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Abstract
The objective of this study was to reduce the uncertainties of correlations for flow characteristics in vertical pipes under flooding at the top end. The void fraction α, pressure gradient dP/dz, and countercurrent flow limitation (CCFL) were previously measured with diameter D = 40 mm and working fluid of air and water. The wall friction and interfacial friction factors (fw and fi) were obtained based on the annular flow model, and CCFL and fw were evaluated in detail. Hence, attention was turned to detailed evaluations of α and fi. Liquid film thickness δ and interfacial friction factor fi for smooth film (SF) due to flooding at the top end were obtained using the previously derived fw correlation and existing dP/dz data with D = 20 to 50.8 mm and pressure P = 0.1 to 4.1 MPa, and empirical correlations for δ and fi were derived. The δ term was well expressed by a function of the liquid Reynolds number ReL, and the uncertainty of the δ correlation was ±0.0062 for α = 0.87 to 0.98. fi was expressed by a function of δ/L (where L is the Laplace length) or the Kutateladze parameter KG*, the dimensionless diameter D* (=D/L), and the density ratio of the gas and liquid phases ρG/ρL. The applicability of the derived correlations to conditions of D = 300 mm and P = 7 MPa was evaluated, and the fi correlation was modified based on fi values computed with the δ correlation. The drift-flux parameters for SF were also considered.
Nomenclature
| C = | = | CCFL constant |
| C0 = | = | distribution parameter |
| D = | = | pipe diameter (m) |
| D* = | = | dimensionless pipe diameter |
| = | interfacial friction factor | |
| = | wall friction factor | |
| g = | = | gravitational acceleration (m/s2) |
| h = | = | water level in the upper tank (m) |
| J = | = | superficial velocity (m/s) |
| J* = | = | Wallis parameter |
| K* = | = | Kutateladze parameter |
| L = | = | Laplace length (m) |
| Lν = | = | length defined by EquationEq. (19) |
| m = | = | slope of CCFL characteristics |
| P = | = | pressure (Pa) |
| Re = | = | Reynolds number |
| Vgj = | = | drift velocity (m/s) |
| Vgj* = | = | dimensionless drift velocity |
| WL = | = | liquid flow rate limited by flooding (m3/s) |
| z = | = | axial coordinate (m) |
| Greek | = | |
| α = | = | void fraction |
| δ = | = | liquid film thickness (m) |
| μ = | = | viscosity (Pa·s) |
| ν = | = | kinematic viscosity (m2/s) |
| ρ = | = | density (kg/m3) |
| σ = | = | surface tension (N/m) |
| Subscript | = | |
| B = | = | bottom |
| c = | = | computed |
| G = | = | gas phase |
| i = | = | G or L |
| L = | = | liquid phase |
| m = | = | measured |
| T = | = | top |
| Superscript | = | |
| * = | = | dimensionless form |