Mechanical Engineering - Theses
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ItemThree-dimensional structure and scaling of a canonical turbulent boundary layer( 2021)Wall-bounded turbulent flows are pervasive in nature and are also encountered in many engineering applications; common examples include the flow over an airplane wing, or the atmospheric boundary layer over the Earth's surface, etc. A dominant feature present within these flows is the appearance of recurring eddies or so-called coherent structures that are highly three-dimensional (3-D) in geometry and are statistically significant over a wide range of scales. This has led to the proposal of various coherent structure-based models in the literature, with the attached eddy model (AEM) of wall-turbulence being the most popular amongst them. Their predictive capabilities, however, are still lacking due to the dearth of 3-D information on the coherent motions which they model. The present thesis reports a new and unique set of multi-point hotwire measurements conducted in a frictional Reynolds number, $Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^4$) canonical turbulent boundary layer (TBL) to reconstruct the 3-D statistical picture of these energy-containing motions. The measurements are complemented by performing a similar reconstruction using published direct numerical simulation datasets at $Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^3$), thereby facilitating an examination of the scaling of these structures, in flows spanning over a decade of $Re_{\tau}$. Results of these investigations provide direct empirical support towards the AEM, with the prospect of further enhancing its efficiency by defining the representative eddy geometry based on data-driven estimates. The first part of the thesis focuses on investigating characteristics of the inertially dominated wall-coherent structures (i.e. the ones extending down to the wall), which are responsible for the increased skin-friction in high-$Re_{\tau}$ TBLs. Their geometric characteristics are investigated in the wall-parallel plane by estimating, for the first time, the 2-D cross-spectrum of the streamwise velocity using the synchronous velocity fluctuations measured at a log-region ($z_{o}$) and near-wall ($z_{r}$) location. Constant energy contours of this spectrum, which are representative of the energy distribution across the range of streamwise (${\lambda}_{x}$) and spanwise (${\lambda}_{y}$) wavelengths, are found to follow the ${{\lambda}_{x}}/{z_{o}}$ $\approx$ 7(${{\lambda}_{y}}/{z_{o}}$) relationship in the large-scale range, indicative of geometric self-similarity. This suggests that a self-similar structure conforming to Townsend's attached eddy hypothesis (Townsend 1976) is ingrained in the flow, and can be conceptually modelled using the AEM framework given by Perry \& Chong (1982). The very-large-scale wall-coherent structures (i.e. the superstructures), on the other hand, do not conform to Townsend's attached eddies and are found to have a similar spanwise width as the largest motions in the self-similar hierarchy. This result, which is found via a scale-specific coherence analysis of the velocity fluctuations, also reveals the periodic organization of the superstructures along the spanwise direction. Finally, an analysis of the scale-specific phase of the coherence reveals the streamwise inclination angle of the large wall-coherent motions, which is found to be nominally 45$^{\circ}$. This fulfills the minimum geometric information required to statistically model these energetic wall-coherent motions based on the AEM. The second part of the thesis focuses on investigating the range of energy-containing structures coexisting in the log-region, which contribute significantly to the bulk turbulence production in high-$Re_{\tau}$ wall-bounded flows. Townsend (1961) hypothesized that these structures can be segregated into active and inactive motions, where the active motions are solely responsible for producing the Reynolds shear stress, the key momentum transport term in these flows. While the wall-normal component of velocity is associated exclusively with the active motions, the wall-parallel components of velocity are associated with both active and inactive motions. To test this hypothesis, the present study proposes a methodology to segregate the active and inactive components of the 2-D energy spectrum (${\Phi}_{ii}$, where $i$ denotes the velocity-component) at $z_{o}$, thereby permitting to test the self-similarity characteristics of the former which are central to theoretical models for wall-turbulence. The methodology utilizes the multi-point dataset, in conjunction with a spectral linear stochastic estimation-based procedure, to linearly decompose the total energy at $z_{o}$ (${\Phi}_{ii}$) into contributions predominantly from the active (${\Phi}^{a}_{ii}$) and inactive (${\Phi}^{ia}_{ii}$) motions. This is confirmed by ${\Phi}^{a}_{ii}$ exhibiting wall-scaling for both ${\lambda}_x$ and ${\lambda}_y$. The Reynolds shear stress cospectra, estimated solely from the active contributions, is also found to closely match the one obtained conventionally from the dataset, thereby providing direct empirical support for the concept of active and inactive motions. Both ${\Phi}^{a}_{ii}$ and ${\Phi}^{ia}_{ii}$ contours are found to depict geometric self-similarity in the log-region, suggesting that this entire region can be conceptually modelled using the AEM framework. Inactive contributions from the attached eddies also bring out the pure $k^{-1}$-scaling for the associated 1-D spectra (where $k$ is the streamwise/spanwise wavenumber), lending further empirical support to the AEM.
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ItemTime-varying secondary flows in turbulent boundary layers over surfaces with spanwise heterogeneity( 2020)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.
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ItemTowards modelling the downstream development of a turbulent boundary layer following a rough-to-smooth step change( 2020)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.