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The accurate prediction of pressure loss for two-phase slug flow in pipes with a simple and powerful methodology has been desired. The calculation of pressure loss has generally been performed by complicated mechanistic models, most of which require the iteration of many variables. The objective of this study is to optimize the previously proposed simplified slug flow model for horizontal pipes, extending the applicability to turbulent flow conditions, i.e., high mixture Reynolds number and near horizontal pipes. The velocity field previously measured by particle image velocimetry further supports the suggested slug flow model which neglects the pressure loss in the liquid film region. A suitable prediction of slug characteristics such as slug liquid holdup and translational velocity (or flow coefficient) is required to advance the accuracy of calculated pressure loss. Therefore, the proper correlations of slug liquid holdup, flow coefficient, and friction factor are identified and utilized to calculate the pressure gradient for horizontal and near horizontal pipes. The optimized model presents a fair agreement with 2191 existing experimental data (0.001 ≤ μL ≤ 0.995 Pa∙s, 7 ≤ ReM ≤ 227,007 and −9 ≤ θ ≤ 9), showing −3% and 0.991 as values of the average relative error and the coefficient of determination, respectively.

In this study, we show that complex local flow fields, particularly those near corrugated surfaces, can be accurately reproduced with effective Navier-slip boundary conditions over an imaginary smooth surface, in which the normalized slip length can be considered as a surface property even for non-Newtonian fluid flows. The expression for the normalized slip length was derived analytically using the effective viscosity and effective shear rate in a pressure-driven channel flow with a corrugated surface, based on the two-parameter model by separating geometrical and rheological factors with the effective viscosity concept. Our framework was established on the combination of the force balance approach for slip length characterization and the flow quantification method based on the energy dissipation rate. Effects of corrugated patterns with various aspect ratios were investigated. For verification, an example stick–slip–stick flow problem was tested and the results were compared with those of direct simulations. We report that the dimensionless normalized slip length appears to be almost constant and independent of the flow rate (or pressure drop). This implies that the normalized slip length is nearly independent of rheological properties. In addition, the dimensionless slip length of non-Newtonian fluids was found to be close to that of a Newtonian fluid, and it depends on the flow geometry itself. [ABSTRACT FROM AUTHOR]