Nuclear Engineering and Design 151 (1994) i45-t56. Nuclear. Engineed.ng. andDestgn. Validation of the Engineering Plant Analyzer methodology.
I
Nuclear Engineering and Design 151 (1994) i45-t56
ELSEVIER
Nuclear Engineed.ng andDestgn
Validation of the Engineering Plant Analyzer methodology with Peach Bottom 2 stability tests U.S. Rohatgi, A.N. Mallen, H.S. Cheng, W. Wulfi Brookhaven National Laboratory, Department of Nuclear Energy, Building 475B, Upton, N Y i 1973, USA
Received 5 May 1993
Abstract
The Engineering Plant Analyzer (EPA) had been developed in 1984 at Brookhaven National Laboratory to simulate plant transients in boiling water reactors (BWR). Recently, the EPA with its High-Speed Interactive Plant Analyzer code for BWRs (HIPA-BWR) simulated for the first time oscillatory transients with large, non-linear power and flow amplitudes; transients which are centered around the March 9, 1988 instability at the LaSalle-2 BWR power plant. The EPA's capability to simulate oscillatory transients has been demonstrated first by comparing simulation results with LaSaile-2 plant data (Wulff et ai., NUREG/CR-5816, BNL-NUREG-52312, Brookhaven National Laboratory, 1992). This paper presents an EPA assessment on the basis of the Peach Bottom 2 instability tests (Carmichael and Niemi, EPRI NP-564, Electric Power Research Institute, Palo Alto, CA, 1978). This assessment of the EPA appears to constitute the first validation of a time-domain reactor systems code on the basis of frequency-domain criteria, namely power spectral density, gain and phase shift of the pressure-to-power transfer function. The reactor system pressure was disturbed in the Peach Bottem 2 power plant tests, and in their EPA simulation, by a pseudo-random, binary sequence signal. The data comparison revealed that the EPA predicted for Peach Bottom tests PTI, PT2, and PT4 the gain of the power-to-pressure transfer function with the biases and standard deviations of ( - 10 + 28)%, ( - I + 40)% and ( + 28 + 52)%, respectively. The respective frequencies at the peak gains were predicted with the errors of + 6%, + 3%, and - 28%. The differences between the predicted and the measured phase shift increased with increasing frequency, but stayed within the margin of experimental uncertainty. The code assessment presented here is valid only for small-amplitude oscillations, but it encompasses neutron kinetics, fuel thermal response, coolant thermohydraulics and control-system dynamics. To our knowledge, this assessment of the time-domain HIPA-BWR code by frequency-domain methods and spectral plant data demonstrates for the first time the feasibility of such an assessment.
1. Introduction
* This work was performed under the auspices of the U.S. Nuclear Regulatory Commission. ** By acceptance of this article, the publisher and/or recipient acknowldeges the U.S. Goverment's right to retain a nonexclusire, royalty-free license in and to any copyright covering this paper. Elsevier Science S.A. SSD! 0029-5493(94)00854-R
1.1. Background
On March 9, 1988, the LaSalle C o u n t y Plant, Uni~ 2 ( G E BWR-5) experienced a power and
146
U.S. Rohatgi et al./ Nuclear Enghu,ering and Design 151 (1994) 145-156
flow instability, which was safely terminated by automatic SCRAM. This event renewed an interest in the analysis of BWR kinematic instability, which leads to density waves. The density waves are vapor-void disturbances and can develop in parallel-heated channels with boiling; they can be enhanced in a nuclear reactor by void-reactivity feedback. There are two distinct methods, and corresponding computer codes, for analyzing kinematic wave instability in BWRs. These are the frequency-domain and time-domain methods. The frequency-domain method is for predicting the onset of instability or stability boundary. The method is based on linearized balance equations. By this method, one cannot predict the amplitude of large non-linear oscillations and the feedback from the balance of plant on the flow and power oscillations. The earlier frequency-domain analyses of the density-wave instability were performed for, and supported by, data from test facilities with electricaiiy heated test sections (Ishii, 1971, 1976; Saha, 1974, 1976). The analyses have been further exte.~,.led by including the reactivity feedback effects (Lahey, 1973, 1977; March-Leuba, 1984; Taleyarkhan, 1983). Time-domain codes which integrate the full non-linear form of the modeling equations, such a~ the ~AMONA code (Wulff, 1984a) and the Engineering Plant Analyzer (EPA), are required for predicting non-linear phenomena of oscillatory flows with large amplitude (March-Leuba, 1986a,b; Wulff, 1990). The limit-cycle oscillations, caused by density waves during an ATWS, provide a new challenge to time-domain codes. Generally, the time-domain codes have been designed and assessed for non-oscillatory transients, dominated by strong external agents, such as break flows, valve actions or control-rod movements. Most of these codes have large numerical damping in their time-space integration schemes to achieve numerical stability. However, oscillatory transients, where an instability grow~ owing to internal feedback from minute internal effects anywhere in the system (most likely in the reactor core), must be simulated by a computer code with the smallest possible numerical damping.
Excessive numerical damping overwhelms nascent instabilities and renders the simulation nonconservative, i.e. more stable than the system of interest. Non-linear effects and all feedback mechanisms must also be modeled. The capabilities and the accuracy of timedomain codes must, therefore, be assessed for limit-cycle oscillation~ by comparison against data from experin,ents on oscillatory transients. The data can be either in the time domain, with variables as function of time, or in the frequency domain where the data are evaluated as frequency-dependent gain and phase shift of transfer functions between selected reactor parameters, such as the core inlet flow vs. core power, or core power vs. system pressures. Computer code assessments with frequency-domain data are more stringent than those with time-domain data. Only one publication was found, describing the assessment of a timedomain code, RAMONA-3B, with spectral test data (from the electrically heated FRIGG facility) (Rohatgi, 1993). The RAMONA-3B code has threedimensional neutron-kinetics models and multichannel core hydraulics, but it has the same two-phase flow models and numerical integration methods as HIPA-BWR in the EPA. The HIPABWR assessment presented here is the first frequency-domain assessment, which includes also neutron-kinetics feedback and control systems dynamics.
1.2. EPA s#nulation methodology The HIPA-BWR code in the Engineering Plant Analyzer (EPA) (Wulff, 1984b) is a time-domain code and simulates non-homogeneous, non-equilibrium two-phase flows, two-phase-flow wall friction, form losses, heat transfer and the effects from void and temperature feedback to the fission power. HIPA-BWR simulates also the pressure and feedwater regulating systems and the steamline dynamics. These are prerequisites for simulating the Peach Pottom stability experiments. This code has the four-equation drift-flux formulation with constitutive relationships for the drift-flux formulation (Ishii, 1977), and non-equilibrium vapor generation rate (Wulff, 1984b). The
U.S. Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156
mixture momentum and mass-balance equations are analytically integrated over the flow paths in the reactor vessel. The mixture energy and vapor mass-balance equations are integrated over 55 computational cells in the reactor vessel. The resuiting ordinary differential equations are explicitly integrated with respect to time. The EPA has been used to analyze the LaSalle event and to investigate transients which could arise from SCRAM failures, such as anticipated transient without scram (ATWS) (Wulff, 1992). Therefore, the EPA has shown its capability to analyze instability events.
2. Objective The H I P A - B W R code of the EPA had been developed and tested originally for BWR plant transient simulatio~s. The code has recently been used for the first time to predict oscillatory flows of the type expected during BWR instability transients (including ATWS). Therefore, there is a need to quantify the accuracy of the code for simulating kinematic instabilities. The objective of the EPA validation presented here is to determine the accuracy of the code predictions for oscillatory transients, by utilizing the results of tests performed at the Peach Bottom Unit 2 at the end of cycle 2 (Carmichael, 1978). In particular, the .predicted gain of power-to-pressure tra,sfer function and the predicted phase shift are to be compared with the experimentally determined gain and phase shift.
3. Code validation The EPA assessment, described in the following sections, covers the interactions of neutron kinetics, the fuel heat transfer and the thermohydraulics, as well as the balance of plant dynamics, including the pressure regulator and the feedwater control system.
3. I. Peach Bottom stability experiments The objective of the Peach Bottom core stabliity tests (Carmichael, 1978; Woffinden, 1981) was
147
to show that small pressure perturbations can be used to demonstrate the BWR stability margin, to obtain data for the validation of stability analyses and to demonstrate BWR stability at low-coreflow conditions. Here, we use the data for assessing the capability of the EPA for stability analyses. Two series of tests (Carmichael, 1978; Woffinden, 1981) were performed at Peach Bottom Unit 2. The first series of tests (Carmichael, 1978) were conducted at the end of cycle 2 and the second series (Woffinden, 1981) were conducted during cycle 3. Both tests were performed with the same procedure and the same instrumentation. However, the second series of tests (Woflindcn, 1981) had an additional objective of investigating the effect of exposure on plant stability. There were set of runs for each of the burn-up conditions. The quality of data was the same for the two series. The standard deviations for the core exit pressure data. for the first series of tests varied between 2.2 psi to 3.8 psi, with a mean pressure of the order cf i000 psia. The standard deviation for the core exit pressure for the second series of tests was available only for the one test and it was 1.6 psi. There were curves for coherence function between power and pressure. The curves were similar in the two series. The coherence was close to 0.95 for frequencies of interest ( < 0.8 Hz). The transfer function curves had error bars in the first set, but no error bars in the second set of tests. Furthermore, there were four tests at the same exposure conditions for the first series (Carmichael, 1978), in comparison to the second series of tests (Woffinden, 1981), where the largest number of tests at one exposure condition was only three. In addition, we had earlier modeled turbine trip tests for the end of cycle 2 (EOC-2) (Carmichael, 1978) and have all the neutronic parameters for the core. Based on these considerations, and the objective of this research, the first series of the tests (Carmichael, 1978) were selected for the validation. The Peach Bottom stability tests (Carmichael, 1978) were conducted by maneuvering the reactor into the selected low-flow, steady initial conditions, as listed in Table 1 below, and then by introducing periodic step changes of 0.55 bar
U.S. Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156
148
(8 psi) in the pressure regulator reference set-point setting, starting with a down step. At first the steps were equally spaced at intervals of l0 s. This method was then abandoned in favor of the more advanced pseudo-random binary stepping sequence with a sampling interval of I s (Kerlin, 1974). All the documented results for the first series of tests were 3btained by pseudo-random binary-sequence stepping. The system pressure and the fission power ( A P R M signal) were measured, and the pressureto-fission-power transfer function was calculated from the measurements by non-linear least-square curve fitting, in the frequency range between 0.02 and l Hz. From the calculated transfer function were then obtained the gain and the phase shift as functions of frequency (Carmichael, 1978), as well as the coherence between pressure and fission power. Thc coherence results indicate that the experimental results are valid only up to 0.45 Hz, and beyond this frequency the data are noisy. It should be noted that Test PT3 is reported (Carmichaei, 1978) to have a remarkably low core-inlet subcooling temperature. A simple combination of global mass and energy balances with the mass and energy balances for the downcomer relates (for steady-state conditions) the feedwater enthalpy hFw to the specified total power P, the core inlet mass-flow rate Wet and the specified core inlet subcooling enthalpy ( h r - h o ) by h~-w = h~--
i%
( !)
P
'~",...l(izr-- h,..O - 1 where the liquid saturation enthalpy hf and the
evaporation enthalpy hfg are evaluated at the vessel pressure. After evaluating Eq. (1) for Test PT3, subtracting from the result the feedwater enthalpy rise (9141 J k g - ~) in the feedwater pump and looking up the corresponding feedwater temperature from the steam table, one finds that the feedwater exit temperature at the last feedwater heater would have had to be 59.3 K (106.8 °F) higher than the steam inlet temperature of 469 K (196 '~C, 385 ~F) at the same hez~ter. Since that is impossible (violation of Second Law of Thermodynamics), and since it was impossible to consult with the authors of the test documentation, it was decided to omit Test PT3 from the EPA assessment.
3.2. EPA simulation of Peach Bottmn stabiliO, tests
3.2.1. Input data and initial conditions The EPA was set up for simulating the Peach Bottom Station Unit 2 for Cycle 2, with input data taken from the references listed in Table 2. The Peach Bottom stability tests are documented in the EPRI report (Carmichael, 1978). It was difficult to obtain consistent, plant-specific information from a single, reliable source. It was not available in the test reports (Carmichael, 1978). The information was collected from different sources as shown in the last column of Table 2, and inconsistencies had to be resolved, primarily in the information on core pressure drop and form loss coefficients. The axial power shape was taken directly from documented tables (Carmichael, 1978 (pp. C-2,3
Table 1 Initial reactor conditions for Peach Bottom stability tests (Wulff. 1992 (p. 3 6)) Test no.
Power ........ MWt
Core inlet flow (Ib h ~) %
kg s i PTI PT2 PT3 PT4
1995 1702 1948 1434
Core inlet
60.6 51.7 59.2 43.5
6627 5418 4901 4901
l0t, 52.6 43.0 38.9 38.9
% 51.3 42.0 38.0 38.0
Pressure
Subcooling temperature
bar
psia
'C
'F
68.9 68.4 69.3 68.9
1000 992 1005 999
14.5 15.7 6.4 15.2
26. I 28.3 11.5 27.2
U.S. Rohatgi et aL[ Nuclear Engineering antt Design 151 (1994) 145-156
and 5)). The radial peaking factor was computed by square power weighing of the data reported on the core cross-section (Carmichael, 1978 (pp. C2.3 and 5)). Since it was not possible to obtain reactivity coefficients for Peach Bottom, we approximated the void, moderator and Doppler reactivity coefficients for Peach Bottom by those of the LaSalle 2 power plant, for the same fuel burn-up. This approximation is justified because LaSalle 2 has the same core size, and the reactivities do not strongly depend on geometric fuel parameters. Form losses at core entrance and exit affect the core stability strongly, but they had to be taken from two different publications, since no complete source could be found. As there was no information available for validating directly any of the important pressure regulator parameters, we matched the documented natural frequency of 0.25 Hz of the pressure regu-
lator and the documented power spectral density of the pressure in the steam line (Carmichael, 1978 (p. 6-4)). Steady-state conditions were achieved in the EPA at the same power and pressure levels as in the Peach Bottom tests. Table 1 shows the initial conditions for the three tests, Test nos. PTI, PT2 and PT4, used in this assessment. 3.2.2. Transient simulation The pseudo-random binary-sequence generator was used ia the EPA, to superimpose a binary switching sequence on the pressure setpoint, at the output junction of the integrator to the right of the RPSP block in the pressure regulator schematic shown in Fig. 1. The stepping was controlled to have the mean of zero and the amplitude of 0.276 bar (4 psi), i.e. the same peak-to-peak change as in the experiments, but without the steady-state drift caused in the
Table 2 List of input data references for simulating Peach Bottom stability tests Type of data
References
Neutron lcinetics parameters Void feedback CVOIDI. CVOID2 Axial power shape and 5: radial power distribution (factor for spatial power square.weighing)
(Diederich, 1988 (p. 34)) (Carmichael, 1978 (pp. C-2, 3)) derived from Carmichael and Niemi (1978 (pp. C-2, 3 and 5))
Fuel specifications 75%7x7and 25%8x8 '~678 W m - 2 °K - t 1000 Btu h- t fl-z '~F- i
Standard GE fuel design Gap conductance (constant)
Thermohydraulic parameters Form loss coefficients Core inlet channels Core exit channels Spacers. lower core middle core upper core
29 1.35 2.42 3.63 2.42
(Homik. (Young, (Young, (Young, (Young,
1979 (p. B-4)) 1985 (Table II)) 1985 (Table 11)) 1985 (Table II)) 1985 (Table I1))
Pressure regulator (see Fig. I) Lead/lag comparison parameters Zpl, zr2 Actuator Frequency = coefficient kp~ = 4.15 s -j
Damping coefficient
kp2
_...'=
2.60 s- i
149
(Wulff, 1984 (p. 3-140)) Computed to match natural frequency of 0.25 Hz and PSD function for pressure (Carmichael, 1978 (p. 6-4)). For symbols see Fig. 2 (Wulff, 1984 (p. 3-140)). Normal HIPA value
U.~" Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156
150
N !
+ ,,
--
o
Demand Erro
To Recirculation Flow
~-J
ROSa
I ~
Controller
II I
Press.Se~t.| AUjustmt.
IJ. • i Rt. Of. Change E l ~ i~ Pressure I I s I
,
_. ~ } -%"
II - - ~ - I
TurbineInlet Pressure
-"
L_J Press.SetoLI
el
orl + ~"
I
J -,
D ,.sv-'eq
II
I TC~q'SV I
I
L Open I
.
IMtn|:
" I
I
I
'
'
Actuator
+
"~'$' ,* k-" S * k
SB V~
/
.,v-q ISS I
Actuator
Fig. I. i'ressure control system mode! Engineer..ng Plant AnalyT~r.
Core Pressure Pseudo-random
Binary Sequence
8E-3
r.....
.
-
,
4.41[-3
2.2E-3
a.
,
O.O~O
T
-
i -IE-3
-4.4~-3
, I00
I 105
ilo time, S
~4E-3
,L I15
II~ 120
Fig. 2. Pressure ~gulator set point perturbation with pseudorandom binary sequences.
105
I 11~~,
time, s
115
120
Fig. 3. Sample of core pressure predicted by EPA for pseudorandom binary sequence perturbation in pressure regulator set point.
U.S. Rohatgi et at. / Nuclear Engineering and Design 151 (1994) 145-156
coherence ?PPr is defined by
Core P o w e r ~) 0.12 r,,o "~ 0.04
'~ppr(fDk) =
I ~ -OA2
100
105
110 time, s
115
120
Fig. 4. Sample o f core power predicted by EPA for PRBS perturbation in pressure regulator set point.
experiment by the chosen off-on switching. Figs. 2, 3 and 4 show the pseudo-random binary sequence, core pressure and core power, respectively.
3.2.3. Frequency-domain results Personal computer-based standard programs for spectral analysis were used to calculate the complex transfer function, its gain and phase shift as functions of frequency. The details are given elsewhere (Wulff, 1992 (Appendix E)). The spectral analysis introduces bias and random errors in the results owing to the finite size (number of data points) and the finite number of blocks. The bias error eb is estimated from the following expression (Bendat, 1980 (p. 76)):
lfBe'~2=l( l '~2 'b = 5~,Brr) 3kNftB,)
(2)
where B~ = I/(N~t) denotes the fr-Jquency resolution, Br is the frequency bandwidth associated with the gain equal to i / , / 2 times the maximum gain. 6t is the sampling time interval, and N is the block size. The bias error decreases with the size N of the block, the sampling time interval and the half peak gain bandwidth (Bendat, 1980 (p. 21, Eq. (1.58))). The transfer function also has a random error Er which is estimated from Bendat and Perisol (1980 (p. 274)): (1Er =
7 p p r 2 ) 0'5
.yPi,r~n
C S Dppr( °Jk) * CSDppr( (Ok)
PSDpe( mk) *PS~p~p,(~,,~)
~o -o.o4
~-o.2o
151
(3)
where n is the number of blocks of size N and the
(4)
Furthermore, CSD and PSD are cross-spectral density and power-spectral density functions, respectively. Notice that the random error ¢, decreases as n, the number of blocks, increases. For a fixed sample size nN, and without overlapping of data at the ends of data blocks, any attempt to decrease the bias error Eb by increasing the block size N will lead to a reduction in n, the number of blocks, and thereby an increase in the random error er. The choice of the block size N is governed by the need to control the bias error nb within the limits between 0.5% and 2%. Experience showed (Bendat, 1980 (p. 268)) that this bias error bracket is a reasonable compromise in balancing the two errors Eb and ¢r with opposite trends.
3.2.3.1. Application of spectral analysis to code results. The EPA-computed pressure, fission power and time were transferred from the EPA to a personal computer. For each transient, 10 000 data triplets, consisting of pressure, fission power and time, were transferred. The spectral analyses of all three EPA predictions were performed with the existing personal-computer-based program. This program utilized 8192 of the 10000 supplied data points. The 8i92 data points were divided into four blocks of 2048 points each. Three additional blocks were formed by combining one-half of the points in the first four blocks with the adjacent half of the neighboring block. An eighth block contained the first half of the first and the last half of the fourth block. Thus, there were n = 8 blocks of N = 2048 points. Table 3 summarizes the results of the calculations. In :his table, columns 1 to 7 list the test numbers, the block sizes N and the numbers n of blocks used in the spectral analysis, the sampling time interval 6t, the peak gain Gmax, the frequency to at .... ~" ,1 .~, ~t . LIIK:; peak gain, and the coherence 7 t~L gain, respectively. The remaining two columns show the bias error ¢b and the random error ¢,, respectively. The bias errors are under 2.1%, so
U.S. Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156
152
Table 3 Spectral analysis results and error estimates Test no.
PBTI PBT2 PBT4
Block size (N)
2048 2048 2048
Number n of blocks
8 8 8
Time step 6t (s)
0.0305 0.0305 0.0305
Peak gain (power/pressure)
Frequency (o at peak gain
Gin,,,,
(Hz)
48 69 79
0.34 0.37 0.29
the block size is acceptable. The largest random error is 27.4%.
4. Comparison ~etween EPA and Peach Bottom test results
The pressure regulator model in the EPA was tested by comparing the EPA-predicted power spectral density with the reported power spectral density of the pressure. The result is shown in Fig. 5, and demonstrates that the pressure-control system in the EPA does not filter out or unduly excite the system pressure. While these two effects have, in principle, no impact on the pressure-to-power transfer function, they affect very strongly the signal-to-noise ratio and the coherence.
Coherence 7PPr Bias error % at peak gain (%)
Random error
(%) 0.79 0.82 0.84
0.5 1.06 1.97
27.4 24.4 22.4
Table 4 shows for selected frequencies the experimentally obtained and the EPA-predicted gains and phase shifts, along with the differences. The bold values are the peak values. Unlike the experimental data, the predicted pressure and fission power data were not fitted to "empirical models", but processed directly by fast Fourier transform. The coherence at the computed peak gain is 0.75, 0.70 and 0.82, respectively, for Tests PTI, PT2 and PT4. The table shows that the EPA underpredicted the gain vs. frequency curve by the means and standard deviations of ( - 10_+28)% and of ( - I 4- 40)% for Tests PTI and PT2, respectively, and overpredicted for Test PT4 by ( + 29 + 52)%. The test with the lowest power came out with the lowest signal-to-noise ratio and the largest difference between tes! data and prediction.
Table 4 Comparison of EPA prediction of gain with experimental data from Peach Bottom stability tests Test PTI
Test PT2
Test PT4
Exp.
EPA
Diff.
Exp.
EPA
Diff.
Exp.
Hz
(%)
(%)
(%)
(%)
(%)
(%)
(%)
EPA (%)
(%)
0.04 0.06 0.08 0. l0 0.20 0.29 030 0.32 0.34 0.37 0.38 0.40 0.50
5.0 5.0 5.0 8.0 14.5
2.5 3.9 5.6 7.2 18.0
- 50 - 22 6 - l0 24
4.8 4.8 5.0 7.0 14.0
3.3 3.8 5.4 8,6 23.0
-31 -21 8 23 64
29.0 49.0 46.0
38.0 44.0 48.0
31 - 10 4
38,0
46.0
21
4.2 4.2 5.7 6.6 16.4 38.0 40.0
2,9 4.5 6.0 8.4 29.0 79.O 76.0
-31 7 5 27 77 108 85
53.0 55.0 51.0 93.0
69.0 61.0 34.0 20.0
30 II - 33 - 78
55.0 36,0
32.0 44.0
-41 22
37.0 47.0
28.0 23.G
- 24 - .; I
Diff.
U.S. Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156 ~, 10.4
I
+ ~" 10-5 - I ~ , " ~ Q
~
I
I
i
I
I
I
I
a perturbation o f + 4 psi which is abcat 3% of the pressure fluctuation during the limit.-cycle oscillations. The linearization assumption may contribute to the discrepancy. Figs. 6-8 show the graphical comparison between the data and the prediction for the gain of
I
Experimental
-I-
10.6 10-7
a_ 10.8
~
153
10"9 I
I
I
I
I
0.1
0.2
0.3
0.4
0.5
I
I
0.6 0,7 FREQUENCY(Hz)
I
I
0.8
0.9
120
1.0
Fig. 5. Power spectral density functions: comparison of EPA(solid line) and experimental results ( + ) for testing pressure regulator model in EPA.
computed
,
,
100 =.
80
~
611
=
,
,
,
=
,
1
,
r-'--
Experimental EPA-Computed
o
~
10
The frequency-domain code NUFREQ-NPW has recently been used to predict these Peach Bottom stability tests (Taleyarkhan, 1988). The pressure perturbations were applied directly to the dome pressure, and the transfer function between the core power and the dome pressure was computed. The results from these calculations are the only ones available in the published literature for validation with Peach Bottom tests. The N U F R E Q - N P W code was applied to all four tests. However, we found that the data for the test PT4 (Taleyarkhan, 1988 (Fig. 7a)) did not match with the original data (Carmichael, 1978 (Fig. E-13)). We compared our results with NUFREQNPW results for the remaining two tests, PTI and PT2 from the first series and the tests 2PT3, 3PT2, 3PT3 and 4PT2 from the second series. The results from NUFREQ-NPW were read from Figs. 4(a), 5(a), 8(a), 9(a), 10(a) and l l(a) of the reference (Taleyarkhan, 1988). The N U F R E Q - N P W code overpredicted the gain by the mean and standard deviations of (63 + 13)% and (28-51)% for tests PT! and PT2, respectively. This code was also applied to the second series of tests at Peach Bottom (Woffinden, 1981). The comparison was slightly better than with the first series. The code overpredicted the gain by the mean and standard deviations of 13 _ 31%, 23 + 22%, 38 +44% and 75 +47% for the tests 2PT3, 3PT2, 3PT3 and 4PT1 respectively. A comparison of results from two codes indicates that the EPA results compare better than N U F R E Q - N P W results with the data. It should be recognized that these tests were performed with
2O 0
~
0.1
0.2
0.3
0.4
0.5
0.6
FREQUENCY(Hz) Fig. 6. Gain of power-to-pressure transfer function for Peach Bottom Test PTi: power and pressure are normalized by initial values. 300
I
i
i
I
I
[
I
i
i
i
Experimental EPA-C0mputed
o
25O
I
200 150
100 50
0o
0.2 0.3 0.4 FREQUENCY(Hz)
0.1
0.5
0.6
Fig. 7. Gain of power-to-pressure transfer function for Peach Bottom Test PT2: power and pressure are normalized by initial values. trio
i
i
i
i
i
i
i
i
!
80
/ ~ -
0
~ ' ~ 1
0
I
0.1
t
f
0.2
I
0.3
I
i
i
Experimental EPA-Computed-
o
I
0.4 FREQUENCY(Hz)
I
I
0.5
I
0.6
Fig. 8. Gain of power-to-pressure transfer function for Peach Bottom Test PT4: power and pressure are normalized by initial values.
U.S. Rohatgi et al. Nuclear Engineering and Design 151 (1994) 145-156
154 120
80 60 40
T
1
T
0.1
I
I
I
~
I
I
I
0.2 0.3 0.4 FREQUENCY(Hz)
1
0.5
0.6
Fig. 9. Phase angle of power-to-pressure transfer function for Peach Bottom Test PTI: power and pressure are normalized by initial values. 2(IO
I
i
I
I
o
~'
I
i
I
I
I
Experimental
I
A
~/-J~
lJ.......i
0 -100 • 2(]0
0
I
!
I
I
0.1
I
I
I
f
I
A
0.2 0.3 04 FREQUENCY(Hz)
0.5
0.6
Fig. IO, Phase angle of power-to-pressure transfer function for Peach Bottom Test PT2: power and pressure are normalized by initial values.
120
I
I
I
o
I
I
I
I
|
I
Experimental
|
i
~
//~
I
1
~.~ 40 =
0 -40 -so
-120 0
I
I
0.1
I
I
I
1
I
I
0.2 0.3 0.4 FREQUENCY(Hz}
I
0.5
0.6
Fig. I I. Phase angle of power-lo-pressure transfer function for Peach Bottom Test PT4: power and pressure are normalized by initial values.
the pressure to power transfer function, Figs. 9-11 show the corresponding phase shift comparison. The bars with the open circles in these figures represent the uncertainty in the data. The phase shift between the power and the pressure is a measure of void generation rate and the effect of voids on neutronic power generation. The pressure perturbations affect the void genera-
tion rate, which in turn affects the neutronic power through void feedback effects. As shown in Figs. 9-11, the differences between the data and the prediction for the phase shift is within the experimental uncertainties upto 0.3 Hz. It is concluded that the models for vapor generation and void feedback effect are adequate for the small amplitude transiems represented by the Peach Bottom stability te,~ts.
5. Conclusions
The study reported here shows that: (I) the simulation methodology of the HIPABWR code in the Engineering Plant Analyzer (EPA) can be successfttlly used to predict small-amplitude oscillations, (2) a time-domain systems code can be sucessfully assessed with spectral stability data from a power plant, by using time-domain methods. Key features of HIPA- BWR for stability analyses are its drift-flux model for simulating nonequilibrium, nonhomogeneous two-phase flow, and its explicit algorithms for integrating the field equations. Relative to the plant, the pressure regulator model in HIPA-BWR neither filtered nor excited the system pressure. The predicted power spectral density function of the system pressure matched the experimental data over four decades in the frequency range from 0.04 Hz to. 0.8 Hz. The EPA predicted for Peach Bottom Tests PTI, PT2, and PT4 the gain of the power to pressure transfer function with the biases and standard deviations of ( - l0 _28)%, ( - 1 + 40)% and ( + 28 _ 52)"/o, respectively. In comparison, the reported N U F R E Q - N P W calculations differ by ( 6 3 + 13)% and ( 2 8 _ 5 1 ) % for PTI and PT2 tests and by 13 +31%, 23 + 22%, 38 + 44'70 and 75 +47% for tests 2PT3, 3PT2, 3PT3 and 4PTI. The respective frequencies at peak gain were predicted by the EPA with the errors of + 6%, + 3°/, and - 2 8 % . The discrepancy in the EPA prediction of phase shift is within the uncertainties of the experimental data.
U.S. Rohatgi et aL[ Nuclear Engineering and Design 151 (1994) 145-156
This comparison is for small amplitudes, but it encompasses neutron kinetics, thermal fuel response, coolant thermohydraulics and control systems. It is recommended that EPA should also be assessed with the stability tests performed at Peach Bottom during Cycle 3.
Eb Er 0 09 *
155
bias error random error phase angle frequency cwnplex multiplication
Subscripts Acknowledgements This work was performed under the auspices of the US Nuclear Regulatory Commisssion. The authors would like to thank Dr. Jose March-Leuba of Oak Ridge National Laboratory for providing the computer program for spectral analysis and also for providing timely advice on its use.
Dedication The first author, Upendra Singh Rohatgi, would like to acknowledge the contribution of Dr. Novak Zuber, since 1975, to the author's understanding of the physics of two-phase flow and to developing a critical view of the computer code's ability to predict the phenomena. Dr. Zuber encouraged us to have a healthy skepticism of computer codes and to be wary of getting good results for the wrong reasons. This critical thinking has guided us in the past and will continue to guide us in the future.
Appendix A: Nomenclature Be Br CSD n N P Pr PSD T
frequency resolution half-power-point bandwidth cross spectral density number of blocks block size power pressure power spectral density duration of the transient for one block
Greek letters 6t "~PPr
sampling time internal t coherence between P and Pr
•P Pr
power pressure
References J.S. Bendat and A.G. Piersol, Engineering Applications of Correlation and Spectral Analysis, Wiley, 1980. L.A. Carmichael and R.O. Niemi, Transient and stability tests at Peach Bottom Atomic Power Station Unit 2 at end of Cycle 2, Topical Report, EPRI NP-564, 1978 (Electric Power Research Institute, Palo Alto, CA). G.J. Diederich, Potentially significant event: Unit 2 scram initiated by valving error, LaSalle County Station, letter to N. Kalivianakis, March I I, 1988. K. Hornik and J.A. Naser, RETRAN analysis of the turbine trip tests at Peach Bottom Atomic Power Station Unit 2 at the end of Cycle 2, EPRI Report NP-1076-SR, 1979 (Electric Power Research Institute, Palo Alto, CA). M. Ishii, Thermally induced flow instabilities in two-phase mixtures in thermal equilibrium, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, 1971 (University Microfilms Inc., Ann Arbor, MI). M. Ishii, Study of flow instabilities in two-phase mixtures, ANL-76-23, March 1976. M. Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, ANL-77-47, 1977 (Argonne National Laboratory).) T.W. Kerlin, Frequency Response Testing in Nuclear Reactors, Academic Press, New York, 1974. R.T. Lahey Jr. and G. Yadigaroglu, NUFREQ, A computer program to investigate thermo-hydraulic stability, NEDO13344, 1973 (General Electric Company)• R.T. Lahey Jr. and F.J. Moody, The thermal-hydraulics of a boiling water reactor, 1977 (American Nuclear Society. 5~ North Kensington Avenue, LaGrange Park, iL 60525). J. March-Leuba, Dynamic behavior of boiling water reactors, Ph.D. Dissertation, University of Tennessee, Knoxville, TE, 1984. J Mareh-Leuba, D.G. Cacuci and R.B. Perez, Nonlinear dynamics and stability of boiling water reactors: Part l - qualitative analysis, Nucl. Sci. Eng. 93 (1986a) ! I 1-123. J. March-Leuba, D.G. Cacuci and R.B. Perez, Nonlinear dynamics and stability of boiling water reactors: Part 2 - quantitative analysis, Nucl. Sci. Eng. 93 (1986b) 124-136.
156
U.S. Rohatgi et al. / Nuclear Engineering and Design 151 (1994) 145-156
U.S. Rohatgi, L.Y. Neymotie and W. Wulff, Assessment of RAMONA-3B methodology with oscillatory flow tests, Nucl. Eng. Des. 143 (1993) 69-82. P. Saha, Thermally induced two.phase flow instabilities, including the effect of thermal nonequilibrium between phases, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, GA, 1974 (University Microfilms Inc., Ann Arbor, M1). P. Saha, M. lshii and N. Zuber, An experimental investigation of thermally induced flow oscillations in two-phase systems, J. Heat Transfer, ASME 98 (1976) 616-622. R. Taleyarkhan. M.E. Podowski and R.T. Lahey Jr., An analysis of density-wave oscillations in ventilated channels, NUREG/CR-2972, 1983. R. Taleyarkhan, A.F. McFarland, R.T. Lahey and M.Z. Podowski, Benchmarking and qualification of NUFREQNPW code for best estimate prediction of multi-channel core stability, Trans. Am. Nucl. Soc. 57 (1988) 347349. F.B. Woflinden and R.O. Neimi, Low flow stability tests at Peach Bottom Atomic Power Station Unit 2 During Cycle 3, EPRI-NP-972, April 1981 (Electric Power Research Institute, Palo Alto, CA).
W. Wulff et al., A description and assessment of RAMONA3B MOD.0 Cycle 4: A computer code with three-dimensional neutron kinetics for BWR system transients, NUREG/CR-3664, January 1984a (Brookhaven National Laboratory, Upton, NY). W. Wulff, H.S. Cheng, S.V. Lekach and A.N. Mallen, The BWR Plant Analyzer, NUREG/CR-3943, BNL-NUREG51812, August 1984b. W. Wulff, H.S. Cheng and A.N. Mallen, Causes of instability at LaSalle and consequences from postulated scram failure, Proc. OECD Int. Workshop on Boiling Water Reactor Stability, Holtsville, NY, October 1990, CSNI Report No. 178, Committee on the Safety of Nuclear Installations, 1990 (OECD Nuclear Energy Agency, 38 Boulevard, Sucbet, 75016 Paris, France), W. Wulff, H.S. Cheng, A.N. Mallen and U.S. Rohatgi, BWR Stability analysis with the BNL Engineering Plant Analyzer, NUREG/CR,5816, BNL-NUREG-52312, 1992 (Brookhaven National Laboratory). R.K. Young and S.A. Auve, Steady-state thermal hydraulic analysis of Peach Bottom Units 2 and 3, using the FIBWR computer code, PECO-FMS-001, 1985 (Philadelphia Electric Power Compa~y).
