A drag correlation of fluid particles rising through stagnant liquids in vertical pipes at intermediate Reynolds numbers

A drag correlation for a fluid particle rising along the axis of a vertical pipe at low and intermediate Reynolds numbers, Re, is proposed by making use of available correlations and a numerical database accumulated by interface tracking simulations. The accuracy of the interface tracking method has been verified through comparisons between measured and predicted velocities of single drops in vertical pipes. Being similar to drag model for solid spheres proposed by Michaelides, the developed drag correlation takes into account inertial and wall effects as their linear combination. The correlation gives good estimation of the drag coefficient for fluid particles rising through stagnant liquids in vertical pipes under the conditions of 0.13⩽Eo⩽30, −10.0⩽log M⩽2.0, 0.083⩽Re<200, 0⩽κ⩽10.0 and λ⩽0.6, where Eo is the Eötvös number, M the Morton number, κ the viscosity ratio and λ the ratio of particle diameter to pipe diameter.