Recovery of wall-shear stress to equilibrium flow conditions after a rough-to-smooth step change in turbulent boundary layers

This paper examines the recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early work of Antonia and Luxton (J. Fluid Mech., vol. 53, 1972, pp. 737–757) questioned the reliability of standard smooth-wall methods for measuring wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at Reτ≈4100 that have access to both ‘direct’ and ‘indirect’ measures of the wall-shear stress to understand the recovery to equilibrium conditions of the new surface. Our results reveal that the viscous region ( z+≲4 ) recovers almost immediately to an equilibrium state with the new wall conditions; however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition. Based on these observations, an alternative approach to estimating the wall-shear stress from the premultiplied energy spectrum is proposed

Multi-component velocity measurements in turbulent boundary layers

© 2015 Dr. Rio BaidyaAn experimental investigation of high Reynolds number (Re) turbulent boundary layers is undertaken in this study. The primary focus here is to measure the spanwise and wall-normal velocity components, in addition to the streamwise velocity. This study has been undertaken in an attempt to address the lack of spanwise and wall-normal velocity measurements at high Re, identified in the existing literature. For this purpose, we have utilised a custom dual hot-wire probe that is spatially compact, to reduce the volume occupied by the sensing elements. Measurements at high Re are particularly challenging due to the increased scale separation between the smallest and largest energetic scales. To overcome the challenges of resolving these range of scales, experiments are conducted using a specialised wind tunnel, located at the University of Melbourne, whose 27m length allows a thick boundary layer to be developed. Since Re is equal to the ratio between the largest and smallest scales in the flow, a thicker boundary layer (the largest scale in the flow) equates to a larger permissible physical dimension for sensors to capture the smallest scale, for a fixed Re. We start our study by investigating the effects of finite sensor dimensions on the measured turbulence statistics. In this work, the effects of finite sensor dimensions are simulated numerically using a box filtering process on a three-dimensional velocity field obtained through direct numerical simulation. Two typical dual hot-wire probe configurations, namely V- and X-probes are considered. The simulated results show that X-probes are better suited at measuring the turbulence statistics in a wall-bounded flow compared to V-probes. This is attributed to the wire separation in X-probes, which can be physically configured to be closer than in V-probes. Furthermore, the simulation results suggest that the deviation in the turbulence statistics obtained is a function of utilised sensor dimensions, scaled with viscous units. Therefore, care is taken to match the spatial resolution of the sensor used during the experiments at multiple Re, to avoid contamination from the spatial resolution effects to the Re trends identified. The measured broadband turbulent stresses and cross power spectrogram in the logarithmic region are compared against scaling laws derived using the attached eddy hypothesis. A logarithmic relationship between the streamwise and spanwise turbulence intensities with distance from the wall is observed as predicted by the attached eddy hypothesis. Furthermore, the spanwise, wall-normal and Reynolds shear stress spectrogram obtained are consistent with the notion that the logarithmic region in the wall-bounded flow can be considered to be a collection of self-similar eddies that scale with the wall height; an underlying assumption in the attached eddy hypothesis

The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows

We examine the behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips, where the width of the strips S varies such that 0.32⩽S/δ¯¯⩽6.81, where δ¯¯ is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influences of spanwise variation in wall shear stress over a large S/δ¯¯ range. Hot-wire anemometry and particle image velocimetry (PIV) reveal that the half-wavelength S/δ¯¯ governs the diameter and strength of the resulting mean secondary flows and hence the observed isovels of the mean streamwise velocity. Three possible cases are observed: limiting cases (either S/δ¯¯≪1 or S/δ¯¯≫1), where the secondary flows are confined near the wall or near the roughness change, and intermediate cases (S/δ¯¯≈1), where the secondary flows are space filling and at their strongest. These secondary flows, however, exhibit a time-dependent behaviour which might be masked by time averaging. Further analysis of the energy spectrogram and fluctuating flow fields obtained from PIV show that the secondary flows meander in a similar manner to that of large-scale structures occurring naturally in turbulence over smooth walls. The meandering of the secondary flows is a function of S/δ¯¯ and is most prominent when S/δ¯¯≈1

Secondary flow over surfaces with spanwise heterogeneity

Surfaces with heterogeneous roughness are known to alter the behaviour of canonical turbulent boundary layers. In the case where roughness varies in the spanwise direction, the turbulent boundary layer is modified by secondary flows in the form of counter-rotating streamwise roll modes. Previous studies on various spanwise heterogeneity models have shown that the behaviour of these secondary flows is determined by the type,spacing, and the width of the roughness elements. To examine this further, we here conduct a series of hot-wire anemometry measurements over surfaces with strips of spanwise heterogeneous roughness, where the ratio of the roughness strip widthΛ and the spanwise-averaged boundary layer thickness δ varies in the range of Λ/δ = 0.32–3.63. Our results show that the secondary flow appears to amplify a particular energetic mode in the outer layer (z/δ ≈ 0.5), as evidenced by a peak in the 1-D energy spectra at this wall-normal location for all test cases. This behaviour is observed to be the strongest at Λ/δ ≈ 1. In thecases where Λ/δ approaches its limit (Λ/δ 1 or Λ/δ 1),the magnitude of this spectral peak diminishes and the size and location of the secondary flow are limited by either the spanwise extent of Λ or the height of δ. Outside the region affected by the secondary flow, the behaviour of surfaces with spanwise heterogeneity appears to approach that of homogeneous flow

The instantaneous structure of turbulent boundary layers over surfaces with spanwise heterogeneity

Turbulent flows over surfaces with extensive roughness variation in the spanwise direction induce a secondary flow in the form of streamwise aligned counter-rotating vortices. In this study, we conduct cross-plane stereoscopic particle image velocimetry (SPIV) measurements over surfaces constructed from spanwise-alternating smooth and rough strips to emulate spanwise heterogeneity in a rough-walled surface. The half-spanwise-wavelength of the alternating rough and smooth strips S varies from S/δ = 0.32–3.63,relative to the spanwise-averaged boundary layer thickness,δ. Two limiting cases are observed when S/δ 1 and 1, where the size of secondary flow is limited by δ and S, respectively. Consequently, the regions away from the secondary flow scale according to their local shear stress when S/δ 1 and become spanwise homogeneous when S/δ 1. We observe that when S/δ ≈ 1, the secondary flow is particularly strong and appears to fill the entire wall normal extent of the boundary layer. In this condition, we observe that the spanwise location of the secondary flow is highly time-dependent

A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to 10^4

This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a ‘quiescent core’ in pipe flow, as described by Kwon et al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower , and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and ‘quiescent core’ intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness

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

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