Velocity of Particles Falling in Vertically Oscillating Flow

Abstract

The instantaneous velocity of particles driven by an oscillating flow can be determined by means of Fourier analysis. A simple numerical method based on the principle of least square error is presented to obtain the solutions of the Fourier coefficients. The computed zeroth harmonic term, which is the effective fall velocity and is less than the terminal velocity in still fluid, is in good agreement with experimental observations. The reduced velocity is caused by the nonlinear modification of the drag force exerted on the particle by the fluid because the relative velocity between the particle and the fluid is no longer the constant terminal velocity. There are three parameters that determine the effectiveness of fall velocity reduction: The terminal velocity Reynolds number, the ratio of the flow velocity amplitude to the terminal velocity, and a quantity characterizing the frequency response of the particle to the unsteadiness of the flow motion.