Gravitational fall velocity of sphere in viscous fluid

The gravitational transient fall velocity of a rigid sphere in an otherwise quiescent viscous fluid is studied through examining the physical reasonableness of simulated results and comparing the results to Moorman's 1955 free-fall experiments. The published sphere dynamic equations from low-to-moderate sphere Reynolds number are solved numerically by a fourth order predictor-corrector method and iterations on sphere velocity and acceleration. Among the published sphere dynamic expressions, Mei and Adrian's 1992 expression has the best agreement with Moorman's data. The relative importance of the steady and unsteady drags along the gravitational transient process is also discussed. It is found that neglecting the unsteady drag indeed simplifies the computational procedure, but the accuracy on the time-varying fall velocity is significantly compromised. The added mass and history terms are of great importance at early stages of gravitational transient falling for low sphere-to-fluid density ratio and low sphere Reynolds number.