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Table 7.5-1 (2/2) Nomenclature Symbols Meaning Σ , , ν Σ Macroscopic multi-group cross-section of material m. z m, g f , m, g Σ Macroscopic transport cross-section of material m. tr , m, g Σ Macroscopic energy transfer cross-section of material m. sl, m, g→g ' Σ z , I , g , ν Σ f , I , g Averaged multi-group cross-section of I-th X-Region. Usually one X-Region is assigned to each lattice cell unless a super-cell model is used. Σ s0, I , g→g ' Averaged energy transfer cross-section of I-th X-Region. Σ tr , I , g Averaged transport cross-section of I-th X-Region D I , g Averaged diffusion coefficient χ I ,G Few group fission spectrum Σ z , I , G , ν Σ f , I , G Few group cross-section of I-th X-Region. Σ s0, I , G→G' Few group energy transfer cross-section of I-th X-Region. Σ tr , I , G Few group transport cross-section. D I , G Few group diffusion coefficient. ϕ g ( r) = ∫ ϕ( r,u) du Analytical expression of space dependent flux of group g. Δ ∫ u g ϕ / V Average flux of region i and integrated in group g. i, g = ϕ g ( r) dr Vi i Φ Φ m , g = ∑ ∈ ϕ i, gV i / Vm Average flux of region m of multi-group g. i m , G = ∑ ∈ Φ Average flux of region m of few-group G. m g G m , g Φ I , g = ∑ ∈ ϕ i, gV i / VI Average flux of region I of multi-group g. i I Φ g = ∑ ∈ i cell ϕ V / V Average flux of whole cell of multi-group g. i, g i cell Φ I , G = ∑ ∈ Φ I , g Average flux of region I of few-group G. g G 280
7.5.1 Smearing Smearing or spatial average of cross-sections is achieved in the MIXX routine by using the spatial distribution of the flux ϕ i,g obtained by the cell calculation as described in Sect.7.4. When the second resonance energy range below 130.07eV (or 961.12eV ) is treated by the direct method described in Sect.7.3 using the PEACO routine, the effective cross-sections in each region and the fluxes with multi-group structure obtained by Eq.(7.4.1-1) are replaced by those from the PEACO routine. ∑ Σ z, I , g = Σ V ϕ ( Φ I , gV ) (7.5-1) i∈I ∑ i∈I z, m, g i i, g I ν Σ f , m, g = νΣ V ϕ ( Φ I , gV ) (7.5-2) ∑ f , m, g ∑ i i, g I ∑∑ χ (7.5-3) I , g = χ m, g νΣ f , m, g ' Viϕi, g ' νΣ f , m, g ' Viϕi, g ' i∈I g ' i∈I g' Σ ∑ →g ' = Σ V ϕ ( Φ I , gV ) (7.5-4) sl, I , g sl, m, g→g ' i i, g I i∈I Benoist presented a theory of the diffusion coefficient in reactor lattice, leading to expressions valid in full generality 25) . For the diffusion coefficient of the direction k, omitting the absorption correction and angular terms, this theory gives D ϕ ) . (7.5-5) = ∑∑Vi i, g λ j, g Pijk , g 3∑ k , g ( Vi ϕ i, g i j i where i and j stand for the region number, λ j,g the transport mean free path for region j given by 1/Σ tr,m,g and P ijk,g is a directional first flight collision probability given by Eq.(7.1-16). Three options are provided for calculating the diffusion coefficient D k,g . (1) Optional Process IC17 = 1 The first option is a rather sophisticated one which has been proven by experience to be fairly accurate, and the diffusion coefficient is given by the inverse of the cell averaged transport cross-section, i.e., D h ∑ ∑ , g = Σ i V ϕ 3 V ϕ . (7.5-6) i i, g ( i i, g tr, m, g ) i When the flux ϕ i,g are flat in the whole system and we can assume 281
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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-
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Initial inventory in the restart ca
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(YDIOX(j),j=1,NOWSTP) Fission yield
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(n/cm 2 /sec*cm 3 ), NRR is number
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3.2.1 Common PS Files The following
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3.2.5 PS files for TUD The PS files
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at the first column. Block-1-1 Numb
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= ‘DAYS’ days = ‘YEARS’ yea
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GD156 XGD60001 641560 154.660 0 0 0
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: ZZ050 1.50080E+00 *FP-Yield-Data
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Kr83 Zr95 fission β + decay, EC (n
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Ge73 Ge74 As75 Ge76 fission β + de
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4. Job Control Statements In this c
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~SRAC/tool/lmmake/lmmk/lmmk.sh, whi
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5. Sample Input Several typical exa
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613.0 650.0 760.0 769.0 & cooling 7
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5 5 5 5 5 5 & 5 5 5 5 5 5 & 1 2 3 4
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5.3 S N Transport Calculation (PIJ,
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XFEN0001 2 0 5.78720E-02 XNIN0001 2
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Water reflector Extrapolated B.C. B
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1 1 1 1 1 1 1 2 3 008 -2 1 1 999 /
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Note: This sample is time consuming
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XCRN0008 0 0 1.55546E-02 XNIN0008 0
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****** Input for material specifica
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T-Region R-Region X-Region Reflecti
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6. Utility for PDS File Management
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To read in the microscopic cross-se
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7. Mathematical Formulations 7.1 Fo
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scattering kernel at point r’ fro
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The integration by R between R j- a
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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
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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 ,
Page 281 and 282: We shall discuss the following two
Page 283 and 284: where X = 2R p ( Σ C = 2R πρ R p
Page 285 and 286: • the reduced collision probabili
Page 287 and 288: The root mean square (RMS) residual
Page 289 and 290: group flux and for the fast group f
Page 291: Table 7.5-1 (1/2) Nomenclature Symb
Page 295 and 296: 7.5.2 Spectrum for Collapsing The f
Page 297 and 298: Here, an equivalent relation holds
Page 299 and 300: 1 F = K ∑∫ g * χ g ( r) ϕ g (
Page 301 and 302: M dN i ( t) M = ∑ f j→iλ j N i
Page 303 and 304: 8. Tables on Cross-Section Library
Page 305 and 306: Table 8.1-2 (2/2) Element index (zz
Page 307 and 308: JEFF-3.0 are based on other nuclear
Page 309 and 310: Table 8.2-1 (1/8) List of SRAC publ
Page 317 and 318: 8.3 Energy Group Structure The ener
Page 319 and 320: (4) Upper Boundary of PEACO Routine
Page 321 and 322: References 1) K. Tsuchihashi, H. Ta
Page 323 and 324: Experiment,” J. Nucl. Sci. Techno
Page 325: 75) K. Tasaka : “DCHAIN: Code for
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