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6.3 Other utility programs The following utility programs are available. Since all of the programs utilize PDSMDL, user can easily modify the programs if necessary. (1) MACROEDIT [~SRAC/SRAC/util/pdsmdl/shr/MacroEdit.sh] The MACROEDIT is a utility program to print out the content of the member of macroscopic cross-section file MACRO or MACROWRK. While the direct use of PDSTOTXT for this purpose gives simply printout of one-dimensional array, the use of this MACROEDIT gives tabulated form of macroscopic cross-sections. (2) MICROEDIT [~SRAC/SRAC/util/pdsmdl/shr/MicroEdit.sh] The MICROEDIT is a utility program to print out the content of the member of microscopic cross-section file MICREF. It is used for the same purpose as MACROEDIT but for microscopic cross-sections. (3) FLUXEDIT [~SRAC/SRAC/util/pdsmdl/shr/FluxEdit.sh] The FLUXEDIT is a utility program to print out the content of the member storing neutron flux of fine or coarse group structure. The flux in FLUX is multiplied by the region volume. The volume can be also printed out in addition to the neutron spectrum and its spatial distribution in a tabular form. The usage is almost the same as to use MACROEDT. (4) BNUPEDT [~SRAC/SRAC/util/pdsmdl/shr/BnupEdit.sh] The BNUPEDT is a utility program to print out the information on burn-up calculation (members caseBNUP and caseDNxT) on MACRO or MACROWRK file. The major results of burn-up calculation written on logical unit 98 are reproduced by BNUPEDIT. (5) FLUXPLOT [~SRAC/SRAC/util/pdsmdl/shr/ FluxPlot.sh] The FLUXPLOT is a utility program to provide a table in text form for plotting the neutron spectrum in histogram (log-log ) style graph by reading the energy group structure and flux on FLUX file. Actual plotting is done with a spreadsheet software on the market by feeding the table provided by FLUXPLOT. 220
7. Mathematical Formulations 7.1 Formulations of Collision Probabilities We present in this section the formulations to evaluate the collision probabilities for a multi-region cell expressed by either of three one-dimensional coordinate systems (plane, sphere and cylinder) or two-dimensional cylindrical coordinates. They are expressed in a form suitable to apply a numerical scheme “Ray-Trace” method developed by Tsuchihashi 33) . Description of this chapter will be started by the derivation of the linear equation to solve the Boltzmann equation by the collision probability method (CPM) then followed by the formulations of collision probabilities in various coordinate systems, in which care is paid to evaluate the surface problem and also the directional probabilities to yield the anisotropic diffusion coefficients. For the slab geometry, the formulation of the ordinary collision probabilities expressed by the E i3 function has been given by Honeck 34) starting from the plane transport kernel by E i1 function. Here, we shall start from the basic point kernel, operate first, the double integration along a neutron path (line), finally, achieve the angular integration to yield the general form of the directional collision probabilities expressed by the integral exponential function E in . For the one-dimensional cylinder, the formulation derived by Takahashi 35) needs that the angular integration to scan the collision regions be repeated for each source region. The similar formulation by Honeck used in the THERMOS code 34) approximates the attenuation of neutron emitted from a source region by that from the mid-point of the source region. This approximation could be covered by sub-dividing the system into so many concentric regions. The formulation given in this chapter is a special case of the general two-dimensional cylinder. For an annular geometry, no integration over the azimuthal angle is needed. The main difference between the present formulation and the formers’ is in the sequence and the coordinates for the integration. Owing to the variable transformation, the angular integration appearing in the formers’ is replaced by the integration over the volume element d ρ where ρ is the distance from the center to one of the parallel lines drawn across the system. The number of lines drawn for the integration is quite small compared with that of the THERMOS code to have the same measure of accuracy, partly because no repeated integration by source region is required, partly because the analytic integration along the line in the source region does not need so many sub-division of the system. The formulation for collision probabilities in the spherical system which can be sub-divided into an arbitrary number of spherical shells has been given by Tsuchihashi & Gotoh 36) in the course of 221
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JAEA-Data/Code 2007-004 SRAC2006 :
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Contents 1. General Descriptions ..
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5.5 BWR Fuel Assembly Calculation (
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目次 1. 概要 ................
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5.4 三次元拡散計算 (CI
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1. General Descriptions 1.1 Functio
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essential programs of the integrate
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Sphere (Pebble, HTGR) 1D-Plate (JRR
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ecause the scattering cross-section
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As shown in Fig.1.4-1, one PDS file
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1.5.1 Fast Fission Energy Range (10
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i n m≠n i n i n i n i 1 i i g( C
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mixture(s) having resonant nuclides
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thermal energy range. In the fixed
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1.10 Calculation Scheme In Fig.1.10
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3 2 1 CALL MICREF [20] CALL REACT C
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homogenized P 1 spectrum obtained a
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Consequently next step ’CALL MACR
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1.11 Output Information Major calcu
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(4) A floating number may be entere
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2.2 General Control and Energy Stru
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cell. = 2 The PEACO routine (hyperf
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should be avoided for the core wher
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Note: Usually IC15=1 is used in FBR
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Behrens’ term of the Benoist mode
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Only the first character (capital l
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NET ∑ i= 1 NEGT( i ) =(Total numb
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Block-1 Control integers /18/ 1 IGT
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asymmetric cell is surrounded by en
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= 0 Isotropic (white) reflection =
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degree for the numerical angular in
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3 EPSG Extrapolation criterion 4 R
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Block-10’ Required if IGT=11, or
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= 2 Neutron from moderator = 3 Neut
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Unit Cell Periodic B.C. 4 2 3 1 RX(
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NX=4 NTPIN=6 NAPIN=1 NPIN(1)=6 6 ID
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RDP(1)=0.0 RDP(2) RDP(3) 14 13 12 R
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2.5 ANISN ; One-dimensional S N Tra
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7 IBR Right boundary condition, sam
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22 IPM Angular dependent incident s
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EV = best guess for α or 0.0 when
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Block-04* Positions of interval bou
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2.6 TWOTRAN ; Two-dimensional S N T
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Note: The original TWOTRAN uses two
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= 0 (internally set) 19 IHM Total n
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= 3 R-θ 31 IEDOPT Edit options. =
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= 1 Yes Block-4 Control floating po
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Repeat Block-20 through Block-21, N
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2.7 TUD ; One-dimensional Diffusion
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= 1 Monitor print at each inner ite
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equation is applied to meshes, the
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Pin Plate D2 D2 D1 D1 In cylindrica
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XYZ(1,2) Y-abscissa of the top side
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READ(9) (WORK(J+I),I=1,NDATA) END D
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absorption cross-section, each of w
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ITMX19 The upper limit of CPU time
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corner and there are the same numbe
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NUAC19 Override use of Chebychev po
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NUAC17 > 0 The constant for all gro
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ottom starting with a new card. For
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Card-006-3 Specification of meshes
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4 SIG3 Absorption cross-section (
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2 NFX2 Optional print control = 0 N
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Region 1 Region 2 Left Right X/R/R
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X T 22*11 Meshes 1 Mesh = 1 Region
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2.9 Material Specification ’Mater
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fuel pin: MU08F0U2 and those in MOX
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hydrogen, add character ‘0’ to
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Usually, enter IRES=2 for the heavy
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2.10 Reaction Rate Calculation The
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Block-1 Control integers for reacti
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3 U238 The position of the second n
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2.11 Cell Burn-up Calculation The i
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= 2 Information for debugging = 3 D
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chains under consideration is enlar
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MACROWRK file. 2 INTSTP Step number
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Block-8-1 Required if IBC6=1 /1/ NM
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e avoided. Because U08W and U080 ar
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2.12 PEACO ; The hyperfine Group Re
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3. I/O FILES We shall describe the
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(E(g),g=1,NGF+1) structure. Boundar
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LTH(1) = (LD(1)+1)*LA(1), ordered a
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Background cross-sections Member Yz
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INT(2) = 0 K-member only without sc
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Member name Contents **************
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(WEIGHT(g),g=1,NGF) Lethargy widths
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3.1.5 Fine Group Macroscopic Cross-
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Member mmmmebfM or caseebxM /10*ng+
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Member caseBNUP Material-wise burn-
Page 181 and 182: Initial inventory in the restart ca
Page 183 and 184: (YDIOX(j),j=1,NOWSTP) Fission yield
Page 185 and 186: (n/cm 2 /sec*cm 3 ), NRR is number
Page 187 and 188: 3.2.1 Common PS Files The following
Page 189 and 190: 3.2.5 PS files for TUD The PS files
Page 191 and 192: at the first column. Block-1-1 Numb
Page 193 and 194: = ‘DAYS’ days = ‘YEARS’ yea
Page 195 and 196: GD156 XGD60001 641560 154.660 0 0 0
Page 197 and 198: : ZZ050 1.50080E+00 *FP-Yield-Data
Page 199 and 200: Kr83 Zr95 fission β + decay, EC (n
Page 201 and 202: Ge73 Ge74 As75 Ge76 fission β + de
Page 203 and 204: 4. Job Control Statements In this c
Page 205 and 206: ~SRAC/tool/lmmake/lmmk/lmmk.sh, whi
Page 207 and 208: 5. Sample Input Several typical exa
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Page 211 and 212: 5 5 5 5 5 5 & 5 5 5 5 5 5 & 1 2 3 4
Page 213 and 214: 5.3 S N Transport Calculation (PIJ,
Page 215 and 216: XFEN0001 2 0 5.78720E-02 XNIN0001 2
Page 217 and 218: Water reflector Extrapolated B.C. B
Page 219 and 220: 1 1 1 1 1 1 1 2 3 008 -2 1 1 999 /
Page 221 and 222: Note: This sample is time consuming
Page 223 and 224: XCRN0008 0 0 1.55546E-02 XNIN0008 0
Page 225 and 226: ****** Input for material specifica
Page 227 and 228: T-Region R-Region X-Region Reflecti
Page 229 and 230: 6. Utility for PDS File Management
Page 231: To read in the microscopic cross-se
Page 235 and 236: scattering kernel at point r’ fro
Page 237 and 238: The integration by R between R j- a
Page 239 and 240: G j Pij ( lattice) = Pij ( isolated
Page 241 and 242: We, however, should take care of th
Page 243 and 244: 2 = ρ 2 + x r sin β = ρ R = x
Page 245 and 246: 1 i ∑ − 1 k = j+ 1 λ ij = λ k
Page 247 and 248: where λ λ 1 is 2 is = = N ∑ k k
Page 249 and 250: 2π ri −1 Pij = − Σ ∫ ρdρ
Page 251 and 252: In Fig.7.1-5, the line PQ’ define
Page 253 and 254: pin rod are divided into four regio
Page 255 and 256: the arrays T and II, respectively.
Page 257 and 258: Note that among four terms appearin
Page 259 and 260: If a group-dependent form of Fick
Page 261 and 262: 7.3 Optional Processes for Resonanc
Page 263 and 264: 7.3.2 Table-look-up Method of f-tab
Page 265 and 266: has been introduced for the correct
Page 267 and 268: ϕ i ( 0 u ) = ∑ Pij ( u) W j ( u
Page 269 and 270: Geometry b i m f b f −( γ + γ )
Page 271 and 272: will be seen in the reference 65) .
Page 273 and 274: The lattice cell under study may co
Page 275 and 276: (2) Two resonance-absorbing composi
Page 277 and 278: One of the physical problems associ
Page 279 and 280: and V = V + V , F f m where Σ m ,
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where X = 2R p ( Σ C = 2R πρ R p
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• the reduced collision probabili
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The root mean square (RMS) residual
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group flux and for the fast group f
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Table 7.5-1 (1/2) Nomenclature Symb
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7.5.1 Smearing Smearing or spatial
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7.5.2 Spectrum for Collapsing The f
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Here, an equivalent relation holds
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1 F = K ∑∫ g * χ g ( r) ϕ g (
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M dN i ( t) M = ∑ f j→iλ j N i
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8. Tables on Cross-Section Library
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Table 8.1-2 (2/2) Element index (zz
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JEFF-3.0 are based on other nuclear
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Table 8.2-1 (1/8) List of SRAC publ
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8.3 Energy Group Structure The ener
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(4) Upper Boundary of PEACO Routine
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References 1) K. Tsuchihashi, H. Ta
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Experiment,” J. Nucl. Sci. Techno
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75) K. Tasaka : “DCHAIN: Code for
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