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Numerical investigation and quantitative loss analysis of typical wet steam spontaneous condensation based on two-fluid model

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Abstract

A two-fluid model with the influence of inter-phase velocity-slip taken into account is proposed and a modified realizable k–ε turbulence model is put forward as well to make the equation set of two-fluid model closed. Based on this two-fluid model, numerical simulations are implemented on typical wet steam flow in different cases. Good consistency between numerical result and the experimental result implies that this two-fluid model is provided with high accuracy and wide applicability. The flow field analysis also shows that there exist several particular sites along the flow direction. These particular sites could illustrate the development mechanism of nucleation and droplet growing. In addition, further discussion about the flow in cascade then indicates that the presence of condensation has strong impact on the flow while the impact of inter-phase velocity-slip is relatively weaker. The composition of total pressure loss is present here, the majority of total pressure loss brought by condensation is about 8.78 % of inlet total pressure while the inter-phase velocity-slip just results in a small part of about 0.42 % of inlet total pressure, the rest of the total pressure loss is caused by pneumatic factors and this part is about 3.95 % of inlet total pressure.

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Abbreviations

I :

Nucleation rate (kg−1 s−1)

θ :

Non-isothermal correction factor

σ :

Surface tension (N m−1)

q c :

Condensation coefficient

K b :

Boltzmann’s constant (J K)

M m :

Mass of one water molecule (g mol−1)

γ :

The specific heat ratio

R :

Gas constant (J mol−1 K−1)

\(r^{*}\) :

Critical radius (m)

Kn :

Knudsen number

T g :

Temperature of the ambient vapor (K)

ξ :

Molecule fraction of condensation

p d :

Hypothetical ambient pressure (Pa)

r :

Drop radius (m)

ρ g :

Gas phase conditions of density (kg m−3)

ρ l :

Liquid phase conditions of density (kg m−3)

u i :

i-Wise component of velocity (m s−1)

p eff :

Effective pressure (Pa)

g i :

i-Wise component of acceleration of gravity (m s−2)

e :

Total energy per unit mass (J kg−1)

λ eff :

Effective heat conductivity (W m−2 k−1)

T g :

Temperature for gas phase (K)

μ g :

Dynamic viscosity for gas phase (N s m−2)

μ t :

Eddy viscosity for gas phase

δ ij :

Kronecker symbol

P rt :

Turbulent Prandtl number

S m :

Source term for mass exchange (kg m−3)

S u :

Source term for momentum exchange (kg m−2 s−1)

S e :

Source term for energy exchange (J m−3)

G :

Cunningham correction factor

ρ m :

Local average density of mixed phase (kg m−3)

u pi :

i-Wise component of droplet velocity (m s−1)

Y :

Wetness fraction in mixture

μ p :

Eddy viscosity for liquid phase

N :

Droplet concentration (kg−1)

B(T g ):

Second order virial coefficient

C(T g ):

Third order virial coefficient

k :

Turbulent kinetic energy (m2 s−2)

ε(ε ijk ):

Turbulent dissipation rate (m2 s−3)

h fg :

Latent heat of vaporization (J mol−1)

τ rp :

Particle drag coefficient

Re p :

Relative Reynolds number

ΔT :

Degree of supercooling (K)

Ma :

Mach number

p :

Local static pressure for gas phase (Pa)

p 01 :

Inlet total pressure (Pa)

p 02 :

Outlet total pressure (Pa)

λ g :

Heat conductivity (W m−2 k−1)

h t :

Total enthalpy of gaseous phase (J kg−1)

C p g :

Specific heat at constant pressure (J kg−1 k−1)

C vg :

Specific heat at constant pressure (J kg−1 k−1)

h g :

Specific enthalpy (J kg−1)

s g :

Specific entropy (J kg−1 K−1)

T d :

Droplet temperature (K)

p s :

Flat-film saturation pressure (Pa)

T s :

Saturation pressure (K)

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Acknowledgments

The authors are very grateful to Doctor Liu Huaping in HIT for his very helpful guidance. Besides, the research presented in this article is funded by the Research Groups of the National Natural Science Foundation of China (Grant No. 51121004) as well as the National Natural Foundation of China (Grant No. 50976026).

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Authors and Affiliations

  1. The Institute of Propulsion Theory and Technology, School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Ke Cui, Yan-Ping Song, Huan-Long Chen & Fu Chen

  2. Mitsubishi Heavy Industries, LTD, Takasago, Hyogo, 676-8686, Japan

    Hiroharu Ooyama

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  1. Ke Cui
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  2. Yan-Ping Song
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Correspondence to Ke Cui.

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Cui, K., Song, YP., Chen, HL. et al. Numerical investigation and quantitative loss analysis of typical wet steam spontaneous condensation based on two-fluid model. Heat Mass Transfer 52, 1329–1342 (2016). https://doi.org/10.1007/s00231-015-1657-5

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