10th International Symposium on Turbulence and Shear Flow Phenomena (TSFP10), Chicago, USA, July, 2017
Turbulent-drag reduction by wavy wall
S. Ghebali1∗ , S. I. Chernyshenko1 and M. A. Leschziner1
1: Department of Aeronautics, Imperial College London, Exhibition road, London SW7 2AZ, UK.
∗ Correspondent author: [email protected]
The present work is based on the premise
that a wavy surface, with the waves oblique
to the flow direction, is able to induce a
streamwise-varying spanwise strain field that is
broadly analogous to that provoked by a spanwise moving wall with its motion described by
WSSL (x) = ASSL sin(2π/λx x) and denoted SSL
below. The reason for wishing to passively emulate this active actuation is that the latter gives
rise to a Stokes layer that is observed to be exceptionally effective at reducing near-wall tur- Figure 1. Parameters of the flow configuration, which can equivalently be defined by
bulence and hence the friction drag.
(Aw , θ , λ ) or (Aw , λx , λz ); λx and λz are, respectively, the streamwise- and spanwiseThe wavy-channel geometry being con- projected wavelengths of the wavy wall.
sidered is shown in Fig. 1 and described by
hw (x, z) = Aw sin(2π/λx x + 2π/λz z). A low-cost, semi-empirical model, comprising linearized forms of the RANS equations
with prescribed eddy-viscosity profile, is used to guide DNS computations at Reτ = 360, and to provide a first-order estimate
+
of the dependence of drag reduction on the parameter set (Aw , λ , θ ), with A+
w = O(15) and λ = O(1000). As demonstrated
in Fig. 2, the spanwise-velocity profiles induced by the wavy wall are fairly well predicted by the model, although the velocity
magnitude induced by the waves, at w+ = O(1), is rather low relative to the arbitrarily high spanwise velocity that can be induced
by the moving wall. However, important differences between the two cases exist, because of the spanwise inhomogeneity of the
wavy geometry and the significant periodic variations in the streamwise velocity the waves provoke.
The net drag-reduction level arises as a delicate balance between friction-drag reduction and pressure-drag increase, and this
+
demands extremely high DNS resolution. As shown in Fig. 3, the model suggests, for A+
w ≈ 13, an optimum at λ ≈ 720 and
θ ≈ 70◦ for which the drag-reduction value is ≈ 1%, subject to the assumption that the friction-drag component can be estimated
from the SSL for the same w+ amplitude as that provoked by the waves. Two DNS results are included in Fig. 3 for which the
drag reduction is, respectively, 0.0% and 0.7%. Although correspondence with the model-predicted map is not close – and this
also applies to several other simulations performed –, both model and DNS results obtained so far suggest that the optimum
configuration is unlikely to yield maximum net drag reduction in excess of 1%.
Figure 3. Estimation of the net drag reduction
from the semi-empirical model, assuming a successful emulation of a Stokes layer of forcing am+
Figure 2. Profiles of the spanwise velocity for the flow configuration A+
w = 18, λ = 918, plitude A+ = 1. Drag-reduction levels for two
SSL
θ = 70◦ ; dashed lines: semi-empirical model, continuous lines: DNS.
DNS are reported next to the symbols.