Abstract
A framework for analyzing energy flux in turbulent channel flows is proposed which enables quantification of the drag reduction efficacy by different control methods. In contrast to the FIK [Fukagata, Iwamoto, and Kasagi, Phys. Fluids 14, L73 (2002)] and the RD [Renard and Deck, J. Fluid Mech. 790, 339 (2016)] identities, this framework expresses the skin friction coefficient in terms of the nondimensionalized dissipation rate and the work done by external excitation. We extend the energy-box analysis of Gatti et al. [J. Fluid Mech. 857, 345 (2018)] through a triple decomposition of energy flux and show how mean (), coherent (), and random turbulent () dissipations contribute differently to the drag reduction and the net power saving. Three control methods, including our recently developed spanwise opposed wall-jet forcing (SOJF), the spanwise wall oscillation (SWO), and the opposed wall blowing/suction (OBS) controls, are compared at via direct numerical simulations (DNS). While all methods yield comparable drag reductions (), OBS yields the maximum net power saving, followed by SOJF, and then SWO. Specifically, for SOJF control, (induced by the large-scale swirls) is much smaller than (induced mainly by the small-scale near-wall vortices) and (due to the spanwise vorticity sheet ). In contrast, for SWO control, (caused by the wall oscillation-induced vortex sheet)—much larger than that of SOJF—is comparable to and . For OBS control, is notably suppressed without any introduction of as the energy is injected through the random velocity field. Diagnoses performed at a higher (i.e., 2000) for SWO shows that random turbulent dissipation predominates due to the increasing near-wall vortical structures—hence their suppression should be the target for drag control at high . The analysis also suggests a promising hybrid drag control strategy by incorporating both the random (OBS) and coherent (SOJF or SWO) controls together, an issue for future exploration.
4 More- Received 13 July 2020
- Accepted 17 December 2020
DOI:https://doi.org/10.1103/PhysRevFluids.6.013902
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