On the wake of two transversely counter-rotating inline spheres in a uniform flow

Flows past large particles in various engineering and industrial applications, such as combustion systems, atmospheric flows, chemical industries, transport phenomena, and blood cells in blood vessels, demonstrate interesting features of wake interaction. These interactions modify the wake characteristics and dynamic forces acting on the particles. In the present study, three-dimensional numerical computations are performed on uniform flow over two transversely counter-rotating inline spheres to analyze how the interactions affect the wake and dynamic characteristics. Numerical computations are performed using the Open Source Field Operation and Manipulation for a fixed value of Reynolds number (Re) of 300, which is defined based on the free stream velocity (U∞) and the sphere diameter (D). Spheres are rotated in opposite direction with the same angular velocity ω*=ωD2U∞, which is varied from 0 to 1. Here, ω* is the angular velocity normalized by the free stream velocity and the sphere diameter. The non-dimensionalized spacing (S) between spheres varies from 0.25 to 3. Three-dimensional iso-Q surfaces and streamlines are presented to illustrate the effect of S and ω* on wake structures of both spheres. For S ≤ 1, both upstream and downstream sphere wakes are found to be steady at ω* ≤ 0.4, whereas unsteady for ω* ≥ 0.6. However, the mechanism of unsteadiness for upstream and downstream wakes is different. In the upstream wake, instability is caused by vortex shedding from sphere surface, whereas in the downstream wake vortices are generated due to shear layer instability of the Kelvin–Helmhotz type. Hilbert spectra for lift coefficient signals of both spheres are presented to qualitatively measure the variation in the extent of nonlinearity associated with unsteady wake with a change in the value of S and ω*. The variation in Strouhal number, drag, and lift forces with a change in the value of S and ω* also demonstrated.