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Heat transfer of a spray droplet in a PWR pressurizer

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Abstract

Heat transfer rates to spray droplets under conditions corresponding to those of spray transients in a pressurizer of pressurized water reactor (PWR) have been predicted by a simple droplet model with internal thermal resistance and partial internal mixing. In those processes, the temperature distributions in the droplet have been obtained using the integral method, and the physical properties of the saturated steam-hydrogen gas mixture surrounding the droplets are estimated applying the concept of compressibility factor and using appropriate correlations. Results have been provided for the temporal variations of total heat flux with its convection and condensation heat transfer components, dimensionless droplet bulk temperature and droplet flight distance. The effects of ambient pressure, initial droplet size, concentration of hydrogen gas in the mixture, initial injection velocity, and spray angle on the heat transfer of spray droplets have been discussed.

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Abbreviations

A :

Cross-sectional area of a droplet

Bi :

Biot number (=h t R/k i )

C D :

Drag coefficient

C p :

Specific heat at constant pressure

D :

Derivative with respect to τ(=d/dτ)

D 12 :

Mass diffusivity of steam in a mixture

g :

Gravitational acceleration

H fg :

Latent heat of condensation

h c :

Convection heat transfer coefficient

h t :

Apparent heat transfer coefficient

J s :

Mass flux of steam

k :

Thermal conductivity

M :

Molecular weight

m :

Mass of a droplet

Nu :

Nusselt number (=2h c R/k m )

P :

Pressure

P gm :

Logarithmic mean gas pressure difference

Pr :

Prandtl number (=μ m C ipm/k m )

qL :

Sensible heat flux to a droplet

qs :

Latent heat flux to a droplet

qt :

Total heat flux to a droplet

\(\bar R\) :

Universal gas constant

Re :

Reynolds number (=2ρ m WR/μ m )

γ:

Radial distance in spherical coordinate

Sc :

Schmidt number (=μ/D 12 ρ m )

Sh :

Sherwood number (=2βR/D 12)

T :

Temperature

t :

Time

U :

Horizontal velocity component

V :

Vertical velocity component

\(\bar R\) :

Molar specific volume

ν:

Specific volume

W :

Velocity of a droplet (=U 2+V 2)1/2)

x, y :

Cartesian coordinates

Y :

Flight distance

y i :

Volume fraction of each component in the mixture

Z :

Compressibility factor

α:

Thermal diffusivity

β:

Mass transfer coefficient

Θ b :

Dimensionless droplet bulk temperature (=T b -T 0)/(T ∞-T 0)

θ:

Transformed temperature in dimensionless form

μ:

Dynamic viscosity

ξ:

Dimensionless radial distance in spherical coordinate

ρ:

Density

τ:

Dimensionless time (=α l t/R 2)

ϕ:

Spray angle

ω:

Acentric factor

b :

Bulk

c :

Critical value

g :

Noncondensable gas

i :

At the interface between the droplet and the mixture

l :

Droplet

m :

Mixture

o :

Initial condition

r :

Reduced value

s :

Saturated steam or droplet surface

∞:

Ambient

o :

Low pressure

References

  • Bergles, A.E., Collier, J.C. Delhaye, J.M. Hewitt, G.F. and Mayinger, F., 1981, “Two Phase Flow and Heat Transfer in the Power and Process Industries,” Hemisphere Publishing Co., New York.

    Google Scholar 

  • Brokaw, R.S., 1955, “Estimating Thermal Conductivities for Nonpolar Gas Mixtures,” Ind. Eng. Chem., Vol. 47, No. 11, pp. 2398–2400.

    Article  Google Scholar 

  • Chung, J.N. and Ayyaswamy, P.S., 1977, “The Effect of Internal Circulation on the Heat Transfer of a Nuclear Reactor Containment Spray Droplet,” Nuclear Technology, Vol. 35, pp. 603–610.

    Google Scholar 

  • Clift R., Grace, J.R. and Weber, M.E., 1978, “Bubbles, Drops, and Particles,” Academic Press., New York

    Google Scholar 

  • Colburn, A.P. and Hougen, O.A., 1934, “Design of Cooler Condensers for Mixture of Vapours with Non Condensing Gases,” Ind. Eng. Chem., Vol. 26, pp. 1178–1182.

    Article  Google Scholar 

  • Dawson, R., Khoury, F. and Kobayashi, R., 1970, “Self-Diffusion Measurements in Methane by Pulsed Nuclear Magnetic Resonance” AIChE J., Vol.16, No. 5, pp. 725–729.

    Article  Google Scholar 

  • Dean, D.E. and Stiel, L.I., 1965, “The Viscosity of Nonpolar Gas Mixture at Moderate and High Pressures,” AIChE J., Vol. 11, No. 3, pp. 526–532.

    Article  Google Scholar 

  • Huang, L.J. and Ayyaswamy, P.S., 1987a, “Heat and Mass Transfer Associated with a Spray Drop Experiencing Codensation: A Fully Transient Analysis,” Int. J. Heat Mass Transfer, Vol. 30, No. 5, pp. 881–891.

    Article  MATH  Google Scholar 

  • Huang, L.J. and Ayyaswamy, P.S., 1987c, “Drag Coefficients Associated with a Liquid Drop Experiencing Condensation,” ASME J. Heat Transfer, Vol. 109, pp. 1003–1006.

    Article  Google Scholar 

  • Hughmark, G.A. 1967, “Mass and Heat Transfer from Rigid Sphere,” AIChE Journal, Vol. 13, No. 6, pp. 1219–1221.

    Article  Google Scholar 

  • Kulic, E., Rhodes E. and Sullivan, G., 1975, “Heat Transfer Rates Predictions in Condensation on Droplets From Air-Steam Mixtures,” Can. J. Chemical Engineering, Vol. 53, pp. 252–258.

    Google Scholar 

  • Kulic, E. and Rhodes, E., 1977, “Direct Contact Condensation from Air-Steam Mixtures on a Single Droplet,” Can. J. Chemical Engineering, Vol. 55, pp., 131–137.

    Article  Google Scholar 

  • Lee, B.I. and Kesler, M.G., 1975, “A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States,” AIChE J., Vol. 21, No. 3, pp. 510–527.

    Article  Google Scholar 

  • Linn, J.D.M., Maskell, S.J. and Patrick, M.A., 1988, “A Note on Heat and Mass Transfer to a Spray Droplet,” Nuclear Technology, Vol. 81, pp. 122–125.

    Google Scholar 

  • Özisik, N., 1980, “Heat Conduction,” John Wiley Sons Inc., New York.

    Google Scholar 

  • Reid, R.D., Prausnitz, J.M. and Sherwood, T.K., 1977, “The Properties of Gases and Liquids,” 3rd ed., McGraw-Hill Book Company, New York.

    Google Scholar 

  • Stiel, L.I. and Thodos, G., 1964, “The Thermal Conductivity of Nonpolar Substances in the Dense Gaseous and Liquid Regions,” AIChE J., Vol. 10, No. 1, pp. 26–30.

    Article  Google Scholar 

  • Sundararajan, T. and Ayyaswamy, P.S., 1984, “Hydrodynamics and Heat Transfer Associated with Condensation of a Moving Drop: Solutions for Intermediate Reynolds Numbers,” J. Fluid Mech., Vol. 149, pp. 33–58.

    Article  MATH  Google Scholar 

  • Tanaka, M., 1980, “Heat Transfer of a Spray Droplet in a Nuclear Reactor Containment,” Nuclear Technology, Vol. 47, pp. 268–281.

    Google Scholar 

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Authors and Affiliations

  1. Korea Institute of Nuclear Safety, Daeduk-danji, P.O. Box 16, 305-606, Taejon, Korea

    Jong-Chull Jo, Sang-Kyoon Lee & Won-Ky Shin

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  1. Jong-Chull Jo
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  2. Sang-Kyoon Lee
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  3. Won-Ky Shin
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Jo, JC., Lee, SK. & Shin, WK. Heat transfer of a spray droplet in a PWR pressurizer. KSME Journal 5, 130–139 (1991). https://doi.org/10.1007/BF02953612

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  • DOI: https://doi.org/10.1007/BF02953612

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