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Comparison of film condensation models in presence of non-condensable gases implemented in a CFD Code

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Abstract

Several film condensation models in presence of non-condensable gases are presented. They have been implemented in a CFD code and compared with experimental data. The aim was to improve the code for simulating the gas mixing process in large containment buildings involving steam. The models based on correlation are more robust and simpler, but they work badly out of their experimental conditions. The mechanistic models, based on the diffusion layer theory, work well in numerous conditions but the algorithm are more complicated. Moreover, they run badly when the convective heat transfer is not well predicted by the code.

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Abbreviations

c :

molar density of the mixture (mol/m3)

c p :

specific heat (J/kgK)

D :

diffusion coefficient of the gas mixture (m2/s)

f :

film thickness (m)

f(Y nc ):

degradation factor

g :

acceleration of gravity (m/s2)

Gr :

Grashof number \(\left( {Gr = \frac{{g\rho _\infty (\rho _i - \rho _\infty )L^3 }} {{\mu ^2 }}} \right)\)

h :

heat transfer coefficient

h fg :

latent heat of vaporization (J/kg)

\(h'_{{\text{fg}}} \) :

latent heat of vaporization corrected by the subcooling effect (J/kg)

\(\bar h_{{\text{fg}}} \) :

average latent heat of vaporization (J/kg)

k :

thermal conductivity (W/mK)

k cd :

effective condensation conductivity (W/mK)

K :

mass transfer coefficient (m/s)

L :

surface length (m)

M :

molecular weight (kg/mol)

m′ cd :

condensation mass flux (kg/s)

\(m'_{{\text{cd}}} \) :

condensation mass flus (kg/s)

Nu :

Nusselt number

Pr :

Prandtl number \(\left( {\Pr \frac{{c_{\text{p}} \mu }} {k}} \right)\)

p :

pressure (Pa)

q :

heat flux (W/m2)

R :

universal gas constant (J/kgK)

Ra :

Rayleigh number (Ra =Gr Pr)

Re:

Reynolds number

Sh :

Sherwood number \(\left( {{\text{Sh}} = \frac{{h_{{\text{cd}}} L}} {{k_{{\text{cd}}} }}} \right)\)

Sc :

Schmidt number \(\left( {{\text{Sc}} = \frac{\mu } {{\rho D}}} \right)\)

T :

temperature (K)

u m :

averaged velocity in the film (m/s)

X :

molar fraction

Y :

mass fraction

z :

axial coordinate (m)

Φ:

ratio between steam and non-condensable molar fractions

μ:

viscosity (Pa s)

θ:

wall inclination angle (rad)

Θ:

suction factor

ρ:

density (kg/m2)

σ:

surface tension (N/m)

σ ij :

collision diameter

Ω ij :

collision integral

cd:

condensation

cv:

convection

f:

condensate liquid film

g:

non-condensable gas

i:

single gas species i in the mixture

I:

interface

j:

single gas species j in the mixture

l:

liquid phase

m:

gas mixture

n:

maximum number of single gas species in the mixture

Nu:

pure vapour conditions

rd:

radiation

sat:

saturation conditions

t:

total

v:

steam

w:

wall

δ:

diffusion boundary layer

∞:

bulk gas mixture

=:

horizontal surfaces

ave:

averaged

LOW:

lower condenser

MED:

medium condenser

UP:

upper condenser

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Acknowledgment

Authors wished to acknowledge the support from the Fifth Framework Program of the European Commission under the Energy, Environment and Sustainable Development Contract EVG1-CT-2001-00042 (EXPRO).

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Authors and Affiliations

  1. Department of Nuclear Engineering, Universidad Politécnica de Madrid, College of Industrial Engineering, José Gutiérrez Abascal, 2, E-28006, Madrid, Spain

    J. M. Martín-Valdepeñas, M. A. Jiménez & F. Martín-Fuertes

  2. Departamento de Ingeniería Energética y Fluidomecánica, Universidad Politécnica de Madrid, College of Industrial Engineering, José Gutiérrez Abascal, 2, E-28006, Madrid, Spain

    J. A. Fernández. Benítez

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  1. J. M. Martín-Valdepeñas
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  2. M. A. Jiménez
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  3. F. Martín-Fuertes
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  4. J. A. Fernández. Benítez
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Correspondence to J. M. Martín-Valdepeñas.

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Martín-Valdepeñas, J.M., Jiménez, M.A., Martín-Fuertes, F. et al. Comparison of film condensation models in presence of non-condensable gases implemented in a CFD Code. Heat Mass Transfer 41, 961–976 (2005). https://doi.org/10.1007/s00231-004-0606-5

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