ML20138L579
| ML20138L579 | |
| Person / Time | |
|---|---|
| Site: | University of Michigan |
| Issue date: | 06/30/1984 |
| From: | Kerr W MICHIGAN, UNIV. OF, ANN ARBOR, MI |
| To: | |
| Shared Package | |
| ML20138L505 | List:
|
| References | |
| FOIA-85-587 NUDOCS 8512190304 | |
| Download: ML20138L579 (160) | |
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a Low Enrichment Fuel Evaluation j- ,
and Analysis Program n -
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Summary Report for the Period O]
January,1983 - June,1984 5s D' ~
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-i WILLIAM KERR, Project Director
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.3 di 8512190304 851203 PDR FOIA AFTERGOB5-587 PDR /
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1, LOW ENRICHMENT f FUEL EVALUATION j~ .
AND
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- ANALYSIS PROGRAM a_
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.3 Sununary Report for the Period i] January, 1983 to June, 1984 j-1 .
_ William Kerr, Project Director f; Department of Nuclear Engineering and the
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Michigan-Memorial Phoenix Project l' The University of Michigan j,_ Ann Arbor, Michigan 9- :
-b j' July, 1984
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PROJECT PARTICIPANTS e
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. .4 William Kerr .
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-:b :i i John S. King
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John C. Lee' ?.
William R. Martin 4- i 4
Reed R. Burn
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i Felippe Beaklini 3 . .
g-Clifton Drumm 4.'- ,
f:,l Brent Houser 3 11 -^l
'!. .! Baard Johansen
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, Gerald Munyan l,1
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'. William Wan --,
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David Wehe
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'i-TABLE OF CONTENTS l
y]-. LIST OF FIGURES . .. . . ............. v fj -
o LIST Or TABLES . ... . . ............. vii
- a. . ,
.3 I. INTRODUCTION . .. . . .............
_ 1 s -
II. LEU DEMONSTRATION EXPERIMENTS AT THE FNR ... 5 ij A. SPND Sensitivity Measurements . . . . . . . 5 - '
y- B. SPND Flux Measurements .......... 6 7!,_ C. Temperature Coefficient of Reactivity . .. 9 b.i D. Power Defect of Reactivity ........ 11 d,.
- E. Void Coefficient of Reactivity ...... 12 j7 III. SIMULATION AND ANALYSIS OF THE. TEST DATA . .. 15 a A. Iron Wire Activation Analysis . . . . . .. 15 Q' B. Analysis of SPND Measurements . . ..... 19 -
.1 C. Simulation of Flux Maps . . . ....... 22 D. Non-Lattice Peaking Factor Calculation .. 26 j- E. FNR Fuel Burnup Calculations ....... 27 F. 2DB-UM Eigenvalue Calculations for FNR Core 29 il G. Control Rod Worth Calculations ...... 31 a
H. October 1983 Mixed Critical Loading . . . . 32
/- IV.
I GENERIC METHODS DEVELOPMENT AND VERIFICATION . 37 Y- A. IAEA Benchmark Calculation ........ 37 B. Ex-Core Cr'oss Section Generation with the a .
XSDRN Code . . . ............. 47
,, C. Three-Dimensional Capability for 2DB-UM . . 55 ;
f.,- V.
SUMMARY
AND RECOMMENDATIONS FOR FUTURE WORK .. 62 3,
- REFERENCES . . . . .. . .. ............ 64
". APPENDIX A. Subcadmium Flux Measurements in HEU and ,
LEU Cores Using Rhodium SPND and Wire Ac- '
d, -
tivations 1 APPENDIX B. Operating Experience, Measurements, and cj Analysis of the LEU Whole Core Demonstration i nl at the FNR t;
} -
APPENDIX C. Results of In-Core Spectral Measure- .
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,{ - LIST OF FIGURES
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6
_ and Mixed Cores . . . . . . . . . . . . . 10 a
d 2. SPND West-East Flux Profiles for HEU, LEU and j_ Mixed Cores . . . . . . . . . . . . . . . . 10 h 3. C re Configuration for Void Coefficient of a
Reactivity Experiment - February 1979 HEU
], Core . . . . . . . . . . . . . . . . . . . . 13 u "
- 4. Core Configuration for Void Coefficient of Reactivity Experiment - July 1983 LEU Core . 13 b} s-
- 5. Void Coefficient of Reactivity across an West-3 East Traverse of the FNR Core for LEU and j- HEU Fuels . . . ... . . . . . . . . . . . 14 -
I 6.A. SPND and 2DB-UM Absolute Subcadmium Fluzes - "
5/29/82 NEU Core . *
. . . . . . . . . . . . . 23 6.B. SPMD and 2DB-UM Absolute Subcadmium Fl'uzes 1 ~
Normalized to Iron Wire at L 5/29/82 HEU Core . . . . . . . . . . . . . . . . . . 23 7 7.A. SPND and 2DS-UM Absolute Subcadmium Fluxes -
9/16/83 LEU Cora . . . . . . . . . . . . . .
24
- _; , 7.B. SPND and 2DB-t'd Absolute Subcadmium Fluzes Normalized to Iron Wire at L 9/16/83 l{,_ LEU Core . . . . . . . . . . . . . . . . . . 24 8.A. SPND and 2DT-UM Absolute Subcadmium Fluxes -
- l 10/5/83 Mixed Core . . . . . . . . . . . . . 25 8.B. SPND and 2DB-UM Absolute Subcadmium Fluxes Normalized to Iron Wire at L 10/5/83 Mixed Core . . . . . . . . . . . . . . . . . 25
" 9. Relative Error in 2DB-UM Calculated Power
% Fractions for 2x2 Mesh versus 6x6 Mesh -
L)
December 1981 Critical LEU Core . . . . . . 28 5-- 10.
j_ 2DB-UM South-North Thermal Flux Distribution a
for the October 1983 Mixed Core . . . . . . 35 i
n
- 11. 2DB-UM East-West Thermal Flux Distribution 0- for the October 1983 Mixed Core . . . . . . 36 j 12. Core Cross Section for the IAEA Research ll~ Reactor Benchmark Problem g, . . . . . . . . . 39 l]
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[I ' 13. Fuel and Control Element Unit Cell Geometries
? Used for LEOPARD Calculations 40 Y, l.. . . . . . . . .
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- 15. Reflector Unit Cell Ceometry Used for LEOPARD ^
I)/. Calculations . . . . . . . . . . . . . . . . 44 1 16. D 20-Core Gecmatry Used for XSDRN Calculation 50 J -
,] 17. D2 0-Core Thermal Flux Distribution . . . . . 54 -
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- j 18. IAEA Benchmark Problem configuration . . . . 57
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- 19. "
l Assembly-Averaged Thermal Flux Distribution
{ - UMDIF versus 2DB-UM . . . . . . . . . . . 60
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! 20. UMDIF Calculated Thermal Fluxes . . . . . . . 61 -
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LIST OF TABLES 1~
it
- 2. Comparisons of SPND Sensitivity . . . . . . . 8 2 ~
- 3. Subcadmium Cross sections for Iron Wire . . . 17 d 4. Bare and Cadmium Covered Iron Wire Cross Sections . . .. . . . . . . . . . . . . . . 19 i !
- 5. Subcadmium Cross Sections for Rhodium Wire . 22 1 .
g' 6. Effect of NLPF on Core Eigenvalue . . . .. . 29
- 7. 2DB-UM FNR Eigenvalue Calculations . . . . . . 30 .
6 f,,, 8. Ratio of Full- to Half-Length Rod Worth . . . 32 l
.i 9. Control Rod Worths . . . . . . . . .. . . . . 33 10.
i Specifications for the IAEA Research Reactor 8
_ Benchmark Problem . . . . . .. ... . .. . 38 i 11. Infinite Multiplication Factor for HEU Fuel
, versus U-235 Burnup . . . . .. . . . . . . . 41
- 12. Atom Densities in the Fuel Meat versus U-235
', Burnup [
... . .. . .. . .. . .. . ... 43- i
[ 13. 2- and 3-Group Ex-Core Cross Section y
Comparison . . . . . . . . . . . . . . . . . 45
]~ 14. 2DB-UM Eigenvalue Calculation for IAEA '
Benchmark Core . . . . . . . . . . . . . . . 47
- 15. Summary of Effective Multiplication Factors . 48 q' 16. Comparison of Effective Multiplication Factors 48 L,
- 17. 2-Group Ex-Core Cross Section Comparison . . . 53 k" 18. Comparison of Multiplication Factors - UMDIF Versus 3DB ,
14 . .. . . .. . . . . .. . .. . 56 ,
- 19. 3-D, 2-Group IAEA Benchmark Problem Results . 58
- 3. I C
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I. Introduction M The University of Michigan Department of Nuclear En-F '-
gineering and the Michigan-Memorial Phoenix Project have been engaged in a cooperative effort with Argonne National
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Laboratory to test and analyze low enrichment fuel in the A
Ford Nuclear Reactor (FNR). The effort was begun in 1979,
_ as part of the Reduced Enrichment Research and Test Reactor d (RERTR) Program, to demonstrate, on a whole-core basis, the (M feasibility of enrichment reduction from 934 to below 20% in 1
ma _
WTR-type fuel designs.
p H ,
~
The key technical basis cf the low enrichment uranium .
(LEU) fuel'is to reduce the urtnium enrichment while in- '
f "
creasing, at the same time, the uranium loading of each fuel element in order to compensate for the reactivity loss due to the larger 230 U content.
a The required uranium loading '
7 -
can be achieved by increasing the uranium density in the .
fuel meat and by increasing the fuel volume fraction. At the same time it.is necessary to insure that fuel elements operate within their thermal-hydraulic limits. -
5 _
The first phase in our investigation performed in i: ' ,
preparation for the LEU fuel testing in the FNR core in- '
p cluded (a) initiation of development of experimental and
.j_
5
, analytical techniques applicable for neutronic evaluation of
. <] .
the MTR-type fuel elements, (b) selection of a LEU design
[- for the FNR, (c) preparation of a preliminary FNR license ;
[jh-' amendment, and (d) a thermal-hydraulic testing program for <
the MTR-type fuel elements. The 1979 Summary Report in-h cludes a discussion of this initial phase of the FNR LEU b project. -
(
g subsequent effort during 1980 was devoted to improving pl{ and validating the experimental techniques and analytical methods to be used in characterizing the high enrichment S.--
s uranium (HEU) and LEU cores for the FNR. The experimental t
effort focused on the measurement of in-core and ex-core spatial flux distributions and the measurement of ex-core ,
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- 1 ; spectra. In the analytical area, work has continued to im-a,}. ,
g ~, prove and verify the computer codes and calculational models ~
i used to predict the neutronic behavior of the FNR. In addi- '
y]{ :
tion, a series of thermal / hydraulic tests were performed for the MTR-type fuel elements and an amendment to the FNR i;;. Safety Analysis Report was submitted as part of the required 7 T ! License Amendment to the NRC to permit the use of the LEU ui d- fuel in the FNR. (Approval was granted in February 1981.) _'
? The 1980 Summary Report presents the details of this phase
] a ._ i of the LEU project.
Q j[_ The continuation of the project into 1981 culminated s j with the loading of the LEU core into ,the FNR and the achievement of initial criticality'on December 8, 1981. The I critical loading followed one-for-one replacements of HEU ~
fuel elements with LEU fuel elements in the center and q' j - periphery of th'a FNR core. Following the critical loading, J!
j j approximately six weeks of low power testing of the LEU core -
was performed including measurement of control rod worths,
, full core fluz maps, and spectral measurements in-core and _{ '
g, ex-core. This was then followed by two months of high power p [
testing (2MW), during which sinflar measurements were taken. j
$] The experimental and analytical work performed during this ~
i
?} phase of the LEU demonstration testing has been summarized !
j: in the 1982* Summary Report . ~
4li - Testing of the LEU fuel at the FNR has continued during i
,i
., this reporting period. This included comparison of LEU core ~
yf configurations with mixed HEU-LEU configurations. Unfolding j, of the neutron flux spectra through multiple foil activation j' analysis har been a major undertaking during this phase of yj '
the project. Considerable effort has also been expended N during this period on comparison of subcadmium. flux measured
$ with rhodium self-powered neutron detectors (SPNDs) and with f'Ii wire activations. Simulation and analysis of these flux ~
data have been performed to explain the spatial-spectral de-
- pendence of the SPND sensitivity factor. Measurements and ""
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1 1 l} analysis of reactivity parameters for LEU' core configura-f,-
4 tions have also been undertaken.
i p'- Section II presents the der.onstration experiments and y testing portion of the current project, and discusses the measured differer.ces f.n various neutronic characteristics 1- between the HEU, LF", and mixed HEU-LEU cores. This in-N_ cludes ur. folding of neutron flux spectra through multiple foil activations as well,,as measurements of subcadmium flux
,~ distributions, control rod worths and reactivity coeff1-cients.Section II also presents a comparison of subcadmium i j i fluz measured by SPNDs and iron wire activations, which is
['- still a topic of current investigation, section II makes -
4 extensive reierences to two papers ,5 presentd at the 0
1 1_
International Symposium on the Use and Development of Low and Medium Flux Research Reactors held in Cambridge, MA and ,
S- at the International Conference on Reduced Enrichment for a ,
a Research and Test Reactors held in Tokyo, Japan in October, 4 1983. These two papers are included as Appendices A and B ,
~
i to this Summary Report. Results of the spectral unfolding measurements 6 are taken from D. Wehe's doctoral disserta- ..
g"i tion , and are presented as Appendix C.
,: Section III is devoted to the analysis of the FNR HEU j- and LEU core configurations and comparison with the measured
/ data. The comparisons between calculation and experiment W include subcadmium flux distributions, control rod worths, Y, and core criticality.
Similar to the discussion of the ex-perimental program in Section II,Section III makes exten-y
- r. sive references to Appendices A and B. '
l
] The FNR LEU project has also been involved to a sig- '
y nificant extent in the area of generic methods development 3 for MTR-type research and test reactors.Section IV sun-if marizes the work performed in this area, including analysis
(( of an IAEA research reactor benchmark problem and represen-7 tation of the spectral-spatial coupling for. generation of few-group cross sections for reflectors.
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f- Section V summarizes the current status of the overall
('j project, including a discussion of the tasks currently under '
,; investigation. The principal unresolved issues are iden-
)
tified and recommendations are made for future effort to -
,jl complete the current and planned tasks.
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5 j- II. LEU DEMONSTRATION EXPERIMENTS AT THE FNR 1
j During this 1983-1984 reporting period, the major en-i- phasis in the LEU demonstration has involved performing:
3-<
- 1. Additional subcadmium flux measurements using iron b wire activations and rhodium SPNDs. These measure-
]~
j ments were particularly helpful in improving our understanditg of the SPND detector sensitivity. The et
'1
_ theoretical developments and experimental results
.I were presented at the MIT International Symposium on the Use of Low and Medium Flux Research Reactors in f, October, 1983, and are discussed in Appendix A.
- l. 2. Measurements of the temperature coefficient of reac-11 tivity, power defect and void coefficient of reac-
- tivity, and control rod worth. The results of the ,
11 latter two measurements and comparisons with preliminary calculations of control rod worths were .
L presented at the annual RERTR meeting held in Japan i
l last year. A revised copy of that paper included as Appendix 5 contains minor corrections to Figure 1
- and Table 5. FNR operating experiences with the LEU fuel are also discussed in Appendiz 3.
I4
- 3. The spectral unfolding of the NEU and LEU incore ac-i
- i. tivation data. These measurements included separate 1- unfoldings for the thermal / epithermal spectra, and the fast spectra. These results have been published j- as part of a doctoral thesis, and are included as ,
j- Appendix C.
r
.'il ,
A. SPND Sensitivity Measur nts a.
j!, During this past 1983-1984 reporting period, effort has
- 1. been made to more accurately determine the sensitivity of our rhodium SPND. The SPND sensitivity measurements were (f' primarily performed at two locations, the core center (L-37) f* and the heavy water reflector (D20 tank), and for LEU cores y- and mixed HEU-LEU cores. Measurements in the light water .
[,L reflector (L-40) have also been performed.
a [i p '
To ensure accuracy, both the SPND measurements and the -
p foil activations are performed within a period of 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br />.
t!. The net current from the rhodium emitter wire is measured as '
the SPND, mounted to an Inconel paddle, is held in place by
- j a brace fitted to 'he t top of the fuel element. A complete !
3 Lt ~
SPND axial scan is usually performed. An absolute measure-1
(- 2..:."x.- z: w ..? ~ ;: .. <:1_ . - .u .
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.-. 6 -
3 ment of the subcadmium neutron flux is made by irradiating a 5
.} t bare foil anc* a cadmium covered foil. The bare and cadmium ~
~.; j foils are taped, side by side, to a thin aluminum paddle ~
j ; which is then inserted between the fuel plates of the fuel
't element. The ratio of S,PND net current, corrected for {
1, '.
i
!.i .
epicadmium current and paddle flux depression, to absolute -
l
,"3 subcadmium fluz yields the SPND sensitivity. The 1979 Sum- [
g- mary Report includes a complete description of the SPND and foil activation experimental procedures.
j:
3 l Table 1 presents the sensitivity measurements performed ,
i in this reporting period along with measurements made in r 1982 for a HEU core. Although this work is not completed it j is evident that the measured value of the SPND sensitivity in the heavy water reflector is significantly higher than in the core center fuel element. The large discrepancy between ~~
heavy water reflector measurements made. in the LEU core and -
6 - in the mixed HEU-LEU core is of concern. Further efforts -
underway should determine a more consistent SPND sensitivity L in the heavy water reflector. A complete description of
'
- SPND and foil activation flux measurements is contained in gj Appendices A and B. .
j, - Table 6 in Appendix C gives a comparison of subcadmium ,
~
3 fluxes measured by different reactions. As explained in Ap-i pendix C, there is an apparent inaccuracy in the ENDF-IV
- f. Fe-58 (n,7) cross section. For thermal energies the iron
~
capture cross section is underestimated by approximately ~'
j 12%. When this cross section is adjusted accordingly the '
' in-core SPND sensitivity increases, bringing our quoted -
value of the sensitivity into better agreement with values quoted by other authors. Table 2 of this section is an up-
.] dated table from Appendix A, showing our work along with the 4
?j
- work of other authors. .
B. SPND Flux Measurements a
Several SPND maps have been obtained during this j
reporting period.
The SPND subcadmium flux values for a 38-c f!
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.t - y ,m, , . . - , , _ s _ , . _ . _ _ . _ _ _ .__ __ .- , m
.u..- _. w L w u . 2.. .: . m e m s:. : v i . a _ .
. '. J.- . . :..; - - . ;2...' ail.sL .: % . . .:.J K w.w.... :.:~ **
.. c: -
I' - t I 3 C l1 M C. O l. i O ("'"""] Q ' f*T"1 M g i g i f--") p, C. j~
l 9
J a
Table 1 ~
y e
Measured SPND Sensitivities at 1/4-Core Height for HEU, LEU and Mixed Cores'*'
{
F
's,h Iron Wire Rh Wire SPND M ,
S **8 Location sc 1 '
d 80 Fuel Type a I" ;
(barns) (10'* n/cm*-s)
. f ac (10-** amps /(sc-I"I Y (10-' amps) '
4s 4
.s' Core Regular Element '
HEU'*8 .844 2.52 .81 47.78 1.64 5 LEU .844 1.99 .75 43.32 1.75 F.I Mixed .844 1.78 .75 41.60 1.87 '
d D 2 0 Reflector
.a y HEU'*8 .907 1.96 .90 52.67 2.60 ',' ;
LEU .907 2.44 .89 56.97 2.22 #j Mixed .907 1.90 .89 54.80 2.75 i 4
H 2 O Reflector $
-l
- q Mixed 8*8 .907 1.63 .93 36.90 2.25 i.
.i !.fi t Rhodium emitt.ers were 2.54.cm long and .0508 cm diameter. r) s-88' }
j Measured sensitivity increased by 7% to account for support paddle.
i
.rj i 888 Cross section calculated for LBU spectrum la used for HEU case ff- i p1 8
LEU fuel element at center-of-core lattice position, rG
, g
)
- n' k' ,
. n -
1 th.g -
i i y .
- i. LL7.. M M . ' J; .1 '. c 2 s ._ J .;U.: . ..; . L. 6 . ' L.,6_L wJ LAM.L.2E' J.JJ.5. u M62 .d.1, G.._ ai.u'; Of. L: _
..u.......-~.. -....s.- .. . . ~ . --t-~- - . .a -: . . ~ L G- s . -.-- . - ~ M - . - --~~=-~---;------
o ~ ~ - - - - - ' - - - - - - --
'i.
b b
U N M
h-j
?
L Table 2 N
4 :
h Comparisong Qf SPND Sensitivity I
..T S'
fi -
$ \
U S d-Emitter S 2200 3
Author Diameter (10-**ampa/f -cm) i (mils) (10-88 amps /p2200-C"I 'N, Core DO i
2 ,
Heasurements Warren .020 1.20 .89 i
Kroon .018 .95 b:
.91 - -
.020 .99 .76 .80 os
[:
.i Jebair 020 1.01 -
l Baldwin ,018 .96 -
+
.020 1.048
.77 .83 i This work (LEU) .020 1.04' .77* .97*
i j (D2 0) .020 1.23' -
Calculations
., [
j This Work (VIM-LEU) .020 .99 .73 .78 I (VIM-D2 0) -
.98 -
Warren .020
" fl 1.31 .97 1.04 '
Laaksonen .018 .758 - '
b 020 .888 .64 j Goldstein .020 .68 4 '
1.51 1.12 1.20 -
. ,o.
88' Extrapolated to 20 mils based on Kroon's experiment.
8** !~
1 8 Value interpolated Extrapolation basedoff on graph Laaksonen at %'s=e.030 eV.
stimate. i 8 'l sensitivity updated after correction to iron cap.ture cross section. ,
-Jj
't 1
g
4# ,
.1 L 7 .
.g.,,, ppmumy.g s ., g. q.7%,,.y , .; .~. ,g. , ,, -
O.2: 9 1 .
4-
,1 element HEU core, a 33-element LEU core, and a 34-element j
HEU/ LEU mixed core are shown for a north-south and east-west
- j . traverse in Figures 1 and 2, respectively. The complete
, SPND subcadmium flux maps are presented later in Section a
III.B together with calculated results.
a- <
The replacement of~the large equilibrium HEU core by 4_ the smaller and fresher LEU and mixed cores reduces *M w.*t
], flux and raises the flux in both the H O 2 and D2 O retiectors
] (see D2 0-X in Figure 1), as observed earlier . The in-i creases in reflector peaking are dominated,by the reduced (l? core dimension in the north-south direction associated with
. l ~s
- i the smaller LEU and mixed cores. The large peaks at L-57 in i- Figure 2 are due to the special element waterholes in the j2 HEU and LEU core. -
4 j- As reported in Appendix B of Ref. 3, the replacement of 1J a single fresh HEU element by a fresh LEU element at the jq _
center (L-37) of an equilibrium HEU core produces a local a flux depression.
The ratio of HEU to LEU local flux is
, ~1.19. As seen in Figure 1, compared with the HEU core the la 2
- presence of kn LEU element in the mixed core at L-37 lowers i the subcadmium flux by a factor of 2.15/1.81, or 1.19, as
[ G' expected.
C. Temnerature Coefficient of Reactivity 1 y The temperature coefficient of reactivity measurement is normally performed at the FNR in conjunction with the 1 1 N
calorimetric test. In the experiment reactor power is in-
- creased from low power to 1 MW and stabilized while the sec-ji'
.i.
ondary cooling system remains off. Four thermocouples H
measure bulk pool temperatures at 2' and 20' below the pool s
g, surface, and heat exchanger inlet and exit temperatures.
I',b Pool water temperatures and control rod heights are recorded
'.),, _
t when power first reaches 1 MW and, again, about one hour g later. The reactivity change is calculated from the change j,, in regulating rod position associated with the temperature increases registered at the thermocouples.
- , , . , - - - - , , - , . , - - - , , , . - - - -n--,-, - - . -,m , , , , - ~ ,_ . , , , ,.,-n.n-.
.~ ~ :=r2an mG.71D?:LultynmKr..- '. . -.?. . . ":.~:.=.. T..'.= ......._.,"...""..?a"MW'"* ~~:, .
, r
.i 2
, 10 -
,; -?. :::9 ,
- ^ ?.0 ,
, a. .
y'i g ' b '. '$ ) ." 9 o ; .
s -
t
[e f ~ ~ ::
\-
"i 9:
+
re
'.3 -
w i
\ t.
q.
W x 2.0 -
--.4 e
Element Type =
3
~~
f ,\
N
- Reg-Regular -
- 1. ' ; E - HEU
{ g i
I w \ y ,' L - LEU
~
q g 1,5 . . . . . _ . . . _
j _
a- e +
e m o
a a s^ s -
9 us ,g ' i i
,1 L
1 020-X L-35 L-36 L-37 L-38 L-39 L-4
- 4 HEU Core : - Reg Reg Reg Reg Reg Reg -
1 i
LEU Core : - Reg Reg Reg Reg Reg -
i
~
Mixed Core - L-R L-R L-R L-R H-R - -
i
~
l "
Figure I SPND North-South Flux Proftles '
-l for HEU, LEU and Mixed Cores i ,
r 4
.G e J -
m HEU Core 1- a 4 a =
,., e g
~
$ LEU Core 1.* % b l:
I m c3 -
L,
- e Mixed Core .
v
- + ti I
52 // m Element Type -
r g ,t N Reg-Regular Spec-Special ._
[ $ H - HEU d ._.
1 L - LEU L 4e "
N J
- . o n
a ..
id
- 0
.~
HEU Core : Reg Reg Spec Reg Reg Reg Reg Reg 7.; LEU Core Spec Reg Spec Reg Reg Reg Reg Reg
{,
Mixed Core:H-R H-R H-R L-R L-R L-R H-R H-R e Y.
. Figure 2 SPND West-East Flux Proftles W for HEU, LEU and Mixed Cores e, q
- j
' y .. .. -
s,p;g -%.g.g.n _ ,
..,p,y.y.y p, x ;. y ,,. g g. g ,g.,y. 3,
. pr-+ . -
' 1 j7- .
l a
1, 11 1 s
,j - '
In the temperatura coefficient measurement performed l
)7 for the July, 1983, LEU core [FNR Cycle 227A), the average
~
v
?
temperature rise obtained over a period of one hour and l l 7- three minutes from the four thermocouples was 9.8'F, yield-jL ing a temperature coefficient of reactivity of -7.9 x 10-3 j_ %Ak/k/'F. Earlier. measurements yielded a temperature coef-
) i ~
ficient of reactivity of -7.5 x 10-3 4Ak/k/'F for the March, l 1981, HEU core [FNR Cycle 196A], (-6.111.4) x 10 ~3 %Ak/k/*F l
[' for the April, 1983, mixed core [FNR Cycle 224A), and
(-7.32.9) x 10 -3 %Ak/k/*F for the February, 1984, mixed ,
} (mostly LEU) core [FNR Cycle 234C).
l
(~ D. Power Defect of Reactivity The power defect of reactivity represents the total of
[ 1-all reactivity effects induced by taking the reactor from a cold zero power condition to the normal operating condition.
Two different techniques were utilized to measure the power 4 --
defact. The first method involves measuring the reactivity inserted by the regulating rod as core power is quickly in-creased from 5 kW to 1 MW with the secondary cooling system n- off. Linearly extrapolating the reactivity change to 2 MW
] yields the power defect at full power. In the second method a ~
the secondary cooling system remains.on while power is brought from 50 kW to 2 MW. ,
y- The first method yielded a power defect measurement of
-0.21 %Ak/k for the September, 1979, HEU Core [FNR Cycle
(^ 177], -0.31 4Ak/k for the May, 1982, HEU core [FNR Cycle p 211B] and -0.25 4Ak/k for the .uly, 1983, LEU core [FNR j.
d L
Cycle 227C). Based on the second method the power defect for the August,1983, LEU core [FNR Cycle 227D] was measured
!}L.
w- as -0.23 %Ak/k. Both approaches yield similar results for g the LEU cores. The discrepancy in power defects measured 9
for the HEU cores is currently under investigation, Efforts s-
[ are also underway to simulate these measurements.
I.
1 5,..
e.-e
"~
. & i:u x.;;.::;m.3 = c.. m b:c 3;xy m m;m r .',f.;(.r ~ +.'- + -'"~ ,;~
- . , 12.
- ) . -
'.j k E. Void Coefficient of Reactivity
.n f , In the void coefficient of reactivity experiment the j- void is simulated by inserting an aluminum blade measuring
.040" x 2.25" x 24.0* into the central water channel of the fuel elements. Once the blade is inserted and reactor power ~
-" ;i stabilized at 2 MW the core reactivity change is calculated -
from the change in regulating rod position. ~-
1
[.; The core configurations and control rod positions for ~
.i ' experiments performed on the February, 1979, HEU' core (FNR -
c Cycle 169B} and the July, 1983, LEU core [FNR Cycle 227A] e
- 3 are shown in Figures 3 and 4, respectively. The measured i
?
~d void. coefficients of reactivity for the HEU and the LEU core _
presented in Figure.5 are'similar to one another when uncer-tainties in measurements are considered. The uncertainties r-in the measured void coefficients of reactivity in Figure 5 ei c1 represent the variation in the measurements taken by three j
students during the February,1979, experiment. Figure 5 7' also includes corrections of minor typographical errors -
-. present in Figure 1 of Appendir B. -;
(
- li -
~q .
r' l
-:b :
=
,e C
i4 i 4 '
d L4 e4 .R
'l 3l f ,
I I d -- l 1 ,
f '
1s .? >
/4 - ,
s** '
5 t
=
(
- r . _ . y m _. ._ _
a 1.a .4 s ,.:... u.- ,. n .(. v. n,c ,
, . ,.g. i.,g. 2 a :.;.. h u - .. . _ J_ u ca:" - '. !. ; i - - . - -
' *
- 4 L -
L i 3 s. e i ,- C I. , ! L 4 i.6J L. - . 5 <* D. D** ,
.. T f~
. i' i.
t FtR CYCLE 1698 Ffe CYC1.E 227B Fatsuery 19,1979 .My 22,1985 .
SEAW WATER TMM MAW WATER TMM J. -
d ILS 1ES El 1A L1 19 7.43 425 428 2A2 334 5.80 A C A C '
213 11 743 L25 12.4 tu E2 25 L4 14.2 7.90 SAF 435 2J5 189 2.
u IL4 12 219 11 23 El 12.3 IFA 123 111 L76 195 2A3 356 3.43
( L-77 ) ( L-67 ) ( L-57 ) ( L-47 ) A ( L-27 ) (_ L-17_) ( L-7 ) ( L-77 ) ( L-47 ) ( L-57 ) ( L-47 ) ( L-37 ) ( L-27_) (_1-171 i a e >
11.2 11 LSD L46 4 175 114 53 3.4 12.9 17.1 L96 192 2A2 181 ,"
h
- t, 15.7 4 1ES 9.2 12.4 147 7.84 198 175 142 3.90 19e ;a p-r-9 13 to.1 11.s 14- '
(/,
Alky [me er*n n Ragder Special Esrpty Repder Reqpder Speclet Erryty '
nenunt nemt Laceum . annunt n onent osmers Lac =uan :
e p.m runs ww comencient Fuse wks enervicient - -
state a aumont Huemmenant n Dement Measuremura .d>
M Ebenent Ikara, N b Laceuans WM U Locouans ,)
- A O
Figure 3 Core Configuration for Void Coefft- Figure 4 Core Configuration for Vold Coefft-cient of Reactivity Experiment -
p cient of Reactivity Experiment - ;
February 1979 IIEU Core July 1983 LEU Core i
- I.' .A p I
. tl
.. -- - r._r6tr.c . c2. x;... .. c ,z ;. _ . n _ _mn.g;,gg;r.;.,;;g;;,7,n.p;,hp, f y % gj)
~ 14 -
0.4 Q HEU Core R
- 4. LEU Core ~
4
.0 1
., 1 -
n.i .
.a bl -
F1 -0.t I'.I '. M Y -, ,
i
{ ~
j, 4
-0.8
- r. . ; ,
~
E
.. n t
-1.2 r
m _
1 t -
-1.fr n
.e .
g L-77 L-67 L-57 L-47 L-37 L-27 L-17 L-7 -
}]
j HEU Core: Reg Reg Spec Reg Disp Reg Reg Reg a
'e 4 ,
sa Hn LEU Core: Spec Reg Spec Reg Reg Reg Reg Reg r' Measured S
Uncertaintyst.07 .13 .23 .32 .02 .01 .04 .01 c
- r p Figure 5 Void Coefficient of Reacet' icy Across a West-East l.
. Traverse of the FNR Core for LEU and HEU Fuels ~-
=
t -
i o'[i .
T1 i
e j
Vi
(
- _ ;;L '.< h M YJ.n m .7 % n :
- ri=~- - -- ' - ~ ' ~ - - ' ~ ' - '~' ~ ~~~ ~ ' ~~
, 7 ; z. .. j - - -;a p
~
_ .. ;Q '..;~.~5.7 .v:&tsrn.vy@k'?6'zW:'S%%Y 'N -
Y?
' i N '
.r- *
,h 15
-d m
?
t.
-!w g III. SIMULATION AND ANALYSIS OF THE TEST DATA
/ f A. Iron Wire Activation Analysis t.
Much of the experimental work performed during the LEU
, project involved the determination of subcadmium flux dis-
- j~ tributions by means of iron wire activations and rhodium
.' ) SPND measurements. The determination of the subcadmium flux 9' from the SPND and iron wire measurements is the subject of
- -3 this section of the. report.
- l 4 This section will begin by presenting the methods for
} determining the subcadmium flux from iron wire me'asurements, M which involves the determination of effective subcadmium
-3 cross sections for Fe-58, in spectra corresponding to the
, .5 core center and ex-core regions. Then, the determination of I] ,,,
subcadmium flux distributions from rhodium SPND measurements
,j will be discussed. This includes effective subcadmium cross f.] sections for rhodium in spectra corresponding to the core -
[ and ex-core regions and the flux depression caused by the I(~ rhodium vire.
y The subcadmium flux can be determined from bare and
[ .?.
cadmium covered iron wires as follows: -j a
- i~ Ab~Acd
% dsc " Il}
. d 58
- .9 f; where Ab and A cd are the measured saturated activities per ij-Fe-58 nucleus for bare and cadmium covered iron wires,
!, respectively. Here, a 58 is the effective subcadmium cross i section for Fe-58 defined as follows:
' .'1 i y
4: E 7 j, fc 0
'58(E)d(E)dE i
i
- j o s8 = (2)
E
- 51
.,4 fc p(E)dE
, 0 1
[,,. '
1 l
...~
1 -
,L I '
lA :-i&&&r!Y
..&.. iL=.- 6-- " :T :. Q E T.& s T M i W 2 E El T '2 E
.g 1 ,
1.a 16 n
t)
J vhere a58(E) is the activation cross section for Fe-58, ((E)
] is an approximation to the flux spectrum, and E is the cad-c j mium cutoff energy. Since Fe-58 is a weak absorber, there l4 is no need to consider flux depression in the wire, so all ji that is needed is to determine the unperturbed flux spectrum c.]
r .}
- in the region where the measurement is made.
p The subcadmium cross section for Fe-58 has been deter-4 -
h] mined by utilizing several codes in the SCALE package7 . The ;
M, CSAS code is used to set up the input for the NITAWL and 8
$ XSDRN codes. The iron wire is modelled in cylindrical ld geometry with a surrounding environment to simulate inser-f tion into an LEU core, an HEU core, and penetration X of the t.; heavy water tank. To simulate the core environments, fuel, 4 -
l 1 moderator, clad, and. non-lattice regions are volume averaged and homogenized, with number densities corresponding to the '
q .
values given in Table C-2. of Ref. 2. A .05 cm diameter iron -
wire is surrounded by a light water region of .2 cm outside l
r e
diameter followed by a core region of 16 cm outside <
.i , diameter.
The NITAWI. code is run to perform resonance calcula-byl1 tions for the uranium isotopes with the Nordheim Integral, -
3 Treatment. NITAWI. also sets up a cross section library in a format accessible by the XSDRN code. The XSDRN code is then
]' run in a 123 group, cylindrical geometry calculation, with 4 .
Fi ,
u meshes in the iron wire and 20 meshes in the surrounding
- . region, for a total of 24 meshes. The quadrature order is .
d.
3
~ s-5 and the order of scattering is P-3, with a white outer
- i
.4 boundary condition. The XSDRN code is used to generate a
- f;-
30-group library from the 123 group SCALE library. The 30-d group library generated by the XSDRN code contains one set .-
d of microscopic cross sections for each isotope in each zone
[3 of the problem.
W ~
IU The ICE code 7 is then used to generate a macroscopic m cross section library for use in. the ANISN code. Most of _
j the analysis for both the iron wire activations and for the t;i ;
y I}s -
~
li.
-M d
_ 46A - '-'"* '-
w .. x;
'~~6,NeTF,.7, N _"[-* m .? y y ~- .] 7"]'gy g, vj;;,
a
=j= -, . t
- gg--j - +q- h -gr., '* **
3 17 - -
e s 7$ e r)
-- 17 1 .
l_
SPND measurements are performed with the ANISN code'I utiliz-j] ~
ing the 30-group library generated by the XSDRN and ICE 4- , codes.
i d' In order to determine the subcadmium cross section for 1- Fe-58..in the core region, a .05 cm diameter iron wire.is 1
W surrounded by a .2 cm diameter region of light water and a h .
40 cm diameter region of a homogenized mixture of fuel, j-. clad, moderator, and non-lattice regions. An'S-8, P-1 cal-
?
.3 culation is then performed in 30 groups with the ANISN code g '
to determine the flux weighted, subcadmium cross section for iron. These values are given in Table 3. Since iron is a 1/v absorber in the thermal range, the cross section for Fe-58 can be determined by multiplying the total iron ac- '
1
.k- tivation cross section by the ratio of the Fe-58 2200 m/s cross section to the total iron 2200 m/s cross section, and L
.,- this is also given in Table 3. In this analysis, the iron. 5 E, number density is taken to be .08491/b-cm, and the cadmium
- cutoff energy is .625 ev, with the values for .625 eV ob-tained by interpolating the values at .5488 eV with those at
] .6552 eV available with the 30-group library. '
A y i Table 3 '
s J Subcadmium Cross Sections for Iron Wire (barns) 1 -
j Region a
,l' Fe '58 7'- 2200 m/s 2.58 1.18 3
'- LEU Lattice 1.86 .850 HEU Lattice 1.87 .854 D 2 0-X 2.00 .913 Similar calculations were performed for an iron wire
( inserted into position X in the heavy water tank. A .05 cm
[- diameter iron wire is surrounded by a 2.54 cm diameter
~ region of light water followed by a 12.54 cm region of heavy I
\
. .; . g.. .
- f. .,s.r,;- ; w , ,, n .g -- g . g ,2 , ,
,~ g g .. .. g 1 . .
i -
a 18 s.
)9 1
water. A shell source is input on the boundary of the heavy
?! water region to simulate the incoming current of neutrons n
from the core. The spectrum for the shell source was ob- ~
q tained from a one-dimensional, global core, slab geometry ~
gj. calculation. The spectrum at the core-heavy water tank '
Q interface was used as a shell source input for the iron wire -
j activation calculation. The subcadmium cross section for an 'l 7,
m iron wire inserted into heavy water tank penetration X is _
j also given in Table 3. The a 58 values of Table 3 represent j a slight improvement over the corresponding values given in
!. Table I of Appendix A. -
o] d 3 s-
.i1 Alternatively, the iron wire activations can be L-; analyzed by calculating the activation of bare an~d cadmium j U covered irons wires directly. If the aubcadmium flux is
.i defined as the difference between the total fluz.within a
't [
bare iron wire and. the total flux within a cadmium covered '
iron wire, the subcadmium fluz can be determined as follows.
The subcadmium fluz can be approximated as: 7 L
J M ~
e ~
sc * [#
0 (Z}dE ~ [#cd(E)dE b (3) 0 --
(j #
j i which can be rewritten as:
h' -
A A c
b cd v.y +, c - -
(o -
].
u, 58,b #
58,cd Iqg
..a Here the bare and cadmium covered Fe-58 cross sections are
]5 defined as foilows:
0 3.1 *
.h [dEagg(E)$y(E)
- 0 j "58,b = (5)
IdE*b(E) 3; kk n,
. O
- {
,j. .
1J '
I
!5 f-
, l- *
.c. _w. ~., .. . . a = ~~-.:-. - - - - --- - =- ~ -
- - &qh m surgermrm m%%Bb W C6, EWE 2 "3hTM3YF~h '$ * ?;'
- f. .
3-9 .
- 5. -
19 ii T1 a s 3=
3 j~ dea 58(E)ded(E) 3= , l a-d #
58,cd * .
(0)
?
-g fdEdcd( ,,
y-1 2q where (3(E) and (cd(E) are the spectra seen by a bare and a a cadmium covered iron wire, respectively.
2
- j 3 This method unfortunately requires knowledge of the
$ Fe-58 cross section, which is presently unavai.lable in tiii -
4 --
SCALE package of codes, and since the iron cross sec' t ion is Ul not 1/v in the epithermal region, the Fe-58 cross section y,
1 l cannot be determined from the total iron cross section. The ;
j] bare and cadmium covered iron wires have been modelled by 7
ANISN calculations, however, and the results are given in >
Table 4. The ANISN calculation assumed a .05 cm diameter of iron wire surrounded by a .1 cm diameter region of light l j] water, surrounded by a .2.cm diameter region of cadmium, and l 1.;
o surrounded finally by a region of either core material or
. ',/.
heavy water. .
j
". Table 4 s
Bare and Cadmium Covered Iron Wire Cross Sections (barns)
Li ,
,j,.
y Region a Fe,b # Fe,ed 1 LEU Lattice .533 .0453
.; ; HEU Lattice i
.559 - '
q D2 0-X 1.24 .0837 .
- n 12 e
4
- 3. Analysis of SPND Measurements q-1
><_- The SPND measurements have been analyzed in a similar i
7 manner as the iron wire activations. Analysis of the i,
l*
k l?
t t- . _ _. ,- -_ . _ - - - . - - . - - - - - - - - -
?~ 23" T " ^ : ,
w.a= w:.=u.u=.a.wt.w:. m m . Ca.um = " ~' ,A J* .
'i 20 ,
- s t '
3
} rhodium SPND measurements is complicated by two factors.
-l,] First, since rhodium has a large absorption cross section, '
] 5 the flux is significantly perturbed by the insertion of the SPND into the core. The flux depression caused by the in-r a
0] ;
' sertion of the rhodium SPND must be determined in order to i-
$i .' relate SPND current measurements to subcadmium flux. j 9 i Another complicating factor in the analysis of the SPND ['
~ measurements is that the detector is mounted on an Inconel _
Q' paddle, which also causes a significant perturbation in the
$ flux when the detector is inserted. '
d y .
Several attempts were made to model the Inconel paddle h with the one-dimensional transport thsory codes, ANISN and
?
XSDRN, by cylindricizing the paddle and preserving the [
A{ volume of Inconel. It was decided that it was infeasible to "
j adequately model the complicated geometry of the Inconel ~
paddle in this manner since the flux depression caused by -
the paddle depended sensitively upon. the thickness of water -
between the SPND and the Inconal, and also upon the thick- .b
$ ness of the Inconel paddle. It. was decided to model the
- q. -
g SPND itself, which can be modeled reasonably well in one-y 4 dimensional cylindrical geometry, and to rely upon measure-
/
+ ments to estinate the flux depression caused by th'e Inconel _
3 , paddle. '
d y: '
Given a Det SPND current, Inet, the subcadmium flux can y be determined as follows: -
.} r netf'se o i q #sc " '
a III j'i I sc n -;
l '
f; where the subcadmium current fraction f se defined in Appen-q
(-{ dix A is approximated by the subcadmium activation fraction li
.cSt
.i ==
1
- j .
m j .
~
h:
lf'&
I. P
.j i
i i . . .
. mjo g&sarM-~ ~n wn - -m .. - -e "- * *"h=
" e mM ~" r ' W ' '^ ~ ~ ' ' ' ' ' ' '
~~
yw
~
e p.y , , ,
)
- wo -
Jea.~% s -6:(y, y .. z _. . ) ,g, Q . g ,. y y .
- yg. m ;, 3 +.g p_- n .p f .--..; ,-w -~- +--
J7 - -
1 . . .
l 05- .
l
)L 21 ;
i l 1 _
E d C 4 fdr J dea (E)$p(I,E) -
e V 0 3- f sc
=
(2) 1 '
j'
_ vfdr f 0dea (E)$p(I,E) 6~
j_ and S,e is the detector sensitivity. The detector sen-j _
sitivity depends on the beta escape probability if,c, flux q~
perturbation factor f p and the effective subcadmium cross I
section i for Rh-103 as defined in Appendix A.
The factors i, f,e and i p have been calculated by j i utilizing the codes in the SCALE package. The CSAS code is F
used to set up the input files for the NITAWL and XSDRN codes. The SPND is modeled in cylindrical geometry with the 1
a .05 cm diameter rhodium emitter wire surrounded by the aluminum oxide insulator of .1 cm outer diameter and the In-conel collector of .16 cm outer diameter. The SPND has been modeled in surrounding environments simulating HEU fuel, LEU
. fuel, and heavy water tank penetration X.
} The XSDRN code is used to collapse the 123-group SCALE package library to 30 groups, with the group structure in -
- the collapsed library set up to preserve most of the detail in the vicinity of the rhodium resonance around 1.3 ev. The XSDRN code produces a set of microscopic cross sections for 3- each isotope in each region. The ICE code is then used to j- perform the cross section mixing and to generate a macro-scopic cross section library for use in the ANISN code.
e Most of the transport theory analysis of the SPND detector g; was performed with the ANISN code in 30 group, P-1, S-8 cal-2 culations.
J
} Li' The core and heavy water tank surrounding environ:nents
- j. have been simulated in exactly the same manner as in the j previous section for the analysis of the iron wire activa-tions. The subcadmium cross sections i for Rh-103 calcu-4, -
1ated by the ANISN code are given in Table 5. The cadmium a
j..
l.
- - - - - - - . - - - - - - - - - - - - - ~ ~ ~ ~ ~ ~ ~ ~
. c:w =c*:1T.u:4. 2=.2 " " * ~ ' ' ~ " "2T"L*E Z 7 5 V ^
22 '
t:
]f u;)I
/ .
l cutoff energy is taken to be .625 eV, with values at .625 eV determined by interpolating between the values at .5488 eV and at .6552 eV. The subcadmium fractions f sc for the SPND, lf, !
.,a calculated with the ANISN code, are compared with the ex- *
- M l perimental values also in Table 5. :
w: ,
F.}
- _I ib' Table 5 L d
.ijj Subcadmium Cross Sections for Rhodium Wire (barns)
- : .,.,: 3 .
i! ' f f "A . Region se o -
?] [ ANISN ANISN Measured ANISN ;
q; ; '
. 2200 m/s 150 - - -
- i1 LEU r.attice 114 .80 .75 .75
,x' ~
HEU Lattice 114 .82 .79 .73 ,.
?.i ,
D 2 0-X 120 .90 .90 .72 .
L. .
7 The-fluz. perturbation factors f p for the insertion of
}
1* the SPND have been determined by comparing the fluz in the
~
rhodiunr enritter wire with the flur in the same volume with
^
5 4
the detector removed. The flux spectra have been normalized -
- to be the same far away from the location of the detector <
l ,' j insertion The fluz. perturbation factors are also given in _
q Table 5. The parameters ir, fse, f and S 3,
N p sc calculated with [
the ANISN code compare favorably with those obtained with b! the VIM Monte Carlo code 10 as presented in Table II of Ap-
.. )
[c pendix A.
!3, C. Simulation of Fluz Mana
,3
[g; Figures 6.A, 7.A and 8.A compare the absolute subcad- _,
3' mium fluxes determined from SPND measurements with those determined from 2DB-UM11 calculations for an equilibrium HEU y core, a nearly fresh LEU core, and a mixed HEU-LEU core. -
l
.t SPND current measurements have been converted to subcadmium
,j. fluxes by the methods described in Section III.B of this 7 y; j A1, n .
ii. r
- i
- W
- ! fa b wl . = . = - - - - _ - ._ - - = - -
.. w :
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9.. .
[. ,
4 i Figure 6.A SPND and 2DB-UH Absolute Subcad- Figure 6.B SPND and 2DB-UM Absolute Subcad- f.
mium Fluxes - 5/29/82 ilEU Cor.e alum Fluxes Normalized to Iron ,',
., Wire at L 5/29/82 ilEU Core - i 4
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- i'
> 4 , ,
C y.
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l . . . .
3 . -
vi j .
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~
1; - ? .
k report. The SPND measurements have been made at a quarter
~
(,i s cora height.
[N Absolute subcadmium fluxes for comparison have been
~
N. ., ; .
determined from 2DB-UM calculations as follows. The 2DB-UM Oii code computes absolute subcadmium fluxes corresponding to an ~
S
'i 1 input linear power generation rate. The total power of the "
a i j j FNR. is 2 MW and the core height is 23.5 inches, which cor- -
j responds to an average linear power generation rate of .0335 '
jl NW/cm. In order to convert the average flux to quarter. core
%? height flux, the ratio of the quarter core height flux to _.
N [ the average axial flux has been determined from iron wire j i activation measurements as reported in Ref. 2. This was J, nearly a 54 correction. The 2DB-UM calculations assumed a d _ cadmium cutoff energy of .625 eV and a fission energy of 195 ^
MeV/ fission.
e
~
p .Two additional correction factors were included to com-pare the measured and calculated fluxes. The flux depres-
., .sion due to the Inconel paddle surrounding the SPND was ex -
~
f I .' -
perimentally determined to be 74. The subcadmium flux peak- -
), '
ing; in. the light water tube penetration into the heavy water u
$a ps tank was calculated by means of the ANISN code to be 104. ,.
<i
- q. With these corrections, the measured. and calculated fluxes j-
[ are compared in Figures 6.A through 8.A. In order to better
] compare the results, the SPND and 2DB-UM absolute subcadmium
[, i fluzes have been normalized to the iron wire measurements at H
the core center (L-37). These results are presented in l-Figures 6.R through 8.B. Compared with the SPND measure- j-J. tI t
f' ments it is evident that the 2DB-UM calculated fluz is -
] tilted awar from the vicinity of the D 0 tank 2 and west side j of the core. ,
[ '] D. Non-Lattice Peakina Factor Calculation
(.
l Lk.
L, Earlier calculationa have been made for the non- -
Hi lattice peaking factor (NLPF) to be used as input for the h! LEOPARD code l . A fine-mesh (63x38) two-dimensional 2DB-UM -
i.} i calculation for a 1/4-assembly HECT special element yielded a A c
f i, ;t e j a l ~
l
- _. _ _ . --
,. 1
( ' es%y:: mr5 iy.myx-:mm*p.wwn:M.gw;.tMrM.?M ? % ?,*n ciEM W '7*X'
- D'? 2 'T' W W ' W V U Q}]* *
- h l, 3 27 {
C .
~
d NLPF of 1.16. This value was subsequently used for LEOPARD b~ analysis of LEU special elements.
Three new fuel geometries have been examined with 2DB- 1 UM. They include: (1) the initial, clean LEU critical core of December, 1981, (2) a single LEU special element sur-r rounded by 1/2-LEU regular elements on the sides and 1/4-LEU Ma
}- regular elements'on the corners, and (3) a single LEU spe-cial element. Based on'these calculations, a NLPF=1.35 was ,
y_ obtained for generation of new LEOPARD cross sections for y _ LEU special elements. Repeating these calculations for 5 ; geometries (2) and (3) with LEU elements replaced by HEU fp elements yields a NLPF=1.29 for HEU special elements. With '
2 the new library, the LEU criti'al c configuration of December, y 1981, was reexamined using both a 2x2 and 6x6 mesh struc-t ture. As seen in Figure 9, the new LEOPARD cross sections q:
vith NLPF=1.35 reduce the RMS difference in power fraction .
2 s
r.
between the 2x2 and 6x6 mesh 2DB-UM calculations from 5.88%
- to 3.84%. The relative diff erence for shim rod C is reduced from 11.7% to 5.0%. Table 6 shows the effect of the cross .
$ ~
section set on the calculated core eigenvalue. Using the new LEOPARD library yields a core eigenvalue of 1.0068 for .
the 2x2 mesh calculation, which agrees quite well with the
}T-" value of 1.0071 for the 6x6 mesh. It is also noticed that d- the NLPF negligibly affects the core eigenvalue calculated q- with the 6x6 mesh geometry. '
h'
.y E. FNR Fuel Burnue Calculations
- f 7
s Four years of FNR cycles (141 cycles: September, 1979, py through September, 1983) have been simulated with the 2DB-UM
,.p code with a 2x2 coarse-mesh description. This fuel burnup '
h updating covers both HEU and LEU core configurations. Revi-
{k q sions to the FNR burnup data processing codes (SORT /UPSORT) g permit correct burnup computations for any combination of in-core or ex-core residence times for any type of fuel ele-
?.1 ment.
The 2DB-UM calculation utilizes the latest ENDF/B-IV l library (including the new fission product correlation and n-b.
a
+- '
,; --~,.n
- .snu.n .we.uw.a.aw=ns un.. co= s1 -...: ; . ::.:. . 2 .LX GJ.12: =. : ;.* ~ *~'?.i.V ' 7~I?;i 1 l
l4 j .
1 !
28 -
W 1 i
'S i '
. :n 1 V 4
! 1 4
+
1 I
PEC'A. ELEMENT CROSS SECTICNS AMS DEMATICN XX LEOPMC @4.PF - L16) 5J84 8 xx tea,~o - - 1.= 3m e i FEAW WATER TMM b '$
. -2.89 L57 (L64 L75 -2A7 l -L88 2.77 164 2.95 -L46 t i
.i . A C
- j -3.12 12J6 (L47 1L67 -3.13
-2.cs u5 t39 a.m -2m -
-2.75
^
3.58 L35' 3.5E -3.a5 g .a -2.15 m 237 W -2.25 -
- d n
5 p .t -
-T.3T 9.59 -1198 9.53 -7.51 -
9 3
- -us zu a.as 2.az -643 e e du -
ll r
f9 l1j s
I.-l 1 1
'1.
.9 y -
?g + m WECIM. EP'9TY h'1 ji ~
3: 1 -
a:
.A I
- i _
3 l Figure 9 Relative Error in 2DB-UM Calculated Power ls;
- 73. l Fractions for 2x2 Mesh versus 6x6 Mesh -
if t December 1981 Critical LEU Core -
a
?
1.w eum Y
21 9 -.
i n
9 .
.i .
. J'c we..r ww.na,m - av m.u- me .-u r . . , . - . . - mr, -- 1- - - - -
,%:.s+.~.,.m;w3m m uww wL*?tMTM=MfX%%" M TW M31ST5+..__..
t'"
G3 * *
~
M' -
29 xd..
~
Table 6 a -
4 Effect of NLPF on Core Eigenvalue 3-a 1
5 Core Eigenvalue - 12/81 LEU Critical
_ Cross Sections Used
)M 3,1 -
for Special Elements 2x2 Mesh 6x6 Mesh
'I -
LEOPARD (NLPF=1.16) 1.0117 4 1.0069 d'a_ LEOPARD (NLPF=1.35) 1.0068 1.0071 7
a- non-lattice peaking factors for special elements) and the f-- , XSDRN-calculated 2D O cross sections discussed in Section IV.B. The comparisons of 2DB-UM power distributions in Figure 9 with a 2x2 and 6x6 mesh structure for the initial,
], clean LEU core of December, 1981, illustrate the general '
$ adequacy of the coarse-mesh structure in predicting fuel 4 ,.
[u ._
burnup as compared with the 6x6 structure.
q F. 2DB-UM Eicenvalue Calculations for FNR Core Based on the fuel burnups calculated by 2DB-UM, several h* ~
FNR core configurations were examined using a 6x6 structure j 2DB-UM calculation. Table 7 gives the comparison between j~
the measured core eigenvalue and the calculated core eigen-p}
.a value using both 2DB-UM predicted masses and the masses j- predicted by the FNR burnup code, which uses an empirical 3j.
expression for the FNR flux distribution. Table 7 updates l_ the earlier 2DB-UM FNR eigenvalue calculations presented in
- 1. Appendix B performed with FNR calculated fuel burnups and
( the ENDF/B-IV library with old NLPFs.
M Before determining the absolute bias between the calcu-
[t]l_ lated and measured eigenvalues, two corrections must be made
@[ , to some of the calculations. First, 2DB-UM performs the calculation assuming the core is at full-power. In the case of a critical loading, the eigenvalue is measured at zero-
.q power. Therefore, a power defect correction of -0.23 uk/k k*
k
. . _ _ . - e rarc h d w.c..i l k s s1.u n .:. w '.;a X '- e r
,% ' r ': - -':'- _ - : bud-*^"adairfG k GiX 3'IW"F2Q
. . . .. . ... - - . . . . . . a.- - . . ~ . -. . --
iLt l'
['. s I (v l
j -
g t;.
b li.
n;.
Table 7 (( '
e
?DB-UH FNR 51genvalue Calculations [fi
.A.
Average Burnpp (%) 2pB-UH Eigenvalue Absolute Blas (%Ak/k) fj Core Measured FHR888 2pB838 p,, (%Ak/k) FHR 2DB FHR 2DB i;fl b
te pec 198s.
(
CrkticalI.EU 0.00 0,00 0.45 1.0040 1.0040 .28888 ,288** i:
l . s i
Hay, 1982 '
j's:
Full Power HEU 13,76 14,36 '
1.0499 . 1.0464 1.33888
.j.29 1,018'8 w O f de March, 1983 U Critleal Hixed 12,13 }3,14 Q.10 1.0140 1.0101 1.05888 67888 !;I i
?
June, 1983 II
, Critical LEU 3.03 2.96 0.00 1,0046 1.0048 .1088,'8 ,1288,*8 ij
.. a June, 1983 Ful1 Power LEU 3,48 3.42 .'$ . 2 9 1.0365 1.0366 .118* ,ei ,118* , *8
![
l Oct, 1983 -
Full Power Mixed 12,65 13,31 3.02 1.'0388 1.0364 .598'8 .368*8 i
8 FHR calculated fuel burnup -
888 2DB calculated fuel burnup 8** Corrected for power defect, p =
.23 (%Ak/k)
[k.3::
FD (({i 8'8 Corrected for samarium reactlyity, p g,s = ,13 (%A'g/k) -
1 x
- 9 l
rv 1 'I i ? ' i ' '
.y; ~ ~; . m : w ro n;6: m ck kr.wr w enuw nu MiWl TEM M F W S B 8Q*.26fM5E a,. .
s-
% 31 o; :
y
~
fj (as measured for the August, 1983, LEU core) has been ap-
- plied to these cases. Second, post-shutdown samarium build-
}- up is not handled in 2DB-UM calculations. The effect of 4 -
this limitation on the calculated core eigenvalue was ex-h- amined by simulating the actual history of LEU fuel elements !
with the LEOPARD ccde. For the June, 1983, LEU configura-
]_ tion of the FNR core, it is estimated that the samarium
- f n, reactivity at the beginning of the cycle is 0.13 4Ak/k.
H This correction factor has also been applied to the calcu-J-
i r ..,
lated eigenvalues for the May, 1982, HEU core and the Oc-j tober, 1983, Mixed core. ,
aj ,
Q n- Regardless of the fuel burnup model used, these 2DB-UM l
calculations indicate a substantially higher eigenvalue bias ,
for the configurations containing highly depleted HEU fuel I elements than for LEU configurations with fresh or slightly
- - depleted fuel elements. However, using 2DB burnups reduces
!i -
the absolute bias by about 0.31 %Ak/k for the HEU and Mixed d_ cores as compared,with those based on FNR burnups. The
, variation in fuel burnups calculated by 2DB and by FNR has a i: minimal effect on the core eigenvalue calculated for the
]:- -
June, 1983, cores due to a relatively low burnup in the LEU. -
7,j E fuel. Overall, the core eigenvalues calculated using 2DB k-11 burnups indicate a bias in the range -0.3 to +1.0 4Ak/k.
G. Control Rod Worth Calculations
- 5.
j As reported in Ref. 3, the control rod worth calcula-A[L' tions, especially for rod B, were found to be sensitive to'
] the cross sections used for the heavy water tank. This sec-tion of the report gives the results of control rod worth ,' '
Q}'- calculations with the improved heavy water cross sections ;
Sir q - given in'Section~IV.B of this report. The rod worth cal- f, p culations are compared with measurements for an HEU core, an d
LEU core, and a mixed HEU-LEU core. !
?- The rod worths are calculated by' computing the reac-j tivity difference between a rod-in case and a rod-out case.
The calculations are done with the 2DB-UM code with 6x6 l ~,
- l. _ , _ ._. _.__ - - _ - - - - - -- - - - -- - - ~ ~ ' ~~
- ".^ a' d&.=tK Mb@25
- 1..-.... ' '.L. e .. '.
1 w. +: $ . .
.-'m--
~
" w e ' v "C E.;. S : 3.' & 1.:." . . . -..
e 3}
- r. .
d '
. 32
- 3'i '
p .
/ ,
meshes per assembly with the control rod cross sections ob-j tained with the.EPRI-HAMMER 13 and TWOTRAN 4 codes, as dis-
~
$- cussed in earlier reports.1,2 Gj;i b The rod worths are determined experimentally by measur-h]
~
gi ing the worth of one half of a rod, and multiplying the "
result by a factor of 2.
N-q ;l Several full-length rod worth measurements have been made with the ratio of the full-
{!
1 ,
length rod worth to the half-length rod worths given in p q' Table 8. Since full-length rod worth measurements involves ;
j considerable perturbation in the flux distribution due to h- 1 swapping of shim rods, measured full-length worths are not [
- , directly used in our simulation. The extrapolated full-n L}
w 1ength rod worth data are compared with 2DB-UM calculations ,[
~/ i c a1 for three cores in Table 9. The calculations made use of both the improved heavy water cross sections determined by 7 g j'. means of the XSDRN code as discussed.in Section IV.B and the jj special. element cross sections obtained from the LEOPARD -
q*
jj code using the updated non-lattice peaking factors. The , ,.
- ' . ,l agreement between the measured and calculated rod worths is
_~ _
., l v -- -
much better than that reported'previously in Appendiz 3.
, -j k, -
- Table 8 o, Ratio of Full- to Half-Length Rod Worth _
jj. Core Rod Ratio J
- t. 7 1 ~
1.
,.4 t.4 11 8/18/82 HEIT C 1.88 3
9' 6/21/83 LEU A 1.89 b-l B -
1.90 N 1 C 1.99 m.; -
1:
!,1 d<
J.; -
il ; H. October 1983 Mixed Critical Loadina
[d I ~
[.] i In preparation for the october 3, 1983, loading of a _
f,( mixed HEU-LEU core, fuel loading calculations and rod worth ~
h,1 8,
?. .
[]
!:ho
4 P 1
~.j 3.,. g ;q.g.y y.,m.g,y .3 j 3 :3.q,y m myq. ygyggygcqgg,Qqq g;.+,~ \
. \
l
'd * .
.i J
- j. '
33 l l
d j Table 9 I 0- -
Control Rod Worths 3-a O Measured Extrapolated 2DB-UM Relative
]- Core Rod Half-Rod Full-Rod Calculated Error (%)
!j -
'lJ 9/26/82 HEU A 1.25 2.50 2.41 -3.6
- B 1.06 2.12 2.04 -3.8
)-
j-C 1.18 2.36 2.16 -0.5 7/8/83 LEU A 1.42 2.84 2.72 -4.2 i ,_ B 1.16 2.32 2.26 -2.6
.] C .955 1.91 1.75 -8.4 1
,- 10/3/83 Mixed A 1.36 2.7'2 2.66 -2.2
.7 3 1.07 2.14 2.16 0.9 Ej i C 1.08 2.16 1.97 -8.8
.g IJ calculations.were performed with the 2DB-UM code (utilizing
'F FNR burnups, the LEOPARD library with old NLPFs for the spe-
[Ij7 cial elements and LEOPARD ex-core cross sections) to predict
, a full-power core configuration which would satisfy required shutdown margins. The biases in the core eigenvalue and rod q .,
worths obtained with the 2DB-UM code were estimated by com- paring measured excess reactivity and rod worths for the
]
y April 12, 1983, mixed core with 2DB-UM calculations. Based on a bias f actor of 0.86 %Ak/k in core eigenvalue, a 35-j element core was expected to yield a 2.78 4Ak/k excess reac- [
/. -o tivity. In reality, a 34-element core consisting of 23 HEU regular, seven LEU regular', and four LEU special elements g -
was loaded giving an excess reactivity of 3.02 4Ak/k.
}j Repeating the 2DB-UM calculations for the actual core con-4 ., figuration using 2DB burnups and the new LEOPARD library P., ,
gives an excess reactivity of 3.38 %Ak/k. c.~ y. 4 Several 2DB-UM calculations were performed to inves-1( tigate the offect on the global flux distribution of replac-e ing HEU special elements with LEU special elements at the Y
- g. '.
control rod locations. Figures 10 and 11 compare the t .
- c. y. e . ., , * '
. - 2 w -. . :--+...n 1.v . .,.. + 4 L.. 3~.w
. .... ~ .: ---a. v ~ :+ . c:....?
,z a m =, :;-
+
.: . . .. v . .. . . . . . . '. n. .:
;9 e . .
y . . r r,
/ 34 9
u Pj respective south-north and east-west flux distributions g- through lattice position L-37 at the core center with HEU , t;I n and LEU special elements at the control rod locations. The
;i calculations indicate that a HEU special/ LEU special ex- i change has a minimal affect on the flux distribution in the Core. **
f 4 . 4 - y, . 2-1 I1 h J
- 6
)
a. BE 7
? -
e ~ h .. - r l
,L +--
A
'l I
M o .3 , S:;
.}
w 4
'i .
.1
?! ..
9
- 7 JJ -
r ts p"3 . - a "
.5 Q-:
.. _ ..,,M 'J 1 2. . .~ . J. c . . , , . . :. a ;.t . ._ ., ac ;.a:. . .r. . . L_e. sa . . _ _ . ._.. . .. z . 2 . ; u _ ; R 4 ._ 2 . L l .
! I ~ .~i C~.1 t 3,. , . ,, j 'C
* ' L s . 3 L. B. ..,.. g ,,.pj f--) G [--' 7, 3 , g ; p*
- b . ,
.' rim L :,
9 Te l 10/83 35-ELEMENT sou%teofmf TWomt Fust amp Leo - L.35 . h . [j o LEU Special Elemente {j i ' E I h I . E I A HEU Special Elseents l E I ri l > ' 18 1
'q '
rt l l M i I E I ] I e i ,, I H,0 D,0 l l % jI8 I E I u $ g i j' a i vi
- = i $
g g .. El I
.f m 1
I e}
,C .
g g I I W l 'I W l i.P.
.'y, I '
e i u.
; I e W l 19 i W I V
$ I 18 i r?
I id i n "9 i. q . I E
+ i ?:
e i i W l a I W I 'e ,T-2- i g HEU LEU LEU LEU LEU e g i g
* 'l 3 H0 y Reg Reg Reg, Reg Reg g g g
om
- : :s em so.co som som so.co
. : ! - = : . :' :
J anos g g so.co som moo uom com wom som - J rp
. n.
Figure 10 N.- n 2DB-UM South-North Flux Distribution for the October 1983 Mixed Core A h, - 3
. L.?
. . L C".YZ-
.. M. .'k12. . 5.i W W .:a.Q5:TTTG.E.~.,\ 2 G a'.2,Line,.
. i? - Ch"In '!!k.2.3XJ;t:%3.L'NJ.53.dh% '~ .-LW . it1.; z-Ja
..___.. . . . - . , . . , . . . . . . . . . .. : . . ..m._. ....:.,.._____.,, i
- f. . ..
, b. '. 7, h
li . .. E q b f Q 4 6.. .
.1 l t;'
g 10/83 35-ELEMENT i[;-. ~ EAST-MST Mitp4. FLUK MAP 'gDl ? L77 - L7 'j ' l g
?
I I g 0 1.EU Special Elosenta g' l [f l l l A HEU Spec %el Elemente 1 4 3 1 k g i I i l 8 g ,! J :! e , . t I l - E He l 8 He ' nr , l w ce a
.e ?
I i -- I i a , IJ..- - - ; 0 t g [ , I i-N 3 !
, l N
.s g t4-
.i i
9 I a
- [I,,
I : !. F I l 5( 0 8 HEU HEU. LEU l.EU l.EU HEU HEUl *
*HEU Re t Reg. Reg Ibg Reg Reg Regi
- g
!g Res! I . I. .
8 i !y ano immo foco in.oo 4em som egoo g g som som inoo no.co m op p oo m oo {: i :r . y
~
Figure 11 2DB-UH East-West Flux DLatribution for the October 1983 Htxed Core 'I q
* 'i
*I Q ,, d f 'l l *M ~l 4D i ~l f I O Q l
i f' t ') G M Q s L _ ') l T *l '[
-+.-_ ,-
,__ g p g 3 . f .y s.zy g g.y y y , g ;cf; m .,f;= -
1- ; 2T- - f2
- 37 c ;
~
l3 - IV. GENERIC METHODS DEVELOPMENT AND VERIFICATION
< .7 A. IAEA Benchmark Calculation !;j This section discusses the results of using the Univer- ;j sity of Michigan (UM) reactor analysis code package to a$ '
analyze the IAEA research reactor benchmark problem 15 This benchmark problem was developed at the Consultants Meeting
~
j) on " Preparation of a Programme on Ressarch Reactor Core Con- _ versions to Use LEU instead of HEU", IAEA, June 19-22, 1979 ii-a in Vienna, Austria. Its detailed specifications are given q, in Table 10 and in Figure 12. Briefly, it corresponds to a . 3f 10 MWth, 6XS element core at several uniform depletion j
- stages. The reactor core is reflected by graphite on two opposite sides and surrounded by light water. Standard MTR elements with 23 fuel plates are utilized, with uranium en-1 richments of '934, 45% and 204, corresponding to a U-235 con- .
y-tent of 280, 320, and 190 grams per element, respectively. *
.j
~
This benchmark problem has already been calculated by seven 1-international research centers and their results are sum-marized in Ref. 15. Although we have obtained results only , da u for the HEU case, the analysis model and procedure remain 1_ the same for the MEU and LEU cases. ' E. 1_. 1. Fuel and Control Element Cross Section Calculations I {i Macroscopic cross sections were generated as a function of burnup (in percentage loss of the number of U-235 atoms)
- p. by the LEOPARD code with the ENDF/B-IV library. The unit g cell geometries for LEOPARD are based on the specifications g given in Table 10. Figure 13 illustrates the unit cell 2
geometries for both the fuel element and the control ele- [,[
+
ments. The extra regions (or "non-lattice" regions) in Figure 13 for both the fuel element and the control element q- include the aluminum in the fuel plates beyond the width of y the fuel meat, the water beyond the width of the fuel meat, M the aluminum support plates, and the water surrounding the . .) }. fuel element. Moreover, the non-lattice region for the con-j_ trol element includes the central water channel for the con- .i i
-w-
-- -- y w- ,,9 w pi-v-y-- .- -- - _ , - * - - - - - , - g
- e. ,
, . . e. . v.y 4 -
- u. -~
x..:- w.aw .. m :v=wnNmswaciG2m. -%a x.a.:% 2T?.n. ;'..- u.. . _
- ]
y . . 3 . d - t q:: Table 10 . l Specifications for the IAEA t
;) Research Reactor Benchmark Problem m
p
.i l3 .ggs Camperisse et the dif teesse estaulastee enthode and crose-section dose *
(y, .se. emed to ati!wees lassemori.e.11 1ted e-unemess pub &ams.
=.1 e for r=1 a.m-h Spaniftemasase for theInschadies! ^ L 7,41e. '"
Di t ese and seemiftentismo 4areed Umses N]I '
,~.4 aattee case Reiche 488 em Rusrepeastaan Length SS as (la 80 se 41e8==== free the eere. the anstas-shaped f ans goes se sese)
>T e=8-Ma'== enar ,
5 synes as er1A pleen per feel elemmas 77 == s si m. _ A
.; pum1 e&ammme armes-eematen < 76 en a es.3 mm imm1metas support place /.p A 76 e m 08.8 ewitheme support place .
34 i fe' genes _
.. 63 am a 9.31 mm a 480 m
. - _ . _ .1. ,g . :., ,. .m-3 Q
'4 ; .
r s Theahamse of empport P&ase 4.TS ens og
- 2.[ 3
- em I
{ IImmher et fem 1 places por feel elammets 3 33 3dematana paaems, emmt 1.37 mm thtak , 1 p
,h Emmhur et haL passam per ammasel at-*
,J 12 s h a=2 p&am amah 1.27 mm em L s
TM88==ah at the remataase plane posit of the emmate1 e&ammmas
. 4 pime== ef pmme ah og = 1.F g
- em" . esmh 1.2T em thash .'
$ se ehr f==a**= ef the #1res, the thasd. the ammmey=first and the
-j ummmap=ehisd standmed passe panttisms esser amps haemons the tuo sees w
' se alemsame p&sema. .
N et the diffesent feele (561g=4 Fami) for W.15, *"
*~ Im ammessemedias to the prestaus entendee===a
- r, i ma Emmsmammes SS e/o (em1M I) >238 1i
"
- 23 3 >239 per feel alammes. shtat estrumpseds to 12.174 s >833 per emah feel place
- 31 ole of usamsamn to the salg-d li
- en&y 9=23S and PI38 la the fresh faml )
" i-, . ehm e/e in [.j
;;
- 3ae s > 35 per fe.1 elemana (23 p&asam)
* - 4e e/ se esensam le esse mang-u J + emir PDS and ht38 Se the fresh fes&
iM. ,j [ tar
- Bursahmmer N e/o >33S 300 g PDS per san & elammma (23 p&ases)
I'f
- 72 e/o et asunsen te the eu,*1
] ;. t emar e- 3s aus > 3s la the seash feet (Q them& pomerr W Isth (psmme= kn11dugo W= 3.1 s 1938 fiastem/Jamle) , h.; thammmL hydmum&as emene ,Q _ 38*C
- - umser . ~
ha& ; M*C
- f. ) 7 _er essew 1.F hug f.4 !
l3 Esmus eteens sammemammes samme emmenes servespondtag to _ __. Rity !. ? 'u s k [ .3 1.ed#1 ths== flamme ors =ps and andforflum h=etsretta alame of ers&a (seuthe andtem andev===sry-e==s of crete (sou. of the nee
- ]..
'"** g with o av < s, c o.6 s av e _
(. eu,1them a with e.u3 av < se < s.331 her - T ,. e use s. > s.s31 h.e l.;j f == } . 1 [~ . s.
- -_.,. 2.,
- .7 '_ , ,. ,. . ;. g .-. w _ ,, . g . w .p _ m g,.:.,:,~ g.,g.g .g.pm. _y; ; ..z_ 7. .
. . . . z . #
, -. j 7- -
. i .4 .
- -. 39 a"
i
- outside boundary condition W = 0 :
,~ d6 f I
, Y 3 fuel element width of water reflector
; 2, 231mm ;
.; y - _ gophitegraphite water BOL-Core a; *
;a I
it.~ i outside rn== 25 % 5% woler boundory
} ~3 fuel element width- condilion of water reflector
$mo
'q , 45% 25 % 5% a 243 mm - i Control l Elened - 1
,? =ades 45% 25 % X ,
. a 1
. e-- :
e1 nun 1 1 Burnup step 5% - L 2 EOL-Core j' graphde gaphite water graphite block cross ; 30 % 10 % water section 77mm x Simm 3 }- . graphite density 1.7ger6 30% 50% Control 10 %
- ._ Element unmL 50s,,
\
50 % 30 % ( Bumup definition : (%) means the percentage of loss of the number of U 235-Atoms
. METHODICAL BENr mm
'{~ 10 MW CAsz J. conz caoss szerzow l2-4 - Figure 12 Core Cross Section for'the IAEA Research Reactor Benchmark Problem a "L M
. Ew
-e. w[ -mhamTiem IMea hfew',T h3% Jpg p .
7;8
.. % :'cr i m 3.C . a i "i - --%
e.qditi.Ed., CDPj,v M7 ' . ,.. -- M,, g . .- c$s 40 q?
!y+ -
trol rod as well as the aluminum side plates forming the j channel. _ l, -
- 1 5
$1 d
Extra Region '~' Fuel Al O 25.61 v/o 0 4: Meat Clad Mode ator 74.39 v/o A @d ..
.0255 .038 .1115 .0402 -
- d. E. -
i q Fuel Element (cm) ij q') Extra Region ' Fuel Al O 52.66 v/o H.30
'.] ,
Meat Clad Mode ator 47.34 v/o AI'
~
,j, < > < > < > < > *-
- r .0255 .038 .1115 .1162
- ) T. ~
{.]
- Control Element (cm) I
-?. ... c L Figure 13. Fuel and Control Element Unit Cell .T Geometries Used for LEOPARD Calculations ~ r lf: 2 j- Table 11. presents the infinite multiplication f actors .- ].' for the fuel element as a function of U-235 burnup. The L q table includes results obtained by LEOPARD and by Argonne _ O National Laboratory (ANL). The LEOPARD code uses the ENDF/ y 1-
- . B-IV library and includes a fission product correlation
, [
4 g based on the CINDER code 16 . _- hj The data in Table 11 are plotted in Figure 14. It is ' kg evident that the LEOPARD results agree very well with the E ANL predictions. This comparison seems reasonable because ]- CINDER was utilized by ANL for burnup. Therefore, LEOPARL -
~
? was used to generate the 2-group cross section libraries for ' both the fuel element and the control element. An earlier 7 g ENDF/B-IV version of LEOPARD with an old fission product .f 7
- 3 71 L [
, _ , _, , - - - - - - - - ~ * ~ ' - - ' " ' *
. .m 1 .< . ,
f M .J. .-
. . ., , ,y, ..... . , . .
7.
'i - .. -
3
]s' '.) ,
41 j Table 11 M ei Infinite Multiplication Factor for HEU j" Fuel versus U-235 Burnup 3
)
9 Infinite Multiplication Factor b U-235 j] Burnup (%) LEOPARD'*3 ANL L2 a M a- 0.0 1.7432 1.7370
/ e 5.0 1.6427 1.6370 10.0 1.6203 1.6165 1 1
15.0 1.5979 1.5953 j 7 20.0 1.5745 ij 1.5728 : 25.0 1.5494 1.5485 J.- 30.0 1.5225 1.5223 L.j
" 35.0 1.4932 1.4936 j
40.0 1.4608 1.4620 l 45.0 1.4247 1.4269
, 50.0 1.3842 1.3876 I ,
3,. 888 2 4 ^ ENDF/B-IV with fission product correlation based on ' CINDER. - t correlation tended to underestimate the infinite multiplica-
]
IJ tion factor compared with the ANL result, as seen in Figure .c ; 14. [ In addition to the comparison of k,, comparisons have
;- been made for the predicted atom densities in the fuel meat
?j {
of the fuel element for the LEOPARD calculation as a func-tion of U-235 burnup. The results are tabulated in Table y, 12, along with the results calculated by ANL. As can be
'j, seen, the LEOPARD results compare very well with the ANL j
results. \ j,.
?
- 2. Reflector Cross Section Calculations
"_ Separate LEOPARD calculations were performed to generate the macroscopic cross sections for the light water !
g reflector, the central flux trap and the graphite reflector.
' The problem configuration and the corresponding unit cell used in these LEOPARD calculations are shown in Figure 15.
k ! W .
..,.--.,---..,.---.-.w-
--e~' * - ' ~ = - ~ ' ' " ' " " ' " " " * ^ ' ' ~ " ~ ' ' ^ ' '
k;:-: '
~ i. ..
._. .a.u a.. . > ' ' r-
'"c.LlGLELu'x:CdN . .2.K A.ci d
3 -, 42 e A
- l \
.J ! Y
~
F 1
.I i 1.80 l g .-
n g 1 Q " - _. -i a - LEOPARD wito CINDER f[jt ;, 1.70 -
~
Fission Product -
~
L:i g Correlation '
>:a u a -
o g - ANL c -
- 'j o 1.60 -
.~ u
.I 0 -
a - C. " d u
- g. .
1 a t.sa - [ . LEOPARD with old " 4 3 w Fission Product e
. . - - ,c Correlation 1.40 -
. I
- 1 . >
1 ' 1.30- l 5 u. 0 10 20 30 40 50 I)
~
g U-235 Surnup (%) si Figure 14 Infinite Mticiplication Factor .~l for HEU Fuel versus U-235 Burnup 7I D a e r1 5 L' Wig:::- - ---- -r:- - n .1- m= ' r w"'w M* -
' ' ^ ^ " ~ ^ ^ ^ ~ " ~ ' ' ' ~ ~ ~ ' ' ' ~
1.- m n u m ;_. w. . m . , , .ww.w,..;;. x~ w :___.. .u. ;.u.um.u. . m.maanar.,=w.ua.q;a_: .. j
..;,1, 6 i a l _, ; i L i, i a rc7j g 3 ,3 m i,, , ,, g , ,3
, , ,,,,, ,, A g g - ,, g777) ,
\.
T. 3
'li 21 Table 12
- t)
A
- ' I. .
Atom Densities in the Fuel Heat versus U-235 Burnup i
- p U-235 it -
Burnup Atom Densities (b-cm)-' d Xe-135 (t) Sm-149 U-235 U-236 U-238 Pu-239 Pu-240 Pu-241 ,'1
. LEOPARD '
0.0 0.0 0.0 1.61798-3 0.0 1.2020E-4 0.0 0.0 0.0 5.0 1.7072E-88 1.41678-7 1.5370E-3 1.34855-5 1.19738-4 4.4223E-7 8.2701E-9 1.4831E-10 10.0 1.6472E-8 1.3831E-7 1.4560E-3 2.69115-5 1.1923E-4 i 8.53425-7 3.17175-8 2.1173E-9 25.0 1.4095E-8 1.1567E-7 1.2134E-3 6.6279E-5 1.1769E-4 j. 30.0 1.32795-8 1.0815E-7 1.8227E-6 1.6748E-7 3.6986E-8 'T 1.13248-3 7.9144E-5 1.1716E-4 2.06128-6 2.2867E-7 6.0327E-8 G 45.0 1.0760E-8 8.5706E-8 8.8971E-4 1.1677E-4 1.1549E-4 50.0 9.8972E-9 7.8257E-8 2.53738-6 4.31375-7 1.7023E-7 # M 8.08808-4 1.29008-4 1.1490E-4 2.6169E-6 5.01568-7 2.1671E-7 " j[ n
. ANL Y re 0.0 0.0 0.0 1.61798-3 0.0 1.2020E-4 0.0
;.) -
0.0 0.0 5.0 1.7094E-8 1.3393E-7 1.5370E-3 1.3468E-5'1.1973E-4 4.37695-7 8.5690E-9 3.7780E-10 to - 10.0 1.6416E-8 1.28248-7 l.jf 1.45615-7 2.6885E-5 1.1923E-4 8.4775E-7 3.3247E-8 2.9955E-9 r-25.0 1.4034E-8 1.0755E-7 1.2134E-3 6.62988-5 1.1768E-4 30.0 1.3219E-8 1.00698-7 1.8002E-6 1.7889E-7 3.9914E-8 Nb 1.1325E-3 7.91395-5 1.1715E-4 2.0304E-6 2.4357E'7 6.4686E-8 I5 45.0 1.07095-8 8.01318-8 8.8985E-4 1.1672E-4 1.1546E-4 50.0 9.8497E-9 7.3282E-8 2.4799E-6 4.5967E-7 1.7615E-7 :d 8.0895E-4 1.2890E-4 1.1486E-4 2.5535E-6 5.3381E-7 2.2312E-7 JA -
. ?. . '
I.
- Read as 1.7072 x 10-* *
,,7
,r 9
' , 1,
. . ... ... - 1
- - _+ d-r c r -W i a. ._ f., +--? x ;rx;; ,
. 3 , 3;;;t.;~ . g g ., g g. p -l y d
a , , j 44
.a - .i q
'O The macroscopic cross sections for these regions are taken a y from the non-lattice edits (corresponding to the extra ~ ]: region in Figure 15) of LEOPARD and are assumed to be in-
,;,} dependent of burnup. Both 3-group and 2-group cross sec- -
r M. tions are given in Table 13. ' e, A d F lM. . i_ _q. _ H2 O (or C) Region [i" Fuel Element q (Same Size as ~ 1 Fuel Element)
.i.- _
.A,.'
.3
. Problem Cross Section 5_
.I i e
~j Fuel AI i' Meat %O Moderator H,0 (or C) -
Clad Extra Region
.0255 .038 .1115 7
.2152 , ..
, T. ~ 3, kL ,S 2 Unit Cell (cm) _ ji Figure 15
' Reflector Unit Cell Geometry C
. - Used for LEOPARD Calculations
- d i
t .. H. We have also run the 1-D discrete ordinates codes ,
.1 . XSDRN-PM and ANISN for the global 1-D (i.e. Y-direction in ~~
i lj tt Figure 12) core calculations to generate another set of '.
- i M
'.i macroscopic cross sections for the reflectors. The results ,- l; from these calculations are also given in Table 13. For the h treatment of anisotropic scattering, a P-1 model was used in Ji these calculations, based on earlier calculations which in- _f dicated very little difference between the P-1 and P-3 cal-
;g
. culations. -
") The results calculated by ANL (f'or 3-group) and by u g Switzerland EIR (for,2-group) are also included in Table 13. _l '
.., h
,i m]l ',
i4 6 *
,i ll ., ' . .","O [ N ( '.esqn %W ,
---#^'*~%' '
.. '=l . xn d .u. L ., , i
-^
,a. ,- .; : :........w..
.;la. J _ _
C
*
- 4 L .. i L.m 6 ;. .a [--l j g ,. i i. , g ' .,.a.:
, , , .; m cg :.a
.a a g i x c.. a.aa.
g.,, mgn.c ...".: g g~' g:s .
. . :\ ,
?
. . ~ . N.
i g Table 13. 2- and 3-Group Ex-core Cross Section Comparison 4 a s. Light Water Reflector j Model Group 1 Group 2 Group l'*8 Group 2 r ., . Group 3 fl D E D E D E A<
- 1. a a a D E D E {
a a l $g XSDRN-PM 1.121 5.182E-48 0.153 1.8725-2 1.502 1.960E-4 0.561 1.019E-3 l ANISN'*8 0.824 5.183E-4 0.129 1.8725-2 0.153 1.872E-2 $ 1.186 1.9605-4 0.559 1.020E-3 0.129 1.8725-2 LEOPARD j' h 1.154 4.231E-4 0.168 1.800E-2
' 1.402 2.029E-4 0.597 0.9185-3 0.168 1.8005-2 ANL -
1.729 2.271E-4 0.569 1.0025-3 0.147 1.9015-2 i SWITZERLAND 1.152 4.876E-4 0.165 1.780E-2 - - - - - O, 3 Graphite Reflector q.
.if
- s. }r
! vi ?: XSDRN-PM'*' 1.435 3.5185-5 0.828 2.048E-4 1.646 4.757E-5 0.942 1.1065-5 ANISN'*' 1.193 3.5418-5 0.828 2.0495-4 0.828 2.048E-4 i l LEOPARD 1.382 4.791E-5 0.943 1.107E-5 0.828 2.0495-4 ! 1.327 2.962E-5 0.876 2.1345-4 1.546 3.832E-5 0.873 1.1565-5 0.876 2.1345-4 j!- i i ANL - 1.334 1.160E-5 0.876 1.2975-5 I SWITZERLAND 1.402 0.586E-5 0.886 1.962k-4 - - - - 0.842 2.5105-4 S N j '*8 q j Diffusion coefficient obtained by collapsing the transport cross section through leakage spectrum weighting. ?, 2 ' l '*' Diffusion coefficient based on flux-seighted transport cross section. 888 @ Diffusion coefficient collapsed through flux weighting. " I
- Energy Boundaries XSDRN-PN/ANISN . LEOPARD /ANL/ SWITZERLAND i Group 1: 3.0 5.53 kev < E
! Group 23 0.8 kev < eV <BE" << 20.0 3.0 kev MeV 0.625 ev < E" << 5.53 10.0 MeV kev t Group 3 0.01 meV < E" < 0.8 eV '3 l O eV < E" < 0.625 eV i LG
+ '.
] Read as 5.182 x 10-*. !
- d. -
a } y
- . DJ . , '
MO 1 u 0,
- k. .,
6 ., l . _ . . _ _ _ . _ _ . . ,. ....-...r.,. - .. .. ~ .. -. b
,4
.y--- ~ ~ ~ 2::gm&:s+n N.c , - m :az,,:. _-a . a4.
.....4
. u...
c3--.--Am.**--
. 2.-
2 -. . 5"'**r4 La-
*****'7
~
1 .. . g . a 46 1
- 1 q In general there is reasonable agreement between the ANISN i.} and XSDRN-PM results except for the diffusion coefficients ~
fpg (D), where the different weighting schemes have a large ef-fact on the resultant coefficients. Also, the agreement be-y tween LEOPARD and ANL is reasonable, except for I,,y for the " QN ., graphite. Since this cross section has very little effect - LM on the overall results, we have not examined this in more i l detail. Overall, the comparison seems reasonable.
- 3. Reactor Core Calculations I The quarter core (shown in Figure 12) calculations were ~
h performed with the 2DB-UM code. The fluxes were t Jrmalized
]
- i to a power of 2.5 MW for the quarter core, represented by 12 mesh intervals in the X-direction and 13 in the Y-direction.
- Table 14 presents the 2DB-UM calculated effective -
multiplication f actors for the core at three different burn- i_ N} ; up stages: the fresh core, beginning-of-life (BOL) core; and end-of-life (EOL) core (which are shown in Figure 12). . E since more than one set of cross sections are available for ref. lectors, there are'three cases examined in Table 14: the ., x LEOPARD results were used for both reflectors in case 1, the h XSDRN-PM results for both reflectors in case 2, and the ' " g LEOPARD results for light water reflector, while the XSDRN- 4 N PM results for graphite reflector in case 3. It has been m
- noted that the eigenvalue differences between case 2 md r
e j case 3 are larger than those between case 1 and case 3, in- _ j dicating that the light water reflector has more of an ef-j fact on the core calculations than the graphite reflector, R ' as expected. _ f., . j The effective multiplication factors calculated by the d seven international research centers are given in Table 15, h, in which the results for case 3 in Table 14 are included. [] Following the lead of Ref. 15 wherein the German results are ' L.j chosen as the reference. case, the comparison of the effec- ]1 tive multiplication factors is shown in Table 16. As can be - seen, the deviations- from each other are small, typically d j; 9 i ,
.i
~ ~ ... ,..
, ._..:.-pg-ggggmyggp.ggqw,g . 3 4:gl9l f-y.& .+m
+ ; r .- , :3 p.a >
3 .
~ '
1 -t . * "1,.d , 47 { .
~
Table 14 ~ I 2DB-UM Eigenvalue Calculation for IAEA Benchmark Core 2DB-UM Eigenvalue _ Burnup
, Stage Case 1 Case 2 Case 3 1- LEOPARD'*8 XSDRN-PM888 LEOPARD /XSDRN-PM888
{; :, j_~ Fresh 1.1877 1.1709 1.1842 i i BOL 1.0355 1.0204 1.0323 s EOL 1.0132 0.9985 1.0101
]$,
t*)
/- LEOPARD calculated2H O and graphite reflector cross q sections jI ._
'88 XSDRN-PM calculated2H O and graphite reflector cross sections.
3 t83 ,
'- LEOPARD calculated9 E 0 reflector cross sections.
XSDRN-PM calculated graphite reflector cross j, sections. I h i _' less than 14Ap. b 4. Conclusion }- d The results for the IAEA benchmark core using the UM code package agree very well with the results of the seven
$ _. international research centers.
3 j- B. Ex-Core Cross Section Generation with the XSDRN Code [' This section of the report describes the calculation of the ex-core cross sections used for the analysis of the FNR
;- HEU and LEU cores. Previous reports described the deter-4, mination of ex-core cross sections with the LEOPARD code.
It was found in subsequent calculations that the in-core and ex-core power distributions as well as the core eigenvalue . g. depend sensitively upon the values used for the heavy-water ej tank cross sections, so this work was begun to determine k more accurate ex-core cross sections by means of a one-J~ '4 li .
zu : c:<m e:- iH.tMisiaG YU.ta:.u s!.C.Suaa.'a.: . - : LT. .:.2:W;L 2..Lb : a. .a ; G.a:G%Ma . a
.. .s ,
.i E.$
t if
, i
.l1
- ]
p i3 ' n T4ble 15 ij Summary of Effective Multiplication Factors . 1 Eigenvalue Calculation Burpup /I Stage Germany USA Switzerland Austria France Argentina Japan 1: 2DB-UM (INTERATOM) (AHL) , (BIR) (OSCAE) (CEA) (CHEA) (JAERI) j
, 3 Fresh 1.1842 1.1888 1,1834 1.1939 1.1966 1.2020 1.2002 1,1810 l'
BOL 1.0323 1.0328 1.0233 1.0368 1,0320 1,0404 1.0377 1,0420
- v. <.
h BOL 1.0101 1.0101 1.0004 1.0138 1.0090 1.0170 1.0143 1.0220
- f ,
p r Tgble 16 0 Comparison of Effective Multiplication Factors hl ' Absolute Blas (top) Burnup Germany F! Stage (INTERATOM) USA Switzerland Austria France Argentina Japan 'l 2DB-UH (AHL) (EIR) (OSCAE) (CEA) (CHEA) (JAERI) I p
>' }i .
Fresh 1.1888 -0.39 -0.45 0.43 0,66 1.11 0.96 -0.66 , [. BOL 1.0328 -0.05 -0.92 0.39 -0,08 0.74 0.47 0.89 i ir EOL 1.0101 0.0 0.96 0.37 t t: J-0.11 0.68 0.42 1.18 . U?
's- .
o
. g
. ':'n
. ' ,] ,
-1 1 !
_; -J j uj '
~l O 'l $2.3 (' I i # I 'I ' I Y '
'I
. 2 m
. 2;g ? . % *. *qw &2 To} fGUs**MMM Y W - M*'?E' W @_ 'W # { ?_
a- - g-:. , . 49 1 , ha ,g , dimensional transport calculation with the XSDRN code. The structure of the heavy water tank is shown in j Figures B-1 through B-7 of Ref. 1. As can be seen from the j~ figure, the structure of the heavy water tank is complicated by numerous beam tube void cans and cylindrical penetrations
~
- f. filled with light water. The calculation of the core power j- distributions with the 2DB-UM code requires region-averaged, 2-group t:ross sections for each of the ex-core zones. -
The region-averaged cross sections have been determined
]; by means of several codes in the SCALE package. The CSAS d_
- o. code is used initially to set up the input for the remaining r _ codes in the package. The geometrical configuration of the 3
1
, problem is shown in Figure 16. In the core region, the core 3
~
is homogenized by volume averaging the number densities for a batch HEU and a batch LEU core from the data given in. Table C-2 of Ref. 2. The core and reflector regions are
~
then modelled in one-dimensional slab geometry, as is shown in Figure 16. A 30 cm region of light water simulates the moderator on the south side of the core. The core region consists of a homogenized mixture of LEU or HEU fuel, clad,
- and moderator, with a region thickness corresponding to the l1- ,'
thickness of a five tier core in the north-south direction. 1 The water gap between the core and the heavy water tank, and ll the aluminum wall of the heavy water tank are then f^ represented. The heavy water tank is approximately modelled j] by dividing it into three zones of equal volume, and volume
;; averaging the voids throughout the tank., The actual void p3 fractions for the three heavy water zones in the south-north
[.; direction are .126, .090 and .058, respectively. A three _ zone model of the heavy water tank was used to account more accurately for the spatial distribution of the voids, and to y account for the spatial dependence of the neutron spectrum, 'l ~ which was found to vary quite drastically with penetration
- 1
- J into the tank. The light water reflector on the north side (lr of the core is included as a 20 cm region of light water.
a'l-l4 if~ d_
-e
- eY e a ,, # gg , t *-
e - .
- ) .
n , - - 1 50 a i
;4 .j ;f The cylindrical light water penetrations into the heavy gj water tank are neglected in the generation of average cross J.'j j sections for the heavy water tank, but are included later in 3 the modelling of the SPND and wire activation measurements ~
1.4 ! described in Section II of this report. d1 m il i ~ M , .) = .d. M'O cent Hao m oso Tat H2e .il m-= a a 3,. m-= dj : : : : :: : : 1
- 2 2
3
- ; =
H1 A ans .a .a saa 2a2 2n2 2n. ! [1.I . 3hl E :l 1 1 Unit Cell (cm)
}j Figure 16. D20-Core Geometry Used for XSDRN Calculation 3
The NITAWL. code is used to perform the resonance cal- . culations for the uranium isotopes by means of the Nordheim l . Integral Treatment. The NITAWL code also processes the -
; .; master cross section libraries into a format accessible by -
,3 3- - the XSDRN code, a one-dimensional transport theory code. . y3 ~ The master library contains 123 energy groups, 93 fast )l, l: groups,and 30 thermal groups. g, The spectral calculations and the cross section weight- e
'i >
n ing are performed by the ISDRN code. The geometry for the
]
calculation is shown in Figure 16. A P-3, S-8 calculation N.9 is performed in 123 energy groups with a total of 35 spatial y s . meshes including 12 meshes in the core and 9 meshes in the -. l's
. heavy water tank. Transverse leakage is accounted for by a Oj , geometric buckling. XSDRN determines weighted cross sec- -
f) tions by spectra 11y and spatially weighting the microscopic jj ; cross sections over the calculated fine group flux distribu- - N 'i tion. XSDRN produces a set of coarse group, microscop'ic m g- cross sections for each isotope for each spatial zone of the _ L problem. The group structures are defined as, follows. i.1 For j i, 3 !l n, i .
. ~ . > , S&s ~-
.c;
+: . m p q.y:s q ;y,_,,t.3.r , g f m ;etV W M tta ? s y E W W 6 N 395 E E 1 C f? ? f ~
j ;. M. j;- 51 jj the 2-group cross section generation, group 1 extends from
' ^
14.918 MeV to .6552 ev, and group 2 extends from .6552 eV to j- .004742 eV. For the 4-group cross section generation, group ] 1 extends from 14.92 MeV to .8209 Mev, group 2 from 820.9 1_& kev to 5.531 kev, group 3 from 5.531 kev to .6552 eV, and A group 4 from .6552 eV to .004742 eV. j ., g- The XSDRN code produces fine-group transport cross sec-j tions by integrating the Py , component of the scattering S a- cross section over the current as follows: a Ij . I; = . . .
]-
F fdE ay (E*E ) J(E ) 0 (1)
"tr(E) = at( }- J(E)
} _
A zone-averaged leakage spectrum is defined as follows for 3,. the determination of the fine- and coarse-group transport cross sections: c. N'I _. fdr fdE'L(I,E) d 9 3- r L j,g = (2)
;j fdI 1_ :I $
1 g where g is the fine group index, j is the zone index and
$i~
ri L(I,E) is the leakage spectrum calculated by the code. Coarse-group transport cross sections are then determined
..l for each zone j by weighting the fine group transport cross
% sections over the leakage spectrum as follows: a_ .> ILag tr,g
- d. g
# (3} / tr,G "
.~; . IL jj g 9
=
.I I _ . - _ _ -. -. -- - - --- - - - - - - - - - - - - - - - - -
= :C
,=$r:a.- a :z.m 7ms2E.35EGdt.5Wm - MhMM2RKEGCILM.'.'.5G.C WS$--
. .g - -
M ,. . . ei - 52 JQ't 1 4 -
- id !
}l where G is the coarse group index and the sum is taken over .d1 ! all of the fine groups contained in the coarse group.
Y, j' Macroscopic reflector cross sections are then deter-6] ,1 mined for input to the 2Da-UM code by multiplying the micro-yl, scopic cross' sections bT the appropriate number densities . g for each zone. The 2-group cross sections for the ex-core ~
]'g regions computed with the XSDRN code are compared with those '
calculated with the LEOPARD code in Table 17. - C
^
, several differences can be noted in the cross section '
l) comparisons given in Table 17. The fast group absorption - 13 1 cross sections for aluminum, light water, and* heavy water Nl are significantly overpredicted by the old LEOPARD library. -
'? l The use of the ENDF/E-IV library with the LEOPARD code has I j improved the results for aluminum and light water, but e > LEOPARD is still inaccurate in computing heavy water cross -
di sections. The downscattering cross section for aluminum is .
,' significantly underpredicted in the LEOPARD calculations. ~
The most significant discrepancy occurs in the heavy water ~ i tanic cross sections. The fast group absorption cross sec , - 9; - tion. for heavy water is, overpredicted by an order of mag- -
!I nitude by the LEOPARD code. This is partly due to the in- -
clusion of voids in the ISDRN calculations, and partly due
*l!
to the spatial oepe.,dence of the spectral effects, which _. q .; cannot be adequately modelled with the LEOPARD code. The h downscattering cross section for heavy water was found to be y,j j strongly dependent on the flux spectrum, and much larger ' q when computed with the XSDRN code, as compared with the ~.*q LEOPARD calculations. 7 "q , 'l
,j . The' decrease in the fast absorption cross section of j'lj , heavy water and the increase in the downscattering cross ~~
f, section of heavy water led to a large change in the thermal 9:. . flux distribution in the heavy water tank, as can be seen in - [;l Figure 17. The thermal flux peak is significantly larger in
- f] the D20 tank when the XSDRN cross sections are used in the _
h 2Da-UM calculations. - (R M *
- l *:t
.i t
G
}
,m_.
.rkenni.p w .w. . a. ... . :. . . . . .. . . . . ~ _ . ~ ,__,w _ _ . . , . n.: . 2n.w . w n :ws = . ..:=..g -p.
g
. - i : 1. . I- - 4 & i e i .
C .i i , i... i. -i , i ., i . .i i . i r- g a. , ] .. lll ~j
, i
* * *. W} )%
9 l h
,i ..
[ Table 17 2-Group Ex-core Cross Section Comparison (cm-8) 3,
}.
3 :.
.A i
Group 1 Zone Code Group 2
}j E l.
HEU, LEO OLDLIB a 7.803E-48 .1138 tr s,q-140 a tr s.q-1+a bl Aluminum 0.0 9.556E-3 .09088 5.515E-5 LEO ENDF/B-IV 3.498E-4 .1085 0.0 9.586E-3 .08780 1.463E-4 ~. XSDRN 123 GP 3.933E-4 .1164 0.0 1.051E-2 .09367 2.296E-4 h, ' I HEU, LEO OLDLIB e. 8.691E-4 .2776 0.0 .01853 2.112 .05267 J Light Water LEO ENDF/B-IV 4.914E-4 .2932 0.0 .01830 2.073 .05314 y { XSDRM 123 GP 5.3725-4 .2726 0.0 .01845 2.867 .05963 r ) HEU, LEO OLDLIB .1803 Il S 4.6985-4 0.0 6.651E-5 .3075 5.465E-3 ? Heavy Water LEO ENDF/B-IV 3.312E-4 .1823 0.0 6.535E-5 .2957 5.473E-3 l XSDRN 0-10cm 5.7855-5 M
.2045 0.0 5.8175-5 .3373 6.7465-3 us %
XSDRN 10-20cm 4.084E-5 .2265 0.0 6.222E-5 .3528 1.113E-2 W Jj XSDRN 20-30cm 4'.286E-5 .2416 0.0 6.6685-5 .3682 1.568E-2 Pt .
, LEU, LEO OLDLIB 7.719E-4 .1141 0.0 1.041E-2 .09172 4.844E-5 4
.i Aluminum LEO ENDF/B-IV 3.5288-4 .3088 0.0 1.0518-2 .08872 1.317E-4 XSDRN 123 GP 3.847E-4 .1169 % i 0.0 1.043E-2 .09355 2.1698-4 i l LEU, LEO OLDLIB 7.4155-4 .2636 0.0 .01781 2.009 .04738 Light Water LEO ENDF/B-IV 4.3185-4 .2760 Q i i 0.0 .01781 1.992 .04731 a XSDRN 123 GP 5.320E-4 .2704 '0. 0 .01841 2.869 .05856
! LEU, LEO OLDLIB 4.7215-4 .1800 6.5135-5 r 0.0 .3058 5.391E-3 A i Heavy Water LEO ENDF/B-IV 3.335E-4 .1820 0.0 6.467E-5 .2947 5.388E-3 -
1 XSDRN 0-10cm 5.8145-5 5.7685-5 $.
' .2044 . 0.0 .3366 6.514E-3 9 XSDRM 10-20cm 4.080E-5 .2265 0.0 6.217E-5 .3517 1.103E-2 7
, XSDRN 20-30cm 4.275E-5 .2417 0.0 6.633E-5 .3672 1.565E-2 3 3 8 Read as 7.803 x 10-* LE k.
- 3 l ._._ _.. ._. .
s
...,g. ..,, . . . , _ - -
,,w..m...7.,.,,.. . ., . y
. s.aw.'a s 7..,.g ..,,,7,,.,7y, , , . .
. 3 . . .,*; L s s, . y, ,
;.g,, ..._ ; c,,,..,,.g__.,.,g.g-u --. _~m.: u a ,,,, u ., u ; w, , _ _,g,;g.g,g.g y . ._ 3 , 3 , ;,,.,. , yo _. ,
+
- e l4 . . .
iI * , *
*iW ' 54 f
(-.$
.dj d i d [ *
.h I
?, e J.: . . 8
,' .' t 3
~
% M
$ h 1 i ldI a g ,8 i e .
8 1 . OI f u^I 8 .- yv, s ! O uI ge. bc e 1 * - 3 u g. e-
@ 1.kl o 5., -
J J u y ,u O s j
- wH w C
, . pr}
n e4 e n g O
@l w w a
y "
. Ng g x '
s WJM ."I 4 4 f ' .I 3 s q , ___________________________ _______ g
- u w
- q. i 5
' W ~
- a. . .
s
$]
- Q
- .g a,
,5 n g -
V t , ,,,
] 9 Ca.
't ,
.2 4 a -
.n l}' e
[ I E5555 55555 555555555555555555555E3,
. I l.s
, . , . . _ d o 4 g U
?! h y ,g g ,
\ = m
.s l.s
- I O
S . ,1 f" c. g
',j j
- W -
'y e E @ I ". ) 't l
.w, k t :/
i.. . ; _ om 3
! ~.
- a0
, x a
~
. j. j
,g w j
< . i
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~
j ~ %' q g , S' z .d !
-i - i!
- 4. ll 3: g m;
N. ,b. M E E N N O , O N N N ^~' Er, mIJ 1sument ij 4! u [ 4 "l l:n , M- .2- l "d i 6 \ L3l l* . W l
., a
- t -
ltt. .
;x . . . . - , -
- f. Win %ce.w 3kge,mmuvmmeewwcw*erarmwar?g. TsvmWNN?#
$l\;$' . - h 55 t
~
C. Three-Dimensional CaDability for 2DB-UM l
~
Effort has been expended over the past two years to develop a three-dimensional version of the two-dimensional 1 diffusion theory code 2DB-UM. This ca'pability is needed to analyze control rod worths, axial depletion effects, and , flux distributions in the core and D20 tank. Because the h2 2DB-UM code has been a successful tool for 2-D global 4 diffusion-depletion calculations of the FNR it was decided " h_ to incorporate the three dimensional capability into 2DB-UM h rather than modifying an existing 3-D code (e.g., PDQ-717 , 10 , and 3DB f $ VENTURE I are operational on NTS) to include the f~7 various enhancements that have been made to 2DB-UM over the years, such as the macroscopic depletion scheme,
~
The approach is similar to the 3DB algorithm. Planes
-l -
~
have been added to account for the third dimension and
- another iteration over planes is included to converge the 3- '
M- D solution. The inner iterations still involve calculation for one plane, with the appropriate terms added to account 4,
'1 for the interaction with the neighboring planes. Extensive t changes were needed for the input routines to allow the specification of axial zones as well as changes to the out- '
nfh put routines to allow edits over the axial zones. The ] , modified code, named UMDIF, has been tested extensively, in- 'i cluding comparisons with the original version of 3DB, 9- benchmark calculations of an IAEA test problem, and com- } parisons with 2DB-UM for a mid-core FNR problem. These test
)
0 calculations are described in more detail below. : y 1. Comparisons with 3DB a Il- The 3DB code has been operational on MTS for several i f years and can be used for static 3-D analysis. The 3DB code J- package received from the Argonne Code Center included a Ij sample case for a simple 1/8-reactor consisting of a h homogeneous fast reactor core with a blanket. A two group description was used and three different meshes were calcu-lated - 2x2x2, 4x4x4, and 10x10x10. The resul'ts are tabu-p- . s I; *
, _ , _ _ _ _ _ _ _ _ . . . . _ _ _ _ _ . , _ _ , - _ _ , , _ . . . . _ _ _ _ ,._,,,___.,.--,__._..m__ _ _ _ -_._. ,____. _ . ,_ .,.
l%&h3 N _ - wc & .;;;ya a g r - ,7 ;.; r zc;'~:S;..-a;g;whQw: yY"*Q q 3 . d 56 ' sj '. - b H [ i
~ lated in Table 18, where it is evident that the' codes com-y :, pare very well. Although only multiplication factors are ~
x V! ccapared in Table 18, the point-wise fluxes also agree to Sl wichin 4 decimal points for all cases. -
; a, I
Table 18 . . . Comparison of Multiplication Factors '
; UNDIF Versus 3DB ,
4 i Mesh '" - g , UMDIF 3DB g ] 2x2x2 1.15890 1.15890 , I l 4x4x4 1.06187 1.06188 ( i ~ 10x10x10 1.02167 1.02172 1 - k F 9 ; j R ,
- 2. IAEA Test Problem i ,, The Argonne Benchmark Problem Book 0 contains benchmark ._l problems for many different neutronic configurations, in- _
, cluding a 3-D static diffusion theory problem. This problem 2 ~
is a severe test of a 3-D code, since it consists of a quarter core with several fully inserted control rods and
.j
{% ' one partially inserted control rod, reflected by water on ' ] all sides. Figure 18, taken from Ref. 20, depicts tF / con-ll i figuration. W 4 Table 19 summarizes the results for the benchmark - 1 problem. The UMDIF calculation predicts a multiplication .'I> f actor that agrees to within .01% of the reference VENTURE - i solution, which utilized a Richardson-extrapolation of several VENTURE runs, as summarized in Table 19. The UMDIF j; calculation employed a relatively erude mesh (17x17x29) and i the lack of edits for that particular run did not allow a g determination of a local quantity such as the peak-to-da v- . 2e g,, _ _ , __ , _ _ _ - - - - . , - - =----m-*e"*~ '
*'' -" "-- - ' " ' " " " ' ' " * ' ' ' ' ~ * ' " - - '~
...w.:,1K.Lis'2. C.$r L c..:4L . :s '-
I
- e s'.i J.2. - . a'.'
. aGL'- - -
- s' * ^ ' ' *-
'3dM.L4 Gk A = MMOM- W O,;,+*.*.5
- + i I..i k. , i i a t i I .) M [ ,a L .l l ,6 g 4 g i g i p g ,[* p i .;
.. l q.
1 .. , DDecHMAMIC SOUnCE SITUATI0tl : ** Identification 11
. y of peedsey losessed sed lessenildy nel ,
see ,, i 4 hs3 4 '{ . 4 t see ' ante submitted: June 1976-my: a. a. Lee (es) D. A. Me.1eley (Ontario Nydro) , [k \ g
\ \
h, i.
- 3. Richesleen (missi-Denmark) g gT D. R. Vo.idy (OnasL
- s%
g
. m. R. resner (zwu)~ . .p %
- v. Werner (cas-nun)teh) e, _.i N' \
\ .~
jj
. e ante Accepted: Jesse 1977 By: E.'L. Dodds Jr. (W. of* Tenn.)
- m. v. eresor,y (snL)
\ *
. \s
( fi [ .- % g
. N /- \ $
sescriptive
Title:
Shalti-dimensional (x-y-s) 1 AIR Model , ) i{ 2 h i3, 2 3 &
]
N Suggested Functions: Designed to provide a severe test fo-( 0 eses H the capebilities of coarse mesh g VT M g
- s.,
- seethods and fluz synthesis approxime-. g
\
tiens g $.w configuration ' Three-dinensional configuretion \ k including space dimensions and regteen numbers: 2 Figures g b % 4.g i 3 - g _ s . N s!
,- l s
h N . i
~ Norizontal Cross
. m q , .l 4 ' l seats-N
+ 4 1
j Upper Octant _ g
, 9>
/ 35 38 17 Region Assignments *
- , gg gg,,
)
w } 2 M 32 33 3 r M ants Fuel Assembly
- u f,
j, I 3 27 28 29 30 ' Identification
- f.'
, et 20 21 22 23 24 [,f
; 3 3 so is s2 Yortical Cross Section, y = 0
,, 13 14 IS 46 17
. 2 3 _a i a 7 a e Boundary Conditions:
- e se n se a se se we 'us .we = External Boundaries: Vacuum no incoming current [
4
; ; = synee try sounderles: seneellon, no net currer!* e Figure 18 IAEA Benchmark Problem Configuration %
G M r 1 , Q.
.4 1
- m. Y
'6 j -
y b d . . ;.
. :G 1' f ' Y t. % ".'.1102 3 E 2i? Zl'. C l ? -
d . 58 d! 0 . ij average power density. Although we have concluded that the
.J !
?'1 UMDIF code yields correct 'results for the test problem dis-lj cussed above, we would like to include some additional com-
,, i parisons for completeness, including a finer mesh calcula-l;j - tion (to compare with the 34x34x38 VENTURE calculation in 'Q Table 19) and a comparison of the peak-to-average power den-
) i sity and perhaps other local quantities'such as relative
. flux levels.
Il j Table 19 9 2 3-D, 2-Group IAEA Benchmark Problem Results (Non-Return External Boundary Conditions) 4 IBM-360/91 1l~
- Mesh Poi.nts Multiplication Peak-to-Average Processor (Total Unknowns) Factor Power Density Time (min) j VENTURE 9x9x10 1.03176 2.3765 0.3 to 1 3 -
(1,620)
~"
R , 17x17x19 1.02912 1.5672. 'l.6 to 5
;.] ~ -
(10,982)
~ ~
34x34x38 1.02864
'1 2.5035 49 t, j (87,856) l 68x68x76 1.02887 2.4081 192
~
.j
, (702,848) 1 102x102x114 1.02896 2.3780 360853
~
; , (2,372,112)
Extrapolated 1.02903 2.354 - i.) UwDIF 4 :,
- j ; 17x17x29 1.02897 -
4(*8 ij (16,762) Mi 1 - a a, (*8 IBM 195 -9 i A f83 Amdahl 5860 . Y' I r.: , f I 1.----._. . .
g.w;m.m.. - m ..;;g g.y,
. m mg emw mmum ,~ gy.mm; . . g, ;.
3- - 4 .
%=
- 4 59 y- .
1 g- -
- 3. FNR Test Problem ti 3 Since the objective of the 3-D capability is the g- analysis of the FNR, UMDIF has been applied to a typical FNR j configuration which has been calculated with 2DB-UM. The j- particular configuration examined was an LEU core on Septem-
) ber 16, 1983 (Cycle 229A). The UMDIF thermal fluxes were
; normalized to yield the same core average as calculated by 2DB-UM. Figure 19 summarizes the resultant assembly '
f: . L; n- averaged thermal flux distribution for the core and reflec-
] tors (D20 and H2 O) as well as fast-to-thermal flux ratios } -} for selected regions. As can be seen, the agreement is very 1 good within the core and significant deviations between 2DB- '
UM and UMDIF do not occur until well into the D2 0 tank, ; flC i where one might expect differences between 2-D and 3-D j- predictions due to the non-separability of the flux in the. . j_ D 2 O tank. As a further indication of the non-separability of the flux in the reflectors, Figure 20 summarizes the j , quarter-height and half-height thermal fluxes predicted by UNDIF in the core and reflectors. As can be seen, the difa j~ forence in the thermal flux at these two axial locations is significantly larger in the reflector regions (5-10%) than j'; in the core regions (0-2%). This indicates a substantial 4
& ' difference in the axial profiles in the reflector regions and core regions, hence indicating the importance of the 3-D
, capability.
4
% Effort is still being made to analyze a fine mesh (6x6) model of the above core, in addition to the relatively coarse mesh (2x2) summarized above. This met with some dif-kl_ ficulties due to the large demand on computer memory, and .
y ( this is currently under investigation. - y 3' , = =.
.e 3
g. 1 o_ . . _ _ _ _ _ _ . _ . - _ . _ - . _
, .... ,- g ,, -
% 1. < ' , .-
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. .i Tj LMF varas N ., m u 2
- 4 Mammelv-Awarannst Thermal Fhat ( 10 rVtrn -s) Average Thermal Flux over ;
j (LPCIP Plux termeL1286 in Portions of D O 2 Taroc .> . (*j totat 2De-m flux in core) Locadan 2Ds-m m :. ! m Beces .98 LO6
, :.- g Center 1J5 L42 e!
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... c.
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u .983 1.20 1.41 LU5 N i 1 L39 1A1 -
? .908 1.21 L42 1 28 LO5 s
{ 2.50s/2.50 .a62/.a63 , , .
] .750 A C ,
i is L48 2.43 L77 2.19 L17 J17
.751 I J 12 1A4 2AE L73 2.19 L17 J15 _;
15 g3, A37 l Im 1 11 2.11 1.n , laa 1.17 33 m til 2.11 L79 1A0 1.17 2.154/2.159 D L130/L.W1 L757/2.754
.ld \ 1.52 .9er 125 8
22 1.5r is im h L90 - ,: s s g .9 1a 2, ta 1.= 1m u9x ;p i N s7= No. .,,, 1, im ,,,, ,,,, N u5 ._ !
.; 72 \ L35 1.14
- .m a, -
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.292/.25Zs ur\ 1m 2.440/2.461
.72. N
.39a/.39s s Hi N2= s N= Nur s s Nim s Nui s -Nu s N.9s Ns 7 !
( d. 2.54 479 1.1r 12 IJO La1 .90s Ae6 1
\ \ \ \ \ \ \ \
~
E ._ l t 1 e l.. messar spectet Etmy .,, g? PJament Element Laceuanm . l p, p' 9 L, Figure 19 Assembly-Averageo Therinal Flux L,: Distribution - UMDIF versus ZDB-UM L m-a l} . i-r I, 1* ! cv 14 H ,
.e * ,.
I k
. _ _ . _ ____m__ - __ -- , . _ . --_ _ _ _ _ _g . . _ . . . _ . . , _ _ - , . _ . . . _ ,,
~
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,e .
4 y . 61 A' '
- .j u 2 t.FCF Themiet Fhat Eat ( ID tvem -8)
W rha m to oO Tank g 2
,; . total e thm m care) m if .Heignt v2 % e
.j , 1/4-Malet Back L16 LD6 .976 1 N , center Lss 1A2 L35 vs / U2 - Fest-to-Thermal Front LM 144 140 Fkm Rang) 1
- { -
Heavy Water Tem E a LDO L25 Las ul. 2.30 15 Nu2 N 139 1A1
* .904 L21 1A2 1.28 1.05 %
2.a4/2.50 .a6/.a6
.; A C t .749 LD5 La8 2.41 L73 2.19 L17 J13 1 ; ,, .751 15 Lee 2AO L73 2.19 L17 J15
,9 e 3,,, LDS L1D 2.1D L78 1.59 L16 .350 '
149 1.05 L11 2.11 L79 IJD 1.17 J33 2.7u2.76 '
'~
- B i . .984 . 1.25 2.08 1.51 191 1.D7
!; 39 tas 2m tS2 t2 La 3
'y J74 1.Dg L3 ,,37 m
\ L13
. ]'u. , 1.D5 L14 J79 LDs .963 .726 s
, 2A6/2.a6 .39/.39 N e6 no g.
L t 6
.c Figure 20 UMDIF Calculated Thertaal Fluxes t .I 'w
'. g r: II,t
/ .f*
bM L
as4 s , , a , , y s; . .- . . . x Jb. ? Y.4 . IN e- t A.!. 2. ,,3 L f '- jL...~ .
~
_ _ m. - 3, _ . g . , , B 62 ~ I.Y ' 9 H1 V.
SUMMARY
AND RECOMMENDATIONS FOR FUTURE WORK 1i jj A major emphasis during the past two to three years in the experimental portion of the project has focused on the
;; unfolding of the FNR neutron flux spectra through multiple j y j; foil activations. During the present reporting period, un- '
( folded fluz spectra have been obtained both for LEU and HEU [ $ configurations. This effort covered the entire energy range i Ilj q of interest including thermal and fast energies. The un- - h{ folded flux spectra indicate hardening of the neutron flux $ [I in the LEU configurations as compared with that in the HEU ( environment. This is in agreement with saturation activity i.
@A ,
4 data obtained with wire and foil samples. A comparison of subcadmium fluxes measured with different activation 3 materials has also been made as part of the incore fluz ~ 4
- measurement effort. 7 i -
i
^
e Comparison of the subcadmium flux data obtained with Rh
}
SPNDs and iron wire activations has taken considerable ef- T
), fort during this reporting period. To determine the subcad-o 3 g j -
mium sensitivity factor for the SPNDs, measurements of the - Qj flux depression due to the detector paddle was made in addi- t. 1j ,c . tion to measurements of the subcadmium current fraction and ._
- l. l flux perturbation due to the detector itself. The SPND response, calibrated against iron activations, indicates j
[,1 l considerable sensitivity to the detector environment. i .i . . , Further measurement and analysis of the SPND response j are underway to better understand this observation regarding ?.1 , the SPND sensitivity. Measurement of excore flux spectra at
} selecta.'. beam ports and further comparisons of different M detector materials for subcadmium flux determination are "
also desirable. F M Calculated incore and excore flux distributions are ^ y rather sensitive to few-group cross sections for the heavy y, 7 water tank. An attempt has been made to represent ap- L
? !
9 proximately material heterogeneities.in the tank in space- - 3 f. dependent flux spectrum calculations for generation of heavy h. 1 f !' 4
._mw .c - -- -- -
_ _ - . - --- - - ~
....s. .,. , . _. .--~ , , ..,, mm..m y ,,J.,
.3, gg 4 r.;.,,.y gjg y, ,, .. .
31*
- 4 .
j- 63 i 3 . -
'e -
water cross sections. FNR operation over a period of four j- years has been simulated with the 2DB-UM code to provide a ~
- j .,; better estimate of fuel burnup.for calculation of flux dis-
.] tributions and core eigenvalues. As part of the ongoing ef-j; .-
i fort for validation of our neutronic analysis package used for the LEU project, an IAEA benchmark problem for an HEU J1 t configuration was analyzed. _ :,' , Current effort in the simulation of experimental data i i centers around evaluation of three-dimensional effects in 3 the calculated flux distributions and core eigenvalues. i,] i' This includes study of the effects of distributed fuel burn- t j.f up, and representation of shim and regulating rods partially j;q inserted into the core. Another emphasis will be made in simulation of measured reactivity parameters including L., . temperature coefficient of reactivity and power defect of y reactivity. Analysis of an LEU configuration is also under consideration as part of the IAEA benchmark study. .2
,j Additional tasks in the project include completion and documentation of UM code package, and preparation of a final M; report for the LEU project. These efforts in the last phase ' ! of the project should be of considerable benefit to the Y[D research reactor community.
. fL
'k 3
y 7 ( y
;9
[*h
- s
;1
[;! r 4-b' a - N-l ', . I esp
s, \ .
. :-: , ., . . . . .i . , . ~. ; . , . . ~'
" *2.2 C D:C CP;1m sil.i??J 1 L :_.a. & EX C T ? Yl'11T~;;~~ ~ ".T %.Y,7
" T L;i ,
c, . s 64 '
") -t i
4 REFERENCES h , d 1. W. Kerr, et. al., " Low Enrichment Fuel Evaluation and Analysis Program, Summary Report for the Period y} L; January, 1979 - December, 1979", Department of Nuclear Engineering and Michigan-Memorial Phoenix 3 Fi Project Report- The University of Michigan.(January 1980). r
- 2. W. Kerr, et al., " Low Enrichment Fuel Evaluation and y Analysis Program, Summary Report for the Period f.; January, 1980 - December, 1980", Department of
'j Nuclear Engineering and Michigan-Memorial Phoenix l (1 -
Project Report, The University of Michigan (March '
] 1981).
a ,,
? 3. W. Kerr, et. al., " Low Enrichment Fuel Evaluation and .
M Analysis Program, Summary Report for the Period
- ij January, 1981 - December, 1982", Department of -
Nuclear Engineering and Michigan-Memorial Phoenix t i Project Report, The University of Michigan (January ~ 1983).
~
H ~
] 4. D. K. Wehe, et. al., "Subcadmium Fluz Measurements in - ,: HEU and LEU Cores Using Rhodium SPND and Wire Ac-tivations "", Presented at the International Sym- ~
9 posium on the Use and Development of Low and Medium .
,, Flux Research Reactors, Massachusetts Institute of Technology (October 17-19, 1983). ' ]:.i --
- 5. D. K. Wehe, C. R. bruger, W. R. Martin, and J. C. Lee, 1 " Operating Experience, Measurements, and Analysis of _l 4~ the LEU Whole Core Demonstration at the FNR", i Presented at the International Conference on Reduced J
Enrichment for Research and Test Reactors, Tokyo .! q (October 1983) . -' ,
.; t l5 6. D. K. Wehe, " Measurements of Neutron Spectra in HEU and !
d LEU Fuels," Ph.D. Dissertation, The University of ! Li Michigan (1984).
*g .
- 7. R. M. Westfall et al., " SCALE: A Modular Code System for f
& Performing Standardized Computer Analysis for W Licensing Evaluation,* NUREG CR-0200, Radiation l
, Shielding Information Center, Oak Ridge National j g.. Laboratory (1980). ;j G 8. N. M. Greene and C. W. Crave, Jr., "XSDRN: 'A Discrete '!
$ Ordinates Spectral Averaging CodC , ORNL-TM-2500, _, ; d . Oak Ridge National Laboratory (July 1969). .j u >r I.i 9. W. W. Engle, Jr., "ANISN, A One-Dimensional Discrete Or- ! d dinates Transport Code with Anisotropic scattering", "j 5,j K-1693, Oak. Ridge National Laboratory (March 1966). , M 1 -!
.{ . < ,
1 .
.t - - -
A
- . . 7 w. ; ;; 3 w g: m a c; m w3 n e m m m esu pyyp ysm y .z-yy; g y: ; #
17= - H < .
- s. '
l- ' 65 m. q
}
J:
- 10. L. J. Milton and R. N. Blomquist, " VIM User's Guide",
j_
- Argonne National Laboratory Report (March 1983).
fj -
- 11. W. N. Little, Jr. and R. W. Hardie, "2DB User's Manual-y Revision 1", BNWL-831 REV1, Battelle Pacific d~
- Northwest Laboratory (February 1969). )~
?-
- 12. R. F. 3arry, " LEOPARD-A Spectrum Dependent Non-Spatial Deplet:,on Code", WCAP-3269-26, Westinghouse Electric
( -4 - Corporation (September 1963).
's 13. J. Barhen, W. Rothenstein, E. Taviv, "The HAMMER Code 97, System", NP-565, Electric Power Research Institute 1_ (October 1978).
- l ij ;-
- 14. K. D. Lathrop and F. W. Brinkley, "TWOTRAN-II - An p ~' Interfaced Exportable Version of the TWOTRAN Code
- j. for Two-Dimensional T anapart", LA-4846-M8, Los '
n f Alamos Sclentific Laboratory (1973).
~
- 15. "Research Reactor Core Conversion from the Use of Highly Enriched Uranium to the Use of Low Enriched Uranium
, 7 Fuels Guidebook", IAEA-TECDOC-233, International '
_ Atomic Energy Agency (August 1980).
..jr 16. T. R. England, " CINDER-A One-Point Depletion and Fis-sion Product Program", WAPD-TM-334, Bettis Atomic j
Power Laboratory (August 1962).
~,
- 17. W. R. Cadwell, "PDQ-7 Reference Manual", WAPD-TM-678, y-Westinghouse Electric Corporation (January 1967).
- 18. D. R. Vondy, T.~B. Fowler and G. W. Cunningham, "VEN-g TURE: A~ Code Block for Solving Multigroup j -
Neutronics Problems. Applying the Finite-Difference
; Diffusion Theory Approximation to Neutron y Transport", ORNL-5062, Oak Ridge National Laboratory j- (1975). ) 7 19. R. W. Hardie and W. W. Little, Jr., "3DB, A Three-pm j
Dimensional Diffusion Theory Burnup Code", BNWL-1264, Battelle Northwest Laboratory (1970). 3F bO 20. "Argonne Code Center: Benchmark Problem Book", ANL-7416
?b Supplement 2, Argonne National Laboratory (June ;,1, 1977). ,
1' . i
~
n ir
?.b
~
q e.- }':
- l. L .- :- - +n,5 . .
.,. ,. ,, [ e.g.ye.gymy;.y _ . , -. u:.w.3;,,ven r, gg.<.myg.;y g~ g:;
, 3 * '
f *
! n, .
s= *
.i .
4 1 APPENDIX A E - . S I i s i I- Subcadmium Flux Measurements in HEU and LEU Cores ; Using Rhodium SPND and Wire Activations l
~ ,
. me I e
Q 't . I k{ S
- e. .
9
;e i a '.l M P
M O
>=e m
e N m j -- - -
- 1,,
1 ~ I J [+ *. - _ Y 1m 1 . T
..a D.
i o
' e I
I Y ,m
~~
I.
~
e
.y D .-
4 t 4' i e
* * *= g a +_ 9 ,,,,9,, g - - , , - , -- - - - -
.-u u :> . .,yj.g.4.g.',g-}
. ..y ~ , -
. ~ . ry. . a _. .g..gy.:7 _.,.,,.
y 7,.
- j . , ,
g i ,. .
) ;d\d. -
t
? n b l e- l +- .
d 1 a .:. l . a .35n s l I Aa l
. 1 $7 .s SUSCADMIUM FLUX MEASUREMBITS IN BEU AND LEU CORES d, ,
[u; USING RICDIUM SPMD AND WIRE ACTIVATIONS
. .a e
D.K. Wehe , C.R. Drusst, J.C. Lee,.7.S. King, W.R. Martin
.l The University of Michigan
; 7 Ann Azbor, Michigan
~
7; M.M. Erstacher - I_ Argonne National Laboratory
- j 4 Argonne, T114 anis' . .
1a . AnsTmAcr a . j The sensitivity of a rhodium self-nowered neutron j detector (SPMD) was measured in an MTR core and found .
-. to be significantly smaller than the measurements and . ,, .;. calculaticas of warren would indicate. An analytic j model which incorporates empirical beta escape data ,
was developed, and the calculations tend to support t + 4 these lower measured values. l G l t
)
1 INTRODUCTION e . J 4 As part of the Reduced Enrichment for Research and Test
" Reactors program, the 2 MW Ford Nuclear Reactor (FNR) at the
- l
,,, University of Michigan (UM) is currently WH ag high enriched
,,Fj ,q, uranium (EEU) and low enriched uranium (LEU) MTR type fuels ~. As j a part of the measurements, flux maps using rhodium SPNDs have been
;,, made on a variety pf HEU, LED and mixed cores. However, when the q ]~ SPND flux maps were compared with fluxes obtained from wire activa-tions, differences were noted both in intensity and shape.' Since ]~ the absolute fluses determined frosi the activations are believed '
to be correct, the sensitivity of the detector, S, must be different
,i fh- from the generally accepted values. In order to explain this dif-forence, a simple modal for calculating S was developed, and the 1
i
- results of the calculations are shown to support the revised values l i
of 5 determined from the measurements.
~
1 e ; b - l i . i l Ie e I.I i l$__ _
- I
g - .,- t . . -.=,. a -
- y ,, .: . .
;m. v_ _, __ w, , ,, c, , , , ._.;..,.... .
,,,,,,j..,.,,,.y
,;,,; g
.g. i%_3p 7
q, - m . cI, 2 . d-1; 'l ,' DETECTOR AND CORE CHARACTERISTICS 3' 2e FNR core consists of MTR regular fuel assemblies (18 fuel ]i plates) and special fuel assemblies (9 fuel plates with a central waterhole). The physical dimensions of the HEU and LEU elements 4l Y3j are identical, although the LEU fuel has approximatel/ 20% more - j d .; U-235 per assembly. The core. is surrounded en three faces with a .
~
j! light water reflector, and is bounded by a heavy . rater reflector M . on the fourth face - , ii! ! l 6 ji me operating characteristics of a rhodium SPND are discussed l 9 in reference (1). The SPND's used in these experiments have .020"
~~
~j diameter rhodium emitters, Al 023 and MgG insulators, and .062" outer
': diameters. A background lead running tho' length of the detector cable . ;1 '. was used to determine the background signal strength. Each detec-h' tor is mounted on a 36" x '.625" x .093" inconel paddle for struc-tj tural support. A 1.5" x .25" hole around the emitter reduces the
- !' perturbation caused by paddle.
b' u- . .! 2j MERSURIMDITS OF THE DETECTOR SENSITIVITY I
. The SPND produces a direct current as its output signal. The ' =
i net current signal is proportional to the reaction rata in the emitter, which.in turn is proportional to the flux. S e amount of
- current produced per unit flux is defined to be the sensitivity of the detector. More specifically, if f,e is the fraction of the not '
detector current (Inst) which would be produced by placing the I detector into a flux with a sube-=d=fum component $,c, then the ' subcadmium sensitivity is.. defined by: b
.i S
=
ScnetI .
- se 4,c
] . ,
.L g To detersrf ne the detector sensitivity, the valuesof +sce fsc, and _
a
]j Inst were independently measured at the same location. These g; measurements were performed in the core and D 0 reflector, for both 2
g' . HIU and LEU fuels. The not equilibriunr current was determined by directly measuring ~
; the current (-50 n,anoamps) coming from the emitter lead and sub-I.j ' tracting the current measured at the background lead. Two rhodium .
N* SPND detectors with similar mountings were used dnr4nry the course , j of these measurements. calibrations performed in the core showed ' the detectors' measured net currents were in good agreement. The subcadmium current fraction was measured by activating g j bare and cadmium covered zhodium wires with the same- diamater as the detector emitter. The wires were counted on a GeLi detector, and - [ ,
}
[, i W th !c <.w-Iw _ _ _ . ._ _ ._
<y, . w smf - Sw&-~-mn:~~mt &= wmhedh% O~'T; mob ~':GU=lW&$~~O l l' . e ;
1
- 3 .
,J : ,
I d 2 ' n it can be shown that : I 7 1 sc S f sc
.= 1 - 1/CR 2 f'
- ,,a -
o J m L where CR is the cadmium ratio of rhodium. i J The subcadmium flux was determined by activating bare and cad-l 9 mium covered iron wires,and then counting the activities using a ,
,i
GeLi detector and MD6600 analyser. . Absolute efficiencies are deter- - i F! , mined from an NBS mixed radionuclide standard. The conversion from j
}~ -
saturated activities per unit nucleus (A) to subcadmium flux is made using an LEU spectrum-averaged cross section calculated by a one-d4====ional transport code. Since, 4 A bare -A cadmium
,s c B U^ the sensitivity is directly proportional to this' cross section, 6 which in turn depends on the spectrum. Wille it 'is conventional to use a 2200 m/sec cross section to obtain a sensitivity (5 22 ) which l}a is a current per "2200 m/sec flux", the subcadmium flux is the true quantity of interest. Hence, a spectrum-averaged, snhed=Amius .ll q
group cross section is used in the analysis.- . e, 1 To make these results more generally applicable, experiments "
'j- were performed to separate out the effect of the paddle on the sensi-tivity. Inconel peddles which duplicated the detector support q paddles were constructed and bare iron wires were attached. The ;
f loaded paddles were irradiated and the results of the activation were compared with bare iron wires irradiae.d withoue the paddl.. l'2
] The results show a 7% flux depression at the emitter caused by the ]"- paddle. Since the current from the emitter would be 7% larger with-r out the paddle, the measured sensitivities have ~been increased b by this amount.
Table I shows the sensitivity determined from the measurements ' for the 2.54 cm long emitter with the effect of the support paddle f" removed. The subcadmium sensitivities measured in the HEU and LEU LJ- cores agree reasonably well. Since the HEU spectrum is softer An the core, this agreement would be even better if an HEU spectrum rj averaged cross section were used in the analysis. 1he subcadmium sensitivities measured in the heavy water reflector for HEU and LEU
-q cores differ by -164, which is larger than expected. Comparing the average value of the sensitivity measured in the core to the average j
value measured in the heavy water reflector, it is clear that the [-. detector is significantly more sensitive (-42%) in the reflector. p Interestingly, this conclusion is still true even if the values were "s j a converted to conventional S2200 sensitivities, l-
.I L
? e ,1 } w__ _ _ _
- . n;_;.e,;,., -w . , -- ,- g g , ,, . 'm ,,,,,.,mn _,. ._ , ; ; , _ , ,,;,: ,,y ;l.gcz *T - 1. 3 h g 4
- b 4 .
J . d j COMPARISON WITH PREVIOUS MEASUREMENTS Table III shows a compilation of previous measurements and y calculations of the conventional S2200 sensitivity for rhodium W , SPNDs similar to the ones used in these experiments. These values . j are also converted into subcadmium sensitivities for comparison j: with our measured values. Th'se e conversions were made by using the 3' individual author's interpretation of the 2200 m/sec flux, and mul- 1 93 tiplying by the appropriate ratio 42200/$sc- *
'I 1 . .
3 The present measurements of the LEU core ' sensitivity are con-4 siderably lower than Warren's measurement 3 (22%) and calculation - (29%), and about 10% lower than the measurements reported in * (i references (4), (6) , and (7) . In the heavy water reflector, the
;j present LED measurement is about 9 % lower than Warren's measurement, .
j' but about 6410% larger than the values in references (4), (6), and j (7). 'Ihus in general, the heavy water sensitivity agrees reasonably Q well with previous measurements, but the sensitivity measured in the Jj core is significantly lower (10-22%) than previously reported.
. s CAICULATION OF THE DETECTOR SENSITIVITY y I '
The measured values for the sensitivity of the detector in the
, core disagrees significantly both frona Warren's calculations, and ,,
s the present measurement in the D2 0 reflector. In order to identify -
. the source of theese differences, an analytical model of the. detec- .
?) , tar is developed below. If the detector is placed in a neutron flux, a net equilibritus signal will be produced which can be ~
, written as: ,
1 Inst " "* #8(N!,aC(E)$p(3,E)dEdE -
.i .
where e = ' electron charge, N = number density of nuclei in the d emitter, c(E) = the, Rh-103 activation cross section. $p(r,E) is ,, the actual (perturbed) flux in the emitter at point r and energy E, pS(E) is the probability averaged over the beta spectrum that a beta emitted at point r will contribute to the detector current, and the spatial " l cegral is over the volume v. of the detector. d, Sirae the ulthnate goal is to determine the average unperturbed a I subcadmitan flux <$,e> at the emitter's position without the detector - present, it is convenient to definer U E f.- ' [,Pg(r_)[ cc a(E) $p (r_,E) dEd_r _ E = average probability that a beta S"" L '; a $p(r_,E)dEd_r [,f ce (E) born in the emitter from a sub- !; , cadmium reaction will contribute
~
@ to the current G A l
~
k) 1 .s y, 'll~t 'J e .
. -.,,.m __ , _ . __s -.y-.,._ _
~ u -s - w .s.~ w . m w .,g. w .. ,,.rdi ,z --d. p:a.,equ%g ., ..y my f. :c ;i?1YM4 W
.ps "
1. n .$ E 3* [, P g (r) k cc o(E) (p(r,E) dEd_r 1 f' =
=
= subcadmium current fraction sc
}, g ( Pg(r)[g c(E)$ (r,E)dEd_r
.i
,p . 4f'ec+,(1,E)dEdr o .
i , = flux perturbation factor
}' $,jcc4(5,g}ggg5 n o 37 where (e(I,E) is the, unperturbed flux which would be present at
,,' position r and energy E without the detector present, and f, t===. (E) +,(1,E) dEdt i4 _ .
. a = = subcadmium group crues section j~
a, , [y /o p(1,E)dEdi I il 4 Using these ' definitions, ' flg .s . V I d- - (NVe) $**Of I l not f'e s 8 <$se> - ry -
- 1 I
N, where <$s~e> =v 1 [, of cc$o(r,E)dFAr. - ., i
; Thus, -
- f' I f' I * .
- i se not , se not 9**, , I"*I N 8
. j .;. ec p se -
1 4j where S,e is defined to be,the detector sensitivity. To calculate j the sensitivity, one must then calculate the factors in I se = (NVe) *5se *c S *f . -J-. p . q . ,s. for the detector. d
- M
6 . 3 ,'7 a (1) 6,,. Measurements and calculations of the bwta
.y escape probability indicate a value of .46 is appropriate for our 9 spectrum and ptter geometry. This value is considerably smaller than Warren's calculated value. The SPND insulator space charge g -! effect is calculated ,5 3 to reduce this value by about 204, which is J- reasonable since unasurements2 on an 18-mil emitter show a 14% -
h reduction. Thur , Ise=.37 is adopted. . p (2) a,f.e,f have been calculated using one-dimensional trans- >- port theory (ANIhN)8, and three-di==nsional Monte Carlo simulations g", (VIM)9, and are shown in Table II for an LED core. Because of the J.,,j three dimensional capability, the VIM results are recommended, and l ] compared in Table III with previous calculations. On an absolute l'4-- basis, the model overpredicts the core sensitivity by 6% and under-9 '. predicts the D 20 sensitivity by 114 This agreement is quite
.L , .
es N e. . l I q- l lJ l LL l j-f: l; .w- -.;:p 4-7 m m:.v.=---w : n - . . - _ .., _ . . _ -. ,, , .. , .. _ _ . - _ ._ i
l ,- z~., y ,,ci- . my;;gc.;7m.i:3 y,,,zyf' ;. , &3._ ,
~
.+z r;*,7-- " "~ - ~ -
- -y, .
-Q e a't , ,,
?r,e n , 6 ,- 2 l. N ; N - n - ~ g! reasonable, and tends to support a measured core sensitivity which
.is icwer than one would predict on the basis of Warren's model. The -
l,j principal improvement comes from the lower values of I,e and E. d, , 1l - 23 i CDNCLUSION AND RESULTS Pj 1 a .
; ! As shown in Table I, the s
{3 measured in the FNR core (.67x10~gnsitivity 1 of the rhodium ampe/fsc-cm) SPNDs is lower than values !
j ? '
reported in the literature for similar detectors. The sensitivities i 21 measured in NED and LEU fuels agree reasonably' well in the core (6%
] difference), but are 16% different in, the D20 reflector for reasons M].
which are not known. The sensitivity measured in the core was sub- ,j] stantially smaller than the value measured in the heavy water g, reflector. ,
~
'f; The analytic model predicts sensitivities which are in reason-j
- able agreement with the measurements, although it underestimates the y
~
observed sensitivity change between core 'and D 2 0 reflector. Com-
; paring these results with the results of other approaches, this model yI offers an effective method for predicting subcadmium sensitivities of SPNDs. "
s. 1 } REF N '* - [. ,,
- 1. J.W. Rilborn, Nuclecnics, 22, 2, 69 (1964). '
~
I. 2. M.N. Baldwin, R.H. Clark, and J.E. Bogers, Final report, j BABS-3647-13(1969) . (Sea also BAN-3647-7) . 7 6
- 3. T. Laaksonen and J. Saastamoinen', AECL-5124,111 (1975) . r
' ~
- 4. J. Eroon, AECL-5124,135 (1975)'.
p ! . y 5. R.D. Warren, NSE, & 331-342 (1972). W i 6. M.N. Baldwin and J.E. Bogers, IEEE Trans. Nucl. Sci. , NS-16, p 171 (1969). 4 W N 7. R.P. Debair, M. Grin, and O. Simoni, EVR 4775e, Joint Nuclear [ Research Cente' r , Ispra Establishment-Italy (1972) . ; fj a ! gj 8. W.W. Engle, Jr. , K-1693, Oak Ridge Gaseous Diffusion Plant S (March 1967) . _ n . v' f: 9. F.L. Filmore, ANL ZPR-TM-121, Sept. 20,1972. A N 10. N.P. Goldstein, IEEE Trans. Nucl. Sci. , NS-20, 549 (1973) . A l
- a. ,i
~, S. ) UI ij - l d .._ _
- : .- --~w myw-r~xn _ _. c.Qwpd=tmyg.fw::iyB&C)N.MT. t :' W: n'. :2 ' 2 .N ^ ~ O ''~:' ~ l '
. , e e
- e
.j s
~
7
}*.
l l
- 1 J #
TA8t.E I . Measured spwo sensittelties for MEU and I.EU ruel(3f l 4 ~'
- t Iron wire
't spMD s**g,,
1.ocation Rh utre Fuel TTpe s e** !"'" -21 (10 amps /6** -in) Lj - (borns) (1JI3) I** (20'Isops) Core Regular Element '
- ) - MEU(1) ..... .844 2.52 .81 47.78 1.64 L tEU . . . . . . . .844 1.99 .75 43.32 1.75
$ 5 1- D 0 Rettector 2 III
- MEU ..... .907 '1.96 e .90 52.67 2.60 g I.8U . . . . . . . .907' 2.44 .89 56.97 2.22 ,
(1). Cross section calculated for t.EU spectrum is used for HEU case. (2). Measured sensittelty increesed by 7% to account for support paddle.
,_ . (3). Rhodlue emitters were 2.54 es long and .0508 ce diameter.
1 . 4
~
Table !!. Calculated SPMD Sensittelties ter f.EU ruel
+ ?,
- e(barns) I, t,, 5,,
) -* _ t.ocation (10 -21,,,,f,Q ,
f . ANISM VIM ANISM V!M ANISM VIM MEAS.
.j ANISM V1M I. ) . .
4 Core 1.50 rue! . 114.0 114.1 747 730 80 .83 75 1.90 1.86 0 0 Rettector 120.0 115.8 .719 .768 .89 .93 .89 1.92 1.98 *
', M 0 Soflector 120.6 .733 .95 .91 1.97 1
o a Table III. Camparisons with Previously Quoted Values O7 5 1 3 M Author Smitter -21 (10' amps /$ -cm) Dia. (mits) (10 amps /42200'#'I i Core D02 Measurements
,3 uerren ...... .020 1.20 .89 .95 Eroon . ...... *
.018 .91
.( g Dobair ...... Seldwin . . . . . .
.020
.020
.018
.99 1.01
.96 gg3
.76 .80
.020 1.04 77 .83 This work (f.EU) .. .020 .93 .69 .87 D0 2
...... .020 1.10 Calculations Pwg This work (VIM-LEU) .020 .99 .73 78 D0 .98 uerren2...... ..... .020 1.31(2) .97 1.04
!.aaksonen . . . . . .018 75 g33 7 .020 .88 .64 .68 Goldstein . . . . . .020 1.51 1.12 1.20 a,
f - (1). Estrapolated to 20 o!!s based on Kroon's esperiment. (2). Value interpolated of t graph at E,=.030 ev. L (3). Estrapolation based on t,aaksonen's estieste. A u 4l _ _ , . , _. , . , . _ . , . . . __ ..m _ _ _ _ _ _ _ _ ______m_, . , , , _ .
% y. . ,
- v -m ;. ._ . , _ ,; , . ;g_; ,- . ..,..~egewswmvs m ws m ;m w__ =gg gp yyggg y,y3:--- -
), ,3 l i
;
- I g
.c ,
i
.{, .
i'- - APPENDIX B i ; t. 4- t l 1 e T
- j. Operating Experience, Measurements, and Analysis of [
]-> the LEU Whole Core Demonstration at the FNR
*m f
t . g i e t. t 4
- i. .
i ume 1,'
! e 1 !
\ .
15 9 t .
~
.. k.
6
- N -"
.f_ !
r f k d
- i. ,
k r, . !~ ( r
! L )~ 4 r
l
% t J
t*
.9 l
.- 9 M
a =e a J- i l
?
a 4% i-3 T s ? k' . .:~4 I O
.,w - , - ,_ .. - - , ,
e , _, _ -
s .m s ..a d $.d e% M mneAG %wud h es- w w.w e~ wen e m m er.t j1* . k{ . a-i Operating Experience, Measurements, and Analysis I j~ of the LEU Whole Core Demonstration at the FNR a. d be s- D. K. Wehe, C. R. Drumm, J. S.' King, W. R. Martin, J. C. Lee 1 Department of Nuclear Engineering University of Michigan 9]_ R Ann Arbor, MI 48109 Abstract $"-' ~ The 2-MW Ford Nuclear Reactor at the University of
,. Michigan is serving as the demonstration reactor for the ] MTR-type low enrichment (LEU) fuel for the Reduced Enrichment for Research and Test Reactor program.
si operational experience gained through six months of LEU core d- operation and seven months of mixed HEU-LEU core operation i 1_ is presented. Subcadmium flux measurements perf ormed with 1 rhodium self powered neutron detectors and iron wir.e activations are compared with calculations. Measured j] , reactivity parameters.are compared for HEU and LEU cores. Finally, the benchmark calculations for several HEU, LEU, and mixed HEU-LEU FNR cores and the International Atomic
.j Energy Agen~cy (IAEA) benchmark problem are presented. *
[ Introduction
,' The University of Michigan Department of Nuclear Engineering and the Michigan-Memorial Phoenix Project have t f ...
been engaged in a cooperative effort with Argonne National . Laboratory to test and analyze low enrichment fuel in the Ford Nuclear Reactor (FNR). The ef fort was begun in 1979, J as part of the Reduced-Enrichment Research and Test Reactor i jy (RERTR) Program, to demonstrate on a whole-core. basis, the ( _ feasibility of enrichment r. eduction from 93% to'below 20% in { ,
, MTR-type fuel designs.
J g- The first low enrichment uranium (LEU) core was loaded into the FNR and criticality was achieved on December 8, l _ 1981. The critical loading was followed by a period of l 3 about six weeks of low power testing and 3 months of high . 4 _.
- power testing during which time control rod worths, full l 4
3* core flux maps, and in-core;and ex-core spectral i measurements were made. i
~~ ~
The initial period of LEU operation was followed.by a {j , period of high enriched uranium (MEU) operation (from 5/82 to 12/82), a priod of mixed HEU-LEU core operation- (from q; 12/82 to 6/83), and a second period of LEU operation (f rom 6/83 to 9/83). During these time periods additional
)G '
measurements were taken to characterize and compare the HEU (L: and LEU fuel performance, including incore and excore
.; subcadmium flux measurements wi~th rhodium self-powered y- neutron detectors (SPND's) andw' ire activations, in-core and q-
% _ 1
- p v6 w **c_ epeye merec, .* e,4 =ey e , yo _ _ a - -,,,,
7'zmx.;1;uzr"w m w = v & % h . 7 2 n % 'C ; m: m E;.n ' q C '. d i j,; " ~~2 4, , ,
')
M 2 . 11 ij ex-core spectral measurements with spectral unfolding, il control rod worths, and measurements of various reactivity fj coefficients. ej j Previous reports have described the demonstration G experiments program (1) and the analytical effort (2) to M develop and verify the calculational methods used for ~ M analyzing the FNR HEU and LEU configurations. Preliminary d experimental and analytical results for the LEU core were y' presented at the 1982 RERTR meeting (3-5) at Argenne - g.g National Laboratory (ANL). This paper will focus on y experience gained through an extended period of LEU and' f3 mixed core operation, and the work. which has been performed a to resolve some of the uncertainties identified in the 33 previous papers.
- t 1" 'he T first section of this paper discusses the ~
operational experience that has been gained with the LEU and N. mixed HEU-LEU cores. The next section of the paper 1 describes the demonstration experiments and measurements 9 program with the LEU and mixed HEU-LEU cores. The final i section of the paper discusses the analysis of the LEU and a mixed HEU-LEU core configurations and comparisons with - measured data. .
~
operational Experience i After six months of operation with 'rJEU fuel, and seven i months of operation with a mixed LEU-NEU core, the LEU fuel
- elements have reached an average burnup of 6.4% and 'a -
maximum burnup of 9.7%. The operational experience gained
.1 by the utilization of LEU fuel in these cycles will be gj presented in this section. _
- f. Overall, there have been few problems, and few Fj operational changes required by the use of LEU fuel in place bj of HEU fuel. The mechanical performance of the LEU fuel has i Q been excellent and no fuel has been rejected due to leakage _l p,; or contamination.
HJ : [9 The LEU fuel was designed to be similar to the HEU fuel, , hence all existing fuel handling equipment and procedures l K.ji can be used with the LEU fuel. The similarity in the fuel 1
- b. design greatly simplified the HEU to LEU fuel conversion. ., l
- j The water gap thickness and number of plates per fuel element were unchanged, so that the thermal-hydraulic h,
Dj performance of the-fuels was essentially identical. The - n- enrichment reduction from 93% to 20% was accomplished by B( increasing the U-238 loading from 8.04 grams to 691 grams ji per element, and the loading of U-235 from 140.6 grams to - Lj 167.3 grams per element to account for the resulting M reactivity loss. The extra fuel was accommodated by . [Oj increasing the fraction of uranium in the meat from 14.2% to _ 42.0%, increasing the fuel density from 2.9 gm/cc to 3.8 gm/ {} - 41 d .e m , ]I G ,s - I % 0 .
,,.-m~ --- - - , , - - - -
Q_m.m Q i;yr.:% m.m % f'.M m;mwmg
+Y ;f.
.mw my _ amp,wgy,yy, p.myp pg y .
l 3 ' ' (d
- 3. -
3 - r, i i ec, and increasing the. meat thickness from .056 cm to .081 j- em, with a resulting decrease in clad thickness. j The LEU fuel has in general behaved as expected. The predicted' critical mass of the initial critical loading compared well 1within 1%) with the actual critical mass. 3 Control rod worths, temperature and void coefficients of 1_ reactivity, and power defect are measurably different with 4 the LEU fuel, as predicted, but the changes have been~small
]- enough to allow the reactor operators to use existing o
1 procedures and techniques for routine reactor operation. i . Only minimal administrative changes were required fot
- i" the use of LEU fue'l in the FNR core. The only technical ,
specification requiring revision was a license change to allow the use of 20% enriched fuel. Existing security and
. emergency plans for the facility were adequate for the LEU i _ fuel although fuel accounting procedures had to be broadened Q. to include plutonium production. ~
s -
" Overall, the conversion of the FNR from HEU to LEU fuel has been smooth without surprises. Additional experience
- T will be gained with the approach to an equilibrium LEU cor.e. .
.- Demonstration Experiments ? - .
f Subcadmium fluxes have been measured in the FNR with a
~ rhodium SPND. The rhodium SPND is mounted on an Inconel paddle and produces a current which is proportional to the ).- neutron flux incident on the rhodium emitter wire. In order j to convert the measured current to an unperturbed subcadmium 1- .
flux, several factors must be determined, including the sensitivity of the detector to subcadmium neutrons, the '
?_
fraction of the rhodium activation which is due to subcadmium neutrons, and the flux depression caused by the
', detector and the Inconel paddle. The fraction of the , 'y- activation which is due to subcadmium neutrons is determined 4"
by the activation of bare and cadmium covered rhodium wires. ; The flux depression caused by the Inconel paddle was ' g determined by comparing the activations of iron wires : mounted both on the Inconel paddle and an aluminum paddle. i The flux was found to be depressed by the Inconel paddle by i about 7%. The determination of the detector sensitivity and y flux depression due to the rhodium emitter wire are , n. a. considered in the next section of this report. , i The absolute subcadmium flux has also been determined by f: J- activation of bare and cadmium covered iron wires. The separation distance between the bare and cadmium covered 4 y . wires was chosen to be large enough so that the flux j depression caused by the cadmium sheath does not affect the m-activation of the bare wire. The counting of the activated
, samples is performed using GeLi detectors. Wire samples are counted between two oppositely facing detectors multiplexed a
4-a h_ . - _ _- . _ . . _ _ . . . _ _ _ . _ _ . _ _ . _ _ _ _ _ . _ _ _ . _ _ _ _ _ _ _ . .
. _ _ - . ~ .. . . . _- - _- .
f-d:~= .i=~==dm..=x.zmwnan x..m.c.w = a.Ac2Gr%. $WT$ * * , i d 9
. ,l
- l . 4 , i p i
- .s ! -
3 : together. The sample is positioned by an automatic sample Ig i changer int.o a rotating, cylindrical plexiglass holder. 3 -l Pulse pileup losses are accounted for with a precision - @j pulser fed into the GeLi preamplifier. The amplified and t multiplexed signals are counted using an ND 570 ADC and fed - J J into an ND 6620 analyzer / computer for analysis. Absolute %! efficiencies are determined with a cross-calibration 4j technique at a separate GeLi detector station. . Background - n interference is made negligible for most gamma ray ene'rgies p d -]I
, with 2"-6" of lead shielding around all detectors. The '
saturated activity of the sample is determined from the l' P"; count rate, corrected for the irradiation and wait
, times. (4) -
i' J ' The void coefficient of reactivity was determined by i measuring the reactivity change due to the insertion of an aluminum slat into a fuel element. The void coefficient f i ~ ~~ for
! the nearly fresh LEU core is compared with previous d !
measurements made on an equilibrium HEU core in Figure 1. . b] l "' i Analysis and Comcarison with Excerimental Data [ji @d i 1 The analysis of the subcadmium flux measurements and the - t ;, ~ reactivity measurements will be covered in this section.' O The computational methods that'have been used to analyse the M ; FNR core have been reported previously (2_), and will be y
~
summarized here. Burnup dependent 2 group and 4 group cross _ } i sections for the HEU and LEU MTR-type fuel assemblies have L. been calculated with the LEOPARD code, which is a zero e v T dimensional unit cell spectrum code with an ENDF/B-IV data ~ base (6). , I: 7 3 Burnuc-dependent cross sections for the control elements P : nave been determined by the EPRI-HAMMER code, which is a 1- % ] dimensional integral transport theory code, and TWOTRAN, y[] j L which code. is a 2-dimensional discrete ordinates transport theory The EPRI-HAMMER '. de was used to generate cross Lj d; sections for the TWOTRAh code. The TWOTRAN code was then ]! used to compute reaction rates, which were matched with . ql' those generated by the 2DB-UM code, by adjusting the fast " and thermal abso }y - control regions.petion The and removal 2DB-DM codecross sections forrevised is a substantially the g;i e version of the two-dimensional diffusica code 2DB, which has _ been modified to account for spatially-dependent burnup by interpolation of a depletion dependent library of f macroscopic cross sections generated by LEOPARD. The 2DB-UM 3: code has been used for the Mobal analysis of the core. The _ feature that makets the 2DB-DM code particulaly useful for the analysis of the FNR core is its flexibility and ease of use. With the 2DB-UM code it is quite easy to simulate fi -- d'j several years of FNR operation, including bi-weekly startups g and shutdowns, and fuel shuffles. i Cross sections for the reflector regions have been hs . - ( n
! s
!. 1 - L E. - - _ . - . _
~ - . . . , . .
+b. i5i3 1;;n_,,,_ gm,__._m,mn,ma, & mas mm.mr.n.m :
a- - yqr 6~~. 5 3: .. 4 is {- calculated with the LEOPARD code, assuming a 50% non-lattice 3~ fraction, and a non-lattice peaking factor of 2. This t procedure wa's found to be adequate for the light water
& _ reflector.and aluminum regions. For the heavy water F reflector it was found that the fast absorption and slowing
{ down cross sections were very sensitive to the spectrum,
~ necessitating a more detailed treatment of the heavy water tank; which is difficult because of the complicated structure of the tank (2).
k - In order to determine 2 group and 4 group heavy water cross sections for input to the 2DB-DM code, the entire FNR
)~ core and reflector regions were modelled with the XSDRN code ; _ in 1-dimensional slab geometry and 123 energy groups. The ll XSDRN code is a 1-dimensional, discrete ordinates, transport j ,
theory code. Two group and four group heavy water cross sections were determined by collapsing the fine group cross N" sections.over the ZSDRN calculated spectra. In order to g_ account,for the beam tube voids, the heavy water tank was e divided into 3 regions, and the density of the materials in 3- each region of the tank was uniformly reduced by the volume fraction of voids in that region. C The effect of the water filled irradiation tubes was approximately determined in a separate, cylindrical
- geometry, 1-dimensional transport calulation with the ANISN
~
transport theory code. The geometry of the irradiation tube / was modelled exactly, and the surrounding region was - _ approximated to simulate the environment around the tube. The flux was found to peak by about 10% in the irradiation . ( - tube penetrations. r'N A comparison of the use of the LEOPARD generated..
) _;
reflector cross sections with'the use of' XSDRN calculated a reflector cross sections revealed significant differences in
];- '
the global flux distributions. The use of the LEOPARD d generated heavy water cross sections caused an y- underprediction of the flux in the heavy water tank, which n,. caused an in-core flux tilt away from the heavy water tank, Li b _. as compared with the calculation with the ISDRN heavy water cross sections. The flux tilt affected the contro'i rod d worth calculations, causing the worth of rod B, which is 47 farthest from the heavy water tank, to be overpredicted by
] the 2DB-UM code. ,
The conversion of the SPND current measurements to ' subcadmium flux was found to be a difficult modelling R,- problem. The method used here has been reported previously - (7) and the results will be presented here. t L. The subcadmium flux, 4 can be determined from SPND measured net current, I net,se,y b the following:
.-M
,4
.a 3, . . ._ ._ _. m m_.,, m _
m
- r. g . 4
-d .
g
~ ' ~
' . 3 W ..u.....v ..w .cL..
. ,.,D;w M M .s w M X w..: , . :~L-M.L n; -
- 6 ' .
d . Ui '
, ;. 4,c - 1.07
"'t '
(1) 5
~
i The subcadmium sensitivity factor, S, is proportional to the product of the S escape probability, the effective j . subcadmium absorption cross section for rhodium, o-Rh, and - the rhodium flux depression factor, fp. The B escape
- . probability. is based on a measured value, while o-Rh and fp '
n' - have been determined analytically at Argonne National . Laboratory (ANL) with the VIM Monte-Carlo code and at UM F* -!* with the ANISN code. The sensitivity values are tabulated i in Table 1. The factor of 1.07 in equation (1) accounts for' [2 the flux depression due to the Inconel paddle surrounding
~
the SPND detector. Figures 2-4 compare the measured . subcadmium flux with the 2DB-UM results for an equilibrium HEU core, a nearly fresh LEU core, and a mixed HEU-LEU core, r The' conversion of iron wire activation data to -
; subcadmium flux is much simpler: .
Ab'- Acd - (I $se = . (2) ,
% Fe
$ ]-i j where Ab and Acd are the measured saturated activities per ( Fe-5E nucleus for bare and cadmium covered iron wires. The - 1 effective subcadmium Fe-58 cross sections, o-Fe, have been f3 'i; spectrally aeighted over ANIf r.' calculated spectra in the core and reflector regions by assuming a 1/v cross section y a shape for Fe-58, and a 2200 m/s cross section value of p j i i 1 18h. . ii; . Absolute subcadmium fluxes for iron wire activations and -
$I rhodium SPND measurements and 2DB-UM calculations are Li]
compared in Table-2. The ratios of the flux in the heavy
;.'j i water tank to the flux in the core are compared in Table 3. -
The measurements have been made in lattice position L-37, a i which is at the core center, and in the heavy water tank -- J' penetration X. Measurements and calculations have been " jj j extrapolated to a quarter core height. u ; . 3: Rod wo'rth measurements 'for"an equilbrium HEU core, a mixed HEU-LEU core, and a nearly frash LEU core are - [Q 1 presented and compared with 2DB-UM calculations in Table 4.
"l Full length rod worths have been determined by multiplying measured half rod worths for the bottom half of the core by i -
1
- a. factor of_2_..
3 , i In' order to benchmark the LEOPARD and the 2DB-UM c' odes Nl fo'e'the'neutronics analysis of HEU and LEU fuel in the FNR,
~
] - the calculated eigenvalue has been compared with .
i measurements for several HEU, mixed HEU-LEU, and LEU cores
].
in Table 5. A part of the difference between the 2DB-UM e j - 3i ni . fi a Ll .
x .: n.: .-
, . w w .:. w m m . w - m . w m .,,,,., w & & g g, y 4.gmy. -
d "n O. * *] ,
.1- -
a. gg , J 1 calculation and the measurements was believed to be due to 4" the buildup of samarium in fuel elements that have been
- M removed from the core for some time. Calculations with the M. LEOPARD code indicate that the maximum reactivity change due to the samarium buildup is about .13% ok/k..
jJ ,
'b j' As a further benchmark of the LEOPARD code and the 2DB-
- i . UM code, the IAEA research reactor benchmark problem has
?.$ been solved . The configuration considered was a 10 MW(th) MTR-type research reactor which contains a 6 x 5 array of
- fuel elements, and is reflected by graphite on two faces and is surrounded by light water. Fuel enrichments of 93%, 45%,
- and 20% were modelled, corresponding to HEU, medium enriched j{ uranium (MEU), and LEU fuels, respectively and the results
?- are summarized in Table 6. Figure 5 compares the infinite multiplication factor for the HEU fuel as a function of
? burnup for the cross section generation code LEOPARD with ,
4 ;l the results obtained by ANL. As can be seen, the LEOPARD { . results compare very well with the ANL prediction for k . Finally, Table 6 contains the 2DB-UM calculated effecti,ve
~
multiplication factors for the core at three different c burnup states--a fresh core, a partially depleted core at y beginning of life (BOL), and a depleted core at end of life i ~ (EOL). Also tabulated in the same table are the eigenvalue - q - predictions by several other installations. As can be seen, u our results fall within the range of the other predictions, AP and should be considered acceptable. 2
~
moferences
;- 1. D. K. Wehe and J. S. King. "The RERTR Demonstration Experiments 1 Program at the Ford Nuclear Reactor *. presented at the f International Meeting on Research and Test Reactor Core g Converston from HEU to LEU fuels. Argonne National Laboratory (Novester 12-14 1980). 'l
- 2. D. C. Losey et al.,
- Core Physics Analysts in Support of the FNR HEU-LEU Demonstretton Experimenst*, op. cit.
"'f
- 3. D. K. Wehe and J. 5. King. *FNR Demonstratton Experiments Part I:
. Sean Port Leakage currents and Spectra *. Presented at the International Meeting on Research and Test Reactor Core Converstons from HEU to LEU Fuels. Argonne Nettonal Lacoratory j, (November S-10. 1982).
j- *
- 4 D. K. Wehe and J. 5. King. *FNR Demonstratton Experiments part !!:
Succocantum Neutron Flux Measurements *. op. cit. 5 3 J. A . Rathkopf. C. R. Drumm. W. R. Martin, and J. C. Lee.
- Analysts
;] of the Ford Nuclear Reactor LEU Core *. op. cit.
[
- 4. J. Rathkopf. ' Development of ENDF/B-IV Cross Section Litresey f or the F 7"" LEOPARD Code". M.S. Project Report. Department of Nuclear U Engineering. The University of Mtchts iNovameer 1981).
, ,1 .
r3 7. D . K . Wehe, et. al., *5uecadmium Flux Measurements in HEU and LEU M Cores Using Rhoolum SPND and Wire Activations". presented at the Internettonal Sympostum on Use and Development of Low and Medium" ].;> Flux Research Reactors. Massachusetts Institute of Technology p 2 . ( O.ctober 1983). k e H - d.. 1
~
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~ .
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og A. a a .. . i
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e eg se D . 6 .* .. . .e. g gg
. . O.
j a s ete . .am. . .au.s .
#g gg -- S Oe . . 3 e ge . . .
i'
. 3 M e. Se eg e se e. es fe a= ae - a'* * * ** 3O ====a. ,j e ** ** . e4 . at -
(l. A. e e.d . . 0 gl 'g en j W e & u ==h6 g S 9
.a e .m e6 M
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42 . a em
* ==9 m9 SD f***
- 8.
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at
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.se
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, e e.
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's &. $ .. . .e &. e e.
- =q
. -4 ..We s.e
.. .M
...d.e-.. *
. E.
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.- A.
9*
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. .e . -
e., #.w.
-s e. n . . t a 5 . . - . . - ~
u E E 31 2 .e. 9 5 I. ..u as . u as . u .e. as =, e. e 5 .. 1 E. 3 . a e. , 'w. s
>s
* * - ..a. .. .
3 3 I . . S=3 2 aa;
.s .
3 S. . J.r. 2 .
-d 3 a .
.. .) o s . . -
..8.5 g
..2. .......e...
s .e ds . - s s
- s. e 4, . . e
- 9. .
... ~ . . ., ;
* .j . 3 M.4 MMMMbMb.33 3333 b
w e u .e b , I = e 1 i p= e . o & I t E.
- . . E..~~~. e= - a=
~.~.~.
. w ep se e W e O
.A. 3 ==. 5 4 sw .*
- e .en.. .es. - se ed .ee
.m.
*= .== e en. . . he e . egees 3 e Q
. E.'.
e
. S N 3,$
- f. se to *
.e 3 Pe
- e. .
==. G O O . * *
- E
*/
- A to re R 4 s & E us.e.. e3 5
= 4. .&. S et re fe fe = * "
es a. B Og e
... 4 G se. eG.en
--*
- eA e 3 *
- be e m 4* & ... - e. - a *a=
.* . to en e . e. . . e
- et am 6
., e e ,
8 .* y =e
- e 2 ee r*
.
- De N 3 3 3 S
=. w. ... - . e.e SD M.
.e. e4 -
., 91 ... 45 e t. . . e 4 - a.eam 3
.S
- am a, em A ce O 3. e 9 . . 3 s. a. e ee
.g .= S. S 'Pe G N.* e ,"4 O eh e e 4 e.
A 6 9
=
G 0% R 8D . . 4 A as88 - 4. e *. *** e 4 e - e. O .ea a. . . D. O 3 ** #.* ' 'I.( JJ $. ==. a e. en == - 9 M . *
- et so . m .
( :4 ***
. 3 e ... .e. a e ..
.es, e
eh e. . .* ce a= a= e se .e.m 3
. , ..g.. .e. ah U e e .O .t.e 7.- -4 1 .e=ee ..e. as 3 e.p e
-v s m. e a u a.
. u . * **O
<J'e ' es
-9 a e.w e e B 3 kB -
7 ? ee . . o som I t...; w. .. e u m. a. a. I. e w ** w - ad .4 m ~,1
- e.
.e...
ee e. 3 s-e%. .N 9 4 e. e 3 09N******
'?' == QUe O G %. 9e % e W .....
I
'?" * &
a S Oru e a..% am. 3 e %.**M% %.%e4% . .)I el el 2 e
-8 a a e n%.n= %. .
t*
.; y g % . .%.%
.a am
'J.} .
e4 . I h- l, j - ai 4 k ...
-S -
W. 1 r
] .4
.i i .
e.
+
I A - .'F pP 7 (y _
- . ..,.,. . . ,,. . , g om,,g.. .. , .--.m.m ,;;w yy,y ,.r g.:g.g,n, gmgny py.,pq7.,,n,.
n ,. . .
. . 9 -
,k '"* t .,P i >= Void Coefficient of Reactivity ij . (%Ak/k/%AV/V)
>] 0.4 s i - .a -
6 d A
'4 - A
;d..
.0
,j . .
s _ a d. s _
'i
- LEQ =c
.n Ji -o.4 - EEU '
j a j _- a 1 a o 4
^
, -0.8 -
a
.i 's-s - a 4
21,, -1. 2 - l - o 7 ..
.4
- , a J
i
-1.6 ' ' ' s i
- f. n ,
,jd.. L-77 L-67 L-57 L-47 L-37 L-27 L-17 L-07 4, LEU
- S R S R R R R
-f-i
$!; HEU -* R R R R D R R R
'[ R = Regular
;; S = Special y D = Dispersion (HEU only)
J,i H Figure 1. Void Coefficient of Reactivity across d -- 3 an East-West Traverse of the FNR Core n.- 9 for LEU and HEU Fuels (center of core) )
)
s t
* ~'
~~ '
I *8 ' * * * * * ' s" 4 " ' " * * * ' _y a =
==.9 +,e< -
..,.m,.4,, ,
u,, :;.. s n: . w m--
.e ._.a -
._....~._m._......_m-
. _. . . a . s -.1 .. .- ._n..... .. . . , < . . . - .s.. . . . .-.-..
,j . . . .
- 4. , ,. ,
u 10 . 4 a, y ' see eesarie s ao ensvio.: DO DO TANK 2 TAMC 1 . u.. a n.. 2 ( . n., e n ..
. i g 23.4 C 33.4
=
x .i:". . x
-4 ; 3.n . .s 4
t mer n.s
==
=
~. j i w 1 1.., i.n
's! 1 3.3 La e.
~c j , ...., .u. .
c:N I A s'.*, C A '" C 1.ss 2 ;i .w. i -8 ' a I a.u 1 *
.n s... 3.m 1.w .as i.es i . ., a.as s.n a.u a.., i.te 1. si :.n .s:
'4 .n s.a i.ee s.n s.n s.u .n '" 8 88 LAL-- 8" 8" '" 8" " 2.32 *** '"
-&! : .n.e -se.& .u.s .e.s .u.e -e.e .u.e -n.e ~ " ' *8
- 8* **'* 8
1 - g gn g a.n f)u .*
- 11 s.n 8"
*8
< i.., '" i ..a n -is.e '. sa "
- 7
! 1 l
<j .
; gmu.. m .anu. sm, 33est mem.t Elase gesaf th EDW8F me.m.T ELI E 60Caf!0 n-s.a. s.- .. .
n - ,,,,,, n_ e. ,.,.. u n. . i. u.u- a .
. - . < = - .
.j ; .e.e a .-se .
..; }
m , l'; . en sagttyng i '. 1 D02 TAMC e n.. n.. L - [ g 23.3
- r. ; sus 2.n g an. .a.n l1> y 33.4 .
- a T -
'j .
&.S& A.84 5.e4 1.44 1.?? 1.ee I L
. 4 1.16 8.39 L && t.as 5.34 1.18
.g
, .n., .n., .n.
f.Er
.n . .
har
.u.. .n. . 1.7 '
A 8" 3 1.ee C
- e
*LI.I i.<
- r. 4 t.aB Lar - #
4..*3 1.74 1.78 1.M 1.01 1 43 1.8? 1.M
.M 1.M 1.83 1.47 1.68 Lee 1.38 .92 4
.n.8 .n. ? 50.5 .it 2 4.8 +4.6 *14.4 .is.4 e< ' - i se tar R. s. . 1.5
' s -
/ a -
.M -
t.EOPARD - d
- 4 i.=
i .2, '1 . .. M' .a = '
-]
? : l I L.3 i
.,4 fa 0 20 40 60 r moi. . , , Fuel Burnuo ('r.) 3 ==*" 8'8 =" '*"" Figure 5. Infinite Multiplication l: Factor for tEU Fuel , .3 i i n n. s r n == . = 6su cw _j i ins .e. am
- s. . u e m.. <
s I I h 9 _ _m . r , s -~ u . m .w- -. ...-.a* -- - - - - - - - ' '*'*" ~^~'
4 - , * - u- . -
..- - :2 _ t.wg m m ; w ruw.a msys y v3,n.,g;.~:;vgr,77 r.~;<n y .g,$3 arc'
a 1
3 g
- s-i, i a
0- APPENDIX C
?,
4 ,
]-
k, Results of In-Core Spectral Measurements J:
,k If , i, -
d
= .J 1
I e 8 k i4 l b~ 4
- I ..
i :4. 1-
'4 Ps b
1 9
'$ t, I
a Y Y S
'N 3
J .
-2 . k, i i
e M 4 4= m, I w
>1 .Y p
/.
De 4 e 9 4 9 e* b "*
- w
'e a
9
==#
Yh.
+ !
-4 ,
+4 A
.a h
A ,1 f e w . . --,pe,. , ..n ..n.. -- - - - > - -~ ~ ~
. ** Wue * ' 1
* '
- 1 4,% ' ?" . -. -3 .y 9*
.t * .
'......*g
*' ' '. -.-.A;'
* ['* #g ,k *2 ' '.* Y4,(. * }} 'N * '., f 5-
# [p.c [. +8 5
. 6f er - < -
*. ., . w .a, '
. .w ..: aG.; ;;. A ' .=','y'*04t'eafi,'.t'Q** . w & . n. s,'1 L 0,-g;g;,;,sji
.1::q b4_.,g&
,~~~* 2 &?.:s a G;G $.. W ?.~?ul.W T X i -.-- c . AL.-::i2.'.h
- s >
el l M.;e e i i
. t '.k.
r3 . r 1
> .4 .- .- ,6_ .
2'!
. -1 ji ' . ..-
N,. !' 0!
..O P4 k
M.. e I...
- k. .
l lr a t 7
' f. -
u '4, t' r.- e , l (.-l , - ,. ! e r4
-(* '2 -1 .e 4#'
44b.i
*, j g 'I.e .':1 E
- 1
\:[ .
r
,j p
7 - p t l M t' 4 4
'i em.
s 8
. -se'r N
le ". i eM l4 vesi N
..) '
~
-i l) .'M
. .a, 4 fa li,!-
O 4
*d'd ?* ,-4.h .e.
4 L '.! .. t a.-
% 6 . r.f
- r? +5
., e
..i, 6 .J .=
Is' E n
, 64
$'t
?g a 7 '
r
-11 Ai
$j - C a -
- e. 26 e
~
A I 1 P.
+
i' 4
- a W
. r. -
w
- 1. -
4,4 ., O g - w g y- --=ww w-
e
. :.%. ;:v;y.uygr?;mmg ncm .:msw:mpywquyggr.cseg7ygqqqq:cqyqf:'y. T" i .2 .
[1 7 e
.4 a
q- TABLE OF CONTENTS a
$1 .' +
LIST OF FIGURES . . . . . . . . . . . . . . . . . . v i LIST OF TABLES . . .. . . . . . . . . . . . . . . . vii j I 1. Thermal and Epithermal Flux Reaction Rate M-
. .; Data Measured in HEU and LEU Cores . . . . 1
- 2. Fast Flux Reaction Rate Data Neasured in N)' -
HEU and LEU Cores . . . . . . . . . . . . . 19
,- 3. Thermal and Epithermal Unfolded Spectra . . 22 ' .! 4.
Unfolded Fast Flux . . . . . . . . . . . . 43 y }, 5. Summary and Conclusions . . . . . . . . . . 54 4.. T ,_ REFERENCES . . . . . . . . . . . . .. . . . . . . . 58
, j
- i -
3, . i - i d b 3
-'j ,-
Ml c:
$d e,
L4 > Som M . t-e, , Y l 3 M G~
- H
- t. .'
w .
+- . ?, :b >t' 1
w
']
t 1 iii ( . . . . = _ . . . . .-.~---m-- --;_, --n . _ _
[* - .
- N
/. t . .. < -t l -..4,- . _ . . _ . . - . ,. ,_ . . . . .,, . . , . gg ,. g ..w , ., .. -.
_, . . _a u . . . .
..u d a . ..~.w'.%6...,.,.u .- . . f j
< _ . . ... . -7. .,y,3, -_ _ _ ,.- . +,.
..a_. ..w.a,.wfua, , u . . , _ , _ , . . . ._, , ,.
1 * .
- s
, 8 e 2
4 l .e 4 I h
~ ; h.
' .1 i bl r
= .1 O
- 8) E
.s
~e 4
,e I e I
- .e Y
#e m.-j !
.g . h1,
.d.
,dS O
.i.
1 N
.G O - .>4:
14 =
, .j . . . 1 4
6 4 d b i e
?
L*i 5
+
y e Ammo 4
- .e.
e. 8
.i .A F) 9.
- s* .
,.=
1 I' L1 .. Eg. O
..,9 so
['!
}
=J L e
e n, ' 4
- .e . e
, ene 4 h U
sJ 5
.-k *
.a D +
f/ .. ss - 4 b** 7 1 A v 4
- I
-4 'y. I as . 1 .
s t 's t a j -
'l, ,
l [? , iI
.. - V ~ '::.u :.w. . . - - , .- .- ,, . ~ . - , ._ . - . - , .. -. . . . . . - - . , . - . ..- , . .- . _ _ . . . _ -
- ~
r .
- a. . _ . .
. m. ; .g._..on, , en,% dye:qght- A ;;.i;rcpp;tq.:_ egg gy.g
- isgr"
. s .t,; .
a - - 7" .
?,
0 - LIST OF FIGURES
.5 .
n.-
, 1. Core' Configurations for HEU and LEU Special i~j j Holder Measurements . . . . . . . . . . . . 2 @H -
- 2. Core Configuration for HEU and LEU Regular
-1 y_ Assembly Measurements . . . . . . . . . . . 14 F.)
i-4 ., 3. Core Configurations for Additional LEU [j -
'. Measurements . . . . . . . . . . . . . . . . 16 b- .
- 4. FNR Unfolded HEU Spectrum . . . . . . . . . . 30 l'J 4
j 5. Iterative Unfolding Example Using Mn . . . . .
33 e
- 6. FNR Unfolded LEU Spectrum . . . . . . . . .. 39 j- 7. , Comparison of Normalized HEU and LEU Spectra . 40 -
)7 _
- 8. FNR Measured and Calculated Fast Spectra . . . 50 i.
- 9. FNR Measured Fast Flux . . . . . . . . . . . . 57
.c 4
5
'PW ll .
- g. '
M s.-.) \ .- l l
>e .i y .a, t-0 s.
eg n . l-f " M. 3 q:.. ,
- j
.[-f . ,
- l. I M- i l
;4 W
,s g 4 "0
- q. - l l '?
! V 9
.' .. .- - *... e
..s.>u......,--~- , =m .w ,st
.c--e .,- ,*. y ... ,: x"-n ,8,
*.S A MJ s . _. . . . . . . ._ ..
... .. . . . _ . . r. -
-wma.w ~.v i
e
, <a: k.,,. w*.3..u- ~~:e. m, -
,p,,,
,_..6...._w_.
(M. .) ..
~
!'( F .4 ga G m l .5a 0 e %e e cl . . 0 i% E i I*. 'O e
- k. $.
4
- 1. .~. e j . .i #
l .iI ) 1! ..g
- e '/g h' ..
1-1
,c 3 ,3
.- }
'd S '. t
,4
-t
'1 .
+,
'.'.4
'k
'l , ,
.t i
y3 1 - e t S
.h
.J' 3,- .
e-ba I t A _.
~
- J
' _ .*> N, M
. -1 v
4 4 e e O e Be .
' ,4
- a
') ==
h' .]
- i'}
g.,
.u -
,A
,g :
*4
,'- 1 4 d 6 1
.+ l,
'eed
'. e I
.?
- 6 I * .
7;*. . h*h - TM4we' .e- ' M- . 7 LJ F==T II).7 #'. MN E.L wv., - - - - r. --rar7tw 8 e w. m T'
-n
- N "wTr.**".. ..e s.3 1
', n. _ _ _ . -
.x .- -
. w
_ _;gm. . , ...p.m,m; gg ,gg.
,,_g.pg . . . 3na. . y ,.
7 .' . - 4 0 . M . ' 1: 199
$" LIST OF TABLES '.1 f, Q l.A. Saturated Activities for Reactions Dominated 9 L; by the Thermal / Epithermal Flux at the HEU i special Assembly Sample Holder . . . . . . . ,
3 i' dj 1.B. Saturated Activities for Reactions Dominated f, by the Thermal / Epithermal Flux at the LEU
.) . Special Assembly Sample Holder . . . . . . . 5 ;x <
5- 1.C. Saturated Activities for Reactions Dominated A ,, by the Thermal / Epithermal Flux at the LEU
]
7, Modified Core Special Assembly Sample Holder 6 3 .i
;j 2. Factors Used in Assessing the Uncertainty ,,7 in the Activities . . . . . . . . . . .. . 7 M X T*
- 3. Comparison of Cadmium Ratios for HEU and LEU f, Foils Measured at the Sample Holder . . . . 10 j 1:
iJ 4.A. Comparison 'of HEU Saturated Activities at the
'j Special Assembly Sample Holder Versus Core s ; Center . . . . . . . . . . . . . . . . . . . 12 da ,
4.B. Comparison of LEU Saturated Activities at the
- Special Assembly Sample Holder Versus Core
] Center . . ... . . . . . . .. . . . .. . . 13
-a" 5. Average Iron Cadmium Ratios for HEU and LEU
., a
} Cores . . . . . . ... . ... .. ... . 17 N 6. Comparison of Subcadmium Fluxes Measured by 1m = w Different Reactions . . . . . . . . . . . . 18
; 7. Saturated Activities for Reactions Dominated by
-- the Fast Flux . . . . . . . . . . . . . . . 20
- m. .
'l- 8. Comparison of HEU Unfolded Activities with a,
; Measured Activities . . . . . . . . . . . . 25
'j j 9. HEU Unfolded Sample Holder Thermal and 5 Epithermal Flux . . . . . . . . . . . . . . 26 L
f.j"; 10. Comparison of LEU Unfolded Activities with Measured Activities . . . . . . . . . . . . 34 y. M .- 11. LEU Unfolded Sample Holder Thermal y r, and Epithermal Flux . . . . . . . . . . . . 35
- < ja 12. Broad Group Comparisons of Unfolded HEU and
('i LEU Fluxes . . . . . . . . . . . . . . . . . 42
@' . 13. LEU Unfolded Spectrum Activity Comparisons . . 45 1-a -
U vii ,y 6,s_*
- _ , _ _ _b
- i. <.
..= . - ,, '. .: -?a-a n .+ ;y - -
,. . + -
-q. :w m1,,w... ,..
r ~. a.m.; ,rs,,,
~
<+,%. ,a . .. 2 i
1 4 I O *
.l 14. Comparison of Deviations between Measured and ') Calculated Activities for FNR and ORR Un- ;3 -
foldings . . . . . . . . . . . . . . . . . . 46 A,
- 15. Unfolded Differential Fast Flux . . . . . . . 47 .
",, 16. Analysis of Integral Flux Errors . . . . . . . 49 .
e ll J
-, a I
t-<let ,
; i - >e p $l e 's lT t. ? ~
e-G r r.
'4 2
r a
. 1 e.
G e m e Gib
. - -. n._....
e 4 em 4 4 s'. I
' v.
,?
.b* e T
e
- 1 m
Rama som a 2
- ri 11
.u' - WWD ki 3. O t *. VI.11 '.w ; d 6
,A
~. -feiIN A L.- . - - . - - - - - - * = - - - - -- -- - ' - -- - --- - " ' ' ' ' ' ' " ~ ~ -~
1 m ..
. ~ , - # m.m.-n ,~ . y , .._ e.,,m.m.m .m
,,,m., . . .
jg.p, y g ,,y ,a e
).
?.." . .i .r, i hj "j - y In this Appendix, we present the unfolded HEU and LEU ya spectra. Since the refined saturated activities may be more I j Important to some readers than even the unfold'ed results,
.a some comments on these data are also presented. Although we 1
l
^; .
s have a variety of unfolding approaches at our disposal, we }3_ shall limit our discussion to two unfolding techniques }:.g .
- the semi-empirical method and the integral unfolding '
l l s method. 1. 4
" "hermal and Enithermal Flux Reaction Rate Data Measured c,n HEU and LEU Cores 3
a' , i
'I Multiple foil activations were performed at a sample
[ holder in both the HEU and the LEU cores. Prior to present- [l
'/ 7 ing the data, a few words of caution are necessary. Figure .j -
1 shows the core configurations present for these measure- [' i ments. Note that the HEU measurements were made in a large, i _ equilibrium core. In contrast, the LEU measurements were ! r made in a small, clean core, also shown in Figure 1. Be- f-cause of the differences in the core sizes, one must be ! j~ careful not to erroneously attribute the absolute differen- t ] ces in flux intensities (or activities) solely to the en- [ i f richment differences. '
- - 1.
I Table 1.A shows the saturated activities per unit tar- ' get nucleus for non-threshold reactions measured at the sample holder in an HEU core. The uncertainties in these values are difficult to determine precisely. This is be-I. q- cause the expressions used to determine the saturated ac-a tivity are nonlinear, and can be quite complicated. c ( However, the major factors which contribute to the uncer- -
'(.
tainty can be separated out, and the following expression ;
._ can be used to obtain approximate values for the errors of a (!
1 ji W straightforward isotope production and decay scheme: i
~
2 6Am[6m +6C +6P s +6F +6L 2+6e 2 2 p +6S ik +6f +6Y 2 +6A2 ).5 + 6 s 1 4
).-
- 1 b
,,-gw. % -
M T -' " * * * * '. ~ ~
- = m ... .c a n = w
- w . , n n '
- x -
. " = M. M '=E ei*" i ".."'= '_ # ' # " " """r:..
g. f
,'t i
* -l r a U
i{u
.x f s s
$ November 11, 1981 i january 22, 1982
>j
} HEU Equilibrium Core , i.EU Batch Core (> ' [ CR CR CR CR i _._ n o i CR
~ .-
CR CR CR h
- t t fp B
i - H.
?
- v. ...
d. n..
, D2 0 Reflector D20 Reflector
[i. t, -
) -
,: a,.
.x M
Q CR Control Rod (b) j r ,. i 4 r Sample Q { Figure 1 .. Core configurations for HEU and LED special holder measurements. {"
' .. E j' '
.:.' pj ,
) .[9 8 -
.. s .
"#., ' ) Yl
'l l l l l *'1 L'^1 k ^ ] 8 T '_]
i 1 '*" F 1 *' ' ' ' t
-- x m w o r w ar m w c... u m ; w . g w .
- w - u a_ m;zu.:c,,..;.;.ca m carc:a . 5 L 6 .. i 4 4 . .. J LJ .I L.4i i s. ,
g ,. 3 g.. .: g,... g .,3 g , ,i 'm p g , ,. g3 .. g g .g ' ' g ,, -
, e, . , t.
N *
- li .. !
jj . li U; . 1
- l. e.. Table 1.A 2
'b': Saturated Activities for Reactions Dominated by e 1 the Thermal / Epithermal Flux HEU Special Assembly Sample Holder f:
.i Y
r iti BARE FOILS .> CADMIUM COVERED FOILS C I REACTION CADMIUM i-
] ACTIVITY UNCERTAINTY ACTIVITY THICKNESS UNCERTAINTY 9i (per sec.) (percent) (per sec.) (mils) (percent)
T, _e 4. Pe58(n,y). (FP) .287-10 4 .209-11 20. 4 Co S9(n,y). (PP) .813-09 5
.113,09 20. 5 Au l (n,y) .400-08 8 20. "
.220-08 4 )
Cu 63(n,y). (FP) 4 j(, .833-10 5 .668-118 20. 7 1 Hn55(n,y) .249-09 5 - f h .a Ag 09(n,y) .101-09 8 .273-10 20. 8 d Ta 181(n,y) -
.622-09
- 20. 8 5
p W 186(n,y) .828-09 8 .239-09 20. 8 j_ U O(n,y) .270-09 9 .234-09 20. 9 - h,; (n,y) t,. Na - -
.484-12 40. 11 l U 35(n,fisslon) y
.106-07 10 - - -
I,;'
.f
'.T .
q .',$ I
- 2 G x w xr:.-c56Lhu s?:=r2&G!a.2'." O r % -
" ' . c a- &W M&' WM&M' h" ~ 'NE h'5 ""* y
- a. . . . -
s,
}
t t1 li 14 Y [ p
- i.
q BARE FO!!4 CADMIUM COVERED FOILS f' I REACTION CADMIUM ' t ACTIVITY UNCERTAINTY ACTIVITY THICKNESS UNCERTAINTY '- ! (per sec.) (percent) (per sec.) (mils) (percent) ' i - Pu239(n, fission) I
.185-07 10 - - -
2 f , Th232(n,y) - - 720-10 20. 8 Sc 45(n,y) .470-09 0 .167-10 20. 7 Lu176(n,y) .724-07 7 130-08 20 # 6 ' Dy164(n,y) .414-07 6 571-09 20 7 h Dy 56(n,y) .167-08 5 .106-08 20. 5 l F Ho 98(n,7) - -
.108-10 20.
10 3 Zr 00(n,7) -
,547-12 "i
- 20. 4 Zn64(n,y) -- -
.250-11 20 5 -
Zn 8(n,y) - -
.352-12 20 10 l
Zr 96(n,y) -
.810-11
- 20. 10 ,
Q
'.1 8*8 The Cu 64 branching ratio is uncertain b 10-30% according to the literature. 9 Our evaluations have shown this uncerta nty must be much lower. The cadmium ,
ratio should be reliable since it la independent of the branching ratio, - f pl .
. ...e. , , .
I i
.. 4 2il ,T* 1 'l 'l __] ; _ .. I ) ("DJ !! "I K"
- 1 I""I ~I -'I '" ' " ' ' (
f
__ pap g q. . . . . .
. . q. . . 7 .p_ g .. ._ . ._,. . . . :. . . :.. . . . . . . .__,,.;. .
l
.. n 1
y Table 1.8 Id f; ji Saturated Activities for Reactions Dominated by j the Thermal / Epithermal Flux at the
,j LEU Special Assembly Sample Holder .
1: . 3 BARE FOILS CADMIUM COVERED FOILS (' REACTION ACTIVITY UNCERTAINTY ACTIVITY CADHlUM (per sec.) UNCERTAINTY (percent) (per sec.) (mils) (percent) . 58 gyp), Fe 4 ,,7), .263-10 5 .219-11 25. 5 Co S9(n,y). (PP) .806-09 5 .120-09 25. 5 j Cu 63(n,y). (FP) -
.778-11 "
- 25. 6 g p Hn (n,y). (FP) .261-09 7 .243-10 25. 5 )
Au 9 (n,y) .373-08 8 .224-08 20. 8 t.1 y Il Ag 9(n,y) .103-09 8 .341-10 20. 8 ff U 238(n,y) -
.232-09
- 25. 6 U 235(n,fisslon) .960-08 8 .470-09 25. 8 .
Pu 239(n, fission) .180-07 8 .590-09 25. ' 8
;l Th232(n,7) - -
.800-10 25. 5 3 Sc 45(n,7) .499-9 6 - - -
7'.
**' The abbreviation "FP" means the measurements were made.at full power (2MW). 4 t
I: k-
..r.. ._ . . . . . . ,. . _ . - - - . . _ .
--. .. .; iWuGEE: ..i. x. Md;:.L;WL a%MMW: . m - .. e, :5 ,M,ir.2m.2.4:aMa 2;L::Ls a . L.:..:.
. _ . . . . . . . . . . . . - . . - a. .- .-
t, l'
',.' i-b .}
- i. : ;l 4 I:
I'.i h w ' r
}: -
( Table 1.C - 1
} Saturated Activities for Reactions Dominated by t the Thermal / Epithermal Flux f LEU Special Assembly Sample Holder (Modifled Core) !
g. I t j' BARE FOILS G CADMIUM COVERED FOILS
- 5*
REACTION CADMIUM ACTIVITY UNCERTAINTY ACTIVITY THICKNESS UNCERTAINTY (per sec.) (percent) , (per sec.) (mils) (percent) , 2 Au I (n,7) .428-8 8 ,209-8 20. 8 m Ag109(n,7) 906-9 8 .216-10 20. 8 h jj Ta101(n,y) 905-9 6 ,566-9 20. E 6 }. b
; W186(n,7) .947-9 6 - - -
L g Sc40(n,7) .519-9 7 .168-10 20. 7 .. l Lu 176(n,7) .751-7 6 - - 7 -
?!
1 Dy164(n,y) tt-, i
.430-7 6 ,462-9 20. 6 [i; In115(n,7) -
,292-8 20. 8 h3 l Cu 63(n,y) .792-10 5 .624-11 20, 7 -
Hn 5(n,7) .242-9 5 .166-10 20. 7 R i i
.- t l ,W ei .__J .i ._ )
. ~.. I in~ 1 ': r 1 r 't - '
' li'
,-r s g: ,, _,
af. -
. ..+ ; . a .; .-v -
, sm:, gam,,.y,mmw.,w.,,gmgyjgumP&
9 :' .
??. .. 7 d, '.
3 Table 2 1 i
' Factors Used in Assessing the Uncertainty in the Activities
[i , ,
], - Consideration Symbol Typical Error (%)
J _. f ; Irradiation conditions . .. . . . . . . p-3 1. Power reproducibility (full power) . 6P, 2% i7 Power calibration (low power) . . . . 6% i ; 2. Power ramp corrections . . . . . . . 6F 1-2% j 3. Foil positioning errors . . . . . .. 1-2% i -- o _, Nuclear Parameters . . . . . . . . . . . i t f 1. Half-life . . . . . . . . . . . . 6A 1%
, 7 Effective half-life (Co$ ). . . . . . 4% ]_?
- 2. Gamma branching ratios . . . . . .. 6f 6N y 1-20%
; 3. Number densities, isotopic abundance '
1%~ s- 4. Fission yields . . .- . . . . . . .. 6Y 6-20% i Mass Determination . . . . . . . . . . . 6m I'-
- 1. Mass measurements . . . . . . . . . . 0-1.2% i
)~1
- 2. Fissile / fertile material composition
- 3. Alloy' compositions 1-34 .
L.
. . .... ... 1-24 e Countina Parameters . . . ....... i
;]- 1. Counting Statistics . . . . . . . .. 6C 1-64 a-i
._ 2. Absolute efficiency of detector . . . 6,P 6%
s-
- 3. Count rate corrections . . . . . . . 6L <3-6%
- 4. Sample geometry corrections . . . . . 65 1-10%
j-
- 5. Irradiation, counting,-and wait times <1t n
fj ," Note: Errors are quoted for the 954 confidence level. d', ..?}. A . 1 j~t
- 1 .
Up 'b s ] ,. . .v . 4- '41* ' s
,;*' ? w a z;;;c: s t a w :x: m . x q n :e,m: S 2 b5 2.2T.i. W $k n T M 5~~~l . a.{ & 4 _ D J - 3 8 { 1 .: 3 - 1 m ': E$ 5; The symbols are defined in Table 2 , and the prefix 6 im-plies the relative error in the quantity. In accordance g with the ICRU guidelines, the term 6 g is defined to be the ~ maximum conceivable systematic uncertainty in the measure- - g- l ment. Table 2 shows the factors considered in assessing the r magnitudes of the uncertainties, along with representative I (,j values. Note that we have chosen to quote the uncertainties A .
;,: at the 954 confidence level, so that these values correspond _
j to approximately twice (1.96) the conventional standard er-gj ror. These estimates may appear significantly too large since several completely independent measurements of the L) l . same activity normally agreed to well within the quoted un- ~ certainties. But for the determination of an absolute ac- - tivity, both the relatively.large systematic uncertainty in - the absolute efficiency of the detector and the absolute o re power level can dominate. In addition, while many of the _ d{
- g. other factors are frequently small, the quadrature sum of
( several of these uncertainties together may not be insig-( nificant. In light of our experiences, it would be quite $ (* ? J surprising to find absolute activity measurements quo'ed t g'f with uncertainties on the order of one or two percent. ~ H Table I.A also shows the estimated uncertainties in the - Q measured activities. The full power measurements are noted - (( using the initials "FP". Since these measurements do not a O q require a power calibration factor, they have lower uncer- _. [5 tainties associated with them. As mentioned.above, the ab-solute copper activities should be viewed with caution since )4 q, the gamma branching ratio has a large uncertainty quoted in
~
the literature. q H m The saturated activities presented in Table 1.A are d used directly for our unfolding of the flux. For some h readers, the saturated activities'may be most useful since ~
- these can be used as benchmarks for other unfolding ap-proaches. However, recall that we have incorporated the ef- -
- g. .
a a N 9 dj 7
a.- ay - ,
. . n; , 4; w- ,
" m . &Y. , of W ,& kL W. h$a uk N4C*f*-Q.qQfTs_;<pegp>.tyhq.%:VeR1.h*hAby4 6'y p'*y.
A_ Sq
,3 -
(f, - 9 1.. . facts of self-shielding in the cross sections instead of l correci:ing the activities. Thus, users wishing to employ !
- q. these activities in their own calculations must apply self-j shielding corrections. l d,
os i Table 1.B presents the activities which were measured
- j .
.in the clean LEU core presented in Figure 1, along with an f _
-~ ~-
estimate of the uncertainty in these values. Note that we ' j_ have chosen to present only those reactions which were used a. in the unfoldings. That is, we have not included those ' reactions whose decay schemes or cross sections have very
~,
large uncertainties (such as the Dy 157 capture reaction). Table 1.C presents the activities measured in an even more compact LEU core. In this case, the four fuel elements l' A]- _ along the far right column of the LEU core shown in Figure 1 j.. were removed. Since the larger LEU core shown in Figure 1 3 . 4_ is more comparable to the HEU core, we have chosen the data i of Table 1.5 as being representative of the LEU fuel. m Table 3 presents a comparfson of the measured cadmium ratios for six reactions measured in EEU and LEU fuel. Through comparison of the HEU and LEU measured values, it is ' j~ apparent that the LEU spectrum is measurably harder than the -
]' HEU spectrum.
W This can also be seen in the final column of-a Table 3 which shows the ratio of the HEU to LEU cadmium a'- fractions. The cadmium fraction is the cadmium ratio minus one, and is crudely representative of the ratio of the sub-n cadmium to epicadmium fluxes. Since the ratio of the cad-mium fractions is a ratio of ratios, the uncertainty in
- f. these values is rather large, i.e. 10-154. Nevertheless, the data consistently indicates the harder nature of the LEU
, spectrum. ' st Table 3 also shows the cadmium ratios which are y predicted from the spectra calculated with the HAMMER code. [~
..t_ The effects of self-shielding have been included in these g calculations, so the measured and calculated cadmium ratios F can be directly compared.
These comparisons are quite h ~
~'
. .. .iu.RkMG GX.U.; ti;;221h'.n..AE DH2Dil?LC Lx,. J. ,.iza.L;.k.LL .'r.2!% BC hr:;taLu.2c%.~ ..:.:.;;i
. _ . _ _ . . _ . ...s .. .a 4.
. . _ _ . . . . . ... _.. .... ..-.... .... .. ...-._.:-- - .- a.>. ..- - . i
.t 4 i 'i j U g .. ;j
) P I
;l 1
4 ?i 1 s I. l. Table 3 . jf
'M Comparison of Cadelpm Ratios for HEU and LEU j, i
Foils Heasured at the Sample Holder , f.j , ' h. h HEU LEU CADMIUM FRACTION I ' POWER CADMIUM CADMIUM RATIO REACTION PATIO RATIO (HEU/ LEU) E (FP/t.P)8*8 k~. t HEASURED PREDICTED HEASURED PREDICTED MEASURED 88i PREDICTED j n , Fe (n,7) FP 13,7 9.0 12,0 8.0 1.15 1,14 j l Co (n,7) FP 7,2 6,5 6,7 5.9 1.08 I 1.12 Au ' (n,7) LP 1,8 4,74 1,7 1.66 1.23 1,12 S i Ag109(n,y) LP 3,7 3.0 3.0 N 3 . .) 1.34 1.14 $ bg Hn (n,7) LP 15.28 12,9 10,7 10.3 1.46 1,28 k' l Cu 63g ,,T)- LP 12,5 10. 10,3' 8.9 1.23 u l 1.16 II 8 9 l The abbreviations FP and EP stand for full power and low-power measurements. l 888 The5:sh0 HEU cadmium ratio has a large uncertainty due to a 15% uncertainty {.i i in the cadmium covered activity. $$ j This activity was not used for unfolding.
.y H
888 The low power values have a larger uncertainty (12-15%) due to the additional U I uncertainty introduced in the power calibration. ,]y Q 5 The LEU bare copper data have 4 large uncert.ainty and are not used for l unfolding. . y
' .. >V q
..) :
1 p. . 1 p .c n
, a/1 1 J i ! !
'i ~J
_J : __ )
! 8 5 '1 8 y.q .
(
, v. 46M niw~m- - - - -44 b NhW O d e st m e w1w N " W'*W"!, - i 1gA
=*
l
. 4 .
i k?[
- 11 .
l -(, gll h"4 interesting since they show that the calculated spectrum is jj i- too hard compared to what the measurements indicate. ~ This i!
,i
$'- is most likely due to deficiencies in our analytic model. ), The HMOSR code performs a unit cell calculation with j _ reflective boundary conditions. As a result, the effect of ! [ , leakage on the spectrum is neglected., Since leakage tends i 5 , to soften a spectrum, the~ calculated spectrum.3)23 M be too '! i hard. This is precisely what is observed. Since it is not ! R critical that our calculated spectra agree precisely with i y- our measurements, we have not pursued this further. *I I 7 However, it would be interesting to perform 'a similar cal-E_ [f
;i _
_ culation (for example, using ANISN) with a vacuum boundary condition for comparison, [l i i; i 1- '! Table 4.A' presents a comparison of bare and cadmium ! t
- covered saturated activities measured at the center of an . !
1 ., M core in a regular fuel element, and in the special j f ,,. sample holder in an M core. The HEU core center measure-
', ments were made at'l MW in the core configuration shown in I l
i [ Figure 2(a). Since these two sets of measurements were made i at different core positions in cores with different fuel [>l i configurations, the absolute activities cannot be meaning-fully compared. However, from an examination of the cadmium j j_ ratios, the spectrum can be seen to be slightly harder at ; i, the core center, as correctly predicted by the HM0ER cal- ! L culations. The second half of Table 4.A shows threshold reaction data. While we shall compare the W and LEU threshold reaction data in Section 2 below, it is interest-P ing to compare the data measured in a regular fuel element 4 j ' (l to that measured in the special fuel assembly sample holder. .!
;i b
The HEU core center data has been normalized to the special ! 4 sample holder data for comparison. The normalization factor i was chosen to be the average value of the ratio of measured j activity at the holder to the activity measured at the core l l [ center. If the fast spectrum is the same at both of these ! ) , locations, then the normalized activities should be the same 1 l
- . for the holder and core center measurement.s. The agreement N
1- . . l .
. _pr' ;v U N'a y n'T .
"N~m:.". - : "'6+~e ~ ~~~ ~ p " " P '* i '~ ~ 2 '""'"'N"
^'
j_ , m. .
- a:mience:h.sm. w.,xw = G>:, ~.0 .* .: ud..:e:2C??Lp..W E 'al % :.. , c..w .,,- : t. ~.2%a.w ,
'.) *
,b -
..,- 12 I1 d
Table 4.A U . - A Comparison of HEU Saturated Activities at the Special Assembly Holder
/;..i Versus Core Center (a .
1 A HEU HOLDER HEU CORE CENTER3 1 h) REACTION CADMIUM CADMIUM a BARE El i COVERED BARE COVERED ai a 1 ;. NON-THRESHOLD REACTIONS 3., l , FeII(n,7) .287-10 .209-11 .141-10 .152-11 j Cu63(n,7) .833-10 .668-11 .453-10 .467-11 (a; Ag109(n,7) .101-09 .273-10 .540-10 - i NORMALIZED THRESHOLD REACTIONS - l >:
,1 ! Ti'6(n,p) -
.157-12 -
.160-12 _
~
.f Ti' (n,p) -
.273-12 -
.239-12 l Ti48(n,p) -
.422-14 -
.439-14 -
Fe ( rr,p) -
.117-11 -
.116-11
[j A1 (n,a) -
.961-14 -
.937-14 E
a, Zr gg(n,2n) -
.105-14 -
.104-14
.s,,
! NiS8(n,p) -
.151-11 -
.150-11
, 1
..>I Ni 0(n,2n) - - -
.309-16 -
'Q 1, li 853 These measurements were made on another (see ,.} 4 Figure 2(a)) equilibrium HEU core, but at 1 ,, la Megawatt. The measured saturated activities at the '
- ..j center of this core are normalized to the sample
.4 holder data as described in the text. -;'
g}
.)J - e !
~ii l M.g-
- 3
- i. f I e. ;
[ a]; -Ii ' ! :e 4, )3 .i i- . _ _ . . _ . . _. - . - . _
u .~ -
', ~~ - w.v;. w.w & h;fs .wmudnasmwnekn6mmm.wv mec my.me~y p . y
_ .3-~ a;- a 3.3 i J.
- 9 Table 4.B j Comparison of LEU Saturated Activities
,, at the Special Assembly Sample Holder tj versus Core Center .f' 1 ^-
LEU HOLDER LEU CORE CENTER ('8 REACTION CADNIUM CADMIUM II BARE COVERED BARE COVERED } j NON-THRESHOLD REACTION MEASUREMENTS t y-
- Fe58(n,7) .263-10 .219-11 .251-10 .293-11 y
.217-10* .279-11*
h CoS9(n,7) .806-09 .120-09 .808-09' .158-098
] "l
.838-09 .175-09 THRESHOLD REACTION MEASUREMENTS 8*'
~
Fe' (n,p) -
.128-11 -
.127-11 l Co 59(n,p) -
.217-13 -
.226-13
..a CoS9(n,2n) .301-14
.306-14 '((i
, ,, Ti46(n,p) -
.174-12 -
.185-12
~
j . Ti47(n,p) -
.330-12 -
.303-12 Ti48(n,p) -
.445-14 -
.490-14 i
NiS8(n,p) I { -
.178-11 -
.181-11 P..
k.i (*8
):
_ These LEU measurements were made on a different LEU i core (2/9/84) by B. Houser (see Figure 3). 4 4 3,. (88 These LEU measurements were made on a different LEU ' core (5/10/83) 3..Heuser (see Figure 3). i (88 The saturated activities for the core were
~
decreased by a factor of .595 in order to compare 4 ._ with the sample holder values. The core activities a have an uncertainty of 5-10%. 1-5 (*8
"' These LEU measurements were made on a different LEU j core (10/7/83) by B. Heuser. Other LEU iron cad-mium ratios measured at the core center (6/27/83) q vary from 8.0-8.3.
hi
~
e - - - . . _ -. ._ . . --_ . . . . -
~ 2D;e.asuzwaaiu.x12:Gx.ac;LLE2.01c.s " ,:w .- :xsmmewn.:palme.. ladusxim=.a.Lc
- h
..a-.....s.-..... - = -.: - - .. w .. s : :. . = a ax ~ - =- ."- ="
I l i I I .. .
?.
f.t m 9 t-
;f b
e. j J. t April 8,1980 October 7,1983 1 l _ _ [1 i ' CR CR CR CR 6 L L . I t
. o i. i. - i
- p CR CR CR CRt
- II t t
, Q 3, L L J' ' t;4 1
- h 5
D0 Reflector !! 00 Reflector i 2 2 4, 4
- i. ' . ?
9 (=) CR Control Rod (b) - b _ Sample s. R, V to. Figure 2 core configuration for HEU and LEU regular assembly measurements. {N ' .c] I 4 I
- ll h
. e .J T
.n
.fC . -
? A.~ J g , g ~ ,, n _ m . ~ - ,- - n = =- =remn>m -
weeW O 3- : if," - 15 j3 y 4 between these data is remarkably good, and indicates that .L ..t > above a few MeV the fast spectrum in the special holder can-y not be very different from the fast spectrum in a regular f-i m fuel element. While this is also expected based on the HAM- ?_ MER results, it is nevertheless an exnerimental verification ll_ of our assumptions, as well as adding credibility to the ac-a curacy of the measurements. 3 ~. 9_ 7 Table 4.B presents a comperison of bare and cadmium h 9- covered saturated activities measured at the center of an d~ . . LEU core (shown in Figure 3(a)) and at the special assembly i ; sample holder in the LEU core shown in Figure 1. These measurements also confirm that the spectrum is slightly har-k, der at the core center, as expected. The measured threshold reaction data for the center of the LEU core was normalized i to the LEU special holder data as described above. The LEU
\'
4e core center data have a greater uncertainty than the cor-7
, g- responding LEU holder data due to a larger uncertainty in
[ the absolute detector officiency. As a result, the 3.1% root-mean-squared difference between the LEU core center and LEU special holder of the threshold reaction data is larger [ :r than for the equivalent HEU data discussed above. Neverthe-less, this data provide another verification that the j._ spectrum above a few MeV will not be different from the
.1 spectrum at the core center.
H. . Table 5 shows the average iron cadmium ratios for both l- HEU and LEU cores measured in the sample holder, at the core l
;p, center, and in the heavy and light water reflectors. It is
;j significant that the ratio of the HEU to LEU cadmium frac-a{ tions are the same for the core and the sample holder. This j
~
corroborates our expectation that any spectral shift present .f at the core center will also be present at the special j' holder. Note that there is no spectral change observed in
] the heavy water reflector, and it is doubtful that any g- change would be observed in the light water reflector.
9 Table 6 compares the subcadmium fluxes measured in the e L_ , .. , . .--..-..-.-: - ---- - - - - - - - - -
a s.umswmc.3&ain161=a:GzKnuwa:wmwam.sc.:,we.stmmmaaneic;ua. o p o
- r. w I.
'J l,* .5 - F l 1..
W. p .d Fehuary 6,1984 .c
! April 25,1983 t,
i
- s. i,
- i. F l .. .. .. t b w
L CRL L CRL L L CR CR : 1 L L L L L L 7 t t t 7 (,
) L CRL L CR 'A L L CR CR t ~
l L L L L L s t t Il I:. t-
' 6
, E it l 020 Reflector 00 Reflector 1
, 7 i]
o I,' , i t. -
'a i, t-
'1
() CR Contml Rod L = w a -* n=t (b) i:
- Et 1
s z Sample l*
~
i ' J ,1 1 Figure 3 Core configurations for additional LEU measurements. 'i. o
. . .i-
. e
- y %
M g . $ E E
., r '
j--+
. ' 2.:grw;w.;. r myow.w;.o -wwvEwnwmWMM*mibMMFN?'"#(
a_ ,
.I M
a, . . 71 ~ -
'4, 17 3 ,
j- Table 5 y' . Average Iron Cadmium Ratios for HEU and LEU Cores h .. A e D 0'88 R20888 hj. Core Fuel Sample Core'*8 Holder 2 Reflector Reflector ?r_ HEU Fuel 13.7 9.5 20. - Sp LEU Fuel 12.0* 8.4 20. 26. 4 -
' Cad. Fraction'*8 .
d Ratio (HEU/ LEU) 1.15 1.15 1.0 - e t*8
.=
Measured between fuel plates of a regular fuel J element in the center of the core. Quoted cad-mium ratios are an average of 3 HEU and 2 LEU e measurements made in the core.
- L
'*8 The heavy water reflector is adjacent to the
- 9- edge of the core.
Measurements were made 5 cm. radially into the heavy water reflector.
- 8**
O Measurements were made 2.5 cm. away from the core boundary in the light water reflector. 8*8
,-r-The one. cadmium fraction is the cadmium ratio minus hp 8*8 For comparison, the cadmium ratio in the center 'g[
of a water-filled special assembly was measured w to be 20.
;.1 o
*f sample holder, using each of six capture reactions. The purpose here is to compare the consistency of the cross sec-
~
i L Jj tions and flux measurements. The measured to calculated 7 ratio is determined from: b f5 Ab -A c P . 9 fa(E)G(E)(1-E 0 2 (t(E)))((E)dE 5 t. 'L -l
&dkbQ:&$d.hd? "~.f.. . - l.'.'. n . . =,..... Y +.u. 4::. .. J. c~ . .. .u C.W L'
~~
s ' 9 18 n:. . i ) 1 , ,1, . Table 6 ' '.d i Comparison of'Subcadmium Fluxes '
.) Measured by Different Reactions -
.. ) ' d) , l L'; ' HEU LEU i' u, , REACTION MEASURED / CALCULATED MEASURED / CALCULATED 1
', + 7
{> j Fe (n,7) 1.11 1.14
) CoS9(n,7) 1.01 1.02 Il a
Au18 (n,7) .97 .95
~
- . Ag I(n,7) 1.02 1.02 [
Mn 55(n,7) 1.02 rI
. CuG4(n,7) .97 -
- o
.E where Ab and A are the measured bare and cadmium covered l'
c ~ saturated activities per unit target nucleus, a(E) is the *- ,.c 4 reaction cross section,. G(E) is,the self-shielding factor, - H ,~ . t(E) is the thickness of the cadmium cover measured in mean free paths, E 2 is an exponential integral, and ((E) is _ H- . energy-dependent flux calculated by HAMMER. Note that to N m within a multiplicative constant, the denominator is the ef- u.
., factive subcadmium cross section. While the resulting _
p: ' agreement shown in Table 6 is remarkably good between the q ~ (. :- reactions, we do find that iron is displaced from the ~ p;.1 l ;. i average by about 10%. This difference is also corroborated I
.j ' by measurements made'at the center of HEU and LEU cores .-
- 9
.. , which showed the iron subcadmium flux to be 164 larger than q predicted by copper, and 7% larger than the value determined IQ from cobalt. All of our previous measurements 1-2 which have _ i : s. N made use of the iron cross section will give a subcadmium g flux which is about 10% too high. Thus, we conclude that !!}-1 _ t the ENDF-IV iron capture cross section may be approximately ~ Dj , 10% too small at thermal energies. - N, o
~.
- .A,1
[l; 9 I .
. . _; , vb 5 - . I'b k * ** '
' MIM M* NA "E' #'* *# *#- * "# ' ~ * '
~c n:m,.. ;;. ,:. egg-ape ;,; gig merm;m: Ne 2mtC2'*!Eh";"'"592+WWWEW2'?
y4 1, . N~ - 19 C*' - ., 1 1; P- 2'. Fast Flux Reaction Rate Data Measured in HEU and LFU r .. SSISA n j Threshold reaction data have already been presented in f v Tables 4.A and 4.B for the center of the HEU and LEU, cores. (j We have seen that there is negligible evidence that the fast 5 . - - -- - - - - -spectrum will be different in the sample holder than in a E" and LEU threshold reaction data measured in the sample k; holder, and can' assume these comparisons are valid for
}--
~~
regular fuel elements. Table 7 presents a comprehensive set t g3 of threshold reaction data for measurements made in the spe-yj cial assembly sample holders for the HEU and LEU cores shown
,b,.. in Figure 1. After normalizing the HEU and LEU solid holder 5
a data, the data agree to within a standard deviation of 54. . ( This is significant because it again confirms that down to - kt approximately .5 Mev, there will be very little spectral " difference between the HEU and LEU cores. " Also shown in Table 7 is data taken in the air-filled
.[C sample holder in the LED core shown in Figure 2(b). This data has a larger uncertainty associated with it, but in-Y eludes the interesting Pt 5(n,n') reaction. This reaction l' - has a very low threshold energy (~.1 Mev), and will be help-
% ful in defining the spectrum below 1 MeV when the cross sec-tion is known to greater precision. If the hollow holder i data are normalized to the LEU solid holder data, the two
- 5, , data sets agree to within a standard deviation of 8.84.
q. While this agreement is not as impressive as the comparison ,[ above, it implies that the solid aluminum around the threshold foils does not significantly perturb the fast f spectrum. But recall the shielding correction is given by: j, r,J j, _ e (1-2E3 (I(E)t)) u G(E) = !!j~ 2I(E)t
- m. ,
s) Fi-
?
. _, , ,:. y v ? jM&, ' 5 t]; - \! ' '
M_ f ;__,,,. . . . . . ,_ . . , . . . - . , -
.:> a&"'~
!ad: trin .. '
'. = - . . - - A i --~:- - - w '
}4 ---
s .-. L . d w 20
- I) i li ;
Table 7
$i 41 1 Saturated Activities
..' -I for Reactions Dominated by the
! Fast Flux 11 Qi4 HEU LEU I2U j, REACTION SOLID HOLDER SOLID HOLDER HOLLOW HOLDER ;
n ; i f1 [] f Fe54(n,a)
.115-13 . 132-13 -
d. A: Fe (n,p) .117-11 . 128-11 .101-11 k! Fe 56(n,p) -
. 173-13 .108-13 A i > {
- m ! A127(n,a) .961-14 . 112-13 .742-14 bb \
;ji Tigg(n,p) .157-12 . 174-12 .120-12 c
9 j Ti'7(n,p) .273-12 . 330-12 .236-12 .
#I i I
Ti'I(n,p) .422-14 . 445-14 .308-14 $ g] Zn6 '(n,p)
.484-12 . 503-12 .322-12 -"
l Mg24(n,p) .215-13 . 225-13 .135-13
- Ni I(n,p) .151-11 . 178-11 .112-11 .
f) N Zr90(n,2n) .105-14
. 117-14 -
Np (n, fission) .234-1Q . 265-10 - fjl U238(rr, fission) .432-11 . 490-11 -
,s --
ijI Th232(n, fission) .113-11 . 132-11 - ' f In115(n,n') -
. 307-11 .279-11
~
5' Pt 1 (n,n') -
.518-12 2
M _ (.) > V 51(n,a) -
. 290-15 -
*~
- ? Co O(n,p) -
217-13 - - Mn U(n,2n) -
. 390-14 - '
i i r. Q >; Ni60(n,p) .251-135 -
. 405-13 -
! NiS8(n,2n) -
. 532-16 -
et i -
- 1
?.
r .U f W-1 i'i. r, l . L M- dg A $ A, V,' AA a .. . A A41=*=*d *^C "- * ~ ~ ' ' ' '
?:
et _ss* 4 O _rj {A:Ts. .M ?'1 [. -? r ' - _ . "($((_Of_T h M 'WMT
. A
' t
.s- *
.- 21 ,
J= F 4 HEU LEU LEU
$- REACTION SOLID HOLDER SOLID HOLDER HOLLOW HOLDER } -~
h j_ Co"(n,2n) -
.301-14 -
(*
!1 Cu63(n,a) .600-14 - -
1
']- ~
A127(n,p) -
.635-13 -
4 ,. Rh103(n,p) .155-15 - -
- a i
jT '55 Measured value has a 20% uncertainty associated with ' _ it. a . , i if m b -
- , J 1,
s . I 4
- N d
A t
', 7 1 .
h W . A 4 e 7.
?, !, d 7.
M
.'4 e~s
('. i . s (
,Y .} . ,,i dBY&
59 '4 t!- 1: l' t ( L *
+ na A$bdr ::1ch i m w c. w ..::w. L 'lt Y W ' - D" . . W . . . M; . 2.1 22 d 3 where I(E) is the macroscopic total cross section for g aluminum, and t is the mean chord length for the solid Q holder. Using this expression, one can show that the per-i' a- , turbation of the solid aluminum holder on the fast flux ' should be negligibly small. Thus, the agreement between the j~d ;
.t hollow holder data and the solid holder data is not unex- .
t '; pected. U 3' 3. Thermal and Enithermal Unfolded Soectra q- - i
~
The unfolded HEU and LEU spectra are presented in this -
; section. The semi-empirical unfolding technique was chosen -
for the deconvolutions since this approach allows the ex- [f perimentalist to construct the unfolded spectrum on a foil- . by-foil basis. The advantage of this approach is clearly
][ .,
- j. shown in the discussion of the LEU spectrum below. Since 1' both the LEU and HEU deconvolutions share the same unfolding
; [
parameters, we shall discuss our unfolding philosophy once ' l y1 l. prior to the presentation of both sets of results.
~i The semi-empirical technique iteratively refines the ,J Q* spectrum,until the specified convergence criteria are met. , ,
3- Based on experience, we have chosen to limit the maximum ' [t a number of allowed iterations to convergence to 15, and have - j defined, convergence to occur when the average deviation be- 2 q tween the measured and calculated activities is 54 or less. . LJ a These criteria may appear too relaxed since the fitting y residue would continue to decrease if the number of itera-f:j tions were allowed to increase. However, our experience has N g shown that past a certain point, the unfolded spectra may q develop spurious structure by radically changing the flux in _ f:j energy groups which have relatively little impact on the <' foil activities -- such as between 10 kev and .5 Mov. In 't . c O order to compensate for these unphysical peaks and/or val-N , leys, the spectra are normally " smoothed" (sometimes quite
.I -
heavily) since one expects the flux to be fairly smooth. r4 Q n For instance, the flux at an energy group may be defined to be the average of several points on either side of the L.1 - 1 f; - l' ,' i I L l:
. m m m. , . , z _, . ., m .,,7 , _ _ .m m , , _ _ . _ , , __ _. . .__ _ . . . _
.- '. ~.:n . .
. e ,m e n g & m w c. % w w ,w m g g a g g ; m y g g h W -
3.. 3 i ' y, " - 23 jN group. While the smoothing washas out these erroneous ex-
}- cursions, the resulting spectrum may not necessarily be a j i better approximation to the true spectrum. However, by l
I
] limiting the maximum number of iterations, and defining con- .y vergence to have occurred when the average difference be- l h tween the measured and calculated (based on the unfolded I fI spectrum) activity is 54, the generation of spurious struc-1~ ture caused by the unfolding technimae can be avoided. Be-cause of this conservative approach, the spectra do not need j)) -
to be heavily " smoothed" to remove unphysical features.
]a In the spectra which are presented below, we have /. 2 : chosen to use Monte Carlo error analysis techniques. In g- this approach, the activities, cross sections, and input .
I.j - spectrum are randomly perturbed to within predefined limits, 1 s and then this new unfolding problem is solved. This scheme
];- is repeated 10-20 times, and the results are used to generate the estimates of the uncertainties in the unfolded flux. While the limits of the perturbations on the cross sections and activities are the known uncertainties in these i values, appropriate uncertainty limits for the input j- spectrum are more difficult. It is our belief that the in-put. flux at any one group is known a priori to within a fac-7l _
ter of 2-10. This is an order of magnitude smaller than the inverse sensitivity method would predict. By limiting the
.,j j input flux perturbations to these lower limits, our quoted j
p- uncertainties are believed to be more realistic. q; We have chosen to unfold the detailed fast spectrum 4 separately from the thermal and epithermal spectrum. This -
- ,II is desirable since there is too much activation data to per-
[ form a complete flux unfolding with an associated error . , 3.l 7 analysis. This will not affect the accuracy of the thermal , [;' and epithermal fluxes which are presented. We havg per-L formed the thermal and epithermal flux unfoldings with all S- the measured threshold reactions, but without the error - h analysis, and then compared this result to the unfoldings p; 3 - I')I i 19',_.."**,; ^
;v -_w .w.c m. ...; . Nll _a.. a.ym7g3 - 4y$ h =F A fa j .. . , .
4 24 R
.[t- with only a few threshold reactions. The addition of these 'pa threshold reactions does not change the HEU thermal and ~ $q epithermal results presented below. For the LEU thermal and -
i-y , epithermal spectrum below, the inclusion of all measured - 2 . g, threshold reactions increased the integral fast flux above 1 - dl MeV by 4.0% above the result quoted below, but does not al-91i ter the shape or the magnitude of th'e spectrum below I Mev. 7 [
,! The results of the HEU thermal and epithermal unfold- ,. ;.] i ings are shown-in Tables 8 and 9 and Figure 4. Table 8 Si' .. i shows the non-threshold reactions which were used and the energy span in which 90% of the activity is produced. Also - ] shown is a comparison of the measured activity to the ac-Il tivity calculated with the unfolded spectrum. The final ~
j, column shows the percentage deviation of the measured ac- ' J tivity from the calculated activity. Note that with very y
.i few exceptions, this agreement is quite acceptable (<5%). E q, one particularly interesting result is the Fe58(n,y) cadmium y i covered data shown in the first row of Table 8. This datum Ii
~
j is fit reasonably v' ell by the unfolded spectrum. This im-plies that the iron capture reaction inconsistency shown in ' t. y; Table 6 is probably not related to an error in the isotopic ' .d abundance, but is more likely attributable to the cross sec- 7 [.i ; tion we have used. Kirk 3 et. al. have also noted the d [ . limited accuracy of the Fe58(n,y) cross section. - Figure 4 shows the measured HEU spectrum with the # ' ,4 lethargy dependent fluz plotted on a linear scale. This ,g , - spectrum is harder than the HAMMER calculated spectrum, as m expected. We shall defer comments about the physical mean-1 - L ing of the small fluctuations in the resonance energy region L ?; until after presenting the LEU results. However, without }.; the rather substantial corrections discussed for self-o shielding, gamma counting, and power calibrations, the 1 o spectrum would have large oscillations which would require -' 1
- f. considerable smoothing to remove. -
1 p - Table 9 presents the
- j values for the measured HEU differential and integral
, ; r a (i y* _1 I4 I 4; , g 1 --
;y , - r 3 7 ;
w7q _ ,r. . - , , = -.,- . .
--- - - ' ' ~ ~ '
_. ,_r. ,, u .a .m , ,ww,
..)
g.
,,,. . .. _ ,q .
_:_33 ; :. g w . m . . m u .: n c c w & .- L ' L a a s % : ; -. g g g g g g g, i, p . , . . v , c
; Table 8. Comparison of HEU Unfolded Activities with Nessured Activities
.6 ENERGY LIMITS d
[". FOIL 90% ACTIVITY CALCULATED RATIO DEVIATION I REACTION COVER UNFOLDED NEASURED TO MEASURED FROM i 4 TYPE LONER UPPER ACTIVITY CALCULATED CA14ULATED
!;: ( t (NEV) (NEV) ACTIVITIES A l' ;
. FE58(N,G)FE59 CADMIUM 8.291E-07 3.5095-04 2.140E-12 0.9768 ,
CO59(N G)CO60 -2.32 *
/ BARF 9.315E-09 1.0795-04 7.993E-10 1.0172 1.72 C059(N,G)CO60 CADMIUM 1.476E-06 1.4885-04 .l.143E-10 0.9885 AU197(N,G)AU198 -1.15 4 BARE- 1.626E-08 6.0165-06 4.0625-09 0.9848 AU197(N,G)AU198 CADMIUM 4.324E-06 1.7255-05 2.231E-09 0.9859
-1.52 Q; A U238(N,G)U239 -1.41 t;. ;
BARE 4.2888-08 1.231E-04 2.7605-10 0.9780 k U238(N,G)U239 CADMIUM 6.963E-06 1.4265-04
-2.20 #l
- j. TH232(N,G)TN233 CADMIUM 2.237E-05 1.8828-03 2.210E-10 7.1768-11 1.0600 1.0033 6.00 0.33 k!
F CU63(N,G)CU64 BARE 8.689E-09 3.9345-07 8.9385-11 '0.9711 g,i MI55(N,G)MN56 -2.89 u s-f . SC45(N,G)SC46 BARE 8.620E-09 2.5075-07 BARE 8.361E-09 1.4968-07 2.564E-10 0.9711 -2.89
- 31 3
j 4.8315-10 0.9729 -2.71 y SC45(N,G)SC46 CADMIUM 5.1848-07 3.425E-05 1.721E-11 0.9702 LU176(N,G)LU177 -2.98 S
! BARE 1.8825-08 1.6185-07 7.652E-08 0.9462 i! LU176(N,G)LU177 CADMIUM 1.315E-06 9.0305-05 1.3525-09 0.9614
-5.38
-3.86 -
7. p*
$ DY164(N,G)DY165N BARE 7.923E-09 1.1188-07 4.3088-08 0.9609 l DY164(N,G)DY165M CADMIUM 3.895E-07 4.1065-06 5.4835-10 1.0414
-3.91 4.14 1'
i NA23(N,G)NA24 CADMIUM 7.7585-07 3.164E-03 4.817E-13 1.0049
! U235(N,F)FSPR BARE 7.6575-09 1.4808-07 0.49 %)
l 1.0655-08 -0.9956 -0.44 PU239(N,F)FSPR BARE 1.042E-08 3.176E-07 1.7978-08 d AG109(N,G)AG110M BARE 1.1488-08 5.9265-06 9.801E-11 1.0296 1.0305 2.96 y}! 3 AG109(N,G)AG110M CADNIUM 2.738E-06 2.933E-04 3.05 2i 2.762E-11 0.9884 -1.16 1. TA181(N,G)TA182 CADMIUM 3.252E-06 2.3865-04 6.188E-10 1.0051
; N186(N,G)N187 BARE 1.072E-08 1.847E-05 0.51 .
9.0075-10 0.9192 -8.08 4; J N186(N,G)N187 CADMIUM 6.513E-06 2.8545-05 2.345E-10 1.0193 j NP237(N,F)FSPR 1.93 J. CADMIUM 6.7548-01 4.171E+00 2.3438-11 0.9990 -0.10 p {' 1-a a 3 , 1 - 5
! l
.. 9d l .It ,
9 w
V W w & & w W . % ;. m u, 2 : : .~.- ' 2 2 : w k u s w . u s n & h a x .. t-j a Table 9 f HEU Unfolded Sample Holder Flux 4.- Thersnel and Epithermal ?. -
+
DIFFERENTIAL FLUX INTEGRAL. FLUX j*. GROUP ENERGY - ABOVE E f 2 BELOW E I (MEV) (n/cm -sec-MeV) 4(%) 2 l' ~ (n/cm -sec) 4(t) (n/cm -sec) 4(t) . li 1 1.005-10 9,803E+18 9,1 6.355E+13 6.6 8,917Et09 9.1 i 2 1.00E-09 1.020E+20 7,2 i 6.355E+13 6.6 9,399E+11 7.2 4 3 1.00E-08 2,255E+20 5,8 6,262E+13 6.7 3,922E+12 4 2.30E-08 2.435E+20 4.6 6.1 N 5.963E+13 7.0 1.059Et13 5.1- * , 4 5 5.005-08 1.736E+20 2,8 5.296E+13 7.7 1,514E+13 6 7.60E-08 8.782E+19 7,8 4.1 0-4.842E+13 8.4 1,8515+13 2.9 h.' 7 1.158-07 3.545E+191 10.5 4.505E+13 9.0 2,041E+13
~ 8 1.705-07 1.510Et19 15,9 4.315E+13 9.4 2.167E+13 2.6 2.8 IN 9 2.55E-07 7.4298+18 17,5 4.189E+13 hf 10 3.80E-07 9.5 '2.262E+13 3.1 U2
.4.240E+18 9.1 4.093E+13 9.5 2,340Et13 3.1 11 5.50E-07 2.6988+18 8,0 4.016E+13 [
12 8.40E-07 9.6 2.425E+13 3.0 13 14 1.27E-06 1.90E-06 1.656E+18 1.006E+18 6.744Et17 10.0 19,1 6.2 3,931E+13 3.859E+13 9.7 9.9 2,497Et13 2.555E+13 3.1 3.3 ((}
! s.
*b 3.801E+13 10.2 2.615E+13 3.3 15 2.80E-06 4.411E+17 10.4 3.741E+13 10.4 2.676E+13 h!f 16 4.25E-06 2.860E+17 3.2 '
6' 4.9 3.680E+13 10.6 2.735E+13 3.1 17 6.30E-06 1.9588+17 8.0 3.620E+13 10.7 D 38 9.20E-06 1.343E+17 2.791E+13 3.1 P 12.1 3.564E+13 10.9 2.843E+13 3.2 - d 19 1.35E-05 8.374B+16 21.2 3.513E&l3 11.1 '2.905E+13 20 2.10E-05 5.481E+16 3.0 3 15.7 3.450E+13 11.1 2.955Et13 2.8 21 3.00E-05 3.986E+16 5.7 3.400E+13 11.1 3.016E+13 14 22 4.50E-05 2.564E+16 2.7 1 14.6 3.339E+13 11.3 3.080E+13 2.5 23 6.90E-05 1.739Et16 13.4 3.276E+13 11.4 4 3.134E+13 2.3 lp
!r
..h :
M'
. i r, y ('
, mi r ,< i e- i c- < i na na mi rn rs i :-> " ' ' ' ' " ' "' " ' ' ' '~
n 1._. _r. lir d'is.A 2.w. rQfe;.. c!!.m ? .4 m ' M ... ..hG t h ... , a ! w t. e . dD.: .a iD.::.Fw ;f J&r c..W:1 Kda.hj ,q.G. _. [ 8 . t , .i .s T. a L. . 1 i i 6 .: 1.,, . .: g. e, G g.., m g , ... ; g .; g.a [---] g , m C.
- i:
l J.
.,~ '
V.' i DIFFERENTIAL FLUX INTEU.iAL FLUX l GROUP ENERGY ABOVE E BELOW E iE
- (NEV) (n/cm -sec-MeV) 4(%) ?
(n/cm -sec) 6(%) (n/cm -sec) 4(%) ! 24 1.00E-04 1.341E+16 7.8 3.221E+13 11.5 3.181E+13 2.3 i 25 1.35E-04 1.062E+16 6.5 3.174E+13 11.7 3.2185+13 2.3 # 26 1.70E-04 7. 7188+15 10.5 3.137E+13 11.8 3.255E+13 2.2 27 2.20E-04 6.1165+15 29.3 3.101E+13 0 11.9 3.285E+13 2.1 28 2.80E-04 4.802E+15 26.9 3.071E+13 12.3 3.317E+13 2.1 29 3.60E-04 3.725E+15 11.6 3.038E+13 12.6 3.3498+13 2.0 o 30 4.50E-04 2.912E+15 18.1 3.007E+13 12.6 3.383E+13 2.0 C 31 5.75E-04 2.322E+15 17.3 2.972E+13 12.6 3.4268+13 1.9 E 32 7.60E-04 1.816E+15 16.2 2.930E+13 12.6 3.461E+13 1.9 33 9.60E-04 '1.449E+15 19.1 2.895E+13 12.7 3.504E+13 2.0 Q 34 1.27E-03 1.174E+15 22.0 2.851E+13 y /! - 12.7 3.540E+13 l 2.0 9 W 35 1.60E-03 1.034E+15 24.8 2.816E+13 12.6 3.575E+13 2.1 36 9.4978+14 H: 2.005-03 31.5 2.780E+13 12.6 3.626E+13 '2.3 9 37 2.70E-03 7.179E+14 29.6 2.729E+13 12.7 38 3.405-03 4.550E+14 18.6 2.690E+13 12.8 3.665E+13 2.6 4
~
3.711E+13 2.7 i 39 4.50E-03 3.126E+14 11.6 2.645E+13 12.8 3.742E+13 2.8 [g' 40 5.505-03 2. 2I t?.+14 12.4 2.614E+13 12.9 3.780E+13 2.8 3 41 7.20E-03 1.691E+14 11.1 2.576E+13 13.1 3.815E+13 2.8 d l . 42 9.20E-03 1.397E+14 13.7 2.540E+13 13.3 3.853E+13 2.8
! 43 1.20E-02 1.194E+14 16.1 $
i 2.502E+13 13.5 3.889E+13 2.9 $ 44 1.50E-02 1.026E+14 16.0 2.466E+13 13.6 3.932E+13 3.0 4
- ~
45 1.90E-02 7.602E+13 14.9 2.424E+13 13.6 3.984E+13 3.1 46 2.55E-02 5.1275+13 16.4 2.372E+13 13.7 4.019E+13 3.2 47 3.20E-02 4.169E+13 16.2 2.337E+13 13.7 4.052E+13 3.3
. 24 48 4.00E-02 4.238E+13 17.9 2.303E+13 13.8 4.104E+13 3.4 49 5.258-02 3.957E+13 20.0 hk 2.252E+13 13.9 4.154E+13 3.6 5 50 6.60E-02 2.842E+13 18.6 2.201E+13 14.1 4.216E+13 3.9 j' i s 4-
- ns i H i O pp 1
~MMTi.MM.xM&DSYl3s=3:~muVm.;. 2.132%D:. ~eicR.2 wsT.:ma.=xLwra D
.f..._..
= ._
[
.e l j 1
k d
,t . c.!
l DIFFERENTIAL F(.UX INTEGRAL FI4X : .l 0 I GROUP ENERGY ABOVE E BELOW E i l
' (NEV) (n/cm -sec-HeV) 5(l) 2 !i (n/cm -sec) 6(t) (n/cm2 -sec) 6(t) 13 p
51 8.805-02 2,246Et13 19,1 2,140Etl3 14.2 4,264Etl3 4.0 I 52 1.10E-01 2.128Et13 19.9 2,091Etl3 14.3 4.317Et13 4.2 53 1.35E-01 1.8365t13 20,2 2,039E+13 14.5 4.362Et13 4.4 54 1.608-01 1,579Et13 20,9 1,993Rt13 14.6 4.4085t13 I 4.5 r 55 1.905-01 1.5628t13 21.3 1,947Et13 14.7 4,454E+13 4.7 ; j 56 2.208-01 1,538Et13 21.5 1,902Et13 14.9 4,506E+13 4.9 l 57 2.555-01 1.497Et13 21.2 1,849Et13 15.1 4.5578+13 5.1 w 58 2.905-01 1.444Et13 20.4 1,7988+13 15.3 4.600E+13 5.2 C* .J l 59 3.20E-01 1.369Et13 19.2 1,7565+13 15.4 4.654E+13 5.4 i 60 3.608-01 1.261st13 19,3 ji l 1,701Et13 15.6 4.705E+13 5.5 t. j 61 4.005-01 1.150Et13 20.7 1.6515t13 15.7 4.762E+13 5.6 F 62 4.508-01 1,127Et13 22,7 1,593E+13 15.7 4.819E+13 5.7 h; 63 5.005-01 1.177Bt13 24,5 1,5375+13 IS.7 4,8788+13 5.7 64 5.50E-01 1.194E+13 26.2 1,478Et13 15.6 4.937E+13 5.8 ' I 65 6.00E-01 1.163Et13 27.6 1,418E+13 15.5 5.007E+13 5.9 j. 66 6.60E-01 1.115Et13 28,9 1.348E+13 15.4 5.074Et13 67 7.20E-01 1.055Bt13 30.0 6.0 3 1,282Et13 15.3 5.13GE+13 6.0 !! 68 7.80E-01 9.825E+12 31.1 1,2198+13 15.3 5,195Et13 6.1 0 ! 69 8.40E-01 9.076Et12 32.1 1,160E+13 15.3 5.267E+13 6.2 70 9.20E-01 8.330E+12 30.9 1,0898+13 /} 71 1.00E+00 7.271E612 26.1 1,023E+13 15.6 15.9 5.332E+13 5.473Et13 6.4 .'i t . d 72 1.20st00 6.083E+12 22.1 8.819E+12 16.7 5.591E+13 6.6 b 73 1.40E+00 5.174E+12 6.7 - Cp I i 74 1.60E+00 4.360E+12 21.4 27.3 7,646E+12 6.659E+12 17.6 18.5 5.690E+13 5.769Et13 6.8 6.9 f
. :.l.;
[ 75 1.80E+00 3.862E+12 40.9 5,863E+12 17.7 5.835E+13 76 77 2.00E+00 2.30B+00 3.334E+12 2.685E+12 42.8 28.4 5,206E+12 14.9 5.919E+13 7.0 7.1 Q f.<: 4,36'IEt12 9.6 5.993E+13 7.1 0 j . -, .y
;k-a
. ... Vi F ' ' r .5
. i .'l ,# l l I I l I 'I _}
b'I
- I f*3 I ' I I 'I ' I '
p a.u m r. .:.. ...: ..... i . : 2 .1._ % .. ; . .' . :.& s ::C &J . 2 M.V . ' i.n L e s .
' x :c . . . .a G **)g i I i l' 7 1 i t o. - J C"~1 _. FT I . .; [-~~) [Tl") O g . [----) p ,,. .; g.,.,, g , .; g , ,c, L. .., g ;; , . . . 0 h .
9, y-DIFFERENTIAL FLUX INTEGRAL FLUX Ii' GROUP. ENERGY (HEV) (n/cm -sec-MeV) 8(%) ABOVE E BELOW E 1 3 2 (n/cm _,,c) (n/cm2 -sec) 8(%) 8(%) / si , 78 2.60E+00 2.096E+12 14.8 3.626E+12 6.8 6.055E+13 79 2.90E+00 1.593E+12 7.1 &., 11.0 3.007E+12 6.1 6.119E+13 7.0 i 80 3.30E+00 1.228E+12 10.9 81 3.70E+00 9.752E+11 8.4 2.361E+12 1.853E+12 5.7 5.8 6.170E+13 6.209E+13 6.9 6.8 t! 82 4.10E+00 8.074E+11 7.8 1.463E+12 I l 83 4.50E+00 6.5 6.240B+13 6.8 6.478E+11 6.6 1.157E+12 7.1 6.270E+13 6.7 84 5.00E+00 5.005E+11- 7.4 k' 8.501E+11 7.8 6.294E+13 6.7 Ii 85 5.50E+00 3.739E+11 9.1 86 6.00E+00 2.555E+11 9.3 6.113E+11 4.319E+11 8.1 6.312E+13 6.7 S! 87 6.70E+00 8.1 6.3295+13 6.6 $ 1.536E+11 9.0 2.608E+11 8.6 6.339E+13 6.6 88 7.40E+00 9.188E+10 9.1 N
- 2 1.589E+11 10.0 6.346E+13 6.6 9 89 8.20E+00 5.222E+10 9.t3 8.985E+10 90 9.00E+00 2.7885+10 11.1 5.098E+10 13.0 6.350E+13 6.6 2 18.4 6.353E+13 6.6 -
f 91 1.00E+01 1.427E+10, 10.9 2.529E+10 30.8 6.354E+13 92 1.10E+01 6.6 7.400E+09 16.6 1.229E+10 51.8 6.355E+13 6.6 ,4 93 1.20E+01 3.780E+09 36.8 5.767E+09 80.6 6.355E+13 6.6 '3 94 1.30E+01 1.997E+09 65,.6 2.738E+09 110.5 6.355E+13 95 1.40E+01 6.6 q. 1.138E+09 96.5 1.382E+09 135.4 6.355E+13 6.6 L. 96 1.50E+01 7.630E+08 126.5 7.643E+08 153.4 97 1.60E+01 6.355E+13 6.6 b 6.406E+08 153.9 4.485E+08 165.2 6.355E+13 6.6 i 98 1.70E+01 5.339E*08 7 171.7 2.540E+08 171.9 6.355E+13 6.6 99 1.80B+01 4.3088+08 181.8 1.263E+08 172.1 6.355E+13 Q' 100 1.90E+01 6.6 i 1.434E+08 145.6 3.712E+07 145.6 6.355E+13 6.6 - e i 1 2 9 hi , E; c:4
+ !
.:[ ;
,C=e-----.-miewvwee- w e e-w e-_ +mmie-+* _ _ =--- eer
- u-m--re--r.w---gi-twvF=-----vv>=m-ww-.%.-w
. .; . _ _ i Gidts/23Cfedi'2iinE!.E ~ 72 .iT 21 s J .Ti .1 3 .. ' .. ._ .: e . . 2_ ._ . .. _...,/,,
. a'?.c ...s- . . . .r a.. .G i.T'.> ; > .J .j 6.i . ca 3
x i e. p .,
.t.
t 'i
.i:
t p II: l' [ - l x. 1 .
;i al h
P. 9,'
- b. .
t . t
; F a.
d' r-y , r U i t' P (I h . 9 i i u $ . O t
/ !!
L 'l f .) j i - nn i 1-
- ' 't g ,..
1 . tas-M h 5-8 b m-8 h 5-l bm1 h24 h m-4 h m-3 h g-2 h g-I h28 i ENERGY (t1EV) - Figure,4 FNR unfolded IIEU Spectrum. ' t
.-*.t
. g li.
}
; , p .J g ( '- ". ) -j l 1 't 6- 'l a '1 Sk 1 8- '1
* *"'1 f 8 ' ' ' *
- hp
_g.gm,--. ,m. ,g. g y3 m;j :.pg. ,.,.7,,,.....7. . e p . %. +. ..m _ .. :,- em._m.% . t' - b /'*. !.(} 1 3 '
- 31 l
Sn 7, if l b- fluxes, as well as their uncertainties. Note that the un-3 p, certainties in the differential flux tend to vary sig- {- nificantly between groups for energies above .25 eV and a- below 10 kev. These fluctuations are probably due to the y_ presence of resonances in these groups which serve to en-
- hance the sensitivity of the measurements there. For in- 1
,I 7-...----. stance, the effect of the gold resonance at 4.9 ev is evidenced by a sharply lower uncertainty in that energy group. At energies above 9 Mev, the uncertainty in the un- r folded flux increases dramatically. This is caused by the
~
limited number of reactions which were used to provide sen-g- sitivity in this energy region. In the next section we , shall present more accurate measurements of the differential ,
, i fast fluxes. The last four columns of Table 9 show the in-f_ tegral fluxes above (and including), and below (and includ-l ing) each energy group. These results will be used later to ~
l~ compare the broad group fluxes in the EEU and LEU cores. In *
,, sununary, based on the agreement between the measured and 1" calculated activities, and the reasonable shape of the - '
i, ,. spectrum, we have accepted these results as the measured HEU - q _ -. spectrum., since it has been our experience that the solu-
}, tion of the unfolding problem using one technique is also '
; recognized as a solution using other techniques, we have not compared these results with the results using other ap-proaches.
The LEU thermal and epithermal fluz unfoldings high-l'ight the advantage of using our interactive unfolding ap-
/, proach. Using all the data shown in Table 1.B, there were 3
large unphysical fluctuations in the unfolded flux between
.~ .2 and 10 key. To understand the source of this problem, we .
h began with the twelve reactions with measured to calculated [Li deviations less than five percent, and iteratively added a h a reaction and then performed the unfolding. Each unfolded - e_ spectrum can be used as the input spectrum for the next foil i
} addition. Figure 5 shows the results when the cadmium covered manganese data is entered. This activity was calcu-a(
- l i
- - n =_.x_-,.,-... . - . . . - . . . . . - - -. - -
.%.u w c r. m .sx. a ::.:x. j L ..a u .m 2. nw . - -~ "" _; w 77 !
1 , 1 32 i' lated to be about 6% too large using the spectrum predicted j . by the remaining activation data. The dashed curve
; represents the initial input spectrum, and the solid curve
- ? is the resulting solution spectrum. The fraction of the to- -
j tal cadmium covered manganese activity produced in each j j energy group is also shown superimposed as a dashed curve dl upon the input and. solutiort spectra. The majority of the ]* manganese activity is produced in the 337 e r resonance, and ij '. - to a less rir extent in the 1.080 kev resonance. Since the q' flux was well determined in the group containing the 337 eV ]; resonance, the differential flux had to be perturbed more ~ 3i .: substantially in those groups which were not well deter- ]: mined. Note the significant perturbation which has occu'rred - if,t 3 to the spectrum above 50 kev to compensate for only a 6% ' 3 discrepancy between the measured and calculated manganese . o] activity. This is,a. pathological problem with reactor spectral unfolding. As the number of measured activities increases, the consistency of the activities and cross sec-s p tions must increase to prevent such magnified perturbations. ( Table 10 shows the non-threshold reactions which were I [ n 3 used in the final IR fittings. The fit is not as impres- [0 sive as the HEU unfolding, but still meets the convergence . j!j criteria which were defined. Table 11 presents the LEU results in a comparable format to the HEU results presented - [;i , in Table 9. The uncertainties in these values are com- s [ parable to those presented for the HEU results. Figure 6
- j. shows the unfolded LEU thermal and epithermal fluxes. As g with the HEU results, the spectrum above 1 MeV is unfolded
) in greater detail in the next section. .- 3" j Figure 7 compares the unfolded HEU and LEU spectra. d1 The two spectra ar6 normalizac to have the same integral ..J flux above 1 Mev. Beginning at 1 MeV and moving to lower y energies, note the remarkable similarity between the ~ ha spectra. In the region down to .1 Mev, this is principally j a reflection of the agreement in the HAMMER calculated - M; r 4:a-L nl e il ' l lI _ :. ms u m m _ = ~
7;.;a. w w .*qc;.:.g.casu,y w.c..xiy--
. _ m;. . 2.. ; - 4_._ , _ _ . _..._: ,
.c-..a ,,.. . _ .. . _ . s . . m m . m ,a .g .j. f_ ,_.
> 'I . 'l -
1 l . .f L . , .l [ 3, . . ] l. ,j [ , . , ,l { ,) l jl ,~ a g, j g, g g, g , g g g ,
, ig' f, .
1 k^ i i ,.
.'(i .-
li 4
- rp g
F ,. , t.
- 1. 7 .
i, b- [.
'g tl l1 g --Input 8pectrum 1 I.1 g -Solution Spectrum
'y _
, _ .es .*
5 . s. O _8 - !! .< p s* o 72 l.1 Mn Cadmitas Covered Response ,) o_ai _ 1' x -
, - lL 3, .
>.8 j' 4
L >
- p. gg i,
g *. :; ' i y g* e--
.J .
i
^;
1 j8.o - !l w T i . q I u f M3 !. .l h.
- 2 8
l!l - t
! 1:
I lii '- y w ll. ' ll ( s i 8 .!.!
** .r r
j N --' ( I I,! - p' 1 uj: a l k ,t 1t
.{
,!l ..
.. s :,
. . . T . I[.s r.
h
.4 i 1s 3 ..,
) - ,. : I' 8 g g~ - 3 W ., d ... ut .,
.Q; n n-e nr8 nre n n-i dre ,
nrs nr8 n r2 n r2 n r8 m a' km2 k, > ENERGY ltEV) 4-Figure 5 Iterative unfolding example using Mn. a-
;j-
~..
i e; I I'
- : u. a : . L a e r : a a m u...T. . n :. u:. m n . m a w nu .;c xa - . . . ~ := :+ %1aET.iu .s u2:2iLaaeEw2, c::-r :... =
. . . ...o-e- ----~ -
~-
- ,1 -
1 fl l' 0 i u D ' E 1 - c L 3 Table 10
*t
[ a Comparison of LEU Unfolded Activities with H'easured Activities b
!,i H
ENERGY LIMITS u-f FOIL 90% ACTIVITY CALCULATED RATIO DEVIATION
.?
r REACTION COVER UNFOLDED MEASURED TO HEASURED FROM M TYPE LONER UPPER ACTIVITY CALCULATED CALCULATED dp
) (HEV) (MEV) ACTIVITIES l (%) U .- U235(N,F)PSPR +
BARE 8,0428-09 1,5518-07 1.058E-08 0.9077 -9.23
! PU239(N,F)FSPR BARE 1,094E-08 3,155E-07 1.798E-08 1.0013 h U235(N,F)FSPR 0.13 y
[ CADMIUM 7,997E-07 3.628E-03 4.5238-10 1.0392 PU239(N,F)FSPR 3.92 y CADMIUM 4,080E-07 1.541E-03 5.710E-10 1.0333 3.33 u C NP237(N,F)PSPR CADMIUM 6,760E-01 4.098E+00 2.642E-Il 1.0029 0,29 * ' CU63(N,G)CU64 CADMIUM 1,0448-06 7.6035-03 8,056E-12 0.9657 -3,43 ' HN55(N,G)HN56 BARE 9,130E-09 2.997E-07 2.569E-10 1.0159 1,59 CO59(N,G)CO60 BARE 9,926E-09 ji 1.1095-04 8.058E-10 1.0003 0,03 p CO59(N,G)CO60 CADMIUM 2,104E-06 1.4928-04 1.201E-10 0.9990 -0,10 9 j FE58(N,G)FE59 BARE 9,260E-09 7.367E-07 2.369E-11 1.1102 11,02 - FE58(N,G)FE59 CADMIUM l,'135E-06 3.521E-04 2.349E-12 0.9323 -6.77 lr h U238(N,G)U239 CADHIUM 7,0138-06 1.720E-04 2.377E-10 0.9759 -2,41 f TH232(N,G)TH233 2,257E-05 jf . CADMIUM 1.850E-03 7.920E-11 1.0101 1.01
! AU197(N,G)AU198 BARE 1.711B-08 6.031E-06 4.066E-09 0.9296 -7.04 1 1
( AU197(N,G)AU198 CADMIUM 4.321E-06 1.367E-05 2.245E-09 0.9980 AG109(N,G)AG110H -0.20 BARE 1.207E-08 6.012E-06 9'852E-ll
. 1.0404 4.04 SC45(N,G)SC46 BARE 8.795E-09 1.531E-07 4.807E-10 1.0382 -)
3.82 -, 1 b h
~. I
.l.-
1: i i k. 0 . :..H., e
. I'
!i 1#1 f5=] ,_ _ f :_.I 1 1 - I
- 1 1 '
' i ' ' ' ' " ' '
l
- r. g__. y-w , ~ _ a q, u.r 4 ,.
m,a.c.t
<.p. m.w,.. L .._. _.6 . _ . 4 . u _ u,,2 . u.< .+:es . . ..x a. v_ . _ ._, _. . ;. .-_ .
'- - a : i '
l ; i g. lt Q. w.. .. . .. m ._ .
- i. a r-- i a o
i *s. : i . j Table 11 f h LEU Unfolded Sample Holder Flux $ Thermal and Epithermal, s. l l J
?,
DIFFERENTIAL FLUX INTEGRAt. FLUX ,r' GROUP R $ g ABOVE-E BM E li (n/cm -sec-HeV) 3M) L; gfg,2-sec) 83) (n/cm -sed MO 1 1.005-10 9.4385+18 8.7 6.878E+13 1.00E-09 4.8 8.211E+09 8.7 Y y 2 9.8788+19 6.7 6.877E+13 3 1.005-08 2.201E+20 5.9 6.791E+13 4.8 4.8 8.750E+11 6.7 L' 3.691E+12 6.0 J' 4 2.30E-08 2.424E+20 5.3 6.509E+13 5.0 1.015E+13 5.5 5 5 5.00E-08 1.8095+20 4.7 5.863E+13 5.4 1.480E+13 6 7.605-08 1.001E+20 5.3 3 3.9 5.398E+13 5.9 1.865E+13 4.9 w 7 1.158-07 4.156E+19 4.9 5.013E+13 6.3 2.0898+13
- A, 8 1.70E-07 1.603E+19 14.7 4.4 *-
4.789E+13 6.5 2.222E+13 4.0 $ 9 2.558-07 7.438E+18 20.4 4.656E+13 6.5 2.315E+13 10 .3.80E-07 4.2368+18 3.7 3 13.8 4.563E+13 6.6 2.389E+13 3. 5' f 11 5.50E-07 2.716E+18 7.8 4.489E+13 12 8.405-07 6.8 2.470E+13 3.4 4'
. 1.7588+18 8.0 4.408E+13 6.9 2.546E+13 3.4 13 1.275-06 1.147E+18 8.8 4.332E+13 7.1 2.618E+13 3.3
?$
14 1.90E-06 7.787E+17 7.7 4.261E+13 7.2 2.689E+13 15 2.808-06 5.036E+17 3.3 E 7.7 4.189E+13 7.4 2.765E+13 3.3 16 4.25E-06 2.967E+17 5.9 4.114E+13 l 17 6.30E-06 7.6 2.826E+13 3.2 1.926B+17 8.1 4.052E+13 7.8 2.884E+13 3.1
- 18 9.20E-06 1.371E+17 13.6 3.994E+13 7.9 2.947E+13 t
19 1.35E-05 3.0 ?; . 8.975E+16 10.0 3.932E+13 8.0 3.014E+13 2.9
- 20 2.105-05 6.403E+16 12.7 3.864E+13 3.071E+13 I
21 3.00E-05 4.646E+16 14.7 3.807E+13 8.1 8.1 2.9 $[d 22 4.505-05 3.139E+13 2.8 tij .
- 3.090E+16 10.5 3.739E+13 8.2 3.214E+13 2.9 23 6.908-05 2.110E*16 8.9 3.664B+13 8.2 3.281E+13 j .'
2.9 g, k., l n;i'. . , *y b 1 .h
, ,, .t, - _ - -
t
--. z. : u:.:.2w c . u.L w e w.;.: : 8.:c. u:1.w,: o.2 ' :.'i u * ~ u - -_, - x . y;x e m d5n;uL M :.:..a.... x
.a.. i = , - .a. ; .- - . . u--.: . . . c
- as - 2.- - .~ ~. .
.j s
O f n g , p b 4 9l { DIFFERENTIAL FLUX $- INTEGRAL FLUX - i h 4 l GROUP ENERGY ABOVE E BELOW E
! 2 h (HEV) (n/cm -sec-HeV) 6(%) Q
[ ' (n/cm -sec) 8(t) (n/cm -sec) 6(1) 11 5 i 24 1.00E-04 1.446Bt16 12.1 3.597E+13 8.4 3.332B+13 2.9 f 25 1.35B-04 1.144Etl6 9.2 g.5 3.546Etl3 8.6 3.372E+13_ 2,9 i 26 1.70E-04 7.2775+15 15.5 3.506Et13 8.8 3.410E+13 2.8 27 2.20E-04 5.089Etl5 59,8 3.468Et13 8.9 3.439E+13 2.7 1
! 28 2.808-04 5.7195t15 21.7 3.4398t13 9.1 3.483E+13 2.7 29 3.60E-04 5.275Etl5 12.9 3.395E+13 9.3 3.529E+13 3
2.7 30 4.50E-04 3.062Etl5 16.1 3.350E+13 9.3 3.5675+13 2.7 w jJ
) 31 5.75E-04 2.179Et15 20.8 3.311E+13
- j 9.3 3.607E+13 2.8 D 32 7.60E-04 2.588Etl5 22.5 3.271E+13 9.4 3.655E+13 2.8 N
) 33 9.60E-04 2.495Et15 31.4 3.223Bt13 9.3 3,724Et13 2.9 a 34 1.27E-03 1.461E+15 21.0 3.155E+13 3 8.9 3.769E+13 3.0 a ' 35 1.608-03 1.0025tl5 17.8 3.109E+13 8.8 3.8098+13 3.1 )J y
s 36 2.00E-03 7.157E+14 20.3 3.069E+13 8.8 3.858E+13 3.2 37 2.70E-03 j.i l 6.144E+14 17.8 3.020E+13 8.9 3.901E+13 3.3 M
; 38 3.40E-03 4.523Et14 17.1 2.977E+13 8.8 3.951E+13 39 4.50E-03 2.860Et14 15.7 3.4 d
[' 2.927E+13 8.8 3.980E+13 3.4 B c 40 5.50E-03 2.127E+14 16.3 2.898E+13 8.9 4.018Et13 3.4
! 41 7.20E-03 W 1.696E+14 16.0 2.860Et13 9.1 4.053E+13 3.4 L.
42 9.20E-03 1.343E+14 19.8 2.825E+13 9.2 4.090E+13 3.4 Fj i 43 1.20E-02 1.251E+14 17.5 2.788Et13 9.3 4.127E+13 44 1.50E-02 3.5 h 1.184E+14 17.5 2.751B+13 9.4 4.174E+13 3.6 iF i 45 1.90E-02 9.383E+13 17.3 2.704E+13 9.4 4.235E+13 ' 3.8 !J I 46 2.55E-02 6.265E+13 18.5 2.644E+13 9.5 4.275E+13 3.9 M I 47 3.20E-02 4.736E+13 16.1 2.603E+13 @ 48 4.00E-02 , 4.530E+13 16.7 2.565E+13 9.5 9.5 4.313E+13 4.369E+13 4.0 4.1 d f 49 5.25E-02 4.124E+13 18.0 2,5098+13 9.6 4,425E+13 4.2
'I*
j 50 6.60E-02 3.1898+13 19.2 2,453E+13 9.5 4.496E+13 4.4
. v
. . u.
. F I
L
- i
- t. . i i , .
. ;.ajan. & ?.te g - 24 ' < W.u.1:: ,. . _.u-,- .i ._._:>.,~--' :c.s. ~ x..? cxxw:muc2 :. c.m:.m a . u .u .
.. .T '
a , 4 te s L i f. - i t r- i n r t i i i i - **b. ,-
. .~- f
. i- j q
- c ,
9 s DIFFERENTIAL FLUX INTEGRAL FLUX il GROUP ENERGY ABOVE E BELOW E y (MEV) (n/cm -sec-MeV) 4(%) (n/cm -sec) 8(%) (n/cm2 -sec) 8(%) ^ 51 8.80E-02 0 2.491E+13 20.4 2.382E+13 9.5 4.551E+13 4.5 52 1.10E-01 2.365E+13 22.0 2.327E+13 9.5 4.611E+13 [b ' 53 1.35E-01 4.7 2.063E+13 23.4 2.267E+13 9.4 4.663E+13 4.8 54 1.608-01 1.716E+13 24.2 2.215E+13 9.3 4.715E+13 55 56 1.90E-01 2.20E-01 1.656E+13 1.603E+13 24.8 25.4 2.163E+13 2.112E+13 9.3 4.766E+13 5.0 5.1 f) t,p ' 57 2.55E-01 9.3 4.823E+13 5.3 1.5288+13 25.5 2.056E+13 9.3 4.877E+13 5.5 h 58 2.90E-01 1.450E+13 e 25.1 2.001E+13 9.4 4.922E+13 5.6 59 3.20E-01 1.3588+13 24.1 1.957E+13 4 60 3.60E-01 9.5 4.977E+13 5.8 8 1.234E+13 23.2 1.901E+13 9.6 5.028E+13 5.9 61 4.00E-01 1.109E+13 22.5 1.850E+13 w 5.085E+13 62 63 4.50E-01 5.00E-01 1.070E+13 1.104E+13 22.0 20.8 1.793E+13 1.737E+13 9.7 9.9 5.141E+13 6.1 6.2 %j 10.0 5.198E+13 6.3 j) 64 5.50E-01 1.111E+13 19.1 1.680E+13 10.1 5.256E+13 65 6.005-01 1.075E+13 6.3 % 17.6 1.622E+13 10.2 5.324E+13 6.4 E. 66 6.60E-01 1.024E+13 '16.4 1.554E+13 10.4 5.388E+13 67 6.4 7.205-01 9.632E+12 15.3 1.490E+13 10.6 5.449E+13 68 7.80E-01 8.947E+12 14.5 1.429E+13 10.8 5.505E+13 6.4 6.5 J) i - 69 8.40E-01 8.250E+12 13.7 1.373E+13 11.0 5.575E+13 @bi; 70 9.20E-01 7.623E+12 6.5 12.9 1.303E+13 11.2 71 1.00E+00 6.908E+12 11.8 1.239E+13 11.5 5.639E+13 5.785E+13 6.4 6.4 1'
$d' 72 1.20E+00 6.076E+12 10.7 1.093E+13 12.3 5.914E+13 6.3 d' 73 1.40E+00 5.393E+12 10.2 9.646E+12 13.1 74 1.60E+00 4.762E+12 10.2 8.502E+12 13.9 6.028E+13 6.1295+13 6.2 .
1 75 1.80E+00 4.198E+12 10.6 7.492E+12 14.7 6.1 d 76 2.00E+00 6.218E+13 6.0 P 3.696E+12 11.3 6.602E+12 15.4 6.335E+13 5.8 { 77 2.30E+00 3.203E+12 12.4 $.427E+12 16.5 l 6.437E+13 5.7 [$.
]
Ij ' k-N
~ .... u;.E i.wsa..a:.:w .:a:,.e.. ami.i.aoh .
+
2 =; ' . .a ;L n. .. .a. - c wam:.uw u;aMaa.wa. mu.. , n x , [._
-_ . . . . . . . . . . , . . . . . . . ~ . . . . . . ...t. ..u..._..._,...._...~- -u-.-.. . . .
l' '.1 J ' l [k f. ) L d w - b u
- 9 .
O a e DIFFERENTIAL FLUX INTEGRAL FLUX i I! GROUP ENERGY 2 ABOVE E BELOW E p (MEV) (n/cm -sec-HeV) h 4(%) g I, (n/cm2 -sec) 8(t) (n/cm -sec) 8(t) l! 1 h 78 2.608t00 2.632E+12 13.6 4.409E+12 17.6 6.521R+13 l 79 2.90Bt00 5.5 y'
" 1.9988+12 14.9 3.574B+12 18.7 6.605B+13 5.4 '
80 3.30Bt00 1,4985t12 16.4 2.730E+12 19.9 6.668E+13 5.3 ' l 81 3.70Et00 - 1.1595t12 17.8 2,098E+12 21.0 6.717E+13 5.1 - i 82 4.10Et00 9.044E+11 19.1 1,611E+12 22.0 6.755E+13 83 4.50Et00 6.841B+11 20.4 5.1 84 1,231B+12 22.9 6.791E+13 5.0 ' 5.00Et00~ 5.049E+11 21,S 8.728E+11 23.9 6.817E+13 4.9 w 85 5.50E+00 3.674B+11 23,1 6,091E+11 24.9 " 86 6.00B+00 6.836E+13 4.9 I, 2.505B+11 24,4 4.176E+11 25.7 6.855E+13 4.8 T i 87 6.70B+00 1.618E+11 25.8 2.354E+11 26.7 88 7.405t00 1.033Et11 27,2 6.866E+13 4.8 / 89 1,1815+11 27.6 6.875E+13 4.8 $ 8.20E+00 3.9788+10 28,6 3.275E+10 28.6 6.878E+13 4.8 'l I ib i 15 b h ( u . e j . a
- fU l 3
?.
1 :) n it l . El
.s-O.
l . ,,
. ,- ,V:
H .e7 1 s.* e i . . .' . , i . .
. . ,. . . . t I
i r 1
; -t 4 FLUX (LETHARGY) (X10-103 e 0.00 160.00 320.00 480.00 640.00 800.00 960.00 1120.00 -)
w'< 1 *
, Ee '
e c Dw O k
-f m hf -
'{vr P
H gM "
=
p *k-
*2 -<g _ ,
ses e r m -t C f " hsi -
- i. a E,- -
Lr , f E
'i E
- t g- ,
r - T e; j
. q t ; u?.
6C . et
*I i
- .* . = .. .. .
p fg agg eM D ',.. f M 4 M * *'
-, ; ,; ~ ,11- : .. ' '
a
.tijh;p{q' i;-iA)*;q4. :'v,k t d ri .e4. pp H j,
.l3a aI ' .,. fIIe p!yydsi i
- 41e[1fij(a ;}t - . - -
r- !. 'i 3
>O w
l
- s. E a h r '
t c e ' n-p
- s '
U I E ' i L d n 2 a I
- i U E
H *
- n. ..
,n u
,i n
Q_ i
- d e
z 8 cc ) i i
.au w i 4 Vl
- 1 E am 1
- c. t
( r
.i o Y n
.- 5
- G f m.
i E R o ! N n
- s. -
E o
- s i i w a p
r i _ - 7 m
- a. .
i i o C a
~. .
- _ i 7
w.. s 9 e r u g g h i F i W
- w. (
,g 4M
- u. Ml q F 6_6 p 3 BE- M h
i a u n g a r.
- w. ;
- w. -
w- g g-
- aY' ,w9
- .
,1; P'31 :
- ! <1- ii f: d3j1t,P&pe[,! ! it ,
. . ._ .m.~-xwemw - e- " ~ ~ " ""'" " ** " "
.s .
.~ 2%:. -
l - l; - i j(}.l , fa . 41 b i .n ]- spectra since only the neptunium fission reaction has enough ' j sensitivity in this region to alter the calculated spectra. In the region from 10 kev down to 10 eV, there is relatively j good agreement in the' shape of the spectrum. Both HEU and _ LEU spectra show identical depressions at about .2 kev for reasons which are not understood. Below 10 ev, the spectra i begin to look distinct. It is in this region where the har- ' der nature of the LEU spectrum becomes apparent. This may i be related to the U 238 capture cross section. While the {~ ~~ U 238 capture cross section has many resonances, principal 1
.j 7 resonances appear at 6.7 eV,10.2, and 20 ev. If a sig-IJ%
nificant number of neutrons are absorbed.in slowing down - j- through these resonances, then one might expect the flux to jj be slightly lower in this region. In the thermal energy j,, range, the significantly larger HEU thermal flux is quite
}-
apparent, and not unexpected. j_ Table 12 compares the broad group integral fluxes for
!! - ~ - the HEU and LEU spectra. For et.:h of the three broad 7 -
groups, the integral flux and its uncertainty, and the frac- , tion of the total integral flux are shown. The uncertainty i
}
- j 1ri the collapsed broad group integral flux is smaller than I "' ,
the average of the uncertainties in the groups comprising it . j- because of the strong correlatio,ns between groups. That is, r .. if the differential. flux is unfolded to be too large in one , energy group, it will usually be too small in a nearby ener- i ( gy group so that the integral activity is close to being , l correct. Because of these correlations, the uncertainties [ in integral fluxes are usually much smaller than the uncer-i
- l. tainties in the differential fluxes. For the fast flux, a ,-
[ large uncertainty in the integral flux is quoted based on j N the results shown in Tables 9 and 11. This is because we : p have used very few threshold foils in the unfoldings. In the next section, we shall show that the HEU fast flux is L not different from the value presented in Table 12, and the h LEU f ast flux is only 4% larger than the value presented '
?
b here. Furthermore, the uncertainties in these fast flux b
~
i _w . .. ge._. ne,m-----% -
. izHcost:laLZaczu wmtsfEsamc.anizap mm _pmytrwemmen uywvemm e e, as.: _.q,,,
. . - -. ~ .. ..
f t:- p. 4 .f.1 i,1 {. Ej c [ 5
- t. - l
) Table 12 i
$e '
!.F L} '
Broad Group Comparisons of Unfolded Fluxes n HBU yersus LBU F
,l. .'
HEU RESUhTS LEU RESULTS l ENERGY s. INTBGRAI. INTEGRAL NORMALIZED REGION FLUX FRACTION FLUX FRACTION RATIO 8(%) of 6(%) of HEU/ LEU ( (x1013) TOTAI, (x10I3) TOTAL u W ll j ! l +aC k
' N l (B < .55 eV) 2.339 3.0 ,368 2.389 3.4 .347 1,191.03 a 'I $
h # epi .] (.55 eV< E <1 HeV) 2.993 4.0 3.250 b,1
,471 6.0 .473 1.11 j h i 5,; #f ast
[- g . (E > 1 MeV) 1.023 15.9' .161 1.239 11.0' .180 1.00 si [ f 888 The actual uncertainty in this value is much smaller. i' ' /] These deconvolutions [ used only a few threshold reactions, and hence the results show a large uncer- !: , tainty. The fast flux unfoldings used more reactions, and the integral fast - @ fluxes differ slightly from these values, , n e f' t
~ $
.]I-
[,q,,'1 l i , i , i <- i 0- :: r- i r i ' i l' i f' i (3 l l ." ' 1 f~rt r vi r. , e i e- , il
. &.Qll$$5-a S-i%. Wm -
n r# w & w w w m m M %" ME '" 1
. . , ,. 1
. q. 6 1 4
~
s ' .l. u 7 d ;. - a
.1 values are much lower. The final column of Table 12 shows j -
the values of the HEU to LEU ratio of the integral fluxes r) normalized to the same fast flux. Note that the ratio of j , the subcadmium fluxes would increase to 1.22 using the bet-a
,2 ter value for the LEU fast flux presented in the next s'ac-
- q. _
tion. This is slightly 16rger than the 1.19 value one would jj - expect. j._ 4. . Unfolded Fast Flux .
\
The threshold reaction data shown in Table 7 were used J_ to unfold the HEU and LEU core fast fluxes. As expected, j] the HEU and LEU f ast spectra showed the same general charac-cs - teristics when they were unfolded. In the discussion which
'l '
follows, we shall present the results of the LEU fast . 1_ spectral unfolding, but note any differences from the HEU
.h } results. '
For the fast fluz unfolding, the energy region from 1 ' j1 to 15 MeV was broken into 50 energy groups. A cross section libre y for this energy grid was developed for the threshold reactions. Not all of the measured threshold data reported j -in. Table 7 were used in the unfoldings. In particular, the j _, V 51(n,a), Mn55(n,2n), Ni I(n, 2n) Np ' (n, fission), and Mg 24(n,p) data were excluded from our final unfoldings. The V 51(n,a), Mn55(n,2n), and Ni 0(n,2n) reactions were not used _. because the cross sections are not well known.. When these
' ~
cross sections are better determined, this data should be incorporated into the unfoldings. The Np (n, fission) -. reaction is not included in the fast flux unfoldings :
.y reported here because 36% of the activity is produced below a 1 MeV. We have performed fast flux unfoldings covering the energy range .5 MeV to 15 MeV using Np 3
, and the measured fluxes are consistent with the data reported in Tables 9 and h] 11. This is expected since the same Np 2 data was also (v used in both of those flux unfoldings. Finally, the fa Mg24 (ri,p) reaction was not included because the HEU and LEU 4 solid holder measurements, as well as the LEU hollow holder k.
c t)~ 'fa. _ _ - -= - - ....- . - - - - - - - - - -
^l2 4 d L U W V ; [ 3 _ ).u Q , _
. . , . , , 3;, ,. .;.- y;;3333 s
n . q'
, a j 44 D -
ji-a r.; measurement, support a cross section which is 10% smaller in 3 T1 order to be consistent with other threshold reaction data ', j' covering nearly the same energy region. l j;< Table 13 shows the threshold reactions used, and the f
?! energy range of sensitivity to the flux for each case. '
e i, r These energy bands cover the region above 1.4 MeV complete- r: {;j , ly, and their staggered positions imply the shape of the un- i f.5; a : folded differential flux should be meaningful. In addition, ,- ij the reaction rate per t'arget nucleus which would be calcu- i fj lated using the unfolded flux is shown, along with a com- _ {} parison with the measured activity. The average magnitude . of the deviation is 3.74, which is quite reasonable con-
- +
.. sidering the uncertainties in the cross sections. We have _ # allowed the number of iterations to increase to see if the -
fit would improve, but the solution changed only. minimally. - I" ' From this, we conclude that the solution is stable with ' , respect to the number of iterations used. Furthermore, we - y have also employed two least squares unfolding methods (FER-d RET and STAYSL), but the shapes of the unfolded curves were t -j e
;;. not significantly different. is a result, we shall limit ;
H . our discussion to the unfolded LEU results using the semi- @ empirical method (SANL). Table 14 compares our deviations ~
- j '
between measured and unfolded activities with those one - p would obtain from a more limited set of threshold data -
- c. measured in the ORR . It is interesting that the first -
[, three reactions, which represent some of our worst fit data,
- j, show the same type of disagreements after unfolding as the j ORR data does. This type of similarity tends to strengthen a our confidence in the measured activities, but raises ques-
?!) c.; Y
, tions about our cross sections.
p M Table 15 presents the values of the differential un-l} folded flux, the associated uncertainty for each group (ex- ), m cluding the effects of errors in the cross sections), and 3 the percentage difference between the input spectrum and the M unfolded spectrum. We have deliberately' separated out the 8 9 3! !] 4 .' y d
- - . e w w m:n-w
, x, a u= ' * - - - -. *n~ m m N ~ - ~ ~ '
-~' - - - - - - - ~
c :.- m+= mmt:atescaarnceguw.n . _ a .: w w = = -
=r ms m wno m aew:.i.ap.:.w.,
' I . I i I. .i F-I C i i. 3 (T' l O Q F- I C i. i e. :. i, . O C - h.
'. .A
, ,. M.i Table 13
.j ..
LEU Unfolded Spectrum Activity Comparisons j
. s ENERGY RANGE FOR 90% ACTIVITY UNFOLDED RATIO OF DEVIATION OF ;
REACTION COVER (NEV) ACTIVITY MEASURED j MEASURED j TYPE (1/sec) TO UNFOLDED FROM UNFOLDED (%)
- j. LOWER UPPER ACTIVITY f*
4 IN115(N,N)IN115M CADMIUM 1.374E+00 5.001E+00 3.0515-12 1.0064 TH232(N,F)PSPR 0.64 h. CADMIUM 1.565B+00 5.897E+00 1.213E-12 1.0881 8.81 U238(N,F)PSPR BARE 1.570E+00 5.463E+00 5.2315-12 0.9366 y TI47(N,P)SC47 -6.34 CADMIUM 2.0095+00 6.391E+00 3.552G-13 0.9291 -7.09 NI58(N,P)CO58 ZN64(N,P)CU64 BARE 2.322E+00 6.579E+00 1.6'57E-12 CADMIUM 2.658E+00 6.4075+00 5.191E-13 1.0739 0.9690 7.39
-3.10 3}
! FE54(N,P)54MN BARE 2.669E+00 6.795E+00 1.254E-12 1.0207 "AL27(N,P)HG27 2.07
- f)
F CADMIUM 3.8475+00 8.430E+00 6.711E-14 0.9462
- CO59(N,P)FE59 BARE 3.837E+00 8.512E+00
-5.38 lj TI46(N,P)SC46 2.277E-}4 0.9529 -4.71 !?
f CADMIUM 4.250E+00 8.462E+00 1.6525-13 1.0530 5.30 NI60(N,P)CO60 CADMIUM 5.3185+00 1.002E+01 4.0135-14 q FE54(N,A)CR51 1.0092 0.92 p BARE 5.483E+00 1.071E+01 1.234E-14 1.0695 6.95 FE56(N,P)HN56 l TI48(N,P)SC48 CADMIUM 5.669E+00 1.069E+01 1.739E-14 CADMIUM 6.122E+00 1.181E+01 4.397E-15 0.9950 1.0121
-0.50 1.21
, j AL27(N,A)NA24 CADMIUM 6.751E+00 1.168E+01 1.112E-14 1.0076 ' 4 C059(N,2N)CO58 0.76 BARE 1.153E+01 1.413E+01 2.994E-15 1.0053 0.53 ZR90(N,2N)ZR89 CADMIUM 1.255E+01 1.450E+01 1.176E-15
[d 0.9949 -0.51 1
}
~
q s El g g I. ' 2 O M
a ,- _ ......~ u . M : b k .ui .L 'h i .
- . . = .g, u . . .=
,NY !
i, c) *'.'
-1 :
- l 46 '
j -
- [1 l Table 14 V'. :] -
Comparison of Deviations between Measured and j
- 5) .I Calculated Activities for FNR and ORR Unfoldings !
'd 1 , 43
's Deviation between '
ij 'i Measured Activity Reaction V 9 and Unfolded Activity 5 [L FNR LEU ORR
- ' .i ,
-k. a Fe54(n,c)Cr 1 7. 11. '
a N1 s . i Ti' (n,p)Sc' -7. -18. 4. NiS8(n,p)CoS8 7 6. e $ ! Fe 54(n,p)Mn54 2. Ti40(n,p)Sc48 5. [ 1. di U230(n, fission) -6.
-8.
8.
]
1 I
- . g 1,
, 1 effect of cross section errors on the. uncertainty in the un- !
[]1 folded flux to illustrate the best possible results which w
- f. could be obtained with accurate activation data. However,
- g. ,.
, we have performed the error analysis including estimates of -
;9 ! the cross section uncertainties. For this case, the errors k
[j shown in Table 15 increase by a f actor of ~2-3.5. Thus, the 4 d , . uncertainty in the unfolded flux is dominated by the uncer- e lj' tainties in the cross sections. The uncertainty below 1.5 <i g
- c. , - MeV is larger than at other energies because of the limited F j amount of foil coverage in this region. Also shown for a lq ; q
,.;. reference in Table 15 is the unfolded integral fluz above 3, each energy E. Table 16 shows the errors associated with l d'
<~$ s some integral fluxes. Comparing column 3 with the errors d, N3 shown in Table 15, it is interesting that the errors in the h h integral fluxes are less than the errors in the differential
.a
~'
.. fluxes. This is because of strong correlations between the f
\l
!:.1. I differential errors which tend to cancel out. This is ex- y j; pected since if the fluz is.too large-in one group, it must
- t ! $
\
g 7i a ;
~
^q l <
GWjf k .L LGsMum w:.akT= ?%wu"MrM= """' " ' * * * " * * ~- ^
.[- -..,,.m.,,,
c . m a.a... .w w. amram - c--~- &wmre v:==-Tw?*!*
- 1 M -. ,.
91* W a .
?, - -
47 '+ ,A ~1 .
~ '~
Table 15 4 )) Unfolded Differential Fast Flux
.$ ' 2 Flux (n/cm -sec-MeV)
.Q. Lower Integral fj Group Energy % Diff. Flux [, Number (MeV) Unfolded Uncert. from Above E I i f Setetra (4) Input i 1" d 1 0.100E+01 0.767E+13 16.0 -2.90 0.128E+14 1 I 2 0.125E+01 0.686E+13 Jj
' 12.0 -7.64 0.109E+14 ~- 3 0.150E+01 0.575E+13 9.3 -4.94 0.917E+13 4 0.175E+01 0.483E+13 7.2 0.86 0.773E+13 7 5 0.200E+01 0.424E+13 2.65 5.7 0.652E+13 .
6 0.225E+01 0.360E+13 4.1 2.93 0.546E+13 j ~ 7 0.250E+01 0.296E+13 4.1 2.65 0.456E+13
- i f- 8 0.275E+01 0.235E+13 4.4 3.32 0.382E+13 3 i 9 0.300E+01 0.191E+13 4.6 5.05 0.323E+13 '.
UJ 10 0.325E+01 0.160E+13 4.8 5.83 0.276E+13
; 11 0.350E+01 0.137E+13 2
5.2 5.15 0.236E+13 12 0.375E+01 0.117E+13 5.7 3.60 0.201E+13 ',
. 13 0.400E+01 0.100E+13 5.9 2.18 0.172E+13 14 0.425E+01 0.860E+12 5.8 1.70 ' %- 15 0.147E+13 "-
0.450E+01 0.750E+12 5.9 1.52 0.126E+13
, 16 0.475E+01 0.667E+12 5.6 0.86 0.107E+13 17 0.500E+01 0.579E+12 4.7 0.67 0.901E+12 1_ 18 0.525E+01 0.496E+12 4.1 0.39 0.756E+12 1 l
19 0.550E+01 0.425E+12 4.5 0.77 0.632E+12 "
-. 20 0.575E+01 0.364E+12 6.2 2.08 0.526E+12 d' 21 0.600E+01 0.306E+12 6.8 3.70 0.435E+12 22 0.625E+01 0.250E+12 5.9 5.64 0.359E+12 s 23
'~
s 0.650E+01 0.202E+12 5.6 7.72 0.296E+12 24 0.675E+01 0.165E+12 5.1 9.63 f 25 0.246E+12 0.700E+01 0.136E+12 4.6 11.35 0.204E+12 26 0.725E+01 0.113E+12 4.2 12.86 e- 27 0.170E+12 0.750E+01 0.946E+11 4.4 14.27 0.142E+12 a 28 0.775E+01 0.797E+11 7 4.6 15.47 0.118E+12 29 0.800E+01 0.667E+11 4.5 16.52 30 0.985E+11 0.825E+01 0.553E+11 4.4 17.37 0.819E+11
'. 31 0.850E+01 0.459E+11 4.4 18.07 Ln 32 0.680E+11 0.875E+01 0.382E+11 4.8 18.60 0.566E+11 ih 33 0.900E+01 0.318E+11 ?" 5.8 19.00 0.470E+11 '
34 0.925E+01 0.265E+11 7.6 19.29
$, 35 0.391E+11 0.950E+01 0.221E+11 9.6 19.50 0.325E+11 i dj 36 0.975E+01 0.183E+11 ?a 11.7 19.66 0.270E+11 ',
37 0.100E+02 0.153E+11 13.8 19.86 C' 38 0.224E+11 0.103E+02 0.127E+11 15.8 20.03 0.186E+11 n' 39 0.105E+02 0.106E+11 17.0 19.80 0.154E+11 0 40' O.108E+02 0.894E+10 15.7 18.85 0.127E+11 $~ 41 0.110E+02 0.753E+10 13.2 17.86 j- 42 0.113E+02 0.634E+10 15.4 16.87 0.105E+11 0.861E+10
~
- 1.
- H u
l} c._.,.,..,-.-,.--.~...-... . .---.- -
I. b ES.r s w 8.s.'i-i.i. m si m .vj # m..__-1 _ _ ,,2 . E'OO
. . %9. .; '_' +A~ . -._ ~
- 3. . - _ .
- - . s . r _ _. .' u -v a I i . . ..
j q 1 .
- ._, 48 .
l..! , 'l $ I a, b . Flux (n/cm 2-sec-MeV)
~
d ! Lower Integral - M: Group Energy % Diff. Flux S; Number (HeV) Unfolded Uncert. from Above E y; Spectra (4) Input i .f ,)j ' I
. 43 44 0.ll5E+02 0.532E+10 0.ll8E+02 0.443E+10 19.0 18.9 16.06 16.05 0.703E+10 0.570E+10 9 l 45 0.120E+02 0.333E+10 12.9 18.45 0.459E+10 '
dj j 46 0.125E+02 0.225E+10 7.1 20.63 0.293E+10 - 'f. j 47 0.130E+02 0.154E+10 5.8 22.05 0.180E+10 hj i 48 0.135E+02 0.105E+10 8.1 23.01 0.103E+10 :I
;f i 49 0.140E+02 0.723E+09 10.8 23.60 0.509E+09
. . 50 0.145E+02 0.294E+09 30.7 23.96 0.147E+09
.. 4 1' -
l-l -
~1 , .
3l
~~
e l. '
, e I
- Q' S.i .
.Q - i
-- # i
~f g . .
.. .I
?-
-{
fi :
?.3 -I 411 !
y !. 1
% .a t iI , -f
- . ! 'i l
I . m-.. f
' [
e < :~ ! l
~
~,
';} i
'9 Y.1 -
i Fi
,J * ~k 1;
u; .? 1
'" , '{ :
1 2 n<
- I 1 -
_ _ _ _ , _ _ . 5 ' .T.OT* G}i:5N?5 S WL**'%E' G #d'A**^ ^ 'W'~ * *
- _ . - ..-...z...
. _ , .y, .
2 ,.g.m,m ,mw.1.y...mm .,.,g.w w wg.gqg.,- +S. 7-h. L' : 49 N
>t .'s 1-y be too small in another group so that the integral ac- $ tivities are correct. Because of this cancellation, the unfolding methods excel at predicting integral fluxes over }a arbitrary energy regions. ,a 3 Table 16 0] -
Analysis of Integral Flux Errors J, jj Energy Range (MeV) Integral Flux
;j -
Uncertainty (4)
- a _ From To no 8a823 with 8a883 1 .
d '- 1.5 15.0 2.56 8.24
- b 1.5 4.0 3.60 10.31 4- 4.0 6.0 4.44 11.52 6.0 9.0 4.47 7.60
', 9.0 12.0 9.66 24.80
- 1 i ..
12.0 15.0 7.08 15.13 . .o- - 8*8 i Uncertainties cross sections. exclude the offacts of errors in the 'i-(83
- Uncertainties cross sections.
include the effects of errors in the -i u M~
. Figure 8 shows 4(E) versus energy for the calculated
- measured (solution) spectra. The input and solution spectra 3n are normalized to give the same integral flux above 1 Mev.
At 3.25 Mev, the unfolded flux shows a slight dip relative
'.. to the HAMMER input fluz. Harris 6
attributed a dip in his
- k. proton recoil measurements to the oxygen elastic scattering resonance c' about 3.5 Mev. Since our thermal and epither-fl.. : L. mal measured flux had a greater thermal to epithermal flux c
q,, ratio than the calculations predicted, one might suspect the w; , ...- calculations were based on a model in wBich we underes- [~ . timated the amount of water around the holder. If so, one y might expect the measured flux to be slightly 1cwer than the Sh calcult.ed flux at 3.5 MeV. From 4 to 6 MeV, the unfolded v g'6 , i. spectrum follows the shape of the HAMMER calculation
- .'g . .. . .
M l . . .- i .- . - . . .- _ - a ---. - __. .. - -
.. nis G:i ,a1.. - ai.:.h9 .1La:K.h laLk,G'hihK2. .:c. . . .... .: 2 3 m m ia%.a M t;1: M.r.u.% ;. ..
.. . ... T
.n.. .. . . . ...-:...
)'
's .
i-4..
.. i 70 4 .
n 1. -
- y J.
K , . i I
.. s t
f/ ' 13 't 3- 10 .
'8 g
f3 - N 3, > . x t.
._ n utum earcr= - 8
- t. ,' e.A p
~ A ., a m_. __a.
c_ir~ ,m
.\ e ensnas s Frnas r2 m aareeri its . .d. ' ' I.,e f 12 a..
10 _ f.; u, r.. x, em n , b k r
- I M
k i~ s s N 11 10 A a t --
-{ 'am ,
Y, m V u , ..(l ' t\ O J . i. i~ IJ 5 l E s i V-10 to :s fs u _.s d' n- t h - v.,. -{ x !. k ..k J 9 10 \ ~~
, .:5.; .
o . 1 ; o 8 10 . . 1 . 1.00 2.60 4.29 5.80 7.4 S 00 10.6 0 12.20 13.80 15.40 17.00 RGY BEp y Figure 8 . L;..
,i-FNR measured and calculated fast spectra. ,
- a h-9 Je !
I'
- s i',
e
.* I, b {*Me3
'% I* '* #* #< *. d.
. g .
** ) i f, ,
T , g#r gs"* a a se , g, g g- ,
- . . . _ _ __ ,. .,.,__,..,...s. . y;.ye 3. , .,.g. g._yy,,y,. .
.m ..;, ,
3., q y Q
~.,., .
..p% "
- 1. j * '
51 r,
- 1
'l
.i
'I reasonably well. It is interesting that integral' fast
;,= spectrum measurements using threshold reactions have shown a i 2 large rise in the flux in this region relative to measure-j.3 -. ments made using other techniques. This has been the source fi j of a controversy between direct differential measurements 1] , (e.g., proton recoil, time of flight) and integral measure-d j ments (i.e., foil activation) of the fission spectrum.
l.j Grundl7 , McElroy8, and Fabry 9 have independently reported a j 5. - large (304) " bulge" in the fast flux in the 3-6 MeV range, l' or an equivalent hardening in the " temperature" of the fis-3i sion spectrum from 1.29 MeV to 1.47 Mev. These early . C- measurements used a much smaller set of threshold reaction , f -. data than ours, and cross sections which were presumably ?I3 less accurate. t
?
Figure 8 also shows Harris's proton recoil measurements _ . l .:; for comparison. The calculations, unfolded spectrum, and a
!, proton recoil measurements agree at 4.5 MeV. It is inter- ]
]_j esting that our full spectral unfoldings using the newer _ ENDF-IV cross sections and a more comprehensive set of ac- ' Hj tivation data still appears to show this deviation, although
]~ to a smaller extent. This tends to indicate that this con- ~.
,9 troversy between direct differential measurements and in- .7- tegral methods (i.e., threshold activations), may be direct-ly related to the accuracy of the cross sections known at C _. that time. Above 7 MeV, the unfolded flux is significantly N _, depressed relative to the calculated spectrum. It is in- ,5 : pressive that a depression of the flux in this energy range [ was demanded by .gli of the five (six, if Mg 24 is included) [ M threshold reactions having sensitivity in this region. For i a this reason, it is difficult to dismiss this depression as e ]: an experimental error. For the HEU and the LEU hollow q- holder spectrum unfolded using the FERRET, STAYSL, and SANL
- p. codes, this depression is also present. In this region, our e
calculated spectrum consists of a perturbed fission 7}, { spectrum. The agreement between the measured proton recoil mp-- spectrum and the unfolded spectrum is quite good and lends Ffj
.g -
L i
- g., g g g
~~ ~
K
' ^^ ~
, . *'~ O~~k.w i'..w. . .
. . ._;.;.a.L. = 2 % V'~T$ G C*b.. ?? W ~ '
.g Q. .
l. 1 52 i u ,
-i \
s credence to the shape of the unfolded results. Above 11 I MeV, the agreement between the measured and calculated l fj. spectra remains poor. In this region, the (n,2n) reactions
'f 1 are providing spectral sensitivity, so one would expect the -!
j unfolded results to be meaningful. Above 12 MeV, we do not ! ] have any proton recoil data to compare with our unfolded
-j results. Overall, the unfolded spectrum is quite credible. ,;
5' Below 6 MeV, the unfolded spectrum agrees with the HAMMER , M calculated spectrum reasonably well, but at the lower ener-
] gies, it deviates from the proton recoil data. Since there fj will be neutrons scattering down into these lower energies, '
d one would eqect the flux at these lower energies to be sen-jj sitive to the amount *of water in the vicinity of the detec-tors. Thus, the unfolded flux should exceed the flux seen ' i , at the proton recoil spectrometer at lower energies. Above . >. 6 Mev, the unfolded spectr m. agrees well with the measured I t proton recoil data, but deviates from the calculated .I spectrum. This says that the particular extrapolation that r l 4
) we used to extend the HAMMER calculations was not ap-h-
M propriate, and does not reflect on the accuracy of that set ~ of computer codes. ~ C
~
Q There are three conclusions we can draw from our fast Pj f.Luz unfolding efforts. First, we recognize that spectral ~
] unfolding does not provide the resolution which is available pj with,the direct differential methods, such as proton recoil -
] telescopes. This is inherent in the unfolding method and
] the shape of the cross sections In practice, unfolding , . .] serves as a means for making refinements to one's best es-j timate of the spectrum to become more consistent with the j integral activation measurements. Second, the unfolded j
.t solution doas not appear to be significantly dependent upon T jj the method used for the unfolding. The spectral features ] described above were observed using all three unfolding - ] methods. Solutions from one unfolding method were recog- - ij nized as solutions to the other unfolding methods. This is .- y not surprising since all methods attempt to minimize the ' h
< 7
. g' I .
3 ., g . w w.w.m . . -- c,.~- ------r -- -- ---- - v ~ w -- > - , =
1
,. ~- .:. % ~7 ?._y :w;m5cwaxM,%WLYW%bWXNlT k?P 3 .. ; .m. ~ ~ ,. . .
4 '. 53 d '. . jj - difference between a measured and calculated activity. If [j s one has a good first approximation to the spectrum, then the ].3 changes which must be introduced by the unfolding met! hod (.) . .. 'will be small, and relatively independent of the technique ,i .4 used to infer the change. Third, we have found the shape of the unfolded spectra to be relatively independent of the in- ' ]j_ ~ i put spectrum in those energy regions where there is good
~
foil coverage. We have tried moderately different input j} spectra for the region above 2 MeV to test this sensitivity, y- and the solution exhibited the same characteristics shown in [] Figure 8. Furthermore, it is encouraging that the unfolded ji solution looks more like the previously measured spectrum- : rather than the input spectrum above 6 Mev. This indicates l _ that the unfolded solution is more than just a reflection of f o the input spectrum. Finally, the accuracy of the high ener-
]
gy threshold reaction cross sections are currently the most ., significant obstacle to performing more precise fast flux d ~' unfoldings. Like the thermal and epithermal flux unfold-U ings, increasing the number of reactions used in the unfold- -
- s 7, ings may improve the resolution of the differential unfolded
].I n
spectrum. However, because the cross sections are smoother j and the energy coverage more complete, ona does not require ) j, the same amount of consistency between the measurements and
; cross section sets to prevent unphysical features in the un-i _', folded spectrum. Thus, to some extent, unfolding the fast
(" j7 flux is an easier problem than unfolding the thermal and epithermal fluxes. { (4 But the error analysis has also shown !
- - that the accuracy of the unfolded spectrum is currently S- limited by the accuracy of the threshold cross sections.
3l J The errors in the differential fluxes have been estimated to j, be 15-40%, which is too large to expect to accurately see ' y, small perturbations in the spectrum. A complete set of @ threshold reactions (~15-20) with accurately known cross 5~ sections (~23-5%) is probably required to be able to confi- - h~ dently unfold the differential fission spectrum with good g precision and resolution. ,; While the accuracy of many d" . i L_ 1 __-- --- . r . .g. .... . . . . . . . . . . . , , _ , , _ . , . . , _ _ , . - . _ . . , _ . _ . _ . _ , _ _ . . _ _ , _ _ _ _ _ . _ . . . . _ _ . . _ . , _ , _ . _ _ . . . -
- w. - ,;u. ~
*m-4nw =.=gz m__ . ;-3 . _ . ,
._ . . a.;_3 =n.yt 9-.55.__%73Q, , ,; .&-
.~1 ~ .A f P, -
i
. 5%
- a s.; -
Ly threshold cross sections has improved in the past 15 years, J.j , these. conditions have still not been met. However, con- " 7: sidering the difficulty of inferring differential quantities -i ((] j from integral measurements, it is, impressive that the tech- -l
. nique works even as well as it does. m l
i
; 5. Summary and Conclusions u,
7 S' .., The large number of reaction rate measurements has al- ~
- loved a comparison of the consistency of the cross sections. - "
For most reactions, there is a good agreement between the 2-j fluxes predicted using the measured activities and the cross -l j sections. However, the iron capture reaction at thermal
- l energies appears to be 10% too small when compared with the
- j results of the measurements made using cobalt, gold, silver,
}, i manganese, and copper foils. We have also noted in a
,. separate work that there are inconsistencies in the gold fdL.
_.. y,,gl. cross section at thermal energies which also.need ~ resciution. At higher energies, the Mg24(n,p) cross section 7 yields a fast flux which is inconsistent with the results - 3 i obtained using other threshold reactions. Based upon.our c i, j . measurements, this cross section should be decreased by 10%. 1 d The Zn 64(ri,p) cross section measured' by Argonne National Laboratory is substantially different from the ENDF-IV - C n .$ evaluation. Since only the ANL cross section yields a reli-g able fast flux when applied to our measurements, we suggest I y, the ANL cross section is more accurate. At very high ener- ' u j gies (E>10 Mev), the accuracy of the cross sections in p ij ' general is not particularly good. Precision measurements of k-l' 9- the cross sections at these energies are difficult, but they - g are needed for more accurate deconvolutions of the high ' j energy differential fast flux. U _ ] Regarding the unfolding methodology, we did not find [ much difference between the spectra determined with the . [ semi-empirical and least squares unfolding techniques. This 3 may have been because our initial estimate of the shape of the spectrum was too consistent with the activation measure- [ l . 7' b.i
,A" M
. 7 - -S ' ' '
Ag jY M' e 4 N& " W '
-- ?.. a.x a mm.w m. mn mm N'n n& ':W & = M " ' M CV W Lu:~^Q
,.e =
y
~
s, 55 U.1 -; '1
.- ments, so the amount of change required by the. unfolding N .,
.q codes was not dramatic. We did, however, discover that the
], choice of the input spectrum normalization can affect the h
], ghggg of the unfolded spectrum. This is an area which we ilj s believe has not been generally explored. The interactive ] ,,, semi-empirical unfolding program we have developed is @ .? similar to the SAND-II algorithm, and has the advantages of-j -
. speed, flexibility, convenience, and accuracy. It allows 5 the user to graphically see the effects of each measured ei
, reaction rate on the unfolded flux, and provides a physical {
- j q feel for the solution. The least squares methods we ex-a q- - plored provide the mathematical guarantee of a minimum (f
o variance solution, and a rigorously correct error analysis. j _, - This latter advantage is the practical motivation for.using
- j _, the least squares techniques. However, while the error ,
ij] propagation is rigorous, the resulting errors ^are dependent upon knowledge of the uncertainties in the input spectrum, ~ .; 7 which are not well known. This is an area which has been 9" receiving attention, and may make the least squares methods J 3 even more advantageous in the future. Q" 4 The HEU and LEU spectra were found to be measurably , ?,;!N a different, particularly below the principal.U238 capture. 13 o resonances. For the same integral fast flux, the LEU in-i., . tegral subcadmium flux was measured to be 1923% smaller than 1; the HEU value. This corresponds almost exactly to the dif-h ference in the U 235 number densities. Above 1 Mev, there
- 4. 3
' ' .' were no measurable differences between the HEU and LEU spectrum. The unfolded fast spectrum agrees well with the
^] . measured proton recoil data above 4 Mev. A clean comparison O' of just these measured data is shown in Figure 9 for 'a reference. This level of agreement was achieved by using a f.S large number of accurate threshold reaction data, recent a
p- ENDF-IV and -V cross sections, and the fact that the L., spec,trum is sufficiently smooth (i.e., small second deriva- >2 g-wr tives) at these energies so the lower resolution of the bl.
- e. -
multiple foil method was not critical. From this, we con- }- . l.L
, ,, ,,"#.,e e N * = - * * *'# -
.~ .
f + +: &.' :u....z. ,-M:.: .: .?:.a:a .:c ;. ... mm.,
= ,... ::
. _ _., _ __, ~_. # .
.w . . :.81 .
.-4 - -
- ... ~ .a -
^45 i . -
W .
- a
, 56 Q'J
- 1 y clude that the multiple foil method can be used to measure 1
absolute differential fast spectra reasonably accurately. ~
,n , .4 I ho
- Mi
- 0 -' '
ri Nd c,-
'l l
T/ ; s
.I -
^1
,j*
4 3
?! ' ') i it i ,3 o
p . ,
; 4
. t_
t
. i.
c 8 e y
- _J
.d .}l y -
l 4 - l a-4 b.e e s a e i a , e
. -)
t 1 l'* ..:' s"*.n%:a- .ww,6:iri.m.-v.4%f%v"x:im - ---m-.rm. -. ---- ~ -- -
~ ~ s*" ~
'- ' ~ ~ ' _ - _ _
" L:
I,-22.PMidi.:&r( t . i Q.Wi'. f.c 1 ; '.n-CL52M.w:.::r.
.i O 6
- :.iG3!tc..
- i. .i
. . .' ;..i .:v..J5-m a.sr i . . ..,i 6 g ,3 ; O '%r. W '~:Ela E:4i 2,i M.r.:.D g .
i
. :2::.';w.'
g
':iin.;e.
- g _, j'p.I.
-p a (1 -
4 n . hj 4
~.* a
.s
;j 10 13 - - -- -
9 m c..? . x F.*. x ._ a x m ., ,- encers=
= , f.
sy 3 _ w; m;,- .; __. _ -- - c- _..--..-----a ;; .- ll k . . . . _ l
. 10 12 f
IJ-
^
x i' w h
.( k 'Y
[c . A 7 j a 11 10 .
- Ni:
.l .
'ss D ..
L p;5 ^ h10 - 9.. 10 I. 4 y. W s_ s
' . m4:
)f 1 m ~, 4
\ :
\
9 , l 10
- . L";- ,
\1 'd ':i
.!# >v 4
"-?{
};)~ <.
- {
8 .. /3 10 _
't g.
1.N 2.M 4.20 5.M 7.# IB.M 12.20 13.M 95.# 17.00 - r .
. Figure 9 FNR meas' tired fast flux 1
- 4
, M 3
i, i d h
.3; t
)
. ,. . .. . _ . . . . _ . I'
1-
;~- r=x .L s-=.= tta.m u.- . . :~~ a w, - . . , . . _ . - . . . - . . ,
=-~,a- .H .-&
ua<si . . "7 -- 1 1 Li 58 ~ l 1
) REFERENCES j 1. D. K. W'hee and J. S. King, "FNR Demonstration Experi-
- ments Part II: Subcadmium Neutron Flux Measurements", -
- s. Proc. of the Int'l Meeting on Development, Fabrica-i tion, and Application of Reduced Enrichment Fuels for ~
$ Research and Test Reactors, ANL/RERTR/TM-4, Argonne ,
National Laboratory, Argonne, IL (September 1983). b .
- 2. D. K. Wehe and J. S. King, "FNR Demonstration Experi-f]j . ments - Part I: Beam Port Leakage Currents and '
[
?
Spectra", Proc. of the Int'l Meeting on Development, Fabrication, and Application of Reduced Enrichment d ' H Fuels for Research and Test Reactors, ANL/RERTR/TM-4, - 5 Argonne National Laboratory, Argonne, IL (September ii 1983). ~ 4 i 3. M.'A. Kirk. R. C. Birtcher, T. H. Blewitt, L. R. . q Greenwood, R. J. Popek, and R. R. Heinrich, " Measure- -
]j ments of Neutron Spectra and Fluxes at Spallation- ;i Neutron Sources and Their Application to Radiation Ef-j facts Research", Journal of Nuclear Materials, M (1981) 37-50. _
i
] 4. L. R. Greenwood, personal communication, 1979.
8
- 5. N. A. Frigerio, Nucl. Instr. Math.,M i (1974) 175. ~
- 6. Lawrence Harris, Jr., Measurement of Fast Neutron -
Soectra in Water and Granhite, Ph.D. Thesis, Depart-9 ment of Nuclear Engineering, University of Michigan, 1 Ann Arbor, MI, 1967, p. 68. 3- 7. J. A. Grundl, j "A. Study of Fission-Neutron Spectral vith High-Energy Activation Detectors", Nucl. Sci. ._ g Fglg , H , (1968) p 191-206. s r b 8. W. M. McElroy, " Implications of Recent F'ission- E j Averaged Cross-Section Measurements", Nucl. Sci. Eno.,
.).6,, 109 (1969). ,
9) ? 9. A. Fabry and M. DeCoster, " Integral Test of Capture 4 3 Cross Sections in the Energy Range 0.1-2.0 Mev", - Proceedings of the Second Conference on Neutron Cross f Sections and Technology, Spec. Publ. 299, Vol. 2, p 1 1263, National Bureau of Standards (1968). - k 2 A A.. }. q' * , r h ': .:n.+.:wsm> =~s 3 - -
= .w .~~=u-~~.~-- --~;3-- --3-'--' - - '
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.- w , s . O. s _,. . . . . . _ _ _ ,,
e
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-?
v
.. j .et 4 m
- i .
73 . - 4
- 1 ~ >
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5: N: q . . b., . N,* ,
- )
t
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