TECHNICAL REPORT
IGE–351
A Description of the DRAGON and TRIVAC Version5 Data
Structures
A. Hébert, G. Marleau and R. Roy
Institut de génie nucléaire
Département de génie mécanique
École Polytechnique de Montréal
March 24, 2017
IGE–351
ii
Contents
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Contents of a /macrolib/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1
State vector content for the /macrolib/ data structure . . . . . . . . . . . . .
1.2
The main /macrolib/ directory . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3
The group sub-directory GROUP in /macrolib/ . . . . . . . . . . . . . . . . . .
1.4
The /ADF/ sub-directory in /macrolib/ . . . . . . . . . . . . . . . . . . . . . .
1.5
The /GFF/ sub-directory in /macrolib/ . . . . . . . . . . . . . . . . . . . . . .
1.6
The /SPH/ sub-directory in /macrolib/ . . . . . . . . . . . . . . . . . . . . . .
1.7
Delayed neutron information . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Contents of a /microlib/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
State vector content for the /microlib/ data structure . . . . . . . . . . . . .
2.2
The main /microlib/ directory . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
State vector content for the depletion sub-directory . . . . . . . . . . . . . . .
2.4
The depletion sub-directory /depletion/ in /microlib/ . . . . . . . . . . . . .
2.5
State vector content for the shiba self-shielding sub-directory . . . . . . . . .
2.6
State vector content for the subgroup self-shielding sub-directory . . . . . . .
2.7
The shiba self-shielding sub-directory /selfshield/ in /microlib/ . . . . . . . .
2.8
The subgroup self-shielding sub-directory /selfshield/ in /microlib/ . . . . . .
2.9
Contents of an /isotope/ directory . . . . . . . . . . . . . . . . . . . . . . . .
2.9.1
The probability table directory PT-PHYS in /isotope/ . . . . . . . .
3
Contents of a /geometry/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
State vector content for the /geometry/ data structure . . . . . . . . . . . . .
3.2
The main /geometry/ directory . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
The /BIHET/ sub-directory in /geometry/ . . . . . . . . . . . . . . . . . . . .
4
Contents of a /tracking/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1
State vector content for the /tracking/ data structure . . . . . . . . . . . . .
4.2
The main /tracking/ directory . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
The sybilt dependent records and sub-directories on a /tracking/ directory
4.3.1
The /PURE-GEOM/ sub-directory in sybilt . . . . . . . . . . . . . .
4.3.2
The /DOITYOURSELF/ sub-directory in sybilt . . . . . . . . . . . .
4.3.3
The /EURYDICE/ sub-directory in sybilt . . . . . . . . . . . . . . .
4.4
The excelt dependent records on a /tracking/ directory . . . . . . . . . . . .
4.5
The mccgt dependent records on a /tracking/ directory . . . . . . . . . . . .
4.6
The snt dependent records on a /tracking/ directory . . . . . . . . . . . . . .
4.7
The bivact dependent records on a /tracking/ directory . . . . . . . . . . . .
4.8
The trivat dependent records on a /tracking/ directory . . . . . . . . . . . .
4.9
The /BIHET/ sub-directory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Contents of a /asminfo/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1
State vector content for the /asminfo/ data structure . . . . . . . . . . . . .
5.2
The main /asminfo/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3
The GROUP double-heterogeneity group sub-directory . . . . . . . . . . . . . .
5.4
The GROUP or BIHET group sub-directory . . . . . . . . . . . . . . . . . . . . .
5.4.1
The trafict dependent records on a GROUP directory . . . . . . . .
5.4.2
The sybilt dependent records on a GROUP directory . . . . . . . . .
5.4.3
The mccgt dependent records on a GROUP directory . . . . . . . . .
6
Contents of a /system/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1
State vector content for the /system/ data structure . . . . . . . . . . . . . .
6.2
The main /system/ directory . . . . . . . . . . . . . . . . . . . . . . . . . . .
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IGE–351
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Contents of a /kinet/ directory . . . . . . . . . . . . . . . . . . . . . .
7.1
State vector content for the /kinet/ data structure . . . . . . .
7.2
The main /kinet/ directory . . . . . . . . . . . . . . . . . . . .
Contents of a /fluxunk/ directory . . . . . . . . . . . . . . . . . . . .
8.1
State vector content for the /fluxunk/ data structure . . . . . .
8.2
The main /fluxunk/ directory . . . . . . . . . . . . . . . . . . .
8.3
The harmonic mode sub-directories in /fluxunk/ . . . . . . . .
Contents of a /gptsour/ directory . . . . . . . . . . . . . . . . . . . .
9.1
State vector content for the /gptsour/ data structure . . . . . .
9.2
The main /gptsour/ directory . . . . . . . . . . . . . . . . . . .
Contents of a /edition/ directory . . . . . . . . . . . . . . . . . . . . .
10.1 State vector content for the /edition/ data structure . . . . . .
10.2 The main /edition/ directory . . . . . . . . . . . . . . . . . . .
10.3 The /REF:ADF/ sub-directory in /edition/ . . . . . . . . . . . .
Contents of a /burnup/ directory . . . . . . . . . . . . . . . . . . . .
11.1 State vector content for the /burnup/ data structure . . . . . .
11.2 The main /burnup/ directory . . . . . . . . . . . . . . . . . . .
11.3 The depletion sub-directory /depldir/ in /burnup/ . . . . . . .
Contents of a /multicompo/ directory . . . . . . . . . . . . . . . . . .
12.1 State vector content for the /multicompo/ data structure . . .
12.2 The main /multicompo/ directory . . . . . . . . . . . . . . . .
12.3 The GLOBAL sub-directory in /multicompo/ . . . . . . . . . . .
12.4 The LOCAL sub-directory in /multicompo/ . . . . . . . . . . . .
12.5 The homogenized mixture sub-directory in /multicompo/ . . .
12.6 The TREE sub-directory in a MIXTURES component . . . . . . .
Contents of a /CPO/ directory . . . . . . . . . . . . . . . . . . . . . .
13.1 The main directory . . . . . . . . . . . . . . . . . . . . . . . . .
13.2 The mixture sub-directory . . . . . . . . . . . . . . . . . . . . .
13.3 The burnup sub-directory . . . . . . . . . . . . . . . . . . . . .
Contents of a /saphyb/ directory . . . . . . . . . . . . . . . . . . . . .
14.1 The main /saphyb/ directory . . . . . . . . . . . . . . . . . . .
14.2 The constphysiq sub-directory in /saphyb/ . . . . . . . . . .
14.3 The contenu sub-directory in /saphyb/ . . . . . . . . . . . . .
14.4 The adresses sub-directory in /saphyb/ . . . . . . . . . . . .
14.5 The geom sub-directory in /saphyb/ . . . . . . . . . . . . . . .
14.6 The paramdescrip sub-directory in /saphyb/ . . . . . . . . . .
14.7 The paramvaleurs sub-directory in /saphyb/ . . . . . . . . . .
14.8 The paramarbre sub-directory in /saphyb/ . . . . . . . . . . .
14.9 The varlocdescri sub-directory in /saphyb/ . . . . . . . . . .
14.10 The elementary calculation sub-directory /caldir/ in /saphyb/
14.10.1 The info sub-directory in /caldir/ . . . . . . . . . . .
14.10.2 The divers sub-directory in /caldir/ . . . . . . . . .
14.10.3 The mixture sub-directory /mixdir/ in /caldir/ . . . .
14.10.4 The cinetique sub-directory in /mixdir/ . . . . . . .
Contents of a /mc/ Directory . . . . . . . . . . . . . . . . . . . . . . .
15.1 State vector content for the /mc/ data structure . . . . . . . .
15.2 The main /mc/ directory . . . . . . . . . . . . . . . . . . . . .
Contents of a /draglib/ directory . . . . . . . . . . . . . . . . . . . . .
16.1 The main /draglib/ directory . . . . . . . . . . . . . . . . . . .
16.2 Contents of an /isotope/ directory . . . . . . . . . . . . . . . .
Contents of a /fview/ data structure . . . . . . . . . . . . . . . . . . .
17.1 The state-vector content . . . . . . . . . . . . . . . . . . . . . .
17.2 The main /fview/ directory . . . . . . . . . . . . . . . . . . . .
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IGE–351
iv
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
IGE–351
v
List of Tables
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
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19
20
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41
42
43
44
45
46
47
48
49
50
Main records and sub-directories in /macrolib/ . . . . . . . . . . .
Vectorial cross section records and directories in GROUP . . . . . . .
Example of delayed–neutron records in GROUP . . . . . . . . . . . .
Additional cross section records . . . . . . . . . . . . . . . . . . . .
Scattering cross section records in GROUP . . . . . . . . . . . . . . .
Records in the /ADF/ sub-directory . . . . . . . . . . . . . . . . . .
Records in the /GFF/ sub-directory . . . . . . . . . . . . . . . . . .
Records in the /SPH/ sub-directory . . . . . . . . . . . . . . . . . .
Main records and sub-directories in /microlib/ . . . . . . . . . . .
Examples of isotopes directory in a /microlib/ . . . . . . . . . . .
Main records and sub-directories in /depletion/ . . . . . . . . . . .
Main records and sub-directories in /selfshield/ . . . . . . . . . . .
Main records and sub-directories in /selfshield/ . . . . . . . . . . .
Isotopic cross section identifier records . . . . . . . . . . . . . . . .
Delayed neutron reaction records . . . . . . . . . . . . . . . . . . .
Example of delayed–neutron records in /isotope/ . . . . . . . . . .
Depletion-related information . . . . . . . . . . . . . . . . . . . . .
Example of isotopic vector reaction records . . . . . . . . . . . . .
Additional total cross section records for I = 2 . . . . . . . . . . .
Optional scattering records . . . . . . . . . . . . . . . . . . . . . .
Example of cross section records . . . . . . . . . . . . . . . . . . .
Physical probability tables . . . . . . . . . . . . . . . . . . . . . . .
Group-dependent probability table directories . . . . . . . . . . . .
Main records and sub-directories in /geometry/ . . . . . . . . . . .
Cylindrical correction related records in /geometry/ . . . . . . . .
Cell sub-geometry directory . . . . . . . . . . . . . . . . . . . . . .
Cluster sub-geometry directory . . . . . . . . . . . . . . . . . . . .
Records in the /BIHET/ sub-directory . . . . . . . . . . . . . . . .
Main records and sub-directories in /tracking/ . . . . . . . . . . .
The sybilt records and sub-directories in /tracking/ . . . . . . . .
The contents of the sybilt /PURE-GEOM/ sub-directory . . . . . .
The contents of the sybilt /DOITYOURSELF/ sub-directory . . . .
The contents of the sybilt /EURYDICE/ sub-directory . . . . . . .
The EXCELT: records in /tracking/ . . . . . . . . . . . . . . . . . .
Global geometry records in /NXTRecords/ . . . . . . . . . . . . . .
Cell i = 1 records in /NXTRecords/ . . . . . . . . . . . . . . . . . .
Pin i = 1 records in /NXTRecords/ . . . . . . . . . . . . . . . . . .
Global geometry records in /NXTRecords/ . . . . . . . . . . . . . .
The MCCGT: records in /tracking/ . . . . . . . . . . . . . . . . . . .
The MCCGT: records in /PROJECTION/ . . . . . . . . . . . . . . . .
The snt records in /tracking/ . . . . . . . . . . . . . . . . . . . . .
The snt records in /tracking/ (Cartesian 1-D geometry) . . . . . .
The snt records in /tracking/ (tube 1-D geometry) . . . . . . . . .
The snt records in /tracking/ (spherical 1-D geometry) . . . . . .
The snt records in /tracking/ (Cartesian 2-D and R-Z geometries)
The snt records in /tracking/ (Cartesian 3-D geometry) . . . . . .
The bivact records in /tracking/ . . . . . . . . . . . . . . . . . . .
Description of the /BIVCOL/ sub-directory . . . . . . . . . . . . . .
The trivat records in /tracking/ . . . . . . . . . . . . . . . . . . .
The trivat records in /tracking/ (contd.) . . . . . . . . . . . . . .
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2
4
5
5
7
8
9
10
18
20
21
25
25
25
26
27
27
28
29
31
32
34
34
38
41
43
44
44
46
48
48
50
51
55
56
60
63
65
68
69
71
72
72
73
73
74
76
77
81
82
IGE–351
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
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89
90
91
92
93
94
95
96
97
98
99
100
101
102
The trivat records in /tracking/ (contd.) . . . . . . .
The trivat records in /tracking/ (contd.) . . . . . . .
The contents of the /BIHET/ sub-directory . . . . . . .
Main records and sub-directories in /asminfo/ . . . . .
Records and sub-directories in GROUP . . . . . . . . . .
Records and sub-directories in GROUP . . . . . . . . . .
Collision probability records in GROUP . . . . . . . . .
SYBIL groupwise assembly information in GROUP . . .
MCCG groupwise directories . . . . . . . . . . . . . .
Main records and sub-directories in /system/ . . . . .
Main records and sub-directories in /kinet/ . . . . . .
Main records and sub-directories in /fluxunk/ . . . . .
Component of the harmonic mode directory . . . . . .
Main records and sub-directories in /gptsour/ . . . . .
Main records and sub-directories in /edition/ . . . . .
Example of an editing directory . . . . . . . . . . . . .
Records in the /REF:ADF/ sub-directory . . . . . . . .
Main records and sub-directories in /burnup/ . . . . .
Example of depletion directories . . . . . . . . . . . .
Contents of a depletion sub-directory in /burnup/ . .
Main records in /multicompo/ . . . . . . . . . . . . .
Main records and sub-directories in {/namdir/} . . . .
Contents of sub-directory GLOBAL in /multicompo/ . .
Contents of sub-directory LOCAL in /multicompo/ . . .
Component of the homogenized mixture directory . .
Contents of sub-directory TREE in MIXTURES . . . . . .
Main records and sub-directories in /CPO/ . . . . . .
Example of homogeneous mixture directories . . . . .
Contents of a mixture sub-directory in /CPO/ . . . .
Example of homogeneous mixture directories . . . . .
Contents of a burnup sub-directory in /CPO/ . . . . .
Main records and sub-directories in /saphyb/ . . . . .
Contents of sub-directory constphysiq in /saphyb/ .
Contents of sub-directory contenu in /saphyb/ . . . .
Contents of sub-directory adresses in /saphyb/ . . .
Contents of sub-directory geom in /saphyb/ . . . . . .
Contents of sub-directory outgeom in /geom/ . . . . .
Contents of sub-directory paramdescrip in /saphyb/ .
Contents of sub-directory paramvaleurs in /saphyb/ .
Contents of sub-directory paramarbre in /saphyb/ . .
Contents of sub-directory varlocdescri in /saphyb/ .
Contents of sub-directory /caldir/ in /saphyb/ . . . .
Contents of sub-directory info in /caldir/ . . . . . . .
Contents of sub-directory divers in /caldir/ . . . . .
Contents of sub-directory outflx in /caldir/ . . . . .
Contents of mixture sub-directory /mixdir/ in /caldir/
Contents of sub-directory cinetique in /mixdir/ . . .
Main records and sub-directories in /mc/ . . . . . . .
Main records and sub-directories in /draglib/ . . . . .
Temperature-dependent isotopic records . . . . . . . .
Temperature-dependent isotopic records . . . . . . . .
Records and sub-directories in /fview/ data structure
vi
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82
83
84
86
87
88
89
90
91
93
97
100
102
103
105
107
107
109
110
111
114
114
115
116
116
116
120
121
121
122
122
124
126
126
127
128
128
128
129
130
132
132
133
134
135
135
137
138
140
141
142
144
IGE–351
vii
List of Figures
1
2
3
4
5
6
7
Numbering of scattering elements in ’SCAT’ matrices. . . . . . . . . . . . . . . .
Cylindrical correction in Cartesian geometry . . . . . . . . . . . . . . . . . . . . .
Example of an assembly of hexagons (left) and external faces identification for an
Example of a 5 energy group matrix eigenvalue problem . . . . . . . . . . . . . .
Representation of a multicompo object. . . . . . . . . . . . . . . . . . . . . . .
Parameter tree in a multicompo object . . . . . . . . . . . . . . . . . . . . . . .
Global parameter tree in a saphyb object . . . . . . . . . . . . . . . . . . . . . .
. . . . .
6
. . . . . 41
hexagon 59
. . . . . 93
. . . . . 112
. . . . . 112
. . . . . 123
IGE–351
1
1 Contents of a /macrolib/ directory
A /macrolib/ directory always contains the set of macroscopic multigroup cross sections associated
with a set of mixtures. The structure of this directory, is quite different to that associated with an
/isotope/ directory (see Section 2.9). First, it is multi-level, namely, it contains sub-directories. Moreover
instead of having one directory per mixture which contains the associated multigroup cross section, one
will have one directory component per group containing multi-mixture information. Finally its contents
will vary depending on the operator which was used to create it. Here for convenience we will define the
variable M to identify the creation operator:
0 if the directory is created by the MAC: operator
1 if the directory is created by the LIB: or EVO: operator
M=
2 if the directory is created by the EDI: operator
3 if the directory is created by the OUT: or NCR: operator
In the case where the LIB: or EDI: operator is used to create this directory, it is embedded as a
subdirectory in a /microlib/ or an /edition/ directory. For the other cases, it appears on the root level
of the macrolib data structure.
1.1
State vector content for the /macrolib/ data structure
The dimensioning parameters for the /macrolib/ data structure, which are stored in the state vector
S M , represent:
• The number of energy groups G = S1M
• The number of mixtures Nm = S2M
• The order for the scattering anisotropy L = S3M (L = 1 is an isotropic collision; L = 2 is a linearly
anisotropic collision, etc.)
• The maximum number of fissile isotopes in a mixture Nf = S4M
• The number of additional φ–weighted editing cross sections Ne = S5M
• The transport correction option Itr = S6M
0 do not use a transport correction
1 use an APOLLO-type transport correction (micro-reversibility at all energies)
Itr =
2 recover a transport correction from the cross-section library
4 use a leakage correction based on NTOT1 data.
• The number of precursor groups for delayed neutron Nd = S7M
• The number of physical albedo NA = S8M
• The type of leakage Il = S9M
0 no diffusion/leakage coefficient available
Il =
1 isotropic diffusion/leakage coefficient available
2 anisotropic diffusion/leakage coefficient available.
M
• The maximum Legendre order of the weighting functions Iw = S10
0 use the flux as weighting function for all cross sections
1 use the fundamental current J as weighting function for scattering cross sections with
Iw =
order ≥ 1 and compute both φ– and J –weighted total cross sections.
IGE–351
2
M
• The number of delta cross section sets Istep = S11
used for generalized perturbation theory (GPT)
or kinetics calculations:
0
no delta cross section sets
Istep =
> 0 number of delta cross section sets.
M
• Discontinuity factor flag Idf = S12
:
Idf
0 no discontinuity factor information
=
1 ALBS-type information is available
2 discontinuity factor information (see Section 1.4) is available
M
• Adjoint macrolib flag Iadj = S13
:
Iadj =
0 direct macrolib
1 adjoint macrolib.
M
• SPH-information Isph = S14
:
Isph =
0
1
no SPH information available
SPH information is available.
M
• Type of weighting in EDI: module Ipro = S15
:
Ipro =
0
1
use a flux weighting
use an adjoint–direct (a.k.a., product) flux weighting. Only available if M ≥ 2
M
• Group form factor index Igff = S16
:
Igff =
1.2
0
>0
no group form factor information
number of form factors per mixture and per energy group (see Section 1.5).
The main /macrolib/ directory
The following records and sub-directories will be found on the first level of a /macrolib/ directory:
Table 1: Main records and sub-directories in /macrolib/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
ADDXSNAME-P0
C(Ne ) ∗ 8
Condition
Ne ≥ 1
Units Comment
Signature of the /macrolib/ data structure
(SIGNA =L MACROLIB ).
Vector describing the various parameters associated
with this data structure SiM , as defined in Section 1.1.
Names of the additional φ–weighted editing cross sections (ADDXSk ). These names should not appear in
Tables 2 and 5.
continued on next page
IGE–351
3
Main records and sub-directories in /macrolib/
continued from last page
Name
Type
Condition
Units Comment
FISSIONINDEX
I(Nm , Nf )
Nf ≥ 1, M = 1
ENERGY
DELTAU
ALBEDO
R(G + 1)
R(G)
R(NA )
M≥1
M≥1
NA > 0
VOLUME
FLUXDISAFACT
R(Nm )
R(G)
M≥2
M=2
cm3
LAMBDA-D
R(Nd , Nf )
Nd ≥ 1
s−1
BETA-D
R(Nd , Nf )
Nd ≥ 1
K-EFFECTIVE
K-INFINITY
DIFFB1HOM
B2 B1HOM
B2 HETE
TIMESTAMP
R(1)
R(1)
R(G)
R(1)
R(3)
R(3)
Nf ≥ 1
Nf ≥ 1
M = 2, Il ≥ 1
Il ≥ 1
Il = 2
M=1
GROUP
Dir(G)
STEP
Dir(Istep )
Istep ≥ 1
ADF
GFF
Dir
Dir
Idf ≥ 1
Igff ≥ 1
SPH
Dir
Isph = 1
eV
cm3
cm
cm−2
cm−2
For each mixture i contains the index of each fissile isotope j. The index is pointing to a component
of record ISOTOPESUSED or ISOTOPERNAME of /microlib/.
Energy group limits Eg
Lethargy width of each group Ug
Surface ordered and energy independent physical
albedo βp,j
Volume of region containing this mixture Vm
Ratio of the flux in the fuel to the flux in the cell Fg
after homogenization
Radioactive decay constants of each delayed neutron
precursor group, for each fissile isotope.
Delayed-neutron fraction for each delayed neutron
precursor group, for each fissile isotope.
Effective multiplication constant keff
Infinite multiplication constant k∞
Homogeneous leakage/diffusion coefficient Dg
Homogeneous Buckling Bhom
Directional Buckling Bj
A vector Tj containing three elements. The first element T1 = t is the time in days, the second element
T2 = B is the burnup in MW day T−1 and the third
element T3 = w is the irradiation in Kb−1
List of energy-group sub-directories. Each component of the list is a directory containing the reference macroscopic cross-section information associated with a specific group.
List of GPT or kinetics perturbation sub-directories.
Each component of this list contains a single list
of energy-group sub-directories following the GROUP
specification. This GROUP list contains variations or
derivatives of the reference cross-section set.
ADF–related information as presented in Section 1.4.
Group form factor information as presented in Section 1.5.
SPH–related input data as presented in Section 1.6.
IGE–351
1.3
4
The group sub-directory GROUP in /macrolib/
Each component of the list GROUP is a directory containing cross-section information corresponding
to a single energy group. Inside each groupwise directory, the following records associated with vectorial
cross sections will be found:
Table 2: Vectorial cross section records and directories in GROUP
Name
Type
Condition
Units
NTOT0
NTOT1
TRANC
FIXE
NUSIGF
R(Nm )
R(Nm )
R(Nm )
R(Nm )
R(Nm , Nf )
Nf ≥ 1
CHI
R(Nm , Nf )
Nf ≥ 1
{nusid}
R(Nm , Nf )
Nd ≥ 1
{chid}
R(Nm , Nf )
Nd ≥ 1
FLUX-INTG
FLUX-INTG-P1
R(Nm )
R(Nm )
M≥2
M ≥ 2; Iw ≥ 1
NWAT0
R(Nm )
Ipro = 1
NWAT1
R(Nm )
Iw ≥ 1; Ipro = 1
OVERV
R(Nm )
DIFF
DIFFX
DIFFY
DIFFZ
NSPH
R(Nm )
R(Nm )
R(Nm )
R(Nm )
R(Nm )
M = 2;
M = 2;
M = 2;
M = 2;
M=2
H-FACTOR
R(Nm )
M=2
{/xsname/}
R(Nm )
Ne ≥ 1
M = 2; Iw ≥ 1
Itr = 2
Il
Il
Il
Il
=1
=2
=2
=2
Comment
cm−1
The φ–weighted total cross section Σg0,m
−1
cm
The J –weighted total cross section Σg1,m
−1
cm
The transport correction Σgtc,m
−3 −1
g
cm s Fixed sources Sm
.
−1
cm
The product of Σgf,m , the fission cross section
ss,g
with νm
, the steady-state number of neutron
produced per fission, νΣgf,m
The steady-state energy spectrum of the neutron emitted by fission χss,g
m
cm−1
The product of Σgf,m , the fission cross secD,g
tion with νm,ℓ
, the averaged number of fission–
emitted delayed neutron produced in the precursor group ℓ, νΣD,g
f,m,ℓ
The energy spectrum of the fission–emitted
delayed neutron in the precursor group ℓ, χD,g
m,ℓ
cm s−1 The volume-integrated flux Φgm
cm s−1 The volume-integrated fundamental current
g
Jm
1
The multigroup neutron adjoint flux spectrum
φ∗g
m
1
The multigroup fundamental adjoint current
∗g
spectrum Jm
−1
cm s The average of the inverse neutron velocity
< 1/v >gm
g
cm
The isotropic diffusion coefficient Dm
g
cm
The x-directed diffusion coefficient Dx,m
g
cm
The y-directed diffusion coefficient Dy,m
g
cm
The z-directed diffusion coefficient Dz,m
1
SPH equivalence factors µgm . By default, these
factors are set equal to 1.0. Otherwise, all
the cross sections, diffusion coefficients and integrated fluxes stored on the macrolib are
SPH–corrected.
g
J cm−1 Energy production coefficients Hm
(product of
each macroscopic cross section times the energy emitted by this reaction).
cm−1
Set of cross section records specified by
ADDXSk
IGE–351
5
The set of delayed neutron records {nusid} and {chid} will be composed, using the following FORTRAN instructions, as NUSID and CHID, respectively
WRITE(NUSID,′ (A6, I2.2)′ ) ′ NUSIGF′, ell
WRITE(CHID,′ (A3, I2.2)′ ) ′ CHI′ , ell
for 1 ≤ ell ≤ Nd . For example, in the case where two group cross sections are considered (Nd = 2), the
following records would be generated:
Table 3: Example of delayed–neutron records in GROUP
Name
Type
Condition
Units Comment
NUSIGF01
R(Nm , Nf )
Nd ≥ 1
cm−1 The product of Σgf,m , the fission cross section with
CHI01
R(Nm , Nf )
Nd ≥ 1
NUSIGF02
R(Nm , Nf )
Nd ≥ 2
CHI02
R(Nm , Nf )
Nd ≥ 2
cm−1
D,g
νm,1
, the averaged number of fission–emitted delayed
neutron produced in the precursor group ℓ = 1,
νΣD,g
f,m,1
The energy spectrum of the fission–emitted delayed
neutron in the precursor group ℓ = 1, χD,g
m,1
The product of Σgf,m , the fission cross section with
D,g
νm,2
, the averaged number of fission–emitted delayed
neutron produced in the precursor group ℓ = 2,
νΣD,g
f,m,2
The energy spectrum of the fission–emitted delayed
neutron in the precursor group ℓ = 2, χD,g
m,2
In the case where Ne = 3 and
for k = 1
NG
N2N
for k = 2
ADDXSk =
NFTOT for k = 3
the following reactions will be available in the data structure described in Table 2:
Table 4: Additional cross section records
Name
Type
NG
N2N
NFTOT
Condition
Units
Comment
R(Nm )
R(Nm )
cm−1
cm−1
The neutron capture cross section Σgc,m
The cross section Σg(n,2n),m for the reaction
R(Nm )
−1
cm
+ n →A−1
X + 2n
Z
The neutron fission cross section Σgf,m
A
ZX
IGE–351
6
The information associated with the multigroup scattering matrix, which gives the probability for a
neutron in group h to appear in group g after a collision with an isotope in mixture m is represented by
the form:
h→g ~
~ ′) =
Σs,m
(Ω → Ω
L
X
2l + 1
4π
l=0
~ ·Ω
~ ′ )Σh→g =
Pl (Ω
l,m
L X
l
X
~ lm (Ω
~ ′ )Σh→g
Ylm (Ω)Y
l,m
l=0 m=−l
using a series expansion to order L in spherical harmonic. Assuming that the spherical harmonic are
h→g ~
~′
orthonormalized, we can define Σh→g
l,m in terms of Σs,m (Ω → Ω ) using the following integral:
Z
~
~′
~ ~′
Σh→g
=
d2 Ω Σh→g
s,m (Ω → Ω )Pl (Ω · Ω )
l,m
4π
Note that this definition of Σh→g
l,m is not unique and some authors include the factor 2l + 1 directly in the
different angular moments of the scattering cross section.
Here instead of storing the G × M matrix Σh→g
l,m associated with each final energy group g, a vector
which contains a compress form of the scattering matrix will be considered. We will first define three
integer vectors ngl,m , hgl,m and pgl,m for order l in the scattering cross section, final energy group g and
mixture m. They will contain respectively the number of initial energy groups h for which the scattering
cross section to group g does not vanish, the maximum energy group index for which scattering to the
final group g does not vanishes and the position in the compressed scattering vector where the data
associated with mixture m for each energy group g can be found. Here pgl,m is directly related to ngl,m by
pgl,m
=1+
m−1
X
ngl,k
13
47 46 45
43 42 41
39 38 37 36 35 34 33
32 31 30 29 28 27
26 25 24 23
22 21 20 19 18
44
12
11
10
40
9
8
7
6
5
4
9
3
2
6
3
1
1
thermal groups
secondary group
k=1
17 16
15 14 13 12
11 10
8
7
5
2
4
1
2
3
4
5
6
7
8
IJJ:
1
2
3
4
5
6
7
10 11 13
NJJ:
1
2
3
3
2
4
2
5
9
4
10 11 12 13
primary group
6
12 12 13
8
4
3
Figure 1: Numbering of scattering elements in ’SCAT’ matrices.
Now consider the following 4 groups isotropic scattering cross section matrix associated with mixture
1 and 2 (Nm = 2) respectively:
IGE–351
7
h→g
σ0,m
Mixture m = 1
g=1 g=2 g=3
h=1
h=2
h=3
h=4
hg0,m
ng0,m
pg0,m
a1
0
0
0
1
1
1
a2
a3
a6
a8
4
4
1
g=4
0
a4
a7
0
3
2
1
0
a5
0
a9
4
3
1
Mixture m = 2
g=1 g=2 g=3
b1
b3
0
0
2
2
2
b2
b4
b6
0
3
3
5
0
b5
b7
b8
4
3
3
g=4
0
0
0
b9
4
1
4
The compressed scattering matrix will then take the following form for each final group g:
Σ10,k,c
= (a1 , b3 , b1 )
Σ20,k,c
Σ30,k,c
Σ40,k,c
= (a8 , a6 , a3 , a2 , b6 , b4 , b2 )
= (a7 , a4 , b8 , b7 , b5 )
= (a9 , 0, a5 , b9 )
Finally, we will also save the total scattering cross section vector of order l which is defined as
Σgl,m,s =
G
X
Σg→h
l,m
h=1
and the diagonal element of the scattering matrix:
Σgl,m,w = Σg→g
l,m
In the case where only the order l = 0 and l = 1 moment of scattering cross section are non vanishing
(isotropic and linearly anisotropic scattering) the following records can be found on the group directory.
Table 5: Scattering cross section records in GROUP
Name
Type
SIGS00
Condition
Units
Comment
R(Nm )
cm−1
SIGW00
R(Nm )
cm−1
IJJS00
I(Nm )
NJJS00
I(Nm )
IPOS00
I(Nm )
SCAT00
PNm g
R( m=1
n0,m )
The isotropic component (l = 0) of the total
scattering cross section Σg0,m,s
The isotropic component (l = 0) of the within
group scattering cross section Σg0,m,w
Highest energy group number for which the
isotropic component of the scattering cross
section to group g does not vanish, hg0,m
Number of energy groups for which the
isotropic component of the scattering cross
section to group g does not vanish, ng0,m
Location in the isotropic compressed scattering matrix where information associated with
mixture m begins pg0,m
Compressed isotropic component of the scattering matrix Σg0,k,c
cm−1
continued on next page
IGE–351
8
Scattering cross section records in GROUP
continued from last page
Name
Type
Condition
Units
Comment
SIGS01
R(Nm )
L≥1
cm−1
SIGW01
R(Nm )
L≥1
cm−1
IJJS01
I(Nm )
L≥1
NJJS01
I(Nm )
L≥1
IPOS01
I(Nm )
L≥1
SCAT01
PNm g
R( m=1
n1,m )
L≥1
The linearly anisotropic component of the total scattering cross section Σg1,m,s
The linearly anisotropic component of the
within group scattering cross section Σg1,m,w
Highest energy group number for which the
linearly anisotropic component of the scattering cross section to group g does not vanish,
hg1,m
Number of energy groups for which the linearly anisotropic component of the scattering
cross section to group g does not vanish, ng1,m
Location in the linearly anisotropic compressed scattering matrix where information
associated with mixture m begins pg1,m
Compressed linearly anisotropic component of
the scattering matrix Σg1,k,c
1.4
cm−1
The /ADF/ sub-directory in /macrolib/
Sub-directory containing ADF-type boundary flux edition information. This information can be
used to compute discontinuity factors or to perform Selengut-type normalization with the superhomogénéisation (SPH) method.
Table 6: Records in the /ADF/ sub-directory
Name
Type
Condition
NTYPE
HADF
I(1)
C(NTYPE)∗8
Idf = 2
Idf = 2
ALBS00
R(Nm , G)
Idf = 1
{/type/}
R(Nm , G)
Idf = 2
Units
Comment
Number of ADF-type boundary flux edits.
Name of each ADF-type boundary flux edit. Any
name can be used, but some names are standard.
Standard names are: = FD C: corner flux edition;
= FD B: surface (assembly gap) flux edition; =
FD H: row flux edition (these are the first row of
surrounding cells in the assembly).
averaged fluxes surrounding the geometry. These
values correspond to surfaces where a VOID
boundary condition was replaced by a REFL
boundary condition in DRAGON.
Averaged fluxes in boundary regions. Name type
is a component of HADF array.
IGE–351
1.5
9
The /GFF/ sub-directory in /macrolib/
Sub-directory containing group form factor information. This information can be used to perform
fine power reconstruction over a fuel assembly.
Table 7: Records in the /GFF/ sub-directory
Name
Type
GFF-GEOM
Dir
VOLUME
NWT0
H-FACTOR
R(Nm , Igff )
R(Nm , Igff , G)
R(Nm , Igff , G)
FINF NUMBER
I(Nifx )
{/FINF/}
R(Nm , Igff , G)
Condition
Units
Comment
Macro–geometry directory. This geometry corresponds to an unfolded fuel assembly and is compatible for a discretization with TRIVAC. This directory follows the specification presented in Section 3.2.
cm3
Volumes of homogenized cells Vm
s−1 cm−2 The multigroup neutron flux spectrum φgw
g
J cm−1 Energy production coefficients Hm
(product of
each macroscopic cross section times the energy
emitted by this reaction).
Array containing the Nifx if x indices used by the
user every time the multicompo were “enriched”
with different options.
s−1 cm−2 The diffusion multigroup neutron flux spectrum
d,∞
in an infinite domain ψm,p
. See NAP: module description in IGE344 user guide for details.
The set of diffusion multigroup neutron flux spectrum records {/FINF/} will be composed, using the
following FORTRAN instructions as HVECT,
WRITE(HVECT,′ (5HFINF , I3.3)′ ) ′ ifx′
where ifx is a value chosen by the user (default value is 0). A different value can be chosen every time the
multicompo are “enriched” with different options (homogeneous/heterogeneous, tracking options, etc.).
IGE–351
1.6
10
The /SPH/ sub-directory in /macrolib/
The first level of the macrolib directory may contains a superhomogénéisation (SPH) sub-directory
/SPH/ containing input data:
Table 8: Records in the /SPH/ sub-directory
Name
Type
STATE-VECTOR
I(40)
SPH$TRK
SPH-EPSILON
C∗12
R(1)
Condition
S1sph ≥ 2
S1sph ≥ 2
Units
1
Comment
Vector describing the various parameters associated with this data structure Sisph .
Name of the flux solution door.
Convergence criterion for stopping the SPH iterations.
The dimensioning parameters for this data structure, which are stored in the state vector S sph ,
represent values related to the last editing step:
• Type of SPH equivalence factors: Itype = S1sph
Itype
0 no SPH correction;
1 the SPH factors are read from LCM;
2 homogeneous macro-calculation (non-iterative procedure or Hébert-Benoist
=
SPH-5 procedure);
3
any
type of Pij macro-calculation;
4 any type of diffusion, Sn , Pn or SPn macro-calculation.
• Type of SPH equivalence normalization Inorm = S2sph
Inorm
<0
1
2
=
3
4
5
asymptotic normalization with respect to homoheneous mixture − Inorm ;
average flux normalization;
Selengut normalization using ALBS00 information;
Selengut normalization using FD B boundary fluxes;
Generalized Selengut normalization (EDF-type);
Selengut normalization with surface leakage.
• The maximum number of SPH iterations S3sph
• The acceptable number of SPH iterations with an increase in convergence error before aborting
S4sph
• Flag for forcing the production of a macrolib or microlib at LHS Ilhs = S5sph
Ilhs
0
1
=
2
3
produce
produce
produce
produce
an object of the type of the RHS;
an edition object;
a microlib;
a macrolib.
IGE–351
11
• Type of SPH factors Iimc = S6sph
Iimc
1 factors compatible with diffusion theory, Pn and SPn equations
=
2 factors compatible with other types of transport-theory macro-calculations
3 factors compatible with Pij macro-calculations and Bell acceleration.
• The first group index where the equivalence process is applied S7sph
• The maximum group index where the equivalence process is applied S8sph
1.7
Delayed neutron information
We will present space-time kinetics equations in the context of the diffusion approximation (i.e. using
the Fick law) and equations used in a lattice code to produce condensed and homogenized information.
These equations will be useful to understand the information written in the macrolib specification.
Similar expressions can be obtained in transport theory. Note that delayed neutron information βℓ
and Λ can also be computed at the scale of the complete reactor provided that bilinear direct–adjoint
condensation and homogenization relations are used.
The continuous-energy space-time diffusion equation is written:
∂
1
φ(~r, E, t)
∂t v(E)
=
X
χpr
j (E)
j
+
XX
j
Z
∞
0
dE ′ νjpr (~r, E ′ , t)Σf,j (~r, E ′ , t)φ(~r, E ′ , t)
χD
r , t) + ∇ · D(~r, E, t)∇φ(~r, E, t)
ℓ,j (E)λℓ cℓ,j (~
ℓ
− Σ(~r, E, t)φ(~r, E, t) +
Z
∞
dE ′ Σs0 (~r, E ← E ′ , t)φ(~r, E ′ , t)
(1.1)
0
together with the set of Nd precursor equations:
Z ∞
∂cℓ,j (~r, t)
D
=
dE νℓ,j
(~r, E, t)Σf,j (~r, E, t)φ(~r, E, t) − λℓ cℓ,j (~r, t) ;
∂t
0
ℓ = 1, Nd
(1.2)
where
φ(~r, E, t)= neutron flux
χpr
j (E)= prompt neutron spectrum for a fission of isotope j
νjpr (~r, E, t)= number of prompt neutrons for a fission of isotope j
Σf,j (~r, E, t)= macroscopic fission cross section for isotope j
χD
ℓ,j (E)= neutron spectra for delayed neutrons emitted by precursor group ℓ due to a fission of isotope j
λℓ = radioactive decay constant for precursor group ℓ. This constant is assumed to be independent of
the fissionable isotope j.
cℓ,j (~r, t)= concentration of the ℓ–th precursor for a fission of isotope j
D(~r, E, t)= diffusion coefficient
Σ(~r, E, t)= macroscopic total cross section
Σs0 (~r, E ← E ′ , t)= macroscopic scattering cross section
D
νℓ,j
(~r, E, t)= number of delayed neutrons in precursor group ℓ for a fission of isotope j.
IGE–351
12
The neutron spectrum are normalized so that
Z ∞
dE χss
j (E) = 1
(1.3)
0
and
∞
Z
0
dE χD
ℓ (E) = 1 ; ℓ = 1, Nd
.
(1.4)
After condensation over energy, Eqs. (1.1) and (1.2) are written
#
"
X
X
X pr,g
∂
1−
βℓ,j
νΣhf,j (~r, t)φh (~r, t)
χj
< 1/v >g
φg (~r, t) =
∂t
j
ℓ
h
X X D,g
+
χℓ,j λℓ cℓ,j (~r, t) + ∇ · Dg (~r, t)∇φg (~r, t)
j
ℓ
g
− Σ (~r, t)φg (~r, t) +
X
Σg←h
r , t)φh (~r, t)
s0 (~
(1.5)
h
together with the set of Nd precursor equations:
X
∂cℓ,j (~r, t)
= βℓ,j
νΣhf,j (~r, t)φh (~r, t) − λℓ cℓ,j (~r, t) ;
∂t
ℓ = 1, Nd
(1.6)
h
where
νΣhf,j (~r, t)= product of the number νjss (~r, E) of secondary neutrons (both prompt and delayed) for a
fission of isotope j times the macroscopic fission cross section for a fission of isotope j.
βℓ,j = delayed neutron fraction in precursor group ℓ.
The following condensation formulas have been used:
X
D
νjss (~r, E) = νjpr (~r, E) +
νℓ,j
(~r, E)
(1.7)
ℓ
R∞
D
dE νℓ,j
(~r, E)Σf,j (~r, E)φ(~r, E)
βℓ,j = 0R∞
0
"
1−
R∞
#
βℓ,j = 0R∞
X
ℓ
φg (~r) =
dE νjss (~r, E)Σf,j (~r, E)φ(~r, E)
0
Z
νΣD,g
r )φg (~r)
f,ℓ,j (~
= P g
νΣf,j (~r)φg (~r)
P
g
(1.8)
g
dE νjpr (~r, E)Σf,j (~r, E)φ(~r, E)
dE νjss (~r, E)Σf,j (~r, E)φ(~r, E)
νΣpr,g
r )φg (~r)
f,j (~
g
= P g
νΣf,j (~r)φg (~r)
P
(1.9)
g
Eg−1
dE φ(~r, E)
(1.10)
dE χpr
j (E)
(1.11)
Eg
χpr,g
j
=
χD,g
ℓ,j =
Z
Eg−1
Z
Eg−1
Eg
Eg
dE χD
ℓ,j (E) ;
ℓ = 1, Nd
(1.12)
IGE–351
13
1
g
φ (~r)
< 1/v >g =
Σg (~r) =
1
φg (~r)
Z
Z
Eg−1
dE
Eg
1
φ(~r, E)
v(E)
(1.13)
Eg−1
dE Σ(~r, E) φ(~r, E)
(1.14)
Eg
Σg←h
r) =
s0 (~
1
h
φ (~r)
Z
νΣgf,j (~r) =
1
φg (~r)
Z
Eg−1
dE
Z
Eh−1
dE ′ Σs0 (~r, E ← E ′ ) φ(~r, E ′ )
(1.15)
Eh
Eg
Eg−1
dE νjss (~r, E) Σf,j (~r, E) φ(~r, E) .
(1.16)
Eg
where the variable t has been omitted in order to simplify the notation.
A steady-state fission spectrum (taking into account both prompt and delayed neutrons), for a fission
of isotope j, is also required for solving the static neutron diffusion equation:
#
"
X
X
βℓ,j χD
(1.17)
χss
βℓ,j χpr
ℓ,j (E) .
j (E) = 1 −
j (E) +
ℓ
ℓ
The group-integrated steady-state fission spectrum is therefore given as
#
"
X
X
ss,g
+
βℓ,j χD,g
.
χj = 1 −
βℓ,j χpr,g
j
ℓ,j
(1.18)
ℓ
ℓ
The space-time diffusion equation is generally solved by assuming a unique averaged fissionable isotope. In this case, the variable Nf is set to 1 in the macrolib specification and the summations over j
disapears in Eqs. (1.5) and (1.6):
#
"
X
X
∂
βℓ
νΣhf (~r, t)φh (~r, t)
φg (~r, t) = χpr,g 1 −
< 1/v >g
∂t
ℓ
h
X D,g
+
χℓ λℓ cℓ (~r, t) + ∇ · Dg (~r, t)∇φg (~r, t)
ℓ
− Σg (~r, t)φg (~r, t) +
X
Σg←h
r , t)φh (~r, t)
s0 (~
(1.19)
h
together with the set of nd precursor equations:
X g
∂cℓ (~r, t)
= βℓ
νΣf (~r, t)φg (~r, t) − λℓ cℓ (~r, t) ;
∂t
g
ℓ = 1, Nd
(1.20)
Using additional approximations, the new condensation relations are rewritten as
X
X
νjss (~r, E) Σf,j (~r, E)
νΣf,j (~r, E) =
νΣf (~r, E) =
βℓ =
P
βℓ,j
j
R∞
0
P R∞
j 0
dE νjss (~r, E) Σf,j (~r, E) φ(~r, E)
dE
(1.21)
j
j
νjss (~r, E)
Σf,j (~r, E) φ(~r, E)
P
βℓ,j νΣgf,j (~r) φg (~r)
g
j
= PP g
νΣf,j (~r) φg (~r)
P
j
g
,
(1.22)
IGE–351
χpr,g
14
=
=
P
j
P
j
Eg−1
R∞ ′ ss
R
P
dE χpr
dE νj (~r, E ′ ) Σf,j (~r, E ′ ) φ(~r, E ′ )
1 − βℓ,j
j (E)
ℓ
1−
χD,g
ℓ
=
P
j
ER
g−1
P R∞
j 0
dE νjss (~r, E) Σf,j (~r, E) φ(~r, E)
P
βℓ,j χD,g
ℓ,j
j
Eg
βℓ
P R∞
βℓ
PP
j
h
P
h
(1.23)
h
dE χD
ℓ,j (E)
βℓ,j
j 0
=
P h
P
νΣf,j (~r) φh (~r)
1 − βℓ,j χpr,g
j
h
ℓ
PP h
P
νΣf,j (~r) φh (~r)
1 − βℓ
P
j
βℓ
ℓ
ℓ
and
0
Eg
R∞
0
dE ′ νjss (~r, E ′ ) Σf,j (~r, E ′ ) φ(~r, E ′ )
;
ℓ = 1, Nd
dE νjss (~r, E) Σf,j (~r, E) φ(~r, E)
νΣhf,j (~r) φh (~r)
νΣhf,j (~r) φh (~r)
;
ℓ = 1, Nd
.
(1.24)
The above definitions ensure that the group-integrated steady-state fission spectrum is given as
#
"
X
X
ss,g
βℓ χD,g
.
(1.25)
χ
= 1−
βℓ χpr,g +
ℓ
ℓ
ℓ
A mean neutron generation time can also be written as
Λ=
R∞
0
P R∞
j 0
dE
1 φ(~r, E)
v(E)
dE νjss (~r, E) Σf,j (~r, E) φ(~r, E)
< 1/v >g φg (~r)
= PP g
νΣf,j (~r) φg (~r)
P
g
j
g
.
(1.26)
IGE–351
15
2 Contents of a /microlib/ directory
A /microlib/ directory contains the set of multigroup microscopic cross sections associated with a set
of isotopes. It also includes a /macrolib/ directory where the macroscopic cross sections for the mixtures
to which are associated these isotopes are stored (see Section 1). Finally it may contains a /depletion/
directory (see Section 2.4) which is required for burnup calculation and a /selfshield/ directory which is
generated by the SHI: or USS: operator (see Section 2.8). It is therefore multi-level, namely, it contains
sub-directories. Note that the contents of such a directory will vary depending on the operator which was
used to create or modify it. Here for convenience we will define the variable M to identify the creation
operator:
1 if the microlib is created or modified by the LIB: or EVO: operator
2 if the microlib is created or modified by the EDI: or C2M: operator
M=
3 if the microlib is modified by the SHI: or USS: operator
4 if the microlib is part of a compo object and is created by the COMPO: operator
In the case where the LIB: or C2M: operator is used to create the microlib, it appears on the root
level of the data structure. For the other case it is embedded as a subdirectory of a surrounding data
structure.
2.1
State vector content for the /microlib/ data structure
The dimensioning parameters for the /microlib/ data structure, which are stored in the state vector
S m , represent:
• The maximum number of mixtures Mm = S1m
• The number of isotopes NI = S2m
• The number of groups G = S3m
• The order for the scattering anisotropy L = S4m (L = 1 is an isotropic collision; L = 2 is a linearly
anisotropic collision, etc.)
• The transport correction option Itr = S5m
Itr
0 do not use a transport correction
1 use an APOLLO-type transport correction (micro-reversibility at all energies)
2 recover a transport correction from the cross-section library
=
3 use a WIMS-type transport correction (micro-reversibility below 4eV;
1/E current spectrum elsewhere)
4 use a leakage correction based on NTOT1 data.
• Format of the included /macrolib/ Ip = S6m
Ip =
0 for the direct macroscopic cross sections
1 for the adjoint macroscopic cross sections
• Option for removing delayed neutron effects from the /microlib/ It = S7m
1 include the delayed and prompt neutron effect
2 consider only the prompt neutrons. This option is only available with
It =
MATXS–type libraries.
• The number of independent libraries Nlib = S8m
IGE–351
16
• The number of fast groups without self-shielding Ng,f = S9m
Represents the number of fast energy groups to be treated without including resonance effects. It
is automatically determined from the cross-section libraries. This value, which is only used by the
self-shielding operator, can be modified using the keyword GRMAX.
m
• The maximum index of all groups with self-shielding Ng,e = S10
.
In the case of a WIMS–type library, it represents the total number of energy groups above 4.0 eV.
Otherwise, it is automatically determined from the cross-section libraries. This value, is used by
the self-shielding operator and can be modified locally in this operator using the keyword GRMIN.
m
• The number of depleting isotopes Nd = S11
m
• The number of depleting mixtures Nd,f = S12
m
• The number of additional φ–weighted editing cross sections Ne = S13
m
• The number of mixtures Nm = S14
m
• The number of resonant mixtures Nr = S15
m
• The number of energy-dependent fission spectra Gchi = S16
. By default (Gchi = 0), a unique fission
spectrum is used. The theory of multiple fission spectra is presented in Ref. 2.
m
• Option for processing the cross-section libraries Iproc = S17
Iproc =
−1 skip the library processing (i.e., no interpolation).
0
perform an interpolation in temperature and dilution.
1
perform an interpolation in temperature and compute probability
tables based on the tabulation in dilution.
2
perform an interpolation in temperature and build a new temperatureindependent cross-section library in DRAGON format.
3
perform an interpolation in temperature and compute CALENDF–type
mathematical probability tables based on BIN–type cross sections. Do
not compute the slowing-down correlated weight matrices. Option
compatible with the subgroup projection method (SPM).
4
perform an interpolation in temperature and compute CALENDF–type
mathematical probability tables and slowing-down correlated weight
matrices based on BIN–type cross sections. Option compatible with
the Ribon extended method.
5
perform an interpolation in temperature and compute CALENDF–type
mathematical probability tables based on BIN–type cross sections. This
option is similar to the Iproc = 3 procedure. Here, the base points of the
probability tables corresponding to fission and scattering cross sections
and to components of the transfer scattering matrix are also obtained
using the CALENDF approach.
m
• Option for computing the macrolib Imac = S18
Imac
0
1
=
do not build an embedded macrolib.
build an embedded macrolib. Mandatory if the microlib is to be used to
perform micro-depletion.
m
.
• The number of precursor groups producing delayed neutrons Ndel = S19
m
• The number of fissile isotopes producing fission products with PYIELD data Ndfi = S20
(see Table 17).
IGE–351
17
m
• Option for completing the depletion chains with the missing isotopes Icmp = S21
.
Icmp =
0
1
complete
do not complete
m
• The maximum number of isotopes per mixture MI = S22
.
• An integer index (1, 2, 3 or 4) used to set the accuracy of the CALENDF probability tables. The
m
highest the value, the more accurate are the tables. Nipreci = S23
.
m
• Discontinuity factor flag Idf = S24
. This information is available in /macrolib/ directory (see
Section 1).
Idf
0 no discontinuity factor information
1 ALBS-type information is available
=
2 discontinuity factor information (see Section 1.4) is available
IGE–351
2.2
18
The main /microlib/ directory
The following records and sub-directories will be found on the first level of a /microlib/ directory:
Table 9: Main records and sub-directories in /microlib/
Name
Type
Condition
SIGNATURE
C∗12
STATE-VECTOR
I(40)
ENERGY
DELTAU
CHI-ENERGY
R(G + 1)
R(G)
R(Gchi + 1)
Gchi 6= 0
CHI-LIMITS
I(Gchi + 1)
Gchi 6= 0
ISOTOPESLIST
Dir(NI )
ISOTOPESUSED
C(NI ) ∗ 12
ISOTOPERNAME
C(NI ) ∗ 12
M = 1, 3
ISOTOPESMIX
I(NI )
M=
6 4
ISOTOPESDENS
ISOTOPESTEMP
ISOTOPESTODO
R(NI )
R(NI )
I(NI )
ISOTOPESTYPE
I(NI )
ISOTOPESAWR
R(NI )
ISOTOPESVOL
R(NI )
Units
eV
eV
(cm b)−1
K
M = 1, 3
nau
M = 2, 4
cm3
Comment
Signature of the /microlib/ data structure
).
(SIGNA =L LIBRARY
Vector describing the various parameters associated with this data structure Sim , as defined
in Section 2.1.
Energy groups limits Eg
Lethargy width of each group Ug
Echi (g): Group energy limits defining the
energy-dependent fission spectra. By default,
a unique fission spectra is used.
Nchi (g): Group limit indices defining the
energy-dependent fission spectra. By default,
a unique fission spectra is used.
List of isotope directories. Each component
of this list follows the /isotope/ specification
presented in Tables 14 to 20 and is containing the cross section information associated
with a specific isotope. The name of these
isotopes is specified by NALIASi as given in
record ISOTOPESUSED.
Alias name associated with each isotope
NALIASi . The first eight characters of the
name of a macroscopic residual are set to
’*MAC*RES’.
Reference name associated with each isotope
NISOi
Mixture number associated with each isotope
NI
Isotopic density ρi
Isotope temperature Ti
=0: automatic detection of depletion for isotope i; =1: isotope i is forced to be non depleting (keeps its capability to produce energy);
=2: isotope i is at saturation.
Type index associated with each isotope
ITYPi . = 1: the isotope is not fissile and not
a fission product; = 2: fissile isotope; = 3:
fission product.
Ratio of the isotope mass divided by the neutron mass
Volume occupied by isotope Vi
continued on next page
IGE–351
19
Main records and sub-directories in /microlib/
Units
continued from last page
Name
Type
Condition
Comment
ILIBRARYTYPE
C(NI ) ∗ 8
Nlib ≥ 1
ILIBRARYNAME
C(Nlib ) ∗ 64
Nlib ≥ 1
ILIBRARYINDX
I(NI )
Nlib ≥ 1
ISOTOPESCOH
C(NI ) ∗ 8
Nlib ≥ 1
ISOTOPESINC
C(NI ) ∗ 8
Nlib ≥ 1
ISOTOPESNTFG
I(NI )
Nlib ≥ 1
ISOTOPESHIN
C(NI ) ∗ 12
Nlib ≥ 1
ISOTOPESSHI
I(NI )
Nlib ≥ 1
ISOTOPESDSN
R(NI )
Nlib ≥ 1
Iproc = 0
b
ISOTOPESDSB
R(NI )
Nlib ≥ 1
Iproc = 0
Standard dilution cross section for isotope
σdil,i
b
ISOTOPESNIR
I(NI )
Nlib ≥ 1
ISOTOPESGIR
R(NI )
Nlib ≥ 1
1
MIXTURESVOL
ADDXSNAME-P0
R(Mm )
C(Ne ) ∗ 8
M = 2, 4
Ne ≥ 1
cm3
TIMESPER
R(2 × 3)
M=2
K-EFFECTIVE
B2 B1HOM
MACROLIB
R(1)
R(1)
Dir
*
*
Imac = 1
DEPL-CHAIN
Dir
Nd ≥ 1
Livolant-Jeanpierre dilution cross section for
isotope σLJ,i
Use Goldstein-Cohen factor λi in groups with
index ≥ Niir . Use λ = 1 in other groups
Goldstein-Cohen parameter in low-energy resonant groups λi . Set to -998.0 if Iproc = 3, to
-999.0 if Iproc = 4 and to -1000.0 if Iproc = 5.
Volume occupied by each mixture
Names of the additional φ–weighted editing
cross sections ADDXSk stored on /macrolib/
array Tj,i that contains Tj,1 = t, Tj,2 = B and
Tj,3 = w, the lower (j = 1) and upper bounds
(j = 2) for the reference time in days, burnup in MW day T−1 and irradiation in Kb−1
respectively for which the perturbative expansion is valid
Effective multiplication constant keff
Homogeneous Buckling Bhom
directory containing the /macrolib/ associated with this library, following the specification presented in Section 1.2.
directory containing the /depletion/ associated with this library, following the specification presented in Section 2.4.
Library type associated with each isotope
NLTYi
Name associated with each cross-section library
Index of the cross-section library associated
with each isotope 1 ≤ LLIBi ≤ Nlib
Name of coherent scattering type at thermal
energies NCOHi
Name of incoherent scattering type at thermal
energies NINCi
Number of thermal groups involved in coherent or incoherent scattering Gs,i
Name of resonant isotope associated with each
isotope NSHIi
Resonant mixture associated with each isotope IR,i
cm−2
continued on next page
IGE–351
20
Main records and sub-directories in /microlib/
Name
Type
Condition
SHIBA
Dir
M=3
SHIBA SG
Dir
M=3
INDEX
Dir
*
Units
continued from last page
Comment
directory containing the /selfshield/ associated with this library, following the specification presented in Section 2.7. This data is
used by the SHI: operator.
directory containing the /selfshield/ associated with this library, following the specification presented in Section 2.8. This data is
used by the USS: operator.
directory containing indexing or table-ofcontent data for specific library files
One will find in Section 1 the description of a /macrolib/ directory and in Section 2.9 the contents of
an /isotope/ directory. Note that if NI = 2 and
U235 0001
for i = 1
NALIASi =
Pu239 0003 for i = 2
then {/isotope/} will correspond to the following two directories:
Table 10: Examples of isotopes directory in a /microlib/
Name
Type
U235
0001
Dir
Pu239
0003
Dir
2.3
Condition
Units
Comment
Directory where the microscopic cross sections of
235
U are stored. These are self-shielded cross section already interpolated in temperature. They
correspond to the properties of mixture 1
Directory where the microscopic cross sections
of 239 Pu are stored. These are self-shielded
cross section already interpolated in temperature.
They correspond to the properties of mixture 3
State vector content for the depletion sub-directory
The dimensioning parameters for the depletion sub-directory, which are stored in the state vector S d ,
represent:
• The number of depleting isotopes Ndepl = S1d
• The number of direct fissile isotopes (i.e., producing fission products) Ndfi = S2d
• The number of fission fragments Ndfp = S3d . A fission fragment is produced directly by the fission
IGE–351
21
reaction. A fission product is a fission fragment or a daughter isotope produced by decay or neutroninduced reaction.
• The number of heavy isotopes NH = S4d
This number represents the combination of fissile isotopes and the other isotopes produced from
these isotopes by reactions other than fission.
• The number of fission products Nfp = S5d
This number represents the combination of fission fragments and the other daughter isotopes produced by any reaction (decay or neutron induced).
• The number of other isotopes NO = S6d
This number represents the other depleting isotopes which are not produced by fission or by reaction
with fission isotopes or fission products but have a depletion chain.
• The number of stable isotopes NH = S7d
This number represents the non-depleting isotopes producing energy (mainly by radiative capture).
An isotope is considered to be stable if:
– its radioactive decay constant is zero
– the isotope has no father and no daughter
– energy is produced by the isotope.
• The maximum number of depleting reactions, including radioactive decay and neutron-induced
reactions MR = S8d
• The maximum number of parent isotopes leading to the production of an isotope in the depletion
chain MS = S9d
2.4
The depletion sub-directory /depletion/ in /microlib/
The following records and sub-directories will be found on the first level of a /depletion/ directory:
Table 11: Main records and sub-directories in /depletion/
Name
Type
STATE-VECTOR
I(40)
ISOTOPESDEPL
C(Ndepl ) ∗ 12
CHARGEWEIGHT
I(Ndepl )
DEPLETE-IDEN
DEPLETE-REAC
C(MR ) ∗ 8
I(MR × Ndepl)
Condition
Units
Comment
Vector describing the various parameters associated with this data structure Sid , as defined in
Section 2.3.
Reference name of the isotopes NISODi present
in the depletion chain
6-digit (integer number) nuclide identifier with
atomic number Z (2 digits), mass number A (3
digits) and energy state E (0 for ground state, 1
for first excited level, etc.). This identifier is not
defined for pseudo fission products.
Reference name of the depletion reactions
List of identifier for the depletion of an isotope
d
Kr,i
continued on next page
IGE–351
22
Main records and sub-directories in /depletion/
Name
Type
DEPLETE-ENER
Condition
continued from last page
Units
Comment
R(MR × Ndepl)
Mev
DEPLETE-DECA
PRODUCE-REAC
R(Ndepl )
I(MS × Ndepl )
10−8 s−1
PRODUCE-RATE
R(MS × Ndepl )
1
FISSIONYIELD
R(Ndfi × Ndfp )
1
Energy per reaction associated with each depled
tion reaction Rr,i
Radioactive decay constants
List of identifier for the production of an isotope
p
Ks,i
Branching ratio associated with each production
p
reaction Rs,i
Fission yield for each direct fissile isotope to each
fission fragment Yi→j
An isotope NISOi defined in Section 2.2 is considered to be part of the depletion chain only if one can
find a value of 1 ≤ j ≤ Ndepl such that NISOi = NISODj . Some depleting isotopes may be automatically
added to the /microlib/ directory. In this case, the reference name in record ISOTOPERNAME is taken equal
to its reference name in ISOTOPESDEPL and the alias name in record ISOTOPESUSED is taken equal to the
first 8 characters of its reference name in ISOTOPESDEPL, completed by a 4-digit mixture identifier. If the
reference name contains an underscore, the alias name is truncated at the first underscore. For example,
an isotope present in mixture 2 with a reference name equal to D2O 3 P5 is translated into an alias name
equal to D2O
0002.
d
The contents of the variables Kr,i
is used to identify the type of isotope under consideration. For
each isotope i, r will take successively the values 1 to MD depending on the type of reaction NREADr
one wishes to analyze, namely
NREAD1 =DECAY
NREAD2 =NFTOT
NREAD3 =NG
NREAD4 =N2N
NREAD5 =N3N
NREAD6 =N4N
NREAD7 =NA
NREAD8 =NP
NREAD9 =N2A
NREAD10 =NNP
NREAD11 =ND
NREAD12 =NT
isotope may
isotope may
1
A
0 n +Z X →
isotope may
1
A
0 n +Z X →
isotope may
1
A
0 n +Z X →
isotope may
isotope may
isotope may
isotope may
isotope may
isotope may
isotope may
isotope may
undergo radioactive decay
undergo fission or is a fission fragment
A+1−ν−B
1
U +B
Y V + ν 0n + γ
Z−Y
undergo neutron capture (mt=102)
A+1
X +γ
Z
undergo (n,2n) reaction (mt=16)
A−1
X + 2 10 n + γ
Z
undergo (n,3n) reaction (mt=17)
undergo (n,4n) reaction (mt=37)
undergo (n,α) reaction (mt=107)
undergo (n,p) reaction (mt=103)
undergo (n,2α) reaction (mt=108)
undergo (n,np) reaction (mt=28)
undergo (n,d) reaction (mt=104)
undergo (n,t) reaction (mt=105)
where symbols n, α, p, d and t represent neutron, alpha particle, proton, deuteron and triton, respectively.
d
The contents of the variable Kr,i
is used to specify the properties of reaction r for each isotope i
d
under consideration. Here Kr,i contains two different types of informations, namely d(r) and i(r) which
are defined as follows:
d
d(r) = Kr,i
mod 100
and
i(r) =
d
Kr,i
100
(2.1)
IGE–351
23
where
0
1
2
d(r) =
3
4
5
isotope
isotope
isotope
isotope
isotope
isotope
i
i
i
i
i
i
does not deplete by reaction NREADr
will deplete by reaction NREADr
does not deplete by reaction NREADr but yields energy production
is fissile without fission yield. Valid only for r such that NREADr =NFTOT
is fissile with fission yield. Valid only for r such that NREADr =NFTOT
is a fission fragment. Valid only for r such that NREADr =NFTOT
and i(r) = 0 unless 4 ≤ d(r) ≤ 5. When d(r) = 4, i(r) represents the fissile isotope index while for
d(r) = 5, i(r) represents the fission fragment index. The fractional yield for the production of the fission
d
fragment i(r′ ) from the fissile isotope i(r) is stored in matrix Yi(r)→i(r′ ) . The contents of the vector Rr,i
is the energy in MeV emitted per decay or reaction.
p
is used to identify explicitly the parent isotope which can generate
The contents of the variables Ks,i
p
the current isotope i. The maximum number of parent reaction for this depletion chain is MS . Ks,i
contains two different types of information, namely r(s) and i(s) which are defined as follows:
r(s) =
p
Ks,i
mod 100
and
p
Ks,i
i(s) =
100
(2.2)
where r(s) = 0 indicates that the list of parent isotopes is complete while r(s) > 0 refers to the reaction
type NREADr(s) and can take the following values:
1
isotope i produced by radioactive decay
isotope i produced by fission (this contribution is kept apart from record
2
’FISSIONYIELD’)
r(s) =
3
isotope
i produced by neutron capture
≥ 4 isotope i produced by NREADr(s) reaction
In the case where r(s) > 0, i(s) represents the isotope index associated with the parent isotope and
p
Rs,i
represents the branching ratio in fraction for the production of isotope NISODi from a neutron
reaction with the parent isotope NISODi(s) .
2.5
State vector content for the shiba self-shielding sub-directory
The dimensioning parameters for the self-shielding sub-directory, which are stored in the state vector
S s , represent:
• The first group for which self-shielding takes place Gmin = S1s By default Gmin = Ng,f + 1
• The last group for which self-shielding takes place Gmax = S2s By default Gmax = Ng,e
• The maximum number of iterations in the self-shielding calculation Mr = S3s
• Enabling flag for the Livolant-Jeanpierre normalization Ilj = S4s
• Enabling flag for the use of Goldstein-Cohen parameters Igc = S5s
• The transport correction option used in self-shielding Itc = S6s
0 no transport correction applied in self-shielding calculation
Itc =
1 use transport corrected cross section in self-shielding calculation
• Type of self-shielding model Ilevel = S7s
0 Stamm’ler model without distributed self-shielding effects
1 Stamm’ler model with the Nordheim (PIC) distributed self-shielding model
Ilevel =
2 Stamm’ler model with both Nordheim (PIC) distributed self-shielding model
and Riemann integration method.
IGE–351
24
• The option to indicate whether a specific flux solver or collision probability matrices are used to
perform the self-shielding calculation Iflux = S8s (see PIJ and ARM keyword in SHI: operator input
option)
Iflux =
2.6
1
2
use a specific flux solver (the ARM keyword was selected)
use collision probability matrices (the PIJ keyword was selected)
State vector content for the subgroup self-shielding sub-directory
The dimensioning parameters for the self-shielding sub-directory, which are stored in the state vector
S s , represent:
• The first group for which self-shielding takes place Gmin = S1s By default Gmin = Ng,f + 1
• The last group for which self-shielding takes place Gmax = S2s By default Gmax = Ng,e
• SPH enabling flag Isph = S3s
Isph
0 skip the multigroup equivalence procedure
1 perform a multigroup equivalence procedure (SPH procedure or
=
Livolant-Jeanpierre equivalence)
• The transport correction option used in self-shielding Itc = S4s
Itc =
0 no transport correction applied in self-shielding calculation
1 use transport corrected cross section in self-shielding calculation
• The number of iterations in the self-shielding calculation Mr = S5s
• The option to indicate whether a specific flux solver or collision probability matrices are used to
perform the self-shielding calculation Iflux = S6s (see PIJ and ARM keyword in USS: operator input
option)
Iflux =
1
2
use a specific flux solver (the ARM keyword was selected)
use collision probability matrices (the PIJ keyword was selected)
• The γ factor enabling flag Iγ = S7s . These factors are used to represent the moderator absorption
effect in the Sanchez–Coste self-shielding method.
Iγ =
0 the γ factors are set to 1.0
1 the γ factors are computed
• The simplified self-shielding enabling flag Icalc = S8s
Icalc
0 perform a delailed self-shielding calculation
1 perform a simplified self-shielding calculation using data recovered from the
=
−DATA − CALC− directory
• The flag for ignoring the activation of the mutual resonance shielding model Inoco = S9s
Inoco =
0 follow the directives set by LIB
1 ignore the directives set by LIB
s
• Maximum number of fixed point iterations for the ST scattering source convergence Imax = S10
IGE–351
2.7
25
The shiba self-shielding sub-directory /selfshield/ in /microlib/
Table 12: Main records and sub-directories in /selfshield/
Name
Type
STATE-VECTOR
I(40)
EPS-SHIBA
R(1)
2.8
Condition
Units
Comment
Vector describing the various parameters associated with this data structure Sis , as defined in
Section 2.5.
Value of the relative convergence criterion for the
self-shielding iterations in SHI:
1
The subgroup self-shielding sub-directory /selfshield/ in /microlib/
Table 13: Main records and sub-directories in /selfshield/
Name
Type
STATE-VECTOR
I(40)
-DATA-CALC-
Dir
2.9
Condition
Units
Comment
Vector describing the various parameters associated with this data structure Sis , as defined in
Section 2.6.
name of directory containing the data required by
a simplified self-shielding calculation. This type
of calculation allows the definition of a single selfshielded isotope in several resonant mixtures.
Icalc = 1
Contents of an /isotope/ directory
Each isotope directory always contains a cross section identifier record SCAT-SAVED
used to verify if a given cross section type has been saved for this isotope.
which must be
Table 14: Isotopic cross section identifier records
Name
Type
Condition
ALIAS
C∗12
M≥0
Units
Comment
Alias character*12 name of a microlib isotope.
This record is not provided in draglib objects.
continued on next page
IGE–351
26
Isotopic cross section identifier records
Name
Type
SCAT-SAVED
I(L)
AWR
R(1)
PT-PHYS
Dir
continued from last page
Condition
Units
nau
Iproc = 1, ≥ 3
Comment
Vector κscat
to identify the various type of
k
Legendre-dependent cross sections saved for this
isotope
Ratio of the isotope mass divided by the neutron
mass
Sub-directory containing probability table information, following the specification given in Section 2.9.1. Iproc is defined in Section 2.
Delayed neutron data can be present for some fissile isotopes on the /isotope/ directory. If Ndel ≥ 1
precursor groups are used, the following information is available:
Table 15: Delayed neutron reaction records
Name
Type
Condition
Units
Comment
{nusid}
R(G)
Ndel ≥ 1
b
{chid}
R(G)
Ndel ≥ 1
1
LAMBDA-D
R(Ndel )
Ndel ≥ 1
s−1
D,g
νσf,ℓ
: The product of σfg , the fission cross section
with νℓD,g , the averaged number of fission–emitted
delayed neutron produced in the precursor group
ℓ.
χD,g
ℓ : Delayed fission spectrum, normalized to
one, for the delayed fission neutrons in precursor
group ℓ.
λD
ℓ : Decay constant associated with the precursor
D
group ℓ. We must have 0 < λD
ℓ < λℓ+1 .
The delayed component of the fission yields in each precursor group ℓ is given as νℓD,g . The quantities
π D,g and νℓD,g σfg are defined as
ν D,g σfg
.
π D,g = g g ss
(ν σf )
and
νℓD,g σfg = ωℓ π D,g (ν g σfg )
ss
where the superscript ss indicates steady-state values. The delayed neutron records {nusid} and {chid}
will be composed, using the following FORTRAN instructions, as NUSIGD and CHID:
WRITE(NUSIGD,′ (A6, I2.2)′ ) ′ NUSIGF′, ell
WRITE(CHID,′ (A3, I2.2)′ ) ′ CHI′ , ell
IGE–351
27
for 1 ≤ ell ≤ Ndel. For example, in the case where two group cross sections are considered (Ndel = 2),
the following records would be generated:
Table 16: Example of delayed–neutron records in /isotope/
Name
Type
Condition
Units
Comment
NUSIGF01
R(G)
Ndel ≥ 1
b
NUSIGF02
R(G)
Ndel ≥ 2
b
CHI01
R(G)
Ndel ≥ 1
1
CHI02
R(G)
Ndel ≥ 2
1
D,g
νσf,1
: The product of σfg , the fission cross section
with ν1D,g , the averaged number of fission–emitted
delayed neutron produced in the precursor group 1.
D,g
νσf,2
: The product of σfg , the fission cross section
with ν2D,g , the averaged number of fission–emitted
delayed neutron produced in the precursor group 2.
χD,g
1 : Delayed fission spectrum, normalized to one,
for the delayed fission neutrons in precursor group 1.
χD,g
2 : Delayed fission spectrum, normalized to one,
for the delayed fission neutrons in precursor group 2.
In cases where the /isotope/ directory is produced by the edition module, some depletion-related
information may be available in this directory, in order to facilitate subsequent data processing. This
information is described in Table 17.
Table 17: Depletion-related information
Name
Type
Condition
Units
Comment
MEVG
R(1)
Nd ≥ 1
MeV
MEVF
DECAY
YIELD
R(1)
R(1)
R(G + 1)
Nd ≥ 1
Nd ≥ 1
Nd ≥ 1
MeV
10−8 s−1
1
PIFI
I(Ndfi )
Ndfi ≥ 1
PYIELD
R(Ndfi )
Ndfi ≥ 1
Energy in MeV produced by radiative capture.
Nd is defined in Section 2.
Energy in MeV produced by fission.
Radioactive decay constant
Fission fragment yield per energy group. The first
value is the average yield over all the energy spectrum. This record is given only for fission fragments.
Position in ISOTOPESUSED of the mother fissile
isotopes. This record is given only for fission fragments.
Fission product yield per fissile isotope. This
record is given only for fission fragments.
1
We will first consider the more usual case where constant vector reactions are stored on the isotopic
IGE–351
28
directory. A typical example of the microscopic cross section directory may be:
Table 18: Example of isotopic vector reaction records
Name
Type
NTOT0
Units
Comment
R(G)
b
TRANC
NUSIGF
R(G)
R(G)
b
b
NFTOT
CHI
R(G)
R(G)
Gchi = 0
CHI--01
R(G)
Gchi ≥ 1
CHI--02
R(G)
Gchi ≥ 2
CHI--03
R(G)
Gchi ≥ 3
CHI--04
R(G)
Gchi ≥ 4
NG
R(G)
b
H-FACTOR
R(G)
Jb
N2N
R(G)
b
The φ–weighted multigroup total cross section
σ0g
g
The multigroup transport correction σtc
g
The product of σf , the multigroup fission cross
section with ν g , the steady-state number of
neutron produced per fission, νσfss,g
The multigroup fission cross section σfg
The multigroup energy spectrum of the neutron emitted by fission χg
The first energy-dependent multigroup energy
spectrum of the neutron emitted by fission
χg,1
The second energy-dependent multigroup energy spectrum of the neutron emitted by fission χg,2
The third energy-dependent multigroup energy spectrum of the neutron emitted by fission χg,3
The fourth energy-dependent multigroup energy spectrum of the neutron emitted by fission χg,4
The multigroup neutron capture cross section
σcg
Energy production coefficients H g (product of
each microscopic cross section times the energy emitted by this reaction).
g
The multigroup cross section σ(n,2n)
for the
b
A−1
reaction A
X + 2n
Z X + n →Z
g
The multigroup cross section σ(n,3n)
for the
b
A−2
reaction A
X + 3n
Z X + n →Z
g
The multigroup cross section σ(n,4n)
for the
N3N
N4N
R(G)
R(G)
Condition
b
NP
R(G)
b
NA
R(G)
b
A−3
reaction A
X + 4n
Z X + n →Z
g
The multigroup cross section σ(n,p)
for the reA
A
action Z X + n →Z−1 X + p
g
The multigroup cross section σ(n,α)
for the re-
s−1 cm−2
A−3
action A
Z X + n →Z−2 X + α
The multigroup Goldstein-Cohen parameters
as recovered from GIR array in main /microlib/ directory λg
The multigroup neutron flux spectrum φgw
NGOLD
R(G)
NWT0
R(G)
continued on next page
IGE–351
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Example of isotopic vector reaction records
Name
Type
STRD
Condition
continued from last page
Units
Comment
R(G)
b
STRD-X
R(G)
b
STRD-Y
R(G)
b
STRD-Z
R(G)
b
OVERV
R(G)
cm−1 s
NTOT1
R(G)
b
NWT1
R(G)
s−1 cm−2
NWAT0
R(G)
1
NWAT1
R(G)
1
The multigroup transport cross section hog
mogenized over all directions σstrd
The x−directed multigroup transport cross
g
section σstrd,x
The y−directed multigroup transport cross
g
section σstrd,y
The z−directed multigroup transport cross
g
section σstrd,z
The average of the inverse neutron velocity
< 1/v >gm
The J –weighted multigroup total cross section σ1g
The multigroup fundamental current spectrum Jwg
The multigroup neutron adjoint flux spectrum
φ∗g
w
The multigroup fundamental adjoint current
spectrum Jw∗g
We can also use this isotopic directory to store time dependent cross sections in the form of a power
series expansion:
vkg (t) =
I
X
g i
vk,i
t
(2.3)
i=0
where the presence of these various terms is specified using κk . Note that the last three characters of
each of the records in Table 18 correspond to the extension EXT=’
’ that is associated with term
i = 0 in the power series expansion for the cross sections (see Eq. (2.3)). For i = 1, 2, the extension takes
successively the value EXT=’LIN’ and EXT=’QUA’. For example, if one considers the total cross section
and assumes that Fi (κ1 ) = 1 for i = 0, 2, then this implies the presence of the following additional records
in the /isotope/:
Table 19: Additional total cross section records for I = 2
Name
TOTAL
Type
LIN
R(G)
Condition
Units
Comment
d−1 b
g
array v1,1
= ∆σ g containing the first
order coefficients in the power series expansion for the multigroup total cross
section
continued on next page
IGE–351
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Additional total cross section records for I = 2
Name
TOTAL
Type
QUA
Condition
R(G)
continued from last page
Units
Comment
d−2 b
g
array v1,2
= ∆2 σ g containing the second order coefficients in the power series expansion for the multigroup total
cross section
The multigroup scattering cross section matrix, which gives the probability for a neutron in group h
to appear in group g after a collision with this isotope is represented by the form:
~ →Ω
~ ′) =
σsh→g (Ω
L
X
2ℓ + 1
ℓ=0
4π
~ ·Ω
~ ′ )σ h→g =
Pℓ (Ω
ℓ
L X
ℓ
X
~ m (Ω
~ ′ )σ h→g
Yℓm (Ω)Y
ℓ
ℓ
ℓ=0 m=−ℓ
using a spherical harmonic series expansion to order L − 1. Assuming these spherical harmonic are
orthonormalized, namely:
Z
′
~ m
~
d2 Ω Yℓm (Ω)Y
l′ (Ω) = δm,m′ δℓ,ℓ′
4π
~ →Ω
~ ′ ) using the following integral:
we can define σℓh→g in terms of σsh→g (Ω
Z
~ →Ω
~ ′ )Pℓ (Ω
~ ·Ω
~ ′)
d2 Ω σsh→g (Ω
σℓh→g =
4π
Note that this definition of σℓh→g is not unique and some authors include the factor 2l + 1 directly in
different angular moments of the scattering cross section.
Here instead of storing on these G × G matrices σℓh→g , a vector which contains a compress form for
this matrix will be considered. This choice is justified by the fact that the number of energy groups which
will lead to scattering in a specific group is generally relatively small compared to the total number of
groups in the library and that these groups are clustered around the final energy group. Here we will
first define two different integer vectors ngℓ and hgℓ for each order in the scattering cross section and for
each final energy group g which will contain respectively the number of successive initial energy groups
for which the scattering cross section does not vanish and the maximum energy group number for which
scattering to the final group g does not vanishes. Accordingly, for a scattering cross section of the form:
σ0h→g
h=1
h=2
h=3
h=4
hg0
ng0
g=1
a1
0
0
0
1
1
g=2
a2
a3
a6
a8
4
4
g=3
0
a4
a7
0
3
2
g=4
0
a5
0
a9
4
3
The compress scattering matrix will then contain the following information:
1
1
G
1
2
σℓ,c = σℓh →1 , σℓh −1→1 , . . . , σℓh −n1 +1→1 , σℓh →2 , . . . , σℓh −nG +1→G
which for the example above leads to
σℓ,c = (a1 , a8 , a6 , a3 , a2 , a7 , a4 , a9 , 0, a5 )
IGE–351
31
As a result σℓh→g can
0
0
σℓh→g =
k
σℓ,c
be reconstructed using
if
h > hgℓ
if
h < hgℓ − ngℓ + 1
P
g
h
otherwise k = g−1
h=1 nℓ + hℓ − h + 1
Finally, we will also save the total scattering cross section vector of order ℓ which is defined as
h
σℓ,s
=
G
X
σℓh→g
g=1
In the case where only the order ℓ = 0 moment of scattering cross section is non vanishing (isotropic
scattering) the following records can be found on the isotopic directory.
Table 20: Optional scattering records
Name
Type
SIGS00
R(G)
IJJS00
I(G)
NJJS00
I(G)
SCAT00
PG
R( g=1 ng0 )
Condition
Units
Comment
b
The isotropic component (ℓ = 0) of the multig
group total scattering cross section σ0,s
Highest energy group number for which the
isotropic component of the scattering cross
section to group g does not vanish, hg0
Number of energy groups for which the
isotropic component of the scattering cross
section to group g does not vanish, ng0
Compressed isotropic component of the scatk
tering matrix σ0,c
b
If the scattering cross section is expanded to order L > 1 in Legendre polynomials, additional set
of scattering records similar to those described above will be presentin the cross section directory. The
first four characters and last 6 characters in the names of these records will again be identical to those
described above while character 5 and 6 will differ from level to level. For example, the order ℓ = 5
compressed scattering matrix will be identified by SCAT05
while for order ℓ = 50 we will use
SCAT50
.
The STRD cross sections are normalized in such a way to permit the calculation of a diffusion coefficient
using the following formula:
Dg =
1
3
X
(2.4)
g
Ni σstrd,i
i
g
where Ni is the isotopic density of isotope i and σstrd,i
is the STRD cross section of isotope i in energy
group g. The sum is performed over all isotopes present in the mixture. The STRD cross sections for
isotope i are defined as
g
σstrd,i
=
hφig
1
g
(σ g − σs1,i
)
(µg )2 3 h(Σ1 − Σs1 )J ig 1,i
if a streaming model is used
(2.5)
IGE–351
32
hφi2g
1
g
(σ g − σs1,i
) if no streaming model used
(µg )2 3 hDφig h(Σ0 − Σs1 )φig 0,i
=
(2.6)
where
φg fundamental flux
J g fundamental current
µg SPH equivalence factor
Σg0 φ–weighted macroscopic total cross section of the mixture
Σg1 J –weighted macroscopic total cross section of the mixture
Σgs1 macroscopic P1 scattering cross section of the mixture (J –weighted if a streaming model is used;
φ–weighted if no streaming model used)
Dg diffusion coefficient
g
φ–weighted microscopic total cross section for isotope i
σ0,i
g
σ1,i
J –weighted microscopic total cross section for isotope i
g
σs1.i
microscopic P1 scattering cross section for isotope i (J –weighted if a streaming model is used;
φ–weighted if no streaming model used)
On the other hand the so-called directional cross section STRD X, STRD Y and STRD Z are obtained in
such a way that
Dkg =
1
3
X
g
Ni σstrd,k,i
;
k = x, y or z
.
(2.7)
i
For example, for an isotope with only total and scattering cross sections, we will find the following
records on the cross section directory.
Table 21: Example of cross section records
Name
Type
NTOT0
SIGS00
R(G)
R(G)
IJJS00
I(G)
IJJS00
I(G)
Condition
Units
Comment
b
b
The multigroup total cross section σ g
The isotropic component (ℓ = 1)of the multig
group total scattering cross section σ0,s
Highest energy group number for which the
isotropic component of the scattering cross section to group g does not vanishes, hg0
Highest energy group number for which the first
order perturbation in the isotropic component of
the scattering cross section to group g does not
vanishes, hg0,1
continued on next page
IGE–351
33
Example of cross section records
Name
Type
NJJS00
I(G)
SCAT00
SIGS01
PG
R( g=1 ng0 )
IJJS01
I(G)
NJJS01
I(G)
SCAT01
PG
R( g=1 ng1 )
R(G)
Condition
continued from last page
Units
b
b
b
Comment
Number of energy groups for which the isotropic
component of the scattering cross section to group
g does not vanishes, ng0
Compressed isotropic component of the scattering
k
matrix σ0,c
The linearly anisotropic component (ℓ = 1) of the
g
multigroup total scattering cross section σ1,s
Highest energy group number for which the linearly anisotropic component of the scattering
cross section to group g does not vanishes, hg1
Number of energy groups for which the linearly
anisotropic component of the scattering cross section to group g does not vanishes, ng1
Compressed linearly anisotropic component of
k
the scattering matrix σ1,c
Note that most of these cross sections are not required to perform a cell calculation. In fact, in a
g
typical transport calculation, only σ g , σtc
, νσfg , χg and the isotropic and linearly anisotropic scattering
matrix are used. For burnup calculations, depending on the depletion chain prescribed, the following
g
g
g
g
g
cross sections may be required: σfg , σcg , σ(n,2n)
, σ(n,3n)
, σ(n,4n)
, σ(n,p)
, σ(n,α)
. Finally, when editing
isotopic cross sections, all the cross sections types in the library will be processed.
A final note on the use of the transport correction and the homogenized and directional transport
cross section. In DARGON, the transport correction cross section is used to correct the total and isotropic
scattering cross section using the relations
σcg
g→g
σc,0
=
=
g
σ g − σtc
g
σ0g→g − σtc
2.9.1 The probability table directory PT-PHYS in /isotope/
Physical probability tables (Iproc = 1) are obtained from a least-square fit of the self-shielded cross
sections against dilution. Mathematical probability tables (Iproc ≥ 3) are obtained from Autolib data
using the CALENDF formalism.
IGE–351
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Table 22: Physical probability tables
Name
Type
Condition
GROUP
Dir(G)
NOR
I(G)
NDEL
I(1)
Units
Comment
List of energy-group sub-directories. Each component of the list is a directory containing the
probability-table information associated with a
specific group.
Order nG of the probability table in each energy
group
Number of delayed neutron precursor groups for
this resonant isotope
Table 23: Group-dependent probability table directories
Name
Type
Condition
Units Comment
PROB-TABLE
R(12, Nreact)
SIGQT-SIGS
R(ng )
Iproc = 4
b
SIGQT-SLOW
{/isotope/}
R(ng , ng )
R(ng , mg )
Iproc = 4
*
b
1
ISM-LIMITS
I(2, L)
Probability tables. Nreact is the total number of
reactions represented by probability tables. 12 is
the maximum allowed order of a probability table.
Probability table in secondary slowing-down cross
section.
Slowing-down correlated weight matrix.
Set of records, each containing the correlated
weights between the current total xs and the total
xs of isotope. mg is the order of the probability
table for isotope. (*) This data is optional and
is provided only if Iproc ≥ 3 and if the mutual
self-shielding effect is to be taken into account.
Minimum (index 1) and maximum (index 2) secondary group for each Legendre order of the scattering matrices
IGE–351
35
3 Contents of a /geometry/ directory
The L GEOM specification is used to store structured geometric data, i.e., data characterized by some
regularity in space. Sub-geometries can be embedded at specific node positions to build a more complex
geometry. The following regular geometries can be described with the L GEOM specification:
• Cartesian geometries in 1D, 2D and 3D
• Cylindrical geometries in 1D and 2D (R − Z or R − θ)
• Spherical geometries in 1D
• Hexagonal geometries in 2D/3D
• Various types of cells in 2D/3D Cartesian or hexagonal geometry
• Cells with clusters of fuel rods
• Various synthetic geometries (Do-it-yourself Apollo1 assembly and double-heterogeneity).
This directory contains a compact description of a geometry.
3.1
State vector content for the /geometry/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector S G , represent:
• The type of of geometry Ft = S1G
Ft =
0
1
2
3
4
5
6
7
8
9
10
11
12
13
15
16
17
20
21
22
23
24
25
30
Virtual geometry
Homogeneous geometry
Cartesian 1-D geometry
Tube 1-D geometry
Sphere 1-D geometry
Cartesian 2-D geometry
Tube (R-Z) geometry
Cartesian 3-D geometry
Hexagonal 2-D geometry
Hexagonal 3-D geometry
Tube (R-X) geometry
Tube (R-Y ) geometry
hexagonal 2–D geometry with triangular mesh
z-directed hexagonal 3–D geometry with triangular mesh
Tube (R-θ) 2-D geometry
Triangular 2-D geometry
Triangular 3-D geometry
Cartesian 2-D geometry with annular sub-mesh
Cartesian 3-D geometry with x−directed cylindrical sub-mesh
Cartesian 3-D geometry with y−directed cylindrical sub-mesh
Cartesian 3-D geometry with z−directed cylindrical sub-mesh
Hexagonal 2-D geometry with annular sub-mesh
Hexagonal 3-D geometry with z−directed cylindrical sub-mesh
Do-it-yourself geometry
IGE–351
36
• The number of annular or cylindric mesh intervals in the geometry Nr = S2G
• The number of x−directed mesh intervals, hexagon or triangles in the geometry Nx = S3G
• The number of y−directed mesh intervals in the geometry Ny = S4G
• The number of z−directed mesh intervals in the geometry Nz = S5G
• The total number of mesh intervals in the geometry Nk = S6G
– for Ft =0 or 1, Nk = 1;
– for Ft =2, 5 or 7, Nk = max(Nx , 1) × max(Ny , 1) × max(Nz , 1);
– for Ft =3, 6, 10 or 11, Nk = Nr × max(Nx , 1) × max(Ny , 1) × max(Nz , 1)
– for Ft =4, Nk = Nr ;
– for Ft =8 or 9, Nk = Nx × max(Nz , 1);
– for Ft =12 or 13, Nk = 6 × Nx2 × max(Nz , 1);
– for Ft =20, 21, 22 or 23, Nk = (Nr + 1) × max(Nx , 1) × max(Ny , 1) × max(Nz , 1);
– for Ft =24 or 25, Nk = (Nr + 1) × max(Nz , 1).
• The maximum number of mixtures used in this geometry Mm = S7G
• The cell flag Fc = S8G
Fc =
0 Cell option not activated
1 Cell option present
• The number of sub-geometries defined in this geometry Fg = S9G
G
• The merge flag Fm = S10
Fm =
0
1
Merge option not activated
Merge option present
G
• The split flag Fs = S11
0 Split option not activated
1 Split option present
Fs =
2 Split option present. The embedded tubes are not splitted.
G
• The double heterogeneity flag Fdh = S12
Fdh =
0 Double heterogeneity option not activated
1 Double heterogeneity option present
G
• The number of cluster sub-geometry Ncl = S13
G
• The type of sectorizarion Fsec = S14
. This information may be given only if Ft ≥ 20.
−999 non-sectorized cell processed as a sectorized cell
−1 ×–type sectorization
0 non-sectorized cell
1 +–type sectorization
Fsec =
2 simultaneous ×– and +–type sectorization
3 simultaneous ×– and +–type sectorization shifted by 22.5◦
4 windmill-type sectorization.
IGE–351
37
• Number of tubes that are not splitted by the sectors if Fsec 6= 0. This integer is selected in interval
G
0 ≤ Fsec2 ≤ Nr . Fsec2 = S15
.
G
G
• The pin location option S18
. When S18
> 0, the pin are located according to (r, θ) in 2-D and 3-D
G
(center along the cylinder axis in the cell into which they are inserted) while for S18
< 0, the pin
G
are located according to (x, y) in 2-D and (x, y, z) in 3-D. A value of S18
= 0, implies that there is
no pin in the geometry.
The radii of a CARCEL– or HEXCEL–type geometry are defined as shown in the following figure:
R4
R3
R1
R2
In case where Fsec 6= 0, the elementary cell is splitted with sectors. Mixture indices are specific in
each splitted region. They are defined as in the following two figures (isect≡ Fsec and jsect≡ Fsec2 ):
5
10
6 2
1
3
9
19
10
4 8
6
12
7
11
isect=-1 jsect=0
11
2 1
3 4
7
5
8
9
21
3
1
isect=1
14
jsect=0
4
1
3
9
4
8
isect=-1 jsect=1
2
1 9
8 16
3
13
8
4
9
jsect=1
isect=1
2
3
5
isect=1
3
5
2
1
5
6
16
jsect=1
2
jsect=2
14
17
9
7
16
15
2
6
8
isect=2
9
jsect=2
6
24
7
15
14
23
28
22
13
20
8
isect=3 jsect=2
1
5
14
18
10
2
17
9
8
6
7
16
21
15
4
5
10
9
11
3
4
12
3
1
7
1
8 16
5
21
12
2
6
10
7
17
9
isect=4 jsect=1
4
5
2
12 4
19
8
3
11
isect=4 jsect=0
isect=3 jsect=1
4
1
6
1
6
17
27
2
5
13
9
8
7
15
isect=2
23
10
3
4
20
25
10
19
13
11
12
10
18
26
3
24
isect=3 jsect=0
11
1
6
22
jsect=0
4
14
21
17
9
2
3
1
12 4
8 16
5
7
6
13
15
14
23
6
5
20
15
isect=2
1
4
5
isect=-1 jsect=2
2
6
11
17
24
12
7
5
6 7
22
6
2
7
4
13 5
10
19
10
3 2
12
12
18
18
11
20
10
1
7
13
11
3
9
8
isect=4 jsect=2
14
IGE–351
38
14
9
10
7
4
1
5
2
2
5
10
12
1
1
18
6
4
3
8
3
2
3
15
4
9
13
8
5
11
7
6
16
11
17
isect=-1 jsect=0
8
13
6
7
12
isect=-1 jsect=1
isect=-1 jsect=2
In case of an automatic geometry definition using the NAP: module, the number of mixtures corresponding to assembly in the original core definition is named Nmxa and the number of assembly along X
and Y directions are Nax and Nay respectively.
3.2
The main /geometry/ directory
On its first level, the following records and sub-directories will be found in the /geometry/ directory:
Table 24: Main records and sub-directories in /geometry/
Name
Type
Condition
UnitsComment
SIGNATURE
C∗12
STATE-VECTOR
I(40)
MIX
I(Nk )
HMIX
I(Nk )
*
RADIUS
R(Nr + 1)
Nr ≥ 1
cm
OFFCENTER
R(3)
Nr ≥ 1
cm
MESHX
MESHY
MESHZ
R(Nx + 1)
R(Ny + 1)
R(Nz + 1)
cm
cm
cm
SIDE
R(1)
Nx ≥ 1
Ny ≥ 1
Nz ≥ 1
8 ≤ Ft ≤ 11
24 ≤ Ft ≤ 25
Signature
of
the
data
structure
(SIGNA =L GEOM
)
Vector describing the various parameters associated with this data structure SiG , as defined in
Section 3.1.
Record containing the material mixture index 1 ≤
i ≤ Mm per region (for positive indices) or the
sub-geometry index 1 ≤ |i| ≤ Fg per region (for
negative indices). MIX(I) is set to zero in voided
regions I or in regions located outside the domain.
array Hi containing the virtual (homogenization)
mixtures associated with different regions of the
geometry
The radial mesh Ri position. The first element of
this vector is identical to 0.0
The displacement of the center of the annular
mesh from the center of a Cartesian cell
The x−directed mesh position Xi
The y−directed mesh position Yi
The z−directed mesh position Zi
cm
The width of the side of the hexagon H
continued on next page
IGE–351
39
Main records and sub-directories in /geometry/
continued from last page
Name
Type
Condition
UnitsComment
SPLITR
I(Nr + 1)
Fs × Nr ≥ 1
SPLITX
I(Nx )
Fs × Nx ≥ 1
SPLITY
I(Ny )
Fs × Ny ≥ 1
SPLITZ
I(Nz )
Fs × Nz ≥ 1
SPLITH
I(1)
Ft = 12, 13
IHEX
NCODE
I(1)
I(6)
Ft = 8, 9, 12, 13, 24, 25
ZCODE
R(6)
ICODE
I(6)
NPIN
I(1)
G
|S18
| 6= 0
DPIN
R(1)
G
|S18
| 6= 0
RPIN
R(k)
G
S18
=1
APIN
R(k)
G
S18
=1
Record containing the radial mesh splitting Sr,i .
A negative value permits a splitting into equal
sub-volumes; a positive value permits a splitting
into equal sub-radius spacings
Record containing the x−directed mesh splitting
Sx,i
Record containing the y−directed mesh splitting
Sy,i
Record containing the z−directed mesh splitting
Sz,i
value Sh of the triangular mesh splitting for triangular hexagons in the geometry. This will lead to
a spatial triangular mesh spacing of Hs = H/Nx
The type of hexagonal symmetry βh
Record containing the types of boundary conditions on each surface Nβ,j . NCODE(1): X- or
HBC condition; NCODE(2): X+ or R+ condition;
NCODE(3): Y- condition; NCODE(4): Y+ condition;
NCODE(5): Z- condition; NCODE(6): Z+ condition
Record containing the albedo value on each surface βj
Record containing the albedo index on each surface Iβ,j . The vector βj is used only if Iβ,j > 0
and Nβ,j = 6. In the case where Iβ,j < 0
and Nβ,j = 6 the vector βp,j in the directory
/macrolib/ is used
Number Npin of identical pins in a cluster. All
the pins will see identical flux
cm−3 Relative density dp,r of pins in a cluster. In this
case Npin = −1
cm array Rpin,j containing the radial positions at
which the center of the pins in the cluster are
located with respect to the center of the cell
(k = Npin ). In the case where Rpin,j contains
a single element (k = 1), it is assumed that the
pins are all located at the same radial position
Rref = Rpin,1
rad array θpin,j containing the angular positions at
which the center of the pins in the cluster are
located with respect to the x, y or z axis respectively for TUBEX, TUBEY and TUBEZ geometry
(k = Npin ). In the case where θpin,j contains a
single element (k = 1), it is assumed that the first
pin is located at θref = θpin,1 , the remaining pins
being located at θpin,j = θref + 2(j − 1)π/Npin
continued on next page
IGE–351
40
Main records and sub-directories in /geometry/
continued from last page
Name
Type
Condition
UnitsComment
CPINX
R(Npin )
G
S18
= −1
cm
CPINY
R(Npin )
G
S18
= −1
cm
CPINZ
R(Npin )
G
S18
= −1
cm
BIHET
Dir
Fdh = 1
POURCE
PROCEL
R(S3G )
R(S3G , S3G )
Ft = 30
Ft = 30
CELL
MERGE
C(Fg ) ∗ 12
I(Nk )
Fc = 1
Fm = 1
TURN
I(Nk )
Fc = 1
CLUSTER
C(Fcl ) ∗ 12
Fcl ≥ 1
{/subgeo/}
MIX-NAMES
A-NX
A-IBX
A-ZONE
Dir
C(Mm ) ∗ 12
I(Nay )
I(Nay )
I(Nch )
Fg ≥ 1
*
A-NMIXP
I(1)
array Xpin,j containing the x positions at which
the pins in the cluster are centered with respect
to the center of the cell
array Ypin,j containing the y positions at which
the pins in the cluster are centered with respect
to the center of the cell
array Zpin,j containing the z positions at which
the pins in the cluster are centered with respect
to the center of the cell
Directory containing double-heterogeneity related data. This directory can only be present
on the root directory.
The proportion of each cell type in the lattice Pj
The pre-calculated probability for a neutron leaving a cell of type i to enter in a cell of type j
without crossing any other cell Pi,j
The names of the sub-geometries (CELLk )
The merging index corresponding to each region
Gm,i
The orientation index corresponding to each region Gt,i . Negative values are used to turn a cell
in the Z direction.
The names of the sub-geometries making up the
cluster (CLUSTERk )
Set of sub-directories containing a subgeometry
The names of the mixtures
Number of assemblies on each row
Position of the first assembly on each row
Number of the assembly associated with each
channel. Each assembly may be represented
by several channels if they have been heterogeneously homogenized.
The number of mixtures in one heterogeneously
homogenized assembly. Nmxp . Note for homogeneously homogenized assembly Nmxp = 1.
In the case where a cylindrical correction is applied over a full–core Cartesian calculation, the following
additional data is provided. It is provided if and only if type 20 (CYLI) boundary conditions are set in
the X–Y plane (see Figure 2).
IGE–351
41
ang
rrad
Figure 2: Cylindrical correction in Cartesian geometry
Table 25: Cylindrical correction related records in /geometry/
Name
Type
XR0
Condition
Units
Comment
R(Ncyl )
cm
RR0
R(Ncyl )
cm
ANG
R(Ncyl )
1
Record containing the coordinate of the Z axis
from which the cylindrical correction is applied
to Cartesian geometries. Ncyl is the number of
radii.
Record containing the radius of the real cylindrical boundary (rrad).
Record containing the angle (in radian) of the
cylindrical notch. ang(ir) = π2 by default (i.e.
the correction is applied at every angle).
The type of hexagonal symmetry βh is defined as:
1 S30
2 SA60
3 SB60
4 S90
5 R120
βh =
6 R180
7 SA180
8 SB180
9 COMPLETE
S30, SA60 and COMPLETE symmetries are depicted in the following figures. The other types of
hexagonal symmetries are defined in the DRAGON users guide.[1]
12
CL
S30
9
6
4
8
2
5
1
3
7
21
SA60
11
15
10
10
CL
CL
6
3
9
1
5
2
8
4
7
20
14
19
13
18
12
17
11
16
CL
IGE–351
42
67
66
68
42
69
70
43
24
45
72
12
27
74
13
48
28
75
14
49
76
17
62
38
79
54
81
87
86
85
55
53
80
58
57
56
32
88
35
34
33
31
52
78
21
16
30
51
77
63
39
20
9
91
61
3
8
37
90
4
2
1 19 60
36
89
7
5
18
59
6
15
29
50
22
11
26
47
64
40
10
25
46
73
23
44
71
65
41
84
83
82
COMPLETE
NCODE is a record containing the types of boundary conditions on each surface. In Cartesian geometry,
the 6 components of NCODE are related to sides X-, X+, Y-, Y+, Z- and Z+, respectively. The possibilities
are:
0 side not used
1 VOID: zero re-entrant angular flux. This side is an external surface of the domain.
2
REFL: reflection boundary condition. In most DRAGON calculations, this implies
white
boundary conditions. In DRAGON the cell is never unfolded to take into
account
a REFL boundary condition.
3
DIAG:
diagonal
boundary condition. The side under consideration has the same
properties
as
that
associated with a diagonal through the geometry. Note that two
and
only
two
DIAG
sides must be specified. The diagonal symmetry is only permitted
for
square
geometry
and in the following combinations: (X+ and Y-) or (X- and Y+)
4
TRAN:
translation
boundary
condition. The side under consideration is connected
to
the
opposite
side
of
a
Cartesian
domain. This option provides the facility to treat
an
infinite
geometry
with
translation
symmetry. The only combinations of
translational
symmetry
permitted
are
related to sides (X- and X+) and/or
(Y- and Y+) and/or (Z- and Z+).
Nβ,j =
5 SYME: symmetric reflection boundary condition. The side under consideration is
located outside the domain and that a reflection symmetry is associated with the
adequately directed axis running through the center of the cells closest to this side.
6
ALBE: albedo boundary condition. The side under consideration has an arbitrary
albedo
with a real value given in the record ‘ZCODE’ or indexed by the record
‘ICODE’.
This side is an external surface of the domain.
7
ZERO:
zero
flux boundary condition. This side is an external surface of the domain.
8
PI/2:
π/2
rotation.
The side under consideration is characterized by a π/2 symmetry.
The
only
π/2
symmetry
permitted is related to sides (X- and Y-). This condition can
be
combined
with
a
translation
boundary condition:(PI/2 X- TRAN X+) and/or
(PI/2
YTRAN
Y+).
9 PI: π rotation
10
SSYM: specular relexion boundary condition. Such a condition may be obtained by
unfolding
the geometry.
20 CYLI: use a cylindrical correction in full–core Cartesian geometry
In cylindrical geometry, the 3 components of NCODE are related to sides R+, Z- and Z+, respectively.
The possibilities are: VOID, REFL, ALBE and/or ZERO.
In hexagonal geometry, the 3 components of NCODE are related to sides H+ (the surface surrounding
IGE–351
43
the hexagonal domain in the X–Y plane), Z- and Z+, respectively. The possibilities are: VOID, REFL,
SYME, ALBE and/or ZERO.
We will now describe the exact meaning of the orientation index Gt,i . For Cartesian geometries, the
eight possible orientations are shown in the following figure:
1
3
4
2
7
5
6
8
For hexagonal geometries, the twelve possible orientations are shown in the following figure:
1
2
3
4
5
6
7
8
9
10
11
12
In the case where Fc = 1, the set of directory {/subgeo/} will have the same name as the variable
CELLk . For example, in the case where Fg = 2 and
GEO1 for k = 1
CELLk =
GEO2 for k = 2
then the following directories will also be present in the main geometry directory:
Table 26: Cell sub-geometry directory
Name
Type
GEO1
GEO2
Dir
Dir
Condition
Units
Comment
A first /geometry/ directory
A second /geometry/ directory
In the case where Fcl ≥ 1, the set of directory {/subgeo/} will have the same name as the variable
IGE–351
44
CLUSTERk . For example, in the case where Fcl = 2 and
RODS1 for k = 1
CLUSTERk =
RODS2 for k = 2
then the following directories will also be present in the main geometry directory:
Table 27: Cluster sub-geometry directory
Name
Type
Condition
RODS1
RODS2
Dir
Dir
Fg ≥ 1
Fg ≥ 1
3.3
Units
Comment
A first /geometry/ directory
A second /geometry/ directory
The /BIHET/ sub-directory in /geometry/
The first level of the geometry directory may contains a double-heterogeneity directory /BIHET/ made
of the following records:
Table 28: Records in the /BIHET/ sub-directory
Name
Type
STATE-VECTOR
I(40)
NS
I(S1dh )
RS
R(S2dh , S1dh )
MILIE
I(S3dh )
MIXDIL
I(S3dh )
MIXGR
I(S4dh , S3dh )
FRACT
R(S1dh , S3dh )
Condition
Units
cm
Comment
Vector describing the various parameters associated with this data structure Sidh
The number of sub-regions in the microstructures Nmicro,i
The radii of the tubes or spherical shells making
up the micro-structures Rmicro,i,j
The composite mixture indices used in the definition of the macro-geometry Cmicro,i,j
The mixture indices associated with the diluent in
each composite mixtures of the macro-geometry
Dmicro,i,j
The mixture indices associated with each region
of the micro-structures Mmicro,i,j
The volumetric concentration of each microstructure ρmicro,i,j
The dimensioning parameters for this data structure, which are stored in the state vector S bh , represent:
• The number of different kinds of macro-structures S1dh
• 1 plus the maximum number of annular sub-regions in any micro-structure S2dh
IGE–351
45
• The number of composite mixtures to be included the macro-geometry S3dh
• The maximum number of annular sub-regions in the micro-structure S4dh = (S2dh − 1) × S1dh
• The type of micro-structure S5dh where
S5dh
=
3 Tubular micro-structure
4 Spherical micro-structure
IGE–351
46
4 Contents of a /tracking/ directory
This directory contains the information resulting from an analysis of a geometry using a specific
calculation operator of DRAGON.
4.1
State vector content for the /tracking/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector S, represent:
• The number of regions Nr = S1t
• The number of unknown Nu = S2t
• The leakage flag IL = S3t
IL =
0 Leakage is present
1 Leakage is absent
• The maximum number of mixture used Mm = S4t
• The number of outer surfaces Ns = S5t
t
where
• Flag related to the double-heterogeneity option S40
t
S40
=
4.2
0
1
the double-heterogeneity option is not used
the double-heterogeneity option is used.
The main /tracking/ directory
On its first level, the following records and sub-directories will be found in the /tracking/ directory:
Table 29: Main records and sub-directories in /tracking/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
TRACK-TYPE
C∗12
LINK.GEOM
C∗12
TITLE
MATCOD
C∗72
I(S1t )
Condition
Units Comment
Signature
of
the
data
structure
(SIGNA =L TRACK
).
Vector describing the various parameters associated
with this data structure Sit , as defined in Section 4.1.
Type of tracking considered (CDOOR). Allowed values are: ’EXCELL’, ’SYBIL’, ’MCCG’, ’BIVAC’ and
’TRIVAC’.
Name of the geometry on which the tracking is
based.
Identification title (TITLE)
Region material Mr
continued on next page
IGE–351
47
Main records and sub-directories in /tracking/
Name
Type
KEYFLX
I(S1t , E, F )
Condition
continued from last page
Units Comment
Location in unknown vector of averaged regional flux
Ir The second dimension of this array is
n t
E = M20 if MCCG;
1
otherwise.
The third dimension of this array is
n t
F = M19 if MCCG;
1
otherwise.
cm3
VOLUME
BC-REFL+TRAN
R(S1t )
I(S5t )
S5t
FUNC-TABLES
Dir
*
BIHET
Dir
t
S40
=1
≥1
Region volumes Vr
Reflection/transmission matrix localisation operator
Ts
Directory containing Bickey or/and exponential
function tables.
Sub-directory containing the data related to a double heterogeneity geometry. The specification of this
directory is given in Section 4.9
In addition to the above records, the main /tracking/ directory will also contain information which is
specific to each tracking module. This information will be described in the following sub-sections. Also
note that the contents of the Sit vector for i ≥ 6 will depend on the specific tracking module and will be
defined in the next sub-sections.
4.3
The sybilt dependent records and sub-directories on a /tracking/ directory
When the SYBILT: operator is used (CDOOR=’SYBIL’), the following elements in the vector Sit will
also be defined.
• The main SYBIL model S6t
2 Pure geometry
3 Do-it-yourself geometry
S6t =
4 2-D assembly geometry
• Minimum space required to store tracks for assembly geometry S7t
• Minimum space required to store interface currents for assembly geometry S8t
• Number of additional unknowns holding the interface currents S9t . These unknowns are used if and
only if a current–based inner iterative method is set (with option ARM).
The following sub-directories will also be present on the main level of a /tracking/ directory.
IGE–351
48
Table 30: The sybilt records and sub-directories in /tracking/
Name
Type
Condition
PURE-GEOM
Dir
S6t = 2
DOITYOURSELF
Dir
S6t = 3
EURYDICE
Dir
S6t = 4
Units
Comment
Sub-directory containing the data related to a pure
geometry
Sub-directory containing the data related to a do-ityourself geometry
Sub-directory containing the data related to an assembly geometry
where the sub-directories in Table 30 are described in the following subsections.
4.3.1 The /PURE-GEOM/ sub-directory in sybilt
Table 31: The contents of the sybilt /PURE-GEOM/ sub-directory
Name
Type
Condition
Units Comment
PARAM
I(6)
NCODE
I(6)
ZCODE
XXX
R(6)
R(P4 + 1)
P4 ≥ 1
1
cm
YYY
R(P5 + 1)
P5 ≥ 1
cm
ZZZ
R(P6 + 1)
P6 ≥ 1
cm
SIDE
R(1)
P1 ≥ 8
cm
with the dimension parameter Pi , representing:
Record containing the parameters for a SYBIL tracking on a pure geometry Pi
Record containing the types of boundary conditions
on each surface Nβ,j
Record containing the albedo value on each surface
x−directed mesh coordinates after mesh-splitting for
type 2, 5 and 7 geometries. Region-ordered radius
after mesh-splitting for type 3 and 6 geometries
y−directed mesh coordinates after mesh-splitting for
type 5, 6 and 7 geometries
z−directed mesh coordinates after mesh-splitting for
type 7 and 9 geometries
Side of a hexagon for type 8 and 9 geometries
IGE–351
• The type of geometry P1
2 Cartesian 1-D geometry
3 Tube 1-D geometry
4 Spherical 1-D geometry
5 Cartesian 2-D geometry
P1 =
6 Tube 2-D geometry
7 Cartesian 3-D geometry
8 Hexagonal 2-D geometry
9 Hexagonal 3-D geometry
• The type of hexagonal symmetry βh = P2
1 S30
2 SA60
3 SB60
4 S90
5 R120
βh =
6 R180
7 SA180
8 SB180
9 COMPLETE
• The quadrature parameter P3
• The number of x−directed or radial mesh intervals in the geometry P4
• The number of y−directed mesh intervals in the geometry P5
• The number of z−directed mesh intervals in the geometry P6
The type of boundary conditions used will be defined in the following way
0 Not used
1 Void boundary condition
2 Reflection boundary condition
3 Diagonal reflection boundary condition
Nβ,j =
4 Translation boundary condition condition
5 Symmetric reflection boundary condition
6 Albedo boundary condition
49
IGE–351
50
4.3.2 The /DOITYOURSELF/ sub-directory in sybilt
Table 32:
directory
Name
Type
PARAM
I(3)
NMC
RAYRE
PROCEL
POURCE
SURFA
I(M + 1)
R(Nr + M )
R(M, M )
R(M )
R(M )
The contents of the sybilt /DOITYOURSELF/ sub-
Condition
UnitsComment
cm
cm2
Record containing the parameters for a SYBIL tracking on a do-it-yourself geometry Pi
Offset of the first region in each cell
Radius of the tubes in each cell
Geometric matrix
Weight assigned to each cell
Surface of each cell
with the dimension parameter Pi , representing:
• The number of cells P1 = M
• The quadrature parameter P2
• The statistical option P3
P3 =
0 the statistical approximation is not used. Record ’PROCEL’ is used.
1 use the statistical approximation. Record ’PROCEL’ is not used.
IGE–351
51
4.3.3 The /EURYDICE/ sub-directory in sybilt
Table 33: The contents of the sybilt /EURYDICE/ sub-directory
Name
Type
PARAM
I(16)
XX
YY
LSECT
R(P6 )
R(P6 )
I(P6 )
NMC
NMCR
I(P6 + 1)
I(P6 + 1)
RAYRE
R(Mr )
MAIL
I(2, P6 )
ZMAILI
ZMAILR
IFR
ALB
I(P15 )
R(P16 )
I(P4 , P14 )
R(P4 , P14 )
INUM
I(P4 )
MIX
DVX
IGEN
I(P5 , P14 )
R(P5 , P14 )
I(P5 )
Condition
Units Comment
cm
cm
cm
cm
with the dimension parameter Pi , representing:
• The type of hexagonal symmetry P1
0 Cartesian assembly
1 S30
2 SA60
3 SB60
4 S90
P1 =
5 R120
6 R180
7 SA180
8 SB180
9 COMPLETE
Record containing the parameters for a SYBIL tracking on an assembly geometry Pi
x−thickness of the generating cells
y−thickness of the generating cells
Type of sectorization for each each generating cell.
Equal to zero for non-sectorized cells. Allowed values
are defined as Fsec in Section 3.2
Offset of the first region index in each generating cell
Offset of the first radius index in each generating cell.
Equal to NMC, unless the cell is sectorized.
Radius of the tubes in each generating cell.
Mr =NMCR(P6 + 1)
Offsets of the first tracking information in each generating cell. MAIL(1,:) contains offsets for the integer array ZMAILI; MAIL(2,:) contains offsets for the
real array ZMAILR.
The integer tracking information
The tracking lengths
Index numbers of incoming currents
Albedo or transmission factors corresponding to incoming currents
Index number of the merge cell associated to each
cell of the assembly
Index numbers of outgoing currents
Weights corresponding to outgoing currents
Index number of the generating cell associated to
each merged cell
IGE–351
52
• The type of multicell approximation P2
1 Roth approximation
2 Roth×4 or Roth×6 approximation
P2 =
3 DP-0 approximation
4 DP-1 approximation
• The type of cylinderization P3
1 Askew cylinderization
2 Wigner cylinderization
P3 =
3 Sanchez cylinderization
• The total number of cells P4
• The number of merged cells P5
• The number of generating cells P6
• The number of distinct interface currents P7
• The number of angles for 2-D quadrature P8
• The number of segments for 2-D quadrature P9
• The number of segments for homogeneous 2-D cells P10
• The number of segments for 1-D cells P11
• The track normalization option P12
P12 =
0 Normalize the tracks
1 Do not normalize the tracks
• The type of quadrature in angle and space P13
P13 =
0 Gauss quadrature
1 Equal weight quadrature
• The number of outgoing interface currents per cell P14
• The number of integer array elements in the tracking arrays P15
• The number of real array elements in the tracking arrays P16
IGE–351
4.4
53
The excelt dependent records on a /tracking/ directory
When the EXCELT: modules is used (CDOOR=’EXCELL’), the following elements in the vector Sit will
also be defined.
• S6t is the number of Legendre orders used for the flux expansions, where
S6t =
1
2
isotropic
linearly anisotropic.
• S7t is the specific EXCELL tracking procedure considered where
1
2
t
S7 =
3
4
Cartesian 2D/3D assembly using EXCELT:
hexagonal 2D/3D assembly using EXCELT:
2D cluster geometry using EXCELT:
2D and 3D Cartesian assemblies with clusters using NXT:.
• S8t is the track normalization flag where
−1 direction dependent track normalization to exact volumes;
0 global track normalization to exact volumes;
S8t =
1 no normalization.
• S9t is the tracking type where
S9t =
0
1
means that a standard tracking procedure was considered (TISO);
means that a cyclic tracking procedure was considered (TSPC).
t
is the type of boundary conditions where
• S10
t
S10
=
0
1
means that isotropic (white) boundary conditions will be considered (PISO);
means that mirror-like (specular) boundary conditions will be considered (PSPC).
t
= 1) can be used only if a cyclic tracking procedure
Note that mirror-like boundary conditions (S10
t
was considered (S9 = 1).
t
• S11
= NΩ is the order of the azimuthal (2-D) or solid (3-D) angular quadrature. For 2-D geometry,
the order of the azimuthal quadrature represents:
– the number of equal sectors (trapezoidal quadrature) in the [0, π] range when the EXCELT:
module is used for Cartesian assemblies;
– the number of equal sectors (trapezoidal quadrature) in the [0, 2π/3] range when the EXCELT:
module is used for hexagonal geometries;
t
– the number of equal sectors (trapezoidal quadrature) in the [0, max(S12
, 2) π] range when the
EXCELT: module is used for cluster geometries;
– the number of trapezoidal sectors in the [0, π/2] range when the NXT: module is used.
For 3-D geometry, the order of the solid angle quadrature is:
– the order n of the EQn quadrature in a quadrant (0 ≤ ϕ ≤ π/2 and 0 ≤ θ ≤ π/2) when
the EXCELT: module is used for Cartesian assemblies for Ndir = n(n + 2)/8 direction in each
quadrant;
– the number of equal sectors (trapezoidal quadrature) in the [0, 2π/3] range when the EXCELT:
module is used for hexagonal geometries;
IGE–351
54
– not used for the EXCELT: module in cluster geometries;
– the order n of the EQn , LCn or LTn quadrature in a quadrant with 0 ≤ ϕ ≤ π/2 and
0 ≤ θ ≤ π/2. When the NXT: modules is used, the number Ndir of directions for the azimuthal
(2-D) or solid (3-D) angle quadrature results in Ndir = n(n + 2)/8 directions for the EQn
quadrature, Ndir = 3n(n + 2)/8 for the LCn quadrature and Ndir = 3n2 /2 for the LTn
quadrature.
t
• S12
is the angular symmetry factor;
t
• S13
is the polar quadrature type:
t
S13
0 Gauss-Legendre
1 CACTUS type 1
2 CACTUS type 2
=
3 McDaniel
4 McDaniel with P1 constraint
5 Gauss optimized.
t
• S14
is the order of the polar quadrature.
t
• S15
is the azimuthal (2-D) or solid (3-D) angle quadrature type where
t
S15
1 for a
2
for a
3 for a
4 for a
=
5
for a
6
for
a
7 for a
EQn (3-D) or trapezoidal (2-D) quadrature;
Gauss quadrature (2-D hexagonal geometries);
median angle quadrature;
LCn 3-D quadrature;
LTn 3-D quadrature;
µ1 –optimized level-symmetric 3-D quadrature;
quadrupole range (QR) 3-D quadrature.
t
• S16
is the number of geometric dimensions (1, 2 or 3).
t
• S17
is the number of tracking points on a line.
t
• S18
is the maximum length of a track.
t
• S19
is the total number of tracks generated.
t
• S20
is the total number of track directions processed.
t
• S21
is the line format option for TLM: module, where
t
S21
=
0
1
short format
complete format.
t
• S22
is the vectorization option for computing collision probability matrices where
t
S22
0 scalar algorithm. The tracking is readed for each energy group.
1 vectorial algorithm. The tracking is readed once and the collision probability
matrices are computed in many energy groups.
2 vectorial algorithm of type EXCELL:. The tracking is computed in DOORVP
=
and the collision probability matrices are computed in many energy groups.
3
vectorial algorithm of type NXT:. The tracking is computed in DOORVP
and the collision probability matrices are computed in many energy groups.
IGE–351
55
t
• S23
is the tracking flag, where
t
S23
−1 the LCM object information is used for Monte-Carlo calculations. No
tracking file produced.
0 this option de-activates the tracking file production if TISO or TSPC are
=
specified.
1 this option produces the tracking file.
t
• S39
is the number in a prismatic 3D geometry when a prismatic tracking is considered (0 otherwise).
The following records will also be present on the main level of a /tracking/ directory.
Table 34: The EXCELT: records in /tracking/
Name
Type
Condition
EXCELTRACKOP
R(40)
ICODE
I(6)
ALBEDO
R(6)
EXCELL
Dir
S7t < 4
NXTRecords
PROJECTION
Dir
Dir
S7t = 4
t
S39
>0
Units
Comment
array Ri containing additional EXCELL or NXT
tracking parameters.
array Iβ,k containing the surface albedo index (geometric surface albedo βg,k are used if Iβ,k < 0 while
physical surface albedo βp,k are used if Iβ,k > 0).
array βg,k containing the geometric surface albedo
(used only if Iβ,k ≥ 0).
directory containing additional EXCELT: records for
the cases where S7t = 1 or S7t = 3.
directory containing additional NXT: records.
directory containing the analysis of the projection of
a 3D prismatic geometry.
The record Ri contains the following information:
• R1 is the maximum error allowed on the exponential function.
• R2 is the user requested tracking density in cm−1 and in cm−2 respectively for 2D and 3D calculations.
• R3 is the maximum distance in cm between an integration line and a surface.
• R4 is the computed tracking density in cm−1 and in cm−2 respectively for 2D and 3D calculations
(used only if S7t = 4).
• R5 is the computed line spacing in cm (used only if S7t = 4).
• R6 is the weight of the spatial quadrature (used only if S7t = 4).
• R7 is the minimal radius of the circle (2-D) or sphere (3-D) containing the geometry (used only if
S7t = 4).
• R8 is the x position of the center of the minimal circle (2-D) or sphere (3-D) containing the geometry
(used only if S7t = 4).
IGE–351
56
• R9 is the y position of the center of the minimal circle (2-D) or sphere (3-D) containing the geometry
(used only if S7t = 4).
• R10 is the z position of the center of the minimal circle (2-D) or sphere (3-D) containing the
geometry (used only if S7t = 4).
• R40 user requested tracking density in cm−1 for inline contruction of 3D tracks when a prismatic
t
tracking is considered (only used if S39
> 0).
The /NXTRecords/ directory contains the information required to track the geometry using the NXT:
module module once it has been analyzed. The contents of this directory is presented in Table 35.
Table 35: Global geometry records in /NXTRecords/
Name
Type
Condition
UnitsComment
G00000001DIM
I(40)
G00000001CUF
I(2, N5GG )
G00000001CIS
I(4, N4GG )
G00000001CFE
I(0 : 8, N4GG )
G00000001SMX
GG
D(0 : N13
)
cm
G00000001SMY
GG
D(0 : N14
)
cm
G00000001SMZ
GG
D(0 : N15
)
N1GG = 3
cm
G00000001SMR
D(0 : 1)
N2GG = 1
cm
KEYMRG
GG
GG
I(−N23
: N22
)
MATALB
GG
GG
I(−N23
: N22
)
array NiGG containing the dimensioning information
required to rebuilt the assembly
GG
array Di,j
containing the assembly description of
the geometry in terms of cells and rotations. The
first element (i = 1) identifies the cell number while
the second element identifies the cell rotation
GG
array Si,j
containing the cell intrinsic symmetry
properties. A value of 1 indicates that a center cell
reflexion symmetry is present while a value of 0 indicates that the symmetry is not considered (see below
for a more complete description of this array)
GG
array Fi,j
containing the assembly external surface
identification index (see below for a more complete
description of this array)
array xGG containing the x-directed mesh for the cell
assembly in a Cartesian or Cylindrical geometry and
the x position of the cell center for an hexagonal
assembly (see below for more explanations)
array y GG containing the y-directed mesh for the cell
assembly in a Cartesian or Cylindrical geometry and
the y position of the cell center for an hexagonal
assembly (see below for more explanations)
array z GG containing the z-directed mesh for the cell
assembly (see below for more explanations)
the radius rGG of the outer assembly boundary (see
below for more explanations)
array MRGi containing the merged surface and region number associated with each individual surfaces
and regions in this geometry
array containing the albedo number associated with
each surface and the physical mixture number associated with each region in this geometry
continued on next page
IGE–351
57
Global geometry records in /NXTRecords/
Name
Type
HOMMATALB
GG
GG
I(−N23
: N22
)
SAreaRvolume
GG
GG
D(−N23
: N22
)
Condition
continued from last page
UnitsComment
array containing the albedo number associated with
each surface and the virtual (homogenization) mixture number associated with each region in this geometry
array containing the area (Sα in cm for 2-D and cm2
for 3-D problems) and volume (Vi cm2 for 2-D and
cm3 for 3-D problems) associated with each surface
and region in this geometry
The dimensioning vector for the global geometry contains the following information:
• N1GG number of dimensions for the problem.
• N2GG type of boundary. A value of 0 indicates a Cartesian geometry, a value of 1 indicates a
cylindrical geometry and a value of 2 an hexagonal geometry.
• N3GG first direction to process in the analysis. For cylinder, this is the direction of the first axis of
the plane normal to the cylinder axis. For Cartesian and hexagonal geometries a value of 1 (x-axis)
is selected by default.
• N4GG number of cells in the original geometry (before unfolding).
• N5GG number of cells in the geometry after the original geometry is unfolded according to the
symmetries.
• N6GG diagonal symmetry flag. A value of 0 indicates that this symmetry is not used. A value of
−1 indicates that the symmetry is used for the x− = y+ plane and a value of 1 that the symmetry
is used for the x+ = y plane.
• N7GG flag to identify symmetries with respect to the x-axis (x− or x+ ). A value of 0 indicates that
no symmetry is present, N7GG = ±1 is for a SYME symmetry at the x± plane, N7GG = ±2 represents
a SSYM symmetry at the x± plane and N7GG = 3 implies a translation symmetry is the x direction
(x− = x+ ).
• N8GG flag to identify symmetries with respect to the y-axis (y− or y+ ). A value of 0 indicates that
no symmetry is present, N7GG = ±1 is for a SYME symmetry at the y± plane, N7GG = ±2 represents
a SSYM symmetry at the y± plane and N7GG = 3 implies a translation symmetry is the y direction
(y− = y+ ).
• N9GG flag to identify symmetries with respect to the z-axis (z− or z+ ). A value of 0 indicates that
no symmetry is present, N7GG = ±1 is for a SYME symmetry at the z± plane, N7GG = ±2 represents
a SSYM symmetry at the z± plane and N7GG = 3 implies a translation symmetry is the z direction
(z− = z+ ).
GG
• N10
number of x mesh subdivisions or hexagons in the original geometry.
GG
• N11
number of y mesh subdivisions or hexagons in the original geometry.
GG
number of z mesh subdivisions in the original geometry.
• N12
IGE–351
58
GG
• N13
number of x mesh subdivisions or hexagons in the unfolded geometry.
GG
• N14
number of y mesh subdivisions or hexagons in the unfolded geometry.
GG
• N15
number of z mesh subdivisions in the unfolded geometry.
GG
• N16
maximum number cells required to represent this geometry.
GG
• N17
maximum number of region for this geometry.
GG
• N18
total number of clusters in this geometry.
GG
• N19
maximum number of pins in this geometry.
GG
• N20
maximum dimensions of any mesh array for a cell in this geometry.
GG
• N21
maximum dimensions of any mesh array for a pin in this geometry.
GG
• N22
number of external surfaces for this geometry.
GG
• N23
number of regions for this geometry.
GG
• N24
maximum number of external surfaces in a sub-geometry included in this geometry.
GG
maximum number of regions in a sub-geometry included in this geometry.
• N25
GG
for the axis of symmetry is as follows
The indexing of array Si,j
1. Cartesian assemblies:
• i = 1 refers to a reflexion of the geometry on a plane normal the x-axis;
• i = 2 refers to a reflexion of the geometry on a plane normal the y-axis;
• i = 3 refers to a reflexion of the geometry on the plane x = y;
• i = 4 refers to a reflexion of the geometry on a plane normal the z-axis.
2. Hexagonal assemblies (symmetries not yet programmed).
• i = 1 refers to a reflexion of the geometry on a plane normal the u-axis;
• i = 2 refers to a reflexion of the geometry on a plane normal the v-axis;
• i = 3 refers to a reflexion of the geometry on the plane w;
• i = 4 refers to a reflexion of the geometry on a plane normal the z axis.
GG
GG
represents the
The indexing of array Fi,j
for external surface identification is as follows. First F0,j
GG
can take
number of times the cell appears in the geometry after it has been unfolded. For i > 0, Fi,j
the following values
1 surface associated with direction i of cell j is an external boundary of the assembly
GG
Fi,j
=
0 surface associated with direction i of cell j is not an external boundary of the assembly
with the following planes associated with different values of i:
1. Cartesian assemblies:
• i = 1 surfaces on the x− plane for cell j;
• i = 2 surfaces on the x+ plane for cell j;
• i = 3 surfaces on the y− plane for cell j;
• i = 4 surfaces on the y+ plane for cell j;
• i = 5 surfaces on the z− plane for cell j;
IGE–351
59
26
27
28
12
11
15
31
17
16
32
9
2
7
6
33
21
20
8
19
Face= 3 or -3
U=1
Face= 1 or -5
W=2
Face= 0
U=2
37
36
18
34
Face= 2 or -4
V=1
22
10
1
5
23
3
4
13
29 14
30
24
25
Face= 4 or -2
W=1
Face= 5 or -1
V=2
35
Figure 3: Example of an assembly of hexagons (left) and external faces identification for an hexagon
• i = 6 surfaces on the z+ plane for cell j.
2. Hexagonal assemblies (see Figure 3):
• i = 1 surfaces on the u− plane for cell j;
• i = 2 surfaces on the u+ plane for cell j;
• i = 3 surfaces on the v− plane for cell j;
• i = 4 surfaces on the v+ plane for cell j;
• i = 5 surfaces on the z− plane for cell j;
• i = 6 surfaces on the z+ plane for cell j;
• i = 7 surfaces on the w− plane for cell j;
• i = 8 surfaces on the w+ plane for cell j.
The arrays xGG , y GG , z GG and rGG contain the following information:
1. Cartesian assemblies:
GG
• xGG
are the lower and upper x limits of mesh element i (i = 1, nx );
i−1 and xi
GG
• yj−1
and yjGG are the lower and upper y limits of mesh element j (j = 1, ny );
GG
• zk−1
and zkGG are the lower and upper z limits of mesh element k (k = 1, nz ).
2. Hexagonal assemblies (see Figure 3):
• xGG
= h is the width of one face of the hexagon and xGG
is the position in x of the center of
0
i
cell i in the assembly;
• y0GG = h is the width of one face of the hexagon and yjGG is the position in y of the center of
cell j in the assembly;
GG
• zk−1
and zkGG are the lower and upper z limits of mesh element k (k = 1, nz ).
As we noted above, the global geometry is always an assembly containing cells. For each cell i in this
assembly, several records will be generated in the /NXTRecords/ directory. These records are identified
using a FORTRAN CHARACTER*12 variable as follows
INTEGER
I
CHARACTER*12 NAMREC
CHARACTER*3 NREC
WRITE(NAMREC,’(A1,I8.8,A3)’) ’C’,I,NREC
IGE–351
60
where the variable NREC can take the following values:
• DIM for dimensioning information;
• SMR for the radial mesh description;
• SMX for the x-directed mesh description;
• SMY for the y-directed mesh description;
• SMZ for the z-directed mesh description;
• MIX for physical mixture description;
• HOM for virtual mixture description;
• VSE for areas and volumes results;
• VSI for local surfaces and regions identification;
• RID for final region numbering;
• SID for final surface numbering
• PNT for pin contents description;
• PIN for pins location.
In Table 36, a description of the additional /NXTRecords/ records associated with cell i = 1 can be
found.
Table 36: Cell i = 1 records in /NXTRecords/
Name
Type
Condition
UnitsComment
C00000001DIM
I(40)
C00000001SMR
C00000001SMX
D(N2GC )
D(N3GC )
cm
cm
C00000001SMY
D(N4GC )
cm
C00000001SMZ
D(N5GC )
cm
C00000001MIX
I(N6GC )
C00000001HOM
I(N6GC )
C00000001VSE
D(−N9GC : N8GC )
C00000001VSI
I(4, −N9GC : N8GC )
array NjGC containing the dimensioning information
required to rebuilt the cell
array rjGC containing the cell radial mesh description
array xGC
containing the cell x-directed mesh dej
scription
array yjGC containing the cell y-directed mesh description
array zjGC containing the cell z-directed mesh description
array MjGC containing the cell physical mixture for
each region
array HjGC containing the cell virtual mixture for
each region
GC
array SVGC
containing surface area j (SVGC
j
−j = Sj
2
in cm for 2-D and cm for 3-D problems) and regional
volumes j (SVGC
= VjGC in cm2 for 2-D and cm3 for
j
3-D problems)
array VSIGC
k,j containing the location of a surface (j <
0) and a region (j > 0)
continued on next page
IGE–351
61
Cell i = 1 records in /NXTRecords/
Name
Type
C00000001RID
I(N8GC )
C00000001SID
I(N9GC )
C00000001PNT
C00000001PIN
GC
I(3, N18
)
GC
D(−1 : 4, N18
)
continued from last page
Condition
UnitsComment
index array RIDGC
associating local and global rej
gion numbering
index array SIDGC
j,i associating local and global outer
surface numbering
array PCGC
k,j containing the cell pin contents
array pGC
k,j containing the location of the pins in cell
Note that the record names above are built using the following FORTRAN instructions:
WRITE(NAMREC,’(A1,I8.8,A3)’) ’C’,i,NAMEXT
The cell dimensioning array NiGC for cell i contains the following information:
• N1GC cell geometry type (see the definition of S1G in Section 3.2);
• N2GC dimensions of the radial mesh array;
• N3GC dimensions of the x-directed mesh array;
• N4GC dimensions of the y-directed mesh array;
• N5GC dimensions of the z-directed mesh array;
• N6GC dimensions of the mixture record;
• N7GC geometry level (1 for cell);
• N8GC number of regions in the cell before symmetry considerations;
• N9GC number of surfaces in the cell before symmetry considerations;
GC
• N10
number of regions in the cell after symmetry considerations;
GC
• N11
number of surfaces in the cell after symmetry considerations;
GC
• N12
first global region number for cell;
GC
• N13
last global region number for cell;
GC
• N14
first global surface number for cell;
GC
last global surface number for cell;
• N15
GC
number of pin cluster geometries in cell;
• N16
GC
• N17
first pin cluster geometry associated with cell;
GC
• N18
total number of pins in cell;
GC
• N19
number of times this cell is used in the global cell.
while the remaining elements are not used.
The array xGC
contains the following information:
j
IGE–351
62
• xGC
−1 contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction x. This center is located at:
xc =
GC
xGc
nx + x0
2
where we have used nx = N3GC .
GC
• xGC
are the lower and upper x limits of mesh element j (j = 1, nx ).
j−1 and xj
The array yjGC contains the following information:
GC
• y−1
contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction y. This center is located at:
yc =
GC
ynGC
y + y0
2
where we have used ny = N4GC .
GC
• yj−1
and yjGC are the lower and upper y limits of mesh element j (j = 1, ny ).
The array zjGC contains the following information:
GC
• z−1
contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction z. This center is located at:
zc =
GC
znGC
z + z0
2
where we have used nz = N5GC .
GC
• zj−1
and zjGC are the lower and upper z limits of mesh element j (j = 1, nz ).
The array rjGC contains the following information:
GC
• r−1
= r0GC = 0.
GC
• rj−1
≤ r ≤ rjGC describes the position in r of mesh element j (j = 1, N2GC ).
The array pGC
contains the following information:
j
• pGC
−1 is the angular position of z-, x- or y-directed pin with respect to the x, y or z axis.
• pGC
is the radial position of z-, x- or y-directed pin with respect to the x − y, y − z or z − x center
0
of the cell where the pin is located.
• pGC
is the height of a x-directed pin.
1
• pGC
is the height of a y-directed pin.
2
• pGC
is the height of a z-directed pin.
3
• pGC
is the outer radius of the pin.
4
In Table 37, a description of the additional /NXTRecords/ records associated with pin i = 1 can be
found. These records are identified using a procedure similar to that used for cell records, namely
INTEGER
I
CHARACTER*12 NAMREC
CHARACTER*3 NREC
WRITE(NAMREC,’(A1,I8.8,A3)’) ’P’,I,NREC
where the variable NREC can take the same values as for cell records, except for NREC=PNT and NREC=PIN
which are now forbidden.
IGE–351
63
Table 37: Pin i = 1 records in /NXTRecords/
Name
Type
Condition
UnitsComment
P00000001DIM
I(40)
P00000001SMR
P00000001SMX
D(N2GP )
D(N3GP )
cm
cm
P00000001SMY
D(N4GP )
cm
P00000001SMZ
D(N5GP )
cm
P00000001MIX
I(N6GP )
P00000001HOM
I(N6GP )
P00000001VSE
D(−N9GP : N8GP )
P00000001VSI
I(4, −N9GP : N8GP )
P00000001RID
I(N8GP )
P00000001SID
I(N9GP )
array NjGP containing the dimensioning information
required to rebuilt the pin
array rjGP containing the pin radial mesh description
array xGP
containing the pin x-directed mesh dej
scription
array yjGP containing the pin y-directed mesh description
array zjGP containing the pin z-directed mesh description
array MjGP containing the pin physical mixture for
each region
array HjGP containing the pin virtual mixture for
each region
GP
array SVGP
containing surface area j (SVGP
j
−j = Sj
in cm for 2-D and cm2 for 3-D problems) and regional
volumes j (SVGP
= VjGP in cm2 for 2-D and cm3 for
j
3-D problems)
array VSIGP
k,j containing the location of a surface (j <
0) and a region (j > 0)
index array RIDGP
associating local and global rej
gion numbering
index array SIDGP
j,i associating local and global outer
surface numbering
The pin dimensioning array N GP contains the following information:
GP
• N1,
pin geometry type (see the definition of S1G in Section 3.2);
GP
• N2,
dimensions of the radial mesh array;
GP
• N3,
dimensions of the x-directed mesh array;
GP
• N4,
dimensions of the y-directed mesh array;
GP
• N5,
dimensions of the z-directed mesh array;
GP
• N6,
dimensions of the mixture record;
GP
• N7,
geometry level (2 for pins);
GP
• N8,
number of regions in the pin before symmetry considerations;
GP
• N9,
number of surfaces in the pin before symmetry considerations;
GP
• N10
number of regions in the pin after symmetry considerations;
GP
• N11
number of surfaces in the pin after symmetry considerations;
IGE–351
64
GP
• N12
first global region number for pins in cluster;
GP
• N13
last global region number for pins in cluster;
GP
• N14
first global surface number for pins in cluster;
GP
• N15
last global surface number for pins in cluster;
GP
• N16
first pin cluster geometry for pins in cluster.
GP
• N17
total number of pins in cluster.
while the remaining elements are not used. The array xGP
contains the following information:
j
• xGP
−1 contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction x. This center is located at:
xc =
GP
xGP
nx + x0
2
where we have used nx = N3GP .
GP
• xGP
re the lower and upper x limits of mesh element j (j = 1, nx ).
j−1 and xj
The array yjGP contains the following information:
GP
• y−1
contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction y. This center is located at:
yc =
GP
ynGP
y + y0
2
where we have used ny = N4GP .
GP
• yj−1
and yjGP are the lower and upper y limits of mesh element j (j = 1, ny ).
The array zjGP contains the following information:
GP
• z−1
contains the displacement of the center of the cylindrical region with respect to the center of
the Cartesian mesh in direction z. This center is located at:
zc =
GP
znGP
z + z0
2
where we have used nz = N5GP .
GP
• zj−1
and zjGP are the lower and upper z limits of mesh element j (j = 1, nz ).
The array rjGP contains the following information:
GP
• r−1
= r0GP = 0.
GP
• rj−1
≤ r ≤ rjGP describes the position in r of mesh element j with j = 1, N2GP .
Finally the /NXTRecords/ directory also contains records associated with global identification of the
surfaces and volumes as illustrated in Table 38.
IGE–351
65
Table 38: Global geometry records in /NXTRecords/
Name
Type
TrackingDnsA
t
D(S20
)
TrackingDirc
t
D(N1GG , S20
)
TrackingOrig
t
D(N1GG , Np , S20
)
TrackingWgtD
t
D(S20
)
VTNormalize
GG
D(N22
)
VTNormalizeD
GG
t
D(N22
, S20
)
KEYMRG
MATALB
GG
GG
I(−N23
, N22
)
GG
GG
I(−N23 , N22
)
HOMMATALB
GG
GG
I(−N23
, N22
)
SAreaRvolume
GG
GG
D(−N23
, N22
)
Condition
UnitsComment
cm
cm
S8t = −1
array Di containing the spatial spacing for each track
direction
array αj,i containing the director cosine for axis j for
each track direction
array Lk,j,i containing the origin in space (k =
1, N1GG ) and the direction of the normal plan for each
plane j and track direction i
array Wi containing the integration weight for each
track direction
array Ri containing the ratio of the analytical and
numerical volume for each region
array Ri containing the ratio of the analytical and
numerical volume for region i for each track direction
array MRGi containing the global merging index
array containing the albedo number associated with
each surface and the physical mixture number associated with each region
array containing the albedo number associated with
each surface and the virtual mixture number associated with each region
array containing the area (Sα in cm for 2-D and cm2
for 3-D problems) and volumes (Vi cm2 for 2-D and
cm3 for 3-D problems) of each external surface and
region in the geometry
IGE–351
4.5
66
The mccgt dependent records on a /tracking/ directory
When the MCCGT: module is used (CDOOR=’MCCG’), an additional state vector named MCCG-STATE
is set in EXCELT: data structure. The components Mti of MCCG-STATE are:
• Mt1 : (LCACT) The polar quadrature type used with the method of characteristics
0
1
2
t
M1 =
3
4
5
Gauss-Legendre
CACTUS type 1
CACTUS type 2
McDaniel
McDaniel with P1 constraint
Gauss optimized.
• Mt2 : (NMU) The order of the polar quadrature.
• Mt3 : (KRYL) GMRES acceleration switch:
Mt3 =
0 free inner iterations
≥ 1 GMRES(Mt3 ) acceleration of inner iterations
≤ 1 Bi-CGSTAB acceleration of inner iterations
• Mt4 : (IDIFC) Type of solution operator:
0
1
Mt4 =
transport flux solution selected
CDD diffusion flux solution selected (no inner iterations are performed
in this case, only an ACA resolution is performed)
• Mt5 : (NMAX) The maximum number of elements in a single track.
• Mt6 : (LMCU) The dimension of the connection matrix MCU.
• Mt7 : (IACC) ACA preconditioning switch:
Mt7 =
0
≥1
no ACA preconditioning
ACA preconditioning of inner/multigroup iterations
If the number of inner iterations is set to 1, ACA is used as a rebalancing technique for multigroup
iterations and Mt7 is the maximum number of iterations allowed to solve the ACA system.
• Mt8 : (ISCR) SCR preconditioning switch:
Mt8
=
0
≥1
no SCR preconditioning
SCR preconditioning of inner/multigroup iterations
If the number of inner iterations is set to 1, SCR is used as a rebalancing technique for multigroup
iterations and Mt8 is the maximum number of iterations allowed to solve the SCR system.
• Mt9 : (LPS) The dimension of the surface-to-region collision probabilities array if SCR is used.
• Mt10 : (ILU) The type of preconditioning for the resolution with BICGSTAB of the ACA corrective
system if ACA is used:
0 no preconditioning
1 diagonal preconditioning
Mt10 =
≥ 2 ILU0 preconditioning
IGE–351
67
• Mt11 : (ILEXA) Flag to force the usage of exact exponentials for preconditioner calculation:
Mt11
=
0 not forced
1 forced
• Mt12 : (ILEXF) Flag to force the usage of exact exponentials for flux calculation:
Mt12 =
0 not forced
1 forced
• Mt13 : (MAXI) Maximum number of inner iterations.
• Mt14 : (LTMT) Flag for the usage of a tracking merging technique while building the ACA matrices
in order to obtain a two-step ACA acceleration:
Mt14
=
0 no tracking merging
1 tracking merging
• Mt15 : (STIS) Flag for the flux integration strategy by the characteristics method:
Mt15 =
0 direct approach with asymptotical treatment
1 “Source term isolation” approach: optimized strategy with asymptotical treatment
−1 ”MOCC/MCI”-like approach: optimized strategy without asymptotical treatment
• Mt16 : (NPJJM) Effective number of angular mode-to-mode self-collision probabilities to be calculated
per group and region if Mt15 = 1 e.g.
anisotropy
P0
P1
P2
P3
2D
1
4
13
31
3D
1
7
27
76
• Mt17 : (LMCU0) Effective number of non-diagonal elements to store for the ILU0 decomposition for
ACA preconditioning.
• Mt18 : (IFORW) Flag to set the solution type for the ACA and characteristics system:
Mt18 =
0 direct solution
1 adjoint solution
• Mt19 : (NFUNL) Number of spherical harmonics components used to expand the flux and the sources.
• Mt20 : (NLIN) Number of polynomial components used to expand the flux and the sources in space.
The following records will also be present on the main level of a /tracking/ directory.
IGE–351
68
Table 39: The MCCGT: records in /tracking/
Name
Type
Condition
MCCG-STATE
I(40)
REAL-PARAM
XMU$MCCG
ZMU$MCCG
WZMU$MCCG
PI$MCCG
R(4)
R(Mt2 )
R(Mt2 )
R(Mt2 )
I(Ndim )
INVPI$MCCG
NZON$MCCG
I(S1t + S5t )
I(S1t + S5t )
t
S15
>0
NZONA$MCCG
I(S1t + S5t )
t
S15
>0
V$MCCG
VA$MCCG
KM$MCCG
IM$MCCG
MCU$MCCG
R(S1t + S5t )
R(S1t + S5t )
I(Ndim )
I(Ndim + 1)
I(Mt6 )
JU$MCCG
I(Ndim )
IS$MCCG
I(S5t )
JS$MCCG
I(Mt7 )
ISGNR$MCCG
I(8(S6t )2 )
KEYCUR$MCCG
I(S5t )
KEYFLX$MCCG
I(S1t , F )
KEYANI$MCCG
I((S6t )2 )
t
S15
>0
t
S15
>0
Mt7 > 0
Mt7 > 0
Mt7 > 0
t
S15
>0
Mt3 ≥ 2
Mt1 > 0
Mt1 > 0
S9t = 1
S9t = 1
UnitsComment
Vector describing the various parameters associated
with this data structure Mti , as defined in Section 4.5.
Real parameters Ri for the MCCG tracking.
Inverse of the polar quadrature sines.
Cosines of the polar quadrature set.
Weights of the polar quadrature set.
Permutation array for ACA according to iold =
Π(inew ). The dimension of this array is
t
S1 + S5t if S9t = 0;
Ndim =
S1t
if S9t = 1.
Inverse permutation array for ACA inew = Π(iold )
Index-number of the mixture type assigned to each
volume and the albedo number assigned to each surface.
Index-number of the mixture type assigned to each
volume and the albedo number assigned to each surface (-7 for void boundary conditions).
Volumes and numerical surfaces.
Renumbered Volumes and numerical surfaces.
Connection matrix for ACA.
Connection matrix for ACA.
Connection matrix for ACA.
Used for ILU0 decomposition in the preconditioning
of ACA system.
Connection matrix for surface-to-volume probability
in SCR.
Connection matrix for surface-to-volume probability
in SCR.
Signs for spherical harmonics on the 8 octant angular
modes.
Index for outgoing currents at the domain boundaries.
Index for flux moments. The second dimension of
this array is
t
if S19
= 1;
S6t
t
t
t
F = S6 × (S6 + 1)/2 if S19 = 2;
t 2
t
(S6 )
if S19
= 3.
Index for currents.
continued on next page
IGE–351
69
The MCCGT: records in /tracking/
Name
Type
Condition
PJJIND$MCCG
I(2Mt16 )
Mt15 = 1
IM0$MCCG
I(Ndim + 1)
MCU0$MCCG
I(Mt17 )
continued from last page
UnitsComment
Index of modes connection for non vanishing angular
mode-to-mode self-collision probabilities
Mt7 > 0
Mt3 = 3
Connection matrix for non-diagonal elements of
ILU0-ACA.
Mt7 > 0
Mt3 = 3
Connection matrix for non-diagonal elements of
ILU0-ACA.
with the real parameter Ri , representing:
• Rt1 : Convergence criterion on inner iterations.
• Rt2 : Step characteristics selection criterion:
Rt2 =
0.0 step characteristics scheme
> 0.0 diamond differencing scheme.
• Rt3 : Track spacing in cm for 3D prismatic tracking.
• Rt4 : Tracking symmetry factor for maximum track length calculation during the calculation of a
3D prismatic tracking.
The following records will also be present in the /PROJECTION/ directory of a /tracking/ directory
when a prismatic tracking is considered.
Table 40: The MCCGT: records in /PROJECTION/
Name
Type
Condition
UnitsComment
ZCOORD
IND2T3
R(Mt18 + 1)
I(Nind )
t
S39
>0
t
S39 > 0
cm
VNORF
D(Nnor )
t
S39
>0
The z−directed mesh position
Volume and surfaces index for a 3D prismatic geometry. Its size is Nind = (N2D + 1)(Mt18 + 2) where
N2D is the number of volumes and surfaces in the
initial 2D tracking
Angular dependent normalization factors for a 3D
prismatic extended tracking. Its size is Nnor =
2S1t Mt2 Nangl where Nangl is the number of tracking
angles in the initial 2D tracking
IGE–351
4.6
70
The snt dependent records on a /tracking/ directory
When the SNT: operator is used (CDOOR=’SN’), the following elements in the vector Sit will also be
defined.
• S6t : (ITYPE) Type of SN geometry:
2 Cartesian 1-D geometry
3 Tube 1-D geometry
4 Spherical 1-D geometry
S6t =
5 Cartesian 2-D geometry
6 Tube 2-D geometry (R-Z geometry)
7 Cartesian 3-D geometry
• S7t : (NSCT) Number of spherical harmonics components used to expand the flux and the sources.
• S8t : (IELEM) Order of the spatial approximation:
1 Classical diamond scheme
2 Parabolic diamond scheme
S8t =
3 Cubic diamond scheme
• S9t : (not used)
t
: (not used)
• S10
t
• S11
: (LL4) Number of mesh-centered flux components in one energy group. Generally equal to S2t
t
≤ S2t .
except in cases where surfacic fluxes are appended to the unknown vector. S11
t
• S12
: (LX) Number of elements along the X axis.
t
• S13
: (LY) Number of elements along the Y axis.
t
• S14
: (LZ) Number of elements along the Z axis.
t
• S15
: (NLF) Order of the SN approximation (even number ≥ 2).
t
• S16
: (ISCAT) Number of terms in the scattering sources:
t
S16
1 Isotropic scattering in the laboratory system
2 Linearly anisotropic scattering in the laboratory system
=
n order n − 1 anisotropic scattering in the laboratory system
t
• S17
: (IQUAD) Type of angular quadrature:
t
S17
1
2
3
4
=
5
6
10
Level symmetric, Lathrop and Carlson type
Level symmetric, optimized µ1 values
Level symmetric, compatible with code SNOW
Legendre-Chebyshev quadrature
symmetric Legendre-Chebyshev quadrature
quadrupole range (QR) quadrature
Gauss-Legendre and Gauss-Chebyshev product quadrature
t
• S18
: (IFIX) Flag for negative flux fixup:
t
S18
=
0
1
Non enabled
Enabled
IGE–351
71
t
• S19
: (IDSA) Flag for synthetic diffusion acceleration:
t
S19
=
0
1
Non enabled
Enabled
t
• S20
: (NSTART) Type of acceleration for the scattering iterations:
t
S20
=
0 GMRES non enabled; use a one-parameter Livolant acceleration
> 0 Restarts the GMRES method every NSTART iterations
t
• S21
: (NSDSA) Number if inner flux iterations without DSA in 3-D cases if S8t ≥ 2.
t
• S22
: (MAXI) Maximum number of inner iterations (resp. maximum number of GMRES(m) iterations
t
if S20
> 0).
t
• S23
: (ILIVOL) Flag for enabling/disabling Livolant acceleration method.
t
S23
=
0
1
Non enabled
Enabled
t
• S24
: (icl1) number of free iterations in the Livolant method.
t
: (icl2) number of accelerated iterations in the Livolant method.
• S25
The following records will also be present on the main level of a /tracking/ directory.
Table 41: The snt records in /tracking/
Name
Type
NCODE
I(6)
ZCODE
R(6)
DSA
Dir
EPSI
R(1)
Condition
Units
1
t
S19
=1
1
Comment
Record containing the types of boundary conditions
on each surface. =0 side not used; =1 VOID; =2
REFL; =4 TRAN. NOODE(5) and NOODE(6) are not
used.
Record containing the albedo value (real number) on
each surface. ZOODE(5) and ZOODE(6) are not used.
Sub-directory containing the data related to the diffusion synthetic acceleration using BIVAC (2D) or
TRIVAC (3D). The specification of this directory is
given in Section 4.7 or in Section 4.8
Record containing the convergence criterion on inner
iterations.
If S6t = 2 (Cartesian 1-D geometry), the following records will also be present on the main level of a
/tracking/ directory.
IGE–351
72
Table 42: The snt records in /tracking/ (Cartesian 1-D geometry)
Name
Type
Condition
UnitsComment
U
t
R(S15
)
1
W
PL
t
R(S15
)
t
t
R(S16
, S15
)
1
1
Base points of the angular Gauss-Legendre quadrature.
Weights of the angular Gauss-Legendre quadrature.
Discrete values of the Legendre polynomials on the
quadrature base points.
If S6t = 3 (Tube 1-D geometry), the following records will also be present on the main level of a
/tracking/ directory. The number of discrete directions in two octants Nangl and the number of spherical
t
harmonics components of the flux Npn are given in term of the SN order N = S15
as
1 N 1 + N , if S t < 10;
17
2
2
Nangl =
1 N 2,
otherwise.
2
t
t
S16
1
S16
t
t
1+
+ (1 + S16
) (S16
mod 2)
Npn =
2
2
2
Table 43: The snt records in /tracking/ (tube 1-D geometry)
Name
Type
Condition
UnitsComment
JOP
U
I(N/2)
R(N/2)
1
UPQ
R(Nangl )
1
WPQ
R(Nangl )
1
ALPHA
PLZ
R(Nangl )
R(Npn , N/2)
1
1
PL
R(Npn , Nangl )
1
SURF
t
R(S12
+ 1)
1
Number of base points in each ξ level.
Base points (levels) of the angular quadrature in ξ
(positive values).
Direction cosines of the angular two-octants spherical harmonics quadrature in µ.
Weights of the angular two-octants spherical harmonics quadrature.
Angular redistribution parameters.
Discrete values of the real spherical harmonics on the
zero-weight base points.
Discrete values of the real spherical harmonics on the
quadrature base points.
Surfaces.
If S6t = 4 (Spherical 1-D geometry), the following records will also be present on the main level of a
/tracking/ directory.
IGE–351
73
Table 44: The snt records in /tracking/ (spherical 1-D geometry)
Name
Type
Condition
UnitsComment
U
t
R(S15
)
1
W
ALPHA
PLZ
t
R(S15
)
t
R(S15
)
t
R(S16
)
1
1
1
PL
t
t
R(S16
, S15
)
1
SURF
XXX
t
R(S12
+ 1)
t
R(S12
+ 1)
1
1
Base points of the angular Gauss-Legendre quadrature.
Weights of the angular Gauss-Legendre quadrature.
Angular redistribution parameters.
Discrete values of the Legendre polynomials on the
zero-weight base points at µ = −1.
Discrete values of the Legendre polynomials on the
quadrature base points.
Surfaces.
Mesh-edge radii.
If S6t = 5 (Cartesian 2-D geometry) or S6t = 6 (R-Z geometry), the following records will also be
present on the main level of a /tracking/ directory. The number of discrete directions in four octants
(including zero-weight points) Nangl and the number of spherical harmonics components of the flux Npn
t
are given in term of the SN order N = S15
as
Nangl =
Npn =
1
(N + 4)N
2
t
S16
t
1 + S16
2
Table 45: The snt records in /tracking/ (Cartesian 2-D and R-Z
geometries)
Name
Type
Condition
DU
R(Nangl )
1
DE
R(Nangl )
1
W
R(Nangl )
1
MRM
MRMY
DB
DA
DAL
PL
I(Nangl )
I(Nangl )
t
R(S12
, Nangl )
t
t
R(S12
, S13
, Nangl )
t
t
R(S12 , S13
, Nangl )
R(Npn , Nangl )
1
1
1
1
S6t = 6
UnitsComment
Direction cosines of the angular four-octants spherical harmonics quadrature in µ.
Direction cosines of the angular four-octants spherical harmonics quadrature in η.
Weights of the angular four-octants spherical harmonics quadrature.
Quadrature offsets.
Quadrature offsets.
Diamond-scheme parameter.
Diamond-scheme parameter.
Angular redistribution parameters.
Discrete values of the real spherical harmonics on the
quadrature base points.
IGE–351
74
If S6t = 7 (Cartesian 3-D geometry), the following records will also be present on the main level of
a /tracking/ directory. The number of discrete directions in height octants Nangl and the number of
t
spherical harmonics components of the flux Npn are given in term of the SN order N = S15
as
Nangl = (N + 2)N
t
Npn = 1 + S16
2
Table 46: The snt records in /tracking/ (Cartesian 3-D geometry)
Name
Type
Condition
UnitsComment
DU
R(Nangl )
1
DE
R(Nangl )
1
DZ
R(Nangl )
1
W
R(Nangl )
1
MRMX
MRMY
MRMZ
DC
DB
DA
PL
I(Nangl )
I(Nangl )
I(Nangl )
t
t
R(S12
, S13
, Nangl )
t
t
R(S12 , S14
, Nangl )
t
t
R(S13
, S14
, Nangl )
R(Npn , Nangl )
1
1
1
1
Direction cosines of the angular height-octants spherical harmonics quadrature in µ.
Direction cosines of the angular height-octants spherical harmonics quadrature in η.
Direction cosines of the angular height-octants spherical harmonics quadrature in ξ.
Weights of the angular height-octants spherical harmonics quadrature.
Quadrature offsets.
Quadrature offsets.
Quadrature offsets.
Diamond-scheme parameter.
Diamond-scheme parameter.
Diamond-scheme parameter.
Discrete values of the real spherical harmonics on the
quadrature base points.
IGE–351
4.7
75
The bivact dependent records on a /tracking/ directory
When the BIVACT: operator is used (CDOOR=’BIVAC’), the following elements in the vector Sit will
also be defined.
• S6t : (ITYPE) Type of BIVAC geometry:
2 Cartesian 1-D geometry
3 Tube 1-D geometry
4 Spherical 1-D geometry
S6t =
5 Cartesian 2-D geometry
6 Tube 2-D geometry
8 Hexagonal 2-D geometry
• S7t : (IHEX) Type
0
1
2
3
4
S7t =
5
6
7
8
9
of hexagonal symmetry if S6t = 8:
• S9t : (ICOL) Type
1
2
t
S9 =
3
4
of quadrature used to integrate the mass matrix:
non-hexagonal geometry
S30
SA60
SB60
S90
R120
R180
SA180
SB180
COMPLETE
• S8t : (IELEM) Type of finite elements:
< 0 Order −S8t primal finite elements
> 0 Order S8t dual finite elements. The Thomas-Raviart or Thomas-Raviart-Schneider
S8t =
method is used except if S9t = 4 in which case a mesh-centered finite difference
approximation is used
Analytical integration
Gauss-Lobatto quadrature (finite difference/collocation method)
Gauss-Legendre quadrature (superconvergent approximation)
mesh-centered finite difference approximation in hexagonal geometry
t
: (ISPLH) Type of hexagonal mesh splitting:
• S10
1 No mesh splitting
t
K 6 × (K − 1) × (K − 1) triangles per hexagon with finite-difference approximations
S10
=
3 × K × K losanges per hexagon with Thomas-Raviart-Schneider approximation
t
• S11
: (LL4) Order of the group-wise matrices. Generally equal to S2t except in cases where averaged
t
fluxes are appended to the unknown vector. S11
≤ S2t .
t
• S12
: (LX) Number of elements along the X axis in Cartesian geometry or number of hexagons.
t
• S13
: (LY) Number of elements along the Y axis.
t
• S14
: (NLF) Number of components in the angular expansion of the flux. Must be a positive even
number. Set to zero for diffusion theory. Set to 2 for P1 method.
IGE–351
76
t
• S15
: (ISPN) Type of transport approximation if NLF6= 0:
t
S15
=
0
1
Complete Pn approximation of order NLF−1
Simplified Pn approximation of order NLF−1
t
• S16
: (ISCAT) Number of terms in the scattering sources if NLF6= 0:
t
S16
1 Isotropic scattering in the laboratory system
2 Linearly anisotropic scattering in the laboratory system
=
n order n − 1 anisotropic scattering in the laboratory system
t
A negative value of S16
indicates that 1/3Dg values are used as Σg1 cross sections.
t
• S17
: (NVD) Number of base points in the Gauss-Legendre quadrature used to integrate void boundary
conditions if ICOL = 3 and NLF6= 0:
0 Use a (NLF+1)–point quadrature consistent with PNLF−1 theory
t
1 Use a NLF–point quadrature consistent with SNLF theory
S17
=
2 Use an analytical integration consistent with diffusion theory
The following records will also be present on the main level of a /tracking/ directory.
Table 47: The bivact records in /tracking/
Name
Type
Condition
UnitsComment
NCODE
I(6)
ZCODE
R(6)
SIDE
XX
R(1)
R(S1t )
S6t = 8
S6t 6= 8
cm
cm
YY
R(S1t )
S6t = 5 or 6
cm
DD
R(S1t )
S6t = 3 or 6
cm
KN
I(S1t × Nkn )
QFR
R(S1t × Nsurf )
BFR
MU
R(S1t × Nsurf )
t
I(S11
)
1
Record containing the types of boundary conditions
on each surface. =0 side not used; =1 VOID; =2
REFL; =4 TRAN; =5 SYME; =7 ZERO. NOODE(5)
and NOODE(6) are not used.
Record containing the albedo value (real number) on
each surface. ZOODE(5) and ZOODE(6) are not used.
Side of a hexagon.
Element-ordered X-directed mesh spacings after
mesh-splitting for type 2 and 5 geometries. Elementordered radius after mesh-splitting for type 3 and 6
geometries.
Element-ordered Y -directed mesh spacings after
mesh-splitting for type 5 and 6 geometries.
Element-ordered position used with type 3 and 6 geometries.
Element-ordered unknown list. Nkn is the number of
unknowns per element.
Element-ordered boundary condition. Nsurf = 4 in
Cartesian geometry and = 6 in hexagonal geometry.
Element-ordered boundary surface fractions.
Indices used with compressed diagonal storage mode
matrices.
continued on next page
IGE–351
77
The bivact records in /tracking/
continued from last page
Name
Type
Condition
ZGLOB
t
t 2
I(S12
× (S10
) )
*
BIVCOL
Dir
UnitsComment
Hexagon index assigned to each losange. This information is provided if and only if S6t = 8, S8t >
0 and S9t ≤ 3.
Sub-directory containing the unit matrices (mass,
stiffness, nodal coupling, etc.) for a finite element
discretization.
The following records will be present on the /BIVCOL/ sub-directory:
Table 48: Description of the /BIVCOL/ sub-directory
Name
Type
T
TS
R
RS
Q
QS
V
H
R(L)
R(L)
R(L × L)
R(L × L)
R(L × L)
R(L × L)
R(L × (L − 1))
R(L × (L − 1))
E
RH
QH
RT
QT
R(L × L)
R(6×6)
R(6×6)
R(3×3)
R(3×3)
Condition
UnitsComment
Cartesian linear product vector. L = |S8t | + 1
Cylindrical linear product vector.
Cartesian mass matrix.
Cylindrical mass matrix.
Cartesian stiffness matrix.
Cylindrical stiffness matrix.
Nodal coupling matrix.
Piolat transform coupling matrix (used with
Thomas-Raviart-Schneider method).
Polynomial coefficients.
Hexagonal mass matrix.
Hexagonal stiffness matrix.
Triangular mass matrix.
Triangular stiffness matrix.
IGE–351
4.8
78
The trivat dependent records on a /tracking/ directory
A TRIVAC–type tracking data structure is holding the information related to the ADI partitionning
of the system matrices in 1D, 2D or 3D. A one-speed discretizarion of the diffusion equation leads to a
matrix system of the form
~ =~
AΦ
S
(4.1)
where Φ may contains different types of unknowns: flux values, current values, polynomial coefficients,
etc.
The matrix A can be splitted in different ways. Many TRIVAC discretizations in Cartesian geometry
are based on the following ADI splitting:
⊤
⊤
A = U + Px XP⊤
x + Py YPy + Pz ZPz
where
U=
X, Y, Z =
Px , Py , Pz =
(4.2)
matrix containing the diagonal elements of A
symetrical matrices containing the nondiagonal elements of A
permutation matrices that ensure a minimum bandwidth for matrices X, Y and Z.
Similarly, many discretizations in hexagonal geometry are based on the following ADI splitting:
⊤
⊤
⊤
A = U + Pw WP⊤
w + Px XPx + Py YPy + Pz ZPz
.
(4.3)
The diffusion equation can also be solved using a Thomas-Raviart polynomial basis together with a
mixte-dual variational formulation. In this case, the following splitting will be used in Cartesian geometry:
Ax
0
A=
0
−R⊤
x
0
Ay
0
−R⊤
y
0
0
Az
−R⊤
z
−Rx
−Ry
−Rz
−T
Similarly, we use the following ADI splitting in hexagonal geometry:
Aw
C⊤
Cwy
0
−Rw
xw
Cxw
0
−Rx
Ax
C⊤
yx
⊤
A = Cwy Cyx
Ay
0
−Ry
0
0
0
Az
−Rz
−R⊤
−T
−R⊤
−R⊤
−R⊤
z
y
w
x
(4.4)
(4.5)
When the TRIVAT: operator is used (CDOOR=’TRIVAC’), the following elements in the vector Sit will
also be defined.
• S6t : (ITYPE) Type of TRIVAC geometry:
2 Cartesian 1-D geometry
3 Tube 1-D geometry
5 Cartesian 2-D geometry
6 Tube 2-D geometry
S6t =
7 Cartesian 3-D geometry
8 Hexagonal 2-D geometry
9 Hexagonal 3-D geometry
IGE–351
79
• S7t : (IHEX) Type
0
1
2
3
4
S7t =
5
6
7
8
9
of hexagonal symmetry if S6t ≥ 8:
non-hexagonal geometry
S30
SA60
SB60
S90
R120
R180
SA180
SB180
COMPLETE
• S8t : (IDIAG) Diagonal symmetry flag if S6t = 5 or = 7. S8t = 1 if diagonal symmetry is present.
• S9t : (IELEM) Type of finite elements:
S9t =
< 0 Order −S9t primal finite elements
> 0 Order S9t dual finite elements
t
• S10
: (ICOL) Type
1
t
2
S10
=
3
of quadrature used to integrate the mass matrix:
t
: (ICHX) Type
• S12
1
2
t
S12 =
3
of discretization algorithm:
Analytical integration
Gauss-Lobatto quadrature (finite difference/collocation method)
Gauss-Legendre quadrature (superconvergent approximation)
t
• S11
: (LL4) Order of the group-wise matrices. Generally equal to S2t except in cases where averaged
t
≤ S2t .
fluxes are appended to the unknown vector. S11
Variational collocation method (mesh-corner finite differences or primal finite
elements with Gauss-Lobatto quadrature). Eq. (4.2) or Eq. (4.3) is used.
Dual finite element approximation (Thomas-Raviart or Thomas-Raviart-Schneider
polynomial basis). Eq. (4.4) or Eq. (4.5) is used.
Nodal collocation method with full tensorial products (mesh-centered finite
differences or dual finite elements with Gauss-Lobatto quadrature). Eq. (4.2) or
Eq. (4.3) is used.
t
• S13
: (ISPLH) Type of hexagonal mesh splitting if S6t ≥ 8:
1 No mesh splitting (full hexagons)
t
K 6 × (K − 1) × (K − 1) triangles per hexagon with finite-difference approximations
S13
=
3 × K × K losanges per hexagon with Thomas-Raviart-Schneider approximation
t
• S14
: (LX) Number of elements along the X axis in Cartesian geometry or number of hexagons in
one axial plane.
t
• S15
: (LY) Number of elements along the Y axis.
t
• S16
: (LZ) Number of elements along the Z axis.
t
• S17
: (ISEG) Number of components in a vector register (used for supervectorial operations). Equal
to zero for operations in scalar mode.
t
• S18
: (IMPV) Print parameter for supervectorial operations.
IGE–351
80
t
• S19
: (LTSW) Maximum bandwidth for supervectorial operations (= 2 for tridiagonal matrices).
t
−1 ⊤
• S20
: (LONW) number of groups of linear systems for matrices W + P⊤
Rw
w UPw or Aw + Rw T
(used for supervectorial operations)
t
−1 ⊤
• S21
: (LONX) number of groups of linear systems for matrices X + P⊤
Rx (used
x UPx or Ax + Rx T
for supervectorial operations)
t
−1 ⊤
• S22
: (LONY) number of groups of linear systems for matrices Y + P⊤
Ry (used
y UPy or Ay + Ry T
for supervectorial operations)
t
−1 ⊤
• S23
: (LONZ) number of groups of linear systems for matrices Z + P⊤
Rz (used
z UPz or Az + Rz T
for supervectorial operations)
t
• S24
: (NR0) Number of radii used with the cylindrical correction algorithm for the albedos. Equal
to zero if no cylindrical correction is applied.
t
t
• S25
: (LL4F) Order of matrices T if S12
=2
t
t
• S26
: (LL4W) Order of matrices Aw if S12
=2
t
t
• S27
: (LL4X) Order of matrices Ax if S12
=2
t
t
• S28
: (LL4Y) Order of matrices Ay if S12
=2
t
t
• S29
: (LL4Z) Order of matrices Az if S12
=2
t
• S30
: (NLF) Number of components in the angular expansion of the flux. Must be a positive even
number. Set to zero for diffusion theory. Set to 2 for P1 method.
t
: (ISPN) Type of transport approximation if NLF6= 0:
• S31
t
S31
=
0
1
Complete Pn approximation of order NLF−1 (currently not available)
Simplified Pn approximation of order NLF−1
t
: (ISCAT) Number of terms in the scattering sources if NLF6= 0:
• S32
t
S32
1 Isotropic scattering in the laboratory system
2 Linearly anisotropic scattering in the laboratory system
=
n order n − 1 anisotropic scattering in the laboratory system
t
A negative value of S32
indicates that 1/3Dg values are used as Σg1 cross sections.
t
• S33
: (NADI) Number of ADI iterations at the inner iterative level.
t
• S34
: (NVD) Number of base points in the Gauss-Legendre quadrature used to integrate void boundary
conditions if ICOL = 3 and NLF6= 0:
0 Use a (NLF+1)–point quadrature consistent with PNLF−1 theory
t
1 Use a NLF–point quadrature consistent with SNLF theory
S34
=
2 Use an analytical integration consistent with diffusion theory
The following records will also be present on the main level of a /tracking/ directory.
IGE–351
81
Table 49: The trivat records in /tracking/
Name
Type
Condition
UnitsComment
NCODE
I(6)
ZCODE
R(6)
SIDE
XX
R(1)
R(S1t )
S6t ≥ 8
S6t < 8
cm
cm
YY
R(S1t )
S6t = 5, 6 or 7
cm
ZZ
R(S1t )
S6t = 7 or 9
cm
DD
R(S1t )
S6t = 3 or 6
cm
KN
I(S1t × Nkn )
QFR
R(S1t × Nsurf )
MUW
t
t
I(S11
or S26
)
S6t ≥ 8
IPW
t
I(S11
)
S6t ≥ 8
MUX
t
t
I(S11
or S27
)
S8t = 0
IPX
t
I(S11
)
MUY
t
t
I(S11
or S28
)
S6t ≥ 5
IPY
t
I(S11
)
S6t ≥ 5
MUZ
t
t
I(S11
or S29
)
S6t = 7 or 9
IPZ
t
I(S11
)
S6t = 7 or 9
BIVCOL
Dir
1
Record containing the types of boundary conditions
on each surface. =0 side not used; =1 VOID; =2
REFL; =4 TRAN; =5 SYME; =7 ZERO; =8 CYLI.
Record containing the albedo value (real number) on
each surface.
Side of a hexagon.
Element-ordered X-directed mesh spacings after
mesh-splitting for type 2, 5 or 7 geometries.
Element-ordered radius after mesh-splitting for type
3 or 6 geometries.
Element-ordered Y -directed mesh spacings after
mesh-splitting for type 5, 6 or 7 geometries.
Element-ordered Y -directed mesh spacings after
mesh-splitting for type 7 or 9 geometries.
Element-ordered position used with type 3 and 6
cylindrical geometries.
Element-ordered unknown list. Nkn is the number of
unknowns per element.
Element-ordered boundary condition. Nsurf = 6 in
Cartesian geometry and = 8 in hexagonal geometry.
Indices used with compressed diagonal storage mode
−1 ⊤
matrices W + P⊤
Rw .
w UPw or Aw + Rw T
Permutation vector ensuring minimum bandwidth
−1 ⊤
for matrices W + P⊤
Rw .
w UPw or Aw + Rw T
Indices used with compressed diagonal storage mode
−1 ⊤
matrices X + P⊤
Rx .
x UPx or Ax + Rx T
Permutation vector ensuring minimum bandwidth
−1 ⊤
for matrices X + P⊤
Rx .
x UPx or Ax + Rx T
Indices used with compressed diagonal storage mode
−1 ⊤
matrices Y + P⊤
Ry .
y UPy or Ay + Ry T
Permutation vector ensuring minimum bandwidth
−1 ⊤
for matrices Y + P⊤
Ry .
y UPy or Ay + Ry T
Indices used with compressed diagonal storage mode
−1 ⊤
matrices Z + P⊤
Rz .
z UPz or Az + Rz T
Permutation vector ensuring minimum bandwidth
−1 ⊤
for matrices Z + P⊤
Rz .
z UPz or Az + Rz T
Sub-directory containing the unit matrices (mass,
stiffness, nodal coupling, etc.) for a finite element
discretization. The specification of this directory is
given in Section 4.7
The following records will also be present on the main level of a /tracking/ directory in cases where
t
a Thomas-Raviart or Thomas-Raviart-Schneider polynomial basis is used (S12
= 2):
IGE–351
82
Table 50: The trivat records in /tracking/ (contd.)
Name
Type
Condition
IPF
IPBBW
IPBBX
IPBBY
IPBBZ
WB
t
I(S25
)
t
I(2 S9t × S26
)
t
t
I(2 S9 × S27
)
t
I(2 S9t × S28
)
t
I(2 S9t × S29
)
t
R(2 S9t × S26
)
t
S25
t
S26
t
S27
t
S28
t
S29
t
S26
XB
t
R(2 S9t × S27
)
t
S27
6= 0
YB
t
R(2 S9t × S28
)
t
S28
6= 0
ZB
t
R(2 S9t × S29
)
t
S29
6= 0
ZGLOB
I(Nlos )
S6t ≥ 8
CTRAN
FRZ
D(Npio × Npio )
t
R(S16
)
S6t ≥ 8
S6t ≥ 8
6= 0
6= 0
6= 0
6= 0
6= 0
6= 0
UnitsComment
Localization vector for flux values in unknown vector.
Perdue sparse storage indices for matrices Rw .
Perdue sparse storage indices for matrices Rx .
Perdue sparse storage indices for matrices Ry .
Perdue sparse storage indices for matrices Rz .
Matrix component Rw in Perdue sparse storage
mode.
Matrix component Rx in Perdue sparse storage
mode.
Matrix component Ry in Perdue sparse storage
mode.
Matrix component Rz in Perdue sparse storage
mode.
Hexagon index assigned to each losange. Nlos =
t
t
t 2
S14
× S15
× (S13
)
Piolat current coupling matrix. Npio = (S9t + 1) × S9t
Volume fractions related to the SYME boundary
condition in Z.
The following records will also be present on the main level of a /tracking/ directory in cases where
t
supervectorial operations are used (S17
6= 0):
Table 51: The trivat records in /tracking/ (contd.)
Name
Type
Condition
LL4VW
I(1)
LL4VX
I(1)
LL4VY
I(1)
LL4VZ
I(1)
NBLW
t
I(S20
)
t
S20
6= 0
NBLX
t
I(S21
)
t
S21
6= 0
NBLY
t
I(S22
)
t
S22
6= 0
UnitsComment
Order of a reordered W −matrix, including supervect
torial fill-in. Multiple of S17
Order of a reordered X−matrix, including supervect
torial fill-in. Multiple of S17
Order of a reordered Y −matrix, including supervect
torial fill-in. Multiple of S17
Order of a reordered Z−matrix, including supervect
torial fill-in. Multiple of S17
Number of linear systems per supervector group for
W −matrices
Number of linear systems per supervector group for
X−matrices
Number of linear systems per supervector group for
Y −matrices
continued on next page
IGE–351
83
The trivat records in /tracking/ (contd.)
Name
Type
Condition
NBLZ
t
I(S23
)
t
S23
6= 0
LBLW
t
I(S20
)
t
S20
6= 0
LBLX
t
I(S21
)
t
S21
6= 0
LBLY
t
I(S22
)
t
S22
6= 0
LBLZ
t
I(S23
)
t
S23
6= 0
MUVW
t
t
I(S11
or S26
)
S6t ≥ 8
MUVX
t
t
I(S11
or S27
)
S8t = 0
MUVY
t
t
I(S11
or S28
)
S6t ≥ 5
MUVZ
t
t
I(S11
or S29
)
S6t = 7 or 9
IPVW
t
I(S11
)
S6t ≥ 8
IPVX
t
I(S11
)
IPVY
t
I(S11
)
S6t ≥ 5
IPVZ
t
I(S11
)
S6t = 7 or 9
continued from last page
UnitsComment
Number of linear systems per supervector group for
Z−matrices
Number of unknowns per supervector group for
W −matrices
Number of unknowns per supervector group for
X−matrices
Number of unknowns per supervector group for
Y −matrices
Number of unknowns per supervector group for
Z−matrices
Indices used with W −directed compressed diagonal
storage mode matrices in supervector mode
Indices used with X−directed compressed diagonal
storage mode matrices in supervector mode
Indices used with Y −directed compressed diagonal
storage mode matrices in supervector mode
Indices used with Z−directed compressed diagonal
storage mode matrices in supervector mode
W −directed ADI permutation matrix in supervector
mode
X−directed ADI permutation matrix in supervector
mode
Y −directed ADI permutation matrix in supervector
mode
Z−directed ADI permutation matrix in supervector
mode
The following records will also be present on the main level of a /tracking/ directory in cases where
t
a cylindrical correction of the albedos is used (S24
6= 0):
Table 52: The trivat records in /tracking/ (contd.)
Name
Type
Condition
Units
Comment
RR0
t
R(S24
)
t
S24
6= 0
cm
XR0
t
R(S24
)
t
S24
6= 0
cm
ANG
t
R(S24
)
t
S24
6= 0
1
Radii of the cylindrical boundaries in the cylindrical
correction
Coordinates on principal axis in the cylindrical correction
Angles for applying the cylindrical correction
IGE–351
4.9
84
The /BIHET/ sub-directory
Table 53: The contents of the /BIHET/ sub-directory
Name
Type
PARAM
I(8)
NS
I(P4 )
IBI
I(P3 )
VOLUME
RS
FRACT
R(P3 )
R(P5 + 1, P4 )
R(P4 , P2 )
VOLK
R(P4 , P5 )
IDIL
I(P2 − P1 )
MIXGR
I(P5 , P4 , P2 − P1 )
Condition
Units Comment
cm3
cm
Record containing the parameters related to a
double-heterogeneity tracking Pi
Number of tubes or shells in each kind of micro structure
Type of mixture in each generating region of the
macro geometry
Volumes of the macro geometry
Radii of the micro regions
Volume fraction of each type of micro region in each
mixture
Volume fractions of the tubes or shells in the micro
regions
Elementary mixture indices in the diluent of the composite mixtures
Elementary mixture indices in the micro structures
with the dimension parameter Pi , representing:
• The number of ordinary mixtures pointing to the macrolib. P1
• The number of mixtures, including the composite mixtures (i.e., containing micro structures) P2
• The number of regions in the macro geometry P3
• The number of different kinds of macro structures P4 = S1dh
A kind of macro structure is characterized by the radii of its tubes or shells. All the micro region
of the same kind should own the same nuclear properties in a given macro region.
• The maximum number of regions (tubes or shells) in each kind of macro structure P5 = S2dh − 1
• The type of double-heterogeneity model P6 where
P6 =
1 Sanchez-Pomraning model
2 Hebert model
• The type of micro structures P7 = S5dh where
P7 =
3 Cylinder
4 Sphere
• The quadrature parameter for the 1-D collision probability calculation in the micro structures P8
IGE–351
85
5 Contents of a /asminfo/ directory
This directory contains the multigroup collision probabilities and response matrices required in the
solution of the transport equation.
5.1
State vector content for the /asminfo/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector Sia , represent:
• The type of collision probabilities considered IT = S1a where
1
2
IT =
3
4
Scattering reduced collision probability or response matrix
Direct collision probability or response matrix
Scattering reduced directional collision probability
Direct directional collision probability
• The type of collision probability closure relation used IC = S2a (see NORM keyword in ASM: operator
input option)
IC =
0
1
No closure relation used
Total reflection closure relation
• A parameter related to the albedo leakage model Iβ = S3a (see ALSB keyword in ASM: operator input
option)
Iβ =
0
1
No information is stored
Groupwise escape matrices WIS are stored
• S4a (not used)
• The option to indicate whether response matrix or collision probability matrices are stored on the
structure Ip = S5a (see PIJ and ARM keyword in ASM: operator input option)
Ip =
1 Response matrices will be stored (the ARM keyword was selected)
2 Collision probability matrices will be stored (the PIJ keyword was selected)
• The option to indicate the type of streaming model used Ik = S6a (see PIJK and ECCO keyword in
ASM: operator input option)
1 No streaming model used (a leakage model may or may not be used)
2 Isotropic streaming model used (ECCO model)
Ik =
3 Anisotropic streaming model used (TIBÈRE model)
• The type of collision probability normalization method used In = S7a (see PNOR keyword in ASM:
operator input option)
0 No normalization
1 Gelbard normalization algorithm
2 Diagonal element normalization
In =
3 Non-linear normalization
4 Helios type normalization
IGE–351
86
• Number of energy groups G = S8a
• Number of unknown in flux system Nu = S9a
a
• Number of mixtures Nm = S10
• Number of Legendre orders of the scattering cross sections used in the main transport solution.
a
Nans = S11
a
• Flag for the availability of diffusion coefficients. Idiff = S12
Idiff =
5.2
0 No diffusion coefficients available;
1 Diffusion coefficients are available.
The main /asminfo/ directory
On its first level, the following records and sub-directories will be found in the /asminfo/ directory:
Table 54: Main records and sub-directories in /asminfo/
Name
Type
SIGNATURE
C∗12
LINK.MACRO
C∗12
LINK.TRACK
C∗12
STATE-VECTOR
I(40)
GROUP
Dir(S8a )
Condition
Units
Comment
Signature
of
the
data
structure
).
(SIGNA =L PIJ
Name of the macrolib on which the collision probabilities are based.
Name of the tracking on which the collision probabilities are based.
Vector describing the various parameters associated
with this data structure Sia , as defined in Section 5.1.
List of energy-group sub-directories. Each component of the list is a directory containing the multigroup collision probabilities and response matrices
associated with an energy group. The specification
of this directory is given in Sect. 5.3 or 5.4 depending
if a double-heterogeneity is present or not. A doublet
heterogeneity is present if S40
= 1 in the tracking
object.
IGE–351
5.3
87
The GROUP double-heterogeneity group sub-directory
This directory is containing the following records, corresponding to a single energy group:
Table 55: Records and sub-directories in GROUP
Name
Type
DRAGON-TXSC
R(Nm + 1)
DRAGON-S0XSC
R(Nm + 1, Nans )
NCO
I(M)
RRRR
R(M)
QKOLD
R(P4 , P5 , M)
QKDEL
R(P4 , P5 , M)
PKL
R(P4 , P5 , P5 , M)
COEF
D(F , F , M)
BIHET
Dir
Condition
P6 = 1
Units Comment
cm−1 where Nm = P1 . The total cross section Σgm
for Nm + 1 composite mixtures assuming that
the first mixture represents void (Σgm = 0).
A transport correction may or may not be included. The first component of this array is
always equal to 0.
cm−1 The within group scattering cross section
Σ0,m,w (see Section 1.3) for Nm + 1 composite
mixtures assuming that the first mixture represents void (Σg0,m,w = 0). A transport correction may or may not be included. Many
Legendre orders may be given. The first component of this array, for each Legendre order,
is always equal to 0.
where M = P2 − P1 . Number of composite
mixtures in each macro-mixture.
Group-dependent double-heterogeneity information.
Group-dependent double-heterogeneity information related to the escape probabilities in
the micro-structures.
Group-dependent double-heterogeneity information related to the escape probabilities in
the micro-structures.
Group-dependent double-heterogeneity information related to the collision probabilities in
the micro-structures.
where F = 1 + P4 × P5 . Group-dependent
double-heterogeneity information.
Directory containing collision probability or
response matrix information related to the
macro-geometry (i. e., the geometry with homogenized micro-structures). The specification of this directory is given in Section 5.4.
Note that the value of Nm = P2 in this object
is set to take into account the macro-mixtures.
Similarly, the value Nr = P3 is the number of
macro-volumes.
IGE–351
5.4
88
The GROUP or BIHET group sub-directory
This directory is containing the following records, corresponding to a single energy group:
Table 56: Records and sub-directories in GROUP
Name
Type
Condition
DRAGON-TXSC
R(Nm + 1)
DRAGON-T1XSC
R(Nm + 1)
DRAGON-S0XSC
R(Nm + 1, Nans )
DRAGON-DIFF
R(Nm + 1)
Idiff = 1
STREAMING
Dir
Ik = 2
*
Units Comment
cm−1 The total cross section Σgm for Nm + 1 mixtures assuming that the first mixture represents void (Σgm = 0). A transport correction
may or may not be included. The first component of this array is always equal to 0.
cm−1 where Nm = P1 . The current-weighted total cross section Σg1,m for Nm + 1 composite
mixtures assuming that the first mixture represents void (Σg1,m = 0). The first component
of this array is always equal to 0.
cm−1 The within group scattering cross section
Σ0,m,w (see Section 1.3) for Nm + 1 mixtures assuming that the first mixture represents void (Σg0,m,w = 0). A transport correction may or may not be included. Many
Legendre orders may be given. The first component of this array, for each Legendre order,
is always equal to 0.
g
cm
Diffusion coefficients Dm
for Nm + 1 mixtures assuming that the first mixture repreg
sents void (Dm
= 1.0×1010). The first component of this array is always equal to 1.0 × 1010.
Directory containing P1 information to be
used with the ECCO isotropic streaming
model. This directory uses the same specification as GROUP where P0 information is replaced
with P1 information. Cross sections used in
this directory are not–transport corrected.
5.4.1 The trafict dependent records on a GROUP directory
If a collision probability method is used, the following records will also be found on the group subdirectory:
IGE–351
89
Table 57: Collision probability records in GROUP
Name
Type
Condition
DRAGON-PCSCT
R(Nr , Nr )
Ip = 2
DRAGON1PCSCT
R(Nr , Nr )
Ik = 3
DRAGON2PCSCT
R(Nr , Nr )
Ik = 3
DRAGON3PCSCT
R(Nr , Nr )
Ik = 3
DRAGON1P*SCT
DRAGON2P*SCT
DRAGON3P*SCT
DRAGON-WIS
R(Nr , Nr )
R(Nr , Nr )
R(Nr , Nr )
R(Nr )
Ik
Ik
Ik
Iβ
=3
=3
=3
=1
Units
Comment
The scattering-reduced (IT = 1, 3) collision
probability matrix Wg or direct (IT = 2, 4)
collision probability matrix pg
The x−directed P1 scattering-reduced (IT =
3) collision probability matrix Yx,g or direct
(IT = 4) collision probability matrix px,g
The y−directed P1 scattering-reduced (IT =
3) collision probability matrix Yy,g or direct
(IT = 4) collision probability matrix py,g
The z−directed P1 scattering-reduced (IT =
3) collision probability matrix Yz,g or direct
(IT = 4) collision probability matrix pz,g
∗
The x−directed matrix p−1
g px,g
−1 ∗
The y−directed matrix pg py,g
∗
The z−directed matrix p−1
g pz,g
g
The scattering-reduced leakage matrix Wis
where
• the reduced collision probability matrix is defined as
pg = {pij,g ; ∀i and j}
• the reduced directional probability matrix, used in the first TIBÈRE equation, is defined as
p∗k,g = {p∗ij,k,g ; ∀i and j} ; k = x, y, or z
• the reduced directional probability matrix, used in the second TIBÈRE equation, is defined as
pk,g = {pij,k,g ; ∀i and j} ; k = x, y, or z
.
The total cross sections used to compute this matrix are not–transport corrected.
• the P0 scattering reduced collision probability matrix is defined as
Wg = [I − pg Σs0,g←g ]−1 pg
• the P1 scattering reduced directionnal collision probability matrix is defined as
Yk,g = [I − pk,g Σs1,g←g ]−1 pk,g ; k = x, y, or z
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5.4.2 The sybilt dependent records on a GROUP directory
This information is provided only if the current iteration method of the interface current method is
used in SYBIL. This occurs if the key-word ARM is been used in operators USS: or ASM:. In these cases,
the following records will also be found on the GROUP directory:
The following dimensions will be used:
Number of generating cells:
Ngen =
if S6t = 3 (do-it-yourself geometry)
if S6t = 4 (2D assembly geometry)
P1
P6
Number of entering currents in a cell:
4
12
Nc =
6
18
if
if
if
if
P1t
P1t
P1t
P1t
=0
=0
>0
>0
and
and
and
and
2 ≤ P2t ≤ 3
P2t = 4
2 ≤ P2t ≤ 3
P2t = 4
(DP0
(DP1
(DP0
(DP1
Cartesian cell)
Cartesian cell)
hexagonal cell)
hexagonal cell)
Number of transmission probability elements:
D1 =
P1
P6
Nc × Nc × P6
if S6t = 3
(do-it-yourself geometry)
if S6t = 4 and P2 = 1 (Roth 2D assembly geometry)
if S6t = 4 and P2 ≥ 2 (Other 2D assembly geometries)
Number of escape probability elements:
NMC(P1 + 1) if S6t = 3
NMC(P6 + 1) if S6t = 4 and P2 = 1
D2 =
Nc × NMC(P6 + 1) if S6t = 4 and P2 ≥ 2
(do-it-yourself geometry)
(Roth 2D assembly geometry)
(Other 2D assembly geometries)
Number of collision probability elements:
Ngen
D3 =
X
[NMC(i + 1) − NMC(i)]2
i=1
Table 58: SYBIL groupwise assembly information in GROUP
Name
Type
PSSW$SYBIL
R(D1 )
PISW$SYBIL
R(D2 )
PSJW$SYBIL
R(D2 )
PIJW$SYBIL
R(D3 )
Condition
Units
Comment
Cellwise scattering-reduced transmission
probabilities.
Cellwise scattering-reduced escape probabilities.
Cellwise scattering-reduced collision probabilities for incoming neutrons.
Cellwise scattering-reduced collision probabilities.
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5.4.3 The mccgt dependent records on a GROUP directory
If the characteristic method (MCCG) is used, the following records will also be found on the GROUP
directory:
Table 59: MCCG groupwise directories
Name
Type
Condition
DIAGF$MCCG
CF$MCCG
R(Ndim )
t
R(S26
)
t
S22
>0
t
S22 > 0
ILUDF$MCCG
R(Ndim )
ILUCF$MCCG
t
R(S37
)
DIAGQ$MCCG
CQ$MCCG
R(Ndim )
t
R(S26
)
t
S22
>0
t
S22 > 0
PJJ$MCCG
t
R(S1t S36
)
t
S35
=1
PSJ$MCCG
t
R(S22
)
t
S21
>0
t
S22
>0
t
S23 ≥ 2
t
S22
>0
t
S23 ∈ {2, 3}
Units
Comment
Diagonal elements of the ACA flux matrix.
Non-Diagonal elements of the ACA flux matrix.
Inverse diagonal elements of U from ILU0 decomposition of ACA flux matrix
Non-diagonal elements of U from ILU0 decomposition of ACA flux matrix that differ from
CF
Diagonal elements of the ACA source matrix.
Non-diagonal elements of the ACA source matrix.
Mode-to-mode self-collision probabilities for
SCR or “STIS=1” integration strategy.
Surface-to-volume probabilities for SCR.
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6 Contents of a /system/ directory
The L SYSTEM specification is used to store a set of system matrices (or a set of perturbations on system
matrices) obtained after discretization of the algebraic operators contained in the neutron transport or
diffusion equation. A complete set of matrices can be written on the root directory. Perturbation matrices
corresponding to variations or derivatives of the cross sections can also be found if the STEP directory list
is present.
6.1
State vector content for the /system/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector Sis , represents:
• S1s : the number of energy groups
• S2s : the order of a system matrix
• S3s : the number of delayed neutron precursor groups
• S4s : the storage type of system matrices:
S4s =
1 BIVAC–compatible profile storage matrices for the diffusion theory
2 TRIVAC–compatible matrices compatible with the generic ADI splitting in
Eq. (4.2) or Eq. (4.3)
3 TRIVAC–compatible matrices compatible with the Thomas-Raviart ADI
splitting in Eq. (4.4) or Eq. (4.5) for the diffusion theory
11 BIVAC–compatible profile storage matrices for the simplified Pn method
13 TRIVAC–compatible matrices compatible with the Thomas-Raviart ADI
splitting in Eq. (4.4) or Eq. (4.5) for the simplified Pn method
• S5s : set to 1 in case where matrices ’RM’ are available
• The number of set of perturbation on system matrices Istep = S6s used for perturbation calculations:
Istep =
0
>0
no STEP information available
number of set of perturbation on system matrices.
• S7s : number of material mixtures in the macrolib used to construct the system matrices
• S8s : number of Legendre orders used to represent the macroscopic cross sections with the simplified
Pn method (maximum integer value of IL). Set to zero with the diffusion theory.
• The type of system matrix assemblies Ipert = S9s :
Ipert
6.2
0 calculation of the system matrices
1 calculation of the derivative of these matrices
2 calculation of the first variation of these matrices
=
3 identical to Ipert = 2, but these variation are added to unperturbed system
matrices.
The main /system/ directory
On its first level, the following records and sub-directories will be found in the /system/ directory:
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Table 60: Main records and sub-directories in /system/
Name
Type
Condition
SIGNATURE
C∗12
LINK.MACRO
C∗12
LINK.TRACK
C∗12
STATE-VECTOR
I(40)
{matrix}
{removalxs}
R(Ndim )
R(S7s )
S4s > 10
RM
t
R(S11
)
S5s 6= 0
IRM
t
R(S11
)
S5s 6= 0
STEP
Dir(S6s )
S6s ≥ 1
Units
Comment
Signature
of
the
data
structure
(SIGNA =L SYSTEM
).
Name of the macrolib on which the system matrices
are based.
Name of the tracking on which the system matrices
are based.
Vector describing the various parameters associated
with this data structure Sis , as defined in Section 6.1.
Set of system matrices
Set of removal cross section arrays used with the simplified Pn method
Unit system matrix, i.e., a system matrix corresponding to cross sections all set to 1.0. This matrix is mandatory in space-time kinetics cases. This
block is always located on the root directory.
Inverse of the unit matrix. This record is available
only with BIVAC trackings.
List of perturbation sub-directories. Each component of this list contains a set of perturbation on system matrices corresponding to variations or derivatives of the cross sections. Each STEP component
follows the specification presented in the current Section 6.2.
The signature variable for this data structure must be SIGNA=L_SYSTEM
→
Φ1
A11
–A
→
Φ2
21 A22
–A
→
32 A33
Φ3 –
42 – A43 A44 – A45
Φ4
–A
B11 B12 B13 B14 B15
54 A55
–A
→
B21 B22 B23 B24 B25
1
Keff
→
Φ5
.
Φ1
→
→
→
→
0
Φ2
→
Φ3
0
=
→
0
Φ4
→
→
→
→
Φ5
0
0
Figure 4: Example of a 5 energy group matrix eigenvalue problem
The discretized neutron transport or diffusion equation is assumed to be given in a form similar to
the matrix system represented in Figure 4. Each system matrix {matrix} is stored on a block named
TEXT12, embodying the primary group index IGR and the secondary group index JGR.
The first case corresponds to the following situations:
t
• BIVAC–type discretization (S4s = 1). In this case, the dimension of the matrix is equal to MU(S11
)
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94
• TRIVAC–type discretization of the out-of-group A matrices (IGR6=JGR). In this case, the dimension
t
of the matrix is equal to S11
• TRIVAC–type discretization of the B matrices. In this case, the dimension of the matrix is equal
t
to S11
The character name of the system matrix is build using
WRITE(TEXT12,’(1HA,2I3.3)’) JGR,IGR
WRITE(TEXT12,’(1HB,2I3.3)’) JGR,IGR
or
WRITE(TEXT12,’(1HB,3I3.3)’) IDEL,JGR,IGR
where IDEL is the index of a delayed neutron precursor group (if S3s ≥ 1).
Otherwise, the TRIVAC–type system matrix is splitted according to Eqs. (4.2) to (4.5). The character
name of the system matrix is build using
WRITE(TEXT12,’(A2,1HA,2I3.3)’) PREFIX,IGR,IGR
where PREFIX is a character*2 name describing the component of the system matrix under consideration.
The following values are available:
PREFIX
W
X
Y
Z
WI
XI
YI
ZI
type of matrix
−1 ⊤
matrix component W + P⊤
Rw
w UPw or Aw + Rw T
⊤
−1 ⊤
matrix component X + Px UPx or Ax + Rx T Rx
−1 ⊤
matrix component Y + P⊤
Ry
y UPy or Ay + Ry T
⊤
−1 ⊤
matrix component Z + Pz UPz or Az + Rz T Rz
−1 ⊤
LDL⊤ factors of W + P⊤
Rw
w UPw or Aw + Rw T
⊤
⊤
−1 ⊤
LDL factors of X + Px UPx or Ax + Rx T Rx
−1 ⊤
LDL⊤ factors of Y + P⊤
Ry
y UPy or Ay + Ry T
−1 ⊤
LDL⊤ factors of Z + P⊤
UP
or
A
+
R
T
R
z
z
z
z
z
dimension Ndim
t
t
MUW(S11
) or MUW(S26
)
t
t
MUX(S11 ) or MUX(S27
)
t
t
MUY(S11
) or MUY(S28
)
t
t
MUZ(S11
) or MUZ(S29
)
t
t
MUW(S11
) or MUW(S26
)
t
t
MUX(S11
) or MUX(S27
)
t
t
MUY(S11
) or MUY(S28
)
t
t
MUZ(S11
) or MUZ(S29
)
where all these matrices are stored in diagonal storage mode.
The following values of PREFIX will also be used in cases where a Thomas-Raviart or Thomas-Raviartt
Schneider polynomial basis is used (S12
= 2 and S4s = 3):
PREFIX
TF
WA
XA
YA
ZA
DIFF
type of matrix
matrix component T
matrix component Aw
matrix component Ax
matrix component Ay
matrix component Az
diffusion coefficients used with the Thomas-Raviart-Schneider method
dimension Ndim
t
S25
t
MUW(S26
)
t
MUX(S27
)
t
MUY(S28
)
t
MUZ(S29
)
Nlos
where TF is a diagonal matrix and where WA to ZA are stored in diagonal profiled mode. The dimension
t
t
t 2
of DIFF is related to the number of losanges in the domain: Nlos = S14
× S15
× (S13
) .
Each removal cross section array {removalxs} is stored on a block named TEXT12, embodying the
Legendre order IL, the primary group index IGR and the secondary group index JGR. The block name
TEXT12 is build using
WRITE(TEXT12,’(4HSCAR,I2.2,2I3.3)’) IL-1,JGR,IGR
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for the mixture-ordered components of the removal cross section, and
WRITE(TEXT12,’(4HSCAI,I2.2,2I3.3)’) IL-1,JGR,IGR
for the mixture-ordered components of the inverse removal cross section matrix at each Legendre order.
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7 Contents of a /kinet/ directory
The L KINET specification is used to store the data related to the space-time neutron kinetics calculations. This directory also contains the main calculations results corresponding to the current time step
of a transient.
7.1
State vector content for the /kinet/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector Sik , represent:
• The current time-step index Ntr = S1k
• The number of delayed-neutron precursor groups Ndg = S2k
• The number of energy groups Ngr = S3k
• The type of geometry Igeo = S4k
• The total number of finite elements Nel = S5k
• The total number of unknowns per energy group Nun = S6k
• The number of flux unknowns per energy group Nuf = S7k
• The number of precursors unknowns per delayed group Nup = S8k
• The number of fissile isotopes Nf iss = S9k
k
• The type of system matrices Nsys = S10
k
• Number of free iteration per variational acceleration cycle Nf = S11
k
• Number of accelerated iteration per variational acceleration cycle Na = S12
k
• Type of normalization for the flux Inorm = S13
where
0 No normalization
1 Imposed factor
Inorm =
2 Maximum flux normalization
3 Initial power normalization
k
• Maximum number of thermal (up-scattering) iterations Min = S14
k
• Maximum number of outer iterations Mout = S15
k
• Initial number of ADI iterations in Trivac Madi = S16
k
• Temporal integration scheme for fluxes Iifl = S17
where
1 Implicit scheme (Θf = 1)
Iifl =
2 Crank-Nicholson scheme (Θf = 0.5)
3 General theta method
k
• Temporal integration scheme for precursors Iipr = S18
where
1 Implicit scheme (Θp = 1)
2 Crank-Nicholson scheme (Θp = 0.5)
Iipr =
3 General theta method
4 Analytical integration method for precursors
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97
The main /kinet/ directory
The following records and sub-directories will be found in the /kinet/ directory:
Table 61: Main records and sub-directories in /kinet/
Name
Type
Condition
UnitsComment
SIGNATURE
C∗12
STATE-VECTOR
I(40)
EPS-CONVERGE
TRACK-TYPE
R(4)
C∗12
E-IDLPC
I(Nel )
DELTA-T
TOTAL-TIME
BETA-D
R(1)
R(1)
R(Ndg )
s
s
LAMBDA-D
R(Ndg )
s−1
CHI-D
R(Ndg , Ngr )
E-VECTOR
E-PREC
R(Nuf , Ngr )
R(Nup , Ndg )
E-KEFF
CTRL-FLUX
R(1)
R(1)
CTRL-PREC
R(Nup × Nf iss )
CTRL-IDL
CTRL-IGR
I(1)
I(1)
POWER-INI
E-POW
R(1)
R(1)
Inorm = 3
Inorm = 3
Signature
of
the
data
structure
(SIGNA =L KINET
)
Vector describing the various parameters associated
with this data structure Sik , as defined in Section 7.1.
Convergence parameters ∆ǫi
Type of tracking considered (CDOOR). Allowed values are: ’BIVAC’ and ’TRIVAC’
Position of averaged precursor concentrations in vector E-PREC.
Current time increment.
Total elapsed time from the beginning of a transient.
Delayed-neutron fraction for each delayed-neutron
precursor group.
Radioactive decay constants of each delayed-neutron
precursor group.
Multigroup delayed-neutron fission spectrum in each
precursor group.
Kinetics solution for fluxes at current time step.
Kinetics solution for precursor concentrations at current time step.
Steady-state value of the initial keff .
Maximum value of flux used for the controlling purpose.
Precursor concentrations at location of maximum
flux.
Position of a maximum value within the flux vector.
Energy group number corresponding to a maximum
flux value.
Initial power.
Actual power.
The convergence parameters ∆ǫi represent:
• ∆ǫ1 is the thermal (up-scattering) iteration flux convergence parameter
• ∆ǫ2 is the outer iteration flux convergence parameter
• Θf is the value of theta-parameter for fluxes
• Θp is the value of theta-parameter for precursors
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8 Contents of a /fluxunk/ directory
This directory contains the main flux calculations results, including the multigroup flux, the eigenvalue
for the problem and the diffusion coefficients when computed. The following types of equations can be
solved:
1. Fixed source problem
~ = ~S
AΦ
(8.1)
~ is the source vector and Φ
~ is the unknown vector.
where A is the coefficient matrix, S
2. Direct eigenvalue problem
~α+
AΦ
1
~ α = ~0
BΦ
Keff,α
(8.2)
1
~ α ) is the eigensolution corresponding
where B is the second coefficient matrix and where ( Keff,α
,Φ
to the α–th eigenvalue or harmonic mode. Generally, only the eigensolution corresponding to the
maximum value of Keff,α is found (the fundamental mode).
3. Adjoint eigenvalue problem
~ ∗α +
A⊤ Φ
1
Keff,α
~ ∗α = ~0
B⊤ Φ
(8.3)
where matrices A and B are transposed.
4. Fixed source direct eigenvalue equation (direct GPT)
~α +
AΓ
1
Keff,α
~α = ~
BΓ
S
where
D
E
Φ∗α , ~S = 0
(8.4)
~ is orthogonal to the adjoint flux.
where the direct source vector S
5. Fixed source adjoint eigenvalue equation (adjoint GPT)
~ ∗α +
A⊤ Γ
1
Keff,α
~ ∗α = ~S∗
B⊤ Γ
where
D
E
Φα , ~S∗ = 0
(8.5)
~ ∗ is orthogonal to the direct flux.
where the adjoint source vector S
8.1
State vector content for the /fluxunk/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector Sif , represent:
• The number of energy groups NG = S1f
• The number of unknowns per energy group NU = S2f
• The type of equation considered Ie = S3f = α1 + 10 α2 + 100 α3 + 1000 α4 where
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99
α1
= 0/1: Fixed source (Eq. (8.1)) or Keff (Eq. (8.2)) direct eigenvalue equation
α2
absent/present
= 0/1: Adjoint eigenvalue equation (Eq. (8.3)) absent/present
α3
= 0/1: Direct fixed source eigenvalue equation – or GPT equation (Eq. (8.4))
absent/present
α4
= 0/1: Adjoint fixed source eigenvalue equation – or GPT equation (Eq. (8.5))
absent/present
• The number of harmonics considered Nh = S4f where
Nh =
0
≥1
the harmonic calculation is not enabled
the harmonic calculation is enabled. Nh is the number of harmonics.
• The number of specific GPT equations considered Ngpt = S5f where
Ngpt =
0
≥1
the GPT calculation is not enabled
the GPT calculation is enabled. Ngpt is the number of specific GPT
equations.
• The type of Bn solution considered Is = S6f where
−1 No flux calculation, fluxes taken from input file
0 Fixed source problem, no eigenvalue
1 fixed source eigenvalue problem (GPT type) with fission
2 Keff eigenvalue problem with fission and without leakage
Is =
3 Keff eigenvalue problem with fission and leakage
4 Buckling eigenvalue problem with fission and leakage
5 Buckling eigenvalue problem without fission but with leakage
• The type of leakage model Il = S7f where
Il =
0
1
2
3
4
5
16
26
36
46
56
66
No leakage model
Homogeneous PNLR calculation
Homogeneous PNL calculation
Homogeneous SIGS calculation
Homogeneous ALSB calculation
Leakage with isotropic streaming effects
Leakage with anisotropic streaming effects
Leakage with anisotropic streaming effects
Leakage with anisotropic streaming effects
Leakage with anisotropic streaming effects
Leakage with anisotropic streaming effects
Leakage with anisotropic streaming effects
–
–
–
–
–
–
imposed buckling
X-Buckling search
Y-Buckling search
Z-Buckling search
radial Buckling search
total Buckling search
• Number of free iteration per variational acceleration cycle Nf = S8f
• Number of accelerated iteration per variational acceleration cycle Na = S9f
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100
f
• Thermal rebalancing option Ir = S10
where
Ir =
0 No thermal iteration rebalancing
1 Thermal iteration rebalancing activated
f
• Maximum number of thermal (up-scattering) iterations Min = S11
f
• Maximum number of outer iterations Mout = S12
f
• Initial number of ADI iterations in Trivac Madi = S13
8.2
The main /fluxunk/ directory
On its first level, the following records and sub-directories will be found in the /fluxunk/ directory:
Table 62: Main records and sub-directories in /fluxunk/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
EPS-CONVERGE
K-EFFECTIVE
R(4)
R(1)
S6f ≥ 1
AK-EFFECTIVE
R(1)
S3f
10
K-INFINITY
R(1)
S6f ≥ 2
B2
B1HOM
R(1)
S6f ≥ 1
DIFFB1HOM
R(G)
S6f ≥ 1
B2
R(3)
S7f ≥ 6
GAMMA
R(G)
S7f ≥ 5
FLUX
Dir(S1f )
HETE
Condition
mod 10 = 1
UnitsComment
Signature
of
the
data
structure
(SIGNA =L FLUX
)
Vector describing the various parameters associated
with this data structure Sif , as defined in Section 8.1.
Convergence parameters ∆ǫi
Computed or imposed effective multiplication factor
for direct eigenvalue problem, corresponding to the
fundamental mode
Computed effective multiplication factor for adjoint
eigenvalue problem, corresponding to the fundamental mode. The theoretical value is equal to
’K-EFFECTIVE’ but difference may occurs for numerical reasons.
Computed infinite multiplication constant for eigenvalue problem, corresponding to the fundamental
mode
cm−2 Homogeneous buckling B 2 , corresponding to the fundamental mode
cm Multigroup homogeneous leakage coefficients dg , corresponding to the fundamental mode
−2
cm Directional buckling components Bi2 , corresponding
to the fundamental mode
Gamma factors used with Bn –type streaming models.
List of real arrays. Each component of this list is a
real array of dimension S2f containing the solution
of a fixed source (Eq. (8.1)) or of a direct eigenvalue
(Eq. (8.2)) equation, corresponding to the fundamental mode.
continued on next page
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Main records and sub-directories in /fluxunk/
Name
Type
Condition
AFLUX
Dir(S1f )
S3f
10
MODE
Dir(S4f )
S4f ≥ 1
DFLUX
Dir(S5f )
S3f = 100
ADFLUX
Dir(S5f )
S3f = 1000
mod 10 = 1
continued from last page
UnitsComment
List of real arrays. Each component of this list is a
real array of dimension S2f containing the solution
of an adjoint eigenvalue (Eq. (8.3)) equation, corresponding to the fundamental mode.
List of harmonic mode sub-directories. Each component of this list follows the specification presented in
Section 8.3.
List of direct (explicit) GPT sub-directories. Each
component of this list is a multigroup list of dimension S1f . Each component of the multigroup list is a
real array of dimension S2f containing the solution of
a fixed source direct eigenvalue equation similar to
Eq. (8.4).
List of adjoint (implicit) GPT sub-directories. Each
component of this list is a multigroup list of dimension S1f . Each component of the multigroup list is a
real array of dimension S2f containing the solution of
a fixed source adjoint eigenvalue equation similar to
Eq. (8.5).
The convergence parameters ∆ǫi represent:
• ∆ǫ1 is the thermal (up-scattering) iteration flux convergence parameter
• ∆ǫ2 is the outer iteration eigenvalue convergence parameter
• ∆ǫ3 is the outer iteration flux convergence parameter
• ∆ǫ4 is the relaxation factor of the flux used in multiphysics applications. ∆ǫ4 = 1 is equivalent to no
relaxation.
8.3
The harmonic mode sub-directories in /fluxunk/
Each component of the list named ’MODE’ contains the information relative to a specific harmonic
mode.
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Table 63: Component of the harmonic mode directory
Name
Type
K-EFFECTIVE
R(1)
FLUX
Dir(S1f )
AFLUX
Dir(S1f )
Condition
Units Comment
Computed effective multiplication factor for
eigenvalue problem, corresponding to the α–th
mode
List of real arrays. Each component of this list
is a real array of dimension S2f containing the
solution of the α–th mode of a direct eigenvalue
(Eq. (8.2)) equation.
S3f
10
mod 10 = 1
List of real arrays. Each component of this list
is a real array of dimension S2f containing the
solution of the α–th mode of an adjoint eigenvalue
(Eq. (8.3)) equation.
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9 Contents of a /gptsour/ directory
This directory contains the source components of a fixed source eigenvalue problem, as used in the
generalized perturbation theory (GPT).
9.1
State vector content for the /gptsour/ data structure
The dimensioning parameters for this data structure, stored in the state vector Sigpt , represent:
• The number of energy groups NG = S1gpt
• The number of unknowns per energy group NU = S2gpt
• The number of direct fixed sources ND = S3gpt
• The number of adjoint fixed sources NA = S4gpt
9.2
The main /gptsour/ directory
On its first level, the following records and sub-directories will be found in the /gptsour/ directory:
Table 64: Main records and sub-directories in /gptsour/
Name
Type
Condition
SIGNATURE
C∗12
STATE-VECTOR
I(40)
LINK.FLUX
C∗12
LINK.SYSTEM
LINK.TRACK
C∗12
C∗12
DSOUR
Dir(S3gpt )
S3gpt ≥ 1
ASOUR
Dir(S4gpt )
S4gpt ≥ 1
Units Comment
Signature
of
the
data
structure
(SIGNA =L GPT
)
Vector describing the various parameters associated
with this data structure Sigpt , as defined in Section 9.1.
Name of the unperturbed flux orthogonal to the
fixed sources.
Name of the unperturbed system object.
Name of the tracking object used to construct the
system matrices.
List of direct fixed source sub-directories. Each component of this list is a multigroup list of dimension
S1gpt . Each component of the multigroup list is a
real array of dimension S2gpt containing a direct fixed
source array.
List of adjoint fixed source sub-directories. Each
component of this list is a multigroup list of dimension S1gpt . Each component of the multigroup list is
a real array of dimension S2gpt containing an adjoint
fixed source array
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10 Contents of a /edition/ directory
This directory contains the main editing results. For the purpose of illustration we will assume that
the EDI: module is executed using the following data:
EDITING := EDI: FLUX LIBRARY VOLMAT ::
MERG COMP COND 27 69 ALL SAVE ON EDITCELL2G ;
where EDITING is the final edition data structure. The data structures FLUX, LIBRARY and VOLMAT are
respectively of type fluxunk, microlib and tracking. Assuming that the initial number of regions
in VOLMAT is N and the number of groups in LIBRARY is G = 69, then the final information that will be
stored in the editing data structure will represent a two group (Gc = 2) one mixture Nh /microlib/.
10.1
State vector content for the /edition/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector Siedi , represent:
• The number of homogeneous mixtures saved NH = S1edi for the last editing step
• The number of condensed groups considered MG = S2edi for the last editing step
• Editing flag to indicate the presence of 4 factor editing I4f = S3edi for the last editing step
• Editing flag to indicate that the up-scattering contributions have all been transferred to the diagonal
part of the scattering matrix IU = S4edi for the last editing step
• The number of mixture activated NA = S5edi for the last editing step
• Editing flag to indicate the types of statistics generated by EDI: IS = S6edi for the last editing step
• Editing flag to indicate which boundary flux editions are used in EDI:. These editions are required for computing assembly discontinuity factors (ADF) or to perform some types of superhomogénéisation (SPH) calculations. Iadf = S7edi for the last editing step
Iadf
0 no boundary flux editions;
1 use boundary fluxes obtained using the ALBS keyword in DRAGON;
2 use boundary fluxes obtained from informations located in REF:ADF directory;
=
3 use boundary fluxes obtained from the current iteration method in Eurydice;
4 use boundary flux information recovered from the MACROLIB/ADF directory.
• Editing flag to indicate the type of tracking to be performed on a macro-geometry built by module
EDI:. Icell = S8edi for the last editing step
Icell
1
2
=
3
the macro-geometry is tracked by module SYBILT: or EXCELT:;
the macro-geometry is tracked by module NXT:;
the macro-geometry is tracked by another module.
• The number of extracted isotopes in the output microlib Im = S9edi for the last editing step
edi
• The print level considered Ip = S10
for the last editing step
edi
• Editing flag to indicate the types of cross section saved in EDI: Ix = S11
for the last editing step
edi
• The type of weighting used for P1 cross section information Iw = S12
for the last editing step (= 0:
flux weighting; = 1 current weighting)
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105
edi
• The maximum number of isotopes per mixture MI = S13
edi
• The maximum number of condensed groups in all editing Mg = S14
edi
• The maximum number of homogeneous mixtures in all editing Mh = S15
edi
• The total number of ISOTXS files generated MF = S16
edi
• The maximum number of regions before homogenization Mmax = S17
edi
• Editing flag = 1 for H-factor edition; = 0 otherwise IH−f ac = S18
edi
• Number of delayed neutron precursor groups Ndel = S19
edi
• Geometry index Lgeo = S20
Lgeo =
0
1
the macro geometry is not available
the macro-geometry of the last editing is available
edi
• Type of weighting for homogenization or/and condensation of cross-section information Iadj = S21
Iadj =
0 use direct flux;
1 use adjoint flux.
edi
• Type of current used for P1 weighting if Iw 6= 0. Icurr = S22
Icurr =
1
2
use a current obtained from an heterogeneous leakage model;
use the Todorova flux.
edi
• Number of reactions saved on output microlib Nreac = S23
Nreac =
10.2
0
>0
all available reactions are saved;
only reactions listed in REF:HVOUT array are saved.
The main /edition/ directory
On its first level, the following records and sub-directories will be found in the /edition/ directory:
Table 65: Main records and sub-directories in /edition/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
TITLE
LAST-EDIT
C∗72
C∗12
LINK.GEOM
C∗12
Condition
edi
|S11
|≥2
Units
Comment
Signature
of
the
data
structure
(SIGNA =L EDIT
).
Vector describing the various parameters associated with this data structure Siedi , as defined
in Section 10.1.
Title of the last editing performed (TITLE)
Name of the last editing sub-directory saved
(LAST)
Name of the geometry on which the last edition was based.
continued on next page
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Main records and sub-directories in /edition/
Name
Type
Condition
REF:IMERGE
edi
I(S17
)
REF:VOLUME
edi
R(S17
)
REF:MATCOD
edi
I(S17
)
REF:IGCOND
I(S2edi )
REF:ADF
Dir
S7edi = 2
REF:HVOUT
edi
C(S23
)∗8
edi
S23
>0
CARISO
C(S9edi ) ∗ 12
S9edi ≥ 1
IACTI
I(S5edi )
S5edi ≥ 1
MACRO-GEOM
Dir
edi
S20
=1
LINK.MACGEOM
C∗12
edi
S20
=1
{/micdir/}
Dir
Units
cm3
continued from last page
Comment
Merged region number associated with each of
the original region number Mr
Volume associated with each of the original
region number Vr
Mixture number associated with each of the
original region number Mmix
Reference group limits associated with the
merged groups Cg
ADF–related input data as presented in Section 10.3.
Names of the reactions saved in the output
microlib.
Name of extracted isotopes saved during the
last editing (NAMI)
Original mixture numbers for which activation
data was generated (Am )
Macro–geometry directory.
This geometry may be used to complete the compo
database, for performing a geometry equivalence (equigeom) and/or as the macro–
geometry in SPH calculations. This directory follows the specification presented in Section 3.2.
Name of the macro–geometry on which the
last edition was based.
Set of sub-directories containing the editing
information. This directory follows the specification presented in Section 2.2.
The set of directory {/micdir/} names EDIDIR will be composed according to the following rules. In
the case where the set of keywords SAVE ON are used followed by a directory name as above, the contents
of EDIDIR will be identical the name of the specified directory (e. g., EDITCELL2G ). If the SAVE option is
used without specifying a specific directory, then the first eight characters of EDIDIR (EDIDIR(1:8)) will
be given as REF-CASE while the last four character (EDIDIR(9:12)) will be a unique character variable
representing the successive directory saved. This character variable will be created as follows:
WRITE(EDIDIR(9 : 12),′ (I4.4)′ ) J
where 1 ≤ J represents the J th execution of the EDI: module. In the case above, we would have a
single editing directory of the form:
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107
Table 66: Example of an editing directory
Name
Type
EDITCELL2G
Dir
10.3
Condition
Units
Comment
Two groups /microlib/ sub-directory
The /REF:ADF/ sub-directory in /edition/
Sub-directory containing input data for ADF-type boundary flux edition.
Table 67: Records in the /REF:ADF/ sub-directory
Name
Type
NTYPE
NADF
I(1)
I(NTYPE)
HADF
C(NTYPE)∗4
{/type/}
I(Niadf )
Condition
Units
Comment
Number of ADF-type boundary flux edits.
Niadf : number of regions included in each ADFtype boundary flux edit.
Name of each ADF-type boundary flux edit.
Standard names are: = FD C: corner flux edition;
= FD B: surface (assembly gap) flux edition; =
FD H: row flux edition. These are the first row of
surrounding cells in the assembly.
Set of integer arrays containing the editing information. Indices of the regions of the reference geometry belonging to the flux edition. Name type
is a component of HADF array.
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11 Contents of a /burnup/ directory
This directory contains the main burnup information, namely the multigroup flux and the isotopic
concentration at each time or burnup step.
11.1
State vector content for the /burnup/ data structure
The dimensioning parameters for the /burnup/ data structure, which are stored in the state vector
S b , represent:
• The type of solution considered Is = S1b where
Is =
1 Fifth-order Cash-Karp method
2 Forth-order Kaps-Rentrop method
• The type of burnup considered It = S2b where
0
1
It =
2
3
Out of core or zero flux/power depletion
Constant flux depletion
Constant fuel power depletion
Constant assembly power depletion
• Number of time steps for which burnup properties are present in this directory Nt = S3b
• Total number of isotopes NI = S4b
depl
• Number of depleting mixtures NM
= S5b
• Number of depleting reactions NRdepl = S6b
• Number of depleting isotopes NIdepl = S7b
• Number of mixtures Nm = S8b
• Microscopic reaction rate extrapolation option in solving the burnup equations Ie = S9b where
Ie =
0 Do not extrapolate
1 Perform linear extrapolation
b
• Constant power normalization option for the burnup calculation Ig = S10
where
Ig =
0 Compute the burnup using the power released in fuel
1 Compute the burnup using the power released in the global geometry
This option have an effect only in cases where some non-depleting mixtures are producing energy.
b
• Saturation of initial number densities Is = S11
where
Is =
0 Do not store saturated initial number densities in the burnup object
1 Store saturated initial number densities
This option have an effect only in cases where some depleting isotopes are at saturation.
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109
b
• Type of saturation model Id = S12
where
Id =
0 Do not use Dirac functions in saturated number densities
1 Use Dirac functions in saturated number densities
This option have an effect only in cases where some depleting isotopes are at saturation.
b
• Perturbation flag for cross sections Ip = S13
where
Ip =
0 Time-dependent cross sections will be used if available
1 Time-independent cross sections will be used
b
• Neutron flux recovery flag If = S14
where
0 Neutron flux is recovered from a L FLUX object
1 Neutron flux is recovered from the embedded macrolib present in a
If =
L LIBRARY object
b
• Fission yield data recovery flag Iy = S15
where
11.2
0 Fission yield data is recovered from DEPL-CHAIN directory (see Section 2.4)
1 Fission yield data is recovered from PIFI and PYIELD records in /isotope/
Iy =
directory (see Table 17)
The main /burnup/ directory
On its first level, the following records and sub-directories will be found in the /burnup/ directory:
Table 68: Main records and sub-directories in /burnup/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
EVOLUTION-R
R(5)
LINK.LIB
C∗12
DEPL-TIMES
R(Nt )
FUELDEN-INIT
R(3)
Condition
UnitsComment
Signature of the /burnup/ data structure
(SIGNA =L BURNUP
).
Vector describing the various parameters associated
with this data structure Sib , as defined in Section 11.1.
Vector describing the various parameters associated
with the burnup calculation options Ri
Name of the microlib on which the last depletion
step was based.
108 s Vector describing the various time steps at which
burnup information has been saved Ti
Vector giving the initial density of heavy element in
the fuel ρf (g cm−3 ), the initial mass of heavy element in the fuel mf (g) and the initial mass of heavy
element in the fuel divided by the global geometry
volume (g cm−3 )
continued on next page
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110
Main records and sub-directories in /burnup/
Name
Type
Condition
VOLUME-MIX
FUELDEN-MIX
R(Nm )
R(Nm )
WEIGHT-MIX
R(Nm )
DEPLETE-MIX
I(Nm × NIdepl )
ISOTOPESUSED
ISOTOPESMIX
MIXTURESBurn
C(NI ) ∗ 12
I(NI )
I(Nm )
MIXTURESPowr
I(Nm )
{/depldir/}
Dir
continued from last page
UnitsComment
cm3 Vector giving the mixture volumes
g
Initial mass of heavy element contained in each mixture
g
Initial mass of all the isotopes contained in each mixture
Matrix giving the index in the ISOTOPESDENS record
of each depleting isotope in each mixture.
Alias name of the isotopes
Mixture number associated with each isotope
Depletion flag array. A component is set to 1 to
indicate that a mixture is depleting.
Power flag array. A component is set to 1 to indicate
that a mixture is producing power.
Set of Nt sub-directories containing the properties
associated with each burnup step Ti
The set of directory {/depldir/} names DEPLDIR will be composed according to the following laws.
The first eight character (DEPLDIR(1:8)) will always be given by DEPL-DAT. The last four characters
(DEPLDIR(9:12)) represent the time step saved. For the case where Nt time steps were saved we would
use the following FORTRAN instructions to create the last four characters of each of the directory names:
WRITE(DEPLDIR(9 : 12),′ (I4.4)′ ) J
for 1 ≤ J ≤ Nt with the time stamp associated with each directory being given by TJ . For the case
where (Nt = 2), two such directory would be generated, namely
Table 69: Example of depletion directories
Name
Type
DEPL-DAT0001
Dir
DEPL-DAT0002
Dir
Condition
Units
Comment
Sub-directories which contain the information associated with time step 1
Sub-directories which contain the information associated with time step 2
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11.3
111
The depletion sub-directory /depldir/ in /burnup/
Inside each depletion directory the following records and sub-directories will be found:
Table 70: Contents of a depletion sub-directory in /burnup/
Name
Type
ISOTOPESDENS
Condition
Units
Comment
R(NI )
(cm b)−1
MICRO-RATES
R(N dim )
10−8 s−1
INT-FLUX
FLUX-NORM
R(Nm )
R(1)
cm s−1
1
ENERG-MIX
R(Nm )
Joule
FORM-POWER
R(1)
BURNUP-IRRAD
R(2)
Isotopic densities ρi for each of the isotopes described in the /microlib/ directory where the
order of the isotopes is also specified
Values of the microscopic reaction rate of the
depleting reactions for each depleting isotope
and each mixture. The macroscopic reaction
rate related to the non-depleting isotopes is
stored at location NIdepl + 1. The NRdepl reaction types are stored in the order of the
’DEPLETE-IDEN’ array in Table 11, starting
with the ’NFTOT’ reaction. The flux-induced
power factors are stored in location NRdepl.
The decay power (delayed) factors are stored
in location NRdepl +1 Both flux-induced and decay power are given in units of 10−8 MeV/s.
N dim = (NIdepl + 1) × (NRdepl + 1) × Nm
Integrated flux in each mixture.
Flux normalization constant. It is zero for out
of core depletion and represents the normalization of the flux φgr that is used to ensure
that the cell integrated flux or power is that
required when fixed flux or power burnup is
requested
Energy realeased during the time step in each
mixture
Ratio of the global power released in the complete geometry divided by the power released
in fuel.
Fuel burnup (MW d T−1 ) and irradiation
(Kb−1 ) reached at this time step
It = 3
1
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112
12 Contents of a /multicompo/ directory
This object, shown in Figure 5, is used to collect information gathered from many DRAGON elementary calculations performed under various conditions. Each elementary calculation is characterized by a
tuple of global and local parameters. These parameters are of different types, depending on the nature of
the study under consideration: type of assembly, power, temperature in a mixture, concentration of an
isotope, time, burnup or exposure rate in a depletion calculation, etc. Each step of a depletion calculation
represents an elementay calculation. The multicompo object is often presented as a multi-parameter
reactor database.
‘SIGNATURE’
‘STATE-VECTOR’
‘DEPL-CHAIN’
‘COMMENT’
‘GLOBAL’
namdir
‘LOCAL’
‘MIXTURES’
‘GEOMETRIES’
‘TREE’
‘CALCULATIONS’
(microlib object)
(geometry object)
Figure 5: Representation of a multicompo object.
The multicompo object contains table-of-content information apart from a list of homogenized mixture directories. Each homogenized mixture directory contain a list of elementary calculation directories
whose components are embedded microlib objects containing the useful data. The localization of an
elementary calculation is done using a tuple of global and local parameters. The elementary calculation
indices are stored in a tree with the number of levels equal to the number of global and local parameters.
An example of a tree with three parameters is shown in Figure 6. Each node of this tree is associated
with the index of the corresponding global parameter (positive index) or local parameter (negative index)
and with the reference to the daughter nodes if they exist. The number if leafs is equal to the number of
nodes for the last (third) parameter and is equal to the number of elementary calculations stored in the
multicompo object. The index of each elementary calculation is therefore an attribute of each leaf.
(root)
Parameter nb. 1
Parameter nb. 2
Parameter nb. 3
(leafs)
Figure 6: Parameter tree in a multicompo object
In each embedded microlib directory, the COMPO: module recover cross sections for a number of
particularized isotopes and macroscopic sets named ’*MAC*RES’, a collection of isotopic cross sections
IGE–351
113
weighted by isotopic number densities. Other information is also recovered: multigroup neutron fluxes,
isotopic number densities, fission spectrum and a set of local parameters. The local parameters are values
that characterize each homogenized mixture: local power, burnup, exposure rate, etc.
12.1
State vector content for the /multicompo/ data structure
The dimensioning parameters for this data structure, which are stored in the state vector S cpo ,
represent:
• The number of homogenized mixtures Mm = S1cpo . = 0 for an empty multicompo object.
• The number of groups G = S2cpo
• The exact number of elementary calculations in the multicompo Ncal = S3cpo
• The maximum number of elementary calculations in the multicompo Nmax = S4cpo
• The number of global parameters Nglob = S5cpo
• The number of local parameters Nloc = S6cpo
• The number of global parameters linked with isotopes Ngl iso = S7cpo
• The number of global parameters linked with microlib objects Ngl bib = S8cpo
• The number of local parameters linked with isotopes Nloc iso = S9cpo
cpo
• The number of lines of comment Ndoc = S10
cpo
• Geometry index Lgeo = S11
:
Lgeo =
0
1
the geometries are not available
calculation–ordered homogenized geometries are available
cpo
• Version identificator S12
. Currently equal to 2006. This value will change if the multicompo
specification is to be modified in the future.
cpo
• The number of user-defined particularized isotopes S13
.
gff
• Group form factor index Ngff = S14
:
Ngff
12.2
−1 the group form factors will be recovered from an edition object
0
the group form factors are not processed
=
> 0 number of group form factors per energy group.
The main /multicompo/ directory
On its first level, the following records and sub-directories will be found in the /multicompo/ directory:
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Table 71: Main records in /multicompo/
Name
Type
SIGNATURE
C∗12
{/namdir/}
Dir
Condition
Units
Comment
Signature
of
the
data
structure
(SIGNA =L MULTICOMPO).
Set of sub-directories, each of them containing an
independent multicompo structure
Table 72: Main records and sub-directories in {/namdir/}
Name
Type
STATE-VECTOR
I(40)
DEPL-CHAIN
Dir
∗
COMMENT
NOMISP
GLOBAL
cpo
) ∗ 80
C(N10
cpo
C(S13 ) ∗ 8
Dir
cpo
>0
S10
cpo
S13
≥1
LOCAL
Dir
S6cpo ≥ 1
MIXTURES
Dir(S1cpo )
S1cpo ≥ 1
GEOMETRIES
Dir(S4cpo )
cpo
S11
=1
12.3
Condition
UnitsComment
Vector describing the various parameters associated
with this data structure Sicpo , as defined in Section 12.1.
directory containing the /depletion/ associated with
directory /namdir/, following the specification presented in Section 2.4.
User–defined comments about the data structure
Names of the user-defined particularized isotopes.
Table–of–content for global parameter information:
definition and tabulated values. The specification is
presented in Section 12.3.
Table–of–content for local parameter information.
The specification is presented in Section 12.4.
List of homogenized mixture directories. Each component of this list follows the specification presented
in Section 12.5.
List of homogenized geometry directories. Each component of this list follows the specification presented
in Section 3.2.
The GLOBAL sub-directory in /multicompo/
This directory is a table–of–content for the globals parameters. Its specification follows:
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115
Table 73: Contents of sub-directory GLOBAL in /multicompo/
Name
Type
Condition
PARKEY
C(S5cpo ) ∗ 12
PARTYP
C(S5cpo ) ∗ 4
PARFMT
C(S5cpo ) ∗ 8
PARCHR
C(S7cpo ) ∗ 8
NVALUE
I(S5cpo )
PARCAD
PARPAD
PARMIL
I(S5cpo + 1)
I(S5cpo + 1)
I(S8cpo )
S8cpo ≥ 1
PARBIB
C(S8cpo ) ∗ 12
S8cpo ≥ 1
{/gvaldir/}
R(NVALUE(J))
*
{/gvaldir/}
I(NVALUE(J))
*
{/gvaldir/}
C(NVALUE(J)) ∗ 12
*
UnitsComment
S7cpo ≥ 1
User–defined key-words for the global parameters.
Character identification for the types of global
parameters (eg: TEMP, CONC, IRRA, etc.). Temperatures are given in Kelvin.
Types for the global parameters (eg: REAL,
STRING or INTEGER).
Isotope names linked to type–CONC global parameters.
Number of specific values for a global parameters.
Address of the first element in array PARCHR.
Address of the first element in array PARBIB.
Mixture indices linked to type–TEMP or –CONC
global parameters.
microlib names linked to type–TEMP or –CONC
global parameters.
Set of real global parameter arrays. Each element of {/gvaldir/} contains a real array containing the tabulated values of the J–th global
parameter.
Set of integer global parameter arrays. Each
element of {/gvaldir/} contains an integer array containing the tabulated values of the J–
th global parameter.
Set of character∗12 global parameter arrays. Each element of {/gvaldir/} contains
a character∗12 array containing the tabulated
values of the J–th global parameter.
Item {/gvaldir/} represents a set of S5cpo real, integer or character*12 records. The name of each
{/gvaldir/} record is a character*12 variable (text12) composed using the following FORTRAN instruction:
WRITE(text12,′ (′′ pval′′, I8.8)′ ) J
where J is the index of the global parameter with 1 ≤ J ≤ S5cpo . The global parameter values of type
REAL or INTEGER are sorted.
12.4
The LOCAL sub-directory in /multicompo/
This directory is a table–of–content for the locals parameters. Its specification follows:
IGE–351
116
Table 74: Contents of sub-directory LOCAL in /multicompo/
Name
Type
PARKEY
C(S6cpo ) ∗ 12
PARTYP
C(S6cpo ) ∗ 4
PARCHR
C(S9cpo ) ∗ 8
PARCAD
I(S6cpo + 1)
12.5
Condition
Units
Comment
User–defined key-words for the local parameters.
Character identification for the types of local
parameters (eg: TEMP, IRRA, FLUB, etc.).
Isotope names linked to type–CONC local parameters.
Address of the first element in array PARCHR.
S9cpo ≥ 1
The homogenized mixture sub-directory in /multicompo/
Each component of the list named ’MIXTURES’ contains the parameter tree and a list of directories:
Table 75: Component of the homogenized mixture directory
Name
Type
TREE
Dir
CALCULATIONS
Dir(S4cpo )
12.6
Condition
Units
Comment
Parameter tree. The specification is presented in
Section 12.6.
List of microlib directories. Each component
of this list follows the specification presented in
Section 2.2 with Mm = 1 (1 mixture) and M = 4.
The TREE sub-directory in a MIXTURES component
This directory contains local parameter values and the parameter tree. Its specification follows:
Table 76: Contents of sub-directory TREE in MIXTURES
Name
Type
NCALS
NVP
I(1)
I(2)
NVALUE
I(S6cpo )
Condition
S6cpo ≥ 1
Units
Comment
Number of elementary calculations.
NVP(1): Exact number of nodes in the parameter tree. NVP(2): Maximum number of nodes
in the parameter tree.
Number of specific values for a local parameters.
continued on next page
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117
Contents of sub-directory TREE in MIXTURES
Name
Type
Condition
{/lvaldir/}
R(NVALUE(J))
S6cpo ≥ 1
DEBARB
I(NVP(1)+1)
ARBVAL
I(NVP(1))
ORIGIN
I(S4cpo )
continued from last page
Units
Comment
Set of real local parameter arrays. Each element of {/lvaldir/} contains a real array containing the tabulated values of the J–th local
parameter.
- If the node does not correspond to the last
parameter: index in DEBARB of the first daughter of the node. - If the node correspond to
the last parameter: index in DEBARB where we
recover the index of an elementary calculation.
-For a global parameter: index of the parameter in the {/gvaldir/} record (see Table 73).
-For a local parameter: index of the parameter
in the {/lvaldir/} record
Index of the mother elementary calculation.
This information is useful to follow the historical relation between calculations.
Item {/lvaldir/} represents a set of S6cpo real records. The name of each {/lvaldir/} record is a
character*12 variable (text12) composed using the following FORTRAN instruction:
WRITE(text12,′ (′′ pval′′, I8.8)′ ) J
where J is the index of the local parameter with 1 ≤ J ≤ S6cpo . The local parameter values are sorted.
The parameter tree has the same number of stages as global and local parameters. The local parameters always follow the global parameters. For each value of the i–th parameter, the tree indicates the
beginning position of the (i + 1)–th parameter. The arrays DEBARB and ARBVAL are set to localize the
results of an elementary calculation identified by a specific parameter tuple.
An example of a parameter tree is represented here:
dn = value in DEBARB,
Root
Param. Nb 1
Param. Nb 2
Param. Nb 3
*(0)
!
d2(1)
------------------!
!
d3(1)
4(2)
----------------!
!
!
!
!
d5(1)
6(3)
d7(1) 8(2) 9(3)
Calculation Nb:
DEBARB:
ARBVAL:
(m) = value in ARBVAL
2
0
4
3
1
5
5
1
7 10
2 1
4
3
1
5
1
1
2
2
3
2
3
3
d10
IGE–351
118
The useful dimensions of variables DEBARB, ARBVAL and ORIGIN in Table 76 are respectively equal to
NVP(1)+1, NVP(1) and S3cpo . The allocated sizes may be bigger.
Each elementary calculation is fully identified by a parameter tuple (the Fortran array MUPLET(NPTOT)),
an integer array of dimension NPTOT= S5cpo +S6cpo . The first S5cpo components correspond to global parameter indices; the following S6cpo components correspond to local parameter indices. Here, NVP represents
the useful size of the ARBVAL array. A recursive procedure is required to search the elementary calculation
index ICAL corresponding to this parameter tuple MUPLET. Note that some components of the tuple can
be set to zero in case where the number of global and local parameters is overdetermined. The recursive
function is called using
ICAL=NICAL(1,NVP,NPTOT,DEBARB,ARBVAL,MUPLET)
and is implemented in Fortran-90 as
RECURSIVE INTEGER FUNCTION NICAL(II,NVP,NPTOT,DEBARB,ARBVAL,MUPLET) RESULT(ICAL)
INTEGER II,NVP,NPTOT,DEBARB(NVP+1),ARBVAL(NVP),MUPLET(NPTOT)
IF(NPTOT==0) THEN
ICAL=DEBARB(II+1)
RETURN
ENDIF
NBOK=0
IKEEP=0
DO I=DEBARB(II),DEBARB(II+1)-1
IF((MUPLET(1)==0).OR.(MUPLET(1)==ARBVAL(I))) THEN
JICAL=NICAL(I,NVP,NPTOT-1,DEBARB,ARBVAL,MUPLET(2))
IF(JICAL > 0) THEN
IKEEP=JICAL
NBOK=NBOK+1
ELSE IF(JICAL==-1) THEN
NBOK=2
ENDIF
ENDIF
ENDDO
IF(NBOK > 1) THEN
! Many elementary calculation exist for this tuple.
ICAL=-1
ELSE IF(NBOK==0) THEN
! No elementary calculation exists for this tuple.
ICAL=0
ELSE
ICAL=IKEEP
ENDIF
END FUNCTION NICAL
Similarly, another Fortran program can be used to search the parameter tuple corresponding to the
ICAL–th elementary calculation:
SUBROUTINE COMUPL(NVP,NPTOT,ICAL,NCALS,DEBARB,ARBVAL,MUPLET)
INTEGER NVP,NPTOT,ICAL,NCALS,DEBARB(NVP+1),ARBVAL(NVP),MUPLET(NPTOT)
DO I=NVP-NCALS+1,NVP
IF(DEBARB(I+1)==ICAL) THEN
I0=I
EXIT
ENDIF
IGE–351
ENDDO
MUPLET(NPTOT)=ARBVAL(I0)
DO IPAR=NPTOT-1,1,-1
DO I=1,NVP-NCALS
IF(DEBARB(I+1) > I0) THEN
I0=I
EXIT
ENDIF
ENDDO
MUPLET(IPAR)=ARBVAL(I0)
ENDDO
END SUBROUTINE COMUPL
119
IGE–351
120
13 Contents of a /CPO/ directory
This directory contains a burnup dependent hierarchical reactor database. For the purpose of illustration we will assume that the CPO: module is executed using the following data:
CpoResults := CPO: EdiResults EvoResults ::
BURNUP REF-CASE
EXTRACT ALL
NAME MIXTH ;
where EdiResults is a edition data structure that contains 2 homogeneous mixtures, evaluated and
saved at 2 time steps, EvoResults is a burnup data structure containing information for the successive
burnup calculations used to generate EdiResults and finally CpoResults is the final cpo data structure
that contains the resulting reactor database.
13.1
The main directory
The following records and sub-directories will be found in the /CPO/ directory:
Table 77: Main records and sub-directories in /CPO/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
{/MIXDIR/}
Dir
Condition
Units
Comment
parameter SIGNA containing the signature of the
data structure
array Sic containing various parameters that are required to describe this data structure
list of sub-directories that contain homogeneous mixture information
The signature for this data structure is SIGNA=L_COMPO
information:
. The array Sic contains the following
• S1c = NH contains the total number of homogeneous mixtures saved.
• S2c = MG contains the maximum number of groups considered.
• S3c = MI contains the maximum number of isotopes.
• S4c = ML contains the maximum order for the scattering anisotropy.
• S5c = MB contains the maximum number of burnup steps per mixtures.
The list of directory {/MIXDIR/} names MIXDIR will be composed according to the following laws.
The first eight character (MIXDIR(1:8)) will be identical to the first 8 character of the user data following
the keyword NAME in the CPO: module (here MIXTH
. If the keyword NAME is not used then MIXDIR(1:8)
takes the value COMPO
. The last four characters (MIXDIR(9:12)) represent the various homogeneous
mixture number saved on the edition data structure. For the case where NH such mixtures were
produces the following FORTRAN instructions are used to create the last four character of each of the
directory names:
IGE–351
121
WRITE(MIXDIR(9:12),’(I4)’) J
for 1 ≤ J ≤ NH . For the example given above (NH = 2), two such directories will be generated, namely
Table 78: Example of homogeneous mixture directories
Name
Type
MIXTH
1
Dir
MIXTH
2
Dir
13.2
Condition
Units
Comment
is the sub-directory that contains the information associated with homogeneous mixture 1
is the sub-directory that contains the information associated with homogeneous mixture 2
The mixture sub-directory
Each mixture directory contains the following records and sub-directories will be found:
Table 79: Contents of a mixture sub-directory in /CPO/
Name
Type
TITLE
C∗72
PARAM
I(4)
VOLUME
R(1)
ENERGY
BURNUP
N/KB
R(G + 1)
R(P4cpo )
R(P4cpo )
ISOTOPESNAME
C(P2cpo ) ∗ 12
{/BRNDIR/}
Dir
Condition
Units
Comment
parameter T containing the title of the run
which produced this mixture
array Picpo containing the various parameters
associated with this mixture
cm3
parameter Vi containing the volume of the region associated this homogeneous mixture in
the edition data structure
eV
array Eg containing the energy groups limits
MW d T−1 array Bk containing the burnup steps
Kb−1
array wk containing the fuel irradiation for the
different burnup steps
array ISOi containing the name of the various
isotopes saved for this mixture
list of sub-directories that contain the burnup
dependent cross sections associated with this
homogeneous mixture
The following information is stored in P cpo :
• P1cpo = G contains the number of groups for this homogeneous mixture.
• P2cpo = NI contains the number of isotopes in this mixture.
• P3cpo = NL contains the order of the scattering anisotropy for this mixture.
IGE–351
122
• P4cpo = NB contains the number of burnup steps for this mixture.
The list of directory {/BRNDIR/} names BRNDIR will be composed according to the following FORTRAN instructions:
WRITE(BRNDIR,’(A8,I4)’), ’BURN
’, J
for 1 ≤ J ≤ NB . For the example given above (NB = 2), two such directories will be generated, namely
Table 80: Example of homogeneous mixture directories
Name
Type
BURN
1
Dir
BURN
2
Dir
13.3
Condition
Units
Comment
is the sub-directory that contains the information associated with burnup step 1
is the sub-directory associated with burnup step 2
The burnup sub-directory
A burnup sub-directory contains the following records and sub-directories:
Table 81: Contents of a burnup sub-directory in /CPO/
Name
Type
ISOTOPESDENS
Condition
Units
Comment
R(NI )
(cm b)−1
ISOTOPES-EFJ
R(NI )
J
FLUX-INTG
OVERV
R(G)
R(G)
cm s−1
cm−1 s
FLUXDISAFACT
R(G)
{/ISOTOPE/}
Dir
array ρi containing the density of each isotopes
array Hi containing the energy produced per
fission for each isotope
array Φgm containing the integrated flux
g
array 1/vm
containing the inverse of the average neutron velocity
array Fg containing the ratio of the flux in the
fuel to the flux in the cell
list of NI sub-directories that contain the isotopic microscopic cross section for this burnup
step
The list of directory names is specified by ISODIR = ISOi for i = 1 to NI . The first isotope ISODIR is
named MACR
and represents an equivalent macroscopic isotope with a density of 1.0 (cm b)−1 .
The content of the isotopic multigroup cross section directory is described in Section 2.9.
IGE–351
123
14 Contents of a /saphyb/ directory
This object is used to collect information gathered from many DRAGON elementary calculations
performed under various conditions. Each elementary calculation is characterized by a tuple of global
parameters. These global parameters are of different types, depending on the nature of the study under
consideration: type of assembly, power, temperature in a mixture, concentration of an isotope, time,
burnup or exposure rate in a depletion calculation, etc. Each step of a depletion calculation represents
an elementay calculation. The saphyb object is often presented as a multi-parameter reactor database.
It is used in the SAPHYR code system.
The saphyb object contains table-of-content information apart from a set of specific elementary
calculation directories. These directories are themselve subdivided into homogenized mixture directories.
The localization of an elementary calculation is done using a tuple of global parameters. The elementary
calculation indices are stored in a tree with the number of levels equal to the number of global parameters.
An example of a tree with three global parameters is shown in Figure 7. Each node of this tree is associated
with the index of the corresponding global parameter and with the reference to the daughter nodes if
they exist. The number if leafs is equal to the number of nodes for the last (third) parameter and is equal
to the number of elementary calculations stored in the saphyb object. The index of each elementary
calculation is therefore an attribute of each leaf.
(root)
Parameter nb. 1
Parameter nb. 2
Parameter nb. 3
(leafs)
Figure 7: Global parameter tree in a saphyb object
In each homogenized mixture directory, the SAP: module recovers cross sections for a number of particularized isotopes and macroscopic sets, a collection of isotopic cross sections weighted by isotopic number
densities. Cross sections for particularized isotopes and macroscopic sets are recovered for selected reactions. Other information is also recovered: multigroup neutron fluxes, isotopic number densities, fission
spectrum and a set of local variables. The local variables are values that characterize each homogenized
mixture: local power, burnup, exposure rate, etc. Some local variables are arrays of values (eg: SPH
equivalence factors). Finally, note that cross section information written on the saphyb is not transport
corrected and not SPH corrected.
14.1
The main /saphyb/ directory
On its first level, the following records and sub-directories will be found in the /saphyb/ directory:
IGE–351
124
Table 82: Main records and sub-directories in /saphyb/
Name
Type
SIGNATURE
TITLE
C∗12
C∗80
NOMLIB
DIMSAP
C∗80
I(50)
COMMEN
constphysiq
contenu
geom
adresses
paramdescrip
paramarbre
paramvaleurs
varlocdescri
{/caldir/}
C(N1 ) ∗ 80
Dir
Dir
Dir
Dir
Dir
Dir
Dir
Dir
Dir
sap
Condition
sap
S1
>0
UnitsComment
Signature of the data structure SIGNA
Signature of the data structure (for this level of
specification,=’SAPHYB LIBRARY VER, 0.02’)
User–defined name of the data structure
Vector describing the various parameters associated
with this data structure Sisap
User–defined comments about the data structure
General physical data
Content description
Geometric data
General localization data for the cross sections
General localization data for the global parameters
Global parameter tree
Global parameter values
General localization data for the local variables
sap
Set of S19
sub-directories containing the cross section information associated with a specific elementary calculation.
The signature variable for this data structure must be SIGNA=L_SAPHYB
.
The name of each {/caldir/} directory is a character*12 variable (text12) composed using the
following FORTRAN instruction:
WRITE(text12,′ (′′ calc′′ , I8)′ ) J
sap
where J is the index of the calculation with 1 ≤ J ≤ S19
.
The dimensioning parameters for this data structure, which are stored in the state vector S sap named
DIMSAP, are defined in the following table:
Values in DIMSAP
DIMSAP
sap
S1
NCOMLI
Number of lines of comment
S2sap
NISOTA
Number of isotopes in the reference cross section library
sap
S3
NCHANN∗
Number of types of radioactive decay reactions
sap
S4
NREA∗
Number of neutron–induced reaction
S5sap
NISO∗
Number of particularized isotopes
sap
S6
NMAC∗
Number of macroscopic sets.
S7sap
NMIL
Number of mixtures in the saphyb
S8sap
NPAR
Number of global parameters
sap
S9
NPCHR
Number of global parameters linked with isotopes
sap
S10
NPPNT
Number of global parameters linked with microlib objects
sap
S11
NPARL∗
Number of local variables.
IGE–351
125
Values in DIMSAP (cntd.)
sap
S12
sap
S13
sap
S14
sap
S15
sap
S16
sap
S17
sap
S18
sap
S19
sap
S20
sap
S21
DIMSAP
NPCHRL∗
NPPNTL∗
NISOF∗
NISOP∗
NMGY
NVP
NADRX∗
NCALS
NG
NISOY∗
Number of local variables linked with isotopes
Number of local variables linked with microlib objects
Number of particularized fissile isotopes
Number of particularized fission products
Number of macrogroups for the fission yields (= 1)
Number of nodes in the global parameter tree
Number of address sets in array ADRX
Number of elementary calculations
Number of energy groups in the saphyb
Number of particularized isotopes and macroscopic sets for which fission
yields are provided.
sap
S22
NVERS
Level of saphyb specification (= 2)
sap
S23
(not used)
sap
S24
NSURFS
Number of surfaces in the saphyb
sap
S25
(not used)
sap
S26
(not used)
sap
S27
(not used)
sap
S28
NRT
Number of unknowns in the reference geometry
sap
S29
(not used)
sap
S30
NGA
Number of energy groups in the reference microlib
sap
S31
NPRC∗
Number of delayed neutron precursors groups
sap
S32
NISOTS
Maximum number of isotopes in output tables (NISOTS ≤ NISOTA)
sap
S33
NMILNR∗
Number of mixtures in the saphyb with delayed neutron data
Elements of array DIMSAP identified with “*” may be equal to zero. Consequently, any array using
these dimensions is optional.
IGE–351
14.2
126
The constphysiq sub-directory in /saphyb/
Table 83: Contents of sub-directory constphysiq in /saphyb/
Name
Type
ISOTA
C(S2 ) ∗ 8
ISOTYP
C(S2sap ) ∗ 4
NOMLAM
C(S3 ) ∗ 8
ENRGA
sap
R(S30
+ 1)
MeV
ENRGS
sap
R(S20
+ 1)
MeV
FGYS
I(S16 + 1)
14.3
Condition
Units
sap
sap
sap
S3
≥1
sap
Comment
Alias names of isotopes in the reference microlib.
Types of isotopes in the reference microlib.
=’FISS’: fissile isotope; =’F.P.’: fission
product; =’ ’: otherwise.
Character identification of the available radioactive decay reactions.
Limits of the reference multigroup energy
mesh.
Limits of the saphyb multigroup energy
mesh.
Indices limits in array ENERGS of the multigroup energy mesh for the fission yields.
The contenu sub-directory in /saphyb/
Table 84: Contents of sub-directory contenu in /saphyb/
Name
Type
Condition
NOMISO
NOMMAC
TYPMAC
C(S5sap ) ∗ 8
sap
C(S6 ) ∗ 8
sap
I(S6 )
S5sap ≥ 1
sap
S6 ≥ 1
sap
S6 ≥ 1
NOMREA
C(S4sap ) ∗ 12
S4sap ≥ 1
TOTMAC
I(S7sap )
RESMAC
I(S7 )
sap
Units
Comment
Names of the particularized isotopes.
Names of the macroscopic sets.
Types of the macroscopic sets. = 1: select
all the available isotopes in the macroscopic
set; = 2: remove all the particularized isotope
contributions from the macroscopic set.
Names of the neutron–induced reactions (e.g.:
TOTALE, ABSORPTION, FISSION, etc.).
Indices in array NOMMAC corresponding to total macroscopic sets (with all isotopic contributions). = 0 if a total macroscopic set is not
defined.
Indices in array NOMMAC corresponding to
residual macroscopic sets (with isotopic contributions for the non–particularized isotopes). = 0 if a residual macroscopic set is
not defined.
IGE–351
14.4
127
The adresses sub-directory in /saphyb/
Table 85: Contents of sub-directory adresses in /saphyb/
Name
Type
Condition
ISADRC
I(S7 )
NISOMN
I(S7sap )
ISOMIL
I(N iso )
N iso ≥ 1
ADRX
I(N adrx )
N adrx ≥ 1
sap
Units
Comment
Equal to array ISADRX (in directory info) for
the last elementary calculation.
Number of particularized isotopes in each output mixture for which cross section information is available in at least one elementary calculation.
Array containing the particularized isotope indices in each output mixture.
sap
sap
sap
N iso = (S5 + S6 ) × S7
Offsets in the array RDATAX containing cross
section information. If the first index corresponds to reaction PROFILE, then ADRX is
the offset in the array IDATAP containing the
profile information of the transfer matrix.
sap
N adrx = (S4sap + 2) × (S5sap + S6sap ) × S18
The array ADRX gives the position of the first value of a cross section in array RDATAX or the first value
of profile information in array IDATAP. RDATAX and IDATAP are located in sub-directory mili//’ m’
of the sub-directory calc//’ n’. For a given reaction with index irea in array NOMREA (in subdirectory contenu), for a particularized isotope with index isot in array NOMISO (in sub-directory
contenu), and for an output mixture with index imil, the first cross section value is located at position ADRX(irea,isot,ISADRX(imil)) of array RDATAX. ISADRX is defined in the sub-directory info of
an elementary calculation. If the address is zero, then the corresponding cross sections are not defined.
Information related to Legendre–dependent scattering information is given in the two extra locations
of the ADRX array: ADRX(NREA+1,:,:) contains the number of components for the vectorial scattering
cross sections (order of anisotropy +1); ADRX(NREA+2,:,:) contains the number of components for the
(matrix) transfer cross sections (order of anisotropy +1).
sap
This system is designed in such a way to keep the value of S18 =NADRX as small as possible.
IGE–351
14.5
128
The geom sub-directory in /saphyb/
Table 86: Contents of sub-directory geom in /saphyb/
Name
Type
Condition
NOMMIL
XVOLMT
SURFS
outgeom
C(S7 ) ∗ 20
R(S7sap )
sap
R(S24
)
Dir
Units
sap
sap
S24
≥1
*
cm3
cm2
Comment
Names of the output mixtures.
Volumes of the output mixtures.
Surfaces of the output geometry.
Surfacic data related to discontinuity factor
information.
Table 87: Contents of sub-directory outgeom in /geom/
Name
Type
SURF
R(Nnsurfd )
14.6
Condition
Units
Comment
cm2
Surface assigned to each discontinuity factor.
The paramdescrip sub-directory in /saphyb/
Table 88: Contents of sub-directory paramdescrip in /saphyb/
Name
Type
Condition
NPAR
NPCHR
I(1)
I(1)
PARNAM
PARKEY
C(S8 ) ∗ 80
C(S8sap ) ∗ 4
PARTYP
C(S8 ) ∗ 4
PARFMT
C(S8 ) ∗ 8
PARCHR
C(S9sap ) ∗ 8
NVALUE
I(S8sap )
PARCAD
I(S8
sap
sap
sap
sap
+ 1)
S9sap ≥ 1
Units
Comment
Number of global parameters.
Number of global parameters linked with isotopes.
User–defined names for the global parameters.
User–defined key-words for the global parameters.
Character identification for the types of global
parameters (eg: TEMP, CONC, IRRA, etc.).
User–defined names for the global parameters
(eg: FLOTTANT, CHAINE, ENTIER, etc.).
Isotope names linked to type–CONC global parameters.
Number of specific values for a global parameters.
Address of the first element in array PARCHR.
continued on next page
IGE–351
129
Contents of sub-directory paramdescrip in /saphyb/
Name
Type
Condition
PARPAD
PARMIL
I(S8 + 1)
sap
I(S10
)
sap
S10
≥1
PARBIB
sap
C(S10
) ∗ 12
sap
S10
≥1
Units
sap
continued from last page
Comment
Address of the first element in array PARBIB.
Mixture indices linked to type–TEMP or –CONC
global parameters.
microlib names linked to type–TEMP or –CONC
global parameters.
Types and units of global parameters are defined as follows:
unit
description
o
TEMP
C
Temperature
CONC
1024 /cm3
Number density
IRRA
MW-day/tonne
Burnup
FLUB
n/kb
Neutron exposure
TIME
s
Time
PUIS
MeV/s
Normalization power
MASL
g/cm3
Mass density of heavy elements
FLUX
Volume-averaged, energy-integrated flux
VALE
(not defined)
User-defined parameter
14.7
The paramvaleurs sub-directory in /saphyb/
Table 89: Contents of sub-directory paramvaleurs in /saphyb/
Name
Type
Condition
{/pvaldir/}
R(NVALUE(J))
*
{/pvaldir/}
I(NVALUE(J))
*
{/pvaldir/}
C(NVALUE(J)) ∗ 12
*
Units
Comment
Set of real global parameter arrays. Each element of {/pvaldir/} contains a real array containing the tabulated values of the J–th global
parameter.
Set of integer global parameter arrays. Each
element of {/pvaldir/} contains an integer array containing the tabulated values of the J–
th global parameter.
Set of character∗12 global parameter arrays. Each element of {/pvaldir/} contains
a character∗12 array containing the tabulated
values of the J–th global parameter.
sap
{/pvaldir/} is a set of S8 real, integer or character*12 records. The name of each {/pvaldir/} record
is a character*12 variable (text12) composed using the following FORTRAN instruction:
WRITE(text12,′ (′′ pval′′ , I8)′ ) J
IGE–351
130
where J is the index of the global parameter with 1 ≤ J ≤ S8sap . The global parameter values of type
REAL or INTEGER are sorted.
14.8
The paramarbre sub-directory in /saphyb/
The global parameter tree has the same number of stages as global parameters. For each value of the
i–th global parameter, the tree indicates the beginning position of the (i + 1)–th parameter. The arrays
DEBARB and ARBVAL are set to localize the results of an elementary calculation identified by a specific
parameter tuple.
Table 90: Contents of sub-directory paramarbre in /saphyb/
Name
Type
Condition
NCALS
DEBARB
I(1)
sap
I(S17
+ 1)
ARBVAL
I(S17 )
ORIGIN
I(S19 )
Units
Comment
Number of elementary calculations.
- If the node does not correspond to the last
parameter: index in DEBARB of the first daughter of the node. - If the node correspond to
the last parameter: index in DEBARB where we
recover the index of an elementary calculation.
Index of the corresponding parameter in the
pval//’ n’ record.
Index of the mother elementary calculation.
This information is useful to follow the historical relation between calculations.
sap
sap
An example of a global parameter tree is represented here:
dn = value in DEBARB,
Root
Param. Nb 1
Param. Nb 2
Param. Nb 3
*(0)
!
d2(1)
------------------!
!
d3(1)
4(2)
----------------!
!
!
!
!
d5(1)
6(3)
d7(1) 8(2) 9(3)
Calculation Nb:
DEBARB:
ARBVAL:
(m) = value in ARBVAL
2
0
4
3
1
5
5
1
7 10
2 1
4
3
1
5
1
1
2
2
3
2
d10
3
3
The dimensions of variables DEBARB, ARBVAL and ORIGIN in Table 90 represent the useful size, not the
allocated size which may be bigger. The allocated size of these arrays may be obtained using the LCM
API (LCMLEN with the Fortran API).
IGE–351
131
Each elementary calculation is fully identified by a global parameter tuple, an integer array of disap
mension S8 =NPAR. A recursive program can be used to search the elementary calculation index ICAL
corresponding to a parameter tuple represented in the Fortran array MUPLET(NPAR). The recursive function is called using
ICAL=NICAL(1,NVP,NPAR,DEBARB,ARBVAL,MUPLET)
and is implemented in Fortran-90 as
RECURSIVE INTEGER FUNCTION NICAL(II,NVP,NPAR,DEBARB,ARBVAL,MUPLET) RESULT(ICAL)
INTEGER II,NVP,NPAR,DEBARB(NVP+1),ARBVAL(NVP),MUPLET(NPAR)
IF(NPAR==0) THEN
ICAL=DEBARB(II+1)
RETURN
ENDIF
NBOK=0
IKEEP=0
DO I=DEBARB(II),DEBARB(II+1)-1
IF((MUPLET(1)==0).OR.(MUPLET(1)==ARBVAL(I))) THEN
JICAL=NICAL(I,NVP,NPAR-1,DEBARB,ARBVAL,MUPLET(2))
IF(JICAL > 0) THEN
IKEEP=JICAL
NBOK=NBOK+1
ELSE IF(JICAL==-1) THEN
NBOK=2
ENDIF
ENDIF
ENDDO
IF(NBOK > 1) THEN
! Many elementary calculation exist for this tuple.
ICAL=-1
ELSE IF(NBOK==0) THEN
! No elementary calculation exists for this tuple.
ICAL=0
ELSE
ICAL=IKEEP
ENDIF
END FUNCTION NICAL
Similarly, a Fortran program can be used to search the global parameter tuple corresponding to the
elementary calculation index ICAL:
SUBROUTINE COMUPL(NVP,NPAR,ICAL,NCALS,DEBARB,ARBVAL,MUPLET)
INTEGER DEBARB(NVP+1),ARBVAL(NVP),MUPLET(NPAR)
DO I=NVP-NCALS+1,NVP
IF(DEBARB(I+1).EQ.ICAL) THEN
I0=I
EXIT
ENDIF
ENDDO
MUPLET(NPAR)=ARBVAL(I0)
DO IPAR=NPAR-1,1,-1
DO I=1,NVP-NCALS
IF(DEBARB(I+1).GT.I0) THEN
I0=I
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EXIT
ENDIF
ENDDO
MUPLET(IPAR)=ARBVAL(I0)
ENDDO
END
14.9
The varlocdescri sub-directory in /saphyb/
Table 91: Contents of sub-directory varlocdescri in /saphyb/
Name
Type
NPAR
NPCHR
PARNAM
PARKEY
PARTYP
I(1)
I(1)
sap
C(S11 ) ∗ 80
sap
C(S11 ) ∗ 4
sap
C(S11
)∗4
PARFMT
C(S11 ) ∗ 8
sap
S11 ≥ 1
PARCHR
C(S12 ) ∗ 8
sap
S12 ≥ 1
PARCAD
sap
I(S11
+ 1)
sap
S11
≥1
14.10
Condition
sap
S11 ≥ 1
sap
S11 ≥ 1
sap
S11
≥1
sap
sap
Units
Comment
Number of local variables.
Number of local variables linked with isotopes.
User–defined names for the local variables.
User–defined key-words for the local variables.
Character identification for the types of local
variables (eg: TEMP, IRRA, FLUB, EQUI, etc.).
User–defined names for the local variables (eg:
FLOTTANT, CHAINE, ENTIER, etc.).
Isotope names linked to type–CONC local variables.
Address of the first element in array PARCHR.
The elementary calculation sub-directory /caldir/ in /saphyb/
For each elementary calculation, we define a directory calc//’ n’, where n is the index of the
calculation in the global parameter tree. The results for each output mixture are stored in a directory
mili//’ m’ where m is the position index of the mixture in the array NOMMIL of the sub-directory geom.
Inside each elementary calculation directory /caldir/, the following records and sub-directories will be
found:
Table 92: Contents of sub-directory /caldir/ in /saphyb/
Name
Type
info
Dir
divers
Dir
outflx
Dir
Condition
Nnsurfd > 0
Units
Comment
General informations about the elementary
calculation
Results not related to a specific mixture: interface currents, k∞ , keff , B 2 , etc.
Discontinuity factor information.
continued on next page
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Contents of sub-directory /caldir/ in /saphyb/
Name
Type
{/mixdir/}
Dir
Condition
continued from last page
Units
Comment
sap
Set of S7 sub-directories containing the cross
section information associated with a specific
mixture.
The name of each {/mixdir/} directory is a character*12 variable (text12) composed using the
following FORTRAN instruction:
WRITE(text12,′ (′′ mili′′ , I8)′ ) J
sap
where J is the index of the mixture with 1 ≤ J ≤ S7 .
14.10.1 The info sub-directory in /caldir/
Table 93: Contents of sub-directory info in /caldir/
Name
Type
NLOC
NISOTS
I(1)
I(1)
NISF
I(1)
NISP
I(1)
NISY
I(1)
LOCNAM
LOCKEY
LOCTYP
C(NLOC) ∗ 80
C(NLOC) ∗ 4
C(NLOC) ∗ 4
NLOC≥ 1
NLOC≥ 1
NLOC≥ 1
LOCADR
I(NLOC+1)
NLOC≥ 1
ISOTS
ADRY
sap
C(S32
)∗8
I(NISY)
NISY≥ 1
ISADRX
I(S7 )
sap
Condition
Units
Comment
Number of local variables (0 ≤NLOC≤NPARL).
sap
Number of isotopes in output tables (S32
≡
NISOTS≤NISOTA).
Number of particularized fissile isotopes
(NISF≤NISOF).
Number of particularized fission products
(NISP≤NISOP).
Number of particularized isotopes and macroscopic sets used for computing the fission
yields (NISY≤NISOY).
User–defined names for the local variables.
User–defined key-words for the local variables.
Character identification for the types of local
variables (eg: TEMP, IRRA, FLUB, EQUI, etc.).
Address of the first element in array RVALOC
(sub-directory mili//’ m’) corresponding
to a local variable.
Alias names of isotopes in output tables.
Indices of fissile isotopes (positive values) and
fission products (negative values) in array
YLDS (sub-directory mili//’ m’).
Used to recover the third index in array ADRX
(sub-directory adresses).
continued on next page
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Contents of sub-directory info in /caldir/
Name
Type
Condition
LENGDX
I(S7 )
LENGDP
I(S7 )
continued from last page
Units
sap
Comment
Length of the cross section array RDATAX (subdirectory mili//’ m’).
Length of the transfer matrix profile array
IDATAP (sub-directory mili//’ m’).
sap
14.10.2 The divers sub-directory in /caldir/
Table 94: Contents of sub-directory divers in /caldir/
Name
Type
Condition
NVDIV
IDVAL
I(1)
C(NVDIV) ∗ 4
NVDIV≥ 1
VALDIV
FLXREF
R(NVDIV)
sap
sap
R(S28
× S30
)
NVDIV≥ 1
sap
S28
≥1
SCURM
R(S24 × S20 )
sap
sap
sap
S24 ≥ 1
Units
Comment
Number of values in arrays IDVAL and VALDIV.
Character identification for the values in array
VALDIV (KEFF, KINF or B2).
Values given in the order of the IDVAL array.
Neutron flux values (region– and group–
ordered) in the reference calculation.
Entering partial currents on the surfaces surrounding the geometry. The values are given
in the order of the SURF array (in sub-directory
geom).
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Table 95: Contents of sub-directory outflx in /caldir/
Name
Type
Condition
REGFLX
SURFLX
R(NG)
R(Nnsurfd ×NG)
Units
Comment
Averaged flux in the complete geometry.
Surfacic fluxes (Nnsurfd values per energy
group) integrated over surface. The averaged
values are obtained by dividing these components by those of SURF record in outgeom subdirectory (see Section 14.5).
14.10.3 The mixture sub-directory /mixdir/ in /caldir/
Table 96: Contents of mixture sub-directory /mixdir/ in /caldir/
Name
Type
CONCES
sap
R(S32
)
RVALOC
R(NVLC)
FLUXS
sap
R(S20
)
YLDS
R(N ylds )
DECAYC
R(S3
RDATAX
R(N datax )
N datax ≥ 1
IDATAP
I(N datap )
N datap ≥ 1
cinetique
Dir
sap
S33
≥1
sap
Condition
NLOC≥ 1
NISP≥ 1
sap
× S32 )
sap
S3
≥1
Units
Comment
1024 cm−3 Number density of each isotope in the output
tables. Correspond to isotopes names ISOTS
in Sect. 14.10.1.
Values
of
the
local
variables.
NVLC=LOCADR(NLOC+1)-1
Volume– and energy–integrated neutron
fluxes in the output tables.
The fission product i yield from fissile isotope
k is given as YLDS(ADRY(k),-ADRY(i)). Indices i and k are given in the order of array
NOMISO (in sub-directory contenu). A macroscopic set with a non–vanishing fission cross
section is considered as an averaged fissile isotope. N ylds = (NISF+S6sap )×NISP.
−1
s
Radioactive decay constants for each type of
decay reaction and each isotope of the output
tables.
Cross section data.
N datax =LENGDX(m)
where m is the mixture index.
Profile information of the transfer matrix.
N datap =LENGDP(m) where m is the mixture index.
Delayed neutron data for the mixture.
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ADRX (in sub-directory adresses) contains the offset used to recover information from arrays RDATAX
and IDATAP:
sap
• Starting from this offset, we recover S20 cross section values in RDATAX, except for the scattering
sap
cross section where we recover S20
values for each available Legendre order, and except for the
scattering transfer matrix where we recover N scat values for each available Legendre order. N scat
is defined with the IDATAP array.
sap
• For a PROFILE–type reaction, starting from this offset, we recover 2 × S20 + 7 integer values in
IDATAP.
The transfer matrix elements are stored in the following way. The non-zero values are stored in the
order of the secondary group and, for each secondary group, in the order of the primary groups. The
sap
2 × S20
+ 7 values describing the profile of the transfer matrix are stored in the following order:
FAGG, LAGG, FDGG, WGAL, FAG, LAG, (FDG(g),g=1,NG), (ADR(g),g=1,NG+1)
where
FAGG
(not used)
LAGG
(not used)
FDGG
(not used)
WGAL
set to 0
FAG
First secondary group
LAG
Last secondary group
FDG
First primary group in each secondary group
ADR
Address in the cross section array where data for secondary group g is beginning (the
address is relative to the isotope). The number of elements in a transfer matrix is
N scat =ADR(NG+1)-1.
For an energy transfer g’ → g and for a Legendre order L(≥ 0), the transfer cross section is identified
in the cross section array RDATAX as
g′ →g
σsℓ
= RDATAX( ADRX(irea,isot,ISADRX(imil)) + L*(ADR(NG+1)-1) + I-1 )
with I = ADR(g)+g’-FDG(g).
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14.10.4 The cinetique sub-directory in /mixdir/
Table 97: Contents of sub-directory cinetique in /mixdir/
Name
Type
NPR
I(1)
LAMBRS
R(NPR)
CHIRS
BETARS
INVELS
TGENRS
R(S20 ×NPR)
R(NPR)
sap
R(S20 )
R(1)
sap
Condition
Units
NPR≥ 1
s−1
NPR≥ 1
NPR≥ 1
NPR≥ 1
NPR≥ 1
1
1
cm−1 s
s
Comment
Number of delayed neutron precursors groups
in the mixture.
Radioactive decay constants of the delayed
neutron precursors groups.
Delayed neutron emission spectrums.
Delayed neutron fractions.
Group average of the inverse neutron velocity.
Prompt–neutron lifetime.
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15 Contents of a /mc/ Directory
This directory contains information generated by the MC: multigroup Monte Carlo module.
15.1
State vector content for the /mc/ data structure
The dimensioning parameters for the /mc/ data structure, which are stored in the state vector S mc ,
represent:
• Nominal number of source histories M per Keff cycle Nnsrck = S1mc
• Number of source cycles Ic to skip before Keff accumulation Nikz = S2mc
• Total number of cycles N in the problem Nkct = S3mc
• Initial seed for the random number generator S = S4mc
• N2N processing flag F = S5mc
F =
0 do not use information in the ’N2N and ’N3N records
1 use information in the ’N2N and ’N3N records to perform the random walk
• Type of tallies T = S6mc
0
T =
1
2
no tallies
effective multiplication factor tally
effective multiplication factor and macrolib tallies
• The number of homogenized mixtures in the macrolib tally Mout = S7mc
• The number of condensed energy groups in the macrolib tally Gout = S8mc
• The number of regions in the initial geometry Nin = S9mc
15.2
The main /mc/ directory
The following records and sub-directories will be found on the first level of a /mc/ directory:
Table 98: Main records and sub-directories in /mc/
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
K-EFFECTIVE
K-EFFECTI-SD
R(1)
R(1)
Condition
Units
Comment
Signature
of
the
/mc/
data
structure
(SIGNA =L MC
).
Vector describing the various parameters associated
with this data structure Simc , as defined in Section 15.1.
Effective multiplication factor Keff
Standard deviation of the effective multiplication factor ∆Keff
continued on next page
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Main records and sub-directories in /mc/
Name
Type
Condition
REF:IMERGE
I(Nin )
T =2
REF:IGCOND
I(Gout )
T =2
MACROLIB
Dir
T =2
Units
continued from last page
Comment
Merged region number associated with each of the
original region number in the macrolib tally Mr
Reference group limits associated with the condensed
groups in the macrolib tally Cg
Directory containing the /macrolib/ structure associated with the macrolib tally, following the specification presented in Section 1.2.
IGE–351
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16 Contents of a /draglib/ directory
The draglib format provide an efficient way to store burnup data and multigroup isotopic nuclear
data to be used in a lattice code. A draglib file is a persistent LCM object (an xsm–formatted file)
used to organize the data in a hierarchical format. Therefore, it will be easy to convert back and forth
between the binary direct access format (efficient during a lattice calculation) and the ascii export
format (usefull for backup and exchange purposes). A library in draglib format is generally built
using the dragr module available in an inhouse version of NJOY.[3] The optional capability to define
energy-dependent fission spectra is available, as described in Ref. 2.
A draglib is an LCM object with a depletion chain and a set of isotopic sub-directories located on
the root directory. Each isotopic sub-directory contains infinite dilution nuclear data for a set of absolute
temperatures. Incremental values corresponding to finite dilutions are given on the last directory level.
The first group corresponds to highest energy neutrons. Every cross section is given in barn. Finally,
note that the lagging zeros of any cross section record can be removed from that record in order to save
space on the draglib. The lattice code will therefore have to pack any uncomplete cross section record
with zeros.
16.1
The main /draglib/ directory
On its first level, the following records and sub-directories will be found in the /draglib/ directory:
Table 99: Main records and sub-directories in /draglib/
Name
Type
Condition
SIGNATURE
C∗12
VERSION
C∗12
README
ENERGY
C(N dgl ) ∗ 80
R(G + 1)
CHI-ENERGY
R(Gchi + 1)
Gchi 6= 0
CHI-LIMITS
I(Gchi + 1)
Gchi 6= 0
DEPL-CHAIN
Dir
*
{/isotope/}
Dir
UnitsComment
eV
eV
Signature
of
the
data
structure
).
(SIGNA =L DRAGLIB
Version identification.
Currently equal to
’RELEASE 2003’. This value will change if the
draglib specification is to be modified in the
future.
User–defined comments about the library.
E(g): Group energy limits in eV. Group g is defined
as E(g) < E ≤ E(g − 1).
Echi (g): Group energy limits defining the energydependent fission spectra. By default, a unique fission spectra is used.
Nchi (g): Group limit indices defining the energydependent fission spectra. By default, a unique fission spectra is used.
directory containing the /depletion/ associated with
this library, following the specification presented in
Section 2.4. (*) This data is required if the library
is to be used for burnup calculations.
Set of sub-directories containing the cross section information associated with a specific isotope.
IGE–351
141
where G is the number of energy groups. For design reasons, the draglib object has no state vector
record.
16.2
Contents of an /isotope/ directory
Each /isotope/ directory contains information related to a single isotope. This information is written
using one of the following formats:
• a temperature–independent isotopic data is written using the format described in Tables 14 to 20
of the microlib specification. Such isotopic data is typically produced by the EDI: module.
• a temperature–dependent isotopic data, tabulated for Ntmp temperatures, is written using the
format presented in Table 100.
Table 100: Temperature-dependent isotopic records
Name
Type
Condition
README
AWR
C(N iso ) ∗ 80
R(1)
TEMPERATURE
{/tmpdir/}
R(Ntmp )
Dir
BIN-NFS
I(G)
*
BIN-ENERGY
R(Nbin + 1)
*
Units Comment
nau
K
eV
User–defined comments about the isotope.
Ratio of the isotope mass divided by the neutron
mass
Set of temperatures, expressed in Kelvin.
Set of Ntmp sub-directories, each containing the
cross section information associated with a specific temperature.
Number of fine energy groups nbin,g in each group
g. May be set to zero in some groups. (*) This
data is optional and is useful when advanced selfshielding models are used in the lattice calculation.
Fine group energy limits in eV. Here, Nbin =
P
g nbin,g . (*) This data should be given if and
only if the record ‘BIN-NFS’ is present.
The name of each {/tmpdir/} directory is a character*12 variable (text12) composed using the
following Fortran instruction:
WRITE(text12,′ (′′ SUBTMP′′, I4.4)′ ) J
where J is the index of the temperature with 1 ≤ J ≤ Ntmp .
Each /tmpdir/ directory contains information related to a single isotope at a single temperature. This
information is written using one of the following formats:
• If the isotope contains no self-shielding data (i.e., if the isotope is only present at infinite dilution),
then the isotopic data is written using the format described in Tables 14 to 20 of the microlib
specification.
• If the isotope contains self-shielding data, then the infinite-dilution isotopic data is written using
the format described in Tables 14 to 20 of the microlib specification. In this case, additional
data is required to represent the dilution dependence of the cross sections. This additional data is
presented in Table 101.
IGE–351
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Table 101: Temperature-dependent isotopic records
Name
Type
Condition
Units
Comment
DILUTION
R(Ndil )
b
Set of finite dilutions σe , expressed in barn. Note:
the infinite dilution value (1.0E10) is not given.
Set of Ndil sub-directories, each containing the
incremental cross section information associated
with a specific dilution.
Microscopic total cross sections σ BIN (h) defined
in the fine groups. (*) This data should be
given if and only if the records ‘BIN-NFS’ and
‘BIN-ENERGY’ are present in the parent directory.
BIN
Microscopic diffusion cross sections σscat0
(h) for
an isotropic collision in the laboratory system defined in the fine groups. (*) This data should
be given if and only if the records ‘BIN-NFS’ and
‘BIN-ENERGY’ are present in the parent directory.
{/dildir/}
Dir
BIN-NTOT0
R(Nbin )
*
b
BIN-SIGS00
R(Nbin )
*
b
The name of each {/dildir/} directory is a character*12 variable (text12) composed using the
following Fortran instruction:
WRITE(text12,′ (′′ SUBMAT′′, I4.4)′ ) K
where K is the index of the finite dilution with 1 ≤ K ≤ Ndil .
The fine-group cross sections in records BIN-NTOT0
group values σ(g) and σscat0 (g) in such a way that
1
σ(g) =
ln[E(g − 1)/E(g)]
and BIN-SIGS00
hmin +N BIN (g)
X
σ BIN (h) ln
h=hmin +1
are normalized to the coarse
E BIN (h − 1)
E BIN (h)
and
1
σscat0 (g) =
ln[E(g − 1)/E(g)]
hmin +N BIN (g)
X
BIN
σscat0
(h)
h=hmin +1
BIN
E
(h − 1)
ln
E BIN (h)
where
hmin =
g−1
X
N BIN (i) .
i=1
Nuclear data stored on sub-directory /tmpdir/ is infinite dilution data related to a single isotope at a
single temperature. Nuclear data stored on /dildir/ and corresponding to dilution σe is incremental data
relative to infinite dilution data:
δσx (g, σe ) = Ix (g, σe ) − σx (g, ∞) = σx (g, σe )ϕ(g, σe ) − σx (g, ∞)
and
IGE–351
143
δϕ(g, σe ) = ϕ(g, σe ) − 1
where Ix (g, σe ) is the effective resonance integral and ϕ(g, σe ) is the averaged fine structure function at
dilution σe . Note that ϕ(g, ∞) = 1.
IGE–351
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17 Contents of a /fview/ data structure
This directory contains information generated by the VAL: module used to interpolate the diffusion
flux computed for Cartesian geometries. The following options of calculations are currently implemented:
• 3D geometries tracked with TRIVAT: using PRIM (aka, variational collocation) method
• 3D geometries tracked with TRIVAT: using DUAL (aka, Raviart-Thomas) method
• 3D geometries tracked with TRIVAT: using MCFD (aka, nodal collocation) method
17.1
The state-vector content
• The total number of energy group Ng = S1
• The number of mesh along X direction Nx = S2
• The number of mesh along Y direction Ny = S3
• The number of mesh along Z direction Nz = S4
17.2
The main /fview/ directory
Table 102: Records and sub-directories in /fview/ data structure
Name
Type
SIGNATURE
C∗12
STATE-VECTOR
I(40)
MXI
R(Nx )
MYI
R(Ny )
MZI
R(Nz )
FLUX
Dir(Ng )
Condition
Units
Comment
Signature of the /fview/ data structure
(SIGNA =L FVIEW
).
Vector describing the various parameters associated with this data structure S
array containing the mesh position along Xdirection.
array containing the mesh position along Ydirection.
array containing the mesh position along Zdirection.
List of real arrays. Each component of this
list is a real array of dimension Nx ∗ Ny ∗ Nz
containing the interpolated values of the flux
in the energy group.
IGE–351
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References
[1] G. Marleau, A. Hébert and R. Roy, “A User Guide for DRAGON Version4”, Report IGE-294, École
Polytechnique de Montréal, Institut de Génie Nucléaire (1997).
[2] P. Mosca, C. Mounier, P. Bellier and I. Zmijarevic, “Improvements in Transport Calculations by
the Energy-Dependent Fission Spectra and Subgroup Method for Mutual Self-Shielding,” Nucl. Sci.
Eng., 175, 266-282 (2013).
[3] A. Hébert and H. Saygin, “Development of DRAGR for the Formatting of DRAGON Cross-section
Libraries”, paper presented at the Seminar on NJOY-91 and THEMIS for the Processing of Evaluated
Nuclear Data Files, NEA Data Bank, Saclay, France, April 7-8 (1992).
IGE–351
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Index
/ADF/, 8
/BIHET/, 44, 84
/BIVCOL/, 77
/DOITYOURSELF/, 50
/EURYDICE/, 51
/GFF/, 9
/PURE-GEOM/, 48
/REF:ADF/, 107
/SPH/, 10
ALBS, 104
ALSB, 85, 99
ang, 41
ARM, 24, 47, 85
ASM:, 85
/asminfo/, 85, 86
BIHET, 88
bivact, 75–77
BIVACT:, 75
{/BRNDIR/}, 121, 122
/burnup/, 108–111
burnup, 120
C2M:, 15
/caldir/, 132–135
{/caldir/}, 124
COMPO:, 15
/CPO/, 120–122
cpo, 120
CPO:, 120
CpoResults, 120
/depldir/, 111
{/depldir/}, 110
/depletion/, 15, 19, 21, 22, 114, 140
/dildir/, 142
{/dildir/}, 142
DIMSAP, 124, 125
DOORVP, 54
/draglib/, 140
DUAL, 144
ECCO, 85
EDI:, 1, 15, 104, 106
EdiResults, 120
EDITING, 104
editing, 104
/edition/, 1, 104–107
edition, 104, 120, 121
EVO:, 1, 15
EvoResults, 120
EXCELL:, 54
excelt, 53
EXCELT:, 53, 55, 66
FD B, 8, 107
FD C, 8, 107
FD H, 8, 107
{/FINF/}, 9
FLUX, 104
/fluxunk/, 98, 100, 101
fluxunk, 104
/fview/, 144
/geom/, 128
/geometry/, 35, 38–41, 43, 44
/gptsour/, 103
GRMAX, 16
GRMIN, 16
GROUP, 3–5, 7, 8, 87–91
{/gvaldir/}, 115, 117
{/ISOTOPE/}, 122
/isotope/, 1, 18, 20, 25–27, 29, 33, 141
{/isotope/}, 20, 34, 140
ISOTOPERNAME, 3
ISOTOPESUSED, 3
/kinet/, 96, 97
LIB:, 1, 15
LIBRARY, 104
{/lvaldir/}, 117
MAC:, 1
/macrolib/, 1–4, 8–10, 15, 17, 19, 20, 39, 139
macrolib, 1
/mc/, 138, 139
MC:, 138
mccgt, 66, 91
MCCGT:, 66, 68, 69
MCFD, 144
{/micdir/}, 106
/microlib/, 1, 15, 18–22, 25, 28, 104, 107, 111
microlib, 104
{/MIXDIR/}, 120
/mixdir/, 135, 137
{/mixdir/}, 133
/multicompo/, 112–116
NADRX, 125
/namdir/, 114
{/namdir/}, 114
IGE–351
NAME, 120
NAP:, 9, 38
NCALS, 125
NCHANN, 124
NCOMLI, 124
NCR:, 1
NG, 125
NGA, 125
NISO, 124
NISOF, 125
NISOP, 125
NISOTA, 124
NISOTS, 125
NISOY, 125
NMAC, 124
NMGY, 125
NMIL, 124
NMILNR, 125
NORM, 85
NPAR, 124
NPARL, 124
NPCHR, 124
NPCHRL, 125
NPPNT, 124
NPPNTL, 125
NPRC, 125
NREA, 124
NREC, 62
NRT, 125
NSURFS, 125
NVERS, 125
NVP, 125
NXT:, 54, 56
/NXTRecords/, 56, 57, 59–65
ON, 106
OUT:, 1
PIJ, 24, 85
PIJK, 85
PIN, 62
PISO, 53
PNL, 99
PNLR, 99
PNOR, 85
PNT, 62
PRIM, 144
/PROJECTION/, 69
PSPC, 53
{/pvaldir/}, 129
REFL, 8
/saphyb/, 123, 124, 126–130, 132, 133
147
SAVE, 106
/selfshield/, 15, 20, 25
SHI:, 15, 20, 24
SIGS, 99
snt, 70–74
SNT:, 70
SSYM, 57
STEP, 92
{/subgeo/}, 40, 43
sybilt, 47, 48, 50, 51, 90
SYBILT:, 47
SYME, 57
/system/, 92, 93
TISO, 53, 55
TLM:, 54
/tmpdir/, 141, 142
{/tmpdir/}, 141
/tracking/, 46–48, 53, 55, 66–78, 80–83
tracking, 104
trafict, 88
trivat, 78, 81–83
TRIVAT:, 78, 144
TSPC, 53, 55
TUBEX, 39
TUBEY, 39
TUBEZ, 39
{/type/}, 8, 107
USS:, 15, 20, 24
VAL:, 144
VOID, 8
VOLMAT, 104
WIS, 85
{/xsname/}, 4
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