Interfacial Friction Factors in Vertical Circular Pipes under Flooding Conditions at the Bottom End

Abstract

In our previous study (Goda et al.), we measured the void fraction α, pressure gradient dP/dz, and countercurrent flow limitation (i.e. relationship between superficial velocities, JG and JL) in vertical pipes (diameter D = 20 and 40 mm) under flooding conditions at the square bottom end and working fluids of air and water to obtain the wall friction factor fw and the interfacial friction factor fi based on the annular flow model. Measurements of α in vertical pipes under flooding conditions are few. In this study, therefore, we evaluated fi from the measured dP/dz under flooding at the square bottom end reported by Bharathan et al. with D = 6.4 to 152 mm and air-water and by Ilyukhin et al. with D = 20 mm and working fluids of steam and water at pressures of P = 0.6 to 4.1 MPa. As a result, we found that the fi values obtained from the measured dP/dz and the fw correlation by Goda et al. were well correlated in terms of the gas Kutateladze parameter KG * and the dimensionless diameter D *. The effect of fluid properties was expressed by a revision term with the viscosity ratio of gas and liquid phases (μG/μL).

Gas-liquid Interfacial Friction Factor under Flooding Conditions in Vertical Pipes

“…混相流 Japanese Journal of Multiphase Flow Advance Publication by J-STAGE Sano et al [14] proposed the fi correlation for RF expressed by Eq. ( 10).…”

“…Ilyukhin et al [16] measured dP/dz of steam-water flows in a D = 20 mm pipe with S/S in the pressure range of P = 0.6-4.1 MPa. Takaki et al [8] and Sano et al [14] obtained fi from the dP/dz data [15][16] and the proposed fw correlations. We evaluated a fi correlation for SF and RF (which does not depend on the flow patterns) in this study by using those fi values.…”

Flow characteristics in vertical circular pipes with the square top end under flooding conditions

“…proposed an fi correlation for RF based on data for D = 20 and 40 mm as a function of JG * . Sano et al (2020) proposed an fi correlation for RF based on data for a wide range of D (D = 6.6-152 mm) as a function of KG * . For SF, however, the fi data have not been correlated, and Fig.…”