Drag Crisis on a Smooth Sphere Exposed to Free Stream Turbulence

Flow past a smooth sphere exposed to free stream turbulence intensity (\({T}_{u}\)) of \(0.4\%\) and \(1\%\) in the regime \(5\times {10}^{4}\le \text{Re} \le 5\times {10}^{5}\) is studied via measurement of unsteady forces. The measurements span three flow regimes, namely subcritical, critical and supercritical. As proposed by Deshpande et al. (J Fluid Mech 812:815–840, 2017 [4]), subregimes: I, II and III are also observed in the critical regime. With increase in turbulence intensity, the drag crisis shifts to a lower \(\text{Re}\) and the maximum drag force experienced by the sphere reduces drastically. With increase in \({T}_{u}\), the drop in \({{\overline{C}}_{D}}\) becomes more gradual to the extent that subregime-II is not observed for \({T}_{u}=1\%\). Probability density functions (PDF) of low-pass filtered time histories of the three force coefficients are used to investigate the various flow states in the critical regime. Some of these states are associated with asymmetric lateral forces, indicating non-axisymmetric transition of the boundary layer. It is proposed that this is due to non-axisymmetric formation of the laminar separation bubble (LSB). Towards the end of the critical regime, near-zero lateral forces and very low \({{\overline{C}}_{D}}\) are observed. These indicate that the LSB is axisymmetric at all time instants at this \(\text{Re}\).