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In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re=U∞Dν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity (U∞) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω*=ωD2U∞, viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G=gD between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω*=0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω* and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω*=0 and 1 and decrease for ω*=−1. Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω*=0. On the other hand, it increases for ω*=−1 and decreases for ω*=1. Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω*=0 and 1 and decreases for ω*=−1. In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.
In the present work, the flow over a transversely rotating sphere placed at varying separation from a plane wall at a Reynolds number Re=U∞Dν of 300 is numerically investigated using Open Source Field Operation and Manipulation, where Re is defined based on the free stream velocity (U∞) and the diameter (D) of the sphere. Three values of the non-dimensional rotational speed ω*=ωD2U∞, viz., −1, 0 and 1, have been chosen with ω being the dimensional rotation rate with anticlockwise rotation being positive. The non-dimensional separation gap G=gD between the sphere and the wall is varied from 0.25 to 3.0. Here, g is the dimensional gap between the sphere and the wall. At ω*=0 and G = 0.25, the wall completely suppresses vortex shedding from the sphere, whereas flow is found to be unsteady for other values of ω* and G. As compared to the case in the absence of the wall, the presence of the wall causes an increase in vortex shedding frequency for ω*=0 and 1 and decrease for ω*=−1. Hilbert spectrum reveals that the wake nonlinearity remains unchanged with an increase in G for ω*=0. On the other hand, it increases for ω*=−1 and decreases for ω*=1. Similar to the observation made for vortex shedding, the presence of wall increases drag force on the sphere for ω*=0 and 1 and decreases for ω*=−1. In order to reveal the spatial and temporal behavior of the coherent structures in the unsteady wake, dynamic mode decomposition (DMD) has been performed. For all the values of G, DMD mode 1 is found to be the primary vortex shedding mode.
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.
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