Abstract
Based on the classical droplet nucleation theory along with the droplet growing model, a dual-fluid model considering the effect of velocity-slip between the liquid phase and the gaseous phase is proposed in this paper. Both 2-D and 3-D numerical simulations were then implemented, respectively, on the flow in low pressure cascade and the result showed that this dual-fluid model was provided with relatively high resolution and good reliability on capturing the typical flow characteristics, such as the “Wilson Point” and the “Condensing Shock” (Li Dissertation Submitted to Xi’an Jiaotong University In partial fulfillment of the requirement for the degree of Doctor of Philosophy 1–2, 2002). In addition, both of the 2-D investigation and 3-D investigation implied that the non-equilibrium condensation had great impact on the parameter distribution as well as the loss of the flow field. Meanwhile, because the radius of droplets generated during the condensation might be quite small, the velocity-slip between the liquid phase and the gaseous phase almost has no influence on the flow field compared with condensation.
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Abbreviations
- T s(p) :
-
Saturate temperature (K)
- T d :
-
Temperature of liquid phase (K)
- T :
-
Temperature of gaseous phase (K)
- \(\dot{m}\) :
-
Mass generation rate (kg/(m3 s))
- ρ :
-
Density of gaseous phase (kg/m3)
- ρ p :
-
Density of liquid phase (kg/m3)
- ρ m :
-
Density of mixed phase (kg/m3)
- P :
-
Local static pressure (Pa)
- P 01 :
-
Inlet total pressure (Pa)
- P 02 :
-
Local total pressure (Pa)
- h fg :
-
Latent heat of vaporization (J/kg)
- h t :
-
Total enthalpy of gaseous phase (J/kg)
- τ rp :
-
Drag coefficient, \(\tau_{rp} = \frac{{d_{p}^{2} \rho_{\text{p}} }}{18\mu }\left( {1 + \frac{1}{6}{\text{Re}}_{p}^{{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}}} } \right)^{ - 1}\)(–)
- G :
-
Cunningham correction factor (–)
- I :
-
Nucleation rate (/kg)
- N :
-
Droplet number (/kg)
- r :
-
Radius of droplets (m)
- r * :
-
Critical radius of droplets (m)
- q c :
-
Coefficient of condensation (–)
- K b :
-
Boltzmann’s constant (=1.3807 × 10−23J/kg)
- M m :
-
Molecular mass of water (kg)
- σ :
-
Surface tension coefficient (N/m)
- θ :
-
Non-isothermal correction coefficient (–)
- γ :
-
Volumetric ratio of specific heats (–)
- R :
-
Gas constant (=461.4 J/(kg K))
- C p :
-
Specific heat at constant pressure (J/(kg K))
References
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Acknowledgments
The authors are very grateful to Doctor LIU Huaping in HIT for their 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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Technical Editor: Fernando Alves Rochinha.
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Cui, K., Song, Y., Chen, H. et al. Numerical method for non-equilibrium phase transition in low pressure stage of steam turbine. J Braz. Soc. Mech. Sci. Eng. 38, 2149–2159 (2016). https://doi.org/10.1007/s40430-015-0452-z
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DOI: https://doi.org/10.1007/s40430-015-0452-z