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- 26- 5. DBU, A TWO-DIMENSIONAL MULTI-GROUP DIFFUSION BURN-UP PROGRAMME With the intention of performing two-dimensional multi-group overall burri-up calculations the TWODIM programme was used as a standard block for the flux solution in a diffusion burn-up programme, DBU. The long-term irradiation of the whole reactor is followed in the quasistationary approach by means of a fast approximative interpolation burn-up method. This method as well as the extension to treatment of spatial xenoninduced power oscillations will be described in the following section. A general description of the programme is given with available options and running times. The programme has been used for studying of spatial xenon oscillations for the BHWR-800 NORDIC STUDY (ref. 21 ) of which a summary is given. 5.1. The Interpolation Burn-up Method A fast, approximative method for over-all burn-up analysis is the interpolation burn-up method. It has been used to a great extent in the Scandinavian countries (ref. 22) as well as in England (ref. 23 ), whereas it seems seldom used in, for example, the United States. The time-dependent problem is treated in the quasistationary approach by splitting of the problem into a number of time steps during which the power density distribution is assumed constant in space. The fundamental idea of this method is now that the detailed depletion of the single fuel rod or bundle of fuel rods is avoided in the o- er-all calculation by the use of a tabulation of few-group macroscopic cross sections as a function of irradiation. The conventional calculation procedure for the interpolation burn-up method is applied (ref. 23 ). Each time step is initiated by an over-all diffusion theory calculation giving a local incremental irradiation determined from the local power density and the time step used. The macroscopic cross sections corresponding to the local actual accumulated irradiation are then simply obtained by interpolation of the tabulated cross sections, and a new time step is taken. The tabulated burn-up calculation for the asymptotic rods placed in a regular lattice can then be obtained once and for all with a usual cell or point multi-group depletion programme. The method accounts for changes in isotopic contents as well as spectrum effects and variation of thermal disadvantage factors during irradi-
- 27- ation. This is due to xenon, samarium and other fission product build-up and of course the usual uranium to plutonium conversion. Asymptotic rods all go through the same stages of irradiation in which case the method is exact. However, a lot of fuel rods are situated in geometric asymptotic regions, but do not really have asymptotic behaviour. This is tor example the case for the inner fuel rods in fuel assemblies placed at different positions in the over-all picture. These rods behave in a similar way when they are situated in the same geometric surroundings far from thermalizing water gaps and absorbing control rods. However, the rods may have a considerably different local power level. An increase by a factor of two in power level will immediately increase IT and Pu capture owing to the Doppler effect. Slower effects are the increased moderator temperature and especially the increased xenon concentration, which together will harden the thermal spectrum and thus decrease the local reactivity by about one per cent. The combined power effects can be accounted for in an approximative way by extension of the one-dimensional tabulation to a two-dimensional one with the macroscopic cross sections as a function of burn-up as well as power density. For asymptotic fuel rods at different, but constant power levels during irradiation the outlined method will be correct. In PWR fuel assemblies the usual number of fuel rods is about 200-300. The lattice is very tight with narrow water gaps and zirconium followers are used to replace the control rods when they are withdrawn. Surface and corner fuel rods adjacent to water gaps and control rods constitute only about 10% of the total number of fuel rods, indicating that most rods behave as if they were asymptotic. If furthermore the local power density does not vary too much with irradiation, the interpolation burn-up method seems to be acceptable for treatment of the assembly as a whole. For BWR fuel assemblies the situation Is more difficult owing to the highly inhomogeneous lattice. Each assembly consists of about 50-60 fuel rods surrounded by large water gaps with no use of power flattening zirconium followers. In this case the corner and surface fuel rods constitute about 50% of all fuel rods, and on asymptotic treatment of the whole assembly is unsatisfactory. Instead a more accurate method for the homogenization of the assembly should be applied, resulting in equivalent cross sections for the whole assembly. Strictly speaking, the interpolation burn-up method Involves that fuel rods with equal power density and accumulated burn-up will have the »Bine
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 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 42 and 43: - 40- & - 0. A modification was per
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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