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ABSTRACT
Heat transfer and pressure drop characteristics of condensation for R410A inside horizontal tubes (dh = 0.25, 1, and 4 mm) at saturation temperatures Tsat = 310, 320, and 330 K are investigated numerically. Liquid–vapor interfaces and stream traces are also presented to provide a better understanding of the effect of saturation temperature on the condensation process inside micro tubes. The results indicate that local heat transfer coefficients and pressure drop gradients increase with increasing mass flux and vapor quality and with decreasing tube diameter and saturation temperature. Liquid film thickness also increases with increasing saturation temperature because of the lower surface tension at a higher saturation temperature. When gravity dominates the condensation process, a vortex with its core lying at the bottom of the tube is found in the vapor phase region. For annular flow regime at dh = 0.25 mm, the vortex disappears, and stream traces point from the symmetry plan to the liquid–vapor interface, where the vapor phase turns into the liquid phase. Numerical heat transfer coefficients and pressure drop gradients are compared with available empirical correlations. Two new models for heat transfer coefficients and frictional pressure drop gradients are developed based on the numerical work. A reasonable agreement between predicted and numerical results is obtained.
Nomenclature
| Bo | = | Bond number, [–] |
| C | = | Chisholm number |
| Cp | = | specific heat capacity, Jkg−1 K−1 |
| dh | = | hydraulic diameter, m |
| E | = | specific sensible enthalpy, Jkg−1 |
| f | = | fanning friction factor |
| F | = | surface tension force, N |
| Fr | = | Froude number |
| Fr* | = | modified Froude number |
| g | = | gravitational acceleration, ms−2 |
| G | = | mass flux, kgm−2 s−1 |
| Ga | = | Galileo number, [–] |
| h | = | heat transfer coefficient, wm−2 K−1 |
| hlv | = | latent heat of vaporization, Jkg−1 |
| Ja | = | Jacob number, [–] |
| k | = | thermal conductivity, Wm−1 K−1 |
| m | = | mass source due to phase change, kgm−3 s−1 |
| MAD | = | mean average deviation, [–] |
| MRD | = | mean relative deviation, [–] |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number, [–] |
| Pred | = | reduced pressure, [–] |
| q | = | heat flux, wm−2 |
| r | = | coefficient of mass source, s−1 |
| Re | = | Reynolds number, [–] |
| Su | = | Suratman number, [–] |
| T | = | temperature, K |
| v | = | velocity, ms−1 |
| x | = | vapor quality, [–] |
| Xtt | = | Lockhart–Martinelli parameter |
| α | = | volume fraction, [–] |
| ε | = | void fraction of vapor, [–] |
| κ | = | curvature of the interface, m−1 |
| μ | = | dynamic viscosity, Pas |
| ρ | = | density, kgm−3 |
| σ | = | surface tension, Nm−1 |
| Ф | = | two-phase pressure drop multiplier |
| Subscripts | = | |
| a | = | acceleration |
| annular | = | annular flow regime |
| B | = | free convection |
| cal | = | results predicted by correlation |
| conv | = | convective |
| F | = | forced convection |
| h | = | homogenous |
| l | = | liquid phase |
| lo | = | all refrigerant assumed to be liquid |
| ra | = | Rouhani–Axelsson |
| sat | = | saturation status |
| sim | = | results obtained by simulation |
| strat | = | stratified flow regime |
| tp | = | two phase |
| v | = | vapor phase |
| vo | = | all refrigerant assumed to be liquid |
| wall | = | wall |
Nomenclature
| Bo | = | Bond number, [–] |
| C | = | Chisholm number |
| Cp | = | specific heat capacity, Jkg−1 K−1 |
| dh | = | hydraulic diameter, m |
| E | = | specific sensible enthalpy, Jkg−1 |
| f | = | fanning friction factor |
| F | = | surface tension force, N |
| Fr | = | Froude number |
| Fr* | = | modified Froude number |
| g | = | gravitational acceleration, ms−2 |
| G | = | mass flux, kgm−2 s−1 |
| Ga | = | Galileo number, [–] |
| h | = | heat transfer coefficient, wm−2 K−1 |
| hlv | = | latent heat of vaporization, Jkg−1 |
| Ja | = | Jacob number, [–] |
| k | = | thermal conductivity, Wm−1 K−1 |
| m | = | mass source due to phase change, kgm−3 s−1 |
| MAD | = | mean average deviation, [–] |
| MRD | = | mean relative deviation, [–] |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number, [–] |
| Pred | = | reduced pressure, [–] |
| q | = | heat flux, wm−2 |
| r | = | coefficient of mass source, s−1 |
| Re | = | Reynolds number, [–] |
| Su | = | Suratman number, [–] |
| T | = | temperature, K |
| v | = | velocity, ms−1 |
| x | = | vapor quality, [–] |
| Xtt | = | Lockhart–Martinelli parameter |
| α | = | volume fraction, [–] |
| ε | = | void fraction of vapor, [–] |
| κ | = | curvature of the interface, m−1 |
| μ | = | dynamic viscosity, Pas |
| ρ | = | density, kgm−3 |
| σ | = | surface tension, Nm−1 |
| Ф | = | two-phase pressure drop multiplier |
| Subscripts | = | |
| a | = | acceleration |
| annular | = | annular flow regime |
| B | = | free convection |
| cal | = | results predicted by correlation |
| conv | = | convective |
| F | = | forced convection |
| h | = | homogenous |
| l | = | liquid phase |
| lo | = | all refrigerant assumed to be liquid |
| ra | = | Rouhani–Axelsson |
| sat | = | saturation status |
| sim | = | results obtained by simulation |
| strat | = | stratified flow regime |
| tp | = | two phase |
| v | = | vapor phase |
| vo | = | all refrigerant assumed to be liquid |
| wall | = | wall |