Turbulent shear flow over active and passive porous surfaces

Abstract

The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied numerically. The transpiration is assumed to be proportional to the local pressure fluctuations. It is first shown that the friction coefficient increases by up to 40% over passively porous walls, even for relatively small porosities. This is associated with the presence of large spanwise rollers, originating from a linear instability which is related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral inviscid shear waves of the mean turbulent profile. It is shown that the rollers can be forced by patterned active transpiration through the wall, also leading to a large increase in friction when the phase velocity of the forcing resonates with the linear eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used to further clarify the flow mechanism. This study is motivated by the control of separation in boundary layers.

Compressible turbulent channel flow with impedance boundary conditions

“…The effects on the mean and RMS velocity profiles are qualitatively consistent with the incompressible simulations by Jiménez et al 20 , suggesting, as anticipated in section V A, that tuned IBCs are akin to porous-wall boundary conditions. However, while in the present cases structural flow changes are confined to the near-wall region, Jiménez et al 20 obtained the formation of large, spanwise coherent rollers in the core of the channel, with size comparable to the computational domain, modulating (essentially) unaltered near-wall turbulence.…”

“…Excellent agreement is observed between (20), calculated via numerical integration of (18) in spectral space, and the results from the Navier-Stokes solver (figure 2) in the time domain. The RMS of the difference between the two solutions, evaluated over the interval −0.4 < y < 0.4 and for t = 2, decays initially with forth-order accuracy in space and second-order in time (figure 3), as expected.…”

“…The non-zero limiting behavior of the Reynolds shear-stress gradient at the wall (figure 6b,inset) is responsible for the deviations from the law of the wall of the mean streamwise velocity profiles (figure 6a). This effect was not evident, for example, in the incompressible calculations of Jiménez et al 20 due to the relatively low permeabilities tested, corresponding, at most, to R −1 = 14, for the present M b = 0.05 case. Variations in the log-law's slope are not significant, indicating a substantially unaltered turbulent kinetic energy balance in the outer logarithmic layer 24 (unaltered Kármán constant), with changes in the intercept value merely due to the drag increase.…”

“…Similar problems have been investigated in the incompressible limit with focus on characterizing the structural alterations to wall-bounded turbulence. The interaction between an incompressible turbulent channel flow and a porous wall, for example, has been explored by Jiménez et al 20 using Darcy-type wall boundary conditions. Large Kelvin-Helmholtz spanwise-coherent rollers were observed in the outer layer and found responsible for the increase in overall drag.…”

How linear is wall-bounded turbulence?

“…For example, one of the consequences of that term is that the flow can undergo a Kelvin-Helmholtz instability if U vanishes. That does not happen above the buffer layer, and is inhibited near the wall by the impermeability boundary condition but, if that condition is relaxed by porosity 63 or by other means, 50 the Kelvin-Helmholtz instability reappears, with vertical eigenfunctions that remain localized below x + 2 ≈ 30. 50,64 We have also analyzed the bursts in simulations of fully turbulent flows in computational boxes that are minimal with respect to the structures of the logarithmic layer.…”