Thermal hydraulic considerations of nuclear reactor systems: Past, present and future challenges

  • Guan Heng YeohEmail author
Review Article


Thermal hydraulic analysis of nuclear reactor core and its associated systems can be performed using analysis system, subchannel or computational fluid dynamics (CFD) codes to estimate the different thermal hydraulic safety margins. The safety margins and operating power limits under different conditions of the primary as well as secondary cooling system such as the system pressure, coolant inlet temperature, coolant flow rate, and thermal power and its distributions are considered as key parameters for thermal hydraulic analysis. Considering the complexity of rod bundle geometry, boiling heat transfer and different turbulent scales bring about the many challenges in performing the thermal hydraulic analysis to ensure the safe design and operation of nuclear reactor systems under normal and abnormal conditions. A comprehensive review is presented of past, present and future challenges in state-of-the-art thermal hydraulic analysis c overing various aspects of experimental, analytical and computational approaches.


nuclear reactor systems thermal hydraulic analysis critical heat flux 


  1. Abderrahim, H., Baeten, P., Fernandez, R., De Bruyn, D. 2010. MYRRHA: An innovative and unique irradiation research facility. In: Proceedings of the 11IEMPT.Google Scholar
  2. Abro, E., Johansen, G. 1999. Improved void fraction determination by means of multibeam gamma-ray attenuation measurements. Flow Meas Instrum, 10: 99–108.Google Scholar
  3. Agee, L. J., Duffey, R. B., Hughes, E. D., et al. 1978. Some aspects of two-fluid models for two-phase flow and their numerical solution. In: Proceedings of the 2nd CSNI Specialists Meeting on Transient Two-Phase Flow.Google Scholar
  4. Albrecht, R. W., Crowe, R. D., Dailey, D., Damborg, M. J. 1982. Measurement of two-phase flow properties using the nuclear reactor instrument. Prog Nucl Energy, 9: 37–50.Google Scholar
  5. Anglart, H., Caraghiaur, D. 2011. CFD modeling of boiling annularmist flow for dryout investigations. Multiphase Sci Technol, 23: 22–251.Google Scholar
  6. Anglart, H., Nylund, O. 1996. CFD application to prediction of void distribution in bubbly flows in rod bundles. Nucl Eng Des, 163: 81–98.Google Scholar
  7. Anh, K.-I., Kin, D.-H. 2003. A state-pf-the-art review of the reactor lower head models employed in three representative U.S. severe accident codes. Prog Nucl Energy, 3: 361–382.Google Scholar
  8. Ardron, K. H., Banerjee, S. 1986. Flooding in an elbow between a vertical and a horizontal or near horizontal pipe, Part I. Theory. Int J Multiphase Flow, 12: 543–558.Google Scholar
  9. Asmolov, V. G., Khabenski, V. B., Bechta, S. V., et al. 2003. MA-3 and MA-4 tests: Zirconium and uranium partitioning between oxidic and metallic phases of molten corium. OECD MASCA Project MP-TR-9, Russian Research Center, Kurchatov Institute.Google Scholar
  10. Baglietto, E., Ninokata, H. 2004. CFD modeling of secondary flows in fuel rod bundles. NUTHOS-6.Google Scholar
  11. Baglietto, E., Ninokata, H. 2005. A turbulence model study for simulating flow inside tight lattice rod bundles. Nucl Eng Des, 235: 773–784.Google Scholar
  12. Baglietto, E., Ninokata, H., Misawa, T. 2006. CFD and DNS methodologies development for fuel bundle simulations. Nucl Eng Des, 236: 1503–1510.Google Scholar
  13. Banerjee, S., Chan, A. M. C. 1980. Separated flow model I. Analysis of the averaged and local instantaneous formulations. Int J Multiphase Flow, 6: 1–24.zbMATHGoogle Scholar
  14. Bankoff, S. G., Lee, S. C. 1985. A brief review of countercurrent flooding models applicable to PWR geometries. Nucl Safety, 26: 139–152.Google Scholar
  15. Banowski, M., Beyer, M., Szalinski, L., Lucas, D., Hampel, U. 2016. Comparative study of ultrafast X-ray tomography and wire-mesh sensors for vertical gas-liquid pipe flows. Flow Meas Instrum, 53: 95–106.Google Scholar
  16. Belfroid, S. P. C., Cargnelutti, M. F., Schiferli, W., van Osch, M. 2010. Forces on bends and T-joints due to multiphase flow. In: Proceedings of the ASME 2010 3rd Joint US–European Fluids Engineering Summer Meeting.Google Scholar
  17. Bennett, A. W., Hewitt, G. F., Kearsey, H. A., Keeys, R. K. F., Lacey, P. M. C. 1965. Flow visualization studies of boiling at high pressure. Proc Inst Mech Engrs, 180: 260–270.Google Scholar
  18. Bergles, A. E., Roos, J. P., Bourne, J. G. 1968. Investigation of boiling flow regimes and critical heat flux. NYO-3304-13, Dynatech Corp.Google Scholar
  19. Besnard, D. C., Harlow, F. H. 1988. Turbulence in multiphase flow. Int J Multiphase Flow, 14: 679–699.zbMATHGoogle Scholar
  20. Bestion, D. 2014. The difficult challenge of a two-phase CFD modelling for all flow regimes. Nucl Eng Des, 279: 116–125.Google Scholar
  21. Biemüller, M., Meyer, L., Rehme, K. 1996. Large eddy simulation and measurement of the structure of turbulence in two rectangular channels connected by a gap. In: Proceedings of the 3rd International Symposium on Engineering Turbulence Modelling and Experiments, 249–258.Google Scholar
  22. Bourne, J. A., Bergles, A. E., Tong, L. S. 1973. Review of two-phase flow instabilities. Nucl Eng Des, 25: 165–192.Google Scholar
  23. Boyer, C., Duquenne, A. M., Wild, G. 2002. Measuring techniques in gas–liquid and gas–liquid–solid reactors. Chem Eng Sci, 57: 3185–3215.Google Scholar
  24. Buongiorno, J., Hu, L. W., Kim, S. J., Hannink, R., Truong, B., Forrest, E. 2008. Nanofluids for enhanced economics and safety of nuclear reactors: An evaluation of the potential features, issues, and research gap. Nucl Technol, 162: 80–91.Google Scholar
  25. Burger, M., Cho, S. H., Berg, E. V., Schatz, A. 1995. Breakup of melt jets as pre-condition for premixing: Modeling and experimental verification. Nucl Eng Des, 155: 15–25.Google Scholar
  26. Caraghiaur, D. 2012. On drops and turbulence in nuclear fuel assemblies of boiling water reactors. Ph.D. Thesis. KTH.Google Scholar
  27. Cargenlutti, M. F., Belfroid, S. P. C., Schiferli, W. 2010. Two-phase flow-induced forces on bends in small scale tubes. J Press Vess Technol, 132: 1–7.Google Scholar
  28. Carver, M. B., Tahir, A., Rowe, D. S., Tapucu, A., Ahmad, S. Y. 1984. Computational analysis of two-phase flow in horizontal bundles. Nucl Eng Des, 82: 215–226.Google Scholar
  29. Chabot, J., Farag, H., de Lasa, H. 1998. Fluid dynamics of bubble columns at elevated temperature modelling and investigation with refractive fiber optic sensors. Chem Eng J, 70: 105–113.Google Scholar
  30. Chandra, L., Roelofs, F., Houkema, M., Jonker, B. 2009. A stepwise development and validation of a RANS based CFD modelling approach for the hydraulic and thermal-hydraulic analyses of liquid metal flow in a fuel assembly. Nucl Eng Des, 239: 1988–2003.Google Scholar
  31. Chang, D., Tavoularis, S. 2008. Simulations of turbulence, heat transfer and mixing across narrow gaps between rod-bundle subchannels. Nucl Eng Des, 238: 109–123.Google Scholar
  32. Chelemer, H., Hochreiter, L. E., Boman, L. H., Chu, P. T. 1977. An improved thermal-hydraulic analysis method for rod bundle cores. Nucl Eng Des, 41: 219–229.Google Scholar
  33. Cheng, X., Muller, U. 2003. Review on critical heat flux in water cooled reactors. FZKA-6825, Forschngszentrum Karlsruhe GmbH, Karlsruhe.Google Scholar
  34. Cheung, S. C. P., Vahaji, S., Yeoh, G. H., Tu, J. Y. 2014. Modeling subcooled flow boiling in vertical channels at low pressures— Part 1: Assessment of empirical correlations. Int J Heat Mass Transfer, 75: 736–753.Google Scholar
  35. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2007a. On the modeling of population balance in isothermal vertical bubbly flows—Average bubble number density approach. Chem Eng Proc, 46: 742–756.Google Scholar
  36. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2007b. On the numerical study of isothermal bubbly flow using two population balance approaches. Chem Eng Sci, 31: 164–1072.Google Scholar
  37. Cheung, S. C. P., Yeoh, G. H., Tu, J. Y. 2008. Population balance modelling of bubbly flows considering the hydrodynamics and thermomechanical processes. AIChE J, 54: 1689–1710.Google Scholar
  38. Choi, K. H., Lee, W. K. 1990. Comparison of probe methods for measurement of bubble properties. Chem Eng Commun, 91: 35–47.Google Scholar
  39. Chu, I. C., Chung, H. J., Lee, S. 2011. Flow-induced vibration of nuclear steam generator u-tubes in two-phase flow. Nucl Eng Des, 241: 1508–1515.Google Scholar
  40. Colombo, M., Fairweather, M. 2016. Accuracy of Eulerian–Eulerian, two-fluid CFD boiling models of subcooled boiling flows. Int J Heat Mass Transfer, 103: 28–44.Google Scholar
  41. Cooper, K. D., Hewitt, G. F., Pinchin, B. 1963. Photography of twophase flow. AERE-R4301.Google Scholar
  42. Corradini, M. L. 1991. Vapor explosion: A review of experiments for accident analysis. Nucl Safety, 32: 337–362.Google Scholar
  43. Corradini, M. L., Kim, B. J., Oh, M. D. 1988. Vapor explosions in light water reactor: A review of theory and modeing. Prog Nucl Energy, 22: 1–117.Google Scholar
  44. Crowe, R. D., Eisenhawer, S. W., McAfee, F. D., Albrecht, R. W. 1977. A study of two-phase flow characteristics using reactor noise techniques. Prog Nucl Energy, 1: 85–97.Google Scholar
  45. De Bertodano, M. L. 1994. Countercurrent gas–liquid flow in a pressurized water reactor hot leg. Nucl Sci Eng, 117: 126–133.Google Scholar
  46. Deendarlianto Höhne, T., Lucas, D., Vallée, C. 2010. Numerical simulation of air–water counter-current two-phase flow in a model of the hot-leg of a pressurized water reactor (PWR). In: Proceeding of the 7th International Conference of the Multiphase Flow.Google Scholar
  47. Deendarlianto Höhne, T., Lucas, D., Vierow, K. 2012. Gas–liquid countercurrent two-phase flow in a PWR led: A comprehensive research review. Nucl Eng Des, 243: 214–233.Google Scholar
  48. Deendarlianto Vallée, C., Lucas, D., Beyer, M., Pietruske, H., Carl, H. 2008. Experimental study on the air/water counter-current flow limitation in a model of the hot leg of a pressurized water reactor. Nucl Eng Des, 238: 3389–3402.Google Scholar
  49. Delhaye, J. M., Achard J. L. 1976. On the averaging operators introduced in two-phase flow modelling. In: Proceedings of the CSNI Specialists Meeting on Transient Two-Phase Flow.Google Scholar
  50. Dominguez-Ontiveros, E. E., Hassan, Y. A., Conner, M. E., Karoutas, Z. 2012. Experimental benchmark data for PWR rod bundle with spacer-grids. Nucl Eng Des, 253: 396–405.Google Scholar
  51. Dominguez-Ontiveros, E., Fortenberry, S., Hassan, Y. A. 2010. Experimental observations of flow modifications in nanofluid boiling utilizing particle image velocimetry. Nucl Eng Des, 240: 299–304.Google Scholar
  52. Doroshchuk, V. E., Levitan, I. L., Lantzman, F. P. 1975. Investigation into Burnout in uniformly heated tubes. ASME Paper 75-WA/HT-22.Google Scholar
  53. Drew, D. A. 1983. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech, 15: 261–291.Google Scholar
  54. Drew, D. A., Passman, S. L. 1999. Theory of Multicomponent Fluids. Springer-Verlag, Berlin.zbMATHGoogle Scholar
  55. Feenstra, P., Weaver, D. S., Nakamura, T. 2009. Two-phase flow induced vibration of parallel triangular tube arrays with asymmetric support stiffness. J Press Vess Technol, 131: 1–9.Google Scholar
  56. Fletcher, D. F. 1995. Steam explosion triggering: A review of theoretical and experimental investigation. Nucl Eng Des, 155: 27–36.Google Scholar
  57. Frank, T., Shi, J., Burns, F. A. D. 2004. Validation of eulerian multiphase flow models for nuclear safety application. In: Proceedings of the 3rd Symposium on Two-Phase Modeling and Experimentation.Google Scholar
  58. Geweke, M., Beckmann, H., Mewes, D. 1992. Experimental studies of two-phase flow. In: Proceeding of the European Two-Phase Flow Group Meeting.Google Scholar
  59. Ginox, J. J. 1978. Two-Phase Flows and Heat Transfer with Application to Nuclear Reactor Design Problems. Hemisphere Publishing Corporation.Google Scholar
  60. Glaeser, H. 1992. Downcomer and tie plate countercurrent flow in the upper plenum test facility (UPTF). Nucl Eng Des, 133: 259–283.Google Scholar
  61. Gluck, M. 2007. Sub-channel analysis with F-COBRA-TF-Code validation and approaches to CHF prediction. Nucl Eng Des, 237: 655–667.Google Scholar
  62. Groeneveld, D. C., Leung, L. K. H., Kirillov, P. L., Bobkov, V. P., Smogalov, I. P., Vinogradov, V. N., Huang, X. C., Royer, E. 1996. The 1995 look-up table for critical heat flux in tubes. Nucl Eng Des, 163: 1–23.Google Scholar
  63. Groeneveld, D. C., Shan, J. Q., Vasic, A. Z., Leung, L. K. H., Durmayaz, A., Yang, J., Cheng, S. C., Tanase, A. 2007. The 2006 CHF look-up table. Nucl Eng Des, 237: 1909–1922.Google Scholar
  64. Hewitt, G. F., Roberts, D. N. 1969. Studies of two-phase flow patterns by simultaneous X-ray and flash photography. AERE-M 2159.Google Scholar
  65. Hibiki, T., Ishii, M., Xiao, Z. 2001. Axial interfacial area transport of vertical bubbly flows. Int J Heat Mass Transfer, 44: 1869–1888.Google Scholar
  66. Höhne, T. 2009. Experiments and numerical simulations of horizontal two-phase flow regimes. In: Proceeding of the 7th International Conference on CFD in the Minerals and Process Industries.Google Scholar
  67. Hubbard, M. G., Dukler, A. E. 1966. The characterization of flow regimes for horizontal two-phase flow. In: Proceedings of the 1966 Heat Transfer and Fluid Mechanics Institute, 100–121.Google Scholar
  68. Hibiki, T., Ishii, M. 1999. Experimental study on interfacial area transport in bubbly two phase flows. Int J Heat Mass Transfer, 42: 3019–3035.Google Scholar
  69. Hibiki, T., Ishii, M. 2000. Experimental study on hot-leg U-bend two-phase natural circulation in a loop with a large diameter pipe. Nucl Eng Des, 195: 69–84.Google Scholar
  70. Hibiki, T., Ishii, M. 2002. Development of one-group interfacial area transport equation in bubbly flow systems. Int J Heat Mass Transfer, 45: 2351–2372.zbMATHGoogle Scholar
  71. Hibiki, T., Ishii, M. 2003a. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Int J Heat Mass Transfer, 46: 4935–4948.zbMATHGoogle Scholar
  72. Hibiki, T., Ishii, M. 2003b. One-dimensional drift-flux model for twophase flow in a large diameter pipe. Int J Heat Mass Transfer, 46: 1773–1790.zbMATHGoogle Scholar
  73. IAEA-TECDOC-1451. 2005. Innovative small and medium sized reactors: Design features, safety approaches and R&D trends.Google Scholar
  74. Ishida, I., Kusunoki, T., Murata, H., Yokomura, T., Kobayashi, M., Nariai, H. 1990. Thermal hydraulic behavior of a marine reactor under oscillations. Nucl Eng Des, 120: 213–225.Google Scholar
  75. Ishii, M., Hibiki, T. 2011. Thermo-fluid Dynamics of Two-phase Flow, 2nd edn. Springer-Verlag, Berlin.zbMATHGoogle Scholar
  76. Jones, O. C., Zuber, N. 1974. Statistical methods for measurement and analysis in two-phase flow. In: Proceedings of the 5th International Heat Transfer Conference, 200–204.Google Scholar
  77. Jones, O. C., Zuber, N. 1975. The interrelation between void fraction fluctuations and flow patterns in two-phase flow. Int J Multiphase Flow, 2: 273–306.Google Scholar
  78. Joseph, D. D., Lundgren, T. S., Jackson, R., Saville, D. A. 1990. Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. Int J Multiphase Flow, 16: 35–42.zbMATHGoogle Scholar
  79. JSME. 2003. Flow Induced Vibrations—Classification and Lessons from Practical Experiences. Gihondo-Publishing Co. Ltd.Google Scholar
  80. Kanizawa, F. T., Oliveira, L. P. R., Ribatski, G. 2012. State of the art review on flow patterns, superficial void fraction and flow induced vibration during two-phase flows across tube bundles. In: Proceedings of the ASME 2012 Fluids Engineering Division.Google Scholar
  81. Kinoshita, I., Utanohara, Y., Murase, M., Minami, N., Tomiyama, A. 2009. Numerical calculations on countercurrent gas–liquid flow in a PWR hot leg (2) steam–water flow under PWR plant conditions. In: Proceedings of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.Google Scholar
  82. Kolev, N. I. 2005. Multiphase Flow Dynamics 1: Fundamentals, 2nd edn. Springer-Verlag, Berlin.zbMATHGoogle Scholar
  83. Kondic, N. D., Lassahn, G. D. 1978. Nonintrusive density distribution measurement in dynamic high temperature systems. In: Proceedings of the 24th International Instrumentation Symposium.Google Scholar
  84. Kosaly, G., Albrecht, R. W., Crowe, R. D., Dailey, D. 1982. Neutronic response to two-phase flow in a nuclear reactor. Prog Nucl Energy, 9: 23–36.Google Scholar
  85. Konno, H., Saito, K. 1985. Identification of non-linear random vibration of the structural components in nuclear reactors. Prog Nucl Energy, 15: 331–339.Google Scholar
  86. Krepper, E., Frank, T., Lucas, D., Prasser, H.-M., Zwart, P. J. 2007a. Inhomogeneous MUSIG model—A population balance approach for polydispersed bubbly flows. In: Proceedings of the 6th International Conference on Multiphase Flow.Google Scholar
  87. Krepper, E., Končar, B., Egorov, Y. 2007b. CFD modelling of subcooled boiling-concept, validation and application to fuel assembly design. Nucl Eng Des, 237: 716–731.Google Scholar
  88. Krepper, E., Rzehak, R., Lifante, C., Frank, T. 2013. CFD for subcooled flow boiling: Coupling wall boiling and population balance models. Nucl Eng Des, 255: 330–346.Google Scholar
  89. Kataoka, I., Ishii, M. 1987. Drift-flux model for large diameter pipe and new correlation for pool void fraction. Int J Heat Mass Transfer, 30: 1927–1939.Google Scholar
  90. Kawaji, M., Thomson, L. A., Krishnan, V. S. 1991. Countercurrent flooding in vertical to inclined pipes. Exp Heat Trans, 4: 95–110.Google Scholar
  91. Kawaji, M., Lotocki, P. A., Krishnan, V. S. 1993. Countercurrent flooding in pipes containing multiple elbows and an orifice. JSME Int Ser B, 36: 397–403.Google Scholar
  92. Kocamustafaogullari, G., Ishii, M. 1995. Foundation of the interfacial area transport equation and its closure relations. Int J Heat Mass Transfer, 38: 481–493.zbMATHGoogle Scholar
  93. Krepper, E., Lucas, D., Prasser, H.-M. 2005. On the modelling of bubbly flow in vertical pipes. Nucl Eng Des, 235: 597–611.zbMATHGoogle Scholar
  94. Kurul, N., Podowski, M. Z. 1990. Multi-dimensional effects in forced convection sub-cooled boiling. In: Proceedings of the 9th Heat Transfer Conference, 21–26.Google Scholar
  95. Lahey, R. T. Jr., Drew, D. A. 1988. The three-dimensional time and volume averaged conservative equations of two-phase flow. In: Advances in Nuclear Science and Technology. Lewins, J., Becker, M. Eds. Springer, 1–69.Google Scholar
  96. Lassahn, G. D. 1977. LOFT three-beam densitometer data interpretation. EG&G Idaho, Inc., TREE NUREG-1111.Google Scholar
  97. Lay, J. H., Dhir, V. K. 1995. Shape of a vapor steam during nucleate boiling of saturated liquids. Trans ASME J Heat Transfer, 117: 394–401.Google Scholar
  98. Lee, K., Lee, K. H., Lee, J. I., Jeong, Y. H., Lee, P. S. 2013. A new design concept for offshore nuclear power plants with enhanced safety features. Nucl Eng Des, 254: 129–141.Google Scholar
  99. Lee, Y. G., Won, W. Y., Lee, B. A., Kim, S. 2017. A dual conductance sensor for simultaneous measurement of void fraction and structure velocity of downward two-phase flow in a slightly inclined pipe. Sensors, 17: 1063.Google Scholar
  100. Lo, S. M. 1996. Application of population balance to CFD modeling of bubbly flow via the MUSIG model. AEAT-1096, AEA Technology.Google Scholar
  101. Lo, S., Zhang, D. 2009. Modelling of break-up and coalescence in bubbly two-phase flows. J Comput Multiphase Flow, 1: 23–38.Google Scholar
  102. Mandhane, J. M., Gregory, G. A., Aziz, K. 1974. A flow pattern map for gas–liquid flow in horizontal pipes. Int J Multiphase Flow, 1: 537–553.Google Scholar
  103. Merzari, E., Ninokata, H., Baglietto, E. 2007. Unsteady Reynolds averaged Navier–Stokes simulation for an accurate prediction of the flow insight tight rod bundles. In: Proceedings of the 12th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.Google Scholar
  104. Merzari, E., Ninokata, H., Baglietto, E. 2008. Numerical simulation of flows in tight lattice fuel bundles. Nucl Eng Des, 238: 1703–1719.Google Scholar
  105. Minami, N., Murase, M., Nishiwaki, D., Tomiyama, A. 2008. Countercurrent gas–liquid flow in a rectangular channel simulating a PWR hot leg (2): Analytical evaluation of counter-current flow limitation. Jpn J Multiphase Flow, 22: 413–422.Google Scholar
  106. Minami, N., Murase, M., Tomiyama, A. 2010. Countercurrent gas–liquid flow in a PWR hot leg under reflux cooling (II) numerical simulation of 1/15-scale air–water tests. J Nucl Sci Tech, 47: 149–155.Google Scholar
  107. Minami, N., Utanohara, Y., Kinoshita, I., Murase, M., Tomiyama, A. 2009. Numerical calculations on countercurrent gas–liquid flow in a PWR hot leg (1) air–water flow in a 1/15-scale model. In: Proceeding of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.Google Scholar
  108. Mishima, K., Ishii, M. 1984. Flow regime transition criteria for upward two-phase flow in vertical tubes. Int J Heat Mass Transfer, 27: 723–737.Google Scholar
  109. Mitra, D., Dhir, V. K., Catton, I. 2009. Fluid elastic instability in tube arrays subjected to air-water and steam-water cross-flow. J Fluids Struct, 25: 1213–1235.Google Scholar
  110. Miwa, S., Liu, Y., Hibiki, T., Ishii, M., Kondo, Y., Morita, H., Tanimoto, K. 2014. Two-phase flow induced vibration. In: Proceedings of the 22nd International Conference on Nuclear Engineering.Google Scholar
  111. Moorthi, A., Sharma, A. K., Velusamy, K. 2018. A review of subchannel thermal hydraulic codes for nuclear reactor core and future directions. Nucl Eng Des, 332: 329–344.Google Scholar
  112. Morel, C., Laviéville, J. M. 2009. Modeling of multisize bubbly flow and application to the simulation of boiling flows with the Neptune CFD code. Sci Tech Nucl Installation, 2009: 953527.Google Scholar
  113. Murase, M., Utanohara, Y., Kinoshita, I., Minami, N., Tomiyama, A. 2009. Numerical calculations on countercurrent air–water flow in small-scale models of a PWR hot leg using a VOF model. In: Proceeding of the 17th International Conference on Nuclear Engineering.Google Scholar
  114. Nariai, T., Tomiyama, A., Vallee, C., Lucas, D., Murase, M. 2010. Countercurrent flow limitation in a scale-down model of a PWR hot leg. In: Proceeding of the 8th International Topical meeting on Nuclear Thermal-Hydraulics, Operation and Safety.Google Scholar
  115. Ninokata, H., Atake, N., Baglietto, E., Misawa, T., Kano, T. 2004. Direct numerical simulation of turbulence flows in a subchannel of tight lattice fuel pin bundles of nuclear reactors. Available at Scholar
  116. Ninokata, H., Merzari, E. 2007. Computational fluid dynamics and simulation based-design approach for tight lattice nuclear fuel pin subassemblies. NURETH-12.Google Scholar
  117. Nusret, A. 2007. Selected examples of natural circulation for small break LOCA and some severe accidents. IAEA course on natural circulation in water-cooled nuclear power plants, International Centre for Theoretical Physics, Trieste, Italy.Google Scholar
  118. Ohnuki, A., Adachi, H., Murao, Y. 1988. Scale effects on counter current gas–liquid flow in a horizontal tube connected to an inclined riser. Nucl Eng Des, 107: 283–294.Google Scholar
  119. Ohnuki, A., Akimoto, H. 2000. Experimental study on transition of flow pattern and phase distribution in upward air-water twophase flow along a large vertical pipe. Int J Multiphase Flow, 26: 367–386.zbMATHGoogle Scholar
  120. Okano, Y., Koshizuka, S., Oka, Y. 1997. Safety analysis of a supercritical pressure, light water cooled and moderated reactor with double tube water rods. Ann Nucl Energy, 24: 1447–1456.Google Scholar
  121. Olmos, E., Gentric, C., Vial, Ch., Wild, G., Midoux, N. 2001. Numerical simulation of multiphase flow in bubble column reactors. Influence of bubble coalescence and break-up. Chem Eng Sci, 56: 6359–6365.Google Scholar
  122. Panton, R. J. 1968. Flow properties for the continuum viewpoint of a non-equilibrium gas particle mixture. J Fluid Mech, 31: 273–304.zbMATHGoogle Scholar
  123. Patel, P., Theofanous, T. G. 1976. Universal relations for bubble growth. Int J Heat Mass Transfer, 19: 425–429.Google Scholar
  124. Pettigrew, M. J., Taylor, C. E. 1994. Two-phase flow-induced vibration: An overview. J Press Vess Technol, 116: 233–253.Google Scholar
  125. Pettigrew, M. J., Taylor, C. E., Fisher, N. J., Yetisir, M., Smith, B. A. W. 1998. Flow-induced vibration: Recent findings and open questions. Nucl Eng Des, 185: 249–276.Google Scholar
  126. Pham, Q. T., Kim, T. I., Lee, S. S., Chang, S. H. 2012. Enhancement of critical heat flux using nanofluids for invessel retention-external vessel cooling. Appl Thermal Eng, 35: 157–165.Google Scholar
  127. Piper, T. C. 1974. Dynamic gamma attenuation density measurements. Aerojet Nuclear Co., ANCR-1160.Google Scholar
  128. Pochorecki, R., Moniuk, W., Bielski, P., Zdrojkwoski, A. 2001. Modeling of the coalescence/redispersion processes in bubble columns. Chem Eng Sci, 56: 6157–616.Google Scholar
  129. Pontaza, J. P., Menon, R. G. 2011. Flow-induced vibrations of subsea jumpers due to internal multi-phase flow. In: Proceedings of the 30th International Conference on Ocean, Offshore and Arctic Engineering.Google Scholar
  130. Prasser, H. M., Böttger, A., Zschau, J. 1998. A new electrode-mesh tomograph for gas liquid flows. Flow Meas Instrum, 9: 111–119.Google Scholar
  131. Prassinos, P. G., Liao C. K. 1979. An investigation of two-phase flow regimes in LOFT piping during loss-of-coolant experiments. EG&G Idaho, Inc., NUREG/CR-0606, TREE-1244.Google Scholar
  132. Pasamehmetoglu, K. O., Gunnerson, F. S. 1985. Theoretical considerations of transient critical heat flux. In: Proceedings of the 3rd International Topical Meeting on Reactor-Thermal Hydraulics, 2: Paper 18-F.Google Scholar
  133. Pasamehmetoglu, K. O., Nelson, R. A., Gunnerson, F. S. 1987. A theoretical prediction of critical heat flux in saturated pool boiling during power transients. Nonequilibrium Transport Phenomena, ASME, New York, HTD-77: 57–64.Google Scholar
  134. Prasad, G. V. D., Pandey, M., Kalra, M. S. 2007. Review of research on flow instabilities in natural circulation boiling systems. Prog Nucl Energy, 49: 429–451.Google Scholar
  135. Rahim, R. A., Rahiman, M. F., Chan, K., Nawawi, S. 2007. Non-invasive imaging of liquid/gas flow using ultrasonic transmission-mode tomograph. Sens Actuators A, 135: 337–345.Google Scholar
  136. Roelofs, F., Gopala, V. R., Jayaraju, S., Shams, A., Konen, E. 2013. Review of fuel assembly and pool thermal hydraulics for fast reactors. Nucl Eng Des, 265: 1205–1222.Google Scholar
  137. Rouhani, S. Z., Sohal, M. S. 1983. Two-phase flow patterns: A review of research letters. Prog Nucl Energy, 11: 219–259.Google Scholar
  138. Rowinski, M. K., Zhao, J., White, T. J., Soh, Y. C. 2018. Safety analysis of super-critical water reactors—A review. Prog Nucl Energy, 106: 87–101.Google Scholar
  139. Sasakawa, T., Serizawa, A., Kawara, Z. 2005. Fluid-elastic vibration in two-phase cross flow. Exp Thermal Fluid Sci, 29: 403–413.Google Scholar
  140. Schlegel, J. P., Hibiki, T., Shen, X., Appathurai, S., Subramani, H. 2017. Prediction of interfacial area transport in a coupled two fluid model computation. J Nucl Sci Technol, 54: 58–73.Google Scholar
  141. Schlegel, J. P., Macke, C., Hibiki, T., Ishii, M. 2013. Modified distribution parameter for churn-turbulent flows in large diameter channels. Nucl Eng Des, 263: 138–150.Google Scholar
  142. Schlegel, J. P., Miwa, S., Chen, S., Hibiki, T., Ishiii, M. 2012. Experimental study of two phase flow structure in large diameter pipes. Exp Therm Fluid Sci, 41: 12–22.Google Scholar
  143. Schlegel, J. P., Sawant, P., Paranjape, S., Ozar, B., Hibiki, T., Ishii, M. 2009. Void fraction and flow regime in adiabatic upward twophase flow in large diameter vertical pipes. Nucl Eng Des, 239: 2864–2874.Google Scholar
  144. Seidel, T., Vallée, C., Lucas, D., Beyer, M., Deendarlianto. 2010. Two-phase flow experiments in a model of the hot leg of a pressurised water reactor. Wissenschaftlich-Technische Berichte/Forschungszentrum Dresden-Rossendorf, FZD-531.Google Scholar
  145. Sha, W. T. 1980. An overview of rod-bundle thermal-hydraulic analysis. Nucl Eng Des, 62: 1–24.Google Scholar
  146. Shen, X., HIbiki, T. 2013. One-group interfacial area transport equation and its sink and source terms in narrow rectangular channel. Int J Heat Fluid Flow, 44: 312–326.Google Scholar
  147. Shen, X., Mishima, K., Nakamura, H. 2010a. Measurement of twophase flow in a vertical large diameter pipe using hot-film anemometer. Jpn J Multi-phase Flow, 23: 605–613. (in Japanese)Google Scholar
  148. Shen, X., Mishima, K., Nakamura, H. 2010b. Flow-induced void fraction transition phenomenon in two-phase flow. In: Proceedings of the 18th International Conference on Nuclear Engineering.Google Scholar
  149. Shen, X., Saito, Y., Mishima, K., Nakamura, H. 2006. A study on the characteristics of upward air-water two-phase flow in a large pipe. Exp Therm Fluid Sci, 31: 21–36.Google Scholar
  150. Shen, X., Schlegel, J. P., Hibiki, T., Nakamura, H. 2018. Some characteristics of gas–liquid two-phase flow in vertical largediameter channels. Nucl Eng Des, 333: 87–98.Google Scholar
  151. Shi, J. M., Zwart, P. J., Frank, T., Rohde, U., Prasser, H. M. 2004. Development of a multiple velocity multiple size group model for poly-dispersed multiphase flows. Annual Report of Institute of Safety Research, Forschungszentrum Rossendorf, Germany.Google Scholar
  152. Siddiqui, H., Banerjee, S., Ardron, K. H. 1986. Flooding in an elbow between a vertical and a horizontal or near horizontal pipe, Part I. Experiments. Int J Multiphase Flow, 12: 531–541.Google Scholar
  153. Smith, T. R. 2002. Two-group interfacial area transport equation in large diameter pipes. Ph.D. Thesis. Purdue University.Google Scholar
  154. Smith, T. R., Schlegel, J. P., Hibiki, T., Ishii, M. 2012. Mechanistic modelling of interfacial area transport in large diameter pipes. Int J Multiphase Flow, 47: 1–16.Google Scholar
  155. Son, G., Dhir, V. K. 2008. Numerical simulation of nucleate boiling on a horizontal surface at high heat fluxes. Int J Heat Mass Transfer, 51: 2566–2582.zbMATHGoogle Scholar
  156. Son, G., Dhir, V. K., Ramanujapu, N. 1999. Dynamics and heat transfer associated with a single bubble during nucleate boiling on a horizontal surface. Trans ASME J Heat Transfer, 121: 623–631.Google Scholar
  157. Sorokin, A. P., Efanov, A. D., Ivanov, E. F., Martsinyuk, D. E., Bogoslovskaya, G. P. 1999. Heat transfer during boiling of a liquid metal during emergency cool down of a fast neutron reactor. At Energy, 87: 801–807.Google Scholar
  158. Staub, F. W., Zuber, N. 1964. A program of two-phase flow investigation. General Electric Co., Report, EURAEC 1171, GEAP 4631.Google Scholar
  159. Subbotin, V., Sorokin, D., Kudryavtsev, A. 1970. Generalized relationship for calculating heat transfer in the developed boiling of alkali metals. At Energy, 29: 730–731.Google Scholar
  160. Sun, X., Smith, T. R., Kim, S., Ishii, M., Uhle, J. 2002. Interfacial area of bubbly flow in a relatively large diameter pipe. Exp Therm Fluid Sci, 27: 97–109.Google Scholar
  161. Taitel, Y., Barnea, D., Dukler, A. E. 1980. Modeling flow pattern transitions for steady upward gas–liquid flow in vertical tubes. AIChE J, 26: 345–354.Google Scholar
  162. Taitel, Y., Dukler, A. E. 1976. A model for predicting flow regime transition iii horizontal and near horizontal gas-liquid flow. AIChE J, 22: 47–55.Google Scholar
  163. Takada, N., Misawa, M., Tomiyama, A., Fujiwara, S. 2000. Numerical simulation of two- and three-dimensional two-phase fluid motion by lattice Boltzmann method. Comp Phys Comm, 129: 233–246.MathSciNetzbMATHGoogle Scholar
  164. Taylor, C. E., Pettigrew, M. J. 2001. Effect of flow regime and void fraction on tube bundle vibration. J Press Vess Technol, 123: 407–413.Google Scholar
  165. Thakrar, R., Murallidharan, J., Walker, S. P. 2015. Simulations of high-pressure subcooled boiling flows in rectangular channels. In: Proceedings of the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.Google Scholar
  166. Theofanous, T. G. 1980. The boiling crisis in nuclear reactor safety and performance. Int J Multiphase Flow, 6: 69–95.Google Scholar
  167. Theofanous, T. G., Boher, T. H., Chang, M. C., Patel, P. 1978. Experiments and universal growth relations for vapor bubbles with micro-layers. J Heat Transfer, 100: 41–48.Google Scholar
  168. Theofanous, T. G., Liu, C., Additon, S., Angelini, S., Kynalainen, O., Salmassi, T. 1994. In-vessel coolability and retention of a core melt. DOE/ID-l0460, Vol. 1: Peer Review Version.Google Scholar
  169. Theofanous, T. G., Liu, C., Additon, S., Angelini, S., Kynalainen, O., Salmassi, T. 1995. In-vessel coolability and retention of a core melt. DOE/ID-10460, Vol. 2: Peer Re-Review Version.Google Scholar
  170. Thomas, S., Narayanan, C., Lakehal, D. 2013. Progress in modelling convective boiling flows using the n-phase approach in TransAT. In: Proceedings of the 15th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics.Google Scholar
  171. Todreas, N. E., Kazimi, M. S. 2001. Nuclear Systems II-Elements of Thermal Hydraulic Design. Taylor and Francis.Google Scholar
  172. Tomiyama, A. 1998. Struggle with computational bubble dynamics. Multiphase Sci Tech, 10: 369–405.Google Scholar
  173. Tong, L. S., Hewitt, G. F. 1972. Overall view point of flow boiling CHF mechanisms. ASME Paper 72-HT-54.Google Scholar
  174. Tu, J. Y., Yeoh, G. H. 2002. On numerical modeling of low-pressure subcooled boiling flows. Int J Heat Mass Transfer, 45: 1197–1209.zbMATHGoogle Scholar
  175. Tu, J. Y., Yeoh, G. H., Park, G.-C., Kim, M.-O. 2005. On population balance approach for subcooled boiling flow prediction. ASME J Heat Transfer, 127: 253–264.Google Scholar
  176. Utanohara, Y., Kinoshita, I., Murase, M., Minami, N., Tomiyama, A. 2009. Effects of interfacial friction correlations on numerical calculations for countercurrent gas–liquid flow in a PWR hot leg. In: Proceeding of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics.Google Scholar
  177. Vernier, P., Delhaye, J. M. 1968. General two-phase flow equation applied to the thermohydrodynamics of boiling nuclear reactors. Acta Tech Belg Energie Primaire, 4: 3–43.Google Scholar
  178. Vince, M. A., Lahey, R. T. Jr. 1980. Flow regime identification and void fraction measurement techniques in two-phase flow. Rensselaer Polytechnic Institute, NUREG/CR-1692.Google Scholar
  179. Wang, M. J., Mayinger, F. 1995. Simulation and analysis of thermalhydraulic phenomena in a PWR hot leg related SBLOCA. Nucl Eng Des, 155: 643–652.Google Scholar
  180. Weisman, J., Duncan, D., Gibson, J., Crawford, T. 1979. Effects of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines. Int J Multiphase Flow, 5: 437–462.Google Scholar
  181. Weisman, J., Kang, S. Y. 1981. Flow pattern transitions in vertical and upwardly inclined tubes. Int J Multiphase Flow, 7: 271–291.Google Scholar
  182. Wu, J. M., Zhao, J. 2013. A review of nanofluid heat transfer and critical heat flux enhancement—Research gap to engineering application. Prog Nucl Energy, 66: 13–24.Google Scholar
  183. Wu, Q., Kim, S., Ishii, M., Beus, S. G. 1998. One-group interfacial area transport in vertical bubbly flow. Int J Heat Mass Transfer, 41: 1103–1112.zbMATHGoogle Scholar
  184. Wu, Y. W., Luo, S., Wang, L., Hou, Y., Su, G. H., Tuan, W., Qiu, S. 2018. Review on heat transfer and flow characteristics of liquid sodium (2): Two-phase. Prog Nucl Energy, 103: 151–164.Google Scholar
  185. Wulff, W. 2011. Critical review of conservation equations for twophase flow in the US NRC TRACE code. Nucl Eng Des, 241: 4237–4260.Google Scholar
  186. Yadigaroglu, G. 2014. CMFD and the critical-heat-flux grand challenge in nuclear thermal-hydraulics—A letter to the editor of this special issue. Int J Multiphase Flow, 67: 3–12.Google Scholar
  187. Yadigaroglu, G., Lahey, R. T. Jr. 1976. On the various forms of the conservation equations in two-phase flow. Int J Multiphase Flow, 2: 477–494.zbMATHGoogle Scholar
  188. Yamaji, A., Oka, Y., Ishiwatari, Y., Liu, J., Suzuki, M. 2006. Principle of rationalizing the criteria for abnormal transients of the Super LWR with fuel rod analyses. Ann Nucl Energy, 33: 984–993.Google Scholar
  189. Yamano, H., Tanaka, M., Kimura, N., Ohshima, H., Kamide, H., Watanabe, O. 2011. Development of flow induced vibration evaluation methodology for large diameter piping with elbow in Japan sodium-cooled fast reactor. Nucl Eng Des, 241: 4464–4475.Google Scholar
  190. Yan, B. H. 2017. Review of the nuclear reactor thermal hydraulic research in ocean motions. Nucl Eng Des, 313: 370–385.Google Scholar
  191. Yao, W., Morel, C. 2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. Int J Heat Mass Transfer, 47: 307–328.zbMATHGoogle Scholar
  192. Yeoh, G. H., Cheung, S. C. P., Tu, J. Y., Ho, M. K. M. 2008. Fundamental consideration of wall heat partition of vertical subcooled boiling flows. Int J Heat Mass Transfer, 51: 3840–3853.zbMATHGoogle Scholar
  193. Yeoh, G. H., Tu, J. Y. 2004. Population balance modelling for bubbly flows with heat and mass transfer. Chem Eng Sci, 59: 3125–3139.Google Scholar
  194. Yeoh, G. H., Tu, J. Y. 2005. Thermal-hydrodynamic modelling of bubbly flows with heat and mass transfer. AIChE J, 51: 8–27.Google Scholar
  195. Yeoh, G. H., Tu, J. Y. 2006a. Numerical modelling of bubbly flows with and without heat and mass transfer. Appl Math Model, 30: 1067–1095.zbMATHGoogle Scholar
  196. Yeoh, G. H., Tu, J. Y. 2006b. Two-fluid and population balance models for subcooled boiling flow. Appl Math Model, 30: 1370–1391.zbMATHGoogle Scholar
  197. Yeoh, G. H., Tu, J. Y. 2010. Computational Techniques for Multiphase Flows. Elsevier Science and Technology.Google Scholar
  198. Yeoh, G. H., Tu, J. Y. 2017. Basic theory and conceptual framework of multiphase flows. In: Handbook of Multiphase Flow Science and Technology. Yeoh, G. H. Ed. Springer Science: 1–47.Google Scholar
  199. Yeoh, G. H., Vahaji, S., Cheung, S. C. P., Tu, J. Y. 2014. Modeling subcooled flow boiling in vertical channels at low pressures—Part 2: Evaluation of mechanistic approach. Int J Heat Mass Transfer, 75: 754–768.Google Scholar
  200. Zhang, C., Pettigrew, M. J., Mureithi, N. W. 2007. Vibration excitation force measurements in a rotated triangular tube bundle subjected to two-phase cross flow. J Press Vess Technol, 129: 21–27.Google Scholar
  201. Zhou, L., Ge, C., Zan, Y. F., Yan, X., Chen, B. D. 2015. Study on generation expression for liquid force per unit mass under noninertial reference frame. Nucl Power Eng, 2: 37–41.Google Scholar

Copyright information

© Tsinghua University Press 2019

Authors and Affiliations

  1. 1.School of Mechanical and Manufacturing EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Australian Nuclear Science and Technology Organisation (ANSTO)Kirrawee DCAustralia

Personalised recommendations