Drag reduction in turbulent boundary layers by spanwise traveling waves with wall deformation

Abstract

The drag-reducing effect of a spanwise-traveling wave with wall deformation on a zeropressure-gradient turbulent boundary layer over a flexible sheet was investigated. The test plate placed in the wind tunnel consisted of a flexible sheet section, where the traveling wave motion was generated by a vibration device with a crank via upstream and downstream smooth rigid wall sections. Streamwise and wall-normal velocity components were measured by single and cross hot-wire anemometers. Amplitude and frequency of the spanwise-traveling-wave motion were measured using two laser displacement sensors. The drag reduction ratio was estimated from the friction coefficients through the growth rate of the momentum thickness of the turbulent boundary layer over the flexible sheet section. A maximum drag reduction ratio DR of up to 13% was obtained. The relations between sheet displacement and streamwise and wall-normal velocity fluctuations were compared at a large DR (DR = 8%) and at a very small DR (DR = 2%), which was almost the same as the no drag reduction case, taking into account the experimental uncertainty. For the larger drag reduction, a slow-velocity fluctuation with large amplitude appeared further away from the flexible sheet. Quadrant analysis of streamwise and wall-normal velocity fluctuations revealed that the drag reduction was attributed to a reduction in the sweep event and an increase in the negative contribution of the inward-interaction event to the Reynolds shear stress due to the sheet displacement fluctuation.

Turbulent drag reduction by spanwise traveling ribbed surface waves

“…For a momentum thickness based Reynolds number range of Re θ ≤ 2080. Roggenkamp et al [40] obtained for an aluminum surface excited by a spanwise transversal wave at an amplitude A + ≤ 9 a drag reduction for a turbulent flat plate boundary layer flow of DR ≤ 4% which is comparable to the results of Tamano and Itoh [38] when the lower excitation amplitude is considered.…”

“…As stated in Section 3, the measurement cross section on the smooth surface is located 3 mm downstream of the riblet surface trailing edge corresponding to 75 wall units for Re θ = 1200 and 150 wall units for Re θ = 2080. Tamano and Itoh [38] reported a recovery length of about 80 mm or 2000 wall units in a spanwise traveling wave setup. Fukagata and Kasagi [54] showed that the drag reduction effect was lowered by approximately 10% at 75 wall units and 35% at 150 wall units downstream of the control region.…”

“…Obtaining a maximum drag reduction of 9%, they determined the damping of wall-normal vorticity fluctuations to be the key feature of the drag reducing mechanism. Itoh et al [37] and Tamano and Itoh [38] analyzed the effect of this control method experimentally at momentum based Reynolds numbers of Re θ = 1100 and Re θ = 1450, respectively. Performing cross hot-wire measurements over an excited flexible sheet, they obtained a maximum drag reduction of 13% at a nondimensional amplitude based on the friction velocity of A + = 24 and period of T + = 115 resulting from the positive contribution of sweep events to the Reynolds shear stress.…”

“…Comparison of the distribution of the root-mean-square value of the wall-normal velocity fluctuation (left) and the Reynolds shear stress u ′ v ′ /u 2 τ (right) for the non-actuated smooth surface, the non-actuated riblet wall, and the actuated riblet configurations; Re θ = 1200, A + = 6, 7, 9; the dimensional frequency and wavelength match the Re θ = 1200 values; inner wall units are defined by the nominal friction velocity u τ of the non-actuated smooth surface [22,32,38,34]…”

Impact of transversal traveling surface waves in a non-zero pressure gradient turbulent boundary layer flow

“…They found up to 7.5% drag reduction. In a more recent analysis extending the previous investigation Tamano and Itoh [21] achieved 13% drag reduction. Klumpp et al [8,10] performed large-eddy simulations (LES) of turbulent boundary layers at Re θ = 887 over transversal traveling surface waves.…”