Simultaneous skin friction and velocity measurements in high Reynolds number pipe and boundary layer flows

Abstract

Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. (J. Fluid Mech., vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of $7:1:1$ in the streamwise, spanwise and wall-normal directions, respectively.

On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows

“…It also implies that the symmetric modelling of positive and negative wall-attached structures by Baidya et al. (2019) for the spectrum might be improved by accounting for the flow asymmetries.…”

“…τ x,rms /τ x = 0.298 + 0.018 ln(Re τ ), where Re τ = u τ δ/ν, u τ is the friction velocity, ν is the kinematic viscosity and δ is the boundary-layer thickness (or channel half-height). The Reynolds number dependence of τ x,rms suggests that large-scale energy-containing motions populating the logarithmic and outer regions in high-Reynolds-number wall turbulence have non-negligible influences on the near-wall dynamics and, hence, on the wall friction (Abe et al 2004;Örlü & Schlatter 2011;de Giovanetti, Hwang & Choi 2016;Renard & Deck 2016;Baidya et al 2019;Fan et al 2019a,b).…”

“…2004; Örlü & Schlatter 2011; de Giovanetti, Hwang & Choi 2016; Renard & Deck 2016; Baidya et al. 2019; Fan et al. 2019 a , b ).…”

“…Baidya et al. (2019) measured the instantaneous wall-shear stress in high-Reynolds-number pipes and boundary layers and found that the energy-containing motions are stochastically coherent with skin-friction events. In the present work, we aim to analyse the structure of the wall-shear stress fluctuations and to assess the relationship between the skin-friction events with the wall-attached eddies.…”

Streamwise inclination angle of large wall-attached structures in turbulent boundary layers

“…In the present study, we draw inspiration from the recent work of Baidya et al. (2019) to isolate large wall-attached structures in a TBL by imposing a spanwise offset between the log-region and wall probe to find .…”