Adaptive Kagome Lattices for Near Wall Turbulence Suppression

Bird, James; Santer, Matthew; Morrison, J. F.

doi:10.2514/6.2015-0270

Cited by 1 publication

(3 citation statements)

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“…The wall wave motion given by (1) has also been studied beneath wall-bounded turbulent flows, first via direct numerical simulations in a turbulent channel flow by Quadrio et al [31] and Quadrio and Ricco [32], and experimentally in a pipe with rotating sections by Auteri et al [28] and in a wind-tunnel flow over a deformable Kagome lattice surface by Bird et al [29,30]. Drag reduction or drag increase occurs depending on the forcing parameters λ and U .…”

Section: Travelling Waves For Turbulent Drag Reductionmentioning

confidence: 99%

“…Drag reduction or drag increase occurs depending on the forcing parameters λ and U . For the pipe with rotating sections [28] and the wind-tunnel flow over the Kagome surface [29,30], the bulk Reynolds number is obviously much larger than unity and λ is either comparable or a few times larger than the pipe radius in the case of Auteri et al [28] or the boundary-layer thickness in the case of Bird et al [29,30].…”

Section: Travelling Waves For Turbulent Drag Reductionmentioning

confidence: 99%

“…Following Langer [36,37], we choose iP/ η 2 = η, and hence, upon integration, where κ(y) is given by (29). A uniform asymptotic approximation to W(y) is given by…”

Section: Langer Theorymentioning

confidence: 99%

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Streamwise-travelling viscous waves in channel flows

Riccó

Hicks

2018

J Eng Math

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The unsteady viscous flow induced by streamwise-travelling waves of spanwise wall velocity in an incompressible laminar channel flow is investigated. Wall waves belonging to this category have found important practical applications, such as microfluidic flow manipulation via electro-osmosis and surface acoustic forcing and reduction of wall friction in turbulent wall-bounded flows. An analytical solution composed of the classical streamwise Poiseuille flow and a spanwise velocity profile described by the parabolic cylinder function is found. The solution depends on the bulk Reynolds number R, the scaled streamwise wavelength λ, and the scaled wave phase speed U . Numerical solutions are discussed for various combinations of these parameters. The flow is studied by the boundary-layer theory, thereby revealing the dominant physical balances and quantifying the thickness of the near-wall spanwise flow. The Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) theory is also employed to obtain an analytical solution, which is valid across the whole channel. For positive wave speeds which are smaller than or equal to the maximum streamwise velocity, a turning-point behaviour emerges through the WKBJ analysis. Between the wall and the turning point, the wall-normal viscous effects are balanced solely by the convection driven by the wall forcing, while between the turning point and the centreline, the Poiseuille convection balances the wall-normal diffusion. At the turning point, the Poiseuille convection and the convection from the wall forcing cancel each other out, which leads to a constant viscous stress and to the break down of the WKBJ solution. This flow regime is analysed through a WKBJ composite expansion and the Langer method. The Langer solution is simpler and more accurate than the WKBJ composite solution, while the latter quantifies the thickness of the turning-point region. We also discuss how these waves can be generated via surface acoustic forcing and electro-osmosis and propose their use as microfluidic flow mixing devices. For the electro-osmosis case, the Helmholtz-Smoluchowski velocity at the edge of the Debye-Hückel layer, which drives the bulk electrically neutral flow, is obtained by matched asymptotic expansion.

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