Home Technology CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges
Article
Licensed
Unlicensed Requires Authentication

CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges

  • Yixiang Liao ORCID logo EMAIL logo
Published/Copyright: March 20, 2024
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Kerntechnik
From the journal Kerntechnik Volume 89 Issue 2

Abstract

Because of its relevance for the safety analysis of pressurized water reactors (PWR), many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have been focused on the critical mass flow rate and transient pressure or temperature fluctuations by means of experiments and system codes. Since the beginning of this century, owing to the increase in computer speed and capacity, computational fluid dynamics (CFD) is being used more and more in the investigation of flashing flows, which has the advantage of providing three-dimensional insights in the internal flow structure as well as its evolution. This work presents an overview of relevant flashing scenarios in the nuclear safety analysis, and focuses on the discussion about possibilities and challenges of using CFD modelling. It is shown that a two-fluid model with the thermal phase-change model is superior to a mixture model with pressure phase-change, relaxation and equilibrium models, respectively, in terms of interfacial mass transfer, however, efforts are still required to improve the interphase heat-transfer model. Furthermore, since flashing is accompanied with high void fraction and broad bubble size ranges, a poly-disperse two-fluid model is recommended, but the effect of phase change on bubble coalescence and breakup needs further research. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models remains a challenge.

Keywords: challenges; computational fluid dynamics; flashing flows; nuclear safety analysis; pressurized water reactor
Corresponding author: Yixiang Liao, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden – Rossendorf e.V., Bautzner Landstraße 400, 01328 Dresden, Germany, E-mail:

  1. Research ethics: Not applicable.

  2. Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The author states no conflicts of interest.

  4. Research funding: None declared.

  5. Data availability: Not applicable.

References

Abuaf, N., Wu, B.J., Zimmer, G.A., and Saha, P. (1981). Study of nonequilibrium flashing of water in a converging-diverging nozzle. Volume 1: experimental (No. NUREG/CR-1864-Vol. 1; BNL-NUREG-51317-Vol. 1). Brookhaven National Lab., Upton, NY (USA).Search in Google Scholar

Al Issa, S. (2015). Experimental investigation and CFD validation of two-phase phenomena related to nuclear safety research during LOCA accidents. Doctoral dissertation. Technische Universität München, Munich, Germany.Search in Google Scholar

Al Issa, S., Weisensee, P., and Macián-Juan, R. (2014). Experimental investigation of steam bubble condensation in vertical large diameter geometry under atmospheric pressure and different flow conditions. Int. J. Heat Mass Transf. 70: 918–929.10.1016/j.ijheatmasstransfer.2013.11.049Search in Google Scholar

Antal, S.P. and Podowski, M.Z. (2003). The effect of steam/water properties feedback on flow oscillations in boiling water reactors. In: The Tenth International Topic Meeting on Nuclear Reactor, NURETH-10. Korean Nuclear Society, Seoul, Korea.Search in Google Scholar

Avdeev, A.A. (2016). Bubble systems. Springer, Switzerland.10.1007/978-3-319-29288-5Search in Google Scholar

Bakhmetiev, A.M., Bolshukhin, M.A., and Vakhrushev, V.V. (2009). Experimental validation of the cooling loop of a passive system removing heat from the protective shell of the AES-2006 design on the site of the Leningradskaya nuclear power plant. Atom. Energy 106: 148–152.10.1007/s10512-009-9150-1Search in Google Scholar

Berry, R.A. (2010). Some specific CASL requirements for advanced multiphase flow simulation of light water reactors (No. INL/EXT-10-20529). Idaho National Lab. (INL), Idaho Falls, ID (United States).Search in Google Scholar

Bestion, D. (2008). System code models and capabilities. In: Conference: seminar on the transfer of competence, knowledge and experience gained through CSNI activities in the field of thermal-hydraulics 5–9 May 2008. Int. Nucl. Info. System, Vienna, Austria.Search in Google Scholar

Bestion, D. (2010). Extension of CFD codes application to two-phase flow safety problems. Nucl. Eng. Technol. 42: 365–376, https://doi.org/10.5516/net.2010.42.4.365.Search in Google Scholar

Blinkov, V.N., Jones, O.C., and Nigmatulin, B.I. (1993). Nucleation and flashing in nozzles – 2. Comparison with experiments using a five-equation model for vapor void development. Int. J. Multiphas. Flow 19: 965–986, https://doi.org/10.1016/0301-9322(93)90072-3.Search in Google Scholar

Clift, R., Grace, J., and Weber, M. (1978). Nonspherical rigid particles at higher Reynolds numbers. Bubbles, drops, and particles. Academic Press, New York, NY, USA, pp. 142–168.Search in Google Scholar

Cloppenborg, T., Schuster, C., and Hurtado, A. (2015). Two-phase flow phenomena along an adiabatic riser – an experimental study at the test-facility GENEVA. Int. J. Multiphas. Flow 72: 112–132, https://doi.org/10.1016/j.ijmultiphaseflow.2015.02.003.Search in Google Scholar

Colombo, M. and Fairweather, M. (2016). Accuracy of Eulerian–Eulerian, two-fluid CFD boiling models of subcooled boiling flows. Int. J. Heat Mass Tran. 103: 28–44, https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.098.Search in Google Scholar

Colombo, M., Rzehak, R., Fairweather, M., Liao, Y., and Lucas, D. (2021). Benchmarking of computational fluid dynamic models for bubbly flows. Nucl. Eng. Des. 375: 111075, https://doi.org/10.1016/j.nucengdes.2021.111075.Search in Google Scholar

Dang Le, Q., Mereu, R., Besagni, G., Dossena, V., and Inzoli, F. (2018). Computational fluid dynamics modeling of flashing flow in convergent-divergent nozzle. J. Fluid. Eng. 140: 101102, https://doi.org/10.1115/1.4039908.Search in Google Scholar

Duponcheel, M., Seynhaeve, J.M., and Bartosiewicz, Y. (2015). Implementation and assessment of the delayed equilibrium model for computing flashing choked flows in a multi-field CFD code. In: The sixteenth International Topic Meeting on Nuclear Reactor, NURETH-16. American Nuclear Society (ANS), Chicago, IL.Search in Google Scholar

Elias, E. and Lellouche, G.S. (1994). Two-phase critical flow. Int. J. Multiphas. Flow 20: 91–168, https://doi.org/10.1016/0301-9322(94)90071-X.Search in Google Scholar

Fauske, H.K. (1962). Contribution to the theory of two-phase, one-component critical flow (No. ANL-6633). Argonne National Lab., Ill.10.2172/4749073Search in Google Scholar

Fauske, H.K. (1965). The discharge of saturated water through tubes. Chem. Eng. Prog. Symp. Ser. 61: 210.Search in Google Scholar

Feng, Z.G. and Michaelides, E.E. (2000). A numerical study on the transient heat transfer from a sphere at high Reynolds and Peclet numbers. Int. J. Heat Mass Tran. 43: 219–229, https://doi.org/10.1016/S0017-9310(99)00133-7.Search in Google Scholar

Florschuetz, L.W., Henry, C.L., and Khan, A.R. (1969). Growth rates of free vapor bubbles in liquids at uniform superheats under normal and zero gravity conditions. Int. J. Heat Mass Tran. 12: 1465–1489, https://doi.org/10.1016/0017-9310(69)90028-3.Search in Google Scholar

Furuya, M., Inada, F., and Van der Hagen, T.H.J.J. (2005). Flashing-induced density wave oscillations in a natural circulation BWR – mechanism of instability and stability map. Nucl. Eng. Des. 235: 1557–1569, https://doi.org/10.1016/j.nucengdes.2005.01.006.Search in Google Scholar

Guelfi, A., Bestion, D., Boucker, M., Boudier, P., Fillion, P., Grandotto, M., and Péturaud, P. (2007). NEPTUNE: a new software platform for advanced nuclear thermal hydraulics. Nucl. Sci. Eng. 156: 281–324, https://doi.org/10.13182/NSE05-98.Search in Google Scholar

Henry, R.E. (1970). The compressible flow of two component, two-phase mixtures in nozzles and orifices (No. NASA-TM-X-52729). NASA Lewis Research Center, Cleveland.Search in Google Scholar

Ingle, R., Rao, V.S., Mohan, L.S., Dai, Y., and Chaudhry, G. (2015). Modelling of flashing in capillary tubes using homogeneous equilibrium approach. Proc. IUTAM 15: 286–292, https://doi.org/10.1016/j.piutam.2015.04.040.Search in Google Scholar

Isbin, H.S., Moy, J.E., and Da Cruz, A.J.R. (1957). Two-phase, steam-water critical flow. AIChE J. 3: 361–365, https://doi.org/10.1002/aic.690030315.Search in Google Scholar

Ishigaki, M., Watanabe, T., and Nakamura, H. (2012). Numerical simulation of two-phase critical flow with the phase change in the nozzle tube. J. Power Energy Syst. 6: 264–274, https://doi.org/10.1299/JPES.6.264.Search in Google Scholar

Janet, J.P., Liao, Y., and Lucas, D. (2015). Heterogeneous nucleation in CFD simulation of flashing flows in converging–diverging nozzles. Int. J. Multiphas. Flow 74: 106–117, https://doi.org/10.1016/j.ijmultiphaseflow.2015.04.005.Search in Google Scholar

Jin, M.S., Ha, C.T., and Park, W.G. (2017). Numerical study on heat transfer effects of cavitating and flashing flows based on homogeneous mixture model. Int. J. Heat Mass Tran. 109: 1068–1083, https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.080.Search in Google Scholar

Jo, J.C., Jeong, J.J., Yun, B.J., and Kim, J. (2019). Numerical analysis of subcooled water flashing flow from a pressurized water reactor steam generator through an abruptly broken main feed water pipe. J. Pressure Vessel Technol. 141: 044501, https://doi.org/10.1115/1.4043297.Search in Google Scholar

Jo, J.C., Jeong, J.J., Yun, B.J., and Moody, F.J. (2018). Numerical prediction of a flashing flow of saturated water at high pressure. Nucl. Eng. Technol. 50: 1173–1183, https://doi.org/10.1016/j.net.2018.06.002.Search in Google Scholar

Karathanassis, I.K., Koukouvinis, P., and Gavaises, M. (2017). Comparative evaluation of phase-change mechanisms for the prediction of flashing flows. Int. J. Multiphas. Flow 95: 257–270, https://doi.org/10.1016/j.ijmultiphaseflow.2017.06.006.Search in Google Scholar

Kolev, N.I. (2006). Uniqueness of the elementary physics driving heterogeneous nucleate boiling and flashing. Nucl. Eng. Technol. 38: 175–184.Search in Google Scholar

Kosky, P.G. (1968). Bubble growth measurements in uniformly superheated liquids. Chem. Eng. Sci. 23: 695–706, https://doi.org/10.1016/0009-2509(68)85004-3.Search in Google Scholar

Krepper, E., Rzehak, R., Lifante, C., and Frank, T. (2013). CFD for subcooled flow boiling: coupling wall boiling and population balance models. Nucl. Eng. Des. 255: 330–346, https://doi.org/10.1016/j.nucengdes.2012.11.010.Search in Google Scholar

Kutnjak, J., Kulenovic, R., and Laurien, E. (2011). Experimental investigation and modelling of bulk boiling for CFD application. In: The fourteenth International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-14. Canadian Nuclear Society, Toronto, ON.Search in Google Scholar

Lee, S.W., Heo, S., Ha, H.U., and Kim, H.G. (2017). The concept of the innovative power reactor. Nucl. Eng. Technol. 49: 1431–1441, https://doi.org/10.1016/j.net.2017.06.015.Search in Google Scholar

Levy, S. and Abdollahian, D. (1982). Homogeneous non-equilibrium critical flow model. Int. J. Heat Mass Tran. 25: 759–770, https://doi.org/10.1016/0017-9310(82)90088-6.Search in Google Scholar

Li, J., Liao, Y., Zhou, P., Lucas, D., and Gong, L. (2023a). Numerical simulation of flashing flows in a converging–diverging nozzle with interfacial area transport equation. Processes 11: 2365, https://doi.org/10.3390/pr11082365.Search in Google Scholar

Li, J., Liao, Y., Zhou, P., Lucas, D., and Li, Q. (2023b). Numerical study of flashing pipe flow using a TFM-PBM coupled method: effect of interfacial heat transfer and bubble coalescence and breakup. Int. J. Therm. Sci. 193: 108504, https://doi.org/10.1016/j.ijthermalsci.2023.108504.Search in Google Scholar

Li, J., Liao, Y., Bolotnov, I.A., Zhou, P., Lucas, D., Li, Q., and Gong, L. (2023c). Direct numerical simulation of heat transfer on a deformable vapor bubble rising in superheated liquid. Phys. Fluids 35: 023319, https://doi.org/10.1063%2F5.0137675.10.1063/5.0137675Search in Google Scholar

Liao, Y., Krepper, E., and Lucas, D. (2019). A baseline closure concept for simulating bubbly flow with phase change: a mechanistic model for interphase heat transfer coefficient. Nucl. Eng. Des. 348: 1–13, https://doi.org/10.1016/j.nucengdes.2019.04.007.Search in Google Scholar

Liao, Y. and Lucas, D. (2015). 3D CFD simulation of flashing flows in a converging-diverging nozzle. Nucl. Eng. Des. 292: 149–163, https://doi.org/10.1016/j.nucengdes.2015.06.015.Search in Google Scholar

Liao, Y. and Lucas, D. (2016). Poly-disperse simulation of condensing steam-water flow inside a large vertical pipe. Int. J. Therm. Sci. 104: 194–207, https://doi.org/10.1016/j.ijthermalsci.2016.01.016.Search in Google Scholar

Liao, Y. and Lucas, D. (2017a). Computational modelling of flash boiling flows: a literature survey. Int. J. Heat Mass Tran. 111: 246–265, https://doi.org/10.1016/j.ijheatmasstransfer.2017.03.121.Search in Google Scholar

Liao, Y. and Lucas, D. (2017b). Possibilities and limitations of CFD simulation for flashing flow scenarios in nuclear applications. Energies 10: 139, https://doi.org/10.3390/en10010139.Search in Google Scholar

Liao, Y. and Lucas, D. (2018). Evaluation of interfacial heat transfer models for flashing flow with two-fluid CFD. Fluids 3: 38, https://doi.org/10.3390/fluids3020038.Search in Google Scholar

Liao, Y. and Lucas, D. (2019). Numerical analysis of flashing pipe flow using a population balance approach. Int. J. Heat Fluid Flow 77: 299–313, https://doi.org/10.1016/j.ijheatfluidflow.2019.05.005.Search in Google Scholar

Liao, Y. and Lucas, D. (2021). A review on numerical modelling of flashing flow with application to nuclear safety analysis. Appl. Therm. Eng. 182: 116002, https://doi.org/10.1016/j.applthermaleng.2020.116002.Search in Google Scholar

Liao, Y. and Lucas, D. (2023). CFD modeling of phase change during the flashing-induced instability in a natural circulation circuit. Processes 11: 1974, https://doi.org/10.3390/pr11071974.Search in Google Scholar

Liao, Y., Lucas, D., Krepper, E., and Rzehak, R. (2013). Flashing evaporation under different pressure levels. Nucl. Eng. Des. 265: 801–813, https://doi.org/10.1016%2Fj.nucengdes.2013.09.027.10.1016/j.nucengdes.2013.09.027Search in Google Scholar

Liao, Y., Rzehak, R., Lucas, D., and Krepper, E. (2015). Baseline closure model for dispersed bubbly flow: bubble coalescence and breakup. Chem. Eng. Sci. 122: 336–349, https://doi.org/10.1016/j.ces.2014.09.042.Search in Google Scholar

Liao, Y., Schuster, C., Hu, S., and Lucas, D. (2018). CFD modelling of flashing instability in natural circulation cooling systems. In: 26th international conference on nuclear engineering 51524, ICONE-26, American Society of Mechanical Engineers (ASME), New York City, U.S.10.1115/ICONE26-81787Search in Google Scholar

Lim, S.G., No, H.C., Lee, S.W., Kim, H.G., Cheon, J., Lee, J.M., and Ohk, S.M. (2020). Development of stability maps for flashing-induced instability in a passive containment cooling system for iPOWER. Nucl. Eng. Technol. 52: 37–50, https://doi.org/10.1016/j.net.2019.06.026.Search in Google Scholar

Lo, S. and Zhang, D. (2009). Modelling of break-up and coalescence in bubbly two-phase flows. J. Comput. Multiph. Flows 1: 23–38, https://doi.org/10.1260/175748209787387106.Search in Google Scholar

Lucas, D., Beyer, M., and Szalinski, L. (2011). Experiments on evaporating pipe flow. In: The fourteenth International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-14. Canadian Nuclear Society, Toronto, ON, Canada.Search in Google Scholar

Lucas, D., Beyer, M., and Szalinski, L. (2013). Experimental database on steam–water flow with phase transfer in a vertical pipe. Nucl. Eng. Des. 265: 1113–1123, https://doi.org/10.1016/j.nucengdes.2013.10.002.Search in Google Scholar

Lucas, D., Beyer, M., Szalinski, L., and Schütz, P. (2010). A new database on the evolution of air–water flows along a large vertical pipe. Int. J. Therm. Sci. 49: 664–674, https://doi.org/10.1016/j.ijthermalsci.2009.11.008.Search in Google Scholar

Luo, H. and Svendsen, H.F. (1996). Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 42: 1225–1233, https://doi.org/10.1002/aic.690420505.Search in Google Scholar

Lyras, K., Dembele, S., Vyazmina, E., Jallais, S., and Wen, J. (2018). Numerical simulation of flash-boiling through sharp-edged orifices. Multiphas. Flow Theor. Appl. 6: 176–185.10.2495/CMEM-V6-N1-176-185Search in Google Scholar

Maksic, S. and Mewes, D. (2002). CFD-calculation of the flashing flow in pipes and nozzles. Fluids Eng. Div. Summer Meet. 36150: 511–516, https://doi.org/10.1115/FEDSM2002-31033.Search in Google Scholar

Manera, A., Prasser, H.M., Lucas, D., and Van Der Hagen, T.H.J.J. (2006). Three-dimensional flow pattern visualization and bubble size distributions in stationary and transient upward flashing flow. Int. J. Multiphas. Flow 32: 996–1016, https://doi.org/10.1016/j.ijmultiphaseflow.2006.03.005.Search in Google Scholar

Marsh, C.A. and O’Mahony, A.P. (2009). Three-dimensional modelling of industrial flashing flows. Prog. Comput. Fluid Dynam. Int. J. 9: 393–398, https://doi.org/10.1504/PCFD.2009.02737.Search in Google Scholar

Marshall, W.R. and Ranz, W.E. (1952). Evaporation from drops – Part I. Chem. Eng. Prog. 48: 141–146.Search in Google Scholar

Meller, R., Schlegel, F., and Lucas, D. (2021). Basic verification of a numerical framework applied to a morphology adaptive multifield two-fluid model considering bubble motions. Int. J. Numer. Methods Fluid. 92: 748–773, https://doi.org/10.1002/fld.4907.Search in Google Scholar

Meller, R., Tekavčič, M., Krull, B., and Schlegel, F. (2023). Momentum exchange modeling for coarsely resolved interfaces in a multifield two-fluid model. Int. J. Numer. Methods Fluid. 95: 1521–1545, https://doi.org/10.1002/fld.5215.Search in Google Scholar

Migot, B., Brillant, G., Martin, J., and Morin, S. (2022). DENOPI project devoted to spent fuel pool accidents: overview on the thermal hydraulics experimental facilities. In: The nineteenth International Topical Meeting on Nuclear Reactor Thermalhydraulics, NURETH-19. American Nuclear Society (ANS), Chicago.Search in Google Scholar

Mimouni, S., Boucker, M., Laviéville, J., Guelfi, A., and Bestion, D. (2008). Modelling and computation of cavitation and boiling bubbly flows with the NEPTUNE_CFD code. Nucl. Eng. Des. 238: 680–692, https://doi.org/10.1016/j.nucengdes.2007.02.052.Search in Google Scholar

Palau-Salvador, G., Altozano, P.G., and Arviza-Valverde, J. (2007). Numerical modeling of cavitating flows for simple geometries using FLUENT V6. 1. Spanish J. Agric. Res. 5: 460–469, https://doi.org/10.5424/sjar/2007054-269.Search in Google Scholar

Petrović, M.M. and Stevanović, V.D. (2016). Two-component two-phase critical flow. FME Trans. 44: 109–114, https://doi.org/10.5937/fmet1602109P.Search in Google Scholar

Prince, M.J. and Blanch, H.W. (1990). Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 36: 1485–1499, https://doi.org/10.1002/aic.690361004.Search in Google Scholar

Reitz, R.D. (1990). A photographic study of flash-boiling atomization. Aerosol Sci. Technol. 12: 561–569, https://doi.org/10.1080/02786829008959370.Search in Google Scholar

Riznic, J., Ishii, M., and Afgan, N. (1987). Mechanistic model for void distribution in flashing flow (No. CONF-8705224--1). Vinča Institute of Nuclear Sciences, Vinča, Serbia.Search in Google Scholar

Robert, M., Farvacque, M., Parent, M., and Faydide, B. (2003). CATHARE 2 V2.5 : a fully validated CATHARE version for various applications. In: The Tenth International Topic Meeting on Nuclear Reactor, NURETH-10. Koeran Nuclear Society, Seoul, Korea.Search in Google Scholar

Schmidt, D.P., Gopalakrishnan, S., and Jasak, H. (2010). Multi-dimensional simulation of thermal non-equilibrium channel flow. Int. J. Multiphas. Flow 36: 284–292, https://doi.org/10.1016/j.ijmultiphaseflow.2009.11.012.Search in Google Scholar

Schnerr, G.H. and Sauer, J. (2001). Physical and numerical modeling of unsteady cavitation dynamics. In: Fourth international conference on multiphase flow, 1. ICMF-4, New Orleans, New Orleans.Search in Google Scholar

Schulz, T.L. (2006). Westinghouse AP1000 advanced passive plant. Nucl. Eng. Des. 236: 1547–1557, https://doi.org/10.1016/j.nucengdes.2006.03.049.Search in Google Scholar

Simoneau, R.J. (1975) Maximum two-phase flow rates of sub-cooled nitrogen through a sharp-edged orifice. In: Advances in cryogenic engineering. Springer US, Boston, MA, pp. 299–306.10.1007/978-1-4757-0208-8_39Search in Google Scholar

Singhal, A.K., Athavale, M.M., Li, H., and Jiang, Y. (2002). Mathematical basis and validation of the full cavitation model. J. Fluids Eng. 124: 617–624.10.1115/1.1486223Search in Google Scholar

Staedtke, H., Franchello, G., Worth, B., Graf, U., Romstedt, P., Kumbaro, A., Garcia-Cascales, J., Paillère, H., Deconinck, H., Ricchiuto, M., et al.. (2005). Advanced three-dimensional two-phase flow simulation tools for application to reactor safety (ASTAR). Nucl. Eng. Des. 235: 379–400, https://doi.org/10.1016/j.nucengdes.2004.08.052.Search in Google Scholar

Van Bragt, D.D.B., De Kruijf, W.J.M., Manera, A., Van Der Hagen, T.H.J.J., and Van Dam, H. (2002). Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor. Nucl. Eng. Des. 215: 87–98, https://doi.org/10.1016/S0029-5493(02)00043-2.Search in Google Scholar

Wang, S., Lin, Y.C., Wang, G., and Ishii, M. (2022). Experimental investigation on flashing-induced flow instability in a natural circulation scaled-down test facility. Ann. Nucl. Energy 171: 109023, https://doi.org/10.1016/j.anucene.2022.109023.Search in Google Scholar

Wang, J., Zhu, F., Liu, X., and Li, W. (2017). Multiscale simulation of gas-liquid flows with droplets. In: 2017 international conference on applied mathematics, modelling and statistics application (AMMSA 2017). Atlantis Press, Amsterdam, Netherlands, pp. 21–25.10.2991/ammsa-17.2017.5Search in Google Scholar

Whitaker, S. (1972). Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J. 18: 361–371, https://doi.org/10.1002/aic.690180219.Search in Google Scholar

Wolfert, K., Burwell, M.J., and Enix, D. (1981). Non-equilibrium mass transfer between liquid and vapour phases during depressurization processes. In: Transient two-phase flow. Proceedings of the second CSNI specialists meeting, Paris, 12–14 June 1978, 12. French Alternative Energies and Atomic Energy Commission (CEA), Paris, France.Search in Google Scholar

Xing, J., Song, D., and Wu, Y. (2016). HPR1000: advanced pressurized water reactor with active and passive safety. Engineering 2: 79–87, https://doi.org/10.1016/J.ENG.2016.01.017.Search in Google Scholar

Yan, K. and Che, D. (2010). A coupled model for simulation of the gas-liquid two-phase flow with complex flow patterns. Int. J. Multiphas. Flow 36: 333–348, https://doi.org/10.1016/j.ijmultiphaseflow.2009.11.007.Search in Google Scholar

Yao, W. and Morel, C. (2004). Volumetric interfacial area prediction in upward bubbly two-phase flow. Int. J. Heat Mass Tran. 47: 307–328, https://doi.org/10.1016/j.ijheatmasstransfer.2003.06.004.Search in Google Scholar

Yeoh, G.H. and Tu, J.Y. (2005). A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow. Nucl. Eng. Des. 235: 1251–1265, https://doi.org/10.1016/j.nucengdes.2005.02.015.Search in Google Scholar

Yin, J., Zhang, T., Krull, B., Meller, R., Schlegel, F., Lucas, D., and Liao, Y. (2023). A CFD approach for the flow regime transition in a vane-type gas-liquid separator. Int. J. Multiphas. Flow 159: 104320, https://doi.org/10.1016%2Fj.ijmultiphaseflow.2022.104320.10.1016/j.ijmultiphaseflow.2022.104320Search in Google Scholar

Yoon, H.J., Ishii, M., and Revankar, S.T. (2006). Choking flow modeling with mechanical and thermal non-equilibrium. Int. J. Heat Mass Tran. 49: 171–186, https://doi.org/10.1016/j.ijheatmasstransfer.2005.07.044.Search in Google Scholar

Zhao, X., Liao, Y., Wang, M., Zhang, K., Su, G.H., Tian, W., and Lucas, D. (2021). Numerical simulation of micro-crack leakage on steam generator heat transfer tube. Nucl. Eng. Des. 382: 111385, https://doi.org/10.1016/j.nucengdes.2021.111385.Search in Google Scholar

Zwart, P. J., Gerber, A. G., and Belamri, T. (2004). A two-phase flow model for predicting cavitation dynamics. In: Fifth international conference on multiphase flow, Paper No. 152. ICMF, Yokohama, Japan.Search in Google Scholar
Received: 2023-08-29
Accepted: 2024-02-29
Published Online: 2024-03-20
Published in Print: 2024-04-25

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. The 34th German CFD network of competence meeting: numerical 3D simulation of reactor primary cooling circuit and containment flows
  3. The European GO-VIKING project on flow-induced vibrations: overview and current status
  4. CFD simulation on droplet behaviour in post-dryout region
  5. Coupled AC2-CFD simulations for a high-pressure core melt accident scenario
  6. Validation of coupled ATHLET-OpenFOAM simulation on a large-scale single- and two-phase flow experiment
  7. CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges
  8. Implementation of the preCICE coupling interface for AC2/ATHLET
  9. Large-scale PANDA facility – radiation experiments and CFD calculations
  10. Overview on GRS CFD activities related to containment applications
  11. Calendar of events
https://doi.org/10.1515/kern-2023-0090
Keywords for this article
challenges; computational fluid dynamics; flashing flows; nuclear safety analysis; pressurized water reactor

Articles in the same Issue

  1. Frontmatter
  2. The 34th German CFD network of competence meeting: numerical 3D simulation of reactor primary cooling circuit and containment flows
  3. The European GO-VIKING project on flow-induced vibrations: overview and current status
  4. CFD simulation on droplet behaviour in post-dryout region
  5. Coupled AC2-CFD simulations for a high-pressure core melt accident scenario
  6. Validation of coupled ATHLET-OpenFOAM simulation on a large-scale single- and two-phase flow experiment
  7. CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges
  8. Implementation of the preCICE coupling interface for AC2/ATHLET
  9. Large-scale PANDA facility – radiation experiments and CFD calculations
  10. Overview on GRS CFD activities related to containment applications
  11. Calendar of events
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 11.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/kern-2023-0090/pdf
Scroll to top button