Effect of size and spacing on the wake characteristics of two spheres placed in tandem

Abstract

In the present study, the flow past two spheres placed in a tandem arrangement is investigated numerically using open source field operation and manipulation (OpenFOAM) at a fixed Reynolds number (Re) of 300, where the Reynolds number is defined based on the diameter (D) of the downstream sphere (DS) and the freestream velocity at the inlet. Keeping size of the DS constant, the diameter of the upstream sphere (US) has been varied, so that the diameter ratio, DR (ratio of the diameters upstream and downstream spheres), takes the values of 0.4, 0.6, 0.8, 1.0, and 1.5. The spacing between the spheres (S) is also varied from 1D to 5D. Iso-Q surfaces show that both upstream and downstream wakes undergo various transitions with changes in the values of DR and S. For US, transition from steady symmetric to planar symmetric occurs at DR = 0.6 and S = 1, which corresponds to a local Re of 180. For DR = 0.8, steady to unsteady transition occurs at S = 2, whereas for all other values of S, the wake remains steady. For DR > 0.8 and S > 1, both upstream and downstream wakes are found to be unsteady. Hilbert analysis revealed that unsteady wakes are periodic for DR values of 0.4, 0.8, and 1.0 and are aperiodic for DR = 1.5. In addition, the extent of wake nonlinearity has also been quantified in terms of degree of stationarity. The drag force on both the spheres increases with an increase in spacing between the spheres.