Mechanical Engineering

The behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips is investigated experimentally. The width of the strips S vary such that 0.32 < S/\delta < 6.81, where \delta is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influence of spanwise variation in wall shear stress over a large S/\delta range. Hot-wire anemometry (HWA) and particle image velocimetry (PIV) reveal that the half-wavelength S/\delta governs the diameter and strength of the resulting mean secondary flows. Three possible cases are observed: limiting cases where S/\delta << 1 or S/\delta >> 1 and the secondary flows are either confined near the wall or near the roughness change, respectively, and intermediate cases (S/\delta \approx 1), where the secondary flows fill the entire boundary layer and the outer layer similarity is destroyed. The size and strength of the time-averaged secondary flows are approximately capped by either the boundary-layer thickness \delta or the roughness patch width S. Instantaneously, however, these secondary flows appear very similar to naturally occurring large-scale structures that are spanwise-locked by the roughness transition with a residual meandering tendency about these locations. The efficacy of the roughness to lock the secondary flows in place and the meandering of the secondary flows are a function of S/\delta, most prominent when S/\delta \approx 1. Further analysis of the energy spectrograms and fluctuating flow fields obtained from PIV show that both secondary flows and the naturally occurring large-scale structures formed in turbulence over smooth walls meander in a similar manner and both coexist in the limits where S/\delta << 1 and S/\delta >> 1.

Turbulent boundary layers are important phenomena, affecting the performance of numerous systems in engineering and nature. At most practical Reynolds numbers, these flows occur over rough surfaces and this surface roughness is often distributed heterogeneously (such as biofouling on a ship hull). Understanding the behaviour of the turbulent boundary layer over this type of roughness is essential for improving the estimation of the drag penalty in full-scale systems. In this work, a turbulent boundary layer over a rough-to-smooth change in the surface condition is examined experimentally. A comprehensive dataset is acquired, which allows us to study the effect of the step height, friction Reynolds number and viscous-scaled equivalent sandgrain roughness height separately. Multiple experimental techniques are employed, including hotwire anemometry and high-magnification particle image velocimetry. The recovering wall-shear stress on the smooth surface is measured directly using oil-film interferometry. Early works of Antonia and Luxton (J. Fluid Mech., 53:737–757, 1972) questioned the reliability of standard smooth-wall methods to measure the wall-shear stress immediately downstream of a rough-to-smooth transition, 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 that have access to both ‘direct’ and ‘indirect’ measures of the wall-shear stress to understand the recovery to equilibrium conditions to the new surface. 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. 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 the 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 the larger energetic scales exhibit an over-energised state for many 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. For surfaces with heterogeneous roughness, there can be a change of virtual origin alongside the variation of roughness heights, an extreme case of which is the flow over a forward- or backward-facing step, where no roughness exists but only a height difference is present. In the present study, cases with various step heights between the rough and smooth surfaces behave similarly beyond two boundary layer thicknesses downstream of the roughness transition, and the higher order statistics seem to recover within approximately the same fetch as required for the recovery of the mean velocity profiles, suggesting that the influence of the step height is limited to the vicinity of the roughness transition with no far-field effect. A comparison of the experimental results with a direct numerical simulation of an open-channel flow shows a qualitatively similar effect on the mean velocity profile, and the change in the virtual origin \Delta d is found to be a useful length scale in normalising the recovery length. Dimensional analysis shows that the upstream condition of a turbulent boundary layer over a rough-to-smooth change in the surface condition can be fully described by two non-dimensional numbers: Re_{\tau 0} (friction Reynolds number) and k_{s0}^+ (viscous-scaled equivalent sandgrain roughness height). Therefore, to investigate the dependence of the flow on each parameter separately, we acquire a unique and comprehensive dataset which takes two cuts in the parameter space: one at a fixed k_{s0}^+ with varying Re_{\tau 0}, and the other at a fixed Re_{\tau 0} with varying k_{s0}^+. With the aid of these data, a blending model of the mean velocity profile is developed. The modelled mean velocity profile approaches an equilibrium smooth-wall velocity profile in the near-wall region, and it asymptotes to the upstream rough-wall profile above the IBL (internal boundary layer). The blending model is then incorporated into the original Elliott’s model (Trans. Am. Geophys. Union, 39:1048–1054, 1958) together with further refinements. The refined Elliott’s model leads to a better agreement with the experimental data compared to the original one, permitting an improved prediction of the evolution of a developing turbulent boundary layer downstream of a step change in surface roughness.

Mechanical Engineering - Theses

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