The effects of near-wall/outer regions and domain size on turbulent drag reduction via external body forces

Turbulent flows are well-known to exhibit a wide range of flow motions. Different flow control methods aim to target different motions for drag reduction. In this study, direct numerical simulations are performed up to a friction Reynolds number of 1000 to investigate the effects of different flow regions and domain size on drag reduction via external spanwise body forces. We first show the overall effect of the body force, where the effectiveness of drag reduction diminishes with increasing the Reynolds number (Re), especially around a friction Re of 500. To understand the drag contribution from different flow regions, the Fukagata-Iwamoto-Kasagi (FIK) identity is used. For the no-control case, the contribution of the outer region increases with Re, while the contribution of the near-wall region gradually decreases. However, the body force reduces drag by controlling the outer region, while barely affecting the near-wall region. Lastly, focusing on a friction Re of 500, we attempt to examine the impacts of the domain size on drag reduction. The premultiplied energy spectra are computed, indicating that as the domain size increases, the decrease in the maximum achievable drag reduction is mainly due to the energization of large-scale structures near the channel centerline. This study reemphasizes the need to control the outer region and large-scale motions when designing drag reduction strategies for higher Reynolds number and larger domain flows.