A high precision model for the terminal settling velocity of drops in fluid medium

Abstract

The terminal settling velocity (TSV) calculation of drops and other spherical objects in fluid medium is a classical problem, which has important application values in many fields such as the study of cloud and precipitation processes, the evaluation of soil erosion, and the determination of fluid viscosity coefficient etc. In this paper, a new explicit approximation model of TSV is established, which combines the theoretical solution of N-S equation about fluid motion around spherical objects and the statistical regression of solution dimensionless coefficients with measurement data. This new model can adapt to different values of drop parameters and medium parameters in a large range of Re. By this model, the relative and absolute calculation errors of TSV are in range of −3.42%–+4.34% and −0.271 m/s–+0.128 m/s respectively for drop radius 0.005–2.9 mm. Their corresponding root mean square values are 1.77% and 0.084 m/s respectively, which are much smaller than that of past theoretical and empirical models.

Graphical abstract

Keywords

terminal settling velocity / drag coefficient / viscous resistance / drop / fluid medium

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