Abstract

In best estimate plus uncertainty approach for thermal-hydraulic simulation in nuclear engineering, a crucial step for the qualification of the scenario simulation is the discretization, i.e., the nodalization of nuclear power plants and related integral test facilities (ITFs). Since intermediate break loss-of-coolant accident (IBLOCA) simulation is getting more and more attention in this decade, we focused on the nodalization of an IBLOCA scenario—a primary loop (PKL) I2.2 benchmark delivered by the organization for economic cooperation and development PKL4-project—using the analyses of thermal-hydraulics for leaks and transients (ATHLET) code. This work followed mainly the nodalization methodology of Petruzzi and D'Auria, including both qualitative and quantitative criteria, being divided into three phases for component volume, steady-state, and transient, respectively. The authors used also some specific approaches: (1) for component volume qualification, a volume fractional parameter was introduced, considering not only the relative error of each component but also the volume fraction in the whole system (an 0.2% acceptability level was chosen for this parameter); (2) the experimental data were not used directly as a reference within the nodalization procedure but the calculated results delivered by the most refined nodalization. Based on the estimator of average amplitude in the fast Fourier transform-based method (FFTBM), the convergence, rationality, and an optimized result of nodalization in the simulation of an actual IBLOCA transient benchmark have been judged. After three phases of nodalization qualification, it has been proved that the final nodalization has the necessary degree of convergence for a good reproduction of the benchmark geometry, allowing the proper simulation of involved phenomena. Finally, a middle-refined nodalization was found as being optimal, fulfilling the convergence criteria with a reasonable central processing unit time consumption. The nodalization scheme in this work was not seen as being the single factor influencing the simulated results, but just as a prerequisite to allow further reliable improvements on the models used by ATHLET (aspects not referred to in this particular study). Therefore, the simulated results presented here will match the experimental ones only as general trends; improvements may be further achieved by using new and more precise models (e.g., for critical mass flow, heat transfer, countercurrent flow, etc.) in the system thermal-hydraulic code.

References

1.
Bajs
,
T.
,
Debrecin
,
N.
, and
Krajnc
,
B.
,
1998
, “
Development of the Qualified Plant Nodalization for Safety and Operational Transient Analysis
,”
International Conference of Croatian Nuclear Society: Nuclear Option in Countries With Small and Medium Electricity Grid
, Dubrovnik, Croatia, June 15–18, pp.
219
226
. https://inis.iaea.org/collection/NCLCollectionStore/_Public/29/064/29064397.pdf
2.
Petruzzi
,
A.
, and
D'Auria
,
F.
,
2008
, “
Thermal-Hydraulic System Codes in Nuclear Reactor Safety and Qualification Procedures
,”
Sci. Technol. Nucl. Installat.
,
2008
, pp.
1
16
.10.1155/2008/460795
3.
D'Auria
,
F.
,
2017
, “
A Historical Perspective of Nuclear Thermal-Hydraulics
,”
Thermal-Hydraulics of Water Cooled Nuclear Reactors
,
Woodhead Publishing (WP)
,
Duxford, UK
, pp.
41
87
.
4.
Liang
,
T. K. S.
,
Chang
,
C. J.
, and
Hung
,
H. J.
,
2002
, “
Development and Assessment of the Appendix K Version of RELAP5-3D for LOCA Licensing Analysis
,”
Nucl. Technol.
,
139
(
3
), pp.
233
252
.10.13182/NT02-A3316
5.
D'Auria
,
F.
,
2017
, “
Best-Estimate Plus Uncertainty (BEPU) Approach for Accident Analysis
,”
Thermal-Hydraulics of Water Cooled Nuclear Reactors
,
Woodhead Publishing (WP)
,
Duxford, UK
, pp.
905
950
.
6.
Kovtonyuk
,
A.
,
Petruzzi
,
A.
, and
D'Auria
,
F.
,
2012
, “
A Procedure for Characterizing the Range of Input Uncertainty Parameters by the Use of the FFTBM
,”
Proceedings of ICONE-20 Conference
, Anaheim, CA, July 30–Aug. 3, Paper No. 54025.
7.
Xu
,
H.
,
2020
, “Improvement of PWR (LOCA) Safety Analysis Based on PKL Experimental Data,” Doctoral dissertation, Karlsruhe Technology of Institute, Germany.
8.
Glaeser
,
H.
,
2008
, “
GRS Method for Uncertainty and Sensitivity Evaluation of Code Results and Applications
,”
Sci. Technol. Nucl. Installat.
,
2008
, pp.
1
7
.10.1155/2008/798901
9.
D'Auria
,
F.
, and
Giannotti
,
W.
,
2000
, “
Development of Code With Capability of Internal Assessment of Uncertainty
,”
Nucl. Technol.
,
131
(
2
), pp.
159
196
.10.13182/NT00-5
10.
Ahn
,
S. H.
,
Aksan
,
N.
,
Austregesilo
,
H.
,
Bestion
,
D.
,
Chung
,
B. D.
,
D'Auria
,
F.
,
Emonot
,
P.
,
Gandrille
,
J. L.
,
Hanninen
,
M.
,
Horvatović
,
I.
,
Kim
,
K. D.
,
Kovtonyuk
,
A.
, and
Petruzzi
,
A.
,
2015
, “
FONESYS: The FOrum & NEtwork of SYStem Thermal-Hydraulic Codes in Nuclear Reactor Thermal-Hydraulics
,”
Nucl. Eng. Des.
,
281
, pp.
103
113
.10.1016/j.nucengdes.2014.12.001
11.
IAEA
,
2002
,
Accident Analysis for Nuclear Power Plants
,
IAEA
,
Vienna, Austria
, p.
129
.
12.
D'Auria
,
F.
,
2019
, “
Best Estimate Plus Uncertainty (BEPU) Status and Perspectives
,”
Nucl. Eng. Des.
,
352
, p.
11
.10.1016/j.nucengdes.2019.110190
13.
Šegon
,
V.
,
Bajs
,
T.
,
Debrecin
,
N.
, and
Čavlina
,
N.
,
2001
, “
BETHSY Nodalization Study During MID-LOOP Operation
,”
Proceeding in International Conference Nuclear Energy in Central Europe 2001
, Nuclear Society of Slovenia, Portorož, Slovenia, Sept. 10–13, Paper No. 214.
14.
Bajs
,
T.
,
Debrecin
,
N.
,
Šegon
,
V.
,
Kahn
,
L.
, and
Mahmood
,
A.
,
2000
, “
Assessment of Discretization Approach for RELAP5/MOD3 Computer Code
,”
Proceeding in International Conference Nuclear Energy in Central Europe
, Nuclear Society of Slovenia, Bled, Slovenia, Sept. 11–14, p.
8
.
15.
Petruzzi
,
A.
, and
D'Auria
,
F.
,
2006
, “BEMUSE Programme. Phase 2 Report (Re-Analysis of the ISP-13 Exercise, Post Test Analysis of the LOFT L2-5 Experiment,” OECD/CSNI, Paris, France. Report No. NEA/CSNI/R(2006)2.
16.
Bonuccelli
,
M.
,
D'Auria
,
F.
,
Debrecin
,
N.
, and
Galassi
,
G. M.
,
1993
, “
A Methodology for the Qualification of Thermal-Hydraulic Codes Nodalizations
,”
Proceeding in International Top Meet on Nuclear Reactor Thermal-Hydraulics (NURETH-6)
, Grenoble, France, Oct. 5–8, p.
10
.
17.
Martinez-Quiroga
,
V.
,
Reventos
,
F.
, and
Freixa
,
J.
,
2014
, “
Applying UPC Scaling-Up Methodology to the LSTF-PKL Counterpart Test
,”
Sci. Technol. Nucl. Installat.
,
2014
, pp.
1
18
.10.1155/2014/292916
18.
Petruzzi
,
A.
,
Cherubini
,
M.
, and
D'Auria
,
F.
,
2016
, “
Thirty Years' Experience in RELAP5 Applications at GRNSPG & NINE
,”
Nucl. Technol.
,
193
(
1
), pp.
47
87
.10.13182/NT14-144
19.
Bajorek
,
S. M.
, and
Gingrich
,
C.
,
2011
, “
Uncertainty Methods Framework Development for the TRACE Thermal-Hydraulics Code by the U.S.NRC
,”
OECD/CSNI Workshop on Best Estimate Methods and Uncertainty Evaluations (NEA/CSNI/R(2013)8/PART2)
, Barcelona, Spain, Nov. 16–18, pp.
148
157
.
20.
]
Glaeser
,
H.
,
2011
, “
Summary of Existing Uncertainty Methods
,”
OECD/CSNI Workshop on Best Estimate Methods and Uncertainty Evaluations (NEA/CSNI/R(2013)8/PART2)
, Barcelona, Spain, Nov. 16–18, pp.
5
15
.https://inis.iaea.org/search/search.aspx?orig_q=RN:45107563
21.
Ambrosini
,
W.
,
Bovalini
,
R.
, and
D'Auria
,
F.
,
1990
, “
Evaluation of Accuracy of Thermal Hydraulic Code Calculations
,”
J. Energia Nucleare
,
7
(
2
), pp.
5
16
.https://inis.iaea.org/search/search.aspx?orig_q=RN:23005396
22.
Mavko
,
B.
,
Prošek
,
A.
, and
D'auria
,
F.
,
1997
, “
Determination of Code Accuracy in Predicting Small-Break LOCA Experiment
,”
Nucl. Technol.
,
120
(
1
), pp.
1
18
.10.13182/NT97-A35427
23.
Prošek
,
A.
,
Kvizda
,
B.
,
Mavko
,
B.
, and
Kliment
,
T.
,
2004
, “
Quantitative Assessment of MCP Trip Transient in a VVER
,”
Nucl. Eng. Des.
,
227
(
1
), pp.
85
96
.10.1016/j.nucengdes.2003.07.005
24.
Prošek
,
A.
,
D'Auria
,
F.
,
Richards
,
D. J.
, and
Mavko
,
B.
,
2006
, “
Quantitative Assessment of Thermal–Hydraulic Codes Used for Heavy Water Reactor Calculations
,”
Nucl. Eng. Des.
,
236
(
3
), pp.
295
308
.10.1016/j.nucengdes.2005.07.004
25.
Coscarelli
,
E.
,
2013
, “
An Integrated Approach to Accident Analysis in PWR
,” Ph.D. thesis,
University of Pisa
, Pisa, Italy.
26.
Xu
,
H.
,
Badea
,
A. F.
, and
Cheng
,
X.
,
2020
, “
Sensitivity Analysis of Thermal-Hydraulic Models Based on FFTBM-MSM Two-Layer Method for PKL IBLOCA Experiment
,”
Ann. Nucl. Energy
,
147
, p.
107732
.10.1016/j.anucene.2020.107732
27.
Kim
,
Y. S.
,
Choi
,
K. Y.
,
Song
,
C. H.
, and
Baek
,
W. P.
,
2014
, “
Overview of the Standard Problems of the ATLAS Facility
,”
Ann. Nucl. Energy
,
63
, pp.
509
524
.10.1016/j.anucene.2013.08.028
28.
Bratfisch
,
C.
, and
Koch
,
M. K.
,
2017
, “
Simulation of Water Hammer Phenomena Using the System Code ATHLET
,”
Kerntechnik
,
82
(
3
), pp.
280
283
.10.3139/124.110804
29.
De Luca
,
D.
,
Petruzzi
,
A.
,
Cherubini
,
M.
, and
Parrinello
,
V.
,
2016
, “
RELAP5-3D Analysis of EBR-II Shutdown Heat Removal Test SHRT-17
,”
Proceedings of the 2016 24th International Conference on Nuclear Engineering (ICONE24)
, Charlotte, NC, June 26–30, Paper No. 60629.
30.
Saghafi
,
M.
,
Ghofrani
,
M. B.
, and
D'Auria
,
F.
,
2016
, “
Development and Qualification of a Thermal-Hydraulic Nodalization for Modeling Station Blackout Accident in PSB-VVER Test Facility
,”
Nucl. Eng. Des.
,
303
, pp.
109
121
.10.1016/j.nucengdes.2016.04.012
31.
Austregesilo
,
H.
,
Bals
,
C.
,
Hora
,
A.
, and
Lerchl
,
G.
,
2016
, “ATHLET 3.1A Models and Methods,” Gesellschaft für Anlagenund Reaktorsicherheit (GRS) gGmbH, Garching, Germany.
32.
Bajorek
,
S. M.
,
Petkov
,
N.
,
Ohkawa
,
K.
,
Kemper
,
R. M.
, and
Ginsberg
,
A. P.
,
2001
, “
Realistics Mall- and Intermediate-Break Loss-of-Coolant Accident Analysis Using WCO-BRA/TRAC
,”
Nucl. Technol.
,
136
(
1
), pp.
50
62
.10.13182/NT01-A3228
33.
Laaksonen
,
L.
,
2011
, “
How Can We Assure Nuclear Safety: Is the Risk of Big Technology Controllable
,”
Institute of Applied Energy Symposium
, Kyoto, Japan, Dec. 17, pp.
1
56
.
34.
Takeda
,
T.
, and
Ohtsu
,
I.
,
2018
, “
Uncertainty Analysis of ROSA/LSTF Test by RELAP5 Code and PKL Counterpart Test Concerning PWR Hot Leg Break LOCAs
,”
Nucl. Eng. Technol.
,
50
(
6
), pp.
829
841
.10.1016/j.net.2018.05.005
35.
Tregoning
,
R. L.
,
Abramson
,
L. R.
,
Scott
,
P. M.
, and
Chokshi
,
N.
,
2007
, “
LOCA Frequency Evaluation Using Expert Elicitation
,”
Nucl. Eng. Des.
,
237
(
12–13
), pp.
1429
1436
.10.1016/j.nucengdes.2006.09.036
36.
USNRC
,
2005
, “
10 CFR Part 50 Risk-Informed Changes to Loss-of-Coolant Accident Technical Requirements, Proposed Rule
,”
Fed. Reg
,.
70
(
214
), p.
34
. https://www.govinfo.gov/content/pkg/FR-2005-11-07/pdf/E5-6090.pdf
37.
Schollenberger
,
S. P.
,
2017
, “
OECD/PKL Phase 4 PKL IIIi2.2 Cold-leg IB-LOCA Quick-Look
,” Erlangen, Germany, AREVA NP GmbH, Report No. D02-ARV-01-112-795 Rev. A.
38.
Umminger
,
K.
,
Dennhardt
,
L.
,
Schollenberger
,
S. P.
, and
Schoen
,
B.
,
2012
, “
Integral Test Facility PKL: Experimental PWR Accident Investigation
,”
Sci. Technol. Nucl. Installat.
,
2012
, pp.
1
16
.10.1155/2012/891056
39.
Lerchl
,
G.
,
Austregesilo
,
H.
,
Ceuca
,
S.
,
Glaeser
,
H.
,
Luther
,
W.
, and
Schöffel
,
P.
,
2016
, “ATHLET Validation, GRS-P-1/Vol. 3 Rev. 4,” GRS gGmbH, Garching, p.
287
.
40.
Hollands
,
T.
,
Buchholz
,
S.
, and
Wielenberg
,
A.
,
2019
, “
Validation of the AC2 Codes ATHLET and ATHLET-CD
,”
Kerntechnik
,
84
(
5
), pp.
397
405
.10.3139/124.190069
41.
Wolfert
,
K.
,
1977
, “
New Method to Evaluate Critical Discharge Rates in Blowdown Codes That Are Based on the Lumped‐Parameter Technique
,”
Proceedings of the Topical Meeting on Thermal Reactor Safety
, Vol.
2
, Sun Valley, ID, July 31–Aug. 5, pp.
513
528
.https://inis.iaea.org/search/search.aspx?orig_q=RN:10437555
42.
Schollenberger
,
S. P.
,
2016
, “
Description of the PKL III Test Facility
,” AREVA NP GmbH, Erlangen, Germany, Report No. NTCTP-G_2007_en_0010 rev.B.
43.
Schollenberger
,
S. P.
,
2016
, “
Determination of Masses in the PKL Test Facility
,” AREVA NP GmbH, Erlangen, Germany, Report No. FANP NT31_01_e34 rev. D.
44.
Güneysu
,
R.
,
2017
, “
Determination of Individual Volumes and of Total Volume in the PKL Test Facility (PKL III A–IIIi)
,” AREVA NP GmbH, Erlangen, Germany, Report No. DTICTP-G_2017_en_0002 rev.A.
45.
Schollenberger
,
S. P.
,
2006
, “
Determination of Heat Losses in the PKL III Test Facility
,” AREVA NP GmbH, Erlangen, Germany, Report No. NTT1-G_2006_en_0067 rev. A.
46.
Schollenberger
,
S. P.
,
2006
, “
Determination of the Pressure Losses in the PKL III Test Facility
,” Erlangen, Germany, Report No. NTT1-G/2006/en/0066 AREVA NP GmbH, December.
47.
D'Auria
,
F.
,
Bousbia-Salah
,
A.
,
Petruzzi
,
A.
, and
Nevo
,
A.
,
2006
, “
State of the Art in Using Best Estimate Calculation Tools in Nuclear Technology
,”
Nucl. Eng. Technol.
,
38
(
1
), pp.
11
32
. https://www.researchgate.net/publication/228944689_State_of_the_art_in_using_best_estimate_calculation_tools_in_nuclear_technology
48.
Radaideh
,
M. I.
,
Kozlowski
,
T.
, and
Farawila
,
Y. M.
,
2019
, “
Loss of Coolant Accident Analysis Under Restriction of Reverse Flow
,”
Nucl. Eng. Technol.
,
51
(
6
), pp.
1532
1539
.10.1016/j.net.2019.04.016
49.
Xu
,
H.
,
Badea
,
A. F.
, and
Cheng
,
X.
,
2021
, “
Analysis of Two Phase Critical flow With a Non-Equilibrium Model
,”
Nucl. Eng. Des.
,
372
, p.
110998
.10.1016/j.nucengdes.2020.110998
50.
Xu
,
H.
,
Badea
,
A. F.
, and
Cheng
,
X.
,
2021
, “
Studies on the Criterion for Choking Process in Two-Phase Flow
,”
Prog. Nucl. Energy
,
133
, p.
103640
.10.1016/j.pnucene.2021.103640
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