A stochastic Method in NPP Diagnosis.pdf

7/28/2019 A stochastic Method in NPP Diagnosis.pdf

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A ST O C H AS TIC M E T HO D F O R N U C L E AR P O W E R P LA N T D IA GN O SISR. B. Perez* and R. T. Wood*The University of TennesseeKnoxville, Tennessee 37916

I N T R O D U C T I O NThe value of using neutron noise descriptors, especially the power spectral den-

sities (PSD s) of ex-core detec tors, to monitor core barrel motion and fuel elementvibrations in pressurized water reactors (PWRs) is well established.1 "6 Indeed, in themid-frequency range (1-20 Hz), PWR neutron noise is dominated by vibration peaksin the ne utron PSD tha t result from the motion of reactor internals. A qualitativeexamination of such descriptors from a 1150 MWE Westinghouse PWR plant, re-vealed significant changes in the p lan t's noise signa ture (P SD ) as its firs t fuel cycleproceeded. The purpose of this work is to use a mathematical model of the interac-tion between small mechanical motions and the core neutronics to provide a tool forqua ntitative investigation of the PSD structure in the vibrational frequency range .7The purpose of neutron noise analysis is to provide information on plant condi-

tions by the study of power traces from ex-core detectors. D ue to the action of thecoolant flow through the core and pump induced vibrations, the core barrel, whichis bolted at the top of the reactor vessel, performs a pendular motion with a naturalfrequency determined by the m echanical param eters an d co nstraints of the system.2""5In addition, external forces deform the cylindrical shape of the core barrel by inducingvibrational modes which are excited by the turbulence of the coolant flow and by the"table-shaker" effect of the core barrel motion. As a result of the various mechanicalmotions, the detector response will vary in a manner proportional to the importancefunction at the location of the disturbance.A typical ex-core neutron detector normalized PSD for a 1150 MW E PW R isshown in F ig. 1. Below 1 Hz the PSD is dominated by the feedback therm al hydraulicloop effects which evolve with time constants of the order of seconds. Between 3 Hzand 30 H z, the PSD exhibits a set of resonances arising from the vibrational andpendular modes previously discussed. This disparity in the "natural" frequencies ofthe system is a fortunate break for the noise analyst as one can perform the modelingof the feedback and mechanical effects in a separate fashion.

I D E N T I F I C A T I O N O F P S D S T R U C T U R EIt can be shown7 on the basis of first order perturbation theory that the neutrondetector PS D ,


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DISCLAIMERThis report was prepared as an account of work sponsored by an agency of theUnited Sta tes Government. Neither the United States Government nor any agencythereof, nor any of their employees, m akes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, completeness, or use-fulness of any information, apparatus, product, or process disclosed, or representsthat its use would not infringe privately owned rights. Reference herein to any spe-cific commercial product, process, or service by trade name, trademark, manufac-turer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof.The views and opinions of authors expressed herein do not necessarily state orreflect those of the United States Government or any agency thereof.


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wh ere the subind ex A varies over the frequencies of the m echanical v ibratio ns a ndwhere we introduce the pole strength and asymmetry factors, A\ and D\, respectively.Th e result in E q. (1 ) shows th at the neutron de tector PSD is the superposition ofa set of resonances at the various frequencies v\. The l ine shapes are asymmetricwith respect to the resonance peak because the term (u; v\) changes sign as it goesthrough the resonance maximum. The second term within the bracket in Eq. (1) is anonresonant term arising from the reflection of complex poles at negative frequencies.The parametric model in Eq. (1) has been implemented in the program "CAR-D IO GR AM A" which performs a least squares fit of the functional relation to m easuredneutron P SD da ta. A typical result of the C ardiograma algori thm is shown in F ig. 2,where the da ta points correspond to the PSD of one of the ex-core neutron detectorsat the 1150 MWE PWR SE QUOYAH-1 nuclear power plant . The r es onance at 6 Hzhas been associated w ith the pe ndular motion of the core suppo rt barrel (C SB). T hepeaks at 3.6, 8 and 16 Hz correspond to fuel element vibrations. Two shell mode res-onances have been identified: a core barrel shell mode at 12 Hz and a pump-inducedshell mo de at 20 Hz. Th e evolution of the ne utron PSD as a function of time a ndpower level ha s bee n followed for nearly two full cycles at the S E QU O YA H- 1 pla nt. 5A short-term and several long-term effects have been observed.The short-term effect observed consisted of the shifting of the fuel vibrationalpeaks towards lower energies following a decrease in power, while the core barrel andshell mod el resonance frequencies rem ain unaltere d. Am ong the various long -termeffects, P SD s and C PS D s of the ne utron noise exhibit a resonance at frequency ofappro xima tely 6.7 H z. Ph ases between the cross-core detec tors at this frequencyare always 180 p and the coherence is always greater than 0.8, thereby indicatingpendular CSB motion. Another resonance at 8.0 Hz, having the same coherence andpha se relat ionships can also be resolved in th e PSD s and C SPD s at th e beginning ofthe first fuel cycle. This resonance occurs at approximately the second mode of fuelassembly vibration (the first mode occurs at 3.6 Hz) as deduced from in-core neutronnoise me asurem ents m ade at SE QUO YAH -1 . T he fuel assembly fundamental mod e

decreased in frequency over the first fuel cycle to 3.0 Hz with a corresponding decreasein the second mo de resonant frequency. This second m ode resonance merged with t heCSB resonance (6.7 Hz) to form what appears to be a s ingle broad peak in the 5 to7.5 Hz rang e, as shown in F ig. 3 . The normalized root mea n square (N RM S) of theneutron noise (at nominal full power conditions) in the 5- to 10-Hz frequency rangeincreased by a factor of five from the beginning to the end of the first fuel cycle.At the beginning of the second fuel cycle, the neutron noise amplitude in this samefrequency range decreased, but only to a level somewhat higher than at the beginningof the first cycle and resonances could be distinguished only at 3.0 and 7.0 Hz.R E S U L T S

In this section, we discuss the application of the present stochastic model to theinterpreta t ion of the neu tron PS D in the vibrat ional region. O f the observed long-termeffects the most worrysome one is the "disappearance" of the core barrel resonanceat the end of the first cycle.To answer this question, measured PSD s from SE QUO YAH-1 taken at varioustimes during the first and second fuel cycles were fitted using the stochastic modelth at was developed. Table 1 lists the frequencies an d pole- strength factors for thefirst two fuel element resonances and for the core barrel peak. These results, whichwere obtained from plant signatures at the beginning, middle, and the end of the firstfuel cycle and at the middle of the second fuel cycle, reveal the following features:

(a) the pole strength factors for the first and second fuel resonances increased con-siderably between April '82 and August '82;


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(b) the fuel element peaks shifted towards the low frequency end of the spectrum;and(c) the pole-strength factor for the core barrel peak remained fairly constant sinceApril '82, at a level of about one order of magnitude with respect to the valuefound in April '8 1 .

The large increase in the pole-strength factor and the frequency shift of the secondfuel element vibrational mode account for the disappearing act performed by the corebarrel peak. However, the ability of the stoch astic model to describe the stru ctur eof the n eu tron PSD and to sep arate the various mechanical m otions allowed confir-m ation th at the core barrel motion had not changed. Th is feature of the model isillustrated in F ig. 4 . It can be seen th at the broad peak a roun d 7 Hz was interpretedas the contributions arising from the core barrel peak and the second fuel mode vi-bra tion . N ote tha t th e fitting program would have failed to work properly witho utthe information gathered from earlier data throughout the fuel cycle, where the corebarrel resonance was not masked by the resonance at 8 Hz. In fact , the "C AR D IO -G R A M A " program refused to fit that broad peak with only one resonance. The useof a core barrel contribution, with parameter guesses based on previous experience,was needed to achieve the functioned fit shown in Fig. 4.

E xam inatio n of Tab le 1 reveals two plant "aging" effects: (i) the increase ofthe pole strength function between April '81 and April '82 for the core barrel peakindicates some "loosening" of the core barrel restrictions, and (ii) the shift of the fuelelement resonances towards lower frequencies shows a decrease in the "stiffness" ofthe core's mechanical configuration.C O N C L U S I O N S

In summary, f irs t order perturbation theory has been used to relate the responseof a neutron detector to small mechanical motions of the reactor internals . By math-ematically manipulat ing the model, an equation for the neutron PSD was obtainedthat describes each motion in terms of a pole-strength factor, a resonance skewnessfactor, a vibra tion dam ping factor, and a frequency of vib ration . Th is formulationallows each resonance peak to be quantified in terms of four identifiable parameters.T he mod el was f i tted to measured PS D s obtained from a P W R at various t imes du ringa fuel cycle. The mechanical motion parameters for several resonances were trackedto determine trends that indicated changes in vibrat ions within the reactor core. Inaddit ion, the resonance model gave the abil i ty to separate the resonant componentsof the PSD after th e param eters h as been identified. As a resu lt, the behavior ofseveral vibration peaks were monitored over two fuel cycles.R E F E R E N C E S

1. J . A. Th ie, Power Reactor Noise, (LaG range , IL, Am erican N uclear Society, 1 981 ).2. D . N . Fr y et a l. , "Us e of N eutron N oise to D etect BW R-4 I n-C or e I ns t r umentTube Vibr at ions and I mpact ing " NucL Technol 4 3 ( 1 9 7 9 ) .3. W . Bastl , R. Sunder, D . Wach, "O n-Line Vibration Monitoring of P W R In-ter nals ," Proceedings of ANS/ENS Topical Meeting on Thermal Reactor Safety( 1 9 8 0 ) .4 . R, Sun der, D . W ach, "Rea ctor D iagnosis Using Vib ration and N oise Analysisin PW R s," presented at the International Symposium on O perational Safety ofN uclear Power Plan ts , Marseilles , F rance, 1 983.


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5 . F . J. Sweeney, J. M arch-Leu ba, C . M. Sm ith, "C ontribu tion of F uel Vib rations toE x-C ore N eutron N oise D uring the F irst and Second F uel C ycles of the Sequoyah-1Pressurized Water Reactor," Prog, in Nucl. Energy 1 5 ( 1 9 8 5 ) .6. F . J. Sweeney, J. P. Itenier, "Sensitivity of D etecting In-C ore Vibration s an dBoiling in Pressurized W ater Reactors Using E x-C ore N eutron D etectors,"O R N L / T M - 8 5 4 9 , O a k R id g e N a tio n al L a b o ra to r y (1 9 8 5 ) .7. J. M arch- Leub a, G. de Saussure, and R. 3 . Perez Tran s. Am. Nucl. Soc. 4 4( 1983) .

AcknowledgementResearch sponsored by Office of N uclear Physics, U.S. D ep artm ent of E nergyunder contr act number DE -AC 05-84OR21400 wi th Mar t in Mar iet ta E ner gy Sys tems ,Inc.

"The lubm rtud manuscript h baanauthored by contractor ol tt U.S.Govammant undar contract No. DE-AC0S-B4OH214O0. Accordingly, tha U.S.Govammanl ratains a nonaxckaiva.royarfy-fraa licanw to publish or raproducathe pubtanad form of this contribution, oralow othars to do so. for U.S. GovarnmantpurpoM* -


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Table 1. Vibrational Frequencies, u\ (Hz), and N ormalizedPole Strength Factors , A\ (dimensionless), at Selected TimesD uring the F irst and Second Fuel C yclesD a t eRecorded

Ap ril 81**April 82*Aug. 82*A u g . 8 3 e

F l f l3.553.343.083.07

Frequency(Hz)C B67.035.885.685.97

F 2 c7.827.467.257.26

"Fuel element first vibrational mode.6C or e s uppor t bar r el .cFuel element second vibrational mode.' 'F irst fuel cycle.e Second fuel cycle.

F l4 . 7 8 '6.91'1.04-2.53-

i o - 8l O " 8io - 7io - 7

Pole StrengthD imensionlessC B

8 . 0 7 1 0 - 84 . 3 1 - 1 0 " 73 . 2 5 1 0 " 72 . 8 0 - 1 0 " 7

F 29 . 2 2 - 1 0 "8

4 . 4 8 1 0 "71.3810-6

1.3910"6


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1 0 - 2i - 3

oinc_z

10"

10"

ia"8

1 0 - 3i n - 1 0

1C - 1 1

i i n i i i | i i i i 1 1 ii | i i i n n q i i i i n n j i i 11TTrqi i i m a

3 " i 210"

l i f t n i t i i t i m i l t i i m i l l I I I I I n l i < r m i l l i I I M I M I-3 10i-l 10 it1FREQUENCY (Hz)Figure 1. Power spectral density for an ex-core

neutron detector at a typical Westing-house PWR. The data are normalizedto the steady state power level.

10

10

_ jCor* BarrelBeam M o d *

j9 8 % Power

Pump Induced -Sh* M o d *

ton e q u E N C Y ( M Z )

Figure 2. Ex-core neutron detector power spectraldensity from the Sequoyah-1 NuclearPower Plant. The points correspond tomeasured data. The continuous curve isthe result of a Cardiograma fit.


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_ 10

TEND OF FIRST FUEL CYCLEBEGINNING OF SECOND FUEL CYCLEBEGINNING OF FIRST FUEL CYCLE

FREQUENCY HZ )10

Figure 3. Typical ex-core neutron detector powerspectral densities through the firstand second fuel cycles at the Sequoyah-1Nuclear Power Plant.

a-3

N

a

!*

+ EXPERIMENTAL OATA- FITCONTRIBUTIONS:

1 First fual mods2 Cor* barrel3 Second fuel mode

4 CFREQUENCY (Hz)

Figure A. Cardiograma fit to the ex-core powerspectral density showing the contri-butions from the first and secondfuel vibrational modes and from thecore support barrel pendular motion.

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