Mechanical Engineering - Theses
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ItemCharacteristics of energetic motions in turbulent boundary layers( 2019)In this dissertation, we present the first measurements of two-dimensional (2-D) energy spectra of the streamwise velocity component (u) in high Reynolds number turbulent boundary layers. The measurements in the logarithmic region of turbulent boundary layers give new evidence supporting the self-similarity arguments that are based on Townsend’s (1976) attached eddy hypothesis. The 2-D spectrum is found to be able to isolate the range of self-similar scales from the broadband turbulence, which is not possible with the measurement of a 1-D energy spectrum alone. High Reynolds number flows are characterized by large separation of scales. Therefore, to obtain converged 2-D statistics while resolving the broad spectrum of length and time scales, a novel experimental technique is required. To this end, we devise a technique employing multiple hot-wire probes to measure the 2-D energy spectra of u. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). The validation of the measurement technique is performed at low Reynolds number by comparing against the direct numerical simulation (DNS) data of Sillero et al. (2014). Based on these comparisons, a correction is introduced to account for the spatial resolution associated with the initial separation of the hot-wires. The proposed measurement technique is used to measure the 2-D spectra in the logarithmic region for friction Reynolds numbers ranging from 2400 to 26000. At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λy/z ∼ (λx/z)1/2 behaviour at large scales, which is in agreement with the existing literature. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λy ∼ λx) as required for self-similarity and predicted by the attached eddy hypothesis. Finally, we present a model for the logarithmic region of turbulent boundary layers, which is based on the attached eddy framework and driven by the scaling of experimental 2-D spectra of u. The conventional attached eddy model (AEM), which comprises self-similar wall-attached eddies (Type A) alone, represent the large scale motions at high Reynolds numbers reasonably well. However, the scales that are not represented by the conventional AEM are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study we propose an extended AEM, where in addition to Type A eddies, we also incorporate Type CA and Type SS eddies. These represent the self-similar but wall-detached low-Reynolds number features and the non-self-similar wall-attached superstructures, respectively. The extended AEM is observed to predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components.
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ItemThe turbulent boundary layer studied using novel numerical frameworks( 2018)Numerical simulation of turbulent boundary layers is a challenging task that has prompted the development of different numerical setups. To complement existing techniques, the temporal boundary layer is investigated and found to be a good model for the spatially developing turbulent boundary layer. The remaining temporal development is subsequently eliminated giving a pared-down model yielding the statistically stationary, fully developed boundary layer. A practical use of the temporal boundary layer setup is demonstrated by the addition of free-stream disturbances.
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ItemBoundary layer and bulk dynamics in vertical natural convection( 2017)Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 10^5–10^9 and Prandtl number 0.709 are found to support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for Rayleigh–Bénard convection. In accordance with the GL theory, we show that the normalised mean boundary- layer thicknesses of the velocity and temperature fields obey the laminar-like Prandtl– Blasius–Pohlhausen scaling, corresponding to the “classical” state. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the “bulk” or “background” dissipation of the GL theory, is found to obey the Kolmogorov– Obukhov–Corrsin scaling for fully developed turbulence. The present results suggest that, similar to Rayleigh–Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics. On closer scrutiny of the boundary layers, we find evidence that the boundary layers are undergoing a transition from the classical state to the “ultimate” shear-dominated state. In particular, we observe near-wall higher-shear patches that occupy increasingly larger fractions of the wall-areas. These higher-shear patches exhibit turbulent features, for instance (i) the patches appear streaky, reminiscent of the characteristic near- wall streaks in canonical wall-bounded turbulence, (ii) the local mean temperature profile yields a logarithmic variation, in agreement with the logarithmic law of the wall for mean temperature, and (iii) the local Nusselt number follows an effective Rayleigh number power-law scaling exponent of 0.37, consistent with the logarithmically corrected 1/2 power-law scaling predicted for ultimate thermal convection. We reason that both turbulent and laminar-like boundary layers coexist in the transitional regime of vertical natural convection, consistent with the findings reported for Rayleigh–Bénard convection and Taylor–Couette flows. When the walls are instead removed and boundary layers eliminated, the new setup mimics turbulent bulk-dominated thermal convection. We refer to this new setup as homogeneous vertical natural convection. A direct application of scaling arguments to the governing equations of this new setup yields the asymptotic 1/2 power-law scaling relations for the Nusselt and Reynolds numbers, in accordance to previous theoretical predictions of turbulent bulk-dominated thermal convection. Results from direct numerical simulation of the new setup further supports the predicted 1/2 power- law relations. When employing bulk quantities for the wall-bounded setup, we too find the aforementioned 1/2 power-law scaling. This extended result suggests that the 1/2 power-law scaling relation may even be present at lower Rayleigh numbers provided the appropriate quantities in the turbulent bulk flow are employed for the definitions of the Rayleigh, Reynolds and Nusselt numbers. Lastly, we perform a straightforward assessment of the mixing efficiency in vertical natural convection. The value is predicted and found to be approximately 0.5, which suggests that the dissipation rate of kinetic energy is directly proportional to the rate at which gravitational potential energy is readily available for conversion.
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ItemEvolution of canonical turbulent boundary layers( 2017)An experimental investigation of evolving turbulent boundary layers in a tow tank facility is performed in this study. The main aim here is to investigate the development of a canonical turbulent boundary layer from the trip to a high Reynolds number state. A review of the literature reveals that while the dynamic characteristics of the near-wall turbulent structures are reasonably well understood, the origin, evolution and dynamics of large-scale coherent structures in the logarithmic and outer regions of turbulent boundary layers remain largely unresolved. Unveiling the dynamics of large-scale coherent motions is essential to understanding the complicated physics behind wall-bounded turbulent flows. Therefore, an experimental set-up with a long flat plate mounted on a traversing carriage has been carefully designed and constructed. The spatially developing turbulent boundary layers formed on the bottom surface of the towed plate are investigated using a stationary PIV system, affording a unique frame of reference. Large-field-of-view high-resolution PIV and high-speed PIV techniques are employed to measure the instantaneous streamwise-wall-normal plane of the evolving turbulent boundary layer. The measurement system including the traversing carriage is fully automated such that a large number of passes can be performed to obtain converged statistics. We start our study by validating the flow statistics and canonical-state of the turbulent boundary layers. The statistics are compared with results from DNS datasets at matched Reynolds numbers. In the process of validating the PIV obtained flow statistics, we propose a robust technique to estimate small-scale missing energy due to the spatial resolution issues. The estimation tool is based on arguments that (i) the inner-scaled small-scale turbulence energy is invariant with Reynolds number and that (ii) the spatially under-resolved measurement is sufficient to capture the large-scale information, which is Reynolds number dependent. This tool can be used to diagnose whether PIV statistics are beset by some wider issue. Having validated the measurements in this way, the evolution of mean flow parameters of the developing boundary layers is compared with the predicted evolution of mean flow parameters for canonical turbulent boundary layers proposed in the literature. This assessment determines whether the turbulent boundary layers considered in this study can be classified as being in the canonical state. Good agreement has been observed between the experimental results and the predicted evolution. The unique aspect of the current experiment is that we can observe a time-resolved view of an evolving structure within turbulent boundary layers. Any large-scale coherent motions that have a convection velocity close to the freestream will remain nominally stationary within the field of view, whereas for the conventional frame of reference (i.e. wind tunnels or water channels), coherent structures convect away from the field of view with local flow velocities. Therefore, by obtaining a temporally-resolved view of developing boundary layers in this unique frame of reference, the evolution of large-scale coherent motions has been analysed. It is shown that there is a mismatch in the convection velocities between low- and high-speed regions at a matched wall-height. This convection velocity difference allows the low- and high-speed regions to interact, causing the formation of a strong internal shear layer. Both instantaneous and conditionally averaged velocity fluctuations are examined to support these findings. It is also shown that a local shear layer instability develops as the shear layer evolves. The development of this local shear layer instability leads to a shear layer roll-up process which perturbs low- and high-speed regions, causing the regions to migrate to different wall heights (ejections and sweep like events). Finally, all the dynamic properties and interactions of large-scale coherent motions discovered in this study are incorporated to construct a conceptual model. This model describes the role of shear layers and the effect of dynamic interactions of large-scale coherent motions in the outer layer of turbulent boundary layers. The model is derived with the intention of providing a better understanding of large-scale coherent motions and potentially the dynamics described in the model can be incorporated into existing kinematic models to advance future efforts for a complete model for wall-bounded turbulent flows.
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ItemMulti-component velocity measurements in turbulent boundary layers( 2015)An 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.
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ItemHighly ordered surface roughness effects on turbulent boundary layers( 2015)The effects of highly ordered riblet type surface roughness with convergingdiverging/ herringbone pattern in zero pressure gradient (ZPG) turbulent boundary layers are investigated experimentally. The study is based on a novel investigation by Koeltzsch et al. (2002), where a new class of riblet type surface roughness with converging-diverging/herringbone riblet pattern is applied inside the surface of fully-developed turbulent pipe-flow. Their experimental results show that the unique pattern generates a largescale azimuthal variation in the mean velocity and turbulence intensity. Inspired by these results we intend to extend their study and investigate it in more detail, particularly in zero pressure gradient (ZPG) turbulent boundary layers. The general results from the present study show that the converging region forms a common-flow-up that transfers the highly turbulent and slower nearwall fluid away from the surface, resulting in a low local mean velocity and high local turbulence intensity. The low momentum over the converging region results in a thicker turbulent boundary layer. Over the diverging region the opposite situation occurs, the diverging pattern forms a common-flowdown that forces the faster and less turbulent fluid that originally resides further from the wall to move towards the surface, resulting in a high local mean velocity and low local turbulence intensity. The high local mean velocity over the diverging region results in a thinner turbulent boundary layer. For certain cases, the spanwise variation in boundary layer thickness between the converging and diverging region is almost double. Such large and aggressive variation is uncommon considering that the height of the riblets is ≈ 1% of the boundary layer thickness. The combination of the common-flow-up and common-flow-down regions forms a large scale counter rotating vortices that dominate the entire boundary layer. The resulting magnitude of maximum spanwise and wall-normal velocity components of the counter-rotating vortices are ≈ 2 − 3% of U∞, which is comparable to the lower end strength of typical vortex generators for turbulent flow. Our study reveals that the strength of the spanwise variation depends on several parameters, namely : yaw angle (α), viscous-scaled riblet height (h+), streamwise fetch/development length over the rough surface (Fx), and relaxation distance/development length over the smooth surface (rs). The riblet pattern may offer a unique technique to generate counter-rotating roll-modes within turbulent boundary layers and act as a low-profile flow control mechanism. Analysis of the pre-multiplied energy spectra suggests that the converging and diverging pattern has redistributed the large-scale turbulent features. Over the converging region the large-scales are found to be very dominant in the logarithmic region, which closely resembles the recently discovered ‘superstructures’ by Hutchins and Marusic (2007a,b). The highly ordered surface roughness pattern seems to preferentially arrange and lock the largest scales over the converging region. Further examination of the three-dimensional conditional structures strengthen this view. The conditionally averaged large-scale low-speed feature over the converging region is wider in size and has a stronger magnitude than the equivalent feature over the diverging region. We also look into amplitude modulation over the converging and diverging pattern. Recent reports by Hutchins and Marusic (2007b); Mathis et al. (2009a,b); Marusic et al. (2010b); Chung and McKeon (2010a); Ganapathisubramani et al. (2012) reveal that large-scale structures in turbulent boundary layers modulate the amplitude and frequency of the small-scale energy. The amplitude and frequency magnitude of the near-wall small-scale structures are found to be reduced when low-speed large-scale features are detected. Our analyses show that over the converging region, the reduction in the conditioned small-scale variance/small-scale energy is stronger than over the diverging region. This finding further strengthens our previous observation that the highly ordered riblet pattern preferentially arranges and locks the largest scales over the converging region. Finally, we look into the turbulent and non-turbulent interface (TNTI) of the converging and diverging pattern and found that the interface location experiencing spanwise variation in the same manner as the boundary layer thickness. Furthermore, there are not many differences in the TNTI properties (i.e. interface position and width) between the smooth wall case, converging region, and diverging region when they are scaled with their respective boundary layer thickness.