Discussion: “Correlations for Prediction of Pressure Gradient of Liquid–Liquid Flow Through a Circular Horizontal Pipe” [Dasari, A., Desamala, A. B., Ghosh, U. K., Dasmahapatra, A. K., and Mandal, T. K., 2014, ASME J. Fluids Eng., 136(7), p. 071302

Abstract

The comments present an assessment of formulations for frictional pressure gradient correlation of moderately viscous lubricating oil–water two-phase flow through a horizontal pipe of 0.025 m internal diameter, which was obtained by Dasari et al. [1]. Their modified Lockhart–Martinelli correlation was(1)φW2=0.019X3+0.06X2-0.006X+1.397Recently, Muzychka and Awad [2] developed an alternative approach for predicting two-phase frictional pressure gradients using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. Muzychka and Awad [2] obtained an expression for the two-phase frictional interfacial multiplier for the liquid phase (ϕl,i2) as follows:(2)φl,i2=φl2-1-1X2From Eq. (2), it is clear that ϕl,i2 cannot be negative because their minimum values are zero, which correspond to the case of no contribution to the pressure gradient through phase interaction (i.e., (dp/dx)f,i = 0).It should be noted that the relations of two-phase frictional multiplier for liquid with higher density (water in these comments) and liquid with lower density (lubricating oil in these comments) in two-phase liquid–liquid flow are similar to the relations of two-phase frictional multiplier for liquid and gas in two-phase gas–liquid flow. The two-phase frictional multiplier concept that was introduced by Lockhart and Martinelli [3] for the case of two-phase gas–liquid flow can be used to model the flow of two immiscible liquids such as oil and water. For example, Awad and Butt [4] presented a simple semitheoretical method for calculating the two-phase frictional pressure gradient for liquid–liquid flow in pipes using asymptotic analysis. In their analysis, Awad and Butt [4] used the two-phase frictional multiplier concept that was introduced by Lockhart and Martinelli [3] for the case of two-phase gas–liquid flow to model the flow of two immiscible liquids such as oil and water.Substituting the Dasari et al. [1] correlation, Eq. (1), into the expression of for the two-phase frictional interfacial multiplier, Eq. (2), we obtain(3)φW,i2=0.019X3-0.94X2-0.006X+0.397From Eq. (3), it is clear that the Dasari et al. [1] correlation results in negative values of the two-phase frictional interfacial multiplier in the range of the Lockhart–Martinelli parameter (X) = 0.03–1. This is impossible because its minimum value is zero.Finally, it should be noted that the empirical correlation, i.e., Eq. (1), was developed by Dasari et al. [1] for the range of the Lockhart–Martinelli parameter (X) = 0.1–20, but would not be valid for X < 0.1 as shown by the authors' Eq. (2).