IL SISTEMA DI CALCOLO MODULARE ERANOS EUROPEAN REACTOR

IL SISTEMA DI CALCOLO MODULARE ERANOS (EUROPEAN REACTOR ANALYSIS OPTIMIZED SYSTEM) (Dr. Vincenzo Peluso – ENEA) 1

1. INTRODUCTION • ERANOS 2. 1 is a system of neutron and gamma codes developed within a European framework. • This system meets the needs expressed by the industrialists and the teams working on the design of fast reactors, present and future. • It allows moreover, with the use of the convivial LU user’s language, to perform programs of R&D in reactor physics without systematically needing specific developments. 2

2. ERANOS FUNCTIONS • Fast reactor core, shielding, and fuel cycle calculations can be performed with the ERANOS system. ERANOS is a deterministic code system, so neutron physics calculations are performed at the cell/lattice level and at the core level. • The cell/lattice code ECCO (European Cell COde) is fed by libraries that are in a direct access format in various energy meshes: 1968 groups (all-purpose), 175 groups (shielding purposes), the 172 -group XMAS scheme (refined in the low energy range), and 33 groups (energy mesh generally used for core calculations). • Four sets of libraries can be used: JEF-2. 2 obtained directly from JEF 2. 2 evaluations ERALIB 1 obtained from the JEF-2. 2 libraries by a statistical fitting on integral experiments JEFF-3. 1 obtained directly from JEFF 3. 1 evaluations ENDFB-VI. 8 obtained directly from ENDFB-VI. 8 evaluations. N. B. : The Code HETAIRE and the library CARNAVAL 4 of the old Fast Neutron C. E. A. code system are also available in ERANOS 2. 1. For neutron shielding and gamma propagation and heating applications, the PROPANE and VASCO libraries are also available. 3

2. ERANOS FUNCTIONS • The ECCO code solves the resonant nuclide self-shielding using the sub-group method and computing, with a collision probability method, a fine-group solution of the transport integral equation. The cross-sections can be condensed and homogenized. • ECCO can model the following geometries: Plane, Cylindrical, 2 D rectangular sub-assembly with or without wrapper, 2 D hexagonal sub-assembly with or without wrapper, 3 D slab geometry, useful to model platelet fuel. • The core calculations carried out by ERANOS include reactivity, flux, spatial power distribution, reactivity coefficients, burnup, and control rod worth. Moreover, for very different applications (analysis of experiments, reactivity coefficients, follow-up and management of core loadings), traditional, generalized and harmonics perturbation modules are available. 4

2. ERANOS FUNCTIONS • The ERANOS code system is a very open system, modular, whose objects (SET or EDL) are easy to handle by many modules and the LU user language. This makes possible, using the various available modules, to create procedures for specific types of applications, e. g. to define separately design and reference calculations schemes for respectively scoping and detailed calculations. • Calculations performed by ERANOS are gathered according to the following chapters: Operating Conditions Internal Transfer of nuclear data Release of energy and damage to the structures Diffusion modules 1 D, 2 D (XY , RZ and Hexagonal), 3 D Hexagonal Z Sn transport modules 1 D, 2 D (XY and RZ ) Nodal diffusion and transport modules P 1, P 3, P 5, SP 3, SP 5 (XY, XYZ, Hexagonal and Hexagonal Z) Perturbation modules Burn-up modules 5

3. The ALOS system What’s ALOS ? • The ALOS software provides a complete development environment. • It includes : -a programming language => ESOPE -basic data structures => the SEGMENTs the EDLs (or SETs ) -an utility library to manage memory =>GEMAT -a user command language =>LU -an archiving utility =>ARCHIVE -a relational data base management system => SGBD 6

3. 1 LU language LU is the user language for all software developed under ALOS. It allows: • To handle the variables(integers, reals, strings of characters, pointers…) and the SETs • To call up a program(ESOPE, standard FORTRAN, C, …) • To perform numericaland logical calculationsusing basic mathematical functions : SIN, COS, LOG, EXP … • To make advanced programmingusing loops (POUR, TANTQUE) or conditional execution structures (SI … SINON … FINSI) • To encapsulate complex sequenceof instructions in macro instructions called PROCEDURE • To use archiving utilitiesand the internal relational SGBD 7

3. 2 Basic LU Each term of a LU instruction may be one of the following types: -numeric constant ==> 10 -5 1. 25789 E-05 -text constant ==> 'Martin‘ 'A= ' "Resultat" -keywords ==> ITERATIONS_EXTERNES -result variable ==> ->X -> SIGMA -input variable ==> (X) (SIGMA) -expression ==> (X+1) (SIGMA*SIGMA) • A LU instruction can stand on several lines • The last instruction of a LU program is FIN ; 8

3. 2 Basic LU Each term of a LU instruction may be one of the following types: -numeric constant ==> 10 -5 1. 25789 E-05 -text constant ==> 'Martin‘ 'A= ' "Resultat" -keywords ==> ITERATIONS_EXTERNES -result variable ==> ->X -> SIGMA -input variable ==> (X) (SIGMA) -expression ==> (X+1) (SIGMA*SIGMA) • A LU instruction can stand on several lines • The last instruction of a LU program is FIN ; 9

3. 2 Basic LU • A LU instruction endswith; • Only 80 first characters are valid on a line • A string of characters must not increase more than 500 characters • The text that follows an exclamation mark (!) is ignored (a line that begins with ! is a comment) • Lower cases and upper cases are equivalentexcept in text variable • Tabulations are prohibited 10

3. 3 Arithmetic and logical calculation • Basic operators: + for the addition - for the subtraction / for the division * for the multiplication ** for the power • Comparison operators: = equal < lesser than > greater than /= different from <= lesser or equal >= greater or equal • Logical operators : ET AND OU OR NON NOT 11

3. 3 Arithmetic and logical calculation • We also use the functions : SIN COS TAN ASIN ATAN ACOS EXP LOG 10 ABSENT MOD MAXMIN SOMME PRODUIT TRI • The sequence : ->TAB 7 2 5 4 3 6 1 ; ->SUM SOMME (TAB); ->PRODUIT (TAB); ->I TRI(TAB) ; ->J TAB(TRI(TAB)) ; provides ->SUM 28 ->PROD 5040 ->I 7 2 5 4 3 6 1 ->J 1 2 3 4 5 6 7 12

3. 4 Others functions • REP operator The sequence ->A REP(6); ->B REP(-6); ->C REP(3, 'toto') ; is similar to ->A 1 2 3 4 5 6 ; ->B 6 5 4 3 2 1 ; ->C 'toto‘ ‘toto’; 13

3. 5 The printing utility • Printing a variable with the * operator ->T 1 4 2. E-02 78; * T; provides * 2 T; provides * -1 T; provides ->T 1 4 2. 00000 E-02 78 ->T 1 4 2. 00000 E-02 78 ->T (1) 1 (2) 4 (3) 2. 00000 E-02 (4) 78 14

3. 6 Utilities • Remove a variable / X; • Remove an EDL / (EDL_MACRO); • Duplication of a variable and a SET = -> Y X; ! the variable X is duplicated under a new ! Reference Y = ->NEW_EDL (EDL_MACRO) ; ! the set pointed by the variable ! MACRO_SET isduplicated 15

3. 7 The POUR (FOR) loop • This structure can be used only in a procedure Syntax: ->CONTROL_ROD_POSITION 0. 100. 200. 400. ; POUR->IP 1 2 3 4; GEOMETRY_MODIFICATION-> NEW_GEOMETRY_SET GEOMETRY(GEOMETRY_SET) CORE(CORE_SET) MEDIUM(MEDIUM_SET) NEW_Z_AXIS POSITION 19 18 (CONTROL_ROD_POSITION(IP)) POSITION 23 19 (CONTROL_ROD_POSITION(IP)) POSITION 13 23 (CONTROL_ROD_POSITION(IP)); . . . FLUX_CALCULATION-> NEW_FLUX_SET ->EIGENVALUE NEW_GEOMETRY_SET ; / (NEW_GEOMETRY_SET) (NEW_FLUX_SET); FINPOUR; The instructions between POUR and FINPOUR will be executed 4 times. The variable IP successively takes the values 1, 2, 3 and 4. 16

3. 8 The TANTQUE (WHILST) loop • This structure can be used only in a procedure ->Z_AXIS 0 100. 200. 400. ; ->IP 1 ; TANTQUE (IP <= Z_AXIS() ) ; GEOMETRY_MODIFICATION ->NEW_GEOMETRY_SET GEOMETRY(GEOMETRIE_SET) CORE(CORE_SET) MEDIUM(MEDIUM_SET) NEW_Z_AXIS POSITION 1918 (Z_AXIS(IP)) POSITION 2319 (Z_AXIS(IP)) POSITION 1823 (Z_AXIS(IP)); . . . FLUX_CALCULATION ->NEW_FLUX_SET >EIGENVALUE NEW_GEOMETRY_SET NEW_MACRO_SET; / (NEW_GEOMETRY_SET) (NEW_FLUX_SET); ->IP (IP+1) ; FINTANTQUE ; 17

3. 9 Conditional execution The SI (IF) structure • This structure can be used only in a procedure SI (GEOMETRY_TYPE=‘XY’) ; ! XY case XY_GEOMETRY_CREATION ->EDL_GEOMETRY …. . ; SINONSI (GEOMETRY_TYPE=‘H 2 D’) ; ! H 2 D case H 2 D_GEOMETRY_CREATION ->EDL_GEOMETRY …. . ; SINONSI (GEOMETRY_TYPE=‘RZ’) ; ! RZ case RZ_GEOMETRY_CREATION ->EDL_GEOMETRY …. . ; SINONSI (GEOMETRY_TYPE=‘XYZ’) ; ! XYZ case XYZ_GEOMETRY_CREATION ->EDL_GEOMETRY …. . ; SINON ; ! H 3 D case FINSI; 18

3. 10 The PROCEDURES • A procedure allows to encapsulate a sequence of LU instructions • A procedure is similar to a function • A procedure is a particular SET (SET of type 'PROCEDURE V 1') • A procedure may be store on a permanent file (ARCHIVE file) �� Structure of a procedure: PROCEDURE->procedure_name input 1 input 2 …. inputn ->output 1 …. ->outputn; . . Sequence of LU instructions. . FINPROC; Input and output arguments can be listedin the order you want 19

3. 10 The PROCEDURES • Example (a way to create an EDL_MACRO with micro cross sections) PROCEDURE->CREATE_MACRO_SAMPLE EDL_MICRO EDL_MILIEU ->EDL_MACRO_SAMPLE isotope conc_iso reaction ; SI (CONC_ISO()/=0) ; ->CONCENTRATION (CONC_ISO) ; FINSI ; CALCUL_MACRO ->EDL_MACRO_SAMPLE MICRO (EDL_MICRO) MILIEU (EDL_MILIEU) (CONCENTRATION) SECTION (reaction) PAR_ECHANTILLON (isotope) ; FINPROC; 20

3. 10 The PROCEDURES • Call a procedure ARCHIVE ‘ARFILE’ ->EDL_MILIEU SPX 180 ; ARCHIVE ‘ARFILE’ ->EDL_MICRO SPX 180 ; ->ISOTOPE ‘U 235’ ; ->CONC_ISO 1. ; ->REACTION ‘FISSION’ ; ! The way below to call the procedure is also valid since the names of the variables are similar to those used when the procedure has been created CREATE_MACRO_SAMPLE; 21

3. 11 The ARCHIVE utility • It allows : -to create a file with his name and its initial space, ARCHIVE ‘file_name’ INITIALISER nb-blocs long-blocs ; -to store set in a file with binary format, ARCHIVE ‘file_name’ << REMPLACER>> (FLUX_SET) FLUX TGV ERANOS ; -to get back a set previously stored , ARCHIVE‘file_name’ ->FLUX _SET FLUX TGV ERANOS; -to suppress a set previously stored, ARCHIVE ‘file_name’ SUPPRIMER FLUX TGV ERANOS ; -to print the list of the set stored in a file, ARCHIVE ‘file_name’ CATALOGUE; -to store this list and then utilize it. ARCHIVE‘file_name’CATALOGUE ->CATAL_SET; EDL_NOM (CATAL_SET) ->SET_NAME 22

3. 12 The PARAM file • The way in which the GEMAT data management scheme works depends of memory parameters. These parameters must be placed in an ASCII file named PARAM. • This file is mandatory in the execution environment and contains : ESOPE=nb-words, NTRK=nb-blocks, LTRK=size-blocks nb-words: number of words which allows to allocate the workspace in RAM memory needed by the job. ( 1 word = 4 or 8 bytes depending of the computer) This size cannot exceed the memory space of the microprocessor. nb-blocks: number of blocks of the overflow file size-blocks: size of a block 23

3. 13 The GEMAT errors • MESSAGE ---GEMAT ERROR -----3500000 ALLOCATION MEMOIRE INSUFFISANTE GEMAT 9. 4 (FEV 93) *** DUMP DE LA MEMOIRE GEREE PAR GEMAT *** DONT 0 MOTS LIBRES EN ZONE DYNAMIQUE ET 0 MOTS LIBRES EN ZONE FIXE • CAUSES 1. The ESOPE parameteristoo large 2. The ESOPE parameter has not been defined • REMEDY 1. Decrease the value of ESOPE 2. Assign a value to ESOPE 24

3. 13 The GEMAT errors • MESSAGE ---GEMAT ERROR ---SUBROUTINE : NCMAC ---INSTRUCTION : 91 ---SEGINI , ZAUX 2 ---PAS ASSEZ DE PLACE EN MEMOIRE GEMAT 9. 4 (FEV 93) *** DUMP DE LA MEMOIRE GEREE PAR GEMAT*** • CAUSES The program complains that there is not enough memory space for the calculation it has been asked to perform • REMEDY Increase the value of ESOPE 25

4. The multi-group and multi-temperature LIBRARIES • Four sets of libraries can be used: JEF-2. 2 obtained directly from JEF 2. 2 evaluations ERALIB 1 obtained from the JEF-2. 2 libraries by a statistical fitting on integral experiments JEFF-3. 1 obtained directly from JEFF 3. 1 evaluations ENDFB-VI. 8 obtained directly from ENDFB-VI. 8 evaluations. 26

4. 1 JECCOLIB 2 & ERALIB 1 • The data are mainly coming from JEF 2 evaluations, except for ERALIB 1 libraries which contain ajusted nuclear data values (elastic, inelastic, capture, n, Xn, fission…) for the main nuclei : 235, 238 U, 239, 240, 241, 242 Pu, Zr, Gd, Al, 56 Fe, 58 Ni, 52 Cr, Na, O, C, 10 B, bd. H (H from H 2 O). • There are 3 libraries with various group weighting (structure and flux): the 1 st one contains 41 isotopes (1968 groups), it is used for reference calculations in any kind of application the 2 nd one contains 287 isotopes (172 groups), it is used for design calculations in thermal spectra the 3 rd one contains 287 isotopes (33 groups), it is used for design calculations in fast spectra 27

ASPILIB 2 P The data are mainly coming from JEF 2 evaluations. The library contains 58 isotopes (175 groups VITAMIN-J group structure). Angular distributions for structural materials cross-sections are more detailed than in other libraries. It is used for shielding calculations. DPA (Displacement Per Atom) The values stored are doses for every reaction: capture, fission, elastic, inelastic. There are 3 ASCII libraries (33, 172 and 175 groups), each of them containing 13 isotopes (iron, chromium and nickel elements). There are used for structural damage calculations. KERMA (Kinetic Energy Release in MAterials) The values stored are total (i. e. neutron + gamma) and for every reaction (capture, fission, elastic, inelastic). There are 2 libraries (in ASCII format): KERMA 33 contains 52 isotopes (33 groups) KERMA 175 contains 40 isotopes (175 groups) 28

The following table indicates whether the energy boundaries of the different structure allow a condensation from one to another 1968 175 172 33 15 1968 -- yes yes 175 -- -- no no no 172 -- -- -- yes 33 -- -- yes 15 -- -- -- Structure Energy limits of the different structures (15 groups are used for sensitivity studies) 29

NB OF GROUPS 1968 175 172 33 UPPER E (e. V) 1. 964033 E+07 1 1 1 1. 947734 E+07 2 1 1 1. 931570 E+07 3 1 1 1. 915541 E+07 4 1 1 1. 899644 E+07 5 1 1 1. 883880 E+07 6 1 1 1. 868246 E+07 7 1 1 1. 852742 E+07 8 1 1 1. 837367 E+07 9 1 1 1. 822119 E+07 10 1 1 1. 806998 E+07 11 1 1 1. 792002 E+07 12 1 1 1. 777131 E+07 13 1 1 1. 762383 E+07 14 1 1 1. 747757 E+07 15 1 1 …………………………………. . . 5. 000000 E-02 1958 175 162 33 15 4. 200000 E-02 1959 175 163 33 15 3. 500000 E-02 1960 175 164 33 15 3. 000000 E-02 1961 175 165 33 15 2. 500000 E-02 1962 175 166 33 15 2. 000000 E-02 1963 175 167 33 15 1. 500000 E-02 1964 175 168 33 15 1. 000000 E-02 1965 175 169 33 15 6. 900000 E-03 1966 175 170 33 15 5. 000000 E-03 1967 175 171 33 15 3. 000000 E-03 1968 175 172 33 15 1. 000000 E-04 1969 175 172 33 15 30

4. 2 ECCO libraries JEFF 3. 1 • They are binary files. They can be converted into ASCII format (and vice-versa) by specific ERANOS modules (BITOCI/CITOBI), but they must be in binary format to be used by the ERANOS modules requiring libraries as input data (e. g. ECCO). • The 1968 -group library is rather large although it contains only the most important nuclides for the reactor flux calculations. The 175, 172 and 33 group libraries contain all the isotopes. • They depend on a reference file which allows to associate a given nuclide to its data. This file also contains nuclide characteristics (mass, disintegration constant, released energies) common to all data files. The same reference file may be used with several libraries under the strict condition that nuclides are in the same order. This is the case for the 1968, 172 and 33 group libraries which all depend on a unique file, while the 175 -group library depends on another reference file. 31

4. 2. 1 THE 1968, 172 AND 33 ENERGY GROUPS LIBRARIES The 1968 group library • The 1968 -group library contains fewer nuclides than the other ones: only the 112 first nuclides from H 1 to ccah 2 are present. • 103 nuclides with P 0 and P 1 scattering, 293. 6 573. 6 973. 6 1473. 6 2973. 6 K data, free gas thermal scattering and probability table representation of resonance shielding over the entire energy range + • 9 compounds with P 0 and P 1 scattering, nuclide dependent multi-temperature cross sections, thermal files (H-H 2 O, H-CH 2, H-Zr. Hx, D-D 2 O, Be and Mg metal, Ca-Ca. H 2, H-Ca. H 2 and C-graphite) 32

The 172 group library (XMAS group structure) • 103 nuclides condensed from the 1968 energy groups library: P 0 and P 1 scattering, 293. 6 573. 6 973. 6 1473. 6 2973. 6 K data, free gas thermal scattering and probability table representation of resonance shielding over the entire energy range + • 9 compounds condensed from 1968 energy groups library: P 0 and P 1 scattering, nuclide dependent multi-temperature cross sections, thermal files + • 277 nuclides with P 0 to P 3 scattering, 293. 6 573. 6 973. 6 K data, free gas thermal scattering 33

The 33 energy groups library • 103 nuclides condensed from the 1968 energy groups library: P 0 and P 1 scattering, 293. 6 573. 6 973. 6 1473. 6 2973. 6 K data, free gas thermal scattering and probability table representation of resonance shielding over the entire energy range + • 9 compounds condensed from the 1968 energy groups library: P 0 and P 1 scattering, nuclide dependent multi-temperature cross sections, thermal files + • 277 nuclides condensed from 172 energy groups library, P 0 -P 3 scattering, 293. 6 573. 6 973. 6 K data, free gas thermal scattering + • 57 PSEUDO fission products : 19 global pseudo fission products for Na-cooled FRs (name=fp+fissile nuclide name) 19 solid pseudo fission products for Na-cooled FRs (name=fps+fissile nuclide name) 19 global pseudo fission products for gaz-cooled FRs with large amounts of C containing structure (name=fpg+fissile nuclide name) 34

Nuclides presents only in 33 energy groups libraries: fp. Th 232 fp. U 233 fp. U 234 fp. U 235 fp. U 236 fp. U 238 fp. Np 237 fp. Np 238 fp. Pu 239 fp. Pu 240 fp. Pu 241 fp. Pu 242 fp. Am 241 fp. Am 242 m fp. Am 243 fp. Cm 243 fp. Cm 244 fp. Cm 245 sfp. Th 232 sfp. U 233 sfp. U 234 sfp. U 235 sfp. U 236 sfp. U 238 sfp. Np 237 sfp. Np 238 sfp. Pu 238 sfp. Pu 239 sfp. Pu 240 sfp. Pu 241 sfp. Pu 242 sfp. Am 241 sfp. Am 242 m sfp. Am 243 sfp. Cm 243 sfp. Cm 244 sfp. Cm 245 fpg. Th 232 fpg. U 233 fpg. U 234 fpg. U 235 fpg. U 236 fpg. U 238 fpg. Np 237 fpg. Np 238 fpg. Pu 238 fpg. Pu 239 fpg. Pu 240 fpg. Pu 241 fpg. Pu 242 fpg. Am 241 fpg. Am 242 m fpg. Am 243 fpg. Cm 243 fpg. Cm 244 fpg. Cm 245 35

4. 3 ECCO libraries ENDFB 6. 8 • All data are coming from ENDFB 6. 8 evaluations except Ar 40, Ni 59, In 115 which could not be processed and were taken from JEFF 3. 1 evaluations. • 320 Nuclides. • The 1968 group library: The 1968 -group library contains fewer nuclides than the other ones: only the 95 first nuclides from H 1 to poly are present. 89 nuclides with P 0 and P 1 scattering, 293. 6 573. 6 973. 6 1473. 6 2973. 6 K data…. + 6 compounds with P 0 and P 1 scattering…. • The 172 group library (XMAS group structure): 89 nuclides condensed from the 1968 energy groups library + 6 compounds condensed from 1968 energy groups library + 225 nuclides with P 0 to P 3 scattering, 293. 6 573. 6 973. 6 K…. . 36

• The 33 energy groups library: 89 nuclides condensed from the 1968 energy groups library + 6 compounds condensed from 1968 energy groups library + 225 nuclides condensed from 172 energy groups library…. 4. 4 ECCO libraries JENDL 3. 3 • All data are coming from JENDL 3. 3 evaluations except Au 197 and Nb 93 which could not be processed and were taken from JEFF 3. 1 evaluations. • 338 Nuclides. ……………………………………. . 37

4. 5 Processing scheme • Evaluated libraries in ENDF-6 format. • It mainly relies on two important processing codes; NJOY (resonance integrals, fission spectrum averaged, Graphical plots of cross sections, angular distributions and emitted spectra for all isotopes and elements at all temperatures) CALENDF (convert resolved and unresolved resonance parameters from ENDF-6 structured evaluations, into temperature dependent pointwise cross-sections, it generates "cross-section probability tables“ based on Gauss quadrature. These represent detailed resonance self shielding within any of the groups and can be used directly in the ECCO cell code) and two interface codes: MERGE GECCO all of which have been largely updated since the last ECCOLIB was generated. Some major improvements have been achieved, in the format and physical 38 qualities of the basic JEFF-3. 1 evaluations input.

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The following 40 response functions, types and names, have been included in the ECCO library tape when present in the original evaluation. 41

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5. USER LANGUAGE • It is the LU language of the ALOS system. Its basic instruction is the calling sentence of a module. • The calling sentence is formed as follows: The first word is the module name which identifies the function. The following terms are specified in the directions for use of the module. • Generally , they are : - Created or used SETS , - Directives to describe the data to be given by the user. - The semicolon ; ends the sentence. 43

5. USER LANGUAGE When the module name expresses without ambiguity the waited resulting SET , the LU name of the variable SET , preceded by an arrow , will immediately follow the module name : CREATION_MACRO ->ma When the module name expresses without ambiguity the used SET , the LU name of the used SET , between brackets , will immediately follow the module name : EDITION_MACRO (ma) ; 44

5. USER LANGUAGE MODULE DESCRIPTION STANDARDS <<. . >> means that the data in square brackets are to be given 0 or 1 time <<. . >>0 means that the data in square brackets are to be given 0 or N times <<. . >>1 means that the data in square brackets are to be given 1 or N times !. . . means that the data at the right are exclusive (one, and only one) !!. . . means that the data at the right are optional , that they may exist all together, and that at least one must exist. 45

6. Lattice calculation with ECCO • Summary Basic reactor modeling: medium set creation ���� operating conditions ECCO sentence and steps basic set creation for core calculation Advanced topics: heterogeneous cells ECCO routes ECCO step options 46

• Modeled Reactor Na-cooled (U, Pu)O 2 fast reactor 1250 MW (thermal) / 500 MW (electric) Fuel S/A geometric data: • 169 -pin bundle ; pin pitch = 0. 878 cm • Hexagonal wrapper across-flats = 11. 65 cm (inner) x 12. 37 cm (outer) • S/A pitch = 12. 87 cm ; Fissile height= 100 cm • Integratedaxialblankets(same geometryas fissile) • Lower/upperaxialblanket height= 25/25 cm • Numberof fuel S/Asis the core= 255 Fertile S/A geometric data: • 61 -pin bundle ; pin pitch = 1. 445 cm • Spacer wire diameter= 0. 187 cm • Hexagonal wrapper across-flats = 11. 65 cm (inner) x 12. 37 cm (outer) • S/A pitch = 12. 87 cm Fertile height= 150 cm 47

• Module sequence MEDIUM_CREATION to create materials, medium and cells: • MEDIUM set (output) • Cell description needs medium • Medium description needs materials OPERATING_CONDITION to expand medium (optional): MEDIUM set (input and output) ECCO to perform lattice calculation: MEDIUM set (input) Ecco files (output) BASIC_EDL_CREATION_FROM_ECCO_FILE to create edl: MEDIUM set (input and output) Ecco files (input) MICRO and MACRO set (output) 48

• Global Data !---> EINT/EEXT = inner/outer volume (Pu+Am)O 2/(U+Pu+Am)O 2 in % ->EINT (25. 0*0. 74) ; ->EEXT 25. 0 ; !---> expansion coefficients : ->OXIDE_DIL 100 1. 0528 E-05 200 1. 0553 E-05. . . ; ->STEEL_DIL 100 1. 707 E-05 200 1. 740 E-05. . . ; ->SODIUM_DIL 100 8. 65600 E-5 200 8. 90300 E-5. . . ; ->B 4 C_DIL 100 0. 4344 E-5 200 0. 4468 E-5. . . ; !---> lists for (initial) trace nuclides : ->HN_TRACES 'U 234' 1. 0 E-15 'U 235' 1. 0 E-15 'U 236' 1. 0 E-15 'U 238' 1. 0 E-15. . . ; 49

• MEDIUM_CREATION general 50

• MEDIUM_CREATION simple material 51

• MEDIUM_CREATION mixed material 52

• MEDIUM_CREATION medium 53

• MEDIUM_CREATION homogenous cell • MEDIUM_EDITION 54