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- 40- & - 0. A modification was performed in fig. 23 with a guess of the average flux values within the smaller time steps to ensure a better approximation for the integrated flux. This modification reduces the number of smaller time steps per larger ones by a factor of 5 with the same accuracy. Concerning the required number of smaller time steps per larger ones, both the finite difference approximation in equations (7.2} and {?. S) as well as the smooth change of the flux converted into a stepwise change with time must be accounted for to ensure a proper solution of the depletion problem. After the initial large time step Xe and Sua in turn are assumed to have reached their equilibrium concentrations, a procedure which is commonly used in cell burn-up programmes {ref. 4). * e >-Xe+°a,Xe» "*» ^w" ( ' The reader is referred to section 5.2 for the symbols. A single pseudo fission product is applied which is defined by one fission product produced per fission. The methods described above constitute the basic principles in the burn-up procedure BURN. Verification of the procedure has been made by depletion of a Yankee unit cell, for which the appropriate average fluxes and effective microscopic cross sections for each time step were provided from the LASER programme. There is full agreement between the two depletion methods. With larger time steps of 30 days a relative accuracy better than 10 is obtained even with a subdivision into only 10 smaller time steps, 7. 3. The CEB Programme The one-dimensional (cylinder, slab, sphere) multi-group (maximum ~ 40 groups and 6 meshes) collision probability cell burn-up programme CEB employe the burn-up procedure BURN as well as several blocks from the CELL programme Including the standard flux solution procedure SOLU. A wide range of current cell burn-up problems will be solved efficient-
- 41 - ly with a detailed spatial isotopic depletion. The programme can be provided with multi-group microscopic cross sections in either card or magnetic tape form. Accumulated burn-up, space-dependent flux spectra and number densities as well as reactivity and homogenized few-group macroscopic cross sections for later application in, for example, diffusion theory, are printed for each time step. The CEB programme is written in the ILLINOIS-ALGOL language with dynamic overlay and with link structure shown in fig. 5. Verification of the programme will be given in section 10, where cell burn-up calculations for the Yankee reactor (ref. 20 ) will be compared with calculations performed with LASER as well as with experimental data. With 16 group microscopic cross sections from the LASER-CROSS MICRO complex, a typical Yankee unit cell burn-up calculation requires about 3 sec per time step. A detailed spatial fission product depletion was recently incorporated in the CEB programme (ref. 29). The FIPO procedure accounts for 166 different isotopes distributed on 68 linear chains by means of a combined analytical and numerical method without any further serious computational efforts.
Page 1 and 2: i Risd Report No. 235 S •S s Dani
Page 3 and 4: December, 1970 RisO Report No. 235
Page 5 and 6: - 3 - CONTENTS Page 1. Introduction
Page 7: - 5 - Page 13. Summary and Main Con
Page 10 and 11: - 8- A combined unit cell and over-
Page 12 and 13: - 10 3. THE LASER - CROSS COMPLEX F
Page 14 and 15: -12- jg. g = £g. g . E g > (3 2) w
Page 16 and 17: - 14- where Q g (r) O fer reactivit
Page 18 and 19: - 16- D 6 c* 2J _ x 2A. w, j (4. 9)
Page 20 and 21: - 18- vectors: »j = Vi M "' F 'j-i
Page 22 and 23: - 20- (H(L„)+ u - l) 2 = 11 (LI u
Page 24 and 25: - 22- duced from equation (4.30):
Page 26 and 27: -24- be seen from the slope of the
Page 28 and 29: - 26- 5. DBU, A TWO-DIMENSIONAL MUL
Page 30 and 31: 28 set of cross sections, regardles
Page 32 and 33: -30- 5.3. The DBU Programme The int
Page 34 and 35: -32- 6. CELL, A GENERAL ONE-DIMENSI
Page 36 and 37: - 34 - k .. effective multiplicatio
Page 38 and 39: -36- h gTh E^-*S2 , (6.8) li'Msh D
Page 40 and 41: - 38- into a number of time steps d
Page 44 and 45: -42- 8. CDB, A COMBINED CELL COLLIS
Page 46 and 47: - 44 - programme. The problem with
Page 48 and 49: -46- treated in an approximative wa
Page 50 and 51: -48- Microscopic cross sections can
Page 52 and 53: - 50- column was 230.05 cm and equa
Page 54 and 55: -52- 10. UNIT CELL CALCULATIONS Mic
Page 56: - 54- with the homogeneous B-l tran
Page 59 and 60: - 56 The calculated and measured ur
Page 61 and 62: - 58- This section describes the av
Page 63 and 64: - 60- The Zr followers surrounded b
Page 65 and 66: - 62- within the core, whereas DBU
Page 67 and 68: -64- 238 on the local flux spectrum
Page 69 and 70: 235 The calculated diagonal U - 66-
Page 71 and 72: - 68- 235 For core locations G4-C-f
Page 73 and 74: - 70- The associated average power
Page 75 and 76: - 72- 239 240 ?41 The spent Core II
Page 77 and 78: - 74- The corner fuel rod Phase II
Page 79 and 80: - 76- 13. SUMMARY AND MAIN CONCLUSI
Page 81 and 82: - 78 - 15. REFERENCES 1) H. C. Hone
Page 83 and 84: - 80 - 28) F. W. Todt, Revised GAD,
Page 85 and 86: - 82 - 16. APPENDIX The description
Page 87 and 88: I - 84 - CEBU TIMS MACR DEPL. CEDI
Page 89 and 90: 86 - Table 2 Yankee unit cell descr
Page 91 and 92: - 88 - Table 4 Yankee Core I beginn
Page 93 and 94:
- 90 - Table 7 Yankee control rod c
Page 95 and 96:
- 92 - Table 10 Yankee Core I begin
Page 97 and 98:
Table 13 Uranium inventories of Yan
Page 99 and 100:
- 96 - Table 15 Initial and final u
Page 101 and 102:
Table 17 Normalized uranium and plu
Page 103 and 104:
Table 19 Normalized uranium and plu
Page 105 and 106:
Location Table 22 Normalized uraniu
Page 107 and 108:
MAIN ORIGIN ALFA FATE J | RATE SLOW
Page 109 and 110:
CEB BDM)- ORIGIN ALFA DAPA STEP FID
Page 111 and 112:
MAIN FUICA _ , 1 ROMO 1 FLUC 1 REAC
Page 113 and 114:
Mesh lines Flux points V.Z.9 . X.R
Page 115 and 116:
tmj iKBtXIKB,) t« 1 «,,) s « k -
Page 117 and 118:
- 113 - X'' \X \ \ \ \ V li', V \ \
Page 119 and 120:
-113 I r / ••• h w«x !i ;.',
Page 121 and 122:
» U * P . ».'" P . -.»! P~. , *
Page 123 and 124:
- 119 - Th« positions of th« 305
Page 125 and 126:
- 1 21 - tf" 00 (O-1.855 eV) 4 6 8
Page 127 and 128:
- 123 - 48 44 40 36 - 32 28 24 20
Page 129 and 130:
- 125 - 0-1 = I 2 3 F^/Nf . MMMom (
Page 131 and 132:
o MM»ur«d Phatt I. n and in data
Page 133 and 134:
Fig. 35. U concentrations versus ac
Page 135 and 136:
- 131 - I0- 2 r- »"•I I 1 1 I 00
Page 137 and 138:
133 •O-'cr 10"' I i •o" = A ur'
Page 139 and 140:
Assembly FS Jk 18 2222 cm w 2 SW TT
Page 141 and 142:
- 137 - Assembly J 3 l. 0719 em 1.2
Page 143 and 144:
2 t -— i ^ —m~ ' Ir Canlrol 3 '
Page 145 and 146:
I I UO U» 106 104 102 too 098 . 09
Page 147 and 148:
.i 1 s i .o — LASER (asymptotic)
Page 149 and 150:
- 140 - Q6 OS r 0.7 ai • a § k I
Page 151 and 152:
147 - Control rods 2 Symmetric boun
Page 153 and 154:
Control rod pattern in relation to
Page 155 and 156:
Control rod pattern in relation to
Page 157 and 158:
-15$ - Rg.65. LASER - unit cell bur
Page 159 and 160:
-155 - Fig. 67. CELLcross siction c
Page 161 and 162:
R9 69 -157- TWOCHMover-all flu« so
Page 163 and 164:
- 159 - »ORIGIN »IBLDR COARP »IB
Page 165:
- 161 »ORIGIN »IEDIT »IBLDR CEBU
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