Estimation of the Drop Size in Dispersed Flow

  • N. D. AgafonovaEmail author
  • I. L. Paramonova

The formulas for calculating the characteristic drop size for the mean Sauter diameter have been compared. The question on various forms of the size distribution of drops has been considered. To substantiate the applicability of the compared formulas for calculating the thermohydrodynamics in the circuits of nuclear power plants, experimental data on the wall temperature in a dispersed flow have been used. It has been shown that the Sauter diameter values calculated using the wall temperature in the supercritical region are in good agreement with sparse direct measurements of the drop size in steam–water flows. The drop sizes calculated using the tested formulas obtained for two-component gas–liquid flows or for single-component flows of coolants (various kinds of freons) and liquefied nitrogen turned out to be much lower. It has been shown that it is necessary to recalculate the numerical coefficients in the considered formulas in using them for steam–water flows.


dispersed flow drop size mean diameter distribution function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Styrikovich, Yu. V. Baryshev, M. E. Grigor′eva, and E. M. Konovalova, A model for calculating the heat transfer for steam water disperse at flow, Teplofiz. Vys. Temp., 21, No. 1, 122–129 (1982).Google Scholar
  2. 2.
    E. N. Ganić and W. M. Rohsenow, Dispersed flow heat transfer, Int. J. Heat Mass Transf., 20, No. 8, 855–866 (1977).CrossRefGoogle Scholar
  3. 3.
    O. G. Stonik and I. L. Mostinskii, Account of the interaction of droplets with a hot wall in calculating the heat transfer in the supercritical region of dispersed annular flow, Izv. Ross. Akad. Nauk, Énergetika, No. 5, 132–140 (2008).Google Scholar
  4. 4.
    RELAP5/MOD3. Code Manual. Volume IV: Models and Correlations. NUREG/CR–5535 INEL–95/0174, Idaho National Engineering Laboratory (1995).Google Scholar
  5. 5.
    H. Austregesilo, C. Bals, A. Hora, G. Lerchl, and P. Romstedt, ATHLET Mod 2.1 Cycle A. Models and Methods, Gesellschaft für Anlagenund Reaktorsicherheit (GRS) mbH (2006).Google Scholar
  6. 6.
    J. Miettinen and A. Hämäläinen, GENFLO — A General Thermal Hydraulic Solution for Accident Simulation. VTT Processes. Research Notes 2163, Julkaisija-Utgivare- Publisher, Otamedia Oy, Espoo (2002).Google Scholar
  7. 7.
    J. W. Spore, J. S. Elson, S. J. Jolly-Woodruff, T. D. Knight, J.-C. Lin, R. A. Nelson, K. O. Pasamehmetoglu, R. G. Steinke, and C. Unal, TRAC–M/FORTRAN 90 (Version 3.0). Theory Manual. LA–UR–00–910 — Los Alamos National Laboratory, Los Alamos, New Mexico (2000).Google Scholar
  8. 8.
    Yu. V. Yudov, S. N. Volkova, and Yu. A. Migrov, Closing relations of the thermohydraulic model of KORSAR computational code, Teploénergetika, No. 11, 22–29 (2002).Google Scholar
  9. 9.
    I. Kataoka, M. Ishii, and K. Mishima, Generation and size distribution of droplet in annular two-phase flow, J. Fluids Eng., 105, No. 2, 230−238 (1983).CrossRefGoogle Scholar
  10. 10.
    G. Kocamustafaogullari and M. Ishii, Foundation of the interfacial area transport equation and its closure relations, Int. J. Heat Mass Transf., 38, No. 3, 481–493 (1995).CrossRefzbMATHGoogle Scholar
  11. 11.
    A. W. Bennett, G. F. Hewitt, H. A. Kearsey, and R. K. F. Keeys, Heat transfer to steam–water mixtures flowing in uniformly heated tubes in which the critical heat flux has been exceeded, United Kingdom Atomic Energy Authority, AERE–R5373 (1967).Google Scholar
  12. 12.
    L. Nilsson, Assessment of RELAP5/MOD3 Against Twenty-Five Post-Dryout Experiments Performed at the Royal Institute of Technology, NUREG/IA–0094.STUDS VIK/NS–90/93, Sweden (1993).Google Scholar
  13. 13.
    N. D. Agafonova and I. L. Paramonova, Heat transfer in dispersed steam–water flow in the channel, Teploénergetika, No. 8, 1–5 (2014).Google Scholar
  14. 14.
    D. N. Plummer, O. S. Iloeje, W. M. Rohsenow, P. Griffith, and E. Ganić, Post Critical Heat Transfer to Flowing Liquid in a Vertical Tube, Report No. 72718-91, MIT, Cambridge, Massachusetts (1974).Google Scholar
  15. 15.
    Z. L. Miropol′skii, Heat transfer to superheated vapor with heat input and removal, Teploénergetika, No. 3, 75–78 (1975).Google Scholar
  16. 16.
    S. Whitaker, 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, No. 2, 361–371 (1972).CrossRefGoogle Scholar
  17. 17.
    A. G. Girin, Distribution of dispersed droplets upon breaking of the drop in a high-velocity gas flow, J. Eng. Phys. Thermophys., 84, No. 4, 872–880 (2011).CrossRefGoogle Scholar
  18. 18.
    S. Y. Ahmad, Fluid to fluid modeling of critical heat flux: a compensated distortion model, Int. J. Heat Mass Transf., 16, No. 4, 641–662 (1973).CrossRefGoogle Scholar
  19. 19.
    L. B. Fore, B. B. Ibrahim, and S. G. Beus, Visual measurements of droplet size in gas–liquid annular flow, Int. J. Multiphase Flow, 28, No. 12, 1896–1910 (2002).CrossRefzbMATHGoogle Scholar
  20. 20.
    D. F. Tatterson, J. C. Dallman, and T. J. Hanratty, Drop sizes in annular gas–liquid flows, AIChE J., 23, No. 1, 68–76 (1977).CrossRefGoogle Scholar
  21. 21.
    T. Ueda and K. Kim, Dryout heat flux and size of entrained drops, Bull. JSME, 25, No. 200, 225−233 (1982).CrossRefGoogle Scholar
  22. 22.
    M. Cumo, J. E. Farello, J. Ferrari, and J. Palazzi, High-dispersion two-phase flows, Heat Transf., 96, No. 4, 66–72 (1974).CrossRefGoogle Scholar
  23. 23.
    J. Collier and J. Thome, Convective Boiling and Condensation, Clarendon Press, Oxford (1994).Google Scholar
  24. 24.
    A. J. Ireland, L. E. Hochreiter, and F.-B. Cheung, Droplet size and velocity measurements in a heated rod bundle, The 6th ASME–JSME Thermal Eng. Joint Conf., March 16–20, 2003, TED–AJ03–624.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Peter the Great St. Petersburg Polytechnical UniversitySt. PetersburgRussia

Personalised recommendations