Terminal velocity of a Taylor drop in a vertical pipe

Abstract

A scaling analysis based on the field equations for two phases and the jump conditions at the interface is carried out to deduce a balance of forces acting on a Taylor drop rising through stagnant liquid in a vertical pipe. The force balance is utilized to deduce a functional form of an empirical correlation of terminal velocity of the Taylor drop. Undetermined coefficients in the correlation are evaluated by making use of available correlations for two limiting cases, i.e. extremely high and low Reynolds number Taylor bubbles in large pipes. Terminal velocity data obtained by interface tracking simulations are also used to determine the coefficients. The proposed correlation expresses the Froude number Fr as a function of the drop Reynolds number Re D , the Eötvös number Eo D and the viscosity ratio μ *. Comparisons between the correlation, simulations and experimental data confirm that the proposed correlation is applicable to Taylor drops under various conditions, i.e., 0.002 < Re D < 4960, 4.8 < Eo D < 228, 0 ⩽ μ * ⩽ 70, 1 < N < 14700, −12 < log M < 4, and d/ D < 1.6, where N is the inverse viscosity number, M the Morton number, d the sphere-volume equivalent drop diameter and D the pipe diameter.