Assessment study about the risk of Wilks’ formula for uncertainty quantification of design extension condition scenarios in prototype Gen-IV sodium fast reactor

ABSTRACT

Sensitivity analysis and uncertainty quantification using Wilks’ formula and Monte Carlo for Unprotected Loss of Flow (ULOF) and Unprotected Transient OverPower (UTOP) accidents of prototype Gen-IV sodium-cooled fast reactor were performed. Multi-dimensional analysis for reactor safety for liquid metal reactors code calculations were conducted while simultaneously varying the values of all uncertain parameters according to their distribution using parallel computing platform integrated for uncertainty and sensitivity analysis to obtain uncertainty bands for Figures of Merit (FOM) – coolant, fuel centerline, and cladding temperature at the hottest fuel rod. To specify the uncertainty range of the parameters for each accident scenario, literature survey and expert judgments were consulted. By the sensitivity analysis, the importance ranking of 25 parameters in model identification and ranking table based on phenomena identification and ranking table was identified. Through Monte Carlo calculation, 95% upper limit and 95% confidence level were obtained, and about 2% and 5% under-prediction (risk) of FOM of ULOF and UTOP accidents using Wilks’ formula were confirmed, respectively.

KEYWORDS:

• PGSFR
• MARS-LMR
• PAPIRUS
• uncertainty quantification
• Wilks’ formula
• Monte Carlo
• ULOF
• UTOP

1. Introduction

The safety requirements and licensing of commercial nuclear power plants have been based on a conservative approach since nuclear safety regulations have been developed by U.S. Nuclear Regulatory Commission (USNRC) 10 CFR [1–3]. However, by the 1980s, the large database of experimental and analytical research related to the conservative approach of safety analysis was somewhat misdirected and sometimes even gave non-conservative results [4]. Therefore, by the 1990s, the Code Scaling Applicability and Uncertainty (CSAU) and Phenomena Identification and Ranking Table (PIRT) methodology started to be used to obtain the safety analysis based on the Best Estimate plus Uncertainty (BEPU). Since the 1990s, safety analysis using conservative methods or the BEPU approach has been optionally utilized in the licensing process for nuclear power plants [4,5]. In South Korea, those approaches have also been applied to safety analysis for licensing regarding Large Break Loss of Coolant Accident (LBLOCA) since the 2000s [6].

Several uncertainty methods have been developed to estimate safety margins to justify reactor operation. Within the uncertainty methods considered, uncertainties are evaluated using either CSAU and Gesellschaft fur Anlagen-und Reaktorsicherheit (GRS) methods through uncertainty methods study or Uncertainty Methodology on Accuracy Extrapolation (UMAE), Code with Internal Assessment of Uncertainty (CIAU) through the best estimate methods – uncertainty and sensitivity evaluation program, and so on [5,7–10]. In the CSAU and GRS approaches, the results of propagation of input parameters with specified ranges are considered to determine the uncertainty for accident scenarios of nuclear power plants. In the UMAE and CIAU approaches, uncertainty is obtained by comparing calculation results with significant experimental data.

CSAU was used for application to small break loss of coolant accident and LBLOCA of Pressurized Water Reactor (PWR) using best estimate codes like RELAP5/MOD3, Transient Reactor Analysis Code, and so on [11,12]. Also, CSAU was referred to another methodology to calculate LBLOCA of PWR [13].

A tolerance limit evaluation approach, which is GRS, Wilks’ formula has been widely used to determine the number of calculations from a limited number of code simulations to obtain the uncertainty bands [14]. Wilks’ formula consists of the number of code runs, tolerance, and confidence level. For example, 59, 93, and 124 samples are required in the case of the first, second, and third Wilks’ formula, respectively [15–17].

In the case of Gen-IV reactors, the statistical estimation of uncertainty for super-safe, small, and simple (4S) reactor was performed [18]. Through seven steps, the statistical analyses were conducted in order to estimate the effect of the uncertainties in the sensitive parameters on the major metrics in ULOF and UTOP accidents.

In this research, the CSAU and GRS approaches were used for the uncertainty quantification of the Prototype Gen-IV Sodium-cooled Fast Reactor (PGSFR).

The schematic and nodalization of PGSFR, which is a 150 MWe pool-type Sodium-cooled Fast Reactor (SFR) using U–TRU–Zr metal fuel, are being designed by Korea Atomic Energy Research Institute (KAERI) as shown in Figure 1 [19]. The heat transport systems of the PGSFR consist of the primary heat transport system, intermediate heat transport system with four Intermediate Heat Exchangers (IHX), two system generators, and a power conversion system. The Decay Heat Removal Systems (DHRS) of the PGSFR comprise the Active Decay Heat Removal Systems (ADHRS) and Passive Decay Heat Removal Systems (PDHRS).

Figure 1. Schematic of PGSFR.

Sensitivity analyses and uncertainty quantification for Unprotected Loss of Flow (ULOF) and Unprotected Transient over Power (UTOP) were carried out using Monte Carlo (MC) and compared with the 95% confidence level determined by Wilks’ formula using Multi-dimensional Analysis for Reactor Safety (MARS) for Liquid Metal Reactors, MARS-LMR [20,21].

2. Procedure of statistical process of PGSFR

The statistical process comprised the following steps prior to the sensitivity analysis and uncertainty quantification.

2.1. Specification of scenario

There are several design extension condition (DEC) events of the PGSFR, such as ULOF, UTOP, unprotected loss of heat sink, large partial subassembly blockage, large steam generator tube rupture, large sodium leak, station black out, and so on. Based on PIRT for DEC scenarios and expert discussion, ULOF and UTOP accidents were selected as accident scenarios of the PGSFR.

ULOF is initiated by the loss of core cooling capability due to pumping failure of the primary pumps. When pumping failure occurs, the reactor coolant circulation is stopped by the active equipment after the period of pump coastdown. Instead, natural convection due to the difference in the density generated by temperature gradients between the core and the coolant occurs. UTOP is initiated by a possible malfunction of the reactivity controller due to withdrawal of the control rods, and the core power is rapidly increased by a positive reactivity insertion [19]. This research was assumed to be initiated by reactivity insertion (0.3$) due to control rod withdrawal.

2.2. Figures of merit (FOM)

To ensure the safety of SFR, phase change of sodium is very important. Therefore, the thermal margin of vaporization for coolant temperature at the hottest fuel rod was selected as Figures of Merit (FOM) of PGSFR. The fuel centerline and cladding temperature were also included as an aspect to the safety of fuel. Because the consideration for the fuel centerline, cladding, and coolant temperature is not limited to certain scenario, those can be applied to both ULOF and UTOP accidents.

2.3. Selection of physical models and uncertainty range related to phenomena

PIRT was set up to identify and list important phenomena as shown in Table 1 [22]. PIRT contains phenomena, importance of phenomena, and the knowledge level for each scenario. As shown in Table 1, L, M, H mean low, medium, and high, respectively. When any of the information for physical models is not available from an experimental database or when it is lacking, expert judgment should be considered [8]. Based on the PIRT, Model Identification and Ranking Table (MIRT) of ULOF and UTOP accidents of PGSFR were also developed as shown in Tables 2 and 3 [23]. The phenomena and related model can be divided into four categories based on MIRT. The first category is related to reactor core such as fuel rod heat transfer, reactivity feedbacks, and core pressure drop. The second category includes primary pumps and heat transfer of the internal structure. The primary pumps work under transient conditions during UTOP accident, unlike the case of ULOF accident. Therefore, in the case of UTOP accident, only pump heat generation is considered. However, reactivity insertion is additionally considered during UTOP accident. The third category includes heat transfer of the shell and tube-side in IHX and pressure drop. The final category considers heat transfer of steam generators. The uncertainty band related to the reactivity model such as sodium density, reactivity insertion, core radial and fuel axial expansion reactivity coefficient, control and shutdown rod worth, and Doppler effect are based on the BFS-73-1 critical experiment at the BFS-1 facility at the Institute of Physics and Power Engineering in Russia [24]. The modified-Schad and Aoki correlations are used as the heat transfer model of the core and tube-side including the primary loop [25,26]. The heat transfer model of the shell-side of heat exchanger is Graber–Reiger correlation [27]. The uncertainty band of the fuel thermal conductivity is from the SCDAP/RELAP5/MOD3.3 code manual [28]. The pressure drop of the core is the simplified Cheng and Todreas model [29,30]. The uncertainty bands of the wall roughness of IHX shell-side and spacer grid form loss are determined from Organisation for Economic Co-operation and Development (OECD) report [31]. Except for the uncertainty bands from literature survey, those of other parameters are based on expert judgment.

Table 1. Phenomena identification and ranking table (PIRT)

			Phenomena importance
System	Subsystem/component	Phenomena	UTOP	ULOF	Knowledge level
Reactor core	Core	Fuel rod heat transfer	H	H	M
		Rate of reactivity insertion	H	N/A	H
		Coolant density effect	M	M	H
		Radial core expansion	H	H	M
	Fuel assembly including CRDL	Axial expansion of fuel and cladding	H	H	M
		Control rod drive line expansion	H	H	H
		Doppler reactivity feedback	M	M	H
		Inter assembly heat transfer	M	H	M
	Fuel rod	Core pressure drop	L	H	H
		Fission gas generation	L	L	M
		Fuel-clad eutectic formation	L	L	M
Reactor vessel	PHTS pump	Pump coastdown	N/A	H	M
		Pump heat generation	L	L	H
	PHTS	Natural circulation (one-dimensional global flow)	N/A	H	M
		Primary system pressure drop	L	H	H
		Thermal stratification	L	L	M
		Reactor vessel heat loss	L	M	L
		Internal heat structure heat transfer	L	H	H
		Three-dimensional flow in reactor vessel	L	M	M
System	Subsystem/component	Phenomena	UTOP	ULOF	Knowledge level
IHX	IHX tube-side (secondary-side)	Tube-side pressure drop	L	L	H
		Tube-side heat transfer	H	H	H
	IHX shell-side (primary-side)	Shell-side pressure drop	L	M	H
		Shell-side heat transfer	H	H	H
IHTS	Expansion tank	Sodium volume expansion	N/A	N/A	H
	IHTS pipe	Pressure drop	L	L	H
	IHTS pump	Electro Magneti (EM) pump characteristic curve	N/A	N/A	M
SGS	SG tube-side	SG tube heat transfer	H	H	L
	SG shell-side	SG shell heat transfer	H	H	H
DHRS	ADHRS	Blower characteristic curve	L	L	H
		EM pump characteristic curve	L	L	M
		FHX air tube heat transfer	L	L	M
		FHX air shell heat transfer	L	L	H
		DHX Na–Na tube heat transfer	L	L	H
		DHX Na–Na shell heat transfer	L	L	H
	PDHRS	AHX air tube heat transfer	L	L	H
		AHX air shell tube heat transfer	L	L	M
		DHX Na-Na tube heat transfer	L	L	H
		DHX Na-Na shell heat transfer	L	L	H
		Natural circulation	L	L	M

FHX : Forced-draft sodium-to-air heat exchanger, DHX : Decay heat exchanger, AHX : Natural-draft sodium-to-air heat exchanger

Table 2. Model identification and ranking table (MIRT) of ULOF accident

				Distribution	Uncertainty band	Sr for coolant
System	Phenomena		Related model	function	[2σ for normal distribution]	temperature (min/max)
Reactor core	Fuel rod heat transfer	M1	Fuel conductivity	Normal	±0.58 W/m K	−0.00434/−0.00303
		M2	Convection (modified-Schad)	Normal	±20%	−0.00087
	Coolant density effect	M3	Sodium density reactivity	Normal	±32.6%	−0.01516/−0.01463
	Core radial expansion	M4	GP strain coefficient	Uniform	±10%	0.0
		M5	ACLP strain coefficient	Uniform	±10%	−0.0685/−0.06503
		M6	Reactivity coefficient	Normal	±30.6%	−0.07424/−0.06092
	Axial expansion of fuel and cladding	M7	Fuel density reactivity	Uniform	±10%	0.0
		M8	Cladding strain coefficient	Uniform	±10%	−0.00347
		M9	Reactivity coefficient	Normal	±30.6%	−0.01615/−0.01530
	Control rod drive line expansion	M10	CRDL expansion reactivity coefficient	Uniform	±10%	−0.01734
		M11	RV expansion reactivity coefficient	Uniform	±10%	0.0
		M12	Control and shutdown rod worth	Normal	±19.8%	−0.01752
	Doppler reactivity feedback	M13	Doppler reactivity	Normal	±30%	−0.02052/−0.01936
	Inter assembly heat transfer	M14	HT-9 conduction	Uniform	±10%	−0.00694/−0.00607
	Core pressure drop	M15	Friction model (simplified Cheng and Todreas)	Normal	±30%	0.009827/0.007515
PHTS	Pump	M16	Coastdown curve	Uniform	±10%	−0.0685/−0.07197
		M17	Pump heat generation	normal	±10%	0.000867
	Internal structure heat transfer	M18	Heat capacity	Uniform	±10%	0.0
		M19	Convection (Aoki)	Normal	±20%	−0.00347/−0.00303
IHTS	Tube-side heat transfer	M20	Convection (Aoki)	Normal	±20%	−0.00737/−0.00434
	Shell-side pressure drop	M21	Wall roughness	Uniform	10^−5–2.0 × 10^−4	0.0
		M22	Spacer grid form loss	Uniform	0.5–1.5	0.0
	Shell-side heat transfer	M23	Convection (Graber–Reiger)	Normal	±12.2%	−0.00924/−0.00640
SGS	SG tube heat transfer	M24	Convection (steam)	Normal	±20%	−0.02124/−0.01474
	SG shell heat transfer	M25	Convection (Graber–Reiger)	Normal	±12.2%	−0.00498/−0.00426

Table 3. Model identification and ranking table (MIRT) of UTOP accident

				Distribution	Uncertainty band	Sr for coolant
System	Phenomena		Related model	function	[2σ for normal distribution]	temperature (min/max)
Reactor core	Fuel rod heat transfer	M1	Fuel conductivity	Normal	±0.58 W/m K	0.005509/0.003725
		M2	Convection (modified-Schad)	Normal	±20%	0.001889/−0.01734
	Rate of reactivity insertion	M3	Reactivity insertion	Normal	±19.8%	0.126501/0.129893
	Coolant density effect	M4	Sodium density reactivity	Normal	±32.6%	−0.00892/−0.0085
	Core radial expansion	M5	GP strain coefficient	Uniform	±10%	0.0
		M6	ACLP strain coefficient	Uniform	±10%	−0.0341/−0.03221
		M7	Reactivity coefficient	Normal	±30.6%	−0.03662/−0.03038
	Axial expansion of fuel and cladding	M8	Fuel density reactivity	Uniform	±10%	0.0
		M9	Cladding strain coefficient	Uniform	±10%	−0.00273/−0.00283
		M10	Reactivity coefficient	Normal	±30.6%	−0.01584/−0.01447
	Control rod drive line expansion	M11	CRDL expansion reactivity coefficient	Uniform	±10%	−0.02172/−0.02130
		M12	RV expansion reactivity coefficient	Uniform	±10%	0.0
		M13	Control and shutdown rod worth	Normal	±19.8%	−0.02194/−0.02104
	Doppler reactivity feedback	M14	Doppler reactivity	Normal	±30%	−0.01917/−0.01745
	Inter assembly heat transfer	M15	HT-9 conduction	Uniform	±10%	−0.0086/−0.00808
	Core pressure drop	M16	Friction model	Normal	±30%	0.020147/0.008395
	Pump	M17	Pump heat generation	normal	±10%	0.001154/0.001364
	Internal structure heat transfer	M18	Heat capacity	Uniform	±10%	0.0
		M19	Convection (Aoki)	Normal	±20%	−0.00782/−0.00624
IHTS	Tube-side heat transfer	M20	Convection (Aoki)	Normal	±20%	−0.00881/−0.00546
	Shell-side pressure drop	M21	Wall roughness	Uniform	10^−5–2.0 × 10^−4	0.0
		M22	Spacer grid form loss	Uniform	0.5–1.5	0.0
	Shell-side heat transfer	M23	Convection (Graber–Reiger)	Normal	±12.2%	−0.01084/−0.00774
SGS	SG tube heat transfer	M24	Convection (steam)	Normal	±20%	−0.02513/−0.01716
	SG shell heat transfer	M25	Convection (Graber–Reiger)	Normal	±12.2%	−0.00636/−0.00482

3. Sensitivity analysis

3.1. Relative sensitivity coefficient

The sensitivity analysis considered 25 uncertain parameters, as shown in Tables 2 and 3. The results of the sensitivity analysis indicate the magnitude of the relative sensitivity coefficient (S_r), which is defined as(1) $$\begin{array}{c}\hfill S_r=\frac{\frac{r-r_0}{r_0}}{\frac{p-p_0}{p_0}}\end{array}$$(1) where r₀ and p₀ indicate each FOM value and each uncertain parameter for the nominal case, respectively. Here, 0 means the original value before the uncertainty range is applied. When the relative sensitivity coefficient has a positive sign, the perturbed values of the input parameters and the simulation results have the same direction, i.e. an increase of the values of uncertainty tends to increase the FOM and vice versa. Therefore, the parameter having the higher value of relative sensitivity coefficient has the more influence to change the FOM.

3.2. ULOF

Table 2 shows the relative sensitivity coefficient of FOM for 25 parameters in ULOF accident. The minimum and maximum values of the relative sensitivity coefficient mean the results applying to the minimum and maximum uncertainty values, respectively. The dominant parameters are the Above Core Load Pad (ACLP) strain coefficient (M5), core radial expansion reactivity coefficient (M6), and pump coastdown curve (M16) as an aspect to the magnitude of the relative sensitivity coefficient. The most dominant parameter having the largest absolute value is M16 as a cause of ULOF accident.

3.3. UTOP

Table 3 also indicates the relative sensitivity coefficient of FOM for 25 parameters in UTOP accident. The dominant parameters, the ACLP strain coefficient (M6 in Table 3) and core radial expansion reactivity coefficient (M7 in Table 3) are common to ULOF accident. The most dominant parameter of UTOP accident is reactivity insertion (M3) compared to other parameters.

4. Uncertainty quantification method

Server and client PC systems with the aid of the Parallel computing Platform IntegRated for Uncertainty and Sensitivity analysis (PAPIRUS) [32] were an environment for the MC calculation. The calculations were performed with 18 client PCs (3.50 GHz i7 CPU, Window 7), and 3000 input files with random sampling were generated using the PAPIRUS. The values of the input parameters were simultaneously varied by random sampling according to probability density functions. MC calculations were performed two times for each accident scenario considering all uncertain parameters. The calculation times for ULOF and UTOP accidents were about seven and ten days, respectively.

4.1. ULOF

Figure 2 compares the FOM distributions of the nominal case and those obtained by uncertainty methods, using MC and Wilks’ formula. The results using MC method were obtained from 3000 input files having different perturbed values for each parameter in MIRT. Among the results from 3000 input files, 151st as a maximum value and 2899th as a minimum value of FOM are the 95% confidence level for every time-step as shown in Figure 2. In this case, it used the value of third Wilks’ formula. The primary pump failure occurred at 10 s and after 5 s, DHRS were operated. Therefore, the fuel centerline, cladding, and coolant temperature increase because of loss of primary flow. After 40 s, the temperature decreases because of the operation of ADHRS and PDHRS and negative reactivity feedbacks. The saturation temperature of sodium was calculated by MARS-LMR. In this paper, only minimum saturation temperature was used to calculate the thermal margin. The criteria for the fuel and cladding temperature were obtained from SFR reactor design division of KAERI. It confirmed that the value of the Wilks’ formula was higher than that obtained by MC calculation, and each maximum FOM value was lower than the minimum saturation temperature although the difference was very small. Figure 3 shows the trends of the 95% upper limit of FOM during MC histories of ULOF and UTOP accidents. For example, the first data-points of this figure (number of MC histories = 100) show a 95% upper limit from 1st to 100th cases, and the second data-points (number of MC histories = 200) show the 95% upper limit value up to 200th case and so on. After the 2000th case, it was confirmed that the 95% upper limit of FOM converged on a certain value. Figure 4 only includes values of the third-order obtained using the Wilks’ formula. Each point means the third maximum value among 124 samples (=input files) having different perturbations of parameters. The calculation results obtained by Wilks’ formula compared with the MC for ULOF accident indicate having 2% under-prediction value, as shown in Table 5. Each value in Table 5 means the number of lower values of FOM calculated by the first, second, and third Wilks’ formula compared to the MC calculation. The number of lower values calculated by the third Wilks’ formula also can be confirmed as shown in Figure 4. The Wilks’ formula predicts the lower maximum value of each FOM and therefore, the thermal margin will be increased in the case of getting 2% under-predicted value of FOM compared to other cases. The results are not good as an aspect to the safety of PGSFR.

Figure 2. Comparison of FOM distribution between the nominal case and uncertainty quantification methods in ULOF accident.

Figure 3. Trends of 95% upper limit of FOM during Monte Carlo histories in (a) ULOF and (b) UTOP accident.

Figure 4. Comparison of 95% upper FOM with value of third-order Wilks’ formula in ULOF accident.

4.2. UTOP

The FOM of UTOP accident have a different temperature range compared to that of ULOF accident. The thermal margin is bigger than that of ULOF accident, as shown in Figure 5. Because of the insertion of positive reactivity at 10 s, and after 5 s, DHRS are operated, those of FOM increase but, the primary pumps still operate. Therefore, the maximum values of FOM of UTOP accident are lower than those of ULOF accident. Table 4 compares the maximum FOM obtained by MC calculation and Wilks’ formula considering all parameters in MIRT. Figure 6 compares the 95% upper FOM with the values obtained by third-order Wilks’ formula. The calculation results using first, second, and third-order Wilks’ formula for UTOP accident indicate about maximum 5% under-prediction as an aspect of the thermal margin, as shown in Table 5.

Figure 5. Trends of 95% upper limit of FOM during Monte Carlo histories in UTOP accident.

Table 4. Comparison of maximum temperature between Monte Carlo and Wilks’ formula of ULOF and UTOP accident

			All parameters in MIRT
	Nominal		ULOF			UTOP
FOM	ULOF	UTOP	Monte Carlo		Wilks	Monte Carlo	Wilks
Coolant temperature (K)	1153.2	953.0	Max.	1179.6	1187.6	977.9	986.7
			Min.	1130.8	1126.9	931.1	926.4
Fuel temperature (K)	1172.5	1050.5	Max.	1199.4	1208.4	1078.8	1089.8
			Min.	1149.8	1145.4	1019.4	1013.7
Cladding temperature (K)	1155.8	960.8	Max.	1182.3	1190.2	986.7	995.6
			Min.	1133.2	1129.4	938.2	932.5

Table 5. Number of Wilks’ formula cases with under-predicted 95th percentile FOM of ULOF and UTOP accident

	The order of	1000 trials
FOM	the formula	ULOF	UTOP
Coolant temperature (K)	First	45	47
	Second	42	35
	Third	42	55
Fuel temperature (K)	First	46	42
	Second	42	42
	Third	46	55
Cladding temperature (K)	First	44	48
	Second	43	42
	Third	49	61

Figure 6. Comparison of 95% upper FOM with value of third-order Wilks’ formula in UTOP accident.

5. Conclusion

Sensitivity analyses and uncertainty quantification for ULOF and UTOP accidents of the PGSFR were carried out by MC calculation, and the results were compared with FOM determined by the Wilks’ formula using the PAPIRUS. Before the sensitivity analyses and uncertainty quantification were carried out, the accident scenarios, FOM, and uncertain parameters of each accident based on PIRT and MIRT were selected. The total number of PCs including the server was 19, and about 80 cores were used during the MC calculation. The sensitivity analysis confirmed the ranking of parameters, and the dominant parameters were identified for each accident scenario. In ULOF and UTOP accidents, the most dominant parameters causing each type of accident were the pump coastdown curve (M16) and reactivity insertion (M3), respectively. In the MC calculation, 3000 cases with random sampling were considered. Based on the comparison of the 95% upper limit of MC and the 95% confidence level of Wilks’ formula, the under-predicted results obtained by third Wilks’ formula indicated about 2% and 5% risk as an aspect of the thermal margin in ULOF and UTOP accidents, respectively. Therefore, the MC calculation can provide a reliable 95% limit value if users have sufficient computational capability or time. These results can be applied as a reference in designing the PGSFR.

Acknowledgments

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) [grant number NRF-2015M2A8A4046778], [grant number NRF-2017M2B2B1072555].

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature
ACLP	=	Above Core Load Pad
ADHRS	=	Active Decay Heat Removal Systems
BEMUSE	=	Best Estimate Methods – Uncertainty and Sensitivity Evaluation
BEPU	=	Best Estimate Plus Uncertainty
CIAU	=	Code with Internal Assessment of Uncertainty
CRDL	=	Control Rod Driving Line
CSAU	=	Code Scaling Applicability and Uncertainty
DEC	=	Design Extension Condition
DHRS	=	Decay Heat Removal Systems
FOM	=	Figures of Merit
GP	=	Grid Plate
GRS	=	Gesellschaft fur Anlagen-und Reaktorsicherheit
IHTS	=	Intermediate Heat Transport Systems
IHX	=	Intermediate Heat Exchangers
IPPE	=	Institute of Physics and Power Engineering
MIRT	=	Model Identification and Ranking Table
LBLOCA	=	Large Break Loss of Coolant Accident
PAPIRUS	=	PArallel computing Platform IntegRated for Uncertainty and Sensitivity analysis
PDFs	=	Probability Density Functions
PGSFR	=	Prototype Gen-IV Sodium-cooled Fast Reactor
PHTS	=	Primary Heat Transfer Systems
PIRT	=	Phenomena Identification and Ranking Table
RV	=	Reactor Vessel
SBLOCA	=	Small Break Loss of Coolant Accident
SBO	=	Station Black Out
SFR	=	Sodium-cooled Fast Reactor
SG	=	Steam Generator
SGS	=	Steam Generator Systems
SGTR	=	Steam Generator Tube Rupture
TRAC	=	Transient Reactor Analysis Code
ULOF	=	Unprotected Loss of Flow
ULOHS	=	Unprotected Loss of Heat Sink
UMAE	=	Uncertainty Methodology on Accuracy Extrapolation
UMS	=	Uncertainty Methods Study
UTOP	=	Unprotected Transient OverPower

Additional information

Funding

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT) [grant number NRF-2015M2A8A4046778], [grant number NRF-2017M2B2B1072555].