The Effect of a Spanwise Body Force on Skin-Friction Reduction and its Connections to Low-Drag States in Turbulent Flow

Abstract

Reducing turbulent skin-friction drag is a subject of great interest due to the potential benefits. These benefits are reflected in applications such as aircraft and vehicles for which skin-friction drag constitutes a significant fraction of the total drag. For example, commercial airliners have up to 50% of their fuel consumption associated with turbulent drag. Thus, any drag reduction would result in substantial savings with regards to the operational cost of the airline industry. In this study, we investigated the effects of a spanwise body force on reducing skin-friction drag in turbulent channel flows. To this end, we performed direct numerical simulations (DNS) of turbulent channel flows with an applied spanwise body force. The body force consists of four control parameters: the amplitude of excitation, penetration depth, period of oscillation, and wavelength. A series of DNS were performed to investigate the effect of these parameters on drag reduction. We observed different levels of drag reduction and the magnitude of skin-friction varied considerably. The DNS results showed that the skin friction is reduced by as much as 20% with values for penetration lengths from 0.03 to 0.09 and periods between 10 and 20. An optimal combination of the four adjustable control parameters is yet to be concluded. In addition to skin-friction reduction, we found an intriguing observation from a time series of wall shear stress. When the wall shear stress is sufficiently lower than its mean value (i.e., low-drag intervals), the spanwise body force appears to significantly affect turbulent dynamics to make the wall shear stress not as chaotic as in other intervals. Specifically, the standard deviations of the peak-to-peak magnitudes of the wall shear stress during low-drag intervals are significantly lower than that of other intervals. This observation could be crucial in that it may lead to a further fundamental understanding of the drag reduction process. Moreover, it may aid in the development of more effective control schemes by way of anticipating that low-drag intervals are promising targets for drag reduction.