Effect of mean and fluctuating pressure gradients on boundary layer turbulence

Abstract

This study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolved, have been performed upstream of and within a sink flow for two inlet Reynolds numbers, Re θ (x 1 ) = 3360 and 5285. The corresponding acceleration parameters, K, are 1.3 × 10 −6 and 0.6 × 10 −6 . The time-resolved data at Re θ (x 1 ) = 3360 enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the fluid material acceleration. As expected, all the locally normalized Reynolds stresses in the favourable pressure gradient (FPG) boundary layer are lower than those in the zero pressure gradient (ZPG) domain. However, the un-scaled stresses in the FPG region increase close to the wall and decay in the outer layer, indicating slow diffusion of near-wall turbulence into the outer region. Indeed, newly generated vortical structures remain confined to the near-wall region. An approximate analysis shows that this trend is caused by higher values of the streamwise and wall-normal gradients of mean streamwise velocity, combined with a slightly weaker strength of vortices in the FPG region. In both boundary layers, adverse pressure gradient fluctuations are mostly associated with sweeps, as the fluid approaching the wall decelerates. Conversely, FPG fluctuations are more likely to accompany ejections. In the ZPG boundary layer, loss of momentum near the wall during periods of strong large-scale adverse pressure gradient fluctuations and sweeps causes a phenomenon resembling local 3D flow separation. It is followed by a growing region of ejection. The flow deceleration before separation causes elevated near-wall small-scale turbulence, while high wall-normal momentum transfer occurs in the ejection region underneath the sweeps. In the FPG boundary layer, the instantaneous near-wall large-scale pressure gradient rarely becomes positive, as the pressure gradient fluctuations are weaker than the mean FPG. As a result, the separation-like phenomenon is markedly less pronounced and the sweeps do not show elevated small-scale turbulence and momentum transfer underneath them. In both boundary layers, periods of acceleration accompanying large-scale ejections involve near-wall spanwise contraction, and a high wall-normal momentum flux at all elevations. In the ZPG boundary layer, although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps upstream, others are not. Conversely, in the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. Apparently, the mechanisms initiating these ejections are either different from those involving large-scale sweeps or occur far upstream of the peak in FPG fluctuations.

Interfaces and internal layers in a turbulent boundary layer

“…Independent pitot measurements indicate the acceleration parameter, K = 2 × 10 −8 . As shown by Joshi et al, 31 effects on the turbulence structure in a boundary layer become noticeable at K = 10 −6 . Hence, the pressure gradient will have a negligible influence on the results discussed here.…”

“…This underlines once more that the effect of the pressure gradient in the current measurements is negligible as one of the first observable consequences of a favourable pressure gradient is to decrease the inclination of structures observed based on two-point correlations for u ′ . 31 Moreover, the angle of the shear layers remains relatively constant over the height of the boundary layer (not shown here). Finally, the PDF of the major/minor axis of the internal layers shows that the detected regions of high shear are elongated, i.e., layer-like structures, as their aspect ratio is on an average of 3.6.…”

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

“…the lower U h in the LES causes the scaled velocity fluctuations to be larger than in the experiments. In addition, the small favourable pressure gradient in the experiments reduces the velocity fluctuations in the experimental boundary layer (Joshi et al 2014). Furthermore, a reduction is observed in the mean Reynolds stress in the experiments in the region 2 ≤ z/ h ≤ 5, see Fig.…”

Counter‐rotating vortex shedding generated by acoustic excitations in confined mixing layers

“…7 Elliptical instability induces streamwise vortices of 3D mixing layer, 10 which is also related to Re. Although the vortices due to corner flow instability have also been observed in the mixing chamber, 2 the most unstable frequency is affected by both the pressure gradient 19,20 and Re. 21 Thus, the new observation that f o is independent of Re cannot be explained by these well-known instabilities.…”