Generally-valid optimal Reynolds and Dean numbers for efficient liquid-liquid mixing in helical pipes

Abstract

This work documents optimal flow conditions in terms of Reynolds number Re (and Dean number De) for mixing of two miscible liquids in helical pipes. Extending our previous investigations (Mansour et al., 2017, 2018), many more configurations have been considered with widely different dimensions; as a consequence, generally-valid values for Reopt and Deopt have been obtained. A full-factorial design of experiment (DOE) has been carried out by considering all possible combinations of geometrical parameters studied in Mansour et al. (2018). This leads to a total of 27 different coiled configurations with a wide variety of curvature ratio (0.033–0.214) and dimensionless pitch (0.034–0.273). Additionally, 47 different values of the Reynolds number have been considered within the laminar range of 5–4000, which corresponds to a Dean number range of De = 2–1850. This study involves at the end 1269 distinct numerical simulations. The results reveal that the mixing efficiency as function of the Reynolds number always exhibits two peaks at nearly similar Reynolds numbers. Average values of the two optimal ranges of Reynolds number and Dean number have been deduced from all simulations, leading to Reopt,1≈35 (Deopt,1≈10), and Reopt,2≈650 (Deopt,2≈185). Those can be used to get excellent mixing within any coiled configuration. The first optimal value leads to a much lower pressure drop and a slightly better mixing efficiency, and is therefore recommended to get optimal mixing and power consumption.