Abstract
Annular Poiseuille flows in a transitional regime were investigated by direct numerical simulations with an emphasis on turbulent statistics including the friction factor that are affected by the presence of large-scale transitional structures. Five different radius ratios in the range of 0.1–0.8 and several friction Reynolds numbers in the range of 48–150 were analyzed to consider various flow states accompanied by characteristic transitional structures. Three characteristic structures, namely, turbulent–laminar coexistence referred to as “(straight) puff,”“helical puff,” and “helical turbulence” were observed. The selection of the structures depends on both the radius ratio and the Reynolds number. The findings indicated that despite the transitional state with a turbulent–laminar coexistence, the helical turbulence resulted in a friction factor that was as high as the fully turbulent value. In contrast, with respect to the occurrence of streamwise-finite transitional structures, such as straight/helical puffs, the friction factor decreased in a stepwise manner toward a laminar level. The turbulent statistics revealed asymmetric distributions with respect to the wall-normal direction wherein the profiles and magnitudes were significantly influenced by the occurrence of transitional structures.
Highlights
Turbulent transition in most wall-bounded shear flows is characterized by subcritical scenarios.[1,2] There exists a significant hysteresis between critical Reynolds numbers for global (Reg) and linear instabilities (Rel)
We would show rather simpler transition processes for high and low h, where observed structures are reminiscent of well-known transition scenarios in pPf and cylindrical Poiseuille flow (cPf)
We describe the transition process for intermediate h = 0.3, which seems to combine the features of transitional structures for lower and higher h, as an anomalous case of annular Poiseuille flow (aPf)
Summary
Turbulent transition in most wall-bounded shear flows is characterized by subcritical scenarios.[1,2] There exists a significant hysteresis between critical Reynolds numbers for global (Reg) and linear instabilities (Rel). The cylindrical Poiseuille flow (cPf) and plane Couette flow (pCf) are widely known to be linearly stable for any Reynolds number. Experimental studies demonstrated that both cPf and pCf cannot maintain these laminar states at high Reynolds numbers, no matter how ideal experiment is conducted,[3] because unpreventable finite-amplitude disturbance triggers a subcritical bypass transition for Re (\Rel). The lower bound of this subcritical transitional regime may be defined as Reg.[1] This corresponds to the lowest Reynolds number to sustain turbulence even under a spatiotemporal intermittent state, and this value is important practically and scientifically.
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