One-dimensional drift-flux correlations for two-phase flow in medium-size channels

  • Takashi HibikiEmail author
Review Article


The drift-flux parameters such as distribution parameter and drift velocity are critical parameters in the one-dimensional two-fluid model used in nuclear thermal-hydraulic system analysis codes. These parameters affect the drag force acting on the gas phase. The accurate prediction of the drift-flux parameters is indispensable to the accurate prediction of the void fraction. Because of this, the current paper conducted a state-of-the-art review on one-dimensional drift-flux correlations for various flow channel geometries and flow orientations. The essential conclusions were: (1) a channel geometry affected the distribution parameter, (2) a boundary condition (adiabatic or diabatic) affected the distribution parameter in a bubbly flow, (3) the drift velocity for a horizontal channel could be approximated to be zero, and (4) the distribution parameter developed for a circular channel was not a good approximation to calculate the distribution parameter for a sub-channel of the rod bundle. In addition to the above, the review covered a newly proposed concept of the two-group drift-flux model to provide the constitutive equation to close the modified gas mixture momentum equation of the two-fluid model mathematically. The review was also extended to the existing drift-flux correlations applicable to a full range of void fraction (Chexel-Lellouche correlation and Bhagwat-Ghajar correlation).


drift-flux model interfacial drag force distribution parameter nuclear thermal-hydraulic analysis interfacial transport equation 


  1. Abbs, T., Hibiki, T. 2019. One-dimensional drift-flux correlation for vertical upward two-phase flow in a large size rectangular channel. Prog Nucl Energ, 110: 311–324.CrossRefGoogle Scholar
  2. Andersen, J. G. M., Chu, K. H. 1982. BWR refill-reflood program task 4.7: Constitutive correlations for shear and heat transfer for the BWR version of TRAC (No. NUREG/CR—2134). General Electric Co.Google Scholar
  3. Bajorek, S. 2008. TRACE/V5.0 theory manual; field equations, solutions methods, and physical models. United States Nuclear Regulatory Commission.Google Scholar
  4. Baotong, S., Rassame, S., Nilsuwankosit, S., Hibiki, T. 2019. Drift-flux correlation of oil-water flow in horizontal channels. J Fluid Eng, 141: 031301.CrossRefGoogle Scholar
  5. Barnea, D., Shoham, O., Taitel, Y., Dukler, A. E. 1980. Flow pattern transition for gas-liquid flow in horizontal and inclined pipes. Comparison of experimental data with theory. Int J Multiphase Flow, 6: 217–225.CrossRefGoogle Scholar
  6. Bhagwat, S. M., Ghajar, A. J. 2014. A flow pattern independent drift flux model based void fraction correlation for a wide range of gas-liquid two phase flow. Int J Multiphase Flow, 59: 186–205.CrossRefGoogle Scholar
  7. Borkowski, J. A., Wade, N. L., Rouhani, S. Z., Shumway, R. W., Weaver, W. L., Rettig, W. H., Kullberg, C. L. 1992. TRAC-BF1/MOD1 models and correlations (No. NUREG/CR—4391). Nuclear Regulatory Commission.Google Scholar
  8. Brooks, C. S., Hibiki, T., Ishii, M. 2012a. Interfacial drag force in one-dimensional two-fluid model. Prog Nucl Energ, 61: 57–68.CrossRefGoogle Scholar
  9. Brooks, C. S., Ozar, B., Hibiki, T., Ishii, M. 2012b. Two-group drift-flux model in boiling flow. Int J Heat Mass Transfer, 55: 6121–6129.CrossRefGoogle Scholar
  10. Brooks, C. S., Paranjape, S. S., Ozar, B., Hibiki, T., Ishii, M. 2012c. Two-group drift-flux model for closure of the modified two-fluid model. Int J Heat Fluid Flow, 37: 196–208.CrossRefGoogle Scholar
  11. Chexal, B., Lellouche, G., Horowitz, J., Healzer, J., Oh, S. 1991. The Chexal-Lellouche void fraction correlation for generalized applications. Nuclear Safety Analysis Center of the Electric Power Research Institute, USA.Google Scholar
  12. Chuang, T. J., Hibiki, T. 2015. Vertical upward two-phase flow CFD using interfacial area transport equation. Prog Nucl Energ, 85: 415–427.CrossRefGoogle Scholar
  13. Chuang, T. J., Hibiki, T. 2017. Interfacial forces used in two-phase flow numerical simulation. Int J Heat Mass Transfer, 113: 741–754.CrossRefGoogle Scholar
  14. Colebrook, C. F. 1939. Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. J Inst Civ Eng, 11: 133–156.CrossRefGoogle Scholar
  15. Goda, H., Hibiki, T., Kim, S., Ishii, M., Uhle, J. 2003. Drift-flux model for downward two-phase flow. Int J Heat Mass Transfer, 46: 4835–4844.CrossRefGoogle Scholar
  16. Grossetete, C. 1995. Caractérisation expérimentale et simulations de l’évolution d’un écoulement diphasique à bulles ascendant dans une conduite vertical. Ph.D. Thesis. Châtenay-Malabry, Ecole centrale de Paris, France.Google Scholar
  17. Hibiki, T., Ishii, M. 1999. Experimental study on interfacial area transport in bubbly two-phase flows. Int J Heat Mass Transfer, 42: 3019–3035.CrossRefGoogle Scholar
  18. Hibiki, T., Ishii, M. 2002a. Distribution parameter and drift velocity of drift-flux model in bubbly flow. Int J Heat Mass Transfer, 45: 707–721.Google Scholar
  19. Hibiki, T., Ishii, M. 2002b. Interfacial area concentration of bubbly flow systems. Chem Eng Sci, 57: 3967–3977.CrossRefGoogle Scholar
  20. Hibiki, T., Ishii, M. 2003. One-dimensional drift-flux model for two-phase flow in a large diameter pipe. Int J Heat Mass Transfer, 46: 1773–1790.CrossRefGoogle Scholar
  21. Hibiki, T., Ishii, M. 2009. Interfacial area transport equations for gas-liquid flow. J Comput Multiphase Flows, 1: 1–22.CrossRefGoogle Scholar
  22. Hibiki, T., Ishii, M., Xiao, Z. 2001. Axial interfacial area transport of vertical bubbly flows. Int J Heat Mass Transfer, 44: 1869–1888.CrossRefGoogle Scholar
  23. Hibiki, T., Mishima, K. 2001. Flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels. Nucl Eng Des, 203: 117–131.CrossRefGoogle Scholar
  24. Hibiki, T., Ozaki, T. 2017. Modeling of void fraction covariance and relative velocity covariance for upward boiling flow in vertical pipe. Int J Heat Mass Transfer, 112: 620–629.CrossRefGoogle Scholar
  25. Hibiki, T., Rong, S. T., Ye, M., Ishii, M. 2003. Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow. Int J Heat Mass Transfer, 46: 1409–1423.CrossRefGoogle Scholar
  26. Hibiki, T., Schlegel, J. P., Ozaki, T., Miwa, S., Rassame, S. 2018. Simplified two-group two-fluid model for three-dimensional two-phase flow computational fluid dynamics for vertical upward flow. Prog Nucl Energ, 108: 503–516.CrossRefGoogle Scholar
  27. Information System Laboratories. 2001. RELAP5/MOD3.3 code manual volume IV: Models and correlations. US NRC (NUREG/CR-5535/Rev 1-Vol.IV).Google Scholar
  28. Ishii, M. 1977. One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. Report No. ANL-77-47. Argonne National Laboratory, USACrossRefGoogle Scholar
  29. Ishii, M., Hibiki, T. 2010. Thermo-Fluid Dynamics of Two-Phase Flow, 2nd edn. Springer Science & Business Media.zbMATHGoogle Scholar
  30. Ishii, M., Mishima, K. 1984. Two-fluid model and hydrodynamic constitutive relations. Nucl Eng Des, 82: 107–126.CrossRefGoogle Scholar
  31. Julia, J. E., Hibiki, T. 2011. Flow regime transition criteria for two-phase flow in a vertical annulus. Int J Heat Fluid Flow, 32: 993–1004.CrossRefGoogle Scholar
  32. Julia, J. E., Hibiki, T., Ishii, M., Yun, B. J., Park, G. C. 2009. Drift-flux model in a sub-channel of rod bundle geometry. Int J Heat Mass Transfer, 52: 3032–3041.CrossRefGoogle Scholar
  33. Kalkach-Navarro, S. 1992. The mathematical modeling of flow regime transition in bubbly two-phase flow. Ph.D. Thesis. Rensselaer Polytechnic Institute, USA.Google Scholar
  34. 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.CrossRefGoogle Scholar
  35. Kondo, M., Kumamaru, H., Murata, H., Anoda, Y., Kukita, Y. 1993. Core void fraction distribution under high-temperature high-pressure boil-off conditions (No. JAERI-M-93-200). Japan Atomic Energy Research Institute.Google Scholar
  36. Liu, H., Hibiki, T. 2017. Flow regime transition criteria for upward two-phase flow in vertical rod bundles. Int J Heat Mass Transfer, 108: 423–433.CrossRefGoogle Scholar
  37. Liu, H., Pan, L. M., Hibiki, T., Zhou, W. X., Ren, Q. Y., Li, S. S. 2018. One-dimensional interfacial area transport for bubbly two-phase flow in vertical 5×5 rod bundle. Int J Heat Fluid Flow, 72: 257–273.CrossRefGoogle Scholar
  38. Liu, T. T. 1989. Experimental investigation of turbulence structure in two-phase bubbly flow. Ph.D. Thesis.Northwestern University, USA.Google Scholar
  39. Lokanathan, M., Hibiki, T. 2018. Flow regime transition criteria for co-current downward two-phase flow. Prog Nucl Energ, 103: 165–175.CrossRefGoogle Scholar
  40. Marchaterre, J. F. 1956. The effect of pressure on boiling density in multiple rectangular channels (Report No. ANL-5522). Argonne National Laboratory, USA.CrossRefGoogle Scholar
  41. 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.CrossRefGoogle Scholar
  42. Morooka, S. I., Yoshida, H., Inoue, A., Oishi, M., Aoki, T., Nagaoka, K. 1991. In-bundle void measurement of BWR fuel assembly by X-ray CT scanner. In: Proceedings of the 1st JSME/ASME Joint International Conference on Nuclear Engineering, Paper No. 38.Google Scholar
  43. Ozaki, T., Hibiki, T. 2015. Drift-flux model for rod bundle geometry. Prog Nucl Energ, 83: 229–247.CrossRefGoogle Scholar
  44. Ozaki, T., Hibiki, T. 2018. Modeling of distribution parameter, void fraction covariance and relative velocity covariance for upward steam-water boiling flow in vertical rod bundle. J Nucl Sci Tech, 55: 386–399.CrossRefGoogle Scholar
  45. Ozaki, T., Suzuki, R., Mashiko, H., Hibiki, T. 2013. Development of drift-flux model based on 8×8 BWR rod bundle geometry experiments under prototypic temperature and pressure conditions. J Nucl Sci Tech, 50: 563–580.CrossRefGoogle Scholar
  46. Ozar, B., Dixit, A., Chen, S. W., Hibiki, T., Ishii, M. 2012. Interfacial area concentration in gas-liquid bubbly to churn-turbulent flow regime. Int J Heat Fluid Flow, 38: 168–179.CrossRefGoogle Scholar
  47. Ozar, B., Jeong, J. J., Dixit, A., Julia, J. E., Hibiki, T., Ishii, M. 2008. Flow structure of gas-liquid two-phase flow in an annulus. Chem Eng Sci, 63: 3998–4011.CrossRefGoogle Scholar
  48. Rassame, S., Hibiki, T. 2018. Drift-flux correlation for gas-liquid two-phase flow in a horizontal pipe. Int J Heat Fluid Flow, 69: 33–42.CrossRefGoogle Scholar
  49. Serizawa, A., Kataoka, I., Michiyoshi, I. 1991. Phase distribution in bubbly flow. In: Multiphase Science and Technology, Vol. 6. Hewitt, G. F., Delhaye, J. M., Zuber, N. Eds. Hemisphere, 257–301.CrossRefGoogle Scholar
  50. Taitel, Y., Bornea, D., Dukler, A. E. 1980. Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AIChE J, 26: 345–354.CrossRefGoogle Scholar
  51. Vaidheeswaran, A., Hibiki, T. 2017. Bubble-induced turbulence modeling for vertical bubbly flows. Int J Heat Mass Transfer, 115: 741–752.CrossRefGoogle Scholar
  52. Yang, X., Schlegel, J. P., Liu, Y., Paranjape, S., Hibiki, T., Ishii, M. 2012. Measurement and modeling of two-phase flow parameters in scaled 8×8 BWR rod bundle. Int J Heat Fluid Flow, 34: 85–97.CrossRefGoogle Scholar
  53. Zuber, N., Findlay, J. A. 1965. Average volumetric concentration in two-phase flow systems. J Heat Transfer, 87: 453–468.CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press 2019

Authors and Affiliations

  1. 1.School of Nuclear EngineeringPurdue UniversityWest LafayetteUSA

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