64 1 80 9 06 7 96 4 76 2 31 12 72 8 97 6 66 2 47 15 62 DUAL 3 3 6 12 1 77 1 72 7 89 6 99 2 90 1 87 9 88 8 94 3 37 2 05 12 31 C7 DUAL 2 3 4 13 4 75 1 69 8 88 3 55 4 91 1 47 8 46 9 02 7 93 2 24 16 94 DUAL 3 3 4 39 4 66 1 61 9 05 4 03 3 34 1 25 7 37 11 67 10 84 1 73 22 51 C8 DUAL 2 3 3 09 4 16 1 77 7 25 4 22 6 18 2 60 10 40 6 01
7. 8 30012 8 20012 Transport 0 0102 0108 0104 0106 0108 0107 0 0101 0102 0108 010 0105 010 0107 0 0101 0102 0103 010 0105 0105 0107 0 0101 0102 0108 01001 0105 0106 0107 Heterogeneous Pin by Pin Heterogeneous Pin by Pin homog 4x4 homog 8x8 0 0102 0103 0104 0109 0108 0107 0 010 0102 0108 010 0105 0105 01077 0108 0 0108 0108 0100 0108 0106 0107 0 0102 0100 0104 0105 0106 0100 0108 Heterogeneous Pin by Pin Heterogeneous Pin by Pin heter 4x4 heter 8x8 1 1 hetl mixtures are used FIGURE 10 Transport vs diffusion flux distribution of the cluster case 5 32 IGE 345 33 However the comparison between the different approaches will only be discussed in Section 4 Only the verification of the implementation was looked at in this section IGE 345 34 HFmapT 5 5 4 5 4 3 5 3 2 5 2 30 35 40 45 50 Reference transport pin power distribution HFmapD 5 h0 sl t2 HFmapD 5 h0 s2 t2 5 5 50 50 4 4 45 45 4 4 40 40 3 3 35 a 35 30 2 30 2 2 2 30 35 40 45 50 30 35 40 45 50 homog 4x4 homog 8x8 HFmapD 5 hl sl t2 HFmapD 5 hl s2 t2 5 5 50 50 a a 45 45 4 a 40 40 de 35 3 35 3 30 2 40 2 2 2 30 35 40 45 50 30 35 40 45 50 heter 4x4 heter 8x8 1 1 heterl mixtures are used FIGURE 11 Transport vs diffusion pin power distribution of the cluster case 5 IGE 345 39 HFmapT 5 5 4 5 4 3 5 3 2 5 2 30 35 40 45 50
8. FIGURE 7 Transport vs diffusion pin power distribution comparison SELE_FD and SELE MWG SPH options C8 M60 U10 M40 IGE 345 21 5 Modules and data structures 5 1 DONJON The implementation of pin power reconstruction in DRAGON DONJON has required several changes in the code new module named NAP has been programmed to perform the PPR As seen in the previous sections heterogeneous assemblies are simulated In order to be able to handle these configurations several modifications had to be done to the existing modules These modifications serve two main purposes Automatic geometry definition Pre format results for pin power reconstruction On a practical point of view several modules had to be changed and their user guide updated RESINI This module of DONJON is used to initialize the MAP data structure L_MAP signature This structure contains the description of the fuel channels In PWR cases each channel corresponds to an assembly Using heterogeneous mixtures in one assembly increases the complexity of the geometry However two levels geometries embedded geometry are not possible in the DONJON code The general idea is then to define one channel per mixture for all assemblies All these channels have then to be regrouped by assembly to impose the same burnup This process could be done manually but if the heterogeneity of the cross section is large ex one mixture per pin within a compl
9. as a one level geometry Compute reconstructed pin power During the validation of the method we have emphasized that it is highly recommended to perform an interpolation of the flux within macro regions before projecting it on the pins This interpolation is done using the polynomial representation used by the flux solver such as Raviart Thomas in our case A lower order of the polynomial mainly flat flux approximation can lead to less precise results especially if the macro regions are large and there is a great deal of heterogeneity between and inside assemblies To validate our implementation of the method 12 configurations of 3x3 cluster of PWR 900 assemblies have been simulated They are the same as those used by Fliscounakis in 1 plus two homogeneous clusters First the homogeneous cluster results are very good The difference between transport and diffusion calculations are smaller than 0 15 for UOX and 0 4 for MOX With regards to the SPH homogenization the flux volume normalization has demonstrated large errors and is not recommended even when using an heterogeneous assembly All Selengut methods are better than the flux volume homogenization When compared together the classical Selengut method leads to the smallest range of errors in general which is the main criteria to choose between the SPH homogenization methods On the other hand the Selengut macro calculation water gap method presents better results regarding flux cont
10. be forgotten or added An example of set of input files is provided in rep900EnrichCOMPO 22m It is related to the set of input files rep900het mco z2m The detailed algorithm to enrich a regular MULTICOMPO with the additional data can then be sum marized as follows 0 Define the homogenized geometry It can be recovered from the MULTICOMPO Do not use symmetry nor split For all calculations in MULTICOMPO perform the following 1 Set parameter values 2 Get cross sections from homogenized data and create a MACROLIB NCR MACINI IGE 345 25 3 Compute flux TRIVAT FLUD 4 Project flux on each pin compute 9 This is done with the NAP module with the PROJECTION keyword Here is an example Cpo NAP Cpo Track Flux EDIT O PROJECTION DIRPIN lt lt DirPin gt gt IFX 2 SET burnup lt lt burnup gt gt SET ppmBore lt lt ppmBore gt gt SET TF 8 0000E 02 SET TCA 6 0000E 02 SET DCA 6 5900E 01 We would like to remind here that the pin wise projected flux is normalized using the flux volume technique as described in Section 2 3 Note No fuel is defined with RESINI module All calculations are performed in 2D directly on the geometry A 3 Step 3 0 Define core geometry Geol with a Only ONE mesh along X and Y directions for assemblies Final mesh for the moderator coolant parts b Final mesh along Z direction 1 Define Geometries G
11. min max rms 0 min max rms min max rms min max rms 0 Cl DUAL 2 3 1 71 2 18 1 02 3 89 2 03 5 13 1 78 7 76 2 93 4 54 1 16 7 47 2 32 15 34 3 09 17 67 DUAL 33 1 87 5 56 1 79 7 43 2 57 3 27 1 12 5 84 2 37 15 35 3 14 17 72 C2 DUAL23 1 88 2 09 1 34 3 96 2 31 5 19 1 78 7 50 2 56 3 12 1 41 6 28 2 81 13 88 3 03 16 69 DUAL 33 2 23 5 24 1 78 7 47 2 28 2 96 1 39 5 24 2 86 13 89 3 07 16 75 C3 DUAL23 2 19 1 95 0 91 4 13 3 44 2 49 2 00 5 93 2 61 2 56 1 03 5 17 5 56 6 10 3 87 11 67 DUAL 33 3 45 2 49 2 01 5 94 2 56 2 15 0 92 4 71 5 58 6 13 3 90 11 70 CA DUAL 23 1 25 1 78 1 00 3 02 0 91 0 90 0 38 1 81 1 36 1 84 1 03 3 20 2 97 3 23 0 66 6 20 DUAL 33 0 91 0 90 0 38 1 82 1 24 1 80 1 02 3 04 2 97 3 22 0 66 6 19 C5 DUAL 23 1 48 2 56 0 68 4 05 1 29 4 75 1 4 6 05 2 40 3 23 0 78 5 63 1 73 13 30 2 80 15 03 DUAL 33 gt S 1 30 4 88 1 42 6 17 2 05 3 01 0 73 5 06 1 74 13 32 2 84 15 07 C6 DUAL 23 5 30 1 66 1 48 6 96 7 09 2 13 2 22 9 22 5 97 2 49 1 56 8 45 9 32 2 53 2 99 11 85 DUAL 33 7 02 2 13 2 23 9 15 5 79 1 72 1 51 7 51 9 30 2 51 3 01 11 81 C7 DUAL 2 3 2 58 3 62 1 41 6 20 3 20 1 47 1 24 4 68 3 29 4 62 1 55 7 91 8 35 7 83 3 99 16 17 DUAL33 3 22 1 48 1 24 4 70 3 25 3 90 1 40 7 15 8 40 7 83 4 01 16 24 C8 DUAL 23 2 25 2 84 1 43 5 09 3 58 3 76 2 50 7 34 2 69 3 94 1 56 6 63 5 20 6 52 4 01 11 73 DUAL 33 3 59 3 74 2 52 7 34 2 64 3 26
12. 0 2 0 3 0 3 0 2 0 2 0 3 0 2 0 3 0 6 0 0 0 2 0 2 0 2 0 1 0 2 0 2 0 1 0 5 0 5 0 2 0 2 0 2 0 1 0 2 0 2 0 2 0 1 0 2 0 2 0 3 0 1 0 3 0 3 0 2 0 7 0 1 0 1 0 2 0 1 0 5 0 5 0 5 0 5 0 1 0 3 0 2 0 2 0 2 0 2 0 3 0 2 0 6 0 6 0 2 0 1 0 1 0 1 0 1 0 1 0 2 0 1 0 5 0 5 0 1 0 3 0 1 0 2 0 2 0 3 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 6 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 5 0 4 0 0 0 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 1 0 6 0 1 0 1 0 0 0 2 0 5 0 5 0 5 0 5 0 2 0 1 0 2 0 2 0 2 0 2 0 1 0 3 0 7 0 6 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 4 LF0 4 0 0 0 1 0 1 0 2 0 2 0 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 6 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 4 0 4 0 0 0 1 0 1 0 1 0 1 0 2 0 1 0 2 0 2 0 3 0 2 0 2 0 2 0 3 0 2 0 6 0 1 0 2 0 0 0 1 0 3 0 4 0 4 0 5 0 1 0 2 0 1 0 2 0 2 0 2 0 2 0 2 0 6 0 6 0 2 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 5 0 4 0 1 0 1 0 1 0 0 0 2 0 1 0 2 0 1 0 2 0 2 0 3 0 1 0 2 0 2 0 2 0 6 0 6 0 6 0 6 0 5 0 4 0 2 0 1 0 3 0 3 0 0 0 1 0 1 0 1 0 1 0 1 0 2 0 2 0 1 0 1 0 2 0 2 0 2 0 6 1 5 1 3 1 1 0 9 0 9 0 7 0 1 0 2 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 3 0 2 0 2 0 2 0 3 0 5 Yd 1 9 1 7 1 0 1 5 1 3 0 9 0 1 0 7 0 7 0 3 0 0 0 0 0 1 0 5 0 0 0 0 0 5 0 0 0 1 0 5 0 2 0 2 0 2 0 5 0 9 3 7 3 8 37 3 6 3 6 3 1 1 5 0 0 0 9 1 0 0 7 0 2 0 3 0 4 0 4 0 4 0 4 0 5 0
13. 0 22 DUAL 33 0 10 0 11 0 04 0 22 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 C10 DUAL23 2 01 1 41 0 92 3 42 3 08 1 85 1 01 4 94 3 54 2 29 1 07 5 82 2 46 1 77 0 98 4 23 DUAL 3 3 2 30 1 58 0 99 3 88 2 40 1 71 0 99 4 11 2 13 1 63 0 96 3 75 Cll DUAL 23 2 07 3 19 1 73 5 26 3 15 7 11 2 06 10 26 3 67 7 43 2 20 11 10 4 49 12 95 2 49 17 44 DUAL 33 3 13 7 19 2 07 10 32 2 51 7 42 1 99 9 92 4 18 15 05 2 18 19 24 C12 DUAL 23 0 34 0 35 0 13 0 69 0 34 0 33 0 12 0 67 0 37 0 34 0 13 0 71 0 34 0 33 0 12 0 67 DUAL 33 0 34 0 33 0 12 0 68 0 33 0 33 0 12 0 67 0 34 0 33 0 12 0 67 STE WOI OV TABLE 6 Relative error between reconstruction and transport calculations fine mesh STD option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 8x8 8x8 8x8 min max rms min max rms min max rms min max rms Cl DUAL 23 1 74 3 56 1 25 5 30 3 26 7 33 1 54 10 59 2 82 8 26 1 38 11 08 4 75 17 27 1 65 22 02 DUAL 33 3 30 7 51 1 56 10 81 2 79 8 46 1 39 11 25 4 82 17 29 1 71 22 11 C2 DUAL23 1 98 2 95 1 44 4 93 2 81 6 44 1 63 9 25 2 57 7 26 1 54 9 83 4 47 15 47 1 78 19 93 DUAL 33 2 85 6 59 1 64 9 44 2 51 7 44 1 55 9 96 4 52 15 50 1 82 20 02 C3 DUAL23 1 93 1 39 0 90 3 32 4 60 2 82 1 21 7 41 4 68 3 16 1 08 7 84 8 40 7 35 1 35 15 74 DUAL 3 3
14. 0 80 0 43 0 35 0 15 0 78 0 22 0 31 0 10 0 53 DUAL 33 0 37 0 43 0 15 0 80 0 43 0 35 0 15 0 77 0 22 0 31 0 10 0 52 SPE ADI Sv TABLE 11 Relative error between reconstruction and transport calculations 96 coarse mesh SELE_EDF option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 min max rms 0 min max rms min max rms min max rms Cl DUAL 2 3 1 71 2 18 1 02 3 89 2 43 7 01 1 84 9 44 4 43 5 63 1 62 10 06 2 77 15 76 3 42 18 53 DUAL 33 1 96 6 42 1 86 8 39 2 51 5 07 1 28 7 58 2 45 15 72 3 29 18 17 C2 DUAL23 1 88 2 09 1 34 3 96 2 87 6 24 1 83 9 10 3 66 4 78 1 73 8 45 2 95 13 99 3 25 16 94 DUAL 33 2 27 5 98 1 85 8 26 2 25 4 55 1 51 6 79 2 96 14 21 3 18 17 17 C3 DUAL23 2 19 1 95 0 91 4 13 3 48 3 02 2 05 6 50 2 89 4 39 1 53 7 28 6 11 6 04 4 10 12 15 DUAL 33 3 47 2 97 2 07 6 44 2 97 2 89 1 08 5 86 5 61 6 24 3 99 11 86 CA DUAL 23 1 25 1 78 1 00 3 02 0 91 1 23 0 47 2 15 1 67 2 53 1 10 4 20 2 97 3 16 0 67 6 13 DUAL 33 0 93 0 88 0 39 1 80 1 27 1 79 1 05 3 07 2 97 3 23 0 66 6 20 C5 DUAL 23 1 48 2 56 0 68 4 05 1 30 5 80 1 44 7 10 4 00 4 27 1 11 8 27 2 48 13 09 2 99 15 57 DUAL 33 1 30 5 52 1 47 6 82 2 00 3 93 0 83 5 93 1 77 13 65 2 94 15 41 C6 DUAL23 5 30 1 66 1 48 6 96 8 42 3 13 2 31 11 55 7 39 5 15 2 18 12
15. 1 51 5 91 5 27 6 50 4 06 11 77 C9 DUAL 23 0 14 0 15 0 05 0 29 0 11 0 10 0 04 0 21 0 10 0 11 0 04 0 22 0 17 0 20 0 08 0 37 DUAL 33 0 11 0 11 0 04 0 22 0 11 0 12 0 04 0 22 0 17 0 20 0 08 0 37 C10 DUAL 23 1 79 1 32 0 83 3 11 1 86 1 24 0 76 3 10 2 04 1 44 0 84 3 49 1 44 1 43 0 39 2 87 DUAL 33 1 74 1 22 0 76 2 96 1 85 1 48 0 85 3 33 1 42 1 41 0 39 2 84 Cll DUAL 2 3 1 91 2 65 1 47 4 56 2 40 5 74 1 95 8 14 2 52 4 92 1 53 7 44 2 61 12 48 2 87 15 09 DUAL 33 2 20 5 65 1 96 7 85 2 15 3 30 1 52 5 45 2 59 12 49 2 92 15 08 C12 DUAL 23 0 34 0 35 0 13 0 69 0 22 0 31 0 10 0 53 0 35 0 33 0 13 0 69 0 23 0 31 0 10 0 53 DUAL 33 0 22 0 31 0 10 0 53 0 34 0 33 0 12 0 67 0 22 0 31 0 10 0 53 SPE ADI LV TABLE 13 Range of relative error 6 between reconstruction and transport calculations for all options coarse mesh Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 e E 9 E E E B R 7 E a z a a E E E a a E A E eal g E E td E El rd E E rd tn 4 cal d mM E d mM leal a tn 4 El a a BH E o BH E S B B a B B un sa on v on n n R Cl DUAL 2 3 5 30 11 14 4 47 3 89 11 14 6 39 10 89 9 44 12 03 11 17 10 39 10 06 19 08 14 85 17 43 18 53 DUAL 33 11 26 6 04 9 84 8 39 11 54 10 85 8 34 7 58 22 64 9 60 17 04 18 17 C2 DUAL23 4
16. 10 9 10 7 6 7 10 9 10 4 4 13 12 13 10 9 10 13 12 13 4 4 12 11 12 9 8 9 12 11 12 4 4 13 12 13 10 9 10 13 12 13 4 0 4 4 4 4 4 4 4 4 4 0 w plane o EN Hs Hs Hs NS NS Hs Hs Hs o 4 13 4 12 LA N 13 10 12 9 LO 10 13 12 13 12 11 12 4 Hs m um 00 Ko IGE 345 29 4 13 12 13 10 9 10 13 12 13 4 4 10 9 10 7 6 7 10 9 10 4 4 9 8 9 6 5 6 9 8 9 4 4 10 9 10 7 6 7 10 9 10 4 4 13 12 13 10 9 10 13 12 13 4 4 12 11 12 9 8 9 12 11 12 4 4 13 12 13 10 9 10 13 12 13 4 0 4 4 4 4 4 4 4 4 4 0 plane 4 0 4 4 4 4 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 4 4 4 4 4 4 4 4 4 0 Assembly zones 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 4 4 4 5 5 5 6 6 6 4 4 4 5 5 5 6 6 6 7 7 7T 8 8 8 9 9 9 7 T TT 8 8 8 9 9 9 7 7 7 8 8 8 9 9 9 When the geometry is automatically split at assembly level the fuel mixtures are redefined automati cally as shown in example over In order to keep all the input files coherent several parts have to take into account these new mixture numbers The affected modules are 1 USPLIT where the fuel mixture numbers are defined and stored 2 RESINI where the fuel positions are defined and stored 3 NCR where the fuel cross sections are computed and stored In all these modules keywords hav
17. 12 03 5 39 13 69 2 27 19 08 DUAL 33 3 42 7 84 1 64 11 26 2 83 8 71 1 57 11 54 4 88 17 76 1 90 22 64 C2 DUAL23 1 98 2 95 1 44 4 93 3 00 6 78 1 71 9 78 3 02 7 48 1 84 10 50 4 33 11 82 2 18 16 15 DUAL 33 2 95 6 89 eral 9 84 2 62 7 67 1 69 10 29 4 50 15 92 1 95 20 41 C3 DUAL23 1 93 1 39 0 90 3 32 4 79 3 01 1 33 7 80 4 50 3 63 1 58 8 13 6 34 5 70 2 07 12 04 DUAL 33 4 85 3 07 1 32 7 92 4 78 3 38 1 24 8 16 8 75 7 63 1 57 16 38 C4 DUAL 23 1 28 1 81 0 99 3 09 1 49 2 15 1 03 3 64 1 68 2 52 1 10 4 20 2 60 3 60 1 20 6 20 DUAL 33 1 36 1 81 1 00 3 16 1 64 2 07 1 04 3 71 2 78 3 92 1 18 6 70 C5 DUAL 23 1 06 2 82 0 67 3 88 2 62 6 55 0 98 9 17 3 31 7 21 1 16 10 52 3 89 11 16 1 62 15 06 DUAL 33 2 55 6 66 0 99 9 22 2 42 7 39 0 97 9 81 4 29 15 22 1 33 19 51 C6 DUAL23 512 1 72 1 74 6 85 7 35 2 97 2 11 10 31 8 61 4 78 2 39 13 39 8 97 6 66 2 47 15 62 DUAL 3 3 6 11 1 97 2 07 8 08 6 71 3 10 1 98 9 80 8 94 3 37 2 05 12 31 DUAL23 1 98 2 05 0 75 4 03 5 97 3 87 1 12 9 84 6 25 5 66 1 46 11 91 9 02 7 93 2 24 16 94 KI DUAL 33 6 07 3 94 1 01 10 01 6 61 5 03 1 07 11 65 AER 10 84 1 73 22 51 C8 DUAL 23 2 63 3 18 1 74 5 81 4 20 4 79 2 26 8 98 4 77 6 63 2 61 11 41 6 01 8 50 3 01 14 51 DUAL 3 3 4 23 410 2 25 8 33 4 05 5 85 2 7 9 89 6 85 8 83 2 54 15 69 C9 DUAL 23 0 14 0 15 0 05 0 29 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 0 10 0 12 0 04
18. 2 0 2 0 3 0 6 2 0 2 0 0 1 0 1 0 0 0 1 0 5 0 1 0 1 0 6 0 1 0 2 0 5 0 2 0 2 0 3 0 5 0 9 3 3 34 0 1 0 0 0 3 0 4 0 4 0 4 0 5 0 6 0 5 0 6 0 6 0 6 0 6 0 6 0 9 0 9 1 9 2 2 0 3 0 2 0 2 0 4 0 3 0 4 0 5 0 7 0 5 0 5 0 5 0 6 0 5 0 6 1 0 0 9 0 5 0 1 1 0 7 0 2 0 1 0 3 0 1 0 1 0 7 0 1 0 2 0 5 0 2 0 2 0 3 0 5 0 9 1 5 1 8 1 7 0 9 0 3 0 1 0 0 0 1 0 1 0 2 0 2 0 2 0 2 0 3 0 5 2 0 2 0 1 0 0 2 0 2 0 1 0 2 0 4 0 2 0 1 0 2 0 2 0 2 0 2 0 6 2 1 2 0 2 0 1 2 0 4 0 3 0 1 0 1 0 2 0 2 0 2 0 2 0 2 0 1 0 2 0 2 0 2 0 6 1 8 MT 1 5 0 5 0 2 0 1 0 1 0 1 0 2 0 2 0 2 0 5 0 6 2 0 2 0 2 2 1 0 6 0 3 0 2 0 1 0 1 0 3 0 1 0 2 0 2 0 2 0 1 0 3 0 2 0 5 2 2 2 0 2 3 1 5 0 6 0 3 0 2 0 2 0 2 0 3 0 1 0 1 0 2 0 2 0 2 0 1 0 1 0 6 2 9 2 1 7 0 7 0 4 0 1 0 2 0 1 0 2 0 1 0 2 0 6 0 6 IGE 345 FIGURE 6 Relative error between reconstruction 4x4 DUAL 3 3 and transport calculations for case 18 5 hetO split F0 5 0 5 0 5 0 6 0 6 0 5 0 5 0 9 0 9 0 9 0 9 0 5 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 7 0 6 0 6 1 0 0 9 0 6 0 1 0 1 0 5 0 1 0 2 0 2 0 5 0 9 0 9 0 5 0 3 0 2 0 2 0 6 0 2 0 2 0 7 0 1 0 2 0 6 0 2 0 3 0 3 0 6 1 0 0 1 0 2 0 2 0 2 0 2 0 2 0 5 0 5 0 2 0 2 0 2 0 2 0 3 0 2 0 2 0 3 0 3 0 2 0 3 0 3 0 6 0 1 0 2 0 1 0 2 0 2 0 2 0 2 0 5 0 5 0 2 0 2 0 2 0 2 0 2
19. 24 3 70 0 90 5 94 8x8 C5 DUAL 2 3 2 53 3 56 0 91 6 09 DUAL 33 2 40 3 47 0 90 5 86 min max rms 4x4 C6 DUAL 23 6 42 2 64 1 80 9 06 DUAL 3 3 6 12 1 77 1 72 7 89 8x8 C6 DUAL 2 3 6 48 2 00 1 69 8 48 DUAL 33 5 89 1 93 1 68 7 83 4 3 2 Homogenization geometry Three geometries for homogenization have been tested Their results were compared to the perfor mance obtained with a pin by pin geometry Results are presented in Tab 3 They were obtained with cross section normalized with the classical Selengut method The best option is the heterogeneous geo metry het2 were the two outer rows of pins are used in the heterogeneous homogenization In general the root mean square of the error is the minimum for this option TABLE 3 Relative error between reconstruction and transport calculations 96 coarse mesh SELE FD option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 min max rms 0 min max rms min max rms min max rms Cl DUAL 23 6 15 4 99 1 51 11 14 2 46 3 93 1 35 6 39 5 48 5 70 1 92 11 17 7 70 7 15 1 83 14 85 DUAL 3 3 2 55 3 49 1 31 6 04 4 88 5 97 1 63 10 85 2 97 6 62 1 33 9 60 C2 DUAL23 5 76 4 61 1 67 10 37 2 54 3 42 1 53 5 96 4 52 5 13 1 94 9 65 6 46 6 03 1 81 12 49 DUAL 3 3 2 42 3 31 1 50 5 73 4 46 5 50 1 75 9 95 2 70 5 93 1 50 8 63 DUAL 2
20. 34 2 29 13 77 4 33 5 31 1 71 9 64 C8 DUAL 23 4 25 3 21 1 90 7 46 3 32 3 08 1 64 6 40 4 70 3 49 1 95 8 19 3 19 3 02 1 58 6 22 DUAL33 3 02 3 01 1 64 6 03 4 66 3 36 1 90 8 01 3 18 3 07 1 60 6 25 C9 DUAL 23 0 14 0 15 0 05 0 29 0 10 0 11 0 04 0 22 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 DUAL 33 0 11 0 12 0 04 0 22 0 11 0 12 0 04 0 22 0 10 0 12 0 04 0 22 C10 DUAL 23 1 84 1 31 0 88 3 15 2 08 1 36 0 92 3 44 2 19 1 62 0 87 3 81 1 86 1 33 0 86 3 19 DUAL 33 1 96 1 38 0 92 3 34 1 91 1 48 0 88 3 39 1 88 1 41 0 88 3 29 Cll DUAL 2 3 5 26 4 20 1 77 9 47 2 42 3 32 1 68 5 74 4 31 4 86 1 79 9 17 2 58 5 18 1 60 7 76 DUAL 33 2 42 3 29 1 68 5 71 4 09 4 78 1 78 8 87 2 54 5 19 1 62 7 73 C12 DUAL23 0 34 0 35 0 13 0 69 0 34 0 33 0 12 0 67 0 35 0 33 0 13 0 69 0 34 0 33 0 12 0 67 DUAL 33 0 34 0 33 0 12 0 68 0 34 0 33 0 12 0 67 0 34 0 33 0 12 0 67 SPE ADI sv TABLE 9 Relative error between reconstruction and transport calculations 96 coarse mesh SELE MWG option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 min max rms 0 min max rms min max rms 0 min max rms Cl DUAL 2 3 1 99 2 48 1 05 4 47 2 81 8 08 2 21 10 89 3 64 6 75 1 68 10 39 2 58 14 84 3 17 17 43 DUAL 33 2 36 7 48 2 24 9 84 2 02 6 32 1 38 8 34 2 28 1
21. 4 71 15 84 6 06 10 87 11 70 CA DUAL 2 3 3 09 3 63 2 93 3 02 3 18 3 00 1 89 1 81 3 62 4 08 2 69 3 20 6 65 3 23 5 68 6 20 DUAL 33 3 17 2 97 1 85 1 82 3 66 3 98 2 62 3 04 6 64 3 27 5 68 6 19 C5 DUAL23 3 88 10 85 4 52 4 05 8 65 6 09 7 10 6 05 9 43 10 33 6 19 5 63 18 94 8 01 14 24 15 03 DUAL 33 8 83 5 86 7 32 6 17 9 57 10 05 5 13 5 06 19 01 8 02 14 27 15 07 C6 DUAL 2 3 6 85 12 36 7 38 6 96 7 56 8 48 10 76 9 22 9 03 11 17 8 81 8 45 11 80 7 91 11 41 11 85 DUAL 33 7 56 7 83 10 67 9 15 7 08 10 60 8 05 7 51 11 87 7 81 11 36 11 81 C7 DUAL 2 3 4 03 14 06 6 70 6 20 9 44 9 24 5 99 4 68 11 24 14 01 7 22 7 91 21 85 9 70 15 39 16 17 DUAL33 9 63 8 77 6 02 4 70 11 40 13 77 6 92 7 15 21 94 9 64 15 46 16 24 C8 DUAL23 5 81 7 46 5 20 5 09 7 43 6 40 8 46 7 34 8 87 8 19 6 96 6 63 15 31 6 22 11 25 11 73 DUAL 33 7 59 6 03 8 52 7 34 7 81 8 01 6 39 5 91 15 33 6 25 11 80 11 77 C9 DUAL 23 0 29 0 29 0 29 0 29 0 22 0 22 0 27 0 21 0 22 0 22 0 27 0 22 0 22 0 22 0 34 0 37 DUAL 33 0 22 0 22 0 26 0 22 0 22 0 22 0 27 0 22 0 22 0 22 0 34 0 37 C10 DUAL23 3 42 3 15 3 04 3 11 3 77 3 44 3 48 3 10 3 84 3 81 2 52 3 49 3 49 3 19 2 72 2 87 DUAL 33 3 62 3 34 3 37 2 96 3 64 3 39 2 32 3 33 3 55 3 29 2 68 2 84 Cll DUAL 2 3 5 26 9 47 4 56 4 56 9 69 5 74 9 72 8 14 9 36 9 17 7 87 7 44 18 66 7 76 14 27 15 09 DUAL 33 9 90 5 71 9 43 7 85 9 51 8 87 6 15 5 45 18 75 7 73 14 28 15 08 C12 DUAL 23 0 69 0 69 0 7
22. 5 input file is very similar to testNAPGEO x2m set See Sec A 2 for picture of the geometry Several simulations can be simulated by changing the case number The main characteristics are the following 3 types of assemblies MOX and or UOX at different burnup 3x3 pattern no coolant 1 plane along Z direction several commented lines either to explain or offer an other option for the input file usually the automatic way is active and manual way is commented use of partially automatic generation for the geometries The input file have been created using the bash script allClusterDif run sh B 6 rep900cluster mco x2m This DRAGON 5 input set of files is used to validate the pin power reconstruction Their purpose is to compute reference pin power distribution on 3x3 clusters for several cases with transport theory Results will be compared to the rep900cluster c2m diffusion results to validate the methodology and its implementation The main characteristics are the following 8 types of assemblies MOX and or UOX at different burnup 3x3 pattern infinite domain 2D calculations isotopic content of each assembly MOX and UOX computed with a two previous calls to the rep900het_mco 22m set self shielding and level 1 computations including condensation at 26 energy groups performed at assembly level Final flux calculation is done for the cluster level 2 The input file have been created u
23. 6 0 5 0 9 0 9 0 9 0 9 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 6 0 7 0 6 0 7 0 6 0 6 1 0 1 0 0 6 0 1 0 2 0 5 0 2 0 2 0 3 0 5 1 0 0 9 0 5 0 3 0 3 0 2 0 6 0 2 0 2 0 7 0 1 0 3 0 6 0 3 0 3 0 4 0 6 1 0 0 1 0 3 0 2 0 2 0 2 0 3 0 6 p0 6 0 3 0 2 0 2 0 3 0 3 0 2 0 2 0 4 0 3 0 3 0 3 0 4 0 6 0 2 0 2 0 1 0 2 0 2 0 2 0 2 0 5 0 6 0 2 0 2 0 2 0 2 0 2 0 3 0 3 0 3 0 2 0 3 0 3 0 3 0 3 0 6 0 1 0 2 0 2 0 2 0 1 0 2 0 2 0 2 0 6 0 6 0 2 0 2 0 3 0 1 0 3 0 3 0 3 0 2 0 3 0 3 0 3 0 1 0 3 0 3 0 3 0 7 0 2 0 2 0 2 0 2 0 5 0 5 0 6 0 5 0 2 0 3 0 3 0 2 0 2 0 2 0 3 0 3 0 6 0 6 0 2 0 1 0 2 0 2 0 2 0 1 0 2 0 2 0 5 0 6 0 2 0 3 0 2 0 2 0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 4 0 3 0 7 0 1 0 1 0 1 0 1 0 2 0 2 0 1 0 1 0 5 0 5 0 1 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 3 0 2 0 2 0 3 0 3 0 2 0 1 0 6 0 3 0 3 0 2 0 4 0 7 0 7 0 6 0 6 0 2 0 1 0 2 0 2 0 2 0 3 0 2 0 3 0 7 0 6 0 2 0 2 5 0 1 0 1 0 2 0 2 0 2 0 2 0 3 0 2 0 3 0 2 0 2 0 3 0 3 0 2 0 2 0 6 0 1 0 1 0 1 0 2 0 2 0 2 0 2 0 3 0 2 0 2 0 2 0 3 0 3 0 3 0 2 0 3 0 2 0 6 0 1 0 2 0 5 0 1 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 6 0 6 0 3 0 2 0 1 0 1 0 1 0 0 0 2 0 2 0 2 0 1 0 2 0 2 0 3 0 1 0 2 0 3 0 2 0 6 0 4 0 0 0 1 0 1 0 1 0 2 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 3 0 6 1 2 1 0 0 1 0 0 0 1 0 1 0 2 0 1 0 2 0 3 0 2 0
24. 8 50 3 01 14 51 DUAL 3 3 3 05 3 68 1 69 6 73 3 78 5 58 2 15 9 36 6 85 8 83 2 54 15 69 C9 DUAL 2 3 0 10 0 11 0 04 0 22 0 13 0 14 0 05 0 27 0 10 0 12 0 04 0 22 DUAL 3 3 0 10 0 11 0 04 0 22 0 13 0 14 0 05 0 27 0 10 0 12 0 04 0 22 C10 DUAL 2 3 2 95 1 80 0 97 4 74 2 72 2 27 0 78 4 99 2 46 1 77 0 98 4 23 DUAL 3 3 2 12 1 49 0 95 3 61 1 56 1 09 0 59 2 65 2 13 1 63 0 96 3 75 Cll DUAL 2 3 2 76 4 57 1 76 7 33 3 19 7 29 1 90 10 48 4 49 12 95 2 49 17 44 DUAL 3 3 2 50 4 10 1 73 6 60 2 05 6 79 1 57 8 84 4 18 15 05 2 18 19 24 C12 DUAL23 0 34 0 33 0 12 0 67 0 49 0 35 0 15 0 84 0 34 0 33 0 12 0 67 DUAL 33 0 34 0 33 0 12 0 68 0 42 0 34 0 15 0 77 0 34 0 33 0 12 0 67 GFE H I 61 IGE 345 20 To better understand the performance of those two Selengut options maps of the error have been plot on Fig 7 The graphs show that the flux is more continuous at the assembly interfaces with the Selengut macro calculation water gap This result shows that this new Selengut method has been correctly implemented and that it guaranties the flux continuity at the assembly interface as designed to Transport Diffusion h2 s1 t3 error SELE FD SELE MWG C3 M10 M30 U20 Mo M van on marz 5 h2 a1 ta s so 5 as a o as D a 30 2 E 30 as aa as so marz 6 h2 al ta marz 6 h2 si t3 so a so 2 as as 2 o ao 40 a as 2 as E 5 30 30 a 30 as 40 as sa 30 25 40 as so
25. 93 10 37 4 00 3 96 9 78 5 96 10 25 9 10 10 50 9 65 8 97 8 45 16 15 12 49 16 24 16 94 DUAL 33 9 84 5 13 9 39 8 26 10 29 9 95 8 34 6 79 20 41 8 63 16 48 17 17 C3 DUAL23 3 32 9 88 4 53 4 13 7 80 5 52 7 66 6 50 8 13 10 16 6 58 7 28 12 04 10 00 11 57 12 15 DUAL 33 7 92 5 56 7 59 6 44 8 16 9 47 6 58 5 86 16 38 5 72 11 02 11 86 CA DUAL 2 3 3 09 3 63 2 93 3 02 3 64 3 59 2 33 2 15 4 20 4 63 3 63 4 20 6 20 3 36 5 62 6 13 DUAL 33 3 16 3 13 1 77 1 80 3 71 4 10 2 71 3 07 6 70 3 29 5 68 6 20 C5 DUAL23 3 88 10 85 4 52 4 05 9 17 6 19 8 25 7 10 10 52 10 95 8 49 8 27 15 06 11 50 14 80 15 57 DUAL 33 9 22 5 94 7 96 6 82 9 81 10 41 6 77 5 93 19 51 8 13 14 60 15 4 C6 DUAL 2 3 6 85 12 36 7 38 6 96 10 31 9 06 12 69 11 55 13 39 15 33 12 72 12 54 15 62 12 58 14 42 14 85 DUAL 33 8 08 7 89 11 17 9 70 9 80 11 23 9 88 9 36 12 31 8 20 12 00 12 48 C7 DUAL 2 3 4 03 14 06 6 70 6 20 9 84 8 88 6 25 4 91 11 91 14 57 8 46 9 81 16 94 13 32 13 83 14 64 DUAL 33 10 01 9 05 6 11 4 83 11 65 1415 7 37 7 62 22 51 9 30 15 88 16 65 C8 DUAL 23 5 81 7 46 5 20 5 09 8 98 7 25 10 50 9 29 11 41 10 69 10 40 10 50 14 51 10 47 13 65 14 10 DUAL 33 8 33 6 73 9 59 8 43 9 89 9 77 9 36 8 58 15 69 6 63 11 53 12 01 C9 DUAL 23 0 29 0 29 0 29 0 29 0 22 0 22 0 26 0 22 0 22 0 22 0 27 0 22 0 22 0 22 0 34 0 37 DUAL 33 0 22 0 22 0 25 0 21 0 22 0 22 0 27 0 22 0 22 0 22 0 34 0 37 C10 DUAL23 3 42 3 15 3 04 3 11 4 94 4 74 4 6
26. Pin by pin F0 5 0 5 0 5 0 6 0 6 0 5 0 5 0 9 0 9 0 9 0 9 0 5 0 5 0 6 0 6 0 6 06 0 6 0 6 0 7 0 6 0 7 0 6 0 6 1 0 0 9 0 6 0 1 0 1 0 5 0 1 0 2 0 2 0 5 0 9 0 9 0 5 0 3 0 3 0 2 0 6 0 2 0 2 0 7 0 1 0 2 0 6 0 2 0 3 0 3 0 6 1 0 0 1 0 3 0 2 0 2 0 2 0 2 0 5 0 6 0 2 0 2 0 2 0 3 0 3 0 2 0 2 0 4 0 3 0 3 0 3 0 3 0 6 0 2 0 2 0 1 0 2 0 2 0 2 0 2 0 5 0 5 0 2 0 2 0 2 0 2 0 2 0 3 0 3 0 3 0 2 0 3 0 3 0 3 0 3 0 6 0 1 0 2 0 2 0 2 0 1 0 2 0 2 0 1 0 6 0 6 0 2 0 2 0 2 0 1 0 3 0 2 0 2 0 2 0 2 0 2 0 3 0 1 0 3 0 3 0 2 0 7 0 2 0 2 0 2 0 2 0 6 0 5 0 5 0 6 0 2 0 3 0 2 0 2 0 3 0 2 0 3 0 3 0 6 0 6 0 3 0 1 0 2 0 2 0 1 0 1 0 3 0 1 0 5 p0 6 0 1 0 3 0 1 0 2 0 2 0 3 0 2 0 3 0 2 0 2 0 2 0 2 0 2 0 4 0 2 07 0 1 0 1 0 1 0 1 0 1 0 2 0 1 0 1 0 5 0 5 0 1 0 1 0 2 0 2 0 2 0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 0 1 0 6 0 1 0 2 0 0 0 2 0 6 0 5 0 5 0 6 0 2 0 1 0 3 0 2 0 2 0 3 0 2 0 3 0 7 0 6 FO 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 5 0 5 0 1 0 1 0 2 0 2 0 2 0 1 0 3 0 2 0 3 0 2 0 2 0 2 0 3 0 2 0 2 0 6 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 4 0 5 0 0 0 2 0 1 0 1 0 2 0 2 0 1 0 3 0 2 0 3 0 2 0 2 0 2 0 3 0 2 0 6 0 1 0 2 0 1 0 1 0 3 0 3 0 4 0 5 0 2 0 2 0 2 0 2 0 2 0 2 0 3 0 2 0 6 0 6 lo 5 0 4 0 5 0 3 0 5 0 4 0 2 0 3 0 3 0 3 0 0 0 1 0 1 0 0 0 2 0 1 0 2 0 1 0
27. and Supercell Calculations Report IGE 157 Ecole Polytechnique de Montr al 1993 G Marleau A H bert and R Roy New Computational Methods Used in the Lattice Code DRA GON Top Mtg on Advances in Reactor Physics Charleston SC March 8 11 1992 A H bert G Marleau and R Roy Application of the Lattice Code DRAGON to CANDU Analy sis Trans Am Nucl Soc 72 335 1995 A H bert and R Roy A Programmer s Guide for the GAN Generalized Driver FORTRAN 77 version Report IGE 158 Ecole Polytechnique de Montr al Institut de G nie Nucl aire 1994 R Roy The CLE 2000 Tool Box Report IGE 163 Institut de g nie nucl aire cole Polytechnique de Montr al Montr al Qu bec 1999 A H bert D Sekki and R Chambon A User Guide for DONJON Version5 Report IGE 344 Ecole Polytechnique de Montr al 2014 G Marleau A H bert and R Roy A User Guide for DRAGON Version5 Report IGE 335 cole Polytechnique de Montr al 2014 A H bert G Marleau and R Roy A Description of the DRAGON and TRIVAC Version4 Data Structures Report IGE 295 Ecole Polytechnique de Montr al 2014 A H bert A User Guide for TRIVAC Version4 Report IGE 293 cole Polytechnique de Montr al 2014 A H bert and G Mathonni re Development of a Third Generation Superhomog n isation Method for the Homogenization of a Pressurized Water Reactor Assembly Nuc Sci Eng 115 pp 129 141
28. flux over the macro region and macro group 3 E wep 1 hes 1 Ve gt E Ene 1 Obes 7 Ve g reV keg TGV keg NT ires x die Res T V 7 ref Vi rev First to simplify the notation the upper script g for macro energy group will be shown only at the first occurrence of each quantity Then using these notations it can easily be seen that the reaction rates for the reference calculations Tref and the macro calculations Tm may be different since the reference average flux and the macro flux have been computed with different configuration and methods Tref Xiref Pires Vi f Xi ref 0i Vi Tmc 2 1 To simplify the notations no subscript is used for the flux when it refers to the macro calculations Pi Pime unless specified To overcome the mathematical problem of Eq 2 1 a transport diffusion equivalence theory is used One available method is the super homogenization methodology proposed previously by H bert in F4 To guaranty the reaction rates conservation macroscopic cross sections have to be modified They are multiplied by a factor A written as after and the new value is defined by X Aii ref The macro reaction rate is then given by Tre LiDE Abi ref DM ref 2 2 Using Eq 2 2 to have both reaction rates of Eq 2 1 equal has to be defined as follows rre 2 3 LM R ref 23 Since the diffusion flux distribution depends on the cross sections finding the set of A facto
29. homogeneous IGE 345 8 3 Algorithm This section presents the general algorithm The procedure to perform pin power reconstruction can be summarized in 3 steps as follows 1 Follow the general procedure to compute a MULTICOMPO data structure and add the following features Addition 1 after each flux calculation perform all homogenization types as needed by the NAP module depends on the chosen methodology for reaction rate calculation homogeneous heterogeneous pin by pin It is recommended to save all cross sections in different folder of the same MULTICOMPO data structure Addition 2 add the simplified unfolded geometry used for homogenization in the MULTICOMPO data structure through the EDI module with MGEO keyword See the user guide l for impor tant note on the coarse geometry requirement Compute additional properties in diffusion theory for an assembly in infinite domain Define a simple geometry in DONJON that is the same as the homogenized geometry in DRAGON homogeneous heterogeneous pin by pin For each burnup step in the MULTICOMPO data structure perform the following a Compute the flux in an infinite domaine with the homogeneous or heterogeneous homogenized cross sections b Project the flux on each pin NAP module and store the results with the pin by pin homo genized cross sections L_COMPO dir pin MIXTURES CALCULATIONS L MICRO MACROLIB GROUP At this point an en
30. which are included within the distribution In this section we want to concentrate on the specific changes that have been done to include the specificities required by pin power reconstruction and leads to the new set of input files rep900het mco x2m As previously said two main additions are done 1 Pin power reconstruction requires datas for several types of homogenization as the same time The first change is then to perform several homogenizations after the flux calculation and to store the results in the same MULTICOMPO in different records to facilitate the data handling in the core computations 2 Homogenized geometry must be recorded in the MULTICOMPO Note The included geometry in the multicompo has to be unfolded even if the transport calculations are done on a 1 8th assembly Moreover no split can be defined in the geometry one mesh ONLY per heterogeneous mixture is mandatory The detailed algorithm to compute a regular MULTICOMPO with the additions can then be summarized as follows 0 Define the MULTICOMPO structure parameter names and types Define geometry and tracking for level self shielding 1 2 tracking module SYBILT SYBILT NXT and MCCGT energy groups 281 281 26 Define homogenized geometries to store in the MULTICOMPO GEOTMP homogeneous heterogeneous 1 heterogeneous 2 heterogeneous 3 Pin by pin homog het1 het2 het3 pbp Define homogenization geometries used by the SPH module ASS
31. z2m in the MULTICOMPO enrichment process The main characteristics are then similar to the rep900het mco z2m Since the MULTICOMPO enrichment process can be done several times the 77 names have to be different As described in the NAP module See user guide U a user defined number is associated with each homogenization projection In this example the keyword IFX is set to 2 because the Heter2 is chosen to get the mixtures properties of the homogenized assembly We would recommand to use 0 for homogeneous 1 for Heterl 2 for Heter2 and 3 for Heter3 See Sec A 3 for pictures The input file have been created using the bash script allenrich run sh B 4 testNAPGEO x2m This DONJON 5 input file has mainly been used during the programation of the NAP module to test all the different features The reactor described in this set of input files is really small in order to be able to verify the capability in a decent number of data See Sec A 2 for picture of the geometry The main characteristics are the following 3 types of assemblies 3x3 pattern plus coolant all around top bottom side 4 planes along Z direction coolant fuel x 2 coolant several commented lines either to explain or offer an other option for the input file usually the automatic way is active and manual way is commented use of partially automatic generation for the geometries IGE 345 38 B 5 rep900cluster x2m This DONJON
32. 0 0100 0103 0102 0108 0108 0100 0108 0 01010102010301040105010601070108 8 82 Heterogeneous Pin by Pin Heterogeneous Pin by Pin 5 s e 8 62 fl ux 8 542 E e 5 8 4012 5 s 5 8 32 a a 3 262 30 35 40 as so 35 40 45 50 55 60 as 40 as ss eo 35 40 45 50 55 60 35 40 as 50 55 60 Heapr 8 marz 8 hi sl t2 rar 8 M s1 t2 C8 0 0090 0095 0 01 0 01050 011 0 0090 0095 0 01 0 01050 011 0 0090 0095 0 01 0 01050 011 0 0088 009 00950 010 0108 018 0115 Pin by Pin Heterogeneous Pin by Pin Heterogeneous flux 40 as 50 sS 60 C5 has uniform burnup C8 is completely heterogeneous Diffusion calculation performed with Selengut SELE EDF option FIGURE 3 Transport vs diffusion h1 sl t2 pin power distribution of all clusters IGE 345 13 this case confirm the first point regarding the mandatory to interpolate the flux at every step specially for low polynomial order The third and fourth columns provide results when the options for infinite domain diffusion flux are fixed at the lowest and highest precisions respectively 4x4 and low order or 8x8 and high order All results show that when the infinite domain and core calculations are not performed with consistent options the precision is reduced Then the results presented in Tab 1 show that diffusion calculations have to be performed with the same options for core 9 and infinite domain i p The value presented in Tab 1 were computed using a different normalization of the 9 an
33. 00 C9 12 U 12 U 12 U 2200 C10 0 U 36 U 12 U 1400 C11 20 M O U 40 U 2000 C12 12 M 12 M 12 M 2000 In order to develop an efficient and precise methodology for PPR several parameters were looked as options Three groups of tests were performed before converging to a recommended methodology 1 Flux projection 2 Consistency of methodology for the computation of 5 and i 3 Type geometry and methodology Selengut for homogenization and condensation 4 1 Flux projection Before presenting the results a very important note has to be made regarding the flux projection on the pins from the macro regions The purpose of the PPR is to be able to perform the calculations in a small additional time frame compared to classical diffusion calculations In order to do so the mesh used for the geometry per assembly remains relatively coarse 4x4 or 8x8 and does not fit a pin by pin description 17x17 However most of the time the core flux is computed with advanced method such as Raviart Thomas using finite elements with polynoms of order up to 3 to take into account the flux gradient within a single mesh When the resulting average flux on each mesh computed with these advanced methods is projected on each pin ip the approach is not precise enough for very heterogeneous assemblies or mixes of assemblies In these cases the flux gradient is very important as shown on LHS of Fig 1 configu
34. 00 0 11000 0 11500 0 12000 0 12500 0 13000 0 13500 0 14000 0 14500 0 15000 0 15500 0 16000 0 16500 0 17000 0 17500 0 18000 0 18500 0 19000 0 19500 0 20000 0 22000 0 24000 0 26000 0 28000 0 30000 0 32000 0 34000 0 36000 0 38000 0 40000 0 42000 0 44000 0 46000 0 48000 0 50000 0 52000 0 54000 0 56000 0 58000 0 60000 0 5 boron steps 0 0 600 0 1200 0 1800 0 2400 0 1 fuel temperature 800 0 1 coolant temperature 600 0 1 coolant density 0 659 Several choices of homogenization 1 Assembly homogeneous Saved in record EDI2A 2 PinByPin pin by pin mixtures 45 The water gap is included in the outer pin mixtures Saved in record EDI2B 3 Heterl heterogeneous with 3 mixtures corner side and inner parts The width of the outer mixtures is 1 pin plus the water gap Saved in record EDI2C 4 Heter Same as Heterl except that the width of the outer mixtures is 2 pins plus the water gap Saved in record EDI2D 5 Heter3 Same as Heterl except that the width of the outer mixtures is 3 pins plus the water gap Saved in record EDI2E 6 All all of the above are performed Several choices of homogenization methodology flux volume Selengut Selengut water gap and Selengut type EDE The input file have been created using the bash script allFuel run sh B 3 rep900EnrichCOMPO x2m This DONJON 5 set of input file is the following part of the DRAGON rep900het mco
35. 1 0 69 0 67 0 67 0 80 0 53 0 70 0 69 0 78 0 69 0 67 0 67 0 53 0 53 DUAL 33 0 67 0 68 0 80 0 53 0 67 0 67 0 77 0 67 0 67 0 67 0 52 0 53 GFE H I DT IGE 345 50 C 2 Figure results The distribution of the error for 4x4 homogenization with DUAL 3 3 tracking is presented for all SPH method for all configurations in Fig 13 to 16 IGE 345 C1 M0 UO0 U20 C2 M20 U10 U60 C3 M10 M30 U20 C7 M0 M0 U60 C8 M60 U10 M40 a so so 2 a as D 40 40 2 35 a as 30 id 20 e 20 as 40 as so 20 C10 U0 U36 U12 C11 M20 U0 U40 so so a D as a 40 40 35 as a 30 30 4 30 as m as so FIGURE 13 Transport vs diffusion pin power distribution of all clusters shpnew STD 5l IGE 345 C1 HU C2 M20 U10 U60 C3 M10 M30 U20 C4 M20 A LA and C5 M20 Mon uae C6 U0 M30 M30 C7 MO MO SU C8 M60 U10 S C9 U12 U12 U12 C10 U0 HUE eot C11 M20 bos ee C12 M12 M12 M12 FIGURE 14 Transport vs diffusion pin power distribution of all clusters shpnew SELE_FD marz 9 h2 si 3 o so as 0 5 ao a as as 30 2 30 as 40 as so 92 IGE 345 53 C1 M0 UO0 U20 C2 M20 U10 U60 C3 M10 M30 U20 C5 M20 U20 U20 C6 U0 M30 M30 so 2 E as 8 30 10 30 as 40 as 50 C8 M60 U10 M40 C9 U12 U12 U12 d ao a as as 30 30 as 40 as 50 C11 M20 U0 U40 C12 M12 M12 M12 12 h2 81 t 50 as 0 5 a na as 30 30 35 40 as so FIGURE 15 Transport vs diffusion pin power distribut
36. 2 0 2 0 3 0 1 0 2 0 3 0 2 0 6 1 0 0 9 1 0 0 9 0 8 0 6 0 5 0 1 FO 1 0 1 0 0 0 1 0 2 0 1 0 2 0 2 0 2 0 1 0 2 0 2 0 2 0 3 0 5 1 7 1 6 1 5 1 3 1 2 1 0 0 4 0 1 0 2 0 1 0 0 0 1 0 2 0 1 0 1 0 3 0 2 0 2 0 2 0 3 0 5 2 5 3 1 3 2 4 2 9 2 7 2 4 1 7 0 8 0 3 0 3 0 2 0 1 0 0 0 5 0 0 0 1 0 6 0 1 0 1 0 6 0 2 0 2 0 2 0 5 0 9 5 2 5 3 5 2 5 2 5 1 4 9 4 4 3 2 1 0 0 3 0 1 0 1 0 3 0 4 0 5 0 5 0 5 0 5 0 6 0 5 0 6 0 5 0 6 0 9 0 9 F3 8 3 7 3 7 3 7 3 8 3 9 y 4 2 2 0 8 0 4 01 0 3 0 3 0 4 0 5 0 5 0 5 0 5 0 5 0 6 0 5 0 5 0 9 0 9 0 5 0 1 0 3 0 0 3 0 7 P 3 2 1 7 1 0 0 5 0 3 0 3 0 1 0 0 0 6 0 1 0 1 0 6 0 1 0 2 0 2 0 5 0 9 1 1 0 8 1 0 0 9 4 4 2 4 1 2 0 6 0 2 0 1 0 0 0 1 0 3 0 2 0 2 0 2 0 2 0 5 3 1 5 1 8 1 4 1 4 4 9 2 7 1 3 0 4 0 1 0 1 0 1 0 2 0 2 0 1 0 2 0 2 0 2 0 2 0 5 2 2 1 9 1 9 1 7 1 8 1 4 5 1 2 9 1 5 0 8 0 5 0 1 0 0 0 1 0 0 0 1 0 1 0 2 0 1 0 2 0 2 0 1 0 6 1 9 1 9 1 7 1 4 5 2 2 4 0 9 0 3 0 0 0 1 0 1 0 2 0 2 0 2 0 5 0 6 1 9 2 1 2 0 1 9 1 9 1 8 5 2 3 1 1 6 1 0 0 5 0 2 0 0 0 0 0 2 0 1 0 2 0 2 0 2 0 1 0 3 0 1 0 5 2 1 2 0 2 1 1 9 1 9 1 5 5 3 3 1 1 7 0 9 0 4 0 1 0 1 0 1 0 1 0 1 0 1 0 2 0 2 0 2 0 1 0 1 0 5 2 1 9 2 2 1 3 5 2 2 5 1 0 0 5 0 0 0 1 0 1 0 3 0 1 0 2 0 6 0 5 FIGURE 5 Relative error between reconstruction and transport calculations for case 5 het2 split 4x4 DUAL 3 3 F0 G 0 6 0 5 0 6 0 6 0
37. 2 93 0 90 0 98 0 44 1 89 1 23 1 46 0 81 2 69 2 69 2 99 0 51 5 68 DUAL 33 0 87 0 98 0 43 1 85 1 18 1 44 0 80 2 62 2 69 2 99 0 51 5 68 C5 DUAL 23 1 71 2 81 0 73 4 52 1 51 5 59 1 72 7 10 1 74 4 46 1 06 6 19 1 66 12 58 2 57 14 24 DUAL 33 1 51 5 81 1 73 7 32 1 42 3 71 1 06 5 13 1 67 12 60 2 61 14 27 C6 DUAL 23 5 44 1 94 1 48 7 38 8 16 2 60 2 52 10 76 6 39 2 42 1 75 8 81 8 95 2 46 2 87 11 41 DUAL 33 8 07 2 60 2 52 10 67 6 21 1 83 1 71 8 05 8 93 2 43 2 88 11 36 CT DUAL 23 2 85 3 85 1 45 6 70 4 10 1 89 1 72 5 99 3 64 3 58 1 25 7 22 7 87 7 52 3 60 15 39 DUAL 33 4 11 1 91 1 72 6 02 3 60 3 32 1 16 6 92 7 93 7 53 3 62 15 46 C8 DUAL 2 3 2 38 2 82 1 44 5 20 4 24 4 22 2 96 8 46 2 86 4 10 1 92 6 96 4 97 6 29 3 79 11 25 DUAL 33 4 21 4 31 2 98 8 52 2 83 3 56 1 92 6 39 5 04 6 26 3 84 11 30 C9 DUAL 23 0 15 0 14 0 05 0 29 0 12 0 15 0 04 0 27 0 13 0 14 0 05 0 27 0 15 0 18 0 07 0 34 DUAL 33 0 12 0 14 0 04 0 26 0 13 0 14 0 05 0 27 0 15 0 18 0 07 0 34 C10 DUAL 23 1 75 1 28 0 81 3 04 2 16 1 32 0 85 3 48 1 43 1 09 0 54 2 52 1 42 1 30 0 40 2 72 DUAL 33 2 02 1 35 0 85 3 37 1 23 1 09 0 53 2 32 1 40 1 28 0 41 2 68 Cll DUAL 2 3 1 88 2 68 1 46 4 56 2 78 6 93 2 35 9 72 1 96 5 91 1 40 7 87 2 44 11 84 2 68 14 27 DUAL 33 2 57 6 86 2 36 9 43 1 67 4 47 1 41 6 15 2 44 11 85 2 73 14 28 C12 DUAL23 0 35 0 36 0 13 0 71 0 37 0 43 0 15
38. 20 1 77 9 47 2 76 4 57 1 76 7 33 4 79 6 03 2 19 10 82 6 93 7 26 2 09 14 19 DUAL 3 3 2 50 4 10 1 73 6 60 3 96 5 73 1 91 9 69 2 29 5 51 1 70 7 80 C12 DUAL23 0 34 0 35 0 13 0 69 0 34 0 33 0 12 0 67 0 37 0 34 0 13 0 71 0 34 0 33 0 12 0 67 DUAL 33 0 34 0 33 0 12 0 68 0 33 0 33 0 12 0 67 0 34 0 33 0 12 0 67 STE MOI 91 IGE 345 17 In addition to the four types of diffusion calculations 4x4 8x8 4x4 and 8x8 the flux has also been computed in diffusion for a pin by pin geometry For an easier comparison of the error distribution between the different option that may be chosen in the diffusion calculations three maps of numerical values are presented on Fig 4 to 6 They represent the difference between the transport and diffusion pin power calculations for pin by pin heterogeneous 4x4 het2 and homogeneous 4x4 homogenized assemblies respectively for configuration 5 The cross section normalized with the classical Selengut method SELE_FD were used to performed the diffusion calculations with the Raviart Thomas solver DUAL 3 3 in TRIVAT module As previously mentioned the best results are obtained with the hete rogeneous geometry Results are even generally better than with the pin by pin geometry These results are similar to those obtained by Fliscounakis et al U FIGURE 4 Relative error between reconstruction and transport calculations for case 5
39. 3 4 40 5 48 1 63 9 88 3 01 2 51 1 27 5 52 4 94 5 22 1 97 10 16 4 89 5 11 1 75 10 00 Cs DUAL 33 3 04 2 52 1 21 5 56 5 13 4 34 1 65 9 47 3 03 2 70 1 11 5 72 CA DUAL 23 1 88 1 75 1 08 3 63 1 58 2 01 1 01 3 59 2 17 2 46 1 16 4 63 1 52 1 84 1 09 3 36 DUAL 33 1 50 1 62 0 99 3 13 2 11 1 99 1 11 4 10 1 43 1 86 1 09 3 29 C5 DUAL23 5 59 5 26 1 25 10 85 2 45 3 75 0 94 6 19 4 89 6 06 1 47 10 95 6 12 5 39 1 31 11 50 DUAL 33 2 24 3 70 0 90 5 94 4 25 6 16 1 26 10 41 2 53 5 60 0 89 8 13 C6 DUAL 23 7 37 4 99 1 73 12 36 6 42 2 64 1 80 9 06 9 04 6 29 2 33 15 33 8 86 3 71 2 09 12 58 DUAL 33 6 12 1 77 1 72 7 89 8 57 2 66 1 87 11 23 6 09 2 11 1 58 8 20 C7 DUAL 23 5 76 8 31 2 41 14 06 4 13 4 75 1 69 8 88 6 37 8 20 2 49 14 57 5 90 7 42 2 15 13 32 DUAL 33 4 39 4 66 1 61 9 05 6 80 7 35 2 29 14 15 4 17 5 13 1 62 9 30 C DUAL 23 4 25 3 21 1 90 1 46 3 09 4 16 1 77 7 25 5 02 5 67 2 60 10 69 5 62 4 84 2 37 10 47 A DUAL 3 3 3 05 3 68 1 69 6 73 4 63 5 13 2 07 9 77 2 99 3 64 1 68 6 63 C9 DUAL 23 0 14 0 15 0 05 0 29 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 0 10 0 12 0 04 0 22 DUAL 33 0 10 0 11 0 04 0 22 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 C10 DUAL23 1 84 1 31 0 88 3 15 2 95 1 80 0 97 4 74 3 45 2 26 1 03 5 71 2 41 1 84 0 93 4 25 DUAL 33 2 12 1 49 0 95 3 61 2 24 1 61 0 94 3 85 1 98 1 54 0 91 3 51 Cll DUAL 2 3 5 26 4
40. 4 0 5 0 5 0 5 0 5 0 5 0 9 0 9 2 4 2 5 2 5 23 20 I8 1 1 23 5 6 0 9 0 7 0 1 0 3 0 5 0 4 0 4 0 4 0 0 5 0 5 0 5 0 5 0 5 0 5 0 9 0 9 0 8 1 0 0 8 1 0 1 4 1 0 0 1 1 3 2 3 0 0 0 1 0 7 0 1 0 1 0 3 0 1 0 0 5 0 0 0 1 0 5 0 1 0 2 0 2 0 5 0 9 0 4 0 1 1 1 1 1 0 4 0 1 l l 1 8 0 9 0 9 0 2 0 1 0 1 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 5 5 1 7 1 9 2 4 1 1 1 0 3 1 1 3 0 9 0 0 0 1 0 1 0 1 0 2 0 1 0 1 0 1 0 2 0 2 0 2 0 5 2 6 2 2 2 2 2 0 2 8 2 4 1 1 1 4 3 6 1 5 13 0 4 0A 0 0 0 1 0 0 0 0 0 1 0 1 0 2 0 1 0 2 0 2 0 1 0 6 1 7 1 6 2 0 1 6 1 0 3 6 1 0 0 5 0 0 0 1 0 0 0 1 0 1 0 2 0 2 0 5 0 6 1 6 1 8 1 7 1 6 2 2 1 9 0 1 0 8 3 7 1 7 1 3 0 6 0 1 0 2 0 0 0 0 0 1 0 1 0 1 0 1 0 2 0 1 0 2 0 1 0 5 1 8 1 7 8 1 7 2 2 1 7 0 4 1 0 3 8 1 9 1 5 0 6 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 2 0 2 0 1 0 1 0 5 1 8 L 2 6 1 5 0 8 3 7 1 1 0 6 0 2 0 1 0 0 0 1 0 2 0 0 0 1 0 6 0 5 4 3 3 Homogenization SPH option The last option to compare is the choice of SPH method The results for flux volume STD classical Selengut SELE FD and Selengut macro calculation water gap SELE MWG are presented in Tab 4 This table shows that the flux volume homogenization leads to fairly large errors The smallest range of errors are generally obtained with the classical Selengut option Regarding the error distribution the results for the root mean square obtained with the Selengut macro calculation water gap are compa
41. 4 76 3 01 17 04 C2 DUAL23 1 85 2 14 1 32 4 00 3 04 1 21 2 07 10 25 2 76 6 21 1 67 8 97 2 89 13 35 3 05 16 24 DUAL 33 2 46 6 93 2 09 9 39 2 21 6 13 1 47 8 34 2 91 13 56 2 97 16 48 C3 DUAL23 238 216 0 97 4 53 4 18 3 48 2 51 7 66 2 92 3 66 1 83 6 58 5 79 5 78 3 80 11 57 DUAL 3 3 4 17 3 42 2 54 7 59 3 08 3 51 1 57 6 58 5 26 5 76 3 67 11 02 CA DUAL 2 3 1 22 1 71 1 00 2 93 0 97 1 36 0 52 2 33 1 44 2 19 0 90 3 63 2 69 2 93 0 53 5 62 DUAL 33 0 81 0 95 0 45 1 77 1 27 144 0 83 2 71 2 69 3 00 0 51 5 68 C5 DUAL 23 1 71 2 81 0 73 4 52 1 51 6 75 1 74 8 25 2 91 5 59 1 32 8 49 2 43 12 38 2 77 14 80 DUAL 33 1 51 6 45 1 77 7 96 1 36 5 41 1 16 6 77 1 69 12 91 2 71 14 60 C6 DUAL 23 5 44 1 94 1 48 7 38 9 36 3 33 2 60 12 69 7 96 4 76 2 31 12 72 9 56 4 86 3 18 14 42 DUAL 33 8 57 2 60 2 58 11 17 6 99 2 90 1 87 9 88 9 03 3 01 2 93 12 04 C7 DUAL 23 2 85 3 85 1 45 6 70 4 15 2 10 1 75 6 25 3 55 4 91 1 47 8 46 7 92 5 91 3 82 13 83 DUAL 33 4 14 1 97 1 75 6 11 4 03 3 34 1 25 7 37 8 16 7 71 3 70 15 88 C8 DUAL 2 3 2 38 2 82 1 44 5 20 4 87 5 63 3 05 10 50 4 22 6 18 2 60 10 40 5 93 7 72 4 19 13 65 DUAL 33 4 58 5 02 3 07 9 59 3 78 5 58 2 15 9 36 5 13 6 40 3 99 11 53 C9 DUAL23 0 15 0 14 0 05 0 29 0 12 0 15 0 04 0 26 0 13 0 14 0 05 0 27 0 15 0 18 0 07 0 34 DUAL 33 0 11 0 14 0 04 0 25 0 13 0 14 0 05 0 27 0 15 0 18 0 07 0 34 C10 DUA
42. 5 4 26 5 82 5 71 4 99 5 46 4 23 4 25 3 81 3 96 DUAL 33 3 88 3 61 3 63 3 22 4 11 3 85 2 65 3 80 3 75 3 51 2 59 2 75 Cl DUAL 2 3 5 26 9 47 4 56 4 56 10 26 7 33 11 68 10 09 11 10 10 82 10 48 10 33 17 44 14 19 16 76 17 57 DUAL 33 10 32 6 60 10 42 8 84 9 92 9 69 8 84 7 79 19 24 7 80 14 69 15 48 C12 DUAL 23 0 69 0 69 0 71 0 69 0 67 0 67 0 80 0 53 0 71 0 71 0 84 0 71 0 67 0 67 0 52 0 53 DUAL 33 0 68 0 68 0 79 0 54 0 67 0 67 0 77 0 67 0 67 0 67 0 52 0 53 STE WOI 87 TABLE 14 Range of relative error 6 between reconstruction and transport calculations for all options fine mesh Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 8x8 8x8 8x8 e E Z E E E B R 7 E a z a A gt E E A a E A E E 1 td E E td E E rd E ea rd tn A d YN A a YN El E Nn d E a a BH E o BH E S B B S B B n sa n n in n A n Cl DUAL 2 3 5 30 11 14 4 47 3 89 10 59 5 91 9 19 7 76 11 08 10 95 7 97 T AT 22 02 9 53 16 54 17 67 DUAL 33 10 81 5 51 8 89 7 43 11 25 10 66 6 16 5 84 22 11 9 51 16 60 17 72 C2 DUAL23 4 93 10 37 4 00 3 96 9 25 5 59 8 55 7 50 9 83 9 88 6 85 6 28 19 93 8 56 16 00 16 69 DUAL 33 9 44 5 23 8 61 7 47 9 96 9 62 5 88 5 24 20 02 8 54 16 06 16 75 C3 DUAL23 3 32 9 88 4 53 4 13 7 41 5 92 7 11 5 93 7 84 9 51 5 18 5 17 15 74 6 13 10 83 11 67 DUAL 33 7 58 5 56 7 10 5 94 7 96 9 10 4 73
43. 54 9 92 4 93 3 29 14 85 DUAL 3 3 7 54 2 16 2 28 9 70 6 57 2 79 1 68 9 36 9 40 3 08 3 06 12 48 C7 DUAL 2 3 2 58 3 62 1 41 6 20 3 26 1 65 1 30 4 91 3 21 6 60 1 77 9 81 8 45 6 18 4 18 14 64 DUAL33 3 25 1 59 1 27 4 83 3 69 3 93 1 42 7 62 8 63 8 02 4 09 16 65 C8 DUAL 23 2 25 2 84 1 43 5 09 4 26 5 03 2 60 9 29 4 52 5 98 2 35 10 50 6 12 7 98 4 39 14 10 DUAL33 3 98 4 46 2 61 8 43 3 26 5 32 1 76 8 58 5 37 6 64 4 20 12 01 C9 DUAL 23 0 14 0 15 0 05 0 29 0 11 0 11 0 04 0 22 0 10 0 12 0 04 0 22 0 17 0 20 0 08 0 37 DUAL 33 0 11 0 10 0 04 0 21 0 10 0 11 0 04 0 22 0 17 0 20 0 08 0 37 C10 DUAL 23 1 79 1 32 0 83 3 11 2 67 1 59 0 81 4 26 3 27 2 18 1 01 5 46 1 94 2 02 0 52 3 96 DUAL 33 1 90 1 32 0 79 3 22 2 19 1 61 0 91 3 80 1 40 1 35 0 40 2 75 Cll DUAL 2 3 1 91 2 65 1 47 4 56 2 95 7 14 2 03 10 09 4 09 6 24 1 99 10 33 3 20 14 37 3 22 17 57 DUAL 33 2 30 6 54 2 04 8 84 2 17 5 61 1 69 7 79 2 65 12 83 3 06 15 48 C12 DUAL 23 0 34 0 35 0 13 0 69 0 22 0 31 0 10 0 53 0 37 0 34 0 13 0 71 0 22 0 31 0 10 0 53 DUAL 33 0 23 0 31 0 10 0 54 0 33 0 33 0 12 0 67 0 22 0 31 0 10 0 53 SPE ADI 97 TABLE 12 Relative error between reconstruction and transport calculations fine mesh SELE_EDF option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 8x8 8x8 8x8
44. 90 2 33 7 18 1 81 9 51 4 13 14 62 2 01 18 75 C12 DUAL23 0 34 0 35 0 13 0 69 0 34 0 33 0 12 0 67 0 36 0 33 0 13 0 70 0 34 0 33 0 12 0 67 DUAL 3 3 0 34 0 33 0 12 0 67 0 34 0 33 0 12 0 67 0 34 0 33 0 12 0 67 STE HOI IV TABLE 7 Relative error between reconstruction and transport calculations coarse mesh SELE_FD option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 min max rms 0 min max rms min max rms 0 min max rms Cl DUAL 23 6 15 4 99 1 51 11 14 2 46 3 93 1 35 6 39 5 48 5 70 1 92 11 17 7 70 7 15 1 83 14 85 DUAL 3 3 2 55 3 49 1 31 6 04 4 88 5 97 1 63 10 85 2 97 6 62 1 33 9 60 C2 DUAL23 5 76 4 61 1 67 10 37 2 54 3 42 1 53 5 96 4 52 5 13 1 94 9 65 6 46 6 03 1 81 12 49 DUAL 3 3 2 42 3 31 1 50 5 73 4 46 5 50 1 75 9 95 2 70 5 93 1 50 8 63 C3 DUAL 23 4 40 5 48 1 63 9 88 3 01 2 51 1 27 5 52 4 94 5 22 1 97 10 16 4 89 5 11 1 75 10 00 DUAL 33 3 04 2 52 1 21 5 56 5 13 4 34 1 65 9 47 3 03 2 70 1 11 5 72 CA DUAL 23 1 88 1 75 1 08 3 63 1 58 2 01 1 01 3 59 2 17 2 46 1 16 4 63 1 52 1 84 1 09 3 36 DUAL 33 1 50 1 62 0 99 3 13 2 11 1 99 1 11 4 10 1 43 1 86 1 09 3 29 C5 DUAL 23 5 59 5 26 1 25 10 85 2 45 3 75 0 94 6 19 4 89 6 06 1 47 10 95 6 12 5 39 1 31 11 50 DUAL 33
45. L has been developed to interpolate the flux in diffusion calculations for Cartesian geometries The description of the module is presented in 5 The data structure created by the VAL module has F VIEW as signature It is described in ll An example of the post processing of the results is presented in the my_version5_path Octave data iaea3d m procedure 5 4 Octave Octave is a free software equivalent to the commercial software MATLAB Except for few restrictions the same input files can be used in both softwares A set of procedures named ASCII Ganlibv4 has been developed to facilitate analysis from DRA GON and DONJON results They provide tools to access rapidly and efficiently the content of data structures saved in ASCII format For more details please refers to the readme file in the folder my _version5_path Octave IGE 345 22 6 Conclusions and recommandations In this report we have presented how the generalized pin power reconstruction has been successfully implemented in DRAGON DONJON v5 new module called NAP has been programmed to perform the following tasks Enrich MULTICOMPO to store pin wise projected flux of diffusion calculation of homogenized assem bly in an infinite domain The process can be repeated several times on the same data structure for different homogenization diffusion calculation options Automatic generation of a two level geometry core with heterogeneous assemblies
46. L 23 1 75 1 28 0 81 3 04 2 93 1 72 0 90 4 65 2 72 2 27 0 78 4 99 1 92 1 89 0 53 3 81 DUAL 33 2 17 1 45 0 87 3 63 1 56 1 09 0 59 2 65 1 37 1 22 0 42 2 59 Cll DUAL 2 3 1 88 2 68 1 46 4 56 3 32 8 37 2 42 11 68 3 19 7 29 1 90 10 48 3 04 13 72 3 04 16 76 DUAL 33 2 68 7 74 2 44 10 42 2 05 6 79 1 57 8 84 2 50 12 18 2 86 14 69 C12 DUAL23 0 35 0 36 0 13 0 71 0 37 0 43 0 15 0 80 0 49 0 35 0 15 0 84 0 22 0 31 0 10 0 52 DUAL33 0 37 0 42 0 15 0 79 0 42 0 34 0 15 0 77 0 22 0 31 0 10 0 52 SPE ADI vr TABLE 10 Relative error between reconstruction and transport calculations 96 fine mesh SELE MWG option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 8x8 8x8 8x8 min max rms 0 min max rms min max rms min max rms 0 Cl DUAL 2 3 1 99 2 48 1 05 4 47 2 42 6 77 2 16 9 19 2 42 5 55 1 23 7 97 2 15 14 39 2 81 16 54 DUAL33 2 26 6 62 2 17 8 89 2 08 4 08 1 22 6 16 2 20 14 40 2 87 16 60 C2 DUAL23 1 85 2 14 1 32 4 00 2 51 6 04 2 02 8 55 1 78 5 06 1 34 6 85 2 77 13 23 2 82 16 00 DUAL 33 2 42 6 19 2 03 8 61 1 74 4 14 1 35 5 88 2 81 13 25 2 86 16 06 C3 DUAL23 2 38 2 16 0 97 4 53 4 14 2 97 2 47 7 11 2 71 2 47 1 45 5 18 5 21 5 62 3 55 10 83 DUAL 33 4 15 2 95 2 48 7 10 2 67 2 06 1 43 4 73 5 22 5 64 3 58 10 87 CA DUAL 23 1 22 1 71 1 00
47. MB_HOM IGE 345 24 homogeneous heterogeneous 1 heterogeneous 2 heterogeneous 3 Pin by pin homog het 1 het2 het3 pbp 1 Reference depletion a Set all parameters at reference value b Loop on all burnup steps Compute cross sections Perform self shielding if required Perform flux calculations at level 1 Perform flux calculations at level 2 Perform homogenization and include homogenized geometry GEOTMP EDIOBJ EDI FLUX2 LIBEQ TRACKN2 GEON2 GEOTMP MERG REGI MGEO GEOTMP Perform SPH factor calculations using homogenization geometry ASSMB_HOM Save data in MULTICOMPO isotopic concentration at each burnup step BURNUP structure 2 Perturbation calculations For each parameter loop on each perturbed value except reference value loop on each burnup step Get isotopic concentration from BURNUP structure Compute flux distribution Perform homogenization with ASSMB_HOM and include homogenized geometry GEOTMP Save data in MULTICOMPO A 2 Step 2 This step is closely related to the previous one Knowing the structure of a regular MULTICOMPO is required to enrich it Indeed for each calculation parameter value have to be recover It is recommended to start from the input files used to create the original MULTICOMPO to write the input files used to enrich the MULTICOMPO This way the same loops for all parameter values will be used and none will
48. S S E 2 24 3 70 0 90 5 94 4 25 6 16 1 26 10 41 2 53 5 60 0 89 8 13 C6 DUAL 23 7 37 4 99 1 73 12 36 6 42 2 64 1 80 9 06 9 04 6 29 2 33 15 33 8 86 3 71 2 09 12 58 DUAL 33 6 12 1 77 1 72 7 89 8 57 2 66 1 87 11 23 6 09 2 11 1 58 8 20 C7 DUAL 23 5 76 8 31 2 41 14 06 4 13 4 75 1 69 8 88 6 37 8 20 2 49 14 57 5 90 7 42 2 15 13 32 DUAL 33 4 39 4 66 1 61 9 05 6 80 7 35 2 29 14 15 4 17 5 13 1 62 9 30 C8 DUAL 23 4 25 3 21 1 90 7 46 3 09 4 16 1 77 7 25 5 02 5 67 2 60 10 69 5 62 4 84 2 37 10 47 DUAL 3 3 3 05 3 68 1 69 6 73 4 63 5 13 2 07 9 77 2 99 3 64 1 68 6 63 C9 DUAL 23 0 14 0 15 0 05 0 29 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 0 10 0 12 0 04 0 22 DUAL 33 0 10 0 11 0 04 0 22 0 10 0 11 0 04 0 22 0 10 0 12 0 04 0 22 C10 DUAL 23 1 84 1 31 0 88 3 15 2 95 1 80 0 97 4 74 3 45 2 26 1 03 5 71 2 41 1 84 0 93 4 25 DUAL 33 2 12 1 49 0 95 3 61 2 24 1 61 0 94 3 85 1 98 1 54 0 91 3 51 Cll DUAL 2 3 5 26 4 20 1 77 9 47 2 76 4 57 1 76 7 33 4 79 6 03 2 19 10 82 6 93 7 26 2 09 14 19 DUAL 3 3 2 50 4 10 1 73 6 60 3 96 5 73 1 91 9 69 2 29 5 51 1 70 7 80 C12 DUAL23 0 34 0 35 0 13 0 69 0 34 0 33 0 12 0 67 0 37 0 34 0 13 0 71 0 34 0 33 0 12 0 67 DUAL 33 0 34 0 33 0 12 0 68 0 33 0 33 0 12 0 67 0 34 0 33 0 12 0 67 SPE ADI GV TABLE 8 Relative error between reconstruction and transport calculations 96 fine mesh
49. SELE FD option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 8x8 8x8 8x8 min max rms 0 min max rms 0 min max rms min max rms Cl DUAL 23 6 15 4 99 1 51 11 14 2 95 2 96 1 28 5 91 5 22 5 73 1 56 10 95 3 25 6 28 1 25 9 53 DUAL 33 2 63 2 87 1 28 5 01 4 97 5 68 1 53 10 66 3 22 6 29 1 26 9 51 C2 DUAL23 5 76 4 61 1 67 10 37 2 77 2 82 1 47 5 59 4 70 5 18 1 68 9 88 2 94 5 62 1 45 8 56 DUAL 33 2 51 2 72 1 47 5 23 4 52 5 09 1 66 9 62 2 90 5 64 1 46 8 54 C3 DUAL 23 4 40 5 48 1 63 9 88 3 24 2 68 1 22 5 92 4 81 4 69 1 64 9 51 3 22 2 91 1 12 6 13 DUAL 33 2 93 2 63 1 20 5 56 4 77 4 33 1 57 9 10 3 20 2 86 1 11 6 06 CA DUAL 23 1 88 1 75 1 08 3 63 1 36 1 64 0 98 3 00 2 05 2 03 1 09 4 08 1 43 1 80 1 08 3 23 DUAL 33 1 34 1 63 0 97 2 97 2 00 1 97 1 09 3 98 1 44 1 84 1 08 3 27 C5 DUAL 23 5 59 5 26 1 25 10 85 2 53 3 56 0 91 6 09 4 57 5 75 1 25 10 33 2 73 5 28 0 88 8 01 DUAL 3 3 2 40 3 47 0 90 5 86 4 33 5 71 1 21 10 05 2 72 5 30 0 88 8 02 C6 DUAL23 7 37 4 99 1 73 12 36 6 48 2 00 1 69 8 48 8 01 3 16 1 80 11 17 6 41 1 51 1 57 7 91 DUAL 33 5 89 1 93 1 68 7 83 7 86 2 75 1 74 10 60 6 33 1 48 1 57 7 81 C7 DUAL 23 5 76 8 31 2 41 14 06 4 35 4 89 1 68 9 24 6 47 7 55 2 38 14 01 4 31 5 39 1 75 9 70 DUAL 33 4 02 4 74 1 65 8 77 6 42 7
50. TECHNICAL REPORT IGE 345 Specifications and User Guide for NAP module in DRAGON DONJON VERSION5 Pin Power Reconstruction module R CHAMBON Institut de g nie nucl aire D partement de g nie m canique cole Polytechnique de Montr al 23 octobre 2014 IGE 345 ii Contents COMME unu Logo ek RR nor xd cR ROS EERE RAE a eee ee qox EE Ita ii 1 COMED sak cone eee ee OR OE ER RO OS POR AS ORO Pe uw woo Roo Xe o8 eie des 1 2 Theonueal background lt a g soad sin k Ry ee Ga ue 9 CR mi 2 2 1 Homogenization and condensation ee 2 IAE Equivalence coefficients 3 271 Flux Volume normalisation STD 3 22 2 Selengut normalization SELE FD and SELE EDF 4 2 29 Selengut macro calculation water gap normalization SELE MWG 5 2 3 Pin Power Reconstruction o e eg n pa am R R de E hem tae E e 5 2 3 1 lolo PPM UE Das ARR REPLI UE 5 2 9 2 Computation e s a e soii aoi 5 6404 4 e Rog ER d EO die Re s 6 JS MENU ug gere co dada soe CR x Rer tale RUE Rm EG RR e DE EA Adis 8 4 Validation 2 64444 Rok Rowe edem doo dy So Re RR e Uy RIP RR eo da 9 4 1 Elux L a hee Pe ce POR RR pd Yom P P possumus 9 4 1 1 Flux projection validation cc omo Row Rm x 9 4 1 2 Flux projection results for clusters ccccccccccts 10 4 2 Consistency of geometry and tracking 10 4 3 Homogenization geometry and SPH method
51. ase 8 the more the interpolation is relevant Indeed the range of error decreases from 18 to 9 for case 5 and from 23 to 10 for case 8 4 2 Consistency of geometry and tracking An attempt to simplify the general procedure has been made by studying the requirement for consis tency of methodology for the computation of 9 Tab 1 present the results performed with an hetl type homogenization for cases 7 and 8 The first column represents the reference case where both dif fusion flux are computed with the same options in terms of geometry mesh and Raviar Thomas method polynomial order T he reference results are present in an italic font The second column presents the results with the same options but no interpolation during the computation of 6 is used The results in IGE 345 11 DUAL 13 DUAL 2 3 iaea2d DUAL 1 3 iaea2d DUAL 2 3 0 001 0 0008 0 0006 0 0004 0 0002 e eee ee e 0 0002 0 DUAL 3 3 DUAL 4 2 iaea2d DUAL 3 3 iaea2d DUAL 4 2 0 001 0 001 0 0008 0 0008 0 0006 0 0006 0 0004 0 0004 0 0002 0 0002 0 0 0 0002 0 0002 gt FIGURE 2 Interpolated thermal flux distribution for IAEA2D benchmark various order of Raviart Thomas IGE 345 12 Transport SEL Diff 96 SEL interp Diff Henapr 5 marz 5 hi st t2 srar S hi sl 02 5 as a C5 5 B 2 30 as 40 as so 30 as o 4 o Finapr 5 Prat 0 0100 0103 0108 0108 0105 0109 0108 0 0100 0103 0100 0108 0105 0109 0108
52. d then differs slightly from those in appendix However the conclusions remain the same TABLE 1 Relative error between reconstruction and transport calculations comparison of different options to compute the PPR factor Pin Type het 1 het 1 het 1 het 1 Pip interp yes not yes yes ifx same as Di p same as Qi p fixed at 112 fixed at 123 min max std min max std min max std min max std Heterogeneous 4x4 SPH type SELE_EDF C7 DUAL 23 4 09 6 73 2 04 7 99 7 40 2 77 4 09 6 73 2 04 5 86 7 70 2 35 DUAL 33 4 61 5 12 1 70 4 22 5 85 2 22 5 40 5 31 2 03 4 29 5 17 1 84 C8 DUAL 23 4 38 5 82 2 43 6 70 6 51 2 81 4 38 5 82 2 43 5 40 6 63 2 77 DUAL 33 3 30 5 46 1 87 4 32 5 38 1 93 4 36 6 54 2 02 3 54 5 91 1 95 Heterogeneous 8x8 SPH type SELE EDF CT DUAL23 4 05 5 25 1 87 8 53 7 05 2 85 5 95 5 45 2 14 4 85 5 50 1 98 DUAL 33 3 95 5 08 1 69 4 07 6 81 2 22 5 22 5 21 1 95 3 95 5 08 1 69 C8 DUAL23 3 10 3 93 1 66 7 06 5 93 2 27 4 47 4 03 1 80 3 72 4 50 1 76 DUAL 33 3 11 3 23 1 63 3 38 5 94 1 69 4 28 3 71 1 72 3 11 3 23 1 63 value of ifx XYZ X type of homogeneization Y split level 1 for 4x4 2 for 8x8 Z DUAL value STE WOI VI IGE 345 15 4 3 Homogenization geometry and SPH method The last point to analyze concerns the options of homogenization used to computed the cross sections Two
53. e Q Q Q O Q Q Q Q Q Q Q Q N e Q MO OKO O Q HG MOMO gs T Q e e Q ADAZES N QOC AA S FIGURE 9 Transport geometry of the cluster The pin flux homogenized with surrounding water computed by transport calculations is presented on top of Fig 10 The corresponding flux computed by diffusion calculation is also presented on the four remaining graphs Each graph corresponds to a different configuration homogeneous or heterogeneous mixtures split with 4 or 8 meshes along each direction The left part of the graphs shows the flux distribu tion on the original core geometry and the right part is the projected flux on each pin homogenized with surrounding water Only the top right part of the cluster is presented since the geometry is symmetrical Note that a very important concerning the flux projection on each pin from macro regions is presented in Section 4 The reconstructed pin power is presented on Fig 11 These pin power distributions correspond to the flux distributions presented on Fig 10 The difference with reference transport computations are presented on Fig 12 Results from Fig 10 to 12 show that the GPPR has been correctly implemented Flux are properly projected and pin power relatively agree between transport and diffusion calculations The different homogenizations and splits lead to more or less precise results according to the choices IGE 345 Finapr 5 8 92 Benz 8 72 2 612 2 512 Benz
54. e been added to perform their task for all the new fuel mixtures automatically The detailed modifications and user guide are presented in Ul A 3 Verifications The input files rep900het mco x2m rep900EnrichCOM PO rz2m and rep900cluster x2m have been used to verify the new GPPR capabilities Results obtained with rep900cluster x2m i e for the re constructed pin power are compared to a reference transport calculation programmed in the data set rep900cluster_mco x2m Both transport and diffusion input sets represent a 3x3 cluster with 17x17 pins assemblies Several clusters have been simulated all results and important details are presented in Sec tion 4 In this section only one configuration is used to illustrate the implementation Case 5 This case corresponds to a cluster 3x3 with the following components a MOX assembly at burnup 20 GWd t in the center 4 UOX assemblies at burnup 20 GW d t on the sides 4 UOX assemblies at burnup 20 GWd t on the corners IGE 345 30 A 1 Verification part 1 The first part to verify is the enrich MULTICOMPO step Results were directly looked at in enrich MULTICOMPO and two major points were found new properties are added with the proper names at the right place The following code has been repeated 4 times with lt lt fx gt gt equal 0 to 3 Cpo NAP Cpo Track Flux EDIT 0 PROJECTION DIRPIN lt lt DirPin gt gt IFX lt lt ifx gt gt SET b
55. eol Geol a NAP Heterogeneous assembly Pin by pin assembly option optional split no split DIRGEO 4 GeoH GeoP b USLPIT y y MatexH MatexP c TRIVAT 1 Track Here follows an example of a call to the NAP module GeoH NAP Geol CpoU EDIT 0 DIRGEO lt lt DirHet gt gt MIXASS 3 1 2 3 SPLITX ASS 1 2 1 SPLITY ASS 1 2 1 Notes MULTICOMPO is required to get the homogenization geometry More split at the assembly level along X and Y directions can be defined here 2 Define fuel object with RESINI and embedded NAP modules RESINI y FmapH FmapP IGE 345 26 3 Compute cross sections fuel NCR d y MacroFH MacroFP coolant NCR Macro core MACINI y Macro2H 4 Compute flux distribution TRIVAA ji FLUD Flux 5 Perform Pin Power Reconstruction FmapH FmapP Track MacroFP Flux MatexH NAP y FmapH To perform the pin power reconstruction several cross section flux are requiered for each pin for they current burnup boron concentration and other parameter values The choice has been made to compute these values by the module designed for that NCR which means it is done externaly of the NAP module in order to not duplicate fortran code for better code maintenance This approach implies that the fuel position has to be specified pin by pin at some point hence why there are two geometries and two map structures de
56. ep900cluster mco x2m 2 2 moo ko v ia wo Roe Rom e hom Roy ben AA a 38 Go REIS Sou Lek ee Ar Row ombre ou RON XOU UE agis RE decus A desk Riad 39 Cul ables 2 7 PME Se be Ae ee Bee LE Ge ee E RE SS 39 C2 Pigure results sd eae GS Ee e b dh m Ba 50 References ck ROLE oRor mo ho ek o X3 353 dE A we ee e a nat de 55 IGE 345 1 1 Context In order to better optimize the fuel energy efficiency in PWR the burnup distribution has to be known as accurately as possible ideally in each pin Since full transport calculation on a entire core is not possible within reasonable time as required by operation needs other methodologies have to be followed The usual approach is to use the two steps method where transport calculations are performed at assembly level and homogenized properties are generated to be used at the core level by diffusion calculations in our case The disadvantage of this methodology is mainly the loss of details at assembly and pin levels The pin by pin power reconstruction PPR method can be used to get back those levels of details as accurately as possible in a small additional computing time frame compared to classical core calculations T his methodology can be seen as a de homogenization technique for core calculations using arbitrarily homogenized fuel assembly geometries It was presented originally by Fliscounakis et al Ul as the generalized pin power reconstruction GPPR More details on the method
57. es are the data structures used to store cross sections There are three types CPO FBMXSDB and MULTICOMPO The major difference is that cross sections may depend of the burnup only with the first type whereas with the second and third type additional parameters can vary The second type is dedicated to CANDU reactors calculations and the additional parameter types are fixed The MULTICOMPO was then naturally selected for this application because additional parameters are defined by the user We will present in Section 2 the theory behind the pin power reconstruction including how reaction rates are conserved between assembly and core calculations and how flux continuity is ensured In the same section PPR theory will also be explained Section 3 described the algorithm used the algorithm used in DRAGON and DONJON to perform the PPR Then the test cases used for validation are presented in Section 4 together with the numerical results analyzes Section 5 presents the main changes in the DRAGON DONJON code and introduces a set of procedures to be used for post treatment with Octave Finally conclusions and recommendations are given in Section 6 The implementation and the features of the new module NAP are presented together in the user guide of DONJON ll IGE 345 2 2 Theorical background The purpose of this project is to program the pin power reconstruction in DRAGON and DONJON v 5 As we will see in the algorithm section several steps are in
58. ete core the geometry definition may be too complex This task can be performed automatically by the module NAP NCR This component of the lattice code is dedicated to the interpolation of MICROLIB and MACROLIB data from a MULTICOMPO object the reactor database produced by COMPO In the context of the pin power reconstruction this module has to be slightly modified when the geometry and the embedded geometry of the RESINI object have been modified by the NAP module In that case new mixture numbers have been automatically assigned to the regions thus association between mixture numbers and cross sections in the COMPO objects has to be done automatically to guaranty the coherence USPLIT This module is used to create a MATEX object that will provide a link between the reactor geometry and material index The new options of these modules and the NAP module are described in the DONJON v5 user guide UY The additional information also stored in the data structures is also presented in the user guide 5 2 DRAGON A new methodology has been introduced for cross section homogenization as described in Section 2 2 3 Selengut water gap normalization The SPH module has been changed to perform this approach The description of the news option is presented in the user guide L 1 The geometry data structure stores additional information regarding the assemblies The new features are described in l 5 3 TRIVAC A new module named VA
59. fined in this step of the detail algorithm A 2 Automatic geometry generation When heterogeneous assembly are used in the core calculations the geometry has to match the he terogeneities in order to put the proper mixtures to corresponding regions in the core The geometry description of the core and the fuel becomes rapidly complex The number of mixtures can also be very large To facilitate the process an automatic geometry definition has been introduced It is pro grammed in the NAP module with the keyword GEODIR The sets of input file testNAPGEO x2m and rep900cluster x2m illustrates this function for a core with 4 planes plus coolant and a core with 1 plane no coolant respectively A graphical representation before and after automatic definition is presented in Fig 8 In this module assemblies are split according to the heterogeneity of the homogenization Additional split can be introduced as shown in Step 3 1c of the detailed algorithm and illustrated below for the testNAPGEO z2m exemple Build geometry for homogeneous assembly Geol GEO CAR3D 5 5 4 EDIT 1 X VOID X VOID Y VOID Y VOID Z VOID Z VOID MIX PLANE 1 04440 44444 44444 44444 04440 PLANE 2 04440 43234 42124 IGE 345 27 test NAPGEO x2m Original Split CAR3D 554
60. inuity at assembly interface This result was expected since Selengut macro calculation water gap method is designed to guaranty flux continuity in diffusion whereas classical Selengut is designed to guaranty the flux in transport In conclusion the Flux Volume normalization is not recommended because of unprecise results Al thought the Selengut macro calculation water gap normalization does not produce the most accurate results it should not be completely overlooked because of the promising tendencies regarding flux conti nuity at assembly interfaces Finally we recommend the use of the classical Selengut normalization because it minimizes the maximum and the root mean square errors in a broader range of configurations which makes this method more reliable IGE 345 23 A Detailed algorithm A 1 Detailed algorithm and input file description The detailed algorithm refers to the three main steps of the general algorithm presented previously They can be summarized as follows Step Z1 DRAGON compute usual cross sections for homogeneous heterogeneous and pin by pin assembly Y MULTICOMPO Step 2 DONJON compute flux on infinite domain for each homogenization type MULTICOMPO enriched including 75 Step 3 DONJON Compute core flux and perform pin power reconstruction A 1 Step 1 The general procedure to compute a regular MULTICOMPO for a PWR can be found in the example rep900 mco xz2m and its procedure folder
61. ion of all clusters shpnew SELE MWG C4 M20 M50 MO C7 M0 M0 U60 IGE 345 C1 M0 UO0 U20 C2 M20 U10 U60 C3 M10 M30 U20 so 2 ao a as E 30 30 as 40 as so C5 M20 U20 U20 C6 UO M30 M30 so E 2 a 1 as 30 a 30 35 40 as 50 C8 M60 U10 M40 C9 U12 U12 U12 as 0 5 o a as as 30 30 as 40 as sa C12 M12 M12 M12 12 h2 81 t so as 0 5 a as as E 30 a 30 as 40 as 50 FIGURE 16 Transport vs diffusion pin power distribution of all clusters shpnew SELE_EDF C4 M20 M50 MO C7 M0 M0 U60 C10 U0 U36 U12 IGE 345 55 10 11 12 13 14 R f rences M Fliscounakis E Girardi and T Courau Generalized Pin Power Reconstruction Method for Arbitrary Heterogeneous Geometries M amp C 2011 Rio de Janero Brasil May 8 12 2011 C Brosselard H Leroyer M Fliscounakis E Girardi and D Couyras Normalization Methods for Diffusion Calculations with Various Assembly Homogenizations PHYSOR 2014 Kyoto Japan Sep 28 Oct 3 2014 A H bert Applied Reactor Physics Presses Internationales Polytechnique ISBN 978 2 553 01436 9 424 p Montr al 2009 G Marleau and A H bert A New Driver for Collision Probability Transport Codes Int Top Mtg on Advances in Nuclear Engineering Computation and Radiation Shielding Santa Fe New Mexico April 9 13 1989 G Marleau R Roy and A H bert DRAGON A Collision Probability Transport Code for Cell
62. n this case we can write 2 Pires Vi DEV 2 6 Pret Vtot 5 api X Vi 0 5 i 34 Vi T S Pine Vtot gt a Pref 2 7 Pme Then for the flux volume normalization the macro fluxes in macro regions in each macro group are normalized using o Ji qi CE 2 8 Pme Using this definition and Eq 2 5 the averaged SPH factor ji is equal to one This normalization corres ponds to the STD option in the SPH module of DRAGON The limitation of this approach is that the flux continuity is not guarantied between two different assemblies 2 2 2 Selengut normalization SELE_FD and SELE EDF The idea of the Selengut approach is to guaranty the flux continuity between different assemblies Note that the continuity is for 1D computations however when applied to 2D the methodology calculations provides good results in terms of continuity at assembly interfaces The methodology consists in using a normalization factor a such that the flux at the assembly interface is equal to 1 or any constant On a practical point of view the interface flux is approximated by the flux in a small volume surrounding the assembly usually the water gap For the Selengut normalization the macro fluxes in macro regions i in each macro group are normalized using gap di di a 2 9 Pref ur eds P l Pref 2 10 Pme Pref ratio reference macro flux ratio boundary average reference flux Using this definition and Eq 2 5 the a
63. olated flux These data can be used in Octave procedures to plot the flux distribution To test all these new capabilities before using them in the PPR module NAP we have simulated the benchmark IAEA2D as described in the DRAGON user guide l l The results presented on Fig 2 show clearly that a higher order of Raviart Thomas has to be used to get a proper representation of the real flux distribution in the core Note that small discontinuity are still present between assembly even with higher polynomial order This is an intrinsic feature of the Raviart Thomas method which does not guaranty the continuity at interface when only the flux information is used and not the current 4 1 2 Flux projection results for clusters To illustrate the efficiency of the interpolated compared to the average flux projection the results for two configurations are presented on Fig 3 Calculations were performed with a 4x4 geometry tracked using DUAL 2 3 option in TRIVAT module For each case the first and the second lines correspond to the pin power and one group flux distribution respectively The three columns show the results for transport diffusion with Selengut without flux interpolation and diffusion with Selengut with flux interpolation For diffusion calculations the flux on the macro regions and on the pin are shown As expected the flux presents important discontinuity when the interpolation is not done The more heterogeneous the assemblies are c
64. ology and some improvements were also presented by Brosselard et al Pl The pin by pin power reconstruction methodology has been programmed as a new module called NAP in the neutronic codes DRAGON transport and DONJON diffusion version 5 With this module the pin by pin power reconstruction would be facilitated and made available in an open source environment The NAP module is based on a classical flux factorization approach initially proposed by Fliscounakis et al UJ The computer code DRAGON is a lattice code designed around solution techniques of the neutron transport equation The DRAGON project results from an effort made at cole Polytechnique de Montr al to rationalize and unify into a single code the different models and algorithms used in a lattice code 71 One of the main concerns was to ensure that the structure of the code was such that the development and implementation of new calculation techniques would be facilitated DRAGON is the refore a lattice cell code which is divided into many calculation modules linked together using the GAN generalized driver These modules exchange informations only via well defined data structures Similarly the computer code DONJON l is the core code designed around solution techniques of the neutron diffusion equation The same approach was followed to program the DONJON code as for DRAGON modules defined data structures and the GAN generalized driver The main interface between the two cod
65. parameters are looked at the geometry with four choices as shown in Section A 3 and the SPH methodology Results for all configurations are presented in appendix in Tab 5 to Tab 12 To facilitate the analyze of the results the range of error 6 max min for each configurations options are regrouped in Tab 13 and 14 also presented in appendix In this section only the most pertinent results are presented to illustrate the differences between various options and methodologies 4 3 1 Mesh splitting and tracking polynomial order The first parameter to look at is the convergence of the calculations regarding the mesh splitting and the tracking polynomial order Tab 2 presents the results using cross sections corrected with the classical Selengut for two configurations 5 and 6 Results shows that most of the gain can be obtained either by increasing the mesh splitting from 4x4 to 8x8 or increasing the polynomial order DUAL 2 3 to DUAL 3 3 However not much additional gain is obtained using fine mesh and high polynomial order for the tracking The results with coarse mesh and high polynomial order are used in the remaining part of the report to analyze the different options TABLE 2 Relative error between reconstruction and transport calculations 96 mesh and tracking order influence SELE_FD option in SPH module Heterogeneous het2 min max rms 4x4 C5 DUAL 23 2 45 3 75 0 94 6 19 DUAL 33 2
66. pre calculated Regarding the methodology used to compute the shape factor two important notes have to be made First the macro calculation flux has to be normalized 975 2 The flux volume normalization is used The average reference and macro calculation fluxes over the assembly on one macro energy group are computed Their ratio is used to normalize the projected macro calculation flux on each pin The results would be the same regardless of the SPH method used in the macro calculation on the infinite domain Indeed we can write C ref gt Pref du mcg Fa dee 0 3 Eo oo Pref Es 0 Pref pee 22 The second note concerns the choice of SPH normalization made in DRAGON During the transport calculations at the end of the SPH normalization the cross sections X ref are multiplied by the SPH factor u A a and the reference flux d ref is divided by the same factor The SPH corrected reference flux Qi ref can be defined as follows s p ret p ref 2 Hp Ppiref Ap a IGE 345 7 Then it is important to use the same SPH corrected cross sections fp ref for both the PPR and the normalization of Pip Indeed when SPH corrected flux are used the shape factor in the reaction rate equation Eq 2 14 can be written as follows Pprref o Hp ret Ap 02 oo bp ref oo Pp ret Ap a A o EN Dpt p a oo Ppa ip Li ge Pp ref Le 2 16 Ap 400 mao w op E E a Pip 99 o Pp
67. ration 8 In this figure the black lines represent the geometry mesh 8x8 The error between transport reference and diffusion in larger region clearly presents a gradient as shown by the white arrows This results shows that the flux has to be re interpolated within each mesh as during its calculation to capture the gradient before it is projected on each pin It also shows that finite elements with too low polynomial order may lead to too large error RHS of Fig 1 shows results in the same configuration with the same choices for homogenization and split but using the interpolated flux for both core and infinite domain diffusion flux The interpolated flux is obtained using the Gauss interpolation technique which provides the integral of the flux over the pin plus surrounding water of one lattice pitch plus water gap on border pins IGE 345 10 diff 8 hl s2 t2 50 6 4 45 9 0 40 35 E 30 40 30 35 45 50 L average flux interpolated polynomial flux FIGURE 1 Relative error between transport and diffusion calculation D T T using results of a RT2 calculation case 8 8x8 heterogeneous assembly het1 4 1 1 Flux projection validation To verify the flux projection using the interpolation method Two subroutines have been programmed in TRIVAC to interpolate flux computed with the Raviart Thomas solver in 2D and 3D Moreover a new module VAL has been programmed in TRIVAC to produce a data structure with interp
68. ref ADD Zi As Eq 2 16 shows the a factors can be removed only if the SPH correction is the same for both terms Then using the SPH corrected reference flux in the PPR takes into account the specific value of the SPH correction pin by pin and using it in the normalization of the ref takes into account the average value of these factors Their ratio can then be seen as normalized SPH factor i e their average equals to 1 which are the flux volume SPH factors Note that homogenized cross sections of macro regions are not used to compute final reaction rates but only used during the diffusion calculations Then at the end of the transport calculation two homo genizations are required one to get the macro region properties as usual for diffusion calculations and one to get the properties homogenized on each pin This means that two sets of cross sections would have to be interpolated one for the homogeneous 4x4 or heterogeneous 4x4 based geometry and one for the pin wise geometry The burnup distribution should match between the two geometries When an homogeneous homogenization is performed the method is equivalent to the classical PPR because all projected flux are the same Indeed the diffusion flux is a constant in that case Eq 2 14 can be written as follows for an homogeneous Pin Power Reconstruction PPR 2 17 uis Dp ref OX i with lt pZ P 2 18 Pme where the subscripts are removed since the assembly is
69. riched MULTICOMPO data structure is obtained and ready to be used for core calculations 3 Core calculations a Compute the core flux distribution following the general procedure Warning if heterogeneous cross sections are used the geometry definition has to match the discretization used for homogenization at assembly level in DRAGON This can be done manually or automatically with the NAP module b Compute the corrected reaction rate using the additional properties in the enriched MULTI COMPO data structure Perform the pin power reconstruction if required by the chosen metho dology Note Reaction rates are saved in the MAP data structure and can be printed in the output file for each assembly of the core The detailed algorithm is presented in Appendix see Section A IGE 345 9 4 Validation As previously mentioned several clusters were simulated both in transport and diffusion theory to validate the GPPR A total of 12 cluster configurations was used They can be described as follows Assembly positions by type BIC C BA B CIBC Assembly types by case Case Burn up GWd t Boron ppm A B C C1 O M O U 20 U 1700 C2 20 M 10 U 60 U 715 C3 10 M 30 M 20 U 900 C4 20 M 50 M 0 M 1100 C5 20 M 20 U 20 U 1600 C6 0 U 30 M 30 M 715 C7 O M O M 60 U 1100 C8 60 M 10 U 40 M 9
70. rs that guaranties the same reaction rates is an iterative process IGE 345 3 2 2 Equivalence coefficients In the transport diffusion equivalence theory presented in the previous section the set of coefficients A can be divided by any constant o written as a after This is based on the fact that in an infinite domain if the cross sections X are divided by a factor a X Y a the flux will be multiplied by the same factor J X o ow X thus the reaction rate 7 remains the same as illustrated in the following equation plns ont c Wee E ad 5 c a Q Note that the factor a is different for each energy group but is the same for all the macro regions and all cross section types a can be seen as a normalization coefficient An other quantity is also defined the SPH factors y and the average SPH factor ji written as ju and ji after which are defined by di da Mi where Hi Z Ai a 2 4 and Dae D et oi Vi Viot A Mi 1 Qi Vii d Viot gt a 1 i re Vi a Viot 25 de ref Q then 1 Pref Sa T 2 5 FT Pme eo where Pret is the averaged volumic flux of the reference calculation and Pme is the averaged volumic flux of the macro calculation on macro group g IGE 345 4 2 2 1 Flux Volume normalisation STD One approach to normalize the set is to make sure that the spatially integrated macro calculation flux for each group is the same as in transport calculations I
71. sing the bash script allCluster run sh IGE 345 39 C Results C 1 Tables results The final calculations presented below where all performed using interpolation and consistency for the mesh splitting and Raviart Thomas method during the core and infinite domain flux computations The minimum and maximum errors together with the root mean square of the difference between transport and diffusion calculations are presented in Tab 5 to Tab 12 The column 6 gives the range of error max min Each table corresponds to a different methodology 1 Flux Volume normalization of the cross sections no Selengut STD Tab 5 and 6 2 Selengut normalization of the cross sections classical SELE_FD Tab 7 and 8 3 Selengut normalization of the cross sections macro calculation water gap SELE MWG Tab 9 and 10 4 Selengut normalization of the cross sections SELE EDF type Tab 11 and 12 The range of errors is also presented for all homogenization methods and geometries in Tab 13 and 14 to facilitate the comparison between the different options TABLE 5 Relative error between reconstruction and transport calculations 96 coarse mesh STD option in SPH module Pin by Pin Heterogeneous het2 Heterogeneous het1 Homogeneous 4x4 4x4 4x4 min max rms 0 min max rms min max rms min max rms 0 Cl DUAL 2 3 1 74 3 56 1 25 5 30 3 42 7 71 1 63 11 14 3 52 8 51 1 79
72. the same level than rdragon or rdongon script When input file main z2m is automatically generated the corresponding file main template z2m from the folder mydata is used B 2 rep900het mco x2m The main characteristics of this DRAGON 5 data set are the following UOX or MOX assembly enrichments are 7 56 4 8996 and 2 82 of Pu and 0 25 of U for MOX assembly and 4 of U for UOX assembly The MOX pin enrichment are distributed as follows self shielding geometry two levels of geometry for 281 groups and 26 groups burnup until 60GW t 1 71 steps for MOX 0 0 9 37499 18 7500 37 5000 74 9999 150 000 325 000 500 000 750 000 1000 00 1500 00 2000 00 2500 00 3000 00 4000 00 5000 00 6000 00 7000 00 8000 00 9000 00 10000 0 11000 0 12000 0 13000 0 14000 0 15000 0 16000 0 17000 0 18000 0 19000 0 20000 0 21000 0 22000 0 23000 0 24000 0 25000 0 26000 0 27000 0 28000 0 29000 0 30000 0 31000 0 32000 0 33000 0 34000 0 35000 0 36000 0 37000 0 38000 0 39000 0 40000 0 41000 0 42000 0 43000 0 44000 0 45000 0 46000 0 47000 0 48000 0 49000 0 50000 0 51000 0 52000 0 53000 0 54000 0 55000 0 56000 0 57000 0 58000 0 59000 0 60000 0 IGE 345 37 2 73 steps for UOX 0 0 9 37498 18 7500 37 4999 74 9999 150 000 237 500 325 000 412 500 500 000 625 000 750 000 1000 00 1250 00 1500 00 1750 00 2000 00 2500 00 3000 00 3500 00 4000 00 4500 00 5000 00 5500 00 6000 00 6500 00 7000 00 7500 00 8000 00 8500 00 9000 00 9500 00 10000 0 105
73. urnup lt lt burnup gt gt SET ppmBore lt lt ppmBore gt gt This resulted in the following records in the enrich MULTICOMPO gt 6 12 3 32 lt ADDXSNAME PO 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 NFTOT NG N2N N3N N4N NA NP N2A NNP ND NT TRANC FINF_OOOFINF_001FINF_OO2FINF_003 gt T 12 2 2 lt FINF_000 4 48785095E 01 4 85739851E 00 gt 7 12 2 2 lt FINF_001 4 51128273E 01 4 73293400E 00 gt 7 12 2 2 lt FINF_002 4 55112991E 01 4 36975765E 00 gt 7 12 2 2 lt FINF_003 4 52058678E 01 4 63550901E 00 infinite diffusion projected flux are coherent with original diffusion calculation and normalization is properly done Note that using an edition level at 100 provides a large number of data with several intermediate results in the output in order to verify the calculations A 2 Verification part 2 The second part consists of verifying the automatic geometry spliting This part can be verified again with an edition level equal to 100 It can also be visually verified with the illustrated examples provided in the detailed algorithm description and also in Section A 2 A 3 Verification part 3 Finally the last part of the verification is the pin power reconstruction Two substeps are looked at the flux projection and then the pin power calculation The transport geometry of the cluster is presented IGE 345 31 on Fig 9 O
74. veraged SPH factor 4 is equal to Pret h Gap ref This normalization corresponds to the SELE_FD option in the SPH module of DRAGON In the case of an heterogeneous homogenization the ratio between the assembly average and boundary reference flux may not be the most accurate one second ratio in the RHS of Eq 2 10 Instead of using IGE 345 5 the average flux on the assembly the average on the side surrounding row of pin i e mixtures see Section A 1 can be used Then for the heterogeneous Selengut normalization the macro fluxes in macro regions 7 in each macro group are normalized using n gap Pref ref A R row ref Di Di E 2 11 ratio reference macro flux ratio boundary side reference flux Using this definition and Eq 2 5 the averaged SPH factor ji is equal to row _ ref H gap ref This normalization corresponds to the SELE_EDF option in the SPH module of DRAGON The limitation of this approach is that the flux continuity is guarantied between two different assem blies for the reference flux i e transport calculations and not macro calculations 2 2 3 Selengut macro calculation water gap normalization SELE MWG The Selengut macro calculation water gap normalization is used to ensure the continuity of the re constructed i e diffusion flux at the boundary For this case the macro flux is normalized as follows EP i pi 24S 2 12 Pret d hi 3 ae 2 13
75. volved in the overall calculations and many options can be chosen In this section we will present the theory behind the three main steps Homogenization and condensation requirements Normalization of the equivalence coefficients Pin power reconstruction 2 1 Homogenization and condensation In core calculations the number of neutron energy groups and the spatial mesh are reduced to be able to perform fast computations of the flux power distribution Average properties are then required for each macro region and each macro group To get this information homogenization and condensation methods are used following the more detailed transport calculations at pin assembly level The main concern during this process is to preserve reaction rates i e make sure that the number of reactions occurring in each macro region i and each macro group g is the same whereas it is computed at the core level or at the assembly level The basic method is to compute the following quantities for each macro region i and each macro group g z bi re p the reference flux which is equal to the volume weighted average of the original flux and the sum of all original energy groups E mS 5 Y bres r k V Ge keg 49 the macro calculation flux generally obtained by solving the diffusion equation over macro regions and macro groups Y p the cross sections which are equal to the ratio of the integrated reaction rate divided by its integrated
76. where the subscripts i p represent the projection of the macro calculations flux using general geometry on the pin by pin geometry As expected the reaction rate is the product of the cross section times the flux times the volume However since the flux is only the projection of the macro calculation on each pin it may differ from the reference flux The shape factor introduced previously corrects this approximation It also represents the ratio between the macro calculation fluxes computed on a pin by pin and on a heterogeneous geometries in an infinite domain Physically this ratio can be seen as the relative error made when using a general geometry instead of the pin by pin geometry Using Eq 2 3 the reference flux is introduced The detailed flux is then clearly seen as the product of the macro flux and normalized local flux Eq 2 15 The reaction rate equation is then the same as proposed by Brosselard et al Pl Eq 2 15 can be applied with any homogenization and was presented originally by Fliscounakis et al as the generalized pin power reconstruction GPPR 2 3 2 Computation To perform the GPPR the different components of Eq 2 14 are obtained as follows The cross sections are recovered from the pin by pin wise homogenized data structure The macro calculation flux is projected on each pin Note that it is very important to interpolate the flux as well as we will see later The components of the shape factor are

Specifications and User Guide for NAP : module in DRAGON

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