A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription For more information, please contact the WRAP Team at: wrap@warwick.ac.ukUnder consideration for publication in J. Fluid Mech. 1The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves This paper exploits the turbulent flow control method using streamwise travelling waves ) to study the effect of Reynolds number on turbulent skin-friction drag reduction. Direct numerical simulations of a turbulent channel flow subjected to the streamwise travelling waves of spanwise wall velocity have been performed at Reynolds numbers ranging from Re τ = 200 to 1600. To the best of the authors' knowledge, this is the highest Reynolds number attempted with DNS for this type of flow control. The present DNS results confirm that the effectiveness of drag reduction deteriorates, and the maximum drag reduction achieved by travelling waves decreases significantly as the Reynolds number increases. The intensity of both the drag reduction and drag increase is reduced with the Reynolds number. Another important finding is that the value of the optimal control parameters changes, even in wall units, when the Reynolds number is increased. This trend is observed for the wall oscillation, stationary wave, and streamwise travelling wave cases. This implies that, when the control parameters used are close to optimal values found at a lower Reynolds number, the drag reduction deteriorates rapidly with increased Reynolds number. In this study, the effect of Reynolds number for the travelling wave is quantified using a scaling in the form Re −α τ . No universal constant is found for the scaling parameter α. Instead, the scaling parameter α has a wide range of values depending on the flow control conditions. Further Reynolds number scaling issues are discussed. Turbulent statistics are analysed to explain a weaker drag reduction observed at high Reynolds numbers. The changes in the Stokes layer and also the mean and r.m.s. velocity with the Reynolds number are also reported. The Reynolds shear stress analysis suggests an interesting possibility of a finite drag reduction at very high Reynolds numbers.

The effectiveness of the opposition control method proposed by Choi et al . [H. Choi, P. Moin, and J. Kim, J. Fluid Mech. 262, 75-110 (1994)] has been studied using direct numerical simulations. In this study, the effects of the amplitude and the phase of wall blowing and suction control input were considered separately. It is found that the amplitude of wall blowing and suction as well as the detection plane location played an important role in active control for skin friction drag reduction. By changing the amplitude, a substantial drag reduction was achieved for all detection plane locations considered, and the efficiency of the opposition control was also improved. When the control was effective, the drag reduction was proportional to the wall blowing and suction strength. There existed a maximum wall blowing and suction strength, beyond which the opposition control became less effective or even unstable. Turbulence characteristics affected by various wall blowing and suction parameters were analysed to understand * Corresponding author: Y.M.Chung@warwick.ac.uk the underlying mechanisms for drag reduction. The wall normal velocity and vorticity fluctuations showed a strong correlation with drag reduction.

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A pseudo two-dimensional (P2D) electro-chemical lithium-ion battery model is presented in this paper to study the capacity fade under cyclic charge-discharge conditions. The