Experimental evaluation of the virtual mass of two solid spheres accelerating in fluids

The virtual mass force of two equal spheres is investigated experimentally when both spheres were moving side by side and along the line joining their centers. The velocities of two accelerated spheres rising along the axis of a glass cylindrical column of a 2 m long and a diameter of 0.3 m, under the action of a driving weight, are measured as a function of time and separation distance between spheres centers ranging from about 2 to 7 radii. During the accelerated motion of the spheres, Reynolds number varied between 10 and 103. The spheres employed are made of stainless steel of the following four different diameters: 9.4, 12, 13.5 and 15.4 mm. A main conclusion of this work is that the virtual mass coefficient (CVM) was found to decrease with increasing the instantaneous Reynolds number. For two equal spheres moving side by side, CVM > 0.5 when the spheres touched. As the distance between them increased, CVM decreased and approached the single sphere value of 0.5 when the spheres were separated by more than 3 radii. For two equal spheres moving along the line joining their centers, when the spheres touched, CVM < 0.5. As the distance between them increased, CVM increased and approached the value of 0.5 when the spheres were separated by more than 5 radii. The experimental results compared well with theoretical results found in the literature.