Correlation of entrainment for annular flow in vertical pipes

A correlation for entrainment in vertical gas–liquid annular flows is presented. The experiments cover pipe diameters of 1.06–5.72 cm, superficial gas velocities of 20–119 m/s, superficial liquid velocities of 0.012–1.35 m/s, gas densities of 0.27–35 kg/m3 and surface tensions of 0.01–0.073 N/m. Entrainment is considered to result from a balance between the rate of atomization of the wall layer and the rate of deposition of drops. Both rates decrease with increasing liquid flow. A simplified approach which uses the rate equations for low liquid inputs is adopted. The basic idea is that decreases in the rates compensate one another. An approximate empirical equation is obtained by simply substituting the gas velocity for the ratio of the deposition constant and the slip coefficient of the drops. A theoretical approach which relates the deposition constant to particle turbulence is also explored.