On Upward Flow of Gas-Liquid Mixtures in Vertical Tubes : 2nd Report, Consideration of Frictional Pressure Drop and Void Fraction

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This paper describes the derivation of an expression for predicting the frictional pressure drop of steady-state upward two-phase flow based on an annular flow model. The procedure followed is to express the shear stress at the tube wall as a function of the liquid velocity u_δ at the edge of the laminar sublayer and the void fraction α. The effect of the flow characteristics on u_δ is introduced by defining an equivalent mean velocity of the liquid phase u_m^*. The appropriate relation between u_δ and u_m^* is determined from the experimental data in the prior report. As an extension of this analysis, a prediction is also presented for the frictional pressure drop of bubble flow. In addition, the void fraction α is derived from an empirical expression for the mean velocity of the gas phase.
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