ML19211A498

Thermal Reactors:Calculations of Power Distributions & Reactivities

ML19211A498
Person / Time
Site:	07106581
Issue date:	11/30/1979
From:	Helhaus G, Jenquin J, Votinen V Battelle Memorial Institute, PACIFIC NORTHWEST NATION
To:
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ML19211A494	List: ML19211A493 ML19211A495 ML19211A496 ML19211A498 ML19211A502
References
14897, BNWL-1381-2, NMWL-1381-2, NUDOCS 7912200020
Download: ML19211A498 (7)

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2.0 THERMAL REACTORS

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CALCULATIONS OF POWER DISTRIBUTIONS AND REACTIVITIES

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V. O. Uotinen, G. L. Gelhaus, U.

P. Jenquin and C. R. Gordon 1

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Introduction A detailed analysis is in progress of the critical experiments conducted in the PRCF under a cooperative l

program (1) between the USAEC and the Italian CNEN.

The purpose of this analysis is to evaluate calculational methods and J

models by comparing calculated power distributions and reac-h}

tivities with those measured in the USAEC-CNEN program.

The experimental program comprised a large number of lattice con-figurations using 2.35 wt% enriched UO rods and Pu0 -UO rods 2

2 2

of several enrichments.

The configurations ranged from simple a

}s uniform lattice arrays to arrays which simulated boiling water

, t' reactor fuel bundles with rods of lower enrichments on the

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h edges and corners to reduce power peaking.

i

] j The analysis thus far has been applied to arrays in which a single type of fuel rod was used.

This study comprises a total of 12 loadings, six configurations for each of two fuel j

e 240 types, 2.3S wtt enriched UO and 2 wt% Pu0 -UO (8%

Pu) 2 2

2 rods.

The six configurations were (1) a regular uniform

~

loading of rods; (2) the same loading but with a water hole l

l in the center (i.e., the central fuel rod was removed);

j (3) water slab (a row of fuel rods removed); (4) water cross; (5) a 7 x 7 rod array surrounded by water slots; (6) a simi1*ar

'}

9x 9 rod array.

In these twelve experimento, spatial power distributions f

were measured by gamma-scanning selected fuel rods.

The k,ff for an infinitely-reflected array was also determined for each 4

case.

The main interest in the power distribution measurements 3j was in the rod-to-red distribution, expecially the effects of a

water slots on the power peaking.

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The saries of experiments, ranging from the simplest (regular) array to one simulating a 7 x 7 or 9 x 9 bundle, gf l[k provides a systematic test for the evaluation of calculational O.5 m

methods.

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Calculations R2$

In the analysis of H 0-moderated and reflected experiments w3 2

(especially clean critical experiments) one generally assumes hbf the reactor is composed of two regions:

core and reflector, ff, Few-group cross section.e are calculated, assuming that an j%;

infinite medium spectrum applies in each region.

The few-group

=P cross sections are then used in a diffusion theory calculation 14

• w of k

.fj eff*

[h In an earlier study (2) it was pointed out that such.a two-J,y region, infinite medium model generally does not predict the Qs

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power distribution well, although it may yield a satisfactory 33; value for k In general, this method shows a pronounced eff. $f 4 trend, such that if the power di~stribution is normalized at the dg l center of the core, the power near the core-reflector interface i.] is consistently under-estimated. A simple modification, which .]} resulted in considerably improved correlations, was reported Qj] in Reference 2. This simple modification consisted in intro-j{. ducing an extra reflector region (one lattice unit thick, $$i adj acent to the core) which is represented by cross sections

1. gg averaged over a spectrum characteristic of the core.

esjh The multigroup transport theory codes HRG and Battelle-p;j Revised - THERMOS were used to generate four-group cross c-M5; sections for~ core and reflector regions. These cross sections .n: ~ 2M j were used in the two-dimensional diffusion theory code 2DB in

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gg an x-y calculation of power distributions and keff. le)

ipj Four mesh points per cell were used in the 2DB calcula-

@n,h tions. This mesh description was carried out two lattice units M ene +r 21s 1631 238 c.: .2

r b h BNNL-1381-2 y into the reflector; then the mesh points were more widely spaced. An axial buckling of 8.9 m ' was used consistently. W rj In our current analysis we have compared three variations 0 t I. of our calculational model: ?. G l Model 1. The usual two-region, infinite-medium model (described in previous section); Model 2. A simple modification consisting of an additional reflector region whose cross sections are obtained from cell f: calculations performed for the core (described in the previous p section). In this model all. water gaps also contained these -,y modified reflector cross sections. Model 3. A more detailed representation of the differ-j ences in spectrum in successive rows of fuel and water. This was accomplished with THERMOS calculations in slab geometry, with appropriate homogenized regions of core, reflector and aps; editing was done over the proper spatial points to obtain average cross sections for each " row" of fuel and water. For analysis of the UO 1 adings, five sets of cure cross sec-2 tions were used to represent fuel rods in various locations, and four sets of cross sections were used to represent water. For analysis of the UO -Pu0 loadings, three sets of core cross 2 2 sections and three sets of water cross sections were used. 'l Results r Power Distributions 7 i kJ r Power distributions calculated using the three models h described above were compared with measured distributions.

f h

m j The trend that is so evident in the regular lattices when 1 using Model 1 (i.e., calculated power consistently under-y estimated near core-reflector boundary) was significantly reduced when the modified models were used. The simple 3 i 1631 239 i 2.3

r t. g 9 -5 l i BNWL-1381-2 J e i. I modification used in Model 2 gives a better correlation than p k the more refined modifi ation used in Model 3. This is evident k especially in the case uf the mixed oxide loading. hr 3 - E The lattice position that one chooses for a normalization h, h l point is rather arbitrary, yet this choice can affect the } trends that one sees as well as the overall goodness or badness [ }(__ of the correlation. The center of the core is one likely [4 f i normalization point. However, if this point is chosen, then h u one is basing his whole correlation on the accuracy of that one lis measurement (since there is only one rod in the center). A M E. better choice might be a location away frora the center and also g g away from water boundaries, a location which would permit four j l or eight symmetrical rods to be measured,. the average of these P;

r l

measurements then providing a more reliable normalization point. 9s i However, multiple symmetrical rods were not measured in every b 4 l Furthermore, no matter what point one chooses, there are case. l always nonuniformities in the fuel rods, in the lattice plates, s, { and bowing of fuel rods, etc., which introduce unknown errors nij 8 into the normalization. j 4 l To eliminate this arbitrariness, and to provide a meaning-ij j ful and consistent criterion for comparison of methods, we .y chose to represent the goodness of each correlation by a stan-d i dard deviation, e, defined by(i) l,f N j

1) h (N - 1)

{ (6 -6 o j i d h l f where N is the number of rods measured, h P - P for the i

rod, in !?J calc meas th 6

= t -- 1 Pmeas i f $ h ) N M. I C and 5={6 i 1631 240 l i s: I, 2.4 .[ 2 I

o u, l

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BNWL-1381-2 ]v i fj The definition of a implies an " effective" normalization such ) that the average fractional deviation, 6, is zero. This defi-h nition thus makes e independent of the particular choice of gf f{j U normalization, and provides us a meaningful, consistent measure y for purposes of comparing methods. (* v

9.,

The o's for the various cases are given in Table 2.1. We y can make the following general observations: n In every case a was significantly reduced when modifica-p Q tions were made to the simple two-region, infinite d medium model (Model 1). !b + In most cases, Model 2 gives the best correlation. y The significant improvement, and the goodness of the correla-hf tions obtained with the simple modification -(Model 2), as well its simplicity, make this model attractive for calculating 2j as j'y power distributions in H O cores. 2 m l} Calculation of kdf F The modifications that were introduced to the two-region, id i' finite-medium model to improve power distribution correla-This L tions resulted in increases in calculated values of keff. 7 1: is consistent with comparisons betwe'en transport and diffusion li theory results(3) which indicate that transport theory gives Q higher values of k,gg. That is, when one represents the core-M reflector boundary with a better model (be it transport theory 1 or a modification to diffusion theory) this results in higher values of k The calculated values of k are listed in p ] eff. eff gf j Table 2.2. 81 ] For the UO 1 adings, the k calculated using Model 1 2 eff d[i were consistently low, with discrepancies ranging from 0.24 1' v 9 to 1.7%. Best agreement between measured and calculated keff L y ] values was obtained using Model 2, with discrepancies ranging j fron +0.34% to -0.17%. Model 3 gave consistently high values fk .j egg (by 1.0% to 1.7%). 4 i: 1631 241 2 2.5 h A

4 h oNWL-1381-2 TABLE 2.1. Standard Deviation (%) in Power Distributions I a ,... a UO Pu0 -UO k 2 2 2 ] f Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 .1 I {o { Regular 2.09 1.18 1.05 3.37 1.86 2.17 g M H 0-hole 1,48 0.98 1.14 2.48 1.78 2 j H 0 Slab 1.95 1.48 1.56 1.60 1.38 1.13 } 2 H 0 Cross 1.57 1.37 1.21 2.13 1.40 h 2 I c-l 7x7 1.96 1.72 2.16 2.26 1.69 1.78 a 9x9 2.91 2.67 3.12 2.29 1.90 [i il l !? 1 b I N i 4 e O TABLE *2.2. Value3 of k eff h. UO Pu0 -UO 2 2 2 Model Model Model Model Model Model Exp. 1 2 3 Exp. 1 2 3 j; 6 Regular 1.0032 1.0008 1.0051 1.0164 1.0006 0.9960 1.0080 1.0009l H O Hole 1.0025 1.0000 1.0046 1.0161 1.0020 0.9973 1.0096 [] 2 i; H O Slab 1.0018 0.9957 1.0044 1.0162 1.0068 0.9982 1.0182 1.0063 - 2 L~ H O Cross 1.0010 0.9924 1.0039 1.0161 1.0054 0.9956 1.0231 i# 2 f -E 7x7 1.0010 0.9888 1.0044 1.0175 1.0038 0.9867 1.0220 1.0007 ' mj k I 9x9 1.0027 0.9858 1.0010 1.0133 1.0078 0.9928 1.0245 h I) I: 1,P c 4 T E r 1631 242 E I I 2.6 t L

i BNWL-1381-2 loadings, the k calculated using For the PuO -UO2 eff 2 Model 1 were consistently low, with the discrepancies ranging from 0.5 to 1.7%. The k calculated using Model 2 were con- {+{ ^ eff sistently high, with discrepancies ranging from 0.7 to 1.8%; p values. Model 3 gave the closest agreement with measured keff { Conclusions .r The simple modification incorporated in Model 2 of our analysis significantly improved power distribution correlations for the twelve configurations that were analy. zed. i This improvement, together with the simplicity of this method, makes this method attractive for calculating power dis-tributions in H O cores. The simplicity of the model comes 2 about because cross sections for the modifie'd water regions 1 (water gaps and the. reflector adjacent to the core) are j obtained directly from cell calculations for the core. No 3 additional calculations are necessary. The method will next be used to calculate power distribu-tions in more complex loadings which contain fuel rods of several enrichments. References 1. P. Loizzo, et al. 2:verimental and Calculated Results for UO and UO,-Puo, Fueled H O-Moderated Loadinas, g g To be published, Battelle-Norchuest. 2. V. O.

Uotinen, G.

L. Gelhaus, S. R. Duivedi. "A n aly tical Correlations of Measured Pouer Dis tributions, " Plutonium v ? ? Y]N Utilization Proaram Technical Activities Report, March, April, Mau 1969, B NWL-110 6, Battelle-Northuest. July 1969. l h {' 3. S. R. Duivedi. " Multiplication Dependence on Energy and i Angular Detail in Transport Theory Calculations, " Plutonium Utilization Proaram Technical Activities Quarterly Report, ,t June, July, August 1969, BNWL-1224, Battelle-Northuest \\(, ~ .k. October 1969. f 1631 243 I 2,7 -}}