The power consumption of impellers is a fundamental parameter for the design, operation, and scale‐up of stirred vessels. While numerous power correlations have been reported for various impellers in cylindrical tanks, no correlation has been established for crescent‐shaped impellers commonly used in round‐bottom flasks at the laboratory scale. In this study, a power correlation for crescent‐shaped impellers installed in round‐bottom flasks was developed, with particular attention to the effect of impeller mounting position. Power measurements were conducted using six crescent‐shaped impellers of different geometries under various liquid heights without baffles. To examine the influence of impeller clearance from the vessel bottom, additional experiments were performed using paddle and Rushton turbine impellers installed at different vertical positions in a flat‐bottom cylindrical vessel. The results revealed that, even under laminar flow conditions, the power number increased significantly when the impeller was installed near the vessel bottom. This increase was attributed to the interaction between the impeller and the laminar boundary layer formed on the vessel bottom. Based on these findings, the existing correlation proposed by Kamei et al. was modified. The turbulent term was adjusted, and the laminar power number was multiplied by a factor of 1.4 to account for bottom installation with minimal clearance. The modified correlation successfully correlated the experimental data for crescent‐shaped impellers over the Reynolds number range of 1 < Re < 10,000, with an average error of 10%. This correlation enables power‐based scale‐up of laboratory‐scale mixing operations using round‐bottom flasks to industrial stirred vessels.
Xueer et al. (Thu,) studied this question.