Calculation of terminal velocity in transitional flow for spherical particle

Abstract The terminal velocity has been widely used in extensive fields, but the complexity of drag coefficient expression leads to the calculation of terminal velocity in transitional flow (1<Re≤1000) with much more difficulty than those in laminar flow (Re≤1) and turbulent flow (Re≥1000). This paper summarized and compared 24 drag coefficient correlations, and developed an expression for calculating the terminal velocity in transitional flow, and also analyzed the effects of particle density and size, fluid density and viscosity on terminal velocity. The results show that 19 of 24 previously published correlations for drag coefficient have good prediction performance and can be used for calculating the terminal velocity in the entire transitional flow with higher accuracy. Adapting two dimensionless parameters (w∗, d∗), a proposed explicit correlation, w∗=-25.68654×exp(Formula presented.)+24.89826, is attained in transitional flow with good performance, which is helpful in calculating the terminal velocity.