Optimal Reynolds number for liquid-liquid mixing in helical pipes

Abstract

A computational study has been performed to determine the mixing behaviour of two miscible liquids in helical pipes with different geometrical dimensions. To evaluate the mixing efficiency between the two liquids, the scalar transport technique has been employed. The main objectives are to investigate the influence of the geometrical parameters on the mixing behaviour and to find the optimal values of Reynolds number (Re) corresponding to the highest possible mixing efficiencies, while keeping acceptable pressure drop. The Reynolds number has been varied broadly from Re = 5 to Re = 4000, corresponding to Dean numbers from De = 1 to De = 1500, covering a wide range of laminar flows relevant for practical applications. Three main geometrical parameters of the helical pipe have been considered; the coil pitch, the pipe diameter, and the coil diameter were varied in the ranges of 16–60 mm, 5–15 mm, and 70–150 mm, respectively. The results show that an increase in coil pitch results generally in lower mixing efficiencies, negligibly higher pressure drops, and lower values of optimal Reynolds numbers. Increasing the pipe diameter leads to lower mixing efficiencies but significantly lower pressure drops. Finally, as the coil diameter is increased, the mixing efficiency and the pressure drop are slightly reduced, while the optimal Reynolds number is moderately shifted to higher values. Furthermore, two optimal values of Reynolds number could be obtained for all configurations, leading systematically to high mixing performance, Re ≈ 40 and Re ≈ 750. The pressure drop for the lower value of the Reynolds number is considerably lower than that of the second optimal value, while mixing efficiency is comparable. Therefore, it is recommended to operate liquid-liquid mixing in helical reactors at Re ≈ 40. This value corresponds to the Dean number range of 7 ⩽ De ⩽ 15 for all the considered geometries.