DIMENSIONAL ANALYSIS OF TERMINAL VELOCITY OF A TAYLOR BUBBLE IN A VERTICAL PIPE

Abstract

An empirical correlation of the terminal velocity of a Taylor bubble in a vertical pipe is proposed. A fundamental functional form, Fr = f (ReD, EoD), of the correlation is deduced by carrying out a dimensional analysis based on the local instantaneous field equations and the jump conditions. Here Fr is the Froude number, ReD the bubble Reynolds number, and EoD the Eötvös number. In the two limiting cases, (EoD→∞ and ReD→∞) and (EoD→∞ and ReD → 0), the deduced functional form approaches those of the well-known Fr models. Coefficients appearing in the correlation are determined by making use of the limiting cases and available experimental data. Comparisons between the proposed Fr correlation and the experimental data show that the correlation gives a good estimation of terminal velocities of Taylor bubbles for a wide range of fluid properties and pipe diameters, i.e., 10 -7< Re D < 10 4, 4 < Eo D < 3 ×10 3, 10 -2 < N < 10 5, and -11 < log M < 10, where N is the inverse viscosity number and M the Morton number.