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Nuclear Engineering and Design 239 (2009) 1128–1135

Contents lists available at ScienceDirect

Nuclear Engineering and Design

journa l homepage: www.e lsev ier .com/ locate /nucengdes

otential steam generator tube rupture in the presence of severe accidenthermal challenge and tube flaws due to foreign object wear

. Liao ∗, S. Guentayaboratory for Thermal-Hydraulics, Department of Nuclear Energy and Safety, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland

r t i c l e i n f o

rticle history:eceived 2 December 2008eceived in revised form 27 January 2009ccepted 9 February 2009

a b s t r a c t

This study develops a methodology to assess the probability for the degraded PWR steam generator torupture first in the reactor coolant pressure boundary, under severe accident conditions with counter-current natural circulating high temperature gas in the hot leg and SG tubes. The considered SG tube flawsare caused by foreign object wear, which in recent years has emerged as a major inservice degradationmechanism for the new generation tubing materials. The first step develops the statistical distributions

for the flaw frequency, size, and the flaw location with respect to the tube length and the tube’s tubesheetposition, based on data of hundreds of flaws reported in numerous SG inservice inspection reports. Thenext step performs thermal-hydraulic analysis using the MELCOR code and recent CFD findings to predictthe thermal challenge to the degraded tubes and the tube-to-tube difference in thermal response at theSG entrance. The final step applies the creep rupture models in the Monte Carlo random walk to test the

SG td to e

potential for the degradedprobability can be applie

. Introduction

Severe accident induced steam generator tube rupture (SGTR)s a concern because the steam generator (SG) tubes are partsf the PWR reactor coolant pressure boundary (RCPB) and fail-re of the SG tubes may lead to fission products bypassing theontainment. The SG tube integrity may be challenged by high tem-erature and high pressure conditions and may have a potential to

ail due to creep rupture in a broad category of station blackoutevere accident scenarios represented by the TMLB’ sequence. Inhe TMLB’ sequence, the primary side pressure is maintained highy the repeated cycling of the pressurizer power operated reliefalve (PORV), the secondary side is depleted of coolant inventorynd becomes dry due to loss of auxiliary feed water, and the sec-ndary side pressure is governed by the repeated cycling of theteam relief valve. Once the steam relief valve fails to reclose dur-ng the repeated cycling, the SG tubes would be subjected to the

ost severe temperature and pressure challenges.The potential of severe accident induced SGTR under such con-

itions was recognized early in the U.S. NRC Severe Accident Risks

eport (NRC, 1990), in which the likelihood of severe accident ther-ally induced SGTR assessed by an expert panel could be very

mall for tubes which were flaw free, but could be a concern ifaws pre-existed in SG tubes. For tubes which were flaw free, the

∗ Corresponding author.E-mail address: yehong.liao@psi.ch (Y. Liao).

029-5493/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2009.02.003

o rupture before the surge line. The mean and range of the SG tube rupturestimate large early release frequency in probabilistic safety assessment.

© 2009 Elsevier B.V. All rights reserved.

later detailed thermal-hydraulic analyses (Knudson et al., 1998;Vierow et al., 2004; Liao and Vierow, 2005) also concluded thatthe first RCPB failure would be the surge line or hot leg, thus elim-inating the potential for severe accident induced SGTR. For thecase of pre-existing flaws in SG tubes, a creep rupture model hasbeen developed and validated by tests for the degraded SG tubesunder severe accident conditions (Majumdar, 1999), and the U.S.NRC (NRC, 1998) has developed a general methodology to assessthe severe accident induced SGTR probability, which appeared sig-nificant at least for severely degraded steam generators. Recently, aplant specific analysis based on the U.S. NRC methodology has beencarried out (Da Silva and Kenton, 2008) to estimate the large earlyrelease frequency contributed by severe accident induced SGTR,given a pre-existing through-wall tube defect. Depending on theinitial SG tube flaw size, the SG tube creep rupture failure maylead to a leak only in the flawed tube or a catastrophic rupture notonly in the flawed tube but probably also in the adjacent tubes dueto cascading failures. Both experimental and analytical evidence(Majumdar et al., 2002) have shown that if the initial flaw size issufficiently small, jet impingement erosion from the induced tubeleaking could not damage the adjacent tubes and therefore leak-ing from a single tube could not depressurize the primary system.In such a single tube failure case with a high primary pressure

maintained even after the SG tube failure, the surge line or hot legwill be expected to fail also within minutes following the SG tubefailure, and therefore the fission product release into the SG sec-ondary side will be greatly reduced. On the other hand, large earlyrelease of fission product into the environment may be assumed if a

Y. Liao, S. Guentay / Nuclear Engineering

Fe

cct

atAtpofi(tawrttpcsdttpiawa

Fn

ig. 1. Temperature fields and distribution of degraded tubes at the steam generatorntrance.

atastrophic rupture is induced in the flawed tube with a suffi-iently large flaw size and causes cascading failures in the adjacentubes.

The U.S. NRC analysis (NRC, 1998) has identified a number ofreas of uncertainty that need to be further addressed, includinghe thermal-hydraulic analysis and the SG tube flaw distribution.s the gas temperature drops gradually while recirculating along

he tube length in the hot leg counter-current natural circulationhenomenon, the most severe thermal challenge to the SG tubesccurs at the top of the inlet plenum tubesheet. The temperatureeld at the top of the tubesheet can be divided into three regionsFig. 1): the hot region with the hot gas leaving the inlet plenum,he cold region with the cold gas returning to the inlet plenum,nd the hottest region. A SG tube with a sufficiently large flaw sizeill fail earlier if its location is in the hottest region than in other

egions. Since the distribution of the flaw location with regard to theube’s tubesheet position was not considered, and strictly speaking,he one dimensional severe accident analysis code alone could notredict the temperature in the hottest region with a high level ofonfidence, it was pointed out in the U.S. NRC work (NRC, 1998) thatome uncertainties were introduced in their methodology whichid not consider the case of a degraded tube that might be located inhe hottest region. Another aspect of large thermal-hydraulic uncer-ainties is about mixing of the hot and cold gases in the SG inletlenum (Fig. 2). Significant mixing tends to reduce the heat loads

mposed on the SG tubes and delay the tube rupture. The severeccident analysis codes generally used a simplied mixing modelith three mixing parameters derived from experiments to char-

cterize the mixing phenomenon in the inlet plenum: the mixing

ig. 2. Steam generator inlet plenum mixing during the hot leg counter-currentatural circulation.

and Design 239 (2009) 1128–1135 1129

fraction, the recirculation ratio and the fraction of tubes carrying thehot gas. The U.S. NRC analysis (NRC, 1998) has performed the mix-ing parameter sensitivity studies on the thermal response of the SGtube, by either varying individually the mixing parameter, or vary-ing simultaneously the three mixing parameters while assumingindependence among the parameters. For the former case, it wasargued that not all mixing parameters had varied over their entireplausible ranges (NRC, 2001), which implies that the temperatureuncertainties might be under-estimated. For the later case, it waspointed out in the U.S. NRC work (NRC, 1998) that the temperatureuncertainties had been over-estimated, since the inter-dependenceamong the mixing parameters was not considered.

The current work addresses these unsolved issues by developingmethods to establish the thermal loads imposed on the SG tubesin the hottest region, the inter-dependence among three mixingparameters used to investigate the mixing parameters’ synergisticeffect on thermal-hydraulic calculation uncertainties, and the dis-tribution of degraded tubes among the three regions at the inletplenum tubesheet. To follow the recent trend of the steam genera-tor operating experience, the current work focuses on the tube flawscaused by foreign object wear, which is a major inservice degrada-tion mechanism for the Alloy 690 new generation tubing materials(Karwoski et al., 2007). The current work sets up the statistical dis-tributions for the flaw frequency, size, as well as the flaw locationwith respect to the tube length and the tube’s tubesheet positionbased on a survey of a few hundred flaws found in numerous steamgenerator inservice inspection reports. As the probability distribu-tion of the severe accident induced SGTR has not been discussed inthe previous studies (NRC, 1998; Da Silva and Kenton, 2008), solvingthese issues allows for the current work to develop a Monte Carlorandom walk technique to estimate the distribution, which alongwith the mean probability should be required for the power plantprobabilistic safety assessment of the large early release frequency.The current work is complementary to the ARTIST internationalconsortium project (Guentay et al., 2004) which experimentallyinvestigates the aerosol fission product retention in the steam gen-erator secondary side once large early release occurs.

2. Background of severe accident thermal challenge tosteam generator tubes

Once the reactor core starts to heatup during the hypotheticalTMLB’ station blackout severe accident, the hot leg counter-currentgas natural circulation would be established (Fig. 2) if the cold legloop seal is plugged with water, transferring heat from the reactorcore to the pipings of the hot leg, surge line and steam generator. Thehot leg counter-current natural circulation consists of an outboundflow and a return flow. The outbound flow starts from the reactorvessel upper plenum to the SG outlet plenum, carrying the relativelyhot gas in the hot leg upper part with a temperature Th and in afraction of the SG tubes (hot tubes) with a temperature Tht. Thereturn flow carries the relatively cold gas in the remaining SG tubes(cold tubes) with a temperature Tct and in the hot leg lower part.The SG inlet plenum is where the outbound flow mixing with thereturn flow takes place.

The computational fluid dynamics (CFD) investigations of the SGinlet plenum mixing phenomenon (Boyd and Hardesty, 2003; Boydet al., 2004) have revealed detailed information about the fluid andthermal dynamic processes which occur simultaneously and inter-act to complicate the behavior of natural circulation of gas. Thehot stream forms a rising plume in the SG inlet plenum once exit-

ing the hot leg upper part. The cold stream returning from the SGoutlet plenum cools the gas surrounding the hot plume. The hotplume entrains a large fraction of the return cold flow when ris-ing and therefore its temperature decreases. Once travelling to thebottom of the tubesheet surface, the hot plume partially penetrates

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130 Y. Liao, S. Guentay / Nuclear Engine

nto the SG tubes and partially spreads radially in all directions. Theart entering the tubes transfers heat to the tubes and displaces thepstream cooler gas. As a result, density gradients along the tube

ength and from tube to tube are established for buoyancy drivingorce to pull the inlet plenum mixture into the tubes. The recircula-ion flow rate in the tubes is governed by buoyancy driving forcehich depends on the hot plume temperature at the tubesheet

ntrance and heat transfer to the tube wall. Conversely, the hotlume temperature at the entrance is affected by the amount of theecirculation flow entrained into the plume, and the amount of heatransfer to the tube wall depends on the recirculation flow rate andemperature. As part of the result of these coupling fluid and ther-

al dynamic processes, the mixture temperature (Tm) is lower thanhe hot leg temperature (Th) and the SG tubes experience less severehermal challenges than the hot leg and surge line, therefore creepupture failure occurs earlier in the hot leg or surge line if the SGubes are flaw free. On the other hand, if the SG tubes are degradedo that flaws exist, the SG tubes may have a potential to fail earlierhan the hot leg and surge line, depending on the severity of theube degradation and the magnitude of the SG inlet plenum mix-ng. If the RCPB components other than the steam generator tubesail first, the potential for SGTR is suppressed since the primary sideill be depressurized due to a failure at other RCPB components.

he probability that the degraded SG tubes fail earlier than otherCPB components is the main theme of the current work.

The magnitude of the SG inlet plenum mixing can be character-zed by three experimentally observed mixing parameters, which

ere used by the severe accident analysis code to simulate the mix-ng phenomenon with a simplified mixing model for the transientalculations (NRC, 1998). Generally speaking, the severe accidentnalysis codes such as MELCOR and SCDAP/RELAP5 cannot com-ute the inlet plenum mixing directly, but adjust the inlet plenumixing to have the three mixing parameters match accepted exper-

mental or analytical results. The mixing fraction (F) is defined ashe fraction of the outbound hot leg flow mixed with the returnow at the inlet plenum (Fig. 2). A mixing fraction close to 1 rep-esents complete mixing and thus achieves a minimal temperatureor the gas flow entering the SG hot tubes, therefore making theG tubes less likely to fail first. On the other hand, a mixing frac-ion close to 0 represents little mixing and thus leads to a maximalemperature for the gas flow entering the SG hot tubes, therefore

aking the SG tubes more likely to fail first. The second mixingarameter is the recirculation ratio (R), defined as the ratio of theG tube mass flow rate to the hot leg mass flow rate (mh). The recir-ulation ratio is always greater than 1, since the naturally induceduoyancy force pulls more gas into the tubes than that received byhe inlet plenum from the hot leg upper part. With a larger recircu-ation ratio, there is a larger amount of return cold flow entrainedy the hot plume, therefore reducing the temperature of the flowntering the SG hot tubes and reducing the thermal challenge tohe tubes. The last mixing parameter is the fraction of tubes car-ying hot gas (˛) in the outbound flow. A larger fraction of tubesarrying hot gas represents on average less heat is received by thendividual tube, therefore making the tubes less likely to fail first.he U.S. NRC analysis (NRC, 1998) showed that when the fractionf hot tubes varied from 0.29 to 0.61, the hot tube maximum tem-erature deviation from the base case was 10 K. It is expected thathe temperature deviation would be much smaller when the plantcale values for the fraction of hot tubes ranging from 0.41 to 0.51iven by the CFD study (Boyd et al., 2004) are used in a similarnalysis. The CFD study also showed that the tube temperature in

he hottest region is insensitive to the fraction of hot tubes. It isonsidered that the effect of the fraction of hot tubes on the tubeemperature prediction is minimal.

When varying the three mixing parameters over their respec-ive plausible ranges to explore the temperature ranges that the

and Design 239 (2009) 1128–1135

SG tubes would be likely to experience, the inter-dependenceamong the mixing parameters needs to be considered to avoidusing the unrealistic combination sets of mixing parameter val-ues (Liao and Guentay, 2008a). The inter-dependence results fromthe coupling of the fluid and thermal dynamic processes in the SGinlet plenum mixing phenomenon. For example, when using thesimplified mixing model in the severe accident analysis code, alower mixing fraction is expected to be compensated by a higherrecirculation ratio. With a lower mixing fraction, the mixture tem-perature at the tube entrance could be higher if other things do notchange. The increased entrance temperature could induce largerbuoyancy force to pull more gas into the tubes and therefore ahigher recirculation ratio could be expected. A higher recircula-tion ratio then implies there must have been more ambient fluidentrained into the hot plume and it could have decreased themixture temperature at the tube entrance. Such a process con-tinues until another quasi-steady state is reached with a lowermixing fraction balanced by a higher recirculation ratio. The inter-dependence between the mixing fraction and the recirculation ratioin such a way could be observed in Cases h2 through h6 and CasesI2 through I6 of the CFD study (Boyd et al., 2004), although theaccount of such an inter-dependence may not be so straightfor-ward as for the simplified mixing model, due to the variations ofother parameters in the CFD study. Therefore, it is unrealistic andover-pessimistic to have both the mixing fraction (F) and the recir-culation ratio (R) varied simultaneously to the minimal values intheir respective plausible ranges provided that other conditions arethe same.

When applying these three experimentally observed mixingparameters to plant scale calculations, it was suggested that properupscaling needed to be considered to avoid over-estimating theinlet plenum mixing (NRC, 2001). The computational fluid dynam-ics predictions indicated slightly less mixing in the prototypical SGinlet plenum than in the scaleup configuration of the test facilitydue to a reduced mixing length (Boyd et al., 2004). Since a smallfraction of the hot gas impacts some SG tubes directly without suffi-cient mixing, tube-to-tube temperature variance is expected at theentrance of the SG inlet plenum as depicted in Fig. 1, where the darktubes in the cold region are associated with the cold return flow, thelight tubes in the hot region are associated with the hot outboundflow, and the lightest tubes in the hottest region are associated withthe hottest outbound flow without sufficient mixing. A key achieve-ment of the CFD studies (Boyd et al., 2004) is the predictions of thecontour and the temperature range for the hottest region, enablinga detailed analysis of severe accident induced SGTR provided thatthe distribution of the degraded tubes among the three regions isavailable.

3. Distribution of steam generator tube flaws caused byforeign object wear

As of 2007, around 43% of the US PWR power plants usedthermally treated Alloy 690 steam generator tubes, and 25% usedthermally treated Alloy 600 tubes, with the remaining balancedby power plants using mill annealed Alloy 600 tubes (Karwoski etal., 2007). Unlike mill annealed Alloy 600 tubes, for which stresscorrosion cracking is the major inservice degradation mechanism(MacDonald et al., 1996), wear due to foreign object and tube sup-port is the major inservice degradation mechanism for thermallytreated Alloy 600 and 690 tubes (Karwoski, 2003; Karwoski etal., 2007). For thermally treated Alloy 690 tubes degraded by the

wear mechanism, most of the tube flaws were caused by foreignobject wear, with the remaining caused by tube support wear. Forthermally treated Alloy 600 tubes degraded by the wear mech-anism, the majority of tube flaws were caused by tube supportwear.

ering and Design 239 (2009) 1128–1135 1131

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slightly expanded comparing to the range from 0.5 to 1.0 in. in theNRR distribution used for the NRC analysis (NRC, 1998). The cor-relation tends to predict a longer flaw length than the observedlength for a given flaw depth and therefore it introduces some

Y. Liao, S. Guentay / Nuclear Engine

There has been no occurrence of tube rupture for the U.S. powerlants using thermally treated Alloy 690 or 600 tubes, but a feworced outages have occurred due to primary to secondary leak-ge. Altogether there were only three forced outages due to tubeeakage for power plants using thermally treated Alloy 690 tubesKarwoski et al., 2007): two leakages were caused by foreign objectear and one was caused by a fabrication flaw. There were only

hree forced outages due to tube leakage for power plants usinghermally treated Alloy 600 tubes (Karwoski, 2003): all leakagesere caused by foreign object wear. Therefore the steam generator

perating experience showed that foreign object wear was a rel-tively important inservice degradation mechanism for thermallyreated Alloy 690 and 600 tubes.

The severity of the SG tube degradation is indicated by theumber of flaws existing between two steam generator inservice

nspections (the flaw frequency), the flaw through-wall depth andhe flaw length (the flaw size). The power plant periodic steamenerator inservice inspection reports contain the number of flawndications detected and the flaw size measured using the eddyurrent testing technique. Also reported are the flaw locationsith respect to the tube length and the tube’s tubesheet posi-

ion. A survey of numerous steam generator inservice inspectioneports helped establish statistically the flaw distributions (Liaond Guentay, 2008b). The survey focused on those flaws causedy foreign object wear due to its relative importance for the neweneration tubing materials. As a result of the survey, a databasef 445 SG tube flaws caused by foreign object wear has been setp with the observed flaw frequency, size and location reported inhe steam generator inservice inspection reports from power plantssing the thermally treated Alloy 690 or 600 new generation tubingaterials. Only those steam generators that have ever experienced

oreign object wear were considered in the database. Altogether theatabase consists of about 121 steam generator years (SG Years) ofperating experience.

Foreign objects may be introduced into the steam generatorystem from maintenance activities or degradation in primary orecondary system components. Most foreign objects were foundn the steam generator secondary side and most flaws due tooreign object wear were caused by mechanical impaction. TheG tube degradation mechanism due to foreign object wear isighly unpredictable, which may be affected by the unknown for-ign object size and configuration, the difficulty to predict theross flow field and the flow induced tube vibration, the poten-ial migration of the foreign object in the secondary side, to name

few. Therefore, the best way to set up the flaw distribution iso use statistical analysis based on the observed data. The mainesults on the flaw distributions (Liao and Guentay, 2008b) areeported herein for the purpose to study severe accident inducedGTR.

The distribution of flaw frequency (number of flaws per SG Year)s shown in Fig. 3. The observed data can be best fitted with anxponential probability density function (PDF) using the maximumikelihood algorithm:

DF(x) = exp(−x/5.5000)5.5000

(1)

here x (/SG Year) represents the flaw frequency.The distribution of flaw depth (% through wall) is shown in Fig. 4.

he observed data can be best fitted with a gamma PDF using theaximum likelihood algorithm:

y0.7631−1.0 exp(−y/29.1561)

DF(y) =

29.15610.7631� (0.7631)(2)

here y (% through wall) represents the flaw depth.Since in the power plant technical specification the steam gen-

rator tube plugging limit is generally set with respect to the flaw

Fig. 3. Distribution of flaw frequency.

depth regardless of the flaw length, the flaw length data are gener-ally not reported in the surveyed inservice inspection reports. Forthose flaws with the axial flaw length also reported, Fig. 5 illustratesthe relation between the axial flaw length and the flaw depth. Whileit is not mature to discuss the dependence of the axial flaw lengthon the flaw depth due to the limitedness of data, it is proposed thatthe axial flaw length (in.) can be bounded by the following empiricalcorrelation:

z = 0.2 + y

100(3)

where z (in.) represents the axial flaw length. As shown in Fig. 5,the correlation bounds the observed data for deep flaws, and alsofor shallow flaws with the exception of only one observation. Thecorrelation predicts the axial flaw length ranging from 0.2 to 1.2 in.,

Fig. 4. Distribution of flaw depth.

1132 Y. Liao, S. Guentay / Nuclear Engineering

cd

ttpaowfl

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Fig. 5. Relation of axial flaw length to flaw depth.

onservatism when applied to quantify the severity of the tubeegradation.

The flaw population is partitioned into five sections along theube length in the flow direction: the hot leg top of tubesheet (TTS),he hot leg straight portion, the U-bend region, the cold leg straightortion and the cold leg TTS (Fig. 6). Most of the flaws were locatedt the hot leg TTS (46%) and the cold leg TTS (20%) since the foreignbjects tended to accumulate at the top of tubesheet. More flawsere located at the hot leg TTS than at the cold leg TTS since theow velocity is greatest at the hot leg TTS.

The group of 206 flaws (46% of the total population) at theot leg TTS is of most interest, because the most severe ther-al challenge would be expected to occur there. The distribution

f these 206 flaws (degraded tubes) at the hot leg TTS is par-itioned into the three thermal regions depicted in Fig. 1: mostf the degraded tubes at the hot-leg top of tubesheet are at theeriphery of the tube bundle, where the foreign objects tend to

ccumulate; the fractions of degraded tubes in the hottest region,ot region and cold region are 12.62%, 43.69% and 43.69%, respec-ively.

Fig. 6. Flaw distribution along the tube length.

and Design 239 (2009) 1128–1135

4. Thermal-hydraulic analysis of severe accident thermalchallenges to steam generator tubes

The current thermal-hydraulic analysis uses the Zion PWR asan example to study the severe accident thermal challenges to theRCPB components during the TMLB’ station blackout sequence withthe assumption that the secondary side steam relief valve of thepressurizer loop fails to reclose due to the repeated cycling, becausethis kind of analysis using various severe accident analysis codeshas been well documented (Knudson et al., 1998; Vierow et al.,2004; Liao and Vierow, 2005), and because the CFD full scale powerplant analysis of the SG inlet plenum mixing used the boundaryconditions derived from the Zion case (Boyd et al., 2004). The cur-rent work uses the MELCOR code to predict the thermal challengesimposed on the hot leg, surge line and the SG tubes in the hot regionand the cold region, while coupling the CFD results to the MELCORcode to predict the thermal challenges to the SG tubes in the hottestregion. The MELCOR nodalization with an emphasis to study the hotleg counter-current natural circulation can be found in the author’spublished work (Vierow et al., 2004; Liao and Vierow, 2005).

4.1. Base case study

The MELCOR base case for the Zion PWR is set up by consider-ing the experience gained from the code-to-code comparison study(Vierow et al., 2004) and the sensitivity study to the key parame-ters affecting the thermal challenges to the RCPB components (Liaoand Vierow, 2005). Specifically, the MELCOR base case uses the SGmixing parameters derived from the CFD full scale Westinghousepower plant analysis (Boyd et al., 2004): 0.81 for the mixing frac-tion (F), 2.70 for the recirculation ratio (R) and 0.50 for the fractionof tubes carrying hot gas (˛); the MELCOR momentum exchangelength for the surge line flow path is adjusted so that the predictedpressurizer liquid draining rate is comparable to the results of theSCDAP/RELAP5 code which employs more rigorous two fluid mod-els. The base case predicts the surge line fails first among the hotleg, surge line and SG tubes which are flaw free, but the degradedSG tube has a potential to fail before the surge line if the flaw sizeis sufficiently large.

The MELCOR gas temperatures at the pressurizer loop hot leg,the hot region SG tubes and the cold region SG tubes during the

hot leg counter-current natural circulation phase until the time ofthe surge line creep rupture failure are shown in Fig. 7. The MEL-COR code alone could not calculate the gas temperature at thehottest region directly, but it can be calculated using both MEL-COR and CFD results. A dimensionless temperature was used in the

Fig. 7. Base case gas temperatures at the hot leg and SG entrance.

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Y. Liao, S. Guentay / Nuclear Engine

FD study (Boyd et al., 2004) to indicate the limit of high tempera-ure at the hot leg (dimensionless temperature equal to 1) and theimit of low temperature at the cold region SG tubes (dimension-ess temperature equal to 0). The dimensionless temperatures ofhe SG tubes in the hot and hottest regions were calculated with ainear interpolation between the high and low temperature lim-ts: � = (T − Tct)/(Th − Tct). The distributions of the dimensionlessemperatures at the hot region and the hottest region have beenresented (Boyd et al., 2004), which were used in the current worko derive the gas temperature at the hottest region.

For the low temperature CFD case (with a hot leg gas tempera-ure equal to 1005 K), the mean of the dimensionless temperaturesor all tubes carrying hot gas was derived herein equal to 0.3386. Theottest region dimensionless temperature ranged from 0.4 to 0.67ith a mean estimated to be 0.5034. While the current work movesstep forward over the U.S. NRC study (NRC, 1998) to account for

he tube-to-tube temperature difference between the hot regionnd hottest region, the finer temperature resolution within theottest region is not considered since the SG inlet plenum hot plume

mpacting the hottest region oscillates with time and space, whichends to smooth out the temperature distribution within the hottestegion. Therefore, the temperature peaking factor (the mean of theimensionless temperatures of the hottest region tubes over thatf all tubes carrying hot gas) was used to characterize the over-ll hottest region gas temperature, which was derived herein equalo 1.4867. The temperature peaking factor for the high tempera-ure CFD case (with a hot leg gas temperature equal to 1404 K) waserived similarly and was very close to that for the low tempera-ure CFD case. The gas temperature for the hottest region SG tubeshown in Fig. 7 was obtained using the MELCOR gas temperaturesor the hot leg (Th), the cold region SG tubes (Tct), the hot regionG tubes (Tht) and the hottest region temperature peaking factor of.4867 derived from the CFD study (Boyd et al., 2004).

The MELCOR heat structure temperatures at the surge line, theot region SG tubes and the cold region SG tubes are shown inig. 8. The MELCOR code alone could not calculate the heat struc-ure temperature at the hottest region directly, but the boundedemperature for the hottest region heat structure can be calcu-ated employing the gas temperature information. During the hoteg counter-current natural circulation phase until the time of theurge line failure, the time rates of gas temperature increase for theottest region (b ) and the hot region (b ) can be calculated from

1 2ig. 7. It was demonstrated that the temperature increase from thenitiation of natural circulation to the time of the surge line failureor the hottest region heat structure was bounded by the temper-ture increase for the hot region heat structure times a factor of

ig. 8. Base case heat structure temperatures at the surge line and SG entrance.

and Design 239 (2009) 1128–1135 1133

b1/b2 (Liao and Vierow, 2005). Therefore, the temperature devia-tion of the hottest region heat structure from the hot region heatstructure can be calculated at the time of the surge line failure, andthe temperature deviation at the initiation of natural circulation iszero. Consequently, the hottest region heat structure temperatureplotted in Fig. 8 was calculated by adding the MELCOR hot regionheat structure temperature with the temperature deviation as alinear function of temperature.

During the natural circulation phase the MELCOR primary sidepressure is maintained at the pressurizer PORV set point pressureand the MELCOR secondary side pressure of the pressurizer loopis close to the atmospheric pressure since the steam relief valve isassumed to fail to reclose during the repeated cycling.

4.2. Uncertainty analysis

The SG inlet plenum mixing parameters and the gas to heatstructure heat transfer coefficients were found to be the mostimportant parameters affecting the failure time difference betweenthe surge line and the SG tubes (NRC, 1998). Other parameters suchas the initiation of natural circulation and the core heating-up rateare less important, since they affect the absolute failure times ratherthan the failure time difference. Because the probability of SGTR isgoverned by the failure time difference rather than the absolutefailure time, the uncertainty analysis studies those parameters thatwill affect the SG tube temperature deviation from the base case atthe time of the surge line failure.

When individually varying the mixing parameter over its plau-sible entire range, the worst case was with the mixing fraction(F) assigned its low limit value, which resulted in the SG tubeheat structure temperature deviation from the base case of 20 Kat the time of the surge line failure (NRC, 1998). When simulta-neously varying the three mixing parameters without consideringtheir inter-dependence, the worst case was with all the three mix-ing parameters assigned their respective low limit values, whichresulted in the temperature deviation of 50 K (NRC, 1998). The cur-rent work studies the SG tube heat structure temperature deviationfrom the base case at the time of the surge line failure causedby the mixing parameters’ synergistic effect considering the inter-dependence among the mixing parameters.

The inter-dependence among the three mixing parameters usedin the simplied mixing model can be formulated using the momen-tum equation for the gas recirculating around the SG tubes. Thebuoyancy force caused by the density change along the tube lengthis the driving force for the recirculation flow, which is balanced bythe friction and form losses. Since the buoyancy force depends onthe gas temperature, while the gas temperature at the SG entrancedepends on the mixing fraction (F), the buoyancy force can berelated to F. On the other hand, since the loss terms depends onthe gas velocity, while the gas velocity depends on the recircula-tion ratio (R) and the fraction of tubes carrying hot gas (˛), the lossterms can be related to R and ˛. Therefore, the inter-dependenceamong F, R and ˛ is depicted in the momentum conservation equa-tion. The constitutive equation about F, R and ˛ has been formulatedin such a way and presented as (Liao and Guentay, 2008a):

(F + R)R1.75

(1

˛1.75+ 1

(1 − ˛)1.75

)≈ const (4)

Starting from the set of mixing parameters used for the MELCORbase case, (F,R,˛) = (0.81,2.70,0.50), only two mixing parameters are

free to vary over their respective plausible ranges, while the thirdmixing parameter is not free to vary but must depend on the othertwo according to Eq. (4). The recommended ranges of R and ˛ forWestinghouse plants based on CFD analysis were 2.25 to 2.75 and0.41 to 0.51, respectively, but no similar recommendation was made

1134 Y. Liao, S. Guentay / Nuclear Engineering and Design 239 (2009) 1128–1135

fuespgwit(B

cseb2ie

tsdwtett

5r

tfi(ru∫

wg(t

Fig. 9. Mixing parameter’s synergistic effect on the SG tube temperature.

or F (Boyd et al., 2004). Actually, the range of F could be estimatedsing Eq. (4) to be 0.65 to 1.0 (Liao and Guentay, 2008a), whichncompasses the experimentally observed range and the CFD sen-itivity cases. Therefore, with respect to the mixing parameters’lausible ranges, the worst case of the mixing parameters’ syner-istic effect to have the degraded SG tubes fail as early as possibleould be one of the following three cases, each case with two mix-

ng parameters assigned their respective low limit values and thehird parameter calculated using Eq. (4) (Liao and Guentay, 2008a):F,R,˛) = (0.65,2.25,0.51) for case A, (F,R,˛) = (0.65,2.67,0.41) for case, and (F,R,˛) = (1.0,2.25,0.41) for case C.

The MELCOR heat structure temperatures for the hot tubes areompared in Fig. 9 among the base case, case A, B, and C. Con-idering the mixing parameters’ inter-dependence and synergisticffect, the SG tube heat structure temperature deviation from thease case at the time of the surge line failure is 33 K, comparing to0 K if the synergistic effect was not considered, and to 50 K if the

nter-dependence among the mixing parameters was not consid-red (NRC, 1998).

The U.S. NRC has performed other sensitivity studies to the heatransfer coefficients, the SG tube nodalization and the primary pres-ure, which showed that the SG tube heat structure temperatureeviation from the base case at the time of the surge line failureere 7, 5 and 15 K, respectively. Therefore, accounting for the 33 K

emperature deviation due to the mixing parameters’ synergisticffect, the gross thermal-hydraulic uncertainty in terms of the SGube heat structure temperature deviation from the base case at theime of the surge line failure is around 60 K.

. Severe accident thermally induced steam generator tubeupture probability

Although the SG tubes which are flaw free would not fail beforehe surge line, the degraded SG tubes might have a potential to failrst. To account for the severity of degradation, a penalty factor Mp

stress magnification factor) was developed to be used in the creepupture model to evaluate the life time of the degraded SG tubender severe accident conditions (Majumdar, 1999):

tf

0

dt

tR(T, Mp�)= 1 (5)

here tf is the life time, and tR is the time to creep rupture for aiven temperature (T) and stress multiplied by the penalty factorMp�). The temperature (T) and stress (�) can be calculated usinghe results obtained in Section 4.

Fig. 10. Relation of stress magnification factor to flaw depth.

The stress magnification factor (Mp) is a function of the flawdepth, flaw length and the tube geometry (Majumdar, 1999). Thestress magnification factor is depicted in Fig. 10 as a function ofthe flaw depth, while assuming the flaw length can be related tothe flaw depth by Eq. (3). In the uncertainty study of the stressmagnification factor (NRC, 1998), the 95% confidence value of Mp

was equivalent to the SG tube heat structure temperature deviationof approximately 10 K from the base case at the time of the surgeline failure.

The flaw distributions and the thermal-hydraulic calculationsdeveloped in the current work are used to assess the SGTR proba-bility for the pressurizer loop steam generator in the TMLB’ stationblackout severe accident assuming the steam relief value fails toreclose. The mean and distribution of the SGTR probability areassessed with the Monte Carlo random walk technique consistingof the following steps:

I. Sample the flaw frequency x (/SG Year) according to the distri-bution in Eq. (1). For each flaw repeat the remaining steps.

II. Assume all flaws were located at the hot leg top of tubesheetwhere the thermal challenge is most severe along the tubelength. The assumption introduces some conservatism whenapplied to study the probability for the degraded SG tubes tofail earlier than the surge line. Sample the flaw location amongthe hottest, hot and cold regions according to the distributionset up in Section 3.

III. Sample the SG tube heat structure temperature deviation fromthe base case at the time of the surge line failure assuming the95% confidence value of 70 K (60 K from the thermal hydraulicuncertainties and 10 K from the stress magnification factoruncertainty, as discussed before). Calculate the temperature his-tories of the SG tubes in the hot and cold regions by adding thebase case temperature with the temperature deviation as a lin-ear function of temperature. Calculate the temperature historyof the SG tubes in the hottest region according to the methodintroduced in Section 4.

IV. Sample the Larson Miller parameter uncertainty with the 95%confidence value of 0.7 (NRC, 1998) for the creep rupture model.

i

Calculate the critical stress magnification factor (Mp) to havethe degraded SG tube fail before the surge line using the creeprupture model. The uncertainty of the time of the surge linefailure delayed from the base case in terms of the 95% confidencevalue is assumed to be 20 minutes, since at that time it is delayed

Y. Liao, S. Guentay / Nuclear Engineering

Fl

V

ficcelfi3c6tasad

6

oAM

ig. 11. Distribution of SGTR probability induced by severe accident thermal chal-enge.

so much that the surge line temperature is almost reaching themelting temperature.

V. Use the critical stress magnification factor (Mip) to infer the crit-

ical flaw depth from Fig. 10. The SGTR probability (pi) is theprobability that the flaw depth is greater than the critical flawdepth, which can be obtained using the probability density func-tion in Eq. (2).

I. Calculate the SGTR probability (pi) for each of the x flaws. Theoverall SGTR probability (p) for one random walk is: p = 1 −

x∏i=1

(1 − pi).

With 10,000 random walks, the distribution of the probabilityor steam generator degraded tubes to fail before the surge linen the presence of severe accident thermal challenge and flawsaused by foreign object wear is plotted in Fig. 11 (the 95 percentileonfidence level means the likelihood of the SGTR probability notxceeding the SGTR probability corresponding to this confidenceevel is 95%), with the mean and the range factor (95 percentile con-dence level over 50 percentile confidence level) equal to 0.025 and.8, respectively, comparing to a mean of 0.079 in the U.S. NRC basease study (NRC, 1998) which focused on the mill annealed Alloy00 steam generator tubing materials that are more susceptibleo stress corrosion cracking. The major reason for a lower prob-bility predicted in the current work is that the new generationteam generator tubing materials treated herein have a better oper-ting performance since the number of flaws caused by inserviceegradation has been significantly reduced.

. Conclusion

The current wok developed the flaw distributions using thebserved data in the power plant inservice inspection reports.ccording to the degraded tubes’ tubesheet positions, either theELCOR code was used to calculate the thermal challenges imposed

and Design 239 (2009) 1128–1135 1135

on the degraded tubes in the hot region and the cold region, or theMELCOR code coupled to CFD findings was used for the tubes inthe hottest region. The current work studied the thermal-hydraulicuncertainties taking into account the mixing parameters’ synergis-tic effect and the inter-dependence among the mixing parameters.A new methodology was developed to assess the mean and distri-bution of the severe accident thermally induced SGTR probabilityin the presence of tube flaws caused by foreign object wear, imple-menting the flaw distributions and the thermal-hydraulic analysisas well as the associated uncertainties developed herein. The meanand the range factor of the probability for the steam generatordegraded by foreign object wear to fail before the surge line inthe presence of the TMLB’ station blackout severe accident thermalchallenge are 0.025 and 3.8, respectively. The current analysis dealswith a broad category of steam generators that have ever experi-enced inservice degradation caused by foreign object wear and usesthe Zion PWR as an example. Plant specific analysis should considerthe variations in the plant design and the steam generator operatingexperience.

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