This paper examines how increasing the value of the Reynolds number Re affects the ability of spanwise-forcing techniques to yield turbulent skin-friction drag reduction. The considered forcing is based on the streamwise-travelling waves of spanwise wall velocity (Quadrio et al. J. Fluid Mech., vol. 627, 2009, pp. 161-178). The study builds upon an extensive drag-reduction database created with Direct Numerical Simulation of a turbulent channel flow for two, 5-fold separated values of Re, namely Re τ = 200 and Re τ = 1000. The sheer size of the database, which for the first time systematically addresses the amplitude of the forcing, allows a comprehensive view of the drag-reducing characteristics of the travelling waves, and enables a detailed description of the changes occurring when Re increases. The effect of using a viscous scaling based on the friction velocity of either the non-controlled flow or the drag-reduced flow is described. In analogy with other wall-based drag reduction techniques, like for example riblets, the performance of the travelling waves is well described by a vertical shift of the logarithmic portion of the mean streamwise velocity profile. Except when Re is very low, this shift remains constant with Re, at odds with the percentage reduction of the friction coefficient, which is known to present a mild, logarithmic decline. Our new data agree with the available literature, which is however mostly based on low-Re information and hence predicts a quick drop of maximum drag reduction with Re. The present study supports a more optimistic scenario, where for an airplane at flight Reynolds numbers a drag reduction of nearly 30% would still be possible thanks to the travelling waves.

A fundamental problem in the field of turbulent skin-friction drag reduction is to determine the performance of the available control techniques at high values of the Reynolds number Re. We consider active, predetermined strategies based on spanwise forcing (oscillating wall and streamwisetraveling waves applied to a plane channel flow), and explore via Direct Numerical Simulations (DNS) up to Reτ = 2100 the rate at which their performance deteriorates as Re is increased. To be able to carry out a comprehensive parameter study, we limit the computational cost of the simulations by adjusting the size of the computational domain in the homogeneous directions, compromising between faster computations and the increased need of time-averaging the fluctuating space-mean wall shear-stress.Our results, corroborated by a few full-scale DNS, suggest a scenario where drag reduction degrades with Re at a rate that varies according to the parameters of the wall forcing. In agreement with already available information, keeping them at their low-Re optimal value produces a relatively quick decrease of drag reduction. However, at higher Re the optimal parameters shift towards other regions of the parameter space, and these regions turn out to be much less sensitive to Re. Once this shift is accounted for, drag reduction decreases with Re at a markedly slower rate. If the slightly favorable trend of the energy required to create the forcing is considered, a chance emerges for positive net energy savings also at large values of the Reynolds number. * gatti@csi.tu-darmstadt.de † maurizio.quadrio@polimi.it

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Soft silicone elastomers are used in a generation of dielectric elastomer actuators (DEAs) with improved actuation speed and durability compared to the commonly used, highly viscoelastic polyacrylate 3M VHB™ films. The maximum voltage-induced stretch of DEAs is ultimately limited by their dielectric breakdown field strength. We measure the dependence of dielectric breakdown field strength on thickness and stretch for a silicone elastomer, when voltage-induced deformation is prevented. The experimental results are combined with an analytic model of equi-biaxial actuation to show that accounting for variable dielectric field strength results in different values of optimal pre-stretch and thickness that maximize the DEA actuation.