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Research on the effect of Reynolds correlation in natural convection film condensation

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Abstract

Film condensation is a vital phenomenon in the nuclear engineering applications, such as the gas–steam pressurizer design, and heat removing on containment in the case of postulated accident. Reynolds number in film condensation can be calculated from either the mass relation or the energy relation, but few researches have distinguished the difference between them at present. This paper studies the effect of Reynolds correlation in the natural convection film condensation on the outer tube. The general forms of the heat transfer coefficient correlation of film condensation are developed in different flow regimes. By simultaneously solving a set of the heat transfer coefficient correlations with Re mass and Re energy, the general expressions for Re mass and Re energy and the relation between the corresponding heat transfer coefficients are obtained. In the laminar and wave-free flow regime, Re mass and Re energy are equivalent, while in the laminar and wavy flow regime, Re mass is much smaller than Re energy, and the deviation of the corresponding average heat transfer coefficients is about 30% at the maximum. In the turbulent flow regime, the relation of Re mass and Re energy is greatly influenced by Prandtl number. The relative deviation of their average heat transfer coefficients is the nonlinear function of Reynolds number and Prandtl number. Compared with experimental results, the heat transfer coefficient calculated from Re energy is more accurate.

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Abbreviations

C :

Variable coefficient

Cp:

Constant pressure-specific heat [J/(K kg)]

G :

Acceleration of gravity (m/s2)

h :

Condensation heat transfer coefficient [W/(m2 K)]

h fg :

Latent heat of vaporization (J/kg)

h ′fg :

Modified latent heat of vaporization (J/kg)

\( \bar{h} \) :

Average heat transfer coefficient [W/(m2 K)]

k :

Thermal conductivity (W/m K)

L :

Length (m)

m :

Variable coefficient

n :

Variable coefficient

Pr :

Prandtl number

Re :

Reynolds number

s :

Variable coefficient

T :

Temperature (K)

μ :

Viscosity (Pa s)

Г :

Mass flow rate of condensate (kg/s)

ε :

Coefficient

ρ :

Density (kg/m3)

δ :

Thickness of condensation film (m)

∆:

Difference

1:

Laminar and wavy flow regime

2:

Turbulent flow regime

b:

Bulk

energy:

Based on energy relation

f:

Liquid phase

g:

Gas phase

l:

Liquid phase

mass:

Based on mass relation

sat:

Saturation

w:

Wall

References

  1. J.W. Rose, Condensation heat transfer fundamentals. Chem. Eng. Res. Des. 76(2), 143–152 (1998). doi:10.1205/026387698524712

    Article  Google Scholar 

  2. W. Nusselt, The condensation of steam on cooled surfaces. Z. Ver. Dtsch. Ing. 60, 541–546 (1916)

    Google Scholar 

  3. W.M. Rohsenow, Heat transfer and temperature distribution in laminar film condensation. Trans. Asme. 78, 1645–1648 (1956)

    Google Scholar 

  4. E.M. Sparrow, J.L. Gregg, A boundary layer treatment of laminar film condensation. J. Heat Transf. 81(1), 13–18 (1959)

    Google Scholar 

  5. W.J. Minkowycz, E.M. Sparrow, Condensation heat transfer in the presence of noncondensables, interfacial resistance, superheating, variable properties, and diffusion. Int. J. Heat Mass Transf. 9(10), 1125–1144 (1966). doi:10.1016/0017-9310(66)90035-4

    Article  Google Scholar 

  6. E.M. Sparrow, S.H. Lin, Condensation heat transfer in the presence of a non-condensable gas. J Heat Transf. 86(3), 430–436 (1964). doi:10.1115/1.3688714

    Article  Google Scholar 

  7. L.E. Herranz, A. Campo, Adequacy of the heat-mass transfer analogy to simulate containment atmospheric cooling in the new generation of advanced nuclear reactors: experimental confirmation. Nucl. Technol. 139(3), 221–232 (2002). http://www.ans.org/store/article-3315/

  8. J.C.Y. Koh, An integral treatment of two-phase boundary layer in film condensation. J Heat Transf. 83(3), 359–362 (1961). doi:10.1115/1.3682285

    Article  Google Scholar 

  9. V.E. Denny, A.F. Mills, V.J. Jusionis, Laminar film condensation from a steam-air mixture undergoing forced flow down a vertical surface. J Heat Transf. 93(3), 297–304 (1971). doi:10.1115/1.3449814

    Article  Google Scholar 

  10. M.H. Kim, M.L. Corradini, Modeling of condensation heat transfer in a reactor containment. Nucl. Eng. Des. 118(2), 193–212 (1990). doi:10.1016/0029-5493(90)90057-5

    Article  Google Scholar 

  11. P.F. Peterson, Theoretical basis for the Uchida correlation for condensation in reactor containments. Nucl. Eng. Des. 162(2), 301–306 (1996). doi:10.1016/0029-5493(95)01125-0

    Article  Google Scholar 

  12. L. Wu, Y. Liu, H.J. Jia, Improved diffusion layer model based on real gas state equation for high pressure condensation. Ann. Nucl. Energy 85, 444–452 (2015). doi:10.1016/j.anucene.2015.05.006

    Article  Google Scholar 

  13. S. Kima, Y.G. Lee, D.W. Jerng, Laminar film condensation of saturated vapor on an isothermal vertical cylinder. Int. J. Heat Mass Transf. 83, 545–551 (2015). doi:10.1016/j.ijheatmasstransfer.2014.12.009

    Article  Google Scholar 

  14. S. Mosayebidorcheh, T. Mosayebidorcheh, M.M. Rashidi, Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method. Sci. Res. Essays 9(12), 557–565 (2014). doi:10.13140/2.1.4464.2241

    Article  MATH  Google Scholar 

  15. B.J. Chung, M.C. Kim, M. Ahmadinejad, Film-wise and drop-wise condensation of steam on short inclined plates. J. Mech. Sci. Technol. 22(1), 127–133 (2008). doi:10.1007/s12206-007-1015-8

    Article  Google Scholar 

  16. L. Slegers, R.A. Seban, Laminar film condensation of steam containing small concentrations of air. Int. J. Heat Mass Transf. 13(12), 1941–1947 (1970). doi:10.1016/0017-9310(70)90094-3

    Article  Google Scholar 

  17. S.S. Kutateladze, I.I. Gogonin, Heat transfer in film condensation of slowly moving vapor. Int. J. Heat Mass Transf. 22(12), 1593–1599 (1979). doi:10.1016/0017-9310(79)90075-9

    Article  Google Scholar 

  18. G.M. Hebbard, W.L. Badger, Steam-film heat transfer coefficients for vertical tubes. Ind. Eng. Chem. 26(4), 420–424 (1934). doi:10.1021/ie50292a013

    Article  Google Scholar 

  19. J.W. Rose, Fundamentals of condensation heat transfer-Laminar film condensation. JSME Int. J. 31, 357–375 (1988). http://ci.nii.ac.jp/naid/110002494180/

  20. X.Y. Wei, X.D. Fang, R.R. Shi, A comparative study of heat transfer coefficients for film condensation. Energy Sci. Technol. 3(1), 1–9 (2012). http://www.cscanada.net/index.php/est/article/view/2344

  21. G. Neiils, S. Kliein, Heat transfer (Cambridge University Press, Cambridge, 2009), pp. 799–806

    Google Scholar 

  22. H. Uchida, A. Oyama, Y. Togo, Evaluation of post-incident cooling systems of light water power reactors. (Tokyo University, 1964). http://www.osti.gov/scitech/biblio/4023463

  23. A.A. Dehbi, The effects of noncondensable gases on steam condensation under turbulent natural convection conditions. (Massachusetts Institute of Technology, 1991). http://dspace.mit.edu/handle/1721.1/13905

  24. M.H. Anderson, L.E. Herranz, M.L. Corradini, Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. 185(2), 153–172 (1998). doi:10.1016/S0029-5493(98)00232-5

    Article  Google Scholar 

  25. J.W. Kim, Y.G. Lee, H.K. Ahn et al., Condensation heat transfer characteristic in the presence of noncondensable gas on natural convection at high pressure. Nucl. Eng. Des. 239(4), 688–698 (2009). doi:10.1016/j.nucengdes.2008.12.011

    Article  Google Scholar 

  26. R.I. Pashkevich, P.V. Muratov, Film condensation in a large diameter tube with upward steam flow. Int. J. Heat Mass Transf. 81, 804–810 (2015). doi:10.1016/j.ijheatmasstransfer.2014.11.001

    Article  Google Scholar 

  27. M. Kondo, H. Nakamura, Y. Kukita et al., Primary-side two-phase flow and heat transfer characteristics of a horizontal-tube PCCS condenser. In 14th International Conference on Nuclear Engineering, Miami. 2006, pp. 685–693. doi:10.1115/ICONE14-89652

  28. J.G. Collier, J.R. Thome, Convective boiling and condensation (Oxford University Press, Oxford, 1994), pp. 445–450

    Google Scholar 

  29. T.L. Bergman, A.S. Lavine, F.P. Incropera et al., Fundamentals of Heat and Mass Transfer, 7th edn. (Wiley, Hoboken, 2011), pp. 675–679

    Google Scholar 

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Authors and Affiliations

  1. Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing, 100084, China

    Lei Wu, Hai-Jun Jia, Xi-Zhen Ma, Yang Liu & Xing-Tuan Yang

  2. Engineering Physics Institute, University of Wisconsin Madison, Madison, WI, 53706, USA

    Jun Wang

Authors
  1. Lei Wu
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  2. Hai-Jun Jia
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  3. Xi-Zhen Ma
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  4. Yang Liu
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  6. Jun Wang
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Corresponding author

Correspondence to Yang Liu.

Additional information

This work was supported by Doctoral Fund of Ministry of Education of China (No. 20130002120016), the Science Found for Creative Groups of National Natural Science Foundation of China (No. 51321002), and the project of “Research and validation of key technology and device for NHR200-II nuclear heating reactor”.

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Wu, L., Jia, HJ., Ma, XZ. et al. Research on the effect of Reynolds correlation in natural convection film condensation. NUCL SCI TECH 28, 85 (2017). https://doi.org/10.1007/s41365-017-0240-9

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