NUREG/IA-0456 

International 

 Agreement Report

BEPU Analysis and Benchmark with 

IIST 2% SBLOCA Experiment Using 

TRACE/DAKOTA

 

 

Prepared by: 

Chunkuan Shih*, Jung-Hua Yang*, Jong-Rong Wang*, Hao-Tzu Lin, Show-Chyuan Chiang**, 

Chia-Chuan Liu**

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

**Department of Nuclear Safety, Taiwan Power Company

242, Section 3, Roosevelt Rd., Zhongzheng District, Taipei, Taiwan

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: April 2015

Date Published: September 2015

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0456 

International 

 Agreement Report

BEPU Analysis and Benchmark with 

IIST 2% SBLOCA Experiment Using 

TRACE/DAKOTA

 

 

Prepared by: 

Chunkuan Shih*, Jung-Hua Yang*, Jong-Rong Wang*, Hao-Tzu Lin, Show-Chyuan Chiang**, 

Chia-Chuan Liu**

Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.

1000, Wenhua Rd., Chiaan Village, Lungtan, Taoyuan, 325, Taiwan

*Institute of Nuclear Engineering and Science, National Tsing Hua University

101 Section 2, Kuang Fu Rd., HsinChu, Taiwan

**Department of Nuclear Safety, Taiwan Power Company

242, Section 3, Roosevelt Rd., Zhongzheng District, Taipei, Taiwan

K. Tien, NRC Project Manager 

 

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: April 2015

Date Published: September 2015

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

iii 

ABSTRACT

There are two licensing approaches for evaluation of Loss of Coolant Accidents consequences: 

conservative methodology and best estimate methodology. Recently, the trend of nuclear reactor 

safety analysis reveals an increasing interest to substitute best estimate for conservative 

methodologies to achieve the safety margins and regulate the licensing and operations of 

nuclear reactors. 

The Institute of Nuclear Energy Research Integral System Test (IIST) facility is a test facility to 

simulate the thermal hydraulics of a Westinghouse 3-loop Pressurized Water Reactor at 

Maanshan Nuclear Power Plant. The research purposes of the IIST facility are: (a) to enhance 

the understanding of thermal hydraulics during transients as well as Small Break Loss of Coolant 

Accidents, (b) to contribute to the evaluations and developments of safety computer codes, (c) to 

validate the Emergency Operation Procedures during the transients. The scaling factors of the 

IIST facility for height and volume in the Reactor Coolant System are approximately 1/4 and 

1/400, respectively, and the maximum operating pressure is 2.1 MPa. The scaling of hot leg is 

based on the Froude number criterion to simulate the transition of flow regimes in the horizontal 

pipes during transients and accidents. 

This study is developed the BEPU methodology and the uncertainty results were compared with 

the IIST experiment data. The IIST TRACE model consists of 89 hydraulic components, 243 

control blocks, 39 heat structures and a power component. The data interactions and 

communications between TRACE and DAKOTA were controlled by SNAP. Finally, correlations 

between input parameters and output data are calculated for sensitivity study and ranking to 

investigate what input parameters dominate the contribution of uncertain distribution of PCT. 

There are two tasks in this study. One is benchmark of the simulation capability of IIST TRACE 

model by comparing with the IIST SBLOCA experiment results. The other is BEPU in SBLOCA 

analysis, several important parameters were considered in the uncertainty quantified. The BEPU 

analysis is focused on the discussion of measurement uncertainty and model uncertainty. 

Furthermore, the IIST experimental data were used to benchmark the results of uncertainty 

analysis. There are 5 parameters taken into account in this uncertainty analysis. An uncertainty 

band is formed by the 59 calculations, and the benchmark results show the IIST experimental 

data were located in the uncertainty band. In addition, this study used two methods to calculate 

correlation coefficients between an input and an output variable: Pearson’s correlation coefficient 

and Spearman’s rank correlation. The formula quantifies the correlations between the input and 

output parameter. Even though the Spearman’s rank correlation employs the rank data is 

difference than the Pearson’s correlation, their results are similar trend. The results indicate that 

choked flow coefficient is the most sensitive parameter. The correlation coefficients of Pearson’s 

and Spearman’s are -0.72405 and -0.70199 respectively. Although the measurement error may 

influence the PCT calculated, its effect is smaller than the model uncertainty. 

 
iv 

 
v 

FOREWORD

The US NRC (United States Nuclear Regulatory Commission) is developing an advanced 

thermal hydraulic code named TRACE for nuclear power plant safety analysis. The development 

of TRACE is based on TRAC, integrating RELAP5 and other programs. NRC has determined 

that in the future, TRACE will be the main code used in thermal hydraulic safety analysis, and no 

further development of other thermal hydraulic codes such as RELAP5 and TRAC will be 

continued. A graphic user interface program, SNAP (Symbolic Nuclear Analysis Program) which 

processes inputs and outputs for TRACE is also under development. One of the features of 

TRACE is its capacity to model the reactor vessel with 3-D geometry. It can support a more 

accurate and detailed safety analysis of nuclear power plants. TRACE usually used in the 

nuclear power plants analysis. This report showed TRACE can also do the calculation of small 

system such as dry-storage cask. 

Taiwan and the United States have signed an agreement on CAMP (Code Applications and 

Maintenance Program) which includes the development and maintenance of TRACE. INER 

(Institute of Nuclear Energy Research, Atomic Energy Council, R.O.C.) is the organization in 

Taiwan responsible for the application of TRACE in thermal hydraulic safety analysis, for 

recording user’s experiences of it, and providing suggestions for its development. To meet this 

responsibility, the TRACE IIST model has been built. This study is developed the BEPU 

methodology and the uncertainty results were compared with the IIST experiment data. 
vi 

 
vii 

CONTENTS

Page

ABSTRACT ............................................................................................................................... iii 

FOREWORD .............................................................................................................................. v 

CONTENTS .............................................................................................................................. vii 

FIGURES ................................................................................................................................... ix 

TABLES .................................................................................................................................... xi 

EXECUTIVE SUMMARY ......................................................................................................... xiii 

ABBREVIATIONS .................................................................................................................... xv 

1. INTRODUCTION ................................................................................................................1-1 

2. METHODOLOGY ...............................................................................................................2-1 

3. FACILITY AND MODEL ....................................................................................................3-1 

3.1 Description of IIST Facility .........................................................................................3-1 

3.2 Description of SBLOCA Experiment ..........................................................................3-1 

3.3 Description of IIST TRACE Model .............................................................................3-2 

4. RESULTS AND DISCUSSIONS ........................................................................................4-1 

4.1 Best Estimate Results................................................................................................4-1 

4.2 Uncertainty Analysis ..................................................................................................4-5 

4.3 Correlation Analysis ...................................................................................................4-8 

5. CONCLUSIONS .................................................................................................................5-1 

6. REFERENCES ...................................................................................................................6-1 

 
viii 

 

 
ix 

FIGURES

Page 

Figure 1 The Flowchart of Uncertainty Analysis ...................................................................2-2 

Figure 2 The Schema of IIST Facility. ..................................................................................3-6 

Figure 3 The TRACE IIST Facility Model .............................................................................3-7 

Figure 4 The Comparisons of Break Flow Rate between IIST Data and TRACE Data .........4-2 

Figure 5 The Comparisons of Primary System Pressure between IIST Data and TRACE 

Data .......................................................................................................................4-2 

Figure 6 The Comparisons of Core Water Level between IIST Data and TRACE Data ........4-3 

Figure 7 The Comparisons of Loop-3 Flow Rate between IIST Data and TRACE Data .......4-3 

Figure 8 The Comparisons of Loop-3 Hot-Leg and Cold-Leg Temperature between IIST 

Data and TRACE Data ..........................................................................................4-4 

Figure 9 The Comparisons of Cladding Temperature between IIST Data and TRACE 

Data .......................................................................................................................4-4 

Figure 10 The Break Flow Rates during the SBLOCA ...........................................................4-6 

Figure 11 The PCTs during the SBLOCA ..............................................................................4-7 

Figure 12 The Histograms of the Input Parameters and Resultant PCTs ...............................4-9 

Figure 13 The Pearson’s Correlation Coefficients between Input Parameters and PCT ...... 4-10 

Figure 14 The Spearman’s Correlation Coefficients between Input Parameters and PCT ... 4-11 

 
x 

 

 
xi 

TABLES 

Page

Table 1 The Comparisons of Key Parameters between Maanshan NPP and IIST Facility ...3-3 

Table 2 The Initial Condition of the IIST SBLOCA Experiment .............................................3-4 

Table 3 The Comparison of SBLOCA Experiment Initial Condition between IIST Facility 

and IIST TRACE Model ..........................................................................................3-5 

Table 4 The Important Parameters for the Uncertainty Analysis ..........................................4-6 
xii 

 

 

 

 
xiii 

EXECUTIVE SUMMARY

An agreement which includes the development and maintenance of TRACE has been signed 

between Taiwan and USA on CAMP. INER (Institute of Nuclear Energy Research Atomic Energy 

Council, R.O.C.) is the organization in Taiwan responsible for applying TRACE to thermal 

hydraulic safety analysis in order to provide users’experiences and development suggestions. To 

fulfill this responsibility, the TRACE model of IIST facility is developed. The IIST facility is a 

Reduced-High and Reduced-Pressure test facility to simulate the thermal hydraulics of a 

Westinghouse 3-loop PWR at Maanshan Nuclear Plant since 1992. The scaling factors of the 

IIST facility for height and volume in the Reactor Coolant System are approximately 1/4 and 

1/400, respectively, and the maximum operating pressure is 2.1 MPa. The scaling of hot leg is 

based on the Froude number criterion to simulate the transition of flow regimes in the horizontal 

pipes during transients and accidents. The research purposes of the IIST facility are: (a) to 

enhance the understanding of thermal hydraulics during transients as well as SBLOCAs, (b) to 

contribute to the evaluations and developments of safety computer codes, (c) to validate the 

Emergency Operation Procedures during the transients. 

The codes used in this research are TRACE v5.0p4 and SNAP v2.2.6. There are two tasks in 

this study. One is benchmark of the simulation capability of IIST TRACE model by comparing 

with the IIST SBLOCA experiment results. The other is BEPU in SBLOCA analysis, 5 important 

parameters were considered in the uncertainty quantified. The BEPU analysis is focused on the 

discussion of measurement uncertainty and model uncertainty. Furthermore, the IIST 

experimental data were used to benchmark the results of uncertainty analysis. In addition, this 

study used two methods to calculate correlation coefficients between an input and an output 

variable: Pearson’s correlation coefficient and Spearman’s rank correlation. The formula 

quantifies the correlations between the input and output parameter. Even though the Spearman’s 

rank correlation employs the rank data is difference than the Pearson’s correlation, their results 

are similar trend. The results indicate that choked flow coefficient is the most sensitive parameter. 

Although the measurement error may influence the PCT calculated, its effect is smaller than the 

model uncertainty. 
xiv 

 

 

 
xv 

ABBREVIATIONS

BEPU Best Estimate Plus Uncertainty 

CAMP Code Applications and Maintenance Program 

CCFL Counter-Current Flow Limitation 

CSAU Code Scaling, Applicability and Uncertainty 

EOP Emergency Operation Procedures 

HPI High Pressure Injection 

IIST Institute of Nuclear Energy Research Integral System Test 

INER Institute of Nuclear Energy Research Atomic Energy Council, R.O.C. 

LOCA Loss of Coolant Accidents 

NPP Nuclear Power Plant 

NRC Nuclear Regulatory Commission 

PDFs Probability Distributions Functions 

PWR Pressurized Water Reactor 

RHRP Reduced-High and Reduced-Pressure 

PCT Peak Cladding Temperature 

RCS Reactor Coolant System 

SBLOCA Small Break Loss of Coolant Accident 

SG Steam Generator 

SNAP Symbolic Nuclear Analysis Program 

TRACE TRAC/RELAP Advanced Computational Engine 

US United States 

 
xvi 

 

 
1-1 

1. INTRODUCTION 

There are two licensing approaches for evaluation of Loss of Coolant Accidents (LOCA) 

consequences: conservative methodology and best estimate methodology. The conservative 

methodology refers to the conservative analysis using conservative code and conservative 

assumptions. While the best estimate methodology refers to best estimate (code) calculation that 

includes uncertainty analysis. Recently, the trend of nuclear reactor safety analysis reveals an 

increasing interest to substitute best estimate for conservative methodologies which may apply 

conservative codes or the combination of best-estimate codes and conservative initial and 

boundary conditions to achieve the safety margins and regulate the licensing and operations of 

nuclear reactors [1]. Compared with conservative methodologies, the methodologies of Best 

Estimate Plus Uncertainty (BEPU) adopt best estimate codes and realistic input data with 

uncertainties to quantify the limiting values i.e., Peak Cladding Temperature (PCT) for LOCAs. 

The use of BEPU methods started from 1974. Research during 1974-1988 provided a foundation 

sufficient for use of realistic and physically based analysis methods [2]. Large number of 

experimental programs was completed internationally. The United States Nuclear Regulatory 

Commission (USNRC) developed the Code Scaling, Applicability and Uncertainty (CSAU) 

method[1] and demonstrated a licensing acceptable best estimate method which could bring 

benefit to nuclear plant operators (ex. less conservative, consideration of uncertainties, 

economic gains). After pioneering CSAU in the next five years several new original methods 

were developed, such as UMAE method (Italy), NE method (UK) [3], GRS method (Germany) [4], 

IPSN method (France) etc. All of methods consist of two basic elements which are identification 

and quantification of important parameters as well as analysis to quantify the combined influence 

of these uncertainties on output parameters. Uncertainty quantification methods calculate 

probabilistic information about response functions based on simulations performed according to 

specified input parameter Probability Distributions Functions (PDFs). Sampling methods are 

often used in uncertainty quantification to calculate a distribution on system performance 

measures, and to understand which uncertain inputs contribute most to the variance of the 

outputs. 

The Institute of Nuclear Energy Research Integral System Test (IIST) facility is a test facility to 

simulate the thermal hydraulics of a Westinghouse 3-loop Pressurized Water Reactor (PWR) at 

Maanshan Nuclear Power Plant (NPP). This study is developed the BEPU methodology and the 

uncertainty results were compared with the IIST experiment data. 
1-2 

 
2-1 

2. METHODOLOGY 

Figure 1 shows the BEPU methodology in this study. First, collecting the IIST facility parameters 

is needed, such as the vessel geometry, pipe length, and flow area. Then, the TRACE IIST 

model is established and verified with the experiment data of the IIST facility. If the results of 

benchmark are not consistent with the IIST experiment data, that modify the TRACE IIST model. 

If yes, then do the next step for uncertainty analysis. In order to do uncertainty analysis, it must to 

identify and select the important parameters in the specific transient. Important parameters which 

will affect transient analysis can be divided into three groups, namely initial conditions, accident 

boundary conditions, and system settings. To define the uncertainty of the parameters, not only 

the uncertainty range needs to be quantified, but also the distribution function needs to be 

specified. Three different kinds of elements contribute the total uncertainty of a particular 

parameter, which involve normal operational range, measurement uncertainty, and model 

uncertainty. Once the major parameters have been identified and ranged, random sampling of 

each parameter needs to be performed to generate a run matrix. DAKOTA code is used to 

generate random variable and to evaluate response data generated by TRACE/SNAP. The 

sampling method in DAKOTA could choose the Monte-Carlo or Latin Hypercube method, which 

can be used with probabilistic variables that have the following distributions: normal, lognormal, 

uniform, loguniform, triangular, exponential, beta, gamma, gumbel, frechet, weibull, poisson, 

binomial, negative binomial, geometric, hypergeometric, and user-supplied histograms. With 

Monte-Carlo method, each random variable is produced from its distribution independent of other 

variables. When set to Latin Hypercube method, the distribution is sliced into equally likely bins, 

and a random value is produced from each bin. 

Because the required minimum number of TRACE runs is dependent of the values of confidence 

level and probability, Wilks’ formula[5] was employed to determinate the minimum number of 

runs. The correlations between number of code runs, confidence level, and probability of Wilks’ 

formula are defined: 

 Eg. 1 

where		α is probability, β is the confidence level, and n denotes the number of code runs. 

Since the value of PCT is the safety criterion to ensure the integrity of fuel assemblies for LOCAs, 

the minimum number of 59 was used to generate the maximum bound of PCT which achieve 

95/95 criterion. 

If more than one output needs to be cited from each trial, the Guba’s formula [6] can be used: 

 Eg. 2 

where N is the sample size and P is the number of output variables. 

If output variable is only one, that Guba’s formula will reduce to Wilk’ formula. 

All TRACE runs were defined and executed through SNAP job streams[7-8], and TRACE 

calculation results were read by AptPlot script. The data interactions and communications 

between TRACE and DAKOTA[9-10] were controlled by SNAP. Finally, correlations between 

input parameters and output data (ex. PCT) are calculated for sensitivity study and ranking to 

investigate what input parameters dominate the contribution of uncertain distribution of PCT. 
2-2 

Figure 1 The Flowchart of Uncertainty Analysis 
3-1 

3. FACILITY AND MODEL 

3.1 Description of IIST Facility

The IIST facility is a Reduced-High and Reduced-Pressure (RHRP) test facility to simulate the 

thermal hydraulics of a Westinghouse 3-loop PWR at Maanshan Nuclear Plant since 1992 [11]. 

The comparisons of key parameters between Maanshan NPP and IIST facility are listed in Table 

1. The research purposes of the IIST facility are: (a) to enhance the understanding of thermal 

hydraulics during transients [12,13] as well as Small Break Loss of Coolant Accidents (SBLOCAs) 

[14], (b) to contribute to the evaluations and developments of safety computer codes [15,16], (c) 

to validate the Emergency Operation Procedures (EOP) during the transients [17]. 

The scaling factors of the IIST facility for height and volume in the Reactor Coolant System (RCS) 

are approximately 1/4 and 1/400, respectively, and the maximum operating pressure is 2.1 MPa. 

The scaling of hot leg is based on the Froude number criterion to simulate the transition of flow 

regimes in the horizontal pipes during transients and accidents. As shown in Figure 2, the IIST 

facility consists of a pressure vessel and 3 loops. The pressure vessel has 3 inlet and 3 outlet 

nozzles. Coolant enters the vessel through the inlet nozzles and flows down through the 

downcomer, and flows up through the heater rods to the outlet nozzles. The bypass flow from the 

upper plenum to the downcomer is simulated by three external tubes connected with the valves. 

Each loop has a steam generator and a coolant pump, and the 3 loops are identical, except that 

there is a pressurizer in the loop 1. The pressurizer connected with loop 1 equips an electrical 

heater, spray nozzle and pressure relief valves. The capacity of electrical heater is 10 kW, and 

the penetrations of spray nozzle and pressure relief valves are located on the top of pressurizer. 

There are 30 U-tubes in each steam generator. However, the steam dome of a steam generator 

doesn’t contain separators and dryers, because the steam velocity in the steam dome is not 

strong enough to entrain liquid into seam line at the low core power during simulation of the 

decay heat level. The secondary feedwater flow rate is controlled by flow control valve actuated 

by the water level controller of each steam generator. The IIST facility incorporates a data 

acquisition system which measures temperature, pressure, flow rate, liquid level, and differential 

pressure. 

3.2 Description of SBLOCA Experiment 

The experiment of IIST facility was performed in order to simulate a 2% cold-leg break (the break 

area is 2% of the scaled cold-leg cross-section area) with total High Pressure Injection (HPI) 

failure[18,19]. A horizontal break nozzle was installed in the cold-leg of loop 2 which is not 

connected with pressurizer. The initial conditions of this experiment are listed in Table 2. The 

SBLOCA experiment started from the break occurred at 0s and the primary pressure of IIST 

facility dropped until it became only a little higher than the secondary-side pressure of IIST facility. 

The air flowed through the hot-leg into the SG-1 U-tubes after emptying the pressurizer at 128s. 

After 164s of the break, the loop 1 flow rate suddenly dropped to near zero, which indicates the 

decrease of the heat removal capability of SG-1. The noncondensable air obviously slowed the 

temperature rise in both the primary and secondary sides of SG-1 and caused the sudden 

decrease of the natural-circulation flow rate in loop 1. The collapsed liquid level of core 

decreased sharply after the break occurred due to the subcooled liquid discharge in the time 

period between 0s to 146s. Then, the collapsed liquid level of core decreased slowly when the 

break flow became a two-phase mixture from 146s to 400s. (Finally, because of no coolant 

makeup, the core was uncovered with heatup at 1734s.) This experiment was terminated at 1734 

s because the uncovering of the core was caused by continuous boil-off of vessel coolant 

inventory without the actuation of coolant makeup system. 
3-2 

3.3 Description of IIST TRACE Model

The IIST TRACE model, which consists of 89 hydraulic components, 243 control blocks, 39 heat 

structures and a power component, is showed in Figure 3. This model has three loops and each 

loop includes the simulation of the hot-leg, Steam Generator (SG) inlet plenum, SG U-tubes, SG 

outlet plenum, crossover leg, coolant pump, and cold-leg. The pressurizer is located in loop 1 

and the break valve is located in loop 2. The models of the three SG are identical, and each of 

the SG consists of downcomer, boiling section and steam dome. The feedwater flow rates are 

simulated by time-dependent junctions, and the downstream condition of each steam line is 

simulated by a break component with constant boundary condition. The steam line is simulated 

by a break component, which simulates the pressure of steam line during the IIST facility 

experiments. The break flow area is simulated using a specific valve with the critical flow option. 

Table 3 shows the comparison of the initial condition between IIST facility and IIST TRACE 

model. The initial conditions of IIST TRACE model are in good agreement with the IIST facility. 

The SNAP v 2.2.6 and TRACE v 5.0p4 were employed in this research. 

 
3-3 

Table 1 The Comparisons of Key Parameters between Maanshan NPP and IIST Facility 

Parameter IIST Maanshan PWR IIST/PWR 

Design pressure (MPa) 

Maximum core power (MW) 

Primary system volume (m3

)

Number of loops 

Core 

Height (m) 

Hydraulic diameter (m) 

Bypass area (m2

) 

Hot leg 

Inner diameter, D (m) 

Length, L (m) 

L / √D (m0.5) 

U-tube in one SG 

Number 

Average length (m) 

Inner diameter (mm) 

Volume (m3

) 

Cold leg 

Inner diameter D (m) 

Length L (m) 

L / √D (m0.5) 

Downcomer 

Flow area (m2) 

Hydraulic diameter (m) 

Pressurizer 

Volume (m3) 

Surge-line flow area (m2

) 

2.1 

0.45 

5.37×10-1

3 

1.0 

1.08×10-1

7.2×10-5

5.25×10-2

2.0 

8.72 

30 

4.08 

15.4 

2.28×10-2

5.25×10-2

5.0 

21.8 

0.0185 

4.12×10-2

9.32×10-2

3.44×10-4

15.6 

2775 

2.15×102

3 

3.6 

1.22×10-2

1.54×10-2

7.35×10-1

7.28 

8.48 

5626 

16.85 

15.4 

18.44 

7.87×10-1

15.7 

17.69 

2.63 

4.8×10-1

39.64 

6.38×10-2

1.35×10-1 

1.62×10-4

2.50×10-3

1 

2.77×10-1

8.85 

4.67×10-3

7.13×10-2

2.75×10-1

1.03 

5.33×10-3

2.24×10-1

1.0 

1.23×10-3

6.67×10-2

3.18×10-1

1.22 

7.03×10-2

8.58×10-2

2.35×10-3

5.39×10-3

 
3-4 

Table 2 The Initial Condition of the IIST SBLOCA Experiment 

Parameter IIST test data

Primary coolant system

Core power (kW) 126 

Pressurizer pressure (MPa) 0.958 

Pressurizer water level (m) 1.459 

Loop flow rate (kg/s) 0.217 

Hot-leg temperature (K) 450 

Cold-leg temperature (K) 409 

Secondary coolant system

Secondary-side pressure (MPa) 0.295 

Secondary-side fluid temperature (K) 407 

 
3-5 

Table 3 The Comparison of SBLOCA Experiment Initial Condition between IIST Facility 

and IIST TRACE Model 

Parameter IIST facility TRACE/error (%) 

Primary coolant system 

Core power (kW) 126 126 

Pressurizer pressure (MPa) 0.958 0.964 /0.6 

Pressurizer water level 

(mm) 

1459 1463 /0.3 

Loop flow rate (kg/s) 

Loop1 0.210 0.219 /4.3 

Loop2 0.217 0.219 /0.9 

Loop3 0.217 0.219 /0.9 

Hot-leg temperature (K) 

Loop1 450 448.7 /0.3 

Loop2 449 448.7 /0.1 

Loop3 451 448.7 /0.5 

Cold-leg temperature (K) 

Loop1 409 409.5 /0.1 

Loop2 408 409.5 /0.4 

Loop3 409 409.5/ 0.1 

Secondary coolant 

system 

 

Secondary-side pressure 

(MPa) 

 

SG-1 0.301 0.303 /0.7 

SG-2 0.295 0.299 /1.4 

SG-3 0.295 0.299 /1.4 

Secondary-side fluid 

temperature (K) 

 

SG-1 407 406.1 /0.2 

SG-2 407 405.6 /0.3 

SG-3 407 405.6 /0.3 
3-6 

Figure 2 The Schema of IIST Facility 
3-7 

Figure 3 The TRACE IIST Facility Model 
3-8 

 
4-1 

4. RESULTS AND DISCUSSIONS 

4.1 Best Estimate Results 

The first task of this study is to benchmark the simulation capability of IIST TRACE model by 

comparing with the IIST SBLOCA experiment results. The parameters including break flow rate, 

system pressure, core water level and peak cladding temperature, etc, which affect the plant 

safety directly should be taken into consideration in SBLOCA analysis. Figure 4 and Figure 5 

show the comparisons of break flow rate and primary system pressure between IIST data and 

TRACE data. The break flow rate and primary system pressure trends of TRACE simulated 

results are similar with the IIST data. Figure 6 shows the comparisons of the core water level 

between IIST data and TRACE data. The trends of their curves are similar. Natural-circulation 

flow rate can be observed in the integral loop (i.e. loop-1 and loop-3) during the IIST SBLOCA 

experiment. Figure 7 shows the comparison of loop-3 flow rate between IIST data and TRACE 

data in the SBLOCA experiment. From the analysis results, there are underpredicted flow rate at 

200~400s and overpredicted flow rate at 400~600s in loop-3. Figure 8 shows the fluid 

temperatures of the cold-leg and hot-leg in loop-3. There is no significant difference in the loop-3 

fluid temperature (hot-leg and cold-leg) between the TRACE prediction and the IIST experiment 

data. Figure 9 shows the comparisons of cladding temperature between IIST data and TRACE 

data. The PCT rising time of IIST experimental data and TRACE calculated are 1782s and 1869s 

respectively. 

In summary, the thermal-hydraulic results calculated by TRACE are in agreement with those of 

IIST facility experiments data. 
4-2 

Figure 4 The Comparisons of Break Flow Rate between IIST Data and TRACE Data 

Figure 5 The Comparisons of Primary System Pressure between IIST Data and TRACE 

Data 

0 400 800 1200 1600 2000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Break flow rate (kg/s)

Time (s)

 IIST data

 TRACE data

0 400 800 1200 1600 2000

0.0

0.5

1.0

1.5

 IIST data

 TRACE data

Primary pressure (MPa)

Time (s)
4-3 

Figure 6 The Comparisons of Core Water Level between IIST Data and TRACE Data 

Figure 7 The Comparisons of Loop-3 Flow Rate between IIST Data and TRACE Data 

0 400 800 1200 1600 2000

-2

-1

0

1

2

3

4

 IIST data

 TRACE data

Core water level (m)

Time (s)

0 400 800 1200 1600 2000

-0.5

0.0

0.5

1.0

 IIST data

 TRACE data

Loop 3 flow rate (kg/s)

Time (s)
4-4 

Figure 8 The Comparisons of Loop-3 Hot-Leg and Cold-Leg Temperature between IIST 

Data and TRACE data 

Figure 9 The Comparisons of Cladding Temperature between IIST Data and TRACE Data 

0 400 800 1200 1600

320

360

400

440

480

520

SG-3 hot leg temperature (K)

Time (s)

Hot-leg temperature

 IIST data

 TRACE data

Cold-leg temperature

 IIST data

 TRACE data

400

420

440

460

480

 SG-3 cold leg temperature (K)
4-5 

4.2 Uncertainty Analysis

In BEPU of LOCA analysis, several important parameters were considered in the uncertainty 

quantified. The uncertainty attributes have been divided for several kinds, such as measurement 

uncertainty, code uncertainty, boundary condition uncertainty, model uncertainty, etc. This study 

is focused on the measurement uncertainty and model uncertainty analysis. Furthermore, the 

IIST experimental data were used to benchmark the results of uncertainty analysis. The 

uncertainties of system pressure and coolant average temperature are major contributed by 

measurement uncertainty (i.e., Venturi tube, thermocouple, etc.). However, the model 

uncertainty is dependent on the coefficient of model by user’s definition. Table 4 lists the 5 

parameters (i.e., primary pressure, core outlet temperature, loop flow rate, choked flow 

coefficient, and Counter-Current Flow Limitation (CCFL) coefficient) taken into account in this 

uncertainty analysis, which are defined as the SNAP user-defined numeric variables and linked 

with uncertainty configuration to generate TRACE input files. By coupling with DAKOTA, the 

important parameters with uncertainties were generated randomly based on specified PDFs. In 

particular, the statistical theory predicts that 59 calculations are required to simultaneously bound 

the 95th percentile of one parameters (PCT) with a 95-percent confidence level. 

In LOCA simulation, the coefficient of choked flow model will influence the calculated results of 

critical flow rate at the break pipe. Except considering the measurement error, the model 

uncertainty was taken into account in this study. Figure 10 displays the 59 break flow rates as a 

function of time. The benchmark results show the IIST experimental data were located in the 

uncertainty band. 

Figure 11 displays the 59 PCTs as a function of time. In BEPU analysis, an uncertainty band is 

formed by the 59 calculations PCTs. The faster PCT rises, the more serious condition in 

transient happens. The minimum and maximum PCT rising time are 1642s and 2237s 

respectively. The IIST experimental data shows the PCT rising time is 1782s. 

 
4-6 

Table 4 The Important Parameters for the Uncertainty Analysis 

Input parameters Nominal 

values 

Uncertainty 

range 

PDFs 

System pressure 1.0293 (MPa) [ -2%, +2% ] ND 

ND 

ND 

UD 

UD 

Hot-leg temperature 440.4 (K) [ -0.3%, +0.3% ]

Loop flow rate 0.217 (kg/s) [ -1.3, +1.3 ] 

Choked flow coefficient 

CCFL coefficient 

1.0 (--) 

0.4 (--) 

[ 0.4, 1.2 ] 

[ 0.2, 0.8 ] 

Note: ND means normal distributions and UD means uniform distributions 

Figure 10 The Break Flow Rates during the SBLOCA 
4-7 

Figure 11 The PCTs during the SBLOCA
4-8 

4.3 Correlation Analysis 

Correlations are always calculated between two sets of sample data. One can calculate 

correlation coefficients between two input variables, between an input and an output variable, or 

between two output variables. Therefore, correlations between input parameters and PCTs 

(output parameters) are calculated for sensitivity study and ranking to investigate what input 

parameters dominate the contribution of uncertain distribution of PCT. In this study, there are two 

methods to present the correlations between input variables and output variables, Pearson’s 

correlation coefficient and Spearman’s rank correlation. The Pearson’s correlation is shown in Eq. 

3. 

r =

∑ 	


	





∑ 	




 ∑ 	

 







 Eq. 3 

where r is the Pearson’s correlation coefficient, n is the number of samples, and x and y denote 

two quantities. 

The formula of Spearman’s rank correlation is the same as Pearson’s; however, the difference is 

that Spearman’s rank correlation employs the rank data which substitute the ranked values for 

raw data. 

Figure 12 shows the distribution histograms of the five input parameters and 59 resultant PCTs. 

The parameters of primary pressure, core outlet temperature, and loop flow rate are uniform 

distribution, but choked flow model and CCFL coefficient are normal distribution. In addition, it 

could see that the PCT distribution is similar to normal distribution. 

Figure 13 (a) shows the calculated results of Pearson’s correlation coefficient, which include the 

correlation of each two parameters. The coefficients represent negative correlation. It means the 

small value of parameter, the quickly time of temperature raised. The correlation between input 

parameters and PCT are shown in Figure 13(b), and the results indicate that choked flow 

coefficient is the most sensitive parameter. The coefficient which user-defined has more 

influence on the PCT calculated results. Although the measurement error may influence the PCT 

calculated, its influence is smaller than the model uncertainty. 

Figure 14 shows the results of Spearman’s correlation coefficient. The calculated results are 

similar to the Pearson’s correlation coefficient. The results also indicate that choked flow 

coefficient is the most sensitive parameter. Pearson’s correlation coefficient and Spearman’s 

correlation coefficient are -0.72405 and -0.70199 respectively. 

By the Pearson’s coefficient and Spearman’s coefficient, it quantifies the correlations between 

the input and output parameter. Even though the Spearman’s rank correlation employs the rank 

data is difference than the Pearson’s correlation, their results are similar trend. 
4-9 

Figure 12 The Histograms of the Input Parameters and Resultant PCTs
4-10 

Figure 13 The Pearson’s Correlation Coefficients between Input Parameters and PCT 
4-11 

Figure 14 The Spearman’s Correlation Coefficients between Input Parameters and PCT 
4-12 

 
5-1 

5. CONCLUSIONS

There are two tasks in this study. One is benchmark of the simulation capability of IIST TRACE 

model by comparing with the IIST SBLOCA experiment results. The parameters including break 

flow rate, system pressure, core water level and peak cladding temperature, etc, which affect the 

plant safety directly should be taken into consideration in SBLOCA analysis. In summary, the 

thermal-hydraulic results calculated by TRACE are in agreement with those of IIST facility 

experiments data. 

The second task is BEPU in SBLOCA analysis, several important parameters were considered in 

the uncertainty quantified. In this study, the BEPU is focused on the discussion of measurement 

uncertainty and model uncertainty analysis. Furthermore, the IIST experimental data were used 

to benchmark the results of uncertainty analysis. There are 5 parameters taken into account in 

this uncertainty analysis. An uncertainty band is formed by the 59 calculations, and the 

benchmark results show the IIST experimental data were located in the uncertainty band. The 

minimum and maximum PCT rising time are 1642s and 2237s respectively. The IIST 

experimental data shows the PCT rising time is 1782s. 

In addition, this study used two methods to calculate correlation coefficients between an input 

and an output variable: Pearson’s correlation coefficient and Spearman’s rank correlation. The 

formula quantifies the correlations between the input and output parameter. Even though the 

Spearman’s rank correlation employs the rank data is difference than the Pearson’s correlation, 

their results are similar trend. The results indicate that choked flow coefficient is the most 

sensitive parameter. The correlation coefficients of Pearson’s and Spearman’s are -0.72405 and 

-0.70199 respectively. Although the measurement error may influence the PCT calculated, its 

effect is smaller than the model uncertainty. 
5-2 

 
6-1 

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NUREG/IA-0252, 2011. 







NUREG/IA

-0456 BEPU Analysis and Benchmark with IIST 2% SBLOCA 

Experiment Using TRACE/DAKOTA