Gallorini, E.

Quadrio, M.

English

Archivio istituzionale della ricerca - Politecnico di Milano

Effect of control discretization on streamwise traveling wavesof spanwise wall velocityE. Gallorini∗ and M. Quadrio∗Since their introduction, streamwise traveling waves (StTW) 1 represented a promis-ing open-loop turbulence control strategy. In the years, the effect of StTW in aturbulent pipe flow was studied experimentally 2, dividing the wall into thin slabsrotating with different velocities. Despite substantial overall agreement in the controlbehavior, differences exist between numerical and experimental results in specific re-gions of the frequency-wavenumber space. The authors linked these differences to thediscrete spatial waveform approximating the continuous wave. Recently, Marusic andcoworkers 3 performed experiments of a controlled boundary layer up to Reτ = 12800using a discrete setup similar to the one described by Auteri et al.Few studies highlight the effect of discretization on control performance. In thefollowing, we present a selection of the results obtained by different Direct NumericalSimulations of a turbulent pipe flow subjected to three types of control: the continuoussine (sin) and sinusoidal waves discretized with three (s3) and six segments (s6).Fig. 1-a shows the effect of discretization in the drag reduction, measured in caseof constant flow rate as R = 1 − Cf/Cf,0. As expected, by increasing the numberof elements approximating the continuous function, the discretization effects reduce,as s3 substantially differs from sin. The main differences are two: first, for negativefrequencies, s3 and s6 show clear wiggles missing in the continuous control. Second, atthe positive frequencies where typically drag increase occurs, s3 exhibits a reductionof R but never a negative value. Incidentally, the discretization prevents also therelaminarization occurring at frequency ω+ = 0.02. Clearly, as shown by Fig. 1-b,the loss of the control continuity affects also uu+, vv+, and uv+.a)-0.3 -0.2 -0.1 0 0.30.20.1-0.100.10.20.30.40.50.6ω+Rsins3s6b)100 101 102-1012345678y+ω+ = −0.08Refsins3s6uu+vv+uv+100 101 102-1012345678y+ω+ = 0.11Refsins3s6uu+vv+uv+Figure 1: (a) R for three types of control: continuous sine (sin) and sinusoidal wavesdiscretized with three (s3) and six segments (s6). ω+ varies while κ+x = 8.4 · 10−3 (b)Wall-normal profile of Reynolds normal and shear stresses.∗Dept. of Aerospace Sciences and Technologies, Politecnico di Milano, via La Masa 34, 20156Milano, Italy1Quadrio et al., J. Fluid Mech 627, 161 (2009).2Auteri et al., Phys. Fluids 22, 115103 (2010)3Maurusic et al., Nat. Commun. 12, 5805 (2021)

Effect of Control Discretization on Streamwise Traveling Waves of Spanwise Wall Velocity

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Effect of Control Discretization on Streamwise Traveling Waves of Spanwise Wall Velocity

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