(630c) Virtual Mass of an Oscillating Sphere

Virtual mass or added mass describes the inertia of the fluid around a submerged body that acts to resist a relative acceleration between the body and the fluid. When the body is a sphere, this mass was determined to be ½ of the mass of the displaced fluid from the inviscid flow theory, under the condition that the relative acceleration is slow and the radius of the sphere is small such that the sphere develops a steady response to the acceleration. This result since then became a broadly accepted term in the equation of motion for spherical particles submerged in fluids.

Not all flows satisfy the condition of this classical result. In this study, we report that for a sphere performing small-amplitude oscillations in gases, its virtual mass is not surprisingly at odds with the classical expression. Sphere was suspended by a spring in a closed cell, the pressure of which was controlled and varied. We triggered oscillation of the sphere magnetically, and then measured the frequency of free oscillation, from which the virtual mass of the sphere was extracted. We found that for three gases CO₂, N₂ and CH₄ at pressures up to 96 bar virtual masses were consistently greater than that from the classical correlation by 30-40%. Simulations of oscillatory flow around sphere show that the flow still possesses an inviscid core, which explains that the observed virtual masses were nearly independent of the viscosities. The shape of the inviscid core, however, is changed by oscillation. Modeling of multiphase flows with strong virtual mass effects could benefit from improving our knowledge on virtual mass. We will also discuss a few practical applications of our oscillatory flow.