stability boiling office of - nrc.gov
TRANSCRIPT
ENCLOSURE
ORNL/NRC/LTR-87/08
Contract Program: Selected Operating Reactors Issues
Subject of Document: Stability Calculations for theGrand Gulf-1 and Susquehanna-2 Boiling Water Reactors
Type of Document: Technical Evaluation Report
Author: Jose March-Leuba
Date of Document: August 1987
Date Published: September 1987
NRC Monitor: T. L. Huang, Office of NuclearReactor Regulation
Prepared forU.S. Nuclear Regulatory Commission
Office of Nuclear Reactor Regulationunder
DOE Interagency Agreement 0544-0544 A1NRC FIN No. A9478, Project 2
Prepared byInstrumentation and Controls Division
OAK RIDGE NATIONAL LABORATORYoperated by
MARTIN MARIETTA ENERGY SYSTEMS, INC.for theU.S. DEPARTMENT OF ENERGY
under Contract No. DE-AC05-840R21400
LIST OF FIGURES.
TABLE OF CONTENTS
Page
LIST OF TABLES ~ ~ ~ ~ ~ ~ viiINTRODUCTION1.1 Objectives1.2 Main results
111
2. GRAND GULF-1 CALCULATIONS2.1 Beginning-of-cycle calculations
2. 1. 1 Modelled conditions2.1.2 Results
2.2 End-of-cycle calculations2.2.1 Modelled conditions2.2.2 Results
2.3 Sensitivity study
2337
12121519
3. SUSQUEHANNA-2 CALCULATIONS3.1 Modelled conditions3.2 Results
232325
4. DISCUSSION OF RESULTS 25
REFERENCES 29
APPENDIX A. SAMPLE LAPUR INPUTS ~ 31
APPENDIX B. DESCRIPTION OF MODELLED OPERATING CONDITIONS 43
LIST OF FIGURES
FigurePage
Degree of control, radial power, and axial powerdistributions for test control GGTP4 . . . . . . . . . 5
2 ~
3.
Calculated close-loop reactivity-to-power transferfunction for test 'point GGTP4 . . . . . . . . . . . . 9
Calculated closed-loop reactivity-to-power transferfunction for test point GGTP4 . . . . . . . . . . . . 10
Measured core-plate-pressure-drop-to-power transferfunction for test point GGTP4 . . . . . . . . . . . . 11
5. Degree of control, radial power, and axial powerdistributions for end-of-cycle conditions modelledin Grand Gulf-1 . . . . . . . . . . . . . . . . . . . 13
6.
7 ~
Comparison between closed-loop reactivity-to-powertransfer functions of test point GGTP4 calculatedfor beginning and end-of-cycle conditions. . . . . . . 17
Comparison between open-loop power-to-void-reactivitytransfer functions of test point GGTP4 calculated forbeginning and end-of-cycle conditions . . . . . . . . 18
8. Calculated constant-decay-ratio lines for end-of-cycleconditions in Grand Gulf-1 . . . . . . . . . . . . . 21
9. Calculated closed-loop reactivity-to-power transferfunction for test point SUSTLO . . . . . . . . . . . . 26
10.
A.l. LAPURX sample input~est GGPT4
A.2. LAPURW sample input~est GGTP4
A.3. LAPURX sample input Zest SUSTLO
A.4. LAPURW sample=-input Zest, SUSTLO
Calculated open-loop power-to-void-reactivitytransfer function for test point SUSTLO 27
33
35
38
40
B.l.
BE 2.
Degree of control, radial power, anddistributions for test point GGTP1
Degree of control, radial power, anddistributions for test point GGTP2
axial power
axial power
45
46
B.3.
B.4.
B. 5.
Degree of control, radial power, and axial powerdistributions for test point GGTP4
Degree of control, radial power, and axial powerdistributions for test point GGTP6
Degree of control, radial power, and axial powerdistributions for test point GGTPB
47
48
49
B.6. Degree of control, radial power, and axial powerdistributions for 8 x 8 fuel in test point SUSTLO. . . 50
B.7.
B. 8.
B.9.
Degree of control, radial power, and axial powerdistributions for 9 x 9 fuel in test point SUSTLO.
Degree of control, radial power, and axial powerdistributions for 8 x 8 fuel in test point SUSSLO.
Degree of control, radial power, and axial powerdistribitions for 9 i 9 fuel in test point SUSSLO.
51
52
53
TableLIST OF TABLES
Page
1. Modelled operating conditions for beginning of cyclein Grand Gulf-1
2. Calculated density reactivity coefficients for beginningof cycle in Grand Gulf-1 . . . . . . . . . . ... . . . 7
3. Comparison between measurements and LAPUR calculationsfor beginning of cycle in Grand Gulf-1
4. Calculated density reactivity coefficients for beginningof cycle in Grand Gulf-1 . . . . . . . . . . . . ~ ~ . 15
5. Comparison between LAPUR calculations for beginning andend of cycle in Grand Gulf-1 . . . . . . . . . . . . . 15
6. Sensitivity of decay ratio to input parameters ofbeginning-of-cycle calculations for Grand Gulf-1 . . . 19
7. Sensitivity of decay ratio to input parameters of end-of-cycle calculations for Grand Gulf-1 . . . . . . . . 20
8. Sensitivity to power and flow for end-of-cycle conditionsin Grand Gulf-1 . . . . . . . . . . . . . . . . . . . . 22
9. Modelled operating conditions for beginning of cycle inSusquehanna-2 . . . . . . . . . . . . . . . . . . . . . 24
10. Calculated density reactivity coefficients for beginningof cycle in Susquehanna-2 . . . . . . . . . . . . . . . 24
11. Comparison between measurements and LAPUR calculationsfor beginning of cycle in Susquehanna-2 . . . . . . . . 25
1. INTRODUCTION
The objective of the present report is to document the results ofa series o f stability calculations per formed using the code
LAPUR-IV for various conditions in the Grand Gulf-1 and
Susquehanna-2 boiling water reactors (BWRs). The main purpose ofthese calculations was to verify whether LAPUR could reproduce
accurately the results obtained during two recent stability testsconducted on these two reactors. In addition, calculations have
been performed for end-of-cycle (EOC) conditions in the Grand
Gulf-1 reactor.
Satisfactory agreement was found between test data and thecalculated stability margins for both reactors. In both tests,the measured decay ratios were low, ranging between 0.2 and 0.4.The calculated values fell within that range and followed trendssimilar to those of the measured values. At one point, though,it was expected that these tests would serve as an open-
literature benchmark case for LAPUR and other codes; however,
given the low-decay-ratio values obtained from the tests,extrapolations of code accuracy at higher values cannot be made
with high confidence. Within this context, we have tocharacterize the results of the present benchmark as
inconclusive.
1n addition, EOC conditions were analyzed for the Grand Gulf-1reactor based on data supplied by System Energy Resources, Inc.(SERI), and the Advanced Nuclear Fuels Corporation (ANF). The
results of the LAPUR modelling of these conditions show that the
Grand Gulf-1 reactor should be stable at the EOC but with a
significantly reduced stability margin as compared with beginningof cycle. For instance, with the nominal conditions of testGGTP6, the LAPUR code calculates a decay ratio (DR) of 0.89 atEOC compared with 0.42 at beginning of cycle. Note, though, thatthe conditions used for the EOC calculations are veryconservative. Based on our engineering judgment, we would notexpect DRs higher than 0.7 should a new series of tests be
performed at the EOC.
1
'
2. GRAND GULF-1 CALCULATIONS
Two sets of LAPUR calculations were performed for the Grand Gulf-1 reactor. The first set corresponds to the operating conditions .
of the stability tests performed at the beginning of cycle 2 on
January 31, 1987. The objective of the second set ofcalculations was to predict the stability of this reactor under
EOC conditions, which were expected to be more unstable.
:.For all these calculations, we relied sonl nuclear and:-'operating-
data .supplied';;;by:,ANF'and.'SERI;;" Input: data, for'he beginning-'of-':: ",
cycle calculations '.are'ar;more reliable;than data .for EOC,:.
because we obtained measurements of the actual operatingconditions during the tests. Nevertheless, there are some
concerns about the accuracy of these input data; in particular,it is well known that flow instrumentation is highly conservative
(and as such, inaccurate) at flow conditions close to naturalcirculation. ~ No attempt has been made to correct the measured
flows for these calculations; thus, the calculated values of the
DR for the lower flow conditions should be expected to be
conservatively high (i.e., the actual values are expected to be
lower).
2.1 Be innin -of-c cle ca culations
2.1.1 Modelled conditionsThe second reload core of Grand Gulf-1 contains 800 fuelassemblies of which 80 are "Type 3" General Electric (GE) 8 x 8
fuel assemblies with 2% Gd, 456 are "Type 7" GE 8 x 8 assemblies
with 5% Gd, and the remaining '264 assemblies are "Type 8" ANF
8 x 8 assemblies. The average exposure of the GE fuel was
approximately 104 MWd/MT, while all the ANF fuel was freshlyloaded and had an approximate exposure of 500 MWd/MT at the timeof the tests.
The radial dependence on power and thermohydraulic
characteristics has been modelled by grouping the 800 assemblies
into six representative channel types. Appendix A contains the
radial power distributions for all the runs, along with the axialdependence of the thermal power and the percentage of controlrods inserted. A representative case for the beginning of cyclecalculations is presented in Fig. 1, which corresponds to testpoint GGTP4 (59% power, 39% flow). It can be observed in thisfigure that, for these beginning-of-cycle conditions, the axialpower shape is fairly uniform and symmetrical. The radial power
distribution, although slightly skewed, shows that the value ofthe average radial peaking factor is less than 1. 2. These two
conditions, along with the high degree of control, which reduces
the density reactivity coefficient, imply that the calculated DRs
should be small.
Table 1 summarizes the operating conditions for the test points.Note that the values given in Table 1 for the flow are theprocess computer values, which are known to underestimate theactual flow at conditions close to natural circulation.
Testpoint
Table 1. Modelled operating conditions forbeginning of cycle in Grand Gulf-1
(MW) (Mlb/h) (psi) ('F) Gain r
GGTP1 1997 44.4GGTP2 2363 50 'GGTP4 2257 44.3GGTP6 1698 29.8GGTPB 1745 33.6
9921000
998986988
509509506498501
-0 '9-0 21-0 '9-0.82-0 '7
0.220 '60.22
-0 ~ 320 ~
28'he
pressure-drop to inlet-flow transfer function is"normalized-'-'. "
by gH/Wo, where''ore. height, Wo = core;;;flow;.~ = Time- constant in s ...
488GGTP4
488 68
ED
388E0
388
~ 288
188
~ 288x
18828
8.8 8.5 1.8 1.5RELATIVE PONER
8 5 18 15CONTROLLED CHANNELS (X)
8 8 8 5 1 8 1 5
RELATIVE POWER
(a) Axial power shape (b) Percentage ofcontrolled channels
(c) Radial power shape
Fig. 1. Degree of control, radial power, and axial powerdistributions for test point GGTP4.
Probably the single most important input parameter for these
calculations is the density reactivity coefficient (DRC). The
LAPUR code estimates a one-dimensional DRC from a two-group cross
section set as a function of void, fuel type, and degree ofcontrol. To calibrate this cross section set, keff calculationsare performed at nominal conditions and at similar conditionswith a +50-psi-pressure increase. The DRC calculated by LAPUR isadjusted by a multiplier to reproduce this calibration. For the
Grand Gulf-1 conditions, the calibration supplied by ANF
corresponded to case GGTP4. At nominal conditions, keff had a
value of 1.00994, with an average void fraction of 0.402354. At+50-psi-pressure conditions, keff increased to 1.01324, with a
decrease of average void fraction to 0.377856, yielding a DRC of13.47 measured in units of %ak/k per unit void change. The LAPUR
calculated value was 13.65 at nominal conditions and 13.16 at+50-psi conditions, which yields an average DRC of 13.41; thus,the DRCs had to be corrected by a factor of less than 0.54.,Table 2 presents the nominal-condition DRCs calculated by LAPUR.
Zt can be observed that the DRCs do not vary greatly between testpoints at the same fuel exposure and similar control rod
positions.
4
Table 2. Calculated density reactivitycoefficients for beginning of cycle in
Grand Gulf-1
Testpoint
Density reactivitycoefficient
(%ok/k / ap)
GGTP1GGTP2GGTP4
+50 psiGGTP6GGTPB
13. 3313.3413.6513.1613.1713.04
The LAPUR code requires a relatively large set of input data
describing the geometry and general characteristics of the
reactor. For completeness in the documentation of these
calculations, a typical input set (for case GGTP4} is presented
in Appendix A.
2.1.2 Results
The main results of these calculations are presented inTable 3, which contains a comparison between the measured and
calculated values of the DR and frequencies of oscillation.Overall, fair agreement has been obtained between the measured
and calculated numbers. For these comparisons, it is important
to realize that, in most cases, neither LAPUR calculations nor
the measurement technique of Ref. 1 has better than a single-digit resolution. Thus, for the small range of DRs observed inthe Grand Gulf-1 tests, we can only extract information about
trends. As long as the calculated DRs are low and the trends
correspond to the measured ones, good agreement has to be
assumed. In other words, the value of the Grand Gulf-1 tests forbenchmarking purposes is limited to the detection of only gross
errors in modelling technique.
Table 3. Comparison between measurements and LAPURcalculations for beginning of cycle in Grand Gulf-1
Test Power Flow Deca atmo atu a f e encpoint (4) (4) Measured LAPUR Measured LAPUR
GGTP6GGTPBGGTP4GGTP1GGTP2
0.350.370.320 '10 '2
44 27 0 '7 0 '546 30 0.40 0.3659 39 0.43 0.4052 39 0.44 0.4062 45 0.44 0.43
For illustration purposes, Figs. 2 and 3 present the calculatedclosed-loop and open-loop reactor transfer functions,respectively, for case GGTP4. Unfortunately, the noise
measurement technique (Ref. 1) for the Grand Gulf-1 tests does
not supply a similar transfer function for comparison. It'wasshown, however, in Refs. 3 and 4 that the transfer function from
the core-plate-pressure-drop signal to the average-power-range
(APRM) signal is related to the calculated transfer function.For purposes of comparison, Fig. 4 presents 'the measured core-.,
- plate-pressure!drop. to: APRM,transfer':function,"„iwh'ich sh'ows', a',"'structure .similar to the one:'in Fig. 2.
18
LVo
188zX
18 1FREQUENCY (Hz)
Fig. 2. Calculated closed-loop reactivity-to-power transferfunction for test point GGTP4.
9
18-1
18 2
-188
-278i8 2 18 1
FREQUENCY'(Hz)188,
Fig. 3. Calculated. open-loop. reactivity-'to-power transfer:,"';,;"function for. test point GGTP4.'l10
181z5
4.
4I
zCK
18-2
CtlfailW
8
-98218 IB
FRKOUENCY (HZ)
Fig. 4. Measured core-plate-pressure-drop-to-power transferfunction for test point GGTP4.11
2.2 End-of-c cle calculations
2.2.1 Modelled conditions
For these series of calculations, we had to rely on ANF's
predictions of operating conditions at the EOC. One of the main
sources of error for predictive stability calculations isprecisely the determination of the most unstable operatingconditions during the core cycle. In this calculation, we used
operating conditions corresponding to a reactor with all controlrods out and with mostly depleted fuel. The nominal power forthese calculations was approximately 60% and the flow 39%, which
are the conditions of test GGTP4 at beginning of cycle.
For the conditions supplied by ANF, the "Type 3" fuel (GE 8 x 8
with 24 Gd) had an average exposure of 1.2 x 104 MWd/MT, the"Type 7" fuel (GE 8 x 8 with 54 Gd) had an exposure of1.8 x 10 MHd/MT, and the "Type 8" fuel (ANF 8 x 8) had
104 MNd/MT of average exposure.
Figure 5 presents the axial and radial power shapes for thenominal EOC condition (604 power, 394 flow). It can be observed;
that both power shapes are heavily skewed. In particular, the;axial power shape is extremely bottom peaked. This fact'.increases the average void fraction in the core, which greatly-reduces; the reactor's stability margin.. The; radial peaking,», " ~
factor, .which is, as high as- 1'.'4", also .forces'ower stability,'--
12
488GGEOC4
8. 18 58
388
I- 288
~ ILI
188
8. 85C0
P. 00C3
UI
-8. 85
48
M38
UJ
28
18
8 -8. 188 8 85 1 8 1.5 -8 188 8%I . 888. 858. 18
RELATIVE POWER CONTROLLED CHANNELS (X)8.8 8.5 1.8 1.5
RELATIVE PONER
(a) Axial power shape (b) Percent,age ofcont, rolled channels
(c) Radial power shape
Fig. 5. Degree of control, radial power, and axial powerdistributions for end of cycle conditions modelled inGrand Gulf-1.
margins (i.e., higher DR). The fraction of controlled channels
is zero, and this increases the DRC, which also has a negativeeffect on the reactor stability.
The main cases analyzed corresponded to the power, flow,. pressureand inlet temperature conditions of the beginning-of-cycle tests(Table 1). We labeled these new conditions GGEOC1 throughGGEOC6, where the last digit indicates the corresponding testpoint conditions at beginning of cycle. Different axial orradial power shapes were not available for the several testcases. For that reason, the power distributions of the nominalcase (60% power, 394 flow) were used for all calculatedconditions at EOC. For the same reason, all of these
calculations were performed assuming no control rods inserted.
According to ANF's calculations for EOC conditions, keff was
1.00068 with an average void fraction of 0.474302. With a +50-
psi-pressure increase, keff changes to 1.0043 with a decreasein'oidsto 0.437054. These numbers imply that the value of the DRC,
should be 9.83 measured in units of 4k/k per unit void change.
Table 4 presents the LAPUR-calculated DRCs for operating powers
and flows equivalent to those of the stability. tests but",under
EOC conditions:.
Table 4. Calculated density reactivitycoefficients for beginning of
cycle in Grand Gulf-1
Testpoint
GGEOC1GGEOC2GGEOC4
+50 psiGGEOC6GGEOCB
Density reactivitycoefficient(%ok/k / ap)
9.389.389 '88.429 '19.28
2.2.2 Results
The main results of the EOC calculations are presented inTable 5, which contains the calcul'ated DRs and the natural
frequencies of oscillation for conditions similar to the ones
during the stability tests. For comparison, the LAPUR-
calculated numbers at beginning of cycle (Table 3) are also shown
in Table 5.
Table 5. Comparison between LAPUR calculationsfor beginning and EOC in Grand Gulf-1
Test Power Flowpoint (4) (4) EOC BOC EOC BOC
GGTP6GGTPBGGTP4GGTP1GGTP2
4446595262
2729393945
0.890 '00 '30.300 '2
0 '20 '20 '20 '80 '2
0 ~ 400 '20.510 '90.54
0 '50 '60 '00 '00 '3
aBOC = Beginning of cycle; EOC = End of cycle.
15
J
I
The comparison in Table 5 indicates that, as expected, conditionsat EOC in Grand Gulf will be more unstable than at beginning ofcycle. The DRs increase approximately by a factor of two, butstill the expected values are below 1.0, indicating stableoperation. The main reason for the increased value of the DR
seems to be the extremely bottom-peaked axial power shape.
,An interesting result of these calculations is that the average
DRC is lower at the EOC than at the beginning of cycle (Tables 2
and 4). This effect is caused by the averaging of severalchannel types: the DRC of the high-power fresh fuel is very high(approximately 30), while the DRC of some of the old fuel is
fnegative, because old fuel assemblies are so burned out that theybehave as if they had their control rods inserted. Due to thisdisparity of cross sections, this condition is rather hard tomodel. Although LAPUR performs an optimal adjoint weighingscheme to account for spacial void feedbacks, the result, for such
a nonhomogeneous core may have poor reliability.
Figures 6 and 7 present a comparison of the reactor transfer.functions for the conditions of test GGTP4 at the beginningversus the EOC. The main difference results on the higherresonance frequency and sharper phase break indicating that theEOC condition is the less .stable.
16„
181
IJICD
I
z 188
F
,-C C
18-1
IIOC,
-45
18 18 1
FREQUENCY (Hz)
Fig. 6. Comparisc.n between closed-loop reactivity-to-powertransfer functions of test point GGTP4 calculated for beginningand end-of-cycle conditions.
18-1
18-2
-188
-27818 2 18-1FREQUENCY.(Hz)'8
Fig. 7. , Comparison'. between'pen-loop",power-to-vo'id-reactivity':.-.transfer ..functions of ..test'oint GGTP4"calculated;for,,b'eginning -.-."'~-".and end-of-cycle conditions.;
18
2.3 Sensitivit stud
Zn addition to the nominal cases presented in Sects. 2.2 and 2.3,we have performed a sensitivity study of the calculated stabilityparameters to changes in LAPUR input parameters. The main
results of this study are presented in Tables 6 and 7, which
indicate the sensitivity 'of the DR and oscillation frequency tochanges in density reactivity coefficient and recirculation loop
parameters.
Table 6. Sensitivity of decay ratio to inputparameters of beginning-of-cyclecalculations for Grand Gulf-1
DRC Gain rTest oint
GGTP1 GGTP2 GGTP4 GGTP6 GGTPB
1.0 1.00.7 1. 00 ~ 8 1.00.9 1.01 ~ 1 1 ~ 01 ~ 2 1.01 ~ 3 1 ~ 01 ' 0.41 ' 0 '1.0 1.31.0 1.61 ' 1 '1 ' 1 '1.0 1.01.0 1 '1.0 1.01 ' 0 '
1.01.01.01.01.01.01 ~ 01 ~ 01.01 ~ 01.00 '0 '1.31.60.00.0
0.180.070.100 '40 '20.270.320.130 '50 '00.220. 160. 170 '80 '80 '40.09
0. 120.040.060.090.160.190 '30.090.110.140.150.110 '20 '30 ~ 130. 100.07
0.220 '90.130 '70.280.330.390.160.190 '50.280.200 '10.230.230 '80.11
0 '20 '00.270.340.490 '60.630.280 '50 '70 '20 '90 '10 '10 '10 '40 '7
0.320.140.200.260.380.450.510.220.27
, 0 '70.400.290.310 '20 '20.260.14
aDRC = Density reactivity coefficient; r = Timeconstant in
S ~
19
Table 7. Sensitivity of decay ratio to inputparameters of end-of-cycle calculations for
Grand Gulf-1
8'*DRC Gain r
Test ointGGTP1 GGTP2 GGTP4 GGTP6 GGTPB
1.00.70.80.91 ~ 11 '1 '1.01.01.01.01.01.01.01.01.01 ~ 0
1.0 1.01.0 1.01 ' 1.01.0 1.01 ' 1 '1.0 1.01 ' 1.00 ' 1.00.7 1 '1 ' 1 '1.6 1.01.0 0 '1.0 0.71.0 1 '1 ' 1.61.0 0 '0.0 0.0
0. 300. 130. 180 ~ 240.360.420.480 '10.260.340.370.300.300.290.280 '90. 15
0.220 '80 '20 '70 '60.320.370 '60 '80.240 '70 '10.220 '10.200 '00 '2
0 '30.300 '80 '50 '00 '70 '40 '00.470.580.630.530.530 '20 '00 '00 '1
0 '90.630 '20 '10 '71 '41 '00 '50.820.951. 010 '80.890 '80.860.830 '3
0.700.440.530.620 '80 '50 '20.570.640.760.800.700.710 '00 '80.660 '60
DRC = Density reactivity coefficient; r = Timeconstant in s 1.
In addition to the above sensitivity study, we have mapped thedecay ratio as a function of power and flow for EOC conditions inthe Grand Gulf-1 reactor. The conditions of test GGTP4 have been
selected as base case for these calculations (i.e., the axial and
radial power shapes have been kept constant for this study). The
results are presented in Table 8 and Fig. 8. The predicted linesof constant DR at the end of cycle 2 are shown in Fig. 8.
20.
88
0$0.5
0.5
(>.2
68
4828 38
FLOW (X)
Fig. 8. Calculated constant-decay-ratio lines for end-of-cycle conditions in grand Gulf-l.
Table 8. Sensitivity to power and flow forend-of-cycle conditions in Grand Gulf-1
Power()
Flow Decay Oscillation(>) ratio . frequency
52
60
68
76
60
39
39
39
39
30
0. 30
0. 53
0. 67
0.82
0 '9
0.49
0.51
0.55
0.57
0.48
We observe from this table that the DR is more sensitive to, changes in flow than to changes in power. Nevertheless, these
4,q
calculations suggest that all the normal operating region of theGrand Gulf-1 reactor will be within the stable domain ofoperation at EOC conditions.
To determine the probable cause of the increase in calculated DR
at the EOC compared with the beginning-of-cycle calculations and
measurements, we performed a calculation with all the EOC
parameters for test GGTP4 except the axial power shape. With a
sinusoidal, symmetric power shape, we obtained a DR value of 0.21and an oscillation frequency of 0.47 Hz. This DR is less thanhalf the one calculated with the EOC power shape and of the same.
order as the DR at beginning of cycle. This .result indicatesthat the main reason for the decreased stability margin at'OC .in- '-Grand Gulf-1 is the!-shift in axial power» shape
toward-ai'.b'ottom-'.'..',",'eaked
distribut'ion.'.
22
3. SUSQUEHANNA-2 CALCULATIONS
LAPUR calculations were performed for the two conditions of the
stability tests performed on November 2 and November 9, 1986,
respectively.1 End-of-cycle conditions were not analyzed for the
Susquehanna™2 reactor due to lack of input data. For the
beginning-of-cycle calculations, we relied on nuclear and reactordata supplied by ANF and the Pennsylvania Power and LightCompany.
3.1 Modelled conditions
The second reload core of Susquehanna-2 contains 764 fuelassemblies of which 8 are "Type 3" General Electric (GE) 8 x 8
fuel assemblies, 432 are "Type 6" GE 8 x 8 assemblies, and theremaining 324 are "Type 12" 9 x 9 ANF assemblies. The average
exposure of the 8 x 8 fuel was 12 ' x 10 MWd/MT< while the 9 x 9
fuel had not been exposed yet.
The radial dependence of power and thermohydraulic
characteristics has been modelled by grouping the 764 assemblies
in five channel types: three of them correspond to 8 z 8 fuel and
the other two are 9 x 9 fuel. The axial and radial power
distributions are shown in Appendix A, along with the percentage
of controlled assemblies. Table 9 summarizes the operatingconditions for the two tests. Test SUSTLO corresponds to the
23
test of November 2, 1986, which was performed with the two
recirculation loops active. Test SUSSLO corresponds to theNovember 9, 1986, test under single-loop operating conditions.Table 10 contains the calculated density reactivity coefficientsfor both conditions. The input parameters for test SUSTLO can be
found in Appendix A.
Table 9. Modelled operating conditions for beginning ofcycle in Susquehanna-2
Test Power Flow Pressure Inlet temp.point (MW) (Mlb/h) (psi) ( F)
Recirc. looGain
SUSTLO 1970 46.8
SUSSLO 1834 43.9
960
955
505
500
-0.36 0.21
-0.36 0.21
The pressure-drop to inlet-flow transfer function isnormalized by gH/Wo, where H = core height, Wo ~ core flow;
= Time constant in s
Table 10. Calculated densityreactivity coefficients for
beginning of cycle in Susquehanna-2
Testpoint
Density reactxvitycoefficient
(Oak/k / ap)
SUSTLO
SUSSLO
12. 07
13.97
24
3.2 Results
The main results of these calculations are presented in Table 11,
which compares the measured and calculated values of the DRs and
frequencies of oscillation. Figures 9 and 10 present the
calculated reactor transfer functions for test SUSTLO.. Similar
arguments to those in Sect. 2.1.2 can be made with respect of the
accuracy of both the measurements and calculations. With that inmind, the benchmarking of LAPUR calculations versus the
Susquehanna-2 test results is inconclusive, in the sense thatboth DRs are low and, as such, good agreement is found between
measurements and calculations. However, extrapolations of the
accuracy of LAPUR calculations for higher DRs based exclusivelyon this benchmark are not possible.
Table 11. Comparison between measurements and LAPURcalculations for beginning of cycle in Susquehanna-2
Testoint
Deca ratioMeasured LAPUR
atu a re e cMeasured LAPUR
SUSTLO
SUSSLO
0.33
0.37
0 ~ 20
0.23
0 '90 ~ 34
0.38
0.42
4. DISCUSSION OF RESULTS
Overall, the results of the present benchmark of the LAPUR-IV
code against the Susquehanna-2 and Grand Gulf-1 stability testsare inconclusive. Given the low decay ratios observed in the
tests and the errors involved in both measurements and
25
181
UJCI
X 188
I:
18 1
-45
-98218 18 1
FREQUENCY (Hz)ie
Fig. 9. Calculated closed-loop.. reactivity-to-power;:transfer„ „
function for test point SUSTLO.26
181
18
18 2
8
-27818-2 18 1
FREQUENCY (Hz)
Fig. 10. Calculated open-loop power-to-void-reactivitytransfer function for test point SUSTLO.
27
calculations, one must conclude that satisfactory agreement isfound as long as the calculated DRs are low. This has been the
case, since both measured and calculated DR values have been less
than 0.4 for all test conditions. The present benchmark has once
more increased our confidence in the general validity of the
LAPUR code, in that if LAPUR had gross modelling errors,agreement might not have been successful over the relativelylarge range of operating conditions and fuel types covered in the
tests.
The modelling of end-of-cycle conditions in the Grand Gulf-1reactor implies that this reactor should be stable at those
conditions, but with a reduced margin as compared with beginning-of-cycle conditions. The highest calculated DR has been 0.89.
Based on our engineering judgment and the conservative nature ofthese calculations, we would not expect the DR to be higher than
0.7 should a second series of tests be conducted at the end ofthe cycle 2.
'I
~ c'c4 ~ <( i5y
28
REFERENCES
1. J. March-Leuba, and D. N. Fry, "Grand Gulf-1 andSusquehanna-2 Stability Tests." Oak Ridge NationalLaboratory Letter Report. ORNL/NRC/LTR-87/Ol (1987).
2. F. B. Woffinden and R. O. Niemi, "Low-Flow Stability Testsat Peach Bottom Atomic Power Station Unit 2 During Cycle 3."EPRI NP-972 (1981).
3. J. March-Leuba, R. T. Wood, P. J. Otaduy, and C. O. McNew,"Stability Tests at Browns Ferry Unit 1 Under Single-LoopOperating Conditions." Nucl. Technol. 74, 38 (1986).
4. J. March-Leuba and P. J. Otaduy, "The Importance of MomentumDynamics in BWR Neutronic Stability: Experimental Evidence."Trans Am. Nucl. Soc. 51, 563 (1985).
29
(13)»» 2 G X SEC TABLE a*
NO. OF FUEL + GD X-SECT TYPES (NFT)»REF. MATER DENS. FOR X-SEC. (LIQUID,
NFT CTRL Dl D2 SIGA1
1 1 1.358K 00 3.208K-01 7.350K-033. 870K-01 l. 159K-01 -5. 900K-042.082E-01 4.607K-01 -1.499E-03
2 1.365K 00 3.227K 01 9.940K-034.030K-01 1.220K-01 -6.600K-042. 157K-01 4. 608K-01 -l.860E-03
2 1 1.360E 00 3.184K-01 7.530E-033. 888K-01 1. 163K-01 -5. 700K-042.093E-01 4. 451K-01 -l. 537K-03
2 1.367K 00 3.201K-01 1.010K-024.046K-01 1.225K-01 -6.600K-042.164K-01 4.448K-01 1.912K-03
3 1 1.365K 00 2.990K-01 7.270K-033.959K-01 9.014K-02 -5.800K-042.264K-01 4.472K-01 -1.398K-03
2 l. 372K 00 2. 998K-01 Q. 910K-034. 121K-01 Q. 655E-02 -6. 700K-042. 331E-01 4. 448E-01 -1. 813K-03
3 NO. OF
STEAH)» 7.3SIGA2
4 . 501K-023.047K-05
-3.676K-035.593K-021.428K-03
-3.765E-034.922K-02
-l.943K-04-4. 514E-036.092K-028.846K-04
-5. 071K-035.987K-02
-5.005K-03-l. 143K-02
7.400K-02-5.393K-03-l.271K-02
~ 4 1 ~ ~ * I *
COEFF. OF X-SEC. POLYNOHIAL EXPAN. (NCOPOL)62E-01 3.790K-02
NUSIGF1 NUSIGF2
3.084E-03 5.490K-02-1. 486K-05 7. 647E-03-6.229K-04 -5.661K-03
3.083E-03 5.841K-02-5.139K-05 6.778E-03-6.782K-04 -7.908K-03
3. 571K-03 6. 397K-02-1.429K-05 7.065K-03-6. 943K-04 -8. 132E-033.554K-03 6.855K-02
-7.023E-OS 5.599K-03-7. 581K-04 -1. 091K-02
4.984K-03 7.320E-02-2.187E-04 -4 '94K-03-9.239K-04 -1.318K-02
4.905E-03 7.928K-02-3.230K 04 -8.417E-03-1. 011E-03 -1. 622K-02
SIGR1-21.994K-02
-l. 441K-025.643K-041.725E-02
-l. 438E 029.586E-041.980K-02
-1.442E"026.095K-041. 712E-02
-1. 438K-02l. 010K-032.006K-02
-1.456E-024.702K-041.'730K-02
-1. 453E-029.044E-04
* * * * P ~ » * *NO.OF CHANN. OF FUEL TYPE (IBT),CH. TYPE (IX) AND HORIZ. NUCL. REGION (J)
J 1 IBT» 1 IX 80 0 0 0
J» 1 IBT» 2 IX»... 0 52 68 88J» 1 IBT» 3 IX»... 0 0 28 52
FUEL TYPE PER BUNDLE (IBT) AND HEIGHT (ZXS) IN CH
IBT» 1 NZX» 1 ZXS 411.291
IBT» 2 NZX» 1 ZXS» 411. 29
2IBT» 3 NZX 1 ZXS» 411.29
3
0
248164
0
0
20
Fig. A2. LAPURW sample input Zest GGTP4 (cont.).
36
5
488GGTP1
488 68
E0
388E0
388
~ 288
Z188
~ 288X
188
W
28C3
8.8 8.5 1.8 1.5RELATIVE POWER
(a) Axial power shape
8 5 18
(b) Per cent,age ofcont, rolled channels
15CONTROLLED CHANNELS (X)
8.8 8.5 1.8 1.5RELATIVE POWER ~
(c) Radial power shape
Fig. Bl. Degree of control, radial power, and axial powerdistributions for test point GGTPl.
488GGTP2
488 68
388E0
~ 288(3
~ LdCh Z
188
E0
388
~ 288
LLJ
18828
8.8 8.5 1.8 1.5—. -- RELATIVE POWER
(a) Axial power shape
8 5
(b) Percent,age ofcont, rolled channels
18 15CONTROLLED CHANNELS (X)
8.8 8.5 1.8 1.5RELATIVE POWER
(c) Radial power shape
t
Fig. B2. Degree of control, radial power, and axial powerdistributions for test point GGTP2.
488GGTP4
488 68
388 388
~ 288
V188
~ 288
18828
8.8 8.5 1.8RELATIVE POWER
8 5 8 15CONTROLLED CHANNELS (X)
8 85 18 158.RELATIVE POWER ~
(a) Axial power shape (b) Percent,age ofcont, r oiled channels
(c) Radial power shape
Fig. B3. Degree of control, radial power, and axial powerdistributions for test point GGTP4.
488GGTP6
488 68
388 388
~ 288C3
c. lV00
188t
~ 288
ILI
18828
8.8 8.5 1 .8 1.5. RELATIVE POWER
(a) Axial power shape
8 5 18 15CONTROLLED CHANNELS (X)
(b) Per cent,age ofcont. rolled channels
8.8 8.5 1.8 1.5RELATIVE PONER
(c) Radial power shape
Fig. B4. Degree of control, radial power, and axial powerdistributions for test point GGTP6.
488GGTPB
488 68
388 388
0r
~ 288- C3.,;
"-'188
~ 288
188z 28
8.8 8.5 1.8 1.5RELATIVE PONER
(a) Axial power shape
8 5 18 15CONTROLLED CHANNELS (X)
(b) Percent.age ofcont,r oiled channels
88.8 8.5 1.8 1.5
RELATIVE POWER
(c) Radial power shape
Fig. B5. Degree of control, radial power, and axial powerdistributions for test point GGTPB.
. 488SUSTLO
488 88
C0
388E0
388 68
~ 288C3
188
~ 288C3
UJ
188
M48
CC
28
88 85 18 15RELATIVE POWER
(a) Axial power shape
8 18 28 38 48 58CONTROLLED CHANNELS (X)
(b) Percent.age ofcont. rolled channels
8.8 8.5 1.8 1.5RELATIVE POWER
(c) Radial power shapee
'ig.
B6. Degree of control, radial power, and axial powerdistributions for 8 x 8 fuel in test point SUSTLO.
488SUSTLO
488 88
ED
388E0
388 68
~ 288(3
~ hJ
188
~ 288
188
48
28
8.8 8.5 1.8 1.5RELATIVE POWER
8 28 48 8868CONTROLLED CHANNELS (X)
8.8 8.5 1.8 1.5RELATIVE POWER ~
(a) Axial power shape (b) Per cent,age ofcont, rolled channels
(c) Radial power shape
Fig. B7. Degree of control, radial power, and axial powerdistributions for 9 x 9 fuel in test point SUSTLO.
488SUSSLO
488 88
388C0
388 68
i 288
~ ill188
~ 288
188
48
28
8.8 8.5 1.8 1.5RELATIVE PONER
(a) Axial power shape
8 18 28 38CONTROLLED CHANNELS (X)
(b) Per cent,age ofcont, rolled channels
8.8 8.5 1.8 1.5RELATIVE PONER
(c) Radial power shape
Fig. B8. Degree of control, radial power, and axial powerdistributions for 8 x 8 fuel in test point SUSSLO.
488SUSSLO
488 88
E0
388 388 68
~ 288C3
~ LIJ4l Z
188
~ 288
188
48Z
28
8.8 8.5 1.8 1.5RELATIVE POWER
(a) Axial power shape
8 18 28 38 48CONTROLLED CHANNELS (X)
(b) Per centage ofcontrolled channels
8.8 8.5 1.8 1.5RELATIVE POWER ~
(c) Radial power shape
Fig. B9. Degree of control, radial= power, and axial powerdistributions for 9 x 9 fuel in test point SUSSLO.
ORNL/NRC/LTR-87/08
INTERNAL DISTRIBUTION
1.2.3.4 ~
5.6.7.8.9.
10
'.E. Clapp
B. G. EadsD. N. FryJ. March-LeubaR. S. StoneR. S. WiltshireM. J. Kopp (Advisor)P. F. McCrea (Advisor)H. M. Paynter (Advisor)J. G. Pruett
11'2.
13 ~
14'5
'6
~
17 ~
J. B. Ball (Advisor)Central Research LibraryY-12 Document Reference
DepartmentZ&C ZPCLaboratory Records DepartmentLaboratory Records
Department, RCORNL Patent Section
EXTERNAL DISTRIBUTION
18. S. Bajva, Division of Engineering and Systems Technology,Office of Nuclear Reactor Regulation, U. S. NuclearRegulatory Commission, P«522, Washington DC 20555
19. T. L. Huang, Division of Engineering and Systems Technology,Office of Nuclear Reactor Regulation, U. S. NuclearRegulatory Commission, P-1022, Washington DC 20555
20. J. B. Henderson, Division of Engineering and SystemsTechnology, Office of Nuclear Reactor Regulation, P-1022,U. S. Nuclear Regulatory Commission, Washington DC 20555
21. L. E. Philips, Division of Engineering and SystemsTechnology, Office of Nuclear Reactor Regulation,U. S. Nuclear Regulatory Commission, P-1022,Washington DC 20555
22. NRC Central File
55