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http://dx.doi.org/10.1016/j.net.2022.07.031

Improvement of the subcooled boiling model using a new net vapor generation correlation inferred from artificial neural networks to predict the void fraction profiles in the vertical channel  

Tae Beom Lee (Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology (KAIST) )
Yong Hoon Jeong (Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology (KAIST) )
Publication Information
Nuclear Engineering and Technology / v.54, no.12, 2022 , pp. 4776-4797 More about this Journal
Abstract
In the one-dimensional thermal-hydraulic (TH) codes, a subcooled boiling model to predict the void fraction profiles in a vertical channel consists of wall heat flux partitioning, the vapor condensation rate, the bubbly-to-slug flow transition criterion, and drift-flux models. Model performance has been investigated in detail, and necessary refinements have been incorporated into the Safety and Performance Analysis Code (SPACE) developed by the Korean nuclear industry for the safety analysis of pressurized water reactors (PWRs). The necessary refinements to models related to pumping factor, net vapor generation (NVG), vapor condensation, and drift-flux velocity were investigated in this study. In particular, a new NVG empirical correlation was also developed using artificial neural network (ANN) techniques. Simulations of a series of subcooled flow boiling experiments at pressures ranging from 1 to 149.9 bar were performed with the refined SPACE code, and reasonable agreement with the experimental data for the void fraction in the vertical channel was obtained. From the root-mean-square (RMS) error analysis for the predicted void fraction in the subcooled boiling region, the results with the refined SPACE code produce the best predictions for the entire pressure range compared to those using the original SPACE and RELAP5 codes.
Keywords
Subcooled boiling; Void fraction; Net vapor generation; Artificial neural network; SPACE; RELAP5;
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1 L. Smith, A Disciplined Approach to Neural Network Hyper-Parameters: Part 1 - Learning Rate, Batch Size, Momentum, and Weight Decay, US Naval Research Laboratory, 2018. Technical Report 5510-026, arXiv : 1803.09820vols. 2, 2018. 
2 Y.G. Lee, et al., Measurement of local two-phase flow parameters in an annulus under low-pressure subcooled boiling condition, Trans. Korean Soc. Mech. Eng. B 42 (12) (2018) 813-824.    DOI
3 H. Christensen, Power-to-void Transfer Functions," ANL-6385, Argonne National Laboratory, 1961. 
4 J.K. Ferrell, et al., Low Pressure Steam-Water Flow in a Heated Vertical Channel. Final Report Volume II on A Study of Convection Boiling inside Channels, North Carolina State University, Raleigh, 1966 (Dept. of Chemical Engineering). 
5 H. Umekawa, et al., The influence of the heating condition on the void fraction in a boiling channel, Phys. Procedia 69 (2015) 599-606, https://doi.org/10.1016/j.phpro.2015.07.085.    DOI
6 M. Shoukri, et al., Experiments on subcooled flow boiling and condensation in vertical annular channels, in: Phase-interface Phenomena in Multiphase Flow, Hemisphere Publishing Corporation, 1991, pp. 413-422. 
7 B. Donevski, et al., Experimental Study of Subcooled Flow Boiling and Condensation in an Annular Channel, McMaster University, 1989. Report No. ME/89/TFRI. 
8 G. Dimmick, et al., A Dynamic Model for Predicting Subcooled Void: Experimental Results and Model Development, EUROTHERM seminar, Pisa, Italy, 1990. 
9 M. Bartel, et al., Interfacial area measurements in subcooled flow boiling, Nucl. Eng. Des. 210 (2001) 135-155, https://doi.org/10.1016/S0029-5493(01)00415-0.    DOI
10 D.H. Kang, et al., Two-phase Flow Regime Maps in Horizontal and Vertical Tubes, Transactions of the Korean Nuclear Society Spring Meeting, Pyeong Chang, Korea, 2007. October 25-26. 
11 P.G. Kroeger, N. Zuber, An analysis of the effects of various parameters on the average void fractions in subcooled boiling, Int. J. Heat Mass Tran. 11 (2) (1968) 211-233, https://doi.org/10.1016/0017-9310(68)90151-8.    DOI
12 S.C. Lee, S.G. Bankoff, A comparison of predictive models for the onset of significant void at low pressures in forced-convection subcooled boiling, KSME Int. J. 12 (3) (1998) 504-513, https://doi.org/10.1007/BF02946366.    DOI
13 D. Maitra, et al., Vapour void fraction in subcooled flow boiling, Nuclear Engineering and Design 32 (1975) 20-28, https://doi.org/10.1016/0029-5493(75)90087-4.    DOI
14 A. Yadav, et al., Axial and radial void fraction measurements in convective boiling, Chem. Eng. Sci. 157 (10) (2017) 127-137, https://doi.org/10.1016/j.ces.2016.04.038.    DOI
15 D Jingyu, Investigation of bubble departure diameter in horizontal and vertical subcooled flow boiling, International Journal of Heat and Mass Transfer 127 (2018) 796-805, https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.019.    DOI
16 H Ivey J, Relationships between bubble frequency, departure diameter and rise velocity in nucleate boiling, International Journal of Heat and Mass Transfer 10 (1967) 1023-1040, https://doi.org/10.1016/0017-9310(67)90118-4.    DOI
17 R McLeod D, Investigation of subcooled void fraction growth in water under low pressure and low flowrate conditions, Carleton University, Ottawa, Ontario, 1986. 
18 J.A. Boure, et al., Review of two-phase flow instability, Nucl. Eng. Des. 25 (1973) 165-192, https://doi.org/10.1016/0029-5493(73)90043-5.    DOI
19 Giustini Giovanni, Modelling of Boiling Flows for Nuclear Thermal Hydraulics Applications-A Brief Review, Inventions 5 (3) (2020) 47-65, https://doi.org/10.3390/inventions5030047.   DOI
20 H. Kantee, Application of RELAP5/MOD3.1 to ATWS Analysis of Control Rod Withdrawal from 1% Power Level, ADAMS (Agencywide Documents Acess and Management System, U.S. NRC, 2000, ML003734249. NUREG/IA-0180. 
21 A. Hainoun, et al., Modelling of void formation in the subcooled boiling regime in the ATHLET code to simulate flow instability for research reactors, Nucl. Eng. Des. 167 (1996) 175-191, https://doi.org/10.1016/S0029-5493(96)01233-2.    DOI
22 M.O. Kim, et al., Comparison of void fraction profiles in subcooled boiling of low pressure by 3D measurement and MARS calculation, in: Proceedings of the Korean Nuclear Society Conference, Korean Nuclear Society, 2002. 
23 IAEA, Passive Safety Systems and Natural Circulation in Water Cooled Nuclear Power Plants, 2009. IAEA-TECDOC-1624. 
24 O. Zeitoun, Subcooled Flow Boiling and Condensation, McMaster University, Hamilton, Ontario, 1994. Ph.D. thesis. 
25 W. Kent, et al., NuScale Preliminary Loss-Of-Coolant Accident (LOCA) Thermal-Hydraulic and Neutronics Phenomena Identification and Ranking Table (PIRT)," NP-TR-0610-289-NP Rev 0, ADAMS No, 2010, ML101810013. 
26 J. Zhang, et al., Application of the WCOBRA/TRAC best-estimate methodology to the AP600 large-break LOCA analysis, Nucl. Eng. Des. 186 (1998) 279-301, https://doi.org/10.1016/S0029-5493(98)00279-9.    DOI
27 J.G. Collier, et al., Convective Boiling and Condensation, McGraw-Hill, New York, 1981. 
28 P. Saha, N. Zuber, Point of net vapor generation and vapor void fraction in subcooled boiling, in: Proceedings Fifth International Heat Transfer Conference vol. 4, 1974, pp. 175-179. Tokyo. 
29 U.S. NRC, TRACE-V5.0, Theory Manual-Field Equations, Solution Methods, and Physical Models, ADAMS No, 2007, ML120060218. 
30 D. Bestion, The physical closure laws in the CATHARE code, Nucl. Eng. Des. 124 (1990) 229-245, https://doi.org/10.1016/0029-5493(90)90294-8.    DOI
31 W.R. Zackary, Evaluation Methodology for the Stability of the NuScale Power Module," TR-0516-49417-P-A, Revision 1, NuScale Power LLC, 2020. ADAMS No. ML20078Q094. 
32 A.S. Devkin, A.S. Podosenov, RELAP5/MOD3 Subcooled Boiling Model Assessment, NUREG/IA-0025, U.S. NRC, Washington, D.C, 1998. 
33 R.T. Lahey, A mechanistic subcooled boiling model, in: Proceedings of the 6th International Heat Transfer Conference, Toronto, Canada, vol. 1, 1978, pp. 293-297. 
34 T.W. Ha, et al., Improvement of the MARS subcooled boiling model for low-pressure, low-Pe flow conditions, Ann. Nucl. Energy 120 (2018) 236-245, https://doi.org/10.1016/j.anucene.2018.05.049.    DOI
35 S. Hari, et al., Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes, Nucl. Eng. Des. 216 (1) (2002) 139-152, https://doi.org/10.1016/S0029-5493(02)00050-X.    DOI
36 B. Konꠑcar, et al., Modelling of low-pressure subcooled flow boiling using the RELAP5 code, Nucl. Eng. Des. 198 (3) (2003) 261-286, https://doi.org/10.1016/S0029-5493(02)00385-0.    DOI
37 Caihong Xu, A study on low-pressure subcooled flow boiling using RELAP5/MOD3.4, Energy Procedia 127 (2017) 387-397, https://doi.org/10.1016/j.egypro.2017.08.101.    DOI
38 K.S. Ha, et al., Improvements in predicting void fraction in subcooled boiling, Nucl. Technol. 150 (2005) 283-292, https://doi.org/10.13182/NT05-A3622.    DOI
39 O. Zeitoun, et al., Axial void fraction profile in low pressure subcooled flow boiling, Int. J. Heat Mass Tran. 40 (4) (1997) 869-879, https://doi.org/10.1016/0017-9310(96)00164-0.    DOI
40 S.J. Ha, et al., Development of the SPACE code for nuclear power plants, Nucl. Eng. Technol. 43 (2011) 45-62, https://doi.org/10.5516/NET.2011.43.1.045.    DOI
41 K.Y. Choi, et al., Development of a wall-to-fluid heat transfer package for the SPACE code, Nucl. Eng. Technol. 41 (9) (2009) 1143-1156, https://doi.org/10.5516/NET.2009.41.9.1143.    DOI
42 T.B. Lee, et al., Improvement of the SPACE Subcooled Boiling Model for the High Pressure and Low Flow Conditions, Transactions of the Korean Nuclear Society Spring Meeting, Jeju, Korea, 2020. May 21-22. 
43 M.V.H. Del Valle, et al., Subcooled flow boiling at high heat flux, Int. J. Heat Mass Tran. 28 (10) (1985) 1907-1920, https://doi.org/10.1016/0017-9310(85)90213-3.    DOI
44 H.C. Unal, Maximum bubble diameter, maximum bubble growth time and bubble growth rate, Int. J. Heat Mass Tran. 19 (1976) 643-649, https://doi.org/10.1016/0017-9310(76)90047-8.    DOI
45 R.W. Bowring, Physical Model, Based on Bubble Detachment, and Calculation of Steam Voidage in the Sub-cooled Region of a Heated Channel," OECD Halden Reactor Project Report HPR-10, Institute for Atomenergi, Halden, Norway, 1962. 
46 M.Z. Podowski, Mechanistic Modeling of CHF in Forced-Convection Subcooled Boiling," KAPL-P-000162, KAPL Atomic Power Laboratory, 1997. 
47 R. Cole, A photographic study of pool boiling in the region of the critical heat flux, AIChE J. 6 (4) (1960) 533-538, https://doi.org/10.1002/aic.690060405.    DOI
48 G. Kocamustafaogullari, Pressure dependence of bubble departure diameter for water, Int. Commun. Heat Mass Tran. 10 (1983) 501-509, https://doi.org/10.1016/0735-1933(83)90057-X.    DOI
49 J.T. Rogers, et al., The onset of significant void in up-flow boiling of water at low pressure and velocities, Int. J. Heat Mass Tran. 30 (11) (1987) 2247-2260, https://doi.org/10.1016/0017-9310(87)90218-3.    DOI
50 Y. Taitel, et al., Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes, AIChE J. 26 (3) (1980) 345-354, https://doi.org/10.1002/aic.690260304.    DOI
51 K. Mishima, et al., Flow regime transition criteria for upward two-phase flow in vertical tubes, Int. J. Heat Mass Tran. 27 (5) (1984) 723-737, https://doi.org/10.1016/0017-9310(84)90142-X.    DOI
52 P. Goel, et al., Bubble departure characteristics in a horizontal tube bundle under cross flow conditions, Int. J. Multiphas. Flow 100 (2018) 143-154, https://doi.org/10.1016/j.ijmultiphaseflow.2017.12.013.    DOI
53 B. Chexal, G. Lellouche, et al., A void fraction correlation for generalized applications, Prog. Nucl. Energy 27 (4) (1992) 255-295, https://doi.org/10.1016/0149-1970(92)90007-P.    DOI
54 H. Goda, et al., Drift-flux model for downward two-phase flow, Int. J. Heat Mass Tran. 46 (2003) 4835-4844, https://doi.org/10.1016/S0017-9310(03)00309-0.    DOI
55 N. Zuber, J.A. Findlay, Average volumetric concentration in two-phase flow systems, J. Heat Tran. 87 (1965) 453-468, https://doi.org/10.1115/1.3689137.    DOI
56 T. Hibiki, et al., Interfacial area concentration in boiling bubbly flow systems, Chem. Eng. Sci. 61 (2006) 7979-7990, https://doi.org/10.1016/j.ces.2006.09.009.    DOI
57 C.S. Brooks, et al., Wall nucleation modeling in subcooled boiling flow, Int. J. Heat Mass Tran. 86 (2015) 183-196, https://doi.org/10.1016/j.ijheatmasstransfer.2015.03.005.    DOI
58 R. Situ, et al., Bubble departure frequency in forced convective subcooled boiling flow, Int. J. Heat Mass Tran. 51 (2008) 6268-6282, https://doi.org/10.1016/j.ijheatmasstransfer.2008.04.028.    DOI
59 J.C. Chen, A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow, vol. 5, I & EC Process Design and Development, 1966, pp. 322-327. 
60 ISL, Inc, RELAP5/MOD3.3 Code Manual, Volume IV: Models and Correlations, U.S. NRC, 2016. NUREG/CR-5535/Rev P5-Vol IV. 
61 E. Hisham, et al., Deep Learning Pipeline - Building a Deep Learning Model with TensorFlow, Apress Media LLC, New York, 2020. 
62 B.J. Yun, et al., Characteristics of the local bubble parameters of a subcooled boiling flow in an annulus, Nucl. Eng. Des. 240 (2010) 2295-2303, https://doi.org/10.1016/j.nucengdes.2009.11.014.    DOI
63 S. Bae, et al., Preliminary Assessment of the Interfacial Source Terms in SPACE Code, Transactions of the Korean Nuclear Society Spring Meeting, Gyeongju, Korea, 2009. October 29-30. 
64 S.N. Aksan, et al., Boil-off experiments with the PSI-NEPTUN facility: analysis and code assessment overview report, Nucl. Eng. Des. 143 (1993) 245-264, https://doi.org/10.1016/0029-5493(93)90227-Z.    DOI
65 E. Bibeau, Experimental Investigation of Subcooled Void Growth for Upflow and Downflow at Low Velocities and Low Pressure, British Columbia University, 1988. Thesis of Master Degree. 
66 R. Evangelisti, et al., The void fraction in an annular channel at atmospheric pressure, Int. J. Heat Mass Tran. 12 (1969) 699-711, https://doi.org/10.1016/0017-9310(69)90004-0.    DOI
67 R. Ahmadi, et al., Experimental identification of the phenomenon triggering the net vapor generation in upward subcooled flow boiling of water at low pressure, Int. J. Heat Mass Tran. 55 (2012) 6067-6076, https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.020.    DOI
68 R. Ahmadi, et al., Visualization study on the mechanisms of net vapor generation in water subcooled flow boiling under moderate pressure conditions, Int. J. Heat Mass Tran. 70 (2014) 137-151, https://doi.org/10.1016/j.ijheatmasstransfer.2013.10.073.    DOI
69 Z. Edelman, et al., Void fraction distribution in low flow rate subcooled boiling, Nucl. Eng. Des. 66 (1981) 375-382, https://doi.org/10.1016/0029-5493(81)90167-9.    DOI
70 R. Ahmadi, et al., Influence of surface wettability on bubble behavior and void evolution in subcooled flow boiling, Int. J. Heat Mass Tran. 97 (2015) 114-125, https://doi.org/10.1016/j.ijthermalsci.2015.06.012.    DOI
71 S.Z. Rouhani, Void Measurements in the Regions of Sub-cooled and Low-Quality Boiling, Part 1. Higher Mass Velocities, AB Atomenergi, 1966. No. AE-239. 
72 S.Z. Rouhani, Void Measurements in the Regions of Sub-cooled and LowQuality Boiling, Part 1. Low Mass Velocities, AB Atomenergi, 1966. No. AE-238. 
73 G.G. Bartolomey, et al., Experimental Investigation of Void Fraction at Sub-cooled Boiling Mode in Tubes, Teploenergetika, N3, 1982, pp. 20-22. 
74 F.W. Staub, The void fraction in subcooled boiling-prediction of the initial point of net vapor generation, J. Heat Tran. 90 (1) (1968a) 151-157, https://doi.org/10.1115/1.3597446.    DOI
75 F.W. Staub, et al., Heat Transfer and Hydraulics; the Effects of Subcooled Voids", Final Report, 1968. NYO-3679-8. 
76 J. Marchaterre, et al., Natural and Forced-Circulation Boiling Studies," ANL-5735, Argonne National Laboratory, 1960. 
77 G. Maurer, et al., Bettis Technical Review - A Method of Predicting Steady-State Boiling Vapor Fractions in Reactor Coolant Channels, vol. 19, WAPD-BT-, Bettis, 1960. 
78 R. Egen, et al., Vapor formation and behavior in boiling heat transfer, in: BMI-1163, Battelle Memorial Institute, 1957. 
79 P. Griffith, et al., Void Volumes in Subcooled Boiling Systems, MIT, 1958. MIT Technical Report No. 12, ASME Paper No. 58-HT-19. 
80 J. Foglia, et al., Boiling-water void distribution and slip ratio in heated channels, in: BMI-1517, Battelle Memorial Institute, 1961. 
81 H. Kubota, et al., Dependence of vapor void fraction on fundamental bubble parameters in subcooled flow boiling, in: Proceedings of ICONE14 International Conference on Nuclear Engineering, 2006. July 17-20, Miami, Florida, USA. 
82 J. Kennedy, et al., The onset of flow instability in uniformly heated horizontal microchannels, J. Heat Tran. 122 (2000) 118-125, https://doi.org/10.1115/1.521442.    DOI
83 M. Kureta, et al., Study on point of net vapor generation by neutron radiography in subcooled boiling flow along narrow rectangular channels with short heated length, Int. J. Heat Mass Tran. 46 (2003) 1171-1181, https://doi.org/10.1016/S0017-9310(02)00398-8.    DOI
84 K. Sekoguchi, et al., Prediction of void fraction in subcooled and low quality boiling regions, JSME 23 (183) (1980) 1475-1482, https://doi.org/10.1299/jsme1958.23.1475.    DOI
85 V. Chanturiya, et al., Experimental study of true void fraction when boiling subcooled water in vertical tubes, Teploenergetika 14 (2) (1967) 123-128. 
86 M. Siman-Tov, et al., Static Flow Instability in Subcooled Flow Boiling in Parallel Channels, CONF-950445-2, ORNL, 1995. 
87 R. Martin, et al., Measurement of the local void fraction at high pressure in a heating channel, Nucl. Sci. Eng. 48 (1972) 125-138, https://doi.org/10.13182/NSE72-A22466.    DOI
88 G. Aurelien, Hands-On Machine Learning with Scikit-Learn, Keras, and Ten-sorflow: Concepts, Tools, and Techniques to Build Intelligent Systems, O'Reilly Media, 2019. 
89 T. Okawa, et al., On the rise paths of single vapor bubbles after the departure from nucleation sites in subcooled upflow boiling, Int. J. Heat Mass Tran. 48 (2005) 4446-4459, https://doi.org/10.1016/j.ijheatmasstransfer.2005.05.026.    DOI
90 G. Mayinger, Void Fraction and Pressure Drop in Subcooled Forced Convective Boiling with Refrigent 12, 7th EUROTHERM Seminar, Pisa, Italy, 1989. 
91 J.H. Anthony, Probability and Statistics for Engineers and Scientists, second ed., Thomson Learning Academic Resource Center, Duxbury, 2002. 
92 L. Francisco, et al., Neuron theory, the cornerstone of neuroscience, on the centenary of the Nobel Prize award to Santiago Ramon y Cajal, Brain Res. Bull. 70 (2006) 391-405, https://doi.org/10.1016/j.brainresbull.2006.07.010.    DOI
93 F. Rosenblatt, The perceptron: a probabilistic model for information storage and organization in the brain, Psychol. Rev. 65 (6) (1958) 386-408, https://doi.org/10.1037/h0042519.    DOI
94 Y. LeCun, et al., Deep learning, Review, Nature 521 (2015) 436-444, https://doi.org/10.1038/nature14539.    DOI
95 D.P. Kingma, et al., ADAM: a method for stochastic optimization, in: International Conference on Learning Representations (ICLR) Conference, 2015 arXiv: 1412.6980vol. 9. 
96 S. Pramod, et al., Learn TensorFlow 2.0 - Implement Machine Learning and Deep Learning Models with Python, Apress Media LLC, New York, 2020.