Abstract
An average bubble number density (ABND) model was formulated and numerically resolved for the subcooled flow boiling of liquid nitrogen. The effects of bubble coalescence and breakup were taken into account. Some new closure correlations describing bubble nucleation and departure on the heating surface were selected as well. For the purpose of comparison, flow boiling of liquid nitrogen was also numerically simulated using a modified two-fluid model. The results show that the simulations performed by using the ABND model achieve encouraging improvement in accuracy in predicting heat flux and wall temperature of a vertical tube. Moreover, the influence of the bubble coalescence and breakup is shown to be great on predicting overall pressure beyond the transition point.
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Abbreviations
- A C :
-
Cross sectional area of boiling channel
- a i :
-
Interfacial area concentration
- C pl :
-
Specific heat of the liquid phase at constant pressure
- D b :
-
Bubble diameter
- d bw :
-
Bubble departure diameter
- \(\vec{F}_{lv} ,\,\vec{F}_{vl}\) :
-
Interfacial force (N/m3)
- \(\vec{F}_{D}\) :
-
The drag force (N/m3)
- \(\vec{F}_{L}\) :
-
The lift force (N/m3)
- \(\vec{F}_{TD}\) :
-
The turbulent dispersion force (N/m3)
- \(\vec{F}_{W}\) :
-
The wall lubrication force (N/m3)
- f :
-
Bubble departure frequency
- g :
-
Gravitational acceleration
- h :
-
Inter-phase heat transfer coefficient
- \(h_{fv}\) :
-
Latent heat
- H:
-
Enthalpy
- k :
-
Turbulent kinetic energy (J/kg)
- N′:
-
Active nucleation site density
- n :
-
The bubble number density (bubbles/m3)
- R ph :
-
Source/sink term due to phase change
- t w :
-
Bubble waiting time
- T :
-
Temperature
- \(\Delta T_{\sup }\) :
-
Wall superheating
- \(\vec{U}\) :
-
Velocity (m/s)
- α :
-
Void fraction
- \(\alpha_{\hbox{max} }\) :
-
Maximum allowable void fraction
- ε :
-
Turbulent kinetic energy dissipation
- \(\mu^{e}\) :
-
Effective viscosity (Pa s)
- ρ :
-
Density (kg/m3)
- σ :
-
Surface tension (N/m)
- \(\xi_{H}\) :
-
Heated parameter
- Γ:
-
Mass transfer (kg/m3/s)
- \(\phi_{n}^{RC}\) :
-
Random collision rate
- \(\phi_{n}^{WE}\) :
-
Wake entrainment rate
- \(\phi_{n}^{TI}\) :
-
Turbulent impact rate
- l :
-
The liquid phase
- lv :
-
Transfer of quantities from vapor phase to liquid phase
- Sat:
-
Saturated
- Sub:
-
Subcooled
- Sup:
-
Superheated
- v :
-
The vapor phase
- vl :
-
Transfer of quantities from liquid phase to vapor phase
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Acknowledgments
Financial supports from the National Natural Science Foundation of China under Grant No. 50806042 and from the Science and Technology Commission of Shanghai Municipality under Grant No. 08DZ053300 are gratefully acknowledged.
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Shao, X., Li, X. & Wang, R. Numerical investigation on boiling flow of liquid nitrogen in a vertical tube using bubble number density approach. Heat Mass Transfer 52, 877–886 (2016). https://doi.org/10.1007/s00231-015-1608-1
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DOI: https://doi.org/10.1007/s00231-015-1608-1