Insights into the physics of dominating frequency modes for flow past a stationary sphere: Direct numerical simulations

Abstract

Direct numerical simulations are carried out for an incompressible flow past a stationary sphere, in the range of 100 ≤ Re ≤ 1000. It is found that the first instability occurs as the axisymmetric wake undergoes breakage at Re ≥ 250. Adding small perturbations to the flow showed that the preferred direction of breakage of the axisymmetric wake and the corresponding contribution of the y and z-direction lift coefficients are highly sensitive and get randomly affected even due to slightest perturbations that might get induced. The second instability arises at Re = 300 as large-scale hairpin shaped structures are formed and shed periodically at frequency StVS = 0.134. At Re = 350, the highly regular hairpin shedding pattern undergoes a quasiperiodic change. From the Q-criterion isosurface, we observed that the quasiperiodicity is induced due to the formation and shedding of secondary hairpin structures which are alongside the primary ones. These secondary hairpin structures are of discernable orientations and are shed 4 times slower as compared to the primary hairpins at Re = 350. Identification of these secondary hairpin structures confirms the hypothesis of wake modulation. The low-frequency mode (Stm) is captured when energy spectral analysis is performed on the surface integrated instantaneous force coefficients and on the radial velocities. The low-frequency mode further exists at all higher Re, exhibiting a gradual increase in Stm. At Re ≥ 800, shear layer instabilities are manifested, demonstrating a characteristic peak at StKH = 0.32 in the energy spectra, rendering the mean lift coefficients to become zero again.