Annals of Nuclear Energy 38 (2011) 1225–1230

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Annals of Nuclear Energy

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Assessment methodology for confidence in safety margin for large break lossof coolant accident sequences

Mahendra Prasad ⇑, R.S. Rao, S.K. GuptaAtomic Energy Regulatory Board, Mumbai 400 094, India

a r t i c l e i n f o

Article history:Received 4 August 2010Received in revised form 8 February 2011Accepted 23 February 2011

Keywords:Large break coolant accidentParameter uncertaintyLatin hypercube samplingEvent treeProbability distribution

0306-4549/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.anucene.2011.02.015

Abbreviations: AOO, Anticipated Operational OccuPlus Uncertainty Analysis; CD, Core Damage; DBA, DesAccumulator; HPECCS, High Pressure Emergency CoLarge Break Loss of Coolant Accident; LHS, Latin HypePressure Emergency Core Cooling System; NCD, NonPower Plant; NPS, Normal Power Supply; PCT, PPostulated Initiating Event; RPS, Reactor Protection S⇑ Corresponding author. Address: Safety Analysis a

Atomic Energy Regulatory Board, Niyamak Bhavan –400 094, India. Tel.: +91 022 25990470; fax: +91 022

E-mail address: mprasad@aerb.gov.in (M. Prasad).

a b s t r a c t

Deterministic Safety Analysis and Probabilistic Safety Assessment (PSA) analyses are used to assess theNuclear Power Plant (NPP) safety. The conventional deterministic analysis is conservative. The best esti-mate plus uncertainty analysis (BEPU) is increasingly being used for deterministic calculation in NPPs.The PSA methodology integrates information about the postulated accident, plant design, operating prac-tices, component reliability and human behavior. The deterministic and probabilistic methodologies arecombined by analyzing the accident sequences within design basis in the event trees of a postulated ini-tiating event (PIE) by BEPU. The peak clad temperature (PCT) distribution provides an insight into theconfidence in safety margin for an initiating event.

The paper deals with calculating the safety margin with 95% confidence and 95% probability in large breakloss of coolant accident (LBLOCA). In the present study, five uncertain input parameters were selected. Uni-form probability density function was assigned to the uncertain parameters in the selected range and theseuncertainties are propagated using Latin Hypercube Sampling (LHS) technique. The sampled data for fiveparameters was randomly mixed by LHS to obtain 25 input sets. An event tree for the initiating event,LBLOCA inside containment, has been used from a VVER study on Level-1 PSA and four non-core damage(NCD) accident sequences were identified for this study. In the accident analysis the success and failureof safety systems reflected in event tree was appropriately modeled in the system thermal hydraulics coderuns. The PCT was obtained for each of 25 code runs for each accident sequence. A Kolmogorov – Smirnovgoodness-of-fit test carried out for PCTs indicated that they followed normal distribution for each of theaccident sequences. The probability distribution of safety margin (difference between acceptable valueand PCT) in each accident sequence was also obtained. The values of safety margin for the 95% confidenceand 95% probability are estimated. The robustness of the system can be judged based on this. This paperdescribes the methodology. LBLOCA in a VVER type reactor is considered as an example.

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1. Introduction

Safety analysis for Nuclear Power Plants (NPP) requires evalua-tions with both deterministic and probabilistic assessments as adefense-in-depth principle of safety assessment. The deterministicsafety analysis generally follows two methods – conservative andbest estimate, depending on analysis objectives and issues

ll rights reserved.

rrences; BEPU, Best Estimateign Basis Accident; HA, Hydrore Cooling System; LBLOCA,rcube Sampling; LPECCS, Low-Core Damage; NPP, Nucleareak Clad Temperature; PIE,ystem; SM, Safety Margin.nd Documentation Division,B, Anushaktinagar, Mumbai25990499.

involved. For an NPP, analysis with best estimate approach withuncertainty analysis is increasingly being used.

Safety Margin (SM) is the difference between the referencevalue of any assigned parameter as accepted by the regulatingbody and the calculated value. There are various areas whereassessment of SM is carried out for making regulatory decisionsuch as,

(a) To demonstrate that adequate margins exist for the Postu-lated Initiating Events (PIEs) such as Anticipated OperationalOccurrences (AOOs) and Design Basis Accidents (DBAs) con-sidered in the design.

(b) To show that adequate safety margin exists in the proposedmodification in the plant structures, systems or components.

(c) Re-evaluation/improvement of SM by screening outextra conservatism in input parameters, using lateststate-of-the-art code, latest knowledge about a sensitiveparameter etc.

Table 1Uncertainty parameter values.

Parameter Probability Nominal value Range

1226 M. Prasad et al. / Annals of Nuclear Energy 38 (2011) 1225–1230

In the conservative analysis there is one value of the safety mar-gin corresponding to the single output of a parameter. However,for the best estimate plus uncertainty analysis (BEPU) there is arange and hence a probability distribution for the safety margindue to multiple output values of a parameter. Fig. 1 shows sche-matically the safety margin for deterministic assessment.

In the 1970s and 1980s, when a large number of reactors were de-signed, conservative hypotheses were considered to account for thelack of knowledge and understanding on the existing uncertainties.The rules and criteria fundamental to reactor safety were fixed inseventies (US Nuclear Regulatory Commission, 1978). The ‘‘Appen-dix K’’ requirements defined conservative model assumptions aswell as conservative initial and boundary conditions to arrive at con-servative code results for critical safety parameters. The safety limitsfor three important parameters are 1473 K for peak clad tempera-ture, 17% clad oxidation and 0.01 times the maximum hypotheticalamount of hydrogen that would be generated if all the clad were toget oxidized. Since then extensive thermal–hydraulic experimentalresearch has resulted in a considerable increase in knowledge, andthe development of computer codes whose results are comparablewith experimental evidences. The best estimate calculation usesmodeling that attempts to realistically describe the physical pro-cesses occurring in a NPP. The model provides a realistic calculationof the important parameters associated with a particular phenome-non to the degree practical with the currently available data andknowledge of the thermal hydraulic phenomena. There are manythermal hydraulic codes available such as TRAC-PWR, RELAP5 andCOBRA for the best estimate analysis (US Nuclear RegulatoryCommission, 1989). The uncertainty analysis refers to the uncer-tainty in the analysis methods and input parameters (US NuclearRegulatory Commission, 1978), models, user specific uncertaintyand fuel behavior. The overall uncertainty should reflect a consoli-dated impact of these variables. The procedure for the detailedtransient and accident analysis method has been elaborated in manydocuments (US nuclear Regulatory Commission, 2005; InternationalAtomic Energy Agency, 2009). Different combinations of computercodes, input parameters and availability of systems are used for car-rying out deterministic safety analysis (for e.g. conservative codeand conservative assumption, best estimate code and best estimateinputs). However, currently best estimate code with realistic input isbeing increasingly used. In India, the thermal hydraulic safety anal-ysis for NPP is carried out with conservative methodology. However,the BEPU methodology is being actively pursued.

Sections 2 and 3 presents the uncertain parameters selection forthe best estimate with uncertainty analysis and formulation of de-sign input for the analysis. Section 4 gives the large break loss ofcoolant accident (LBLOCA) event tree. Section 5 outlines the LBLO-CA analysis for all non-core damage accident sequences and PCT. InSection 6 the PCT and SM uncertainty distribution is presented.

Safety Limit

Value by conservative analysis

Uncertainty

Value calculated by BEPU

SM SM

Fig. 1. Safety margin illustration.

Section 7 provides the linear regression analysis for PCT. FinallySection 8 presents conclusion.

2. Estimation of uncertain parameters for LBLOCA

There are a large number of parameters that need to be consid-ered for uncertainty analysis for large break LOCA (IAEA TECDOC -1418, 2004). Some of these are as follows:

– Decay heat.– Reactor operating power level.– Fuel clad gap conductivity.– Fuel thermal conductivity.– Two phase frictional pressure drop coefficient.– Discharge coefficient.– Heat transfer coefficient to the coolant.

In the present study, five parameters were selected on the basisof a sensitivity study to observe their impact on clad temperature.These are reactor power (P), decay power (Pd), discharge coefficient(Cd), fuel conductivity (Kf) and fuel clad gap conductivity (Kg). Theprobability distribution for each of the parameters was assumed tobe uniform due to lack of experimental data. The range of theparameters was based on operating instrumentation and control,literature and judgment. The five selected parameters, their distri-bution, nominal value and range are shown in Table 1.

3. Design matrix formulation

In the present study Latin Hypercube Sampling (LHS) is used forpropagation of uncertainties. LHS is very popular for use with com-putationally demanding models because it allows for the extractionof a large amount of uncertainty and sensitivity information withrelatively small sample size (Sang–Ryeol Park et al., 1992). TheLHS method consists of three steps to obtain (N � K) design matrixwhere N is the planned number of code runs and K is the numberof input variables. The first step is dividing each input variable Xi

(i = 1–K) into N intervals with equal probability of 1/N. The secondstep is obtaining Xij (j = 1–N) for each input variable Xi. The third stepis random coupling of Xji (j = 1–N, i = 1–K). The sample size is greatlyreduced if the LHS technique is used to generate the sample. Thenumber of latin hypercube sample, N, for K input variables issufficient if it is 4/3 K. However, if running time of model is notexcessive then N can vary from 2 K to 5 K. In this study the number

P Uniform 3000MWth 1.0–1.04Pd Uniform 1.0 1.0–1.20Cd Uniform 1.0 1.0–1.20

Kf Uniform T (K) Kf (W/m-K) 0.95–1.10273.0 8.1293.0 8.0

1100.0 3.751700.0 2.502700.0 2.653100.0 3.503300.0 3.50

Kg Uniform T (K) Kg (W/m-K) 0.95–1.05273.0 0.141500.0 0.211700.0 0.278900.0 0.335

1100.0 0.3892500.0 0.389

Table 2Safety systems for LBLOCA event tree.

System Success criteria

Hydro accumulators Operation of three out of four HAsHigh pressure emergency

core cooling systemBoron solution charging into the core by twoHPECCS train when primary pressure is lessthan 7.9 MPa

Normal power supply Power supply available from grid after unitshutdown

Low pressure emergencycore cooling system

Operation of two LPECCS trains for coolantinjection mode

M. Prasad et al. / Annals of Nuclear Energy 38 (2011) 1225–1230 1227

of input variable is 5, hence a sample size of 25 was considered. Acomputer code was used to generate the input design matrix.

4. VVER LBLOCA analysis event tree

The events consisting of LBLOCA include the LOCAs with breakareas such as to lead to rapid depressurization of primary system.The assumptions considered for the event tree are as follows:

(i) Reactor Protection System (RPS) action is not required forachievement and maintaining of reactor sub criticality asthe reactivity feedbacks are negative.

(ii) The possibility of containment sump clogging with heatinsulation of primary pipelines is not considered.

(iii) The possibility of off site power is considered due to gridfailure at sudden unit trip.

The NPP systems that form the four function events are normalpower supply from grid (NPS), hydro accumulators (HA), low pres-sure emergency core cooling system (LPECCS) and high pressureemergency core cooling system (HPECCS). The hydro accumulatorsand LPECCS begin the delivery of water into primary circuit whenthe primary pressure decreases to the designed injection pressure.The safety systems with the success criteria are shown in Table 2.

The event tree is shown in Fig. 2 which indicates the non-coredamage (NCD) accident sequences (AS) and those that lead to coredamage (CD) following second stage HA failure. In the NCD se-quences the clad temperatures are expected to be below 1473 K.

5. LBLOCA accident sequence analysis

The VVER is a 1000 MWe light water cooled and light watermoderated reactor. The reactor consists of reactor pressure vessel,

Fig. 2. Event tree

core barrel, core baffle, in-core instrumentation detectors, protec-tive tube units and other structures. The reactor core consists ofhexahedral Fuel Assemblies (FAs) and each FA comprises of fuelelements. The primary circuit consists of reactor core, downcomer,lower plenum, upper plenum and four loops. Each loop is having ahot leg and a cold leg and reactor coolant pump (RCP) set. There aretwo safety Pulse Safety Devices (PSDs) and one control PSDmounted on the pressurizer relief line. The secondary circuitconsists of four loops and each loop is having a horizontal SteamGenerator (SG) and four steam lines. On each steam line two PulseSafety Devices (PSDs), one Main Steam Isolation Valve (MSIV) andone electrical isolation valve are mounted.

Thermal hydraulics analysis was carried out for 850 mm dou-ble-ended guillotine rupture (LBLOCA) of the cold leg of fourth loopusing system thermal hydraulics code, RELAP 5.

The following assumptions are considered for the analysis.

(1) The first signal on loss of offsite power is ignored.(2) Failure of pressurizer tubular electric heaters is assumed.(3) Operation of SG emergency cool down system is not

considered.(4) Dependence of reactivity on coolant density and fuel tem-

perature are assumed conservatively in the analysis.(5) Under reactor scram, one control rod of highest worth sticks

in the upper position(6) Effective fraction of delayed neutrons and prompt neutron

lifetime are assumed conservatively.

Nodalisation of primary circuit involves reactor, circulationloops and pressurizer. The reactor pressure vessel is simulated byfour elements: reactor core, downcomer, lower plenum and upperplenum. The reactor core is simulated by maximum power chan-nel, average power channel and bypass channel. Each channel is di-vided into 10 volumes. The downcomer is divided into fourvolumes. The lower plenum is simulated by single volume andtwo volumes simulate upper plenum. The primary coolant systemis represented by four circulation loops. Each loop is divided intohot leg (Five volumes), SG hot collector (Three volumes), SG tubing(Fifteen volumes), SG cold collector (Three volumes), main circula-tion coolant pipeline (Eight volumes), Reactor Coolant Pump (RCP)and cold leg (Four volumes). The RCP has been simulated by pumpcharacteristics, rated flow, head and speed. Pump trip is simulatedby coast down speed, which is given as input. The pressurizer is di-vided into 10 volumes. The connecting pipeline between pressur-izer and hot leg is divided into three volumes. Relief line is

for LBLOCA.

MAX CLAD TEMPERATURE

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

TIME (Sec)

TEM

PER

ATU

RE

(K)

Fig. 3a. Clad temperature for accident sequence1 (AS1, Code run No. 23).

1228 M. Prasad et al. / Annals of Nuclear Energy 38 (2011) 1225–1230

simulated by single volume and PSDs are simulated by trip valves.Nodalisation of secondary involves steam generators, steamlines,MSIVs, electrical isolation valve on second steam line, main steam-line header, turbine stop valve and governor valve. Feedwater issimulated as a boundary condition. The steady state has been ob-tained after modeling of the various reactor components. The stea-dy state values are used as the initial conditions for the accidentscenario considered.

The success of NPS, HA and LPECCS is modeled in accident se-quence 1 as shown in Fig. 2. In case of NPS system available, it isassumed that the safety system injection takes place with a delayof 30.0 s (the assumption is slightly conservative as it takes lessertime for pumps to start injection). The reactor coolant pumpswould trip because the margin to saturation temperature in hotlegs will become less due to sudden decrease in the pressure inLOCA condition. The success of HA is modeled by considering avail-ability of three HAs. Similarly, LPECCS and HPECCS success is mod-eled as two train availability for each of these systems. In accidentsequence 2, the success of NPS, HA and HPECCS is modeled asshown in Fig. 2. The failure of LPECCS is modeled by consideringfailure of all four trains. In accident sequence 3, the differencevis-à-vis sequence 1 is that NPS failure is considered. Similarly,in accident sequence 4, the difference vis-à-vis sequence 2 is thatfailure of NPS is considered. The NPS system failure is assumedto bring additional delay in safety system injection. The total delayconsidered in each of the accident sequences AS3 and AS4 is 40 s.

The thermal–hydraulic analysis for LBLOCA is carried for 1000 s.In the present analysis the overall PCT (i.e. considering both theblowdown and reflood regions together) has been obtained.Fig. 3a–3d show the clad temperature variation for the computercode run in which maximum PCT from 25 runs is predicted. Initially,the clad temperature decreases sharply due to large blowdown.Subsequently, the clad temperature rises and later decreases under

MAX CLAD T

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

0.00 200.00 400.00 6

TIM

TEM

PER

ATU

RE

(K)

Fig. 3b. Clad temperature for accident s

the influence of inventory loss due to blowdown and emergencyinjection respectively. Fig. 3a corresponds to code run No. 23 forAS1 (PCT = 1161.1 K), Fig. 3b corresponds to code run No. 22 ofAS2 (PCT = 1279.9 K), Fig. 3c corresponds to code run No. 23 ofAS3 (PCT = 1161.5 K) and Fig. 3d corresponds to code run No. 1of AS4 (PCT = 1282 K). It is to be noted that the clad temperaturevariation is same in the first few seconds of transient for all the 25code runs for all the four NCD accident sequences. This shows thatthe impact of HA is similar for the accident sequences since it ismodeled as available in all of them. HA is passive system notrequiring power and so is independent of the failure of NPS or emer-gency power supply. The time history of temperatures for accidentsequences AS1 and AS3 are having minor variations as shown inFig. 3a and 3c. This difference is due to the different delay consid-ered in actuations of LPECCS pumps in these cases. Similarly,differences in the temperature profile for AS2 and AS4, as shownin Figs. 3b and 3d respectively, are predicted due to same reason.

6. PCT uncertainty estimation

If the population mean and standard deviation are unknown,and the sample mean (ls) and sample standard deviation (rs) areknown, the interval that contains P% of the population measure-ments with confidence coefficient of l � a is determined, by con-sidering a tolerance limit factor, K, (Montgomery and Runger,1994), as (ls � K rs, ls + K rs) where, the value of K is a functionof the number of samples type of probability distribution, N, Pand confidence coefficient 1 � a. These values of K are tabulatedin the form of tables for various values of the variables N, P anda for a particular probability distribution.

To determine the type of probability distribution for the data onPCT Kolgomorov–Sminroff goodness-of-fit test (Ebeling, 2008) wasperformed for all the four accident sequences. In this test the

EMPERATURE

00.00 800.00 1000.00 1200.00

E (Sec)

equence 2 (AS2, Code run No. 22).

MAX CLAD TEMPERATURE

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00TIME (Sec)

TEM

PER

ATU

RE

(K)

Fig. 3c. Clad temperature for accident sequence 3 (AS3, Code run No. 23).

MAX CLAD TEMPERATURE

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00TIME (Sec)

TEM

PER

ATU

RE

(K)

Fig. 3d. Clad temperature for accident sequence 4 (AS4, Code run No. 1).

M. Prasad et al. / Annals of Nuclear Energy 38 (2011) 1225–1230 1229

observed values in the increasing order PCT1 6 PCT2 6 . . .

. . .. . . 6 PCT25 was recorded. Then calculate D1 and D2 for all thePCTs, as defined in Eqs. (1) and (2) respectively below, with anhypothesized probability distribution function f(PCT) (cumulativedistribution function is F(PCT)). The maximum of the D1 and D2

is compared with Dc (critical value of D) for the confidence levelof interest. The values of Dc are tabulated for the Kolgomorov–Sminroff method and depend on N and 1 � a.

D1 ¼maxji=N � FðPCTiÞj for i ¼ 1;2 . . . N ð1Þ

D2 ¼maxjFðPCTiÞ � ði� 1Þ=Nj for i ¼ 1;2 . . . N ð2Þ

D ¼ maxðD1;D2Þ

If D < Dc, then the sample data follows the assumed distribution forwhich the goodness-of-fit test was performed. For testing by Kol-gomorov–Sminroff method, for each of the four accident sequencesthe hypothesis is that the output data follows normal distributionand the goodness-of-fit test indicated that the hypothesis is true.Thus the PCT in each of the accident sequence followed normaldistribution.

Table 3SM parameters for NCD accident sequences.

Accident sequence SM mean (K) SM standard deviation (K) SM95/95 (K)

1 347.812 24.5916 292.00142 263.788 45.2642 161.06083 349.324 24.5992 293.49614 292.688 45.4957 189.4355

In this study, the lower 95% probability value with 95% confi-dence limit on SM is desired. The one sided tolerance limit factor,Kt, was calculated from (NIST/SEMATECH, 2009) with the formula,

Kt ¼ fZ1�P þ ½ðZ1�PÞ2 � a � b�0:5g=a ð3Þ

a ¼ 1� ðZ1�aÞ2=2 � ðN � 1Þ ð4Þ

b ¼ ðZ1�PÞ2 � ðZ1�aÞ2=N ð5Þ

where N = sample size, P = percentage probability, 1 � a = percentageconfidence.

With N = 25, P = 0.95 and 1�a = 0.95, the value of Kt was calcu-lated as 2.269423.

In the study, the safety margin for each of the 25 PCT for theaccident sequence were calculated as

SMi ¼ 1473� PCTi i ¼ 1;2 . . . 25 ð6Þ

The 25 values for SM for each accident sequence would follownormal distribution as the PCT for each accident sequences followsnormal distribution. The maximum likelihood estimator for themean and standard deviation of SM are given as:

l ¼ RSMi=N i ¼ 1;2 . . . 25;N ¼ 25 ð7Þ

Table 4SM parameters from linear regression.

Accident sequence SM mean (K) SM standard deviation (K) SM95/95 (K)

1 347.522 21.062 310.51442 259.772 44.532 181.52993 349.32 21.224 312.03244 290.702 53.337 196.9816

1230 M. Prasad et al. / Annals of Nuclear Energy 38 (2011) 1225–1230

r ¼ ½RðSMi � lÞ2=N � 1�0:5 i ¼ 1;2 . . . 25;N ¼ 25 ð8Þ

The one sided lower confidence limit for SM was calculated forthe four accident sequences as follows:

Accident Sequence (AS1):

SM95=95 ¼ lAS1 � Kt � rAS1 ¼ 347:812� 2:269423 � 24:5916

¼ 292:0014 K

where lAS1 and rAS1 are the mean and standard deviation of thenormal distribution which the SM is following. The mean, standarddeviation and lower limits for SM are shown in Table 3.

The methodology elaborated in this section is a parametric wayfor statistical analysis of thermal hydraulic uncertainty. In LHS, thenumber of samples used is quite limited with the number of uncer-tain input parameters. LHS is preferable to use if the computationaltime and the required resources for an analysis are large. This may,however, compromise the output confidence. In the current sce-nario of availability of very fast computers (overruling the compu-tational complexity), random sampling is preferred to generate alarge number of truly random combination of samples from theuncertain input parameters. Having a larger set of code runs givesa greater confidence on the output uncertainty.

7. Linear regression for PCT

To estimate the relationship between PCT (and hence SM) andinput uncertain parameters, a second order linear regression modelwas used. The form of the model is as shown below:

Y ¼ Ao þ Ai � Xi þ RBi � X2i þ RðRCjk � Xj � XkÞ i ¼ 1 to 5;

j ¼ 1 to 4; k ¼ jþ 1 to 4

where Y is the PCT and Xi are the 5 input uncertain parameters con-sidered in the analysis and Ao, Ai, Bi and Cjk are the regression coef-ficients. In the quadratic terms, all the five input parameters areconsidered and in the product terms, four parameters (except dis-charge coefficient) are considered. The above model was used forall the accident sequences.

With the data available for PCT from 25 code runs, the coeffi-cients were obtained using a FORTRAN program. Having obtainedthe linear equation, a different 25 set of input parameters valuescombinations was generated and PCT was calculated. This was re-peated for 20 times. Thus a total of 25 � 25 = 500 PCT values wereobtained for each accident sequence. Safety margin correspondingto each PCT was obtained. The mean, standard deviation and lower95/95 limit factor for the safety margin data (N = 500) was calcu-lated using the equations in Section 6. These are shown in Table 4.

The linear regression to generate a response surface is anotherway that has been used in lieu of large number of code runs. Theregression methodology suffers from problems of obtaining thebest fit which can be used as a surrogate to the actual relationshipbetween inputs and output(s). A huge number of combinations ofthe uncertain parameters (and the order of the equation) need tobe checked to arrive at an appropriate equation. Usually second or-der linear regression is used for this purpose along with the cross

products (interaction terms). Also, the calculation of the regressionequation gets complicated if a large number of input parametersare used for uncertainty analysis.

8. Conclusion

In the present study, an uncertainty quantification methodusing sampling based method has been used for estimating peakclad temperature and safety margin. For uncertainty quantificationof thermal hydraulic transient analysis with a large computer codewhere limited time and resources are present, the LHS method isvery efficient and useful. The Kolgomorov–Sminroff method good-ness-of-fit test is very simple and useful for probability testing forsmaller data set. In the present uncertainty analysis for LBLOCAonly five parameters were considered. However, for more rigorousanalysis many other uncertain parameters may also need to beconsidered to examine their effect on available SM for more realis-tic and reliable results. However, the study has provided insightsinto the realistic results expected during possible accident se-quence drawn from event tree for LBLOCA. The SM 95/95 for allthe NCD accident sequences is predicted to be above 150 K inLBLOCA. The measure of robustness of the safety system designcan also be judged from the available SM95/95. The minimum ofthe lower tolerance limit for SMs from the accident sequenceswould indicate the 95% confidence with 95% probability of therobustness of the safety systems.

In uncertainty analysis, the type of sampling technique for theparameters along with their range and distribution play an impor-tant role in the estimation of the confidence limits. Generally, ran-dom sampling should be used for generating a truly randomcombination of inputs. A random input selection would producerandom outputs through the thermal hydraulic functional relation-ship. This gives a realistic and reliable estimation of limitingparameter values.

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