Mechanical Engineering - Theses
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ItemMeasurements and analysis of turbulent boundary layers subjected to streamwise pressure gradients( 2021)This thesis details the changes in structure between an adverse pressure gradient turbulent boundary layer (APG TBL), zero pressure gradient (ZPG) TBL, and channel flow by means of the mean momentum balance (MMB). In order to understand the effects of a pressure gradient on a turbulent boundary layer, aspects of the physical flow are studied via mean statistics, turbulence measurements, and spectra analysis. This study uses new experimental measurements that are conducted along an APG ramp as well as measurements downstream of the ramp insert to study the flow as it relaxes towards equilibrium. In the present experimental set-up the boundary layer is under modest APG conditions, where the Clauser pressure-gradient parameter $\beta$ is $\leq 1.8$. Well-resolved hot-wire measurements are obtained at the Flow Physics Facility (FPF) at the University of New Hampshire. Comparisons are made with ZPG TBL experimental data at similar Reynolds number and computational data at lower Reynolds number. Present measurements are also compared to existing APG TBL lower Reynolds number experimental and computational data sets. Finally, it is shown how these findings relate to an analytical transformation. The primary takeaways from the MMB analysis presented herein are $(i)$ distance-from-the-wall scaling can result from an assumption of self-similar mean dynamics, and does not require primacy of a single velocity scale, and $(ii)$ distance-from-the-wall scaling does not necessarily imply a logarithmic mean velocity profile; a power-law velocity scale hierarchy along with self-similar mean dynamics simultaneously produces distance-from-the-wall scaling \textit{and} a power law mean velocity profile. The choice to refer to the (potentially) self-similar subdomain as the `inertial sublayer' in the present study (rather than the `log' layer) is therefore deliberate.
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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 quiescent core of turbulent channel and pipe flows( 2016)A new conceptual view of turbulent channel and pipe flows is presented via the proposition of the `quiescent core', which is analogous to the free-stream in turbulent boundary layers. The quiescent core is detected as a zone of roughly uniform streamwise momentum, which happens to be relatively quiescent compared to the rest of flow, residing in the central region of channel and pipe flows. It occupies a large proportion of the flow and oscillates with the large-scale wavelengths in a predominantly anti-symmetric manner. Within the intermittent region of wall-turbulence, it is observed that the oscillation of the turbulent/non-turbulent interface or quiescent core can contaminate the fluctuating velocity components under the traditional Reynolds decomposition. A new method of decomposing the total velocity is proposed to remove this contamination. The use of this new decomposition method, along with the zone-averaging technique, enables the examination of `true' turbulent structure and scale purely inside the `turbulent shear flow' region (below the free-stream or outside the quiescent core) of both internal (channel and pipe) and external (boundary layer) flows. The results are compared in internal and external flows to reveal that the structure and scale of turbulence in those flows are indeed much more similar than previous studies have concluded. It is shown that the geometry of the pipe core can be well-represented by a few dominant azimuthal Fourier modes. The dominant azimuthal modes of the pipe core are associated with streamwise streaks and roll-modes in axisymmetric arrangements and they often maintain a high degree of spatial coherence along the streamwise direction (for over a pipe radius). The investigation of temporal progression of the pipe core reveals that it simply convects downstream without azimuthal rotation and rapid evolution. The most energetic modes of channel flow are extracted and investigated by means of proper orthogonal decomposition. It is observed that the large-scale wall-normal eigenfunctions appear in pairs which carry comparable amounts of turbulent kinetic energy and Reynolds shear stress. The turbulent kinetic energy and Reynolds shear stress are mostly concentrated in the large-scale modes (with the first 20 modes carrying about a half of these quantities). The most energetic modes represent the large-scale inclined flow structures with symmetric or anti-symmetric arrangements between the top and bottom channel walls, which can efficiently replicate the associated large-scale geometry of the channel core.
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ItemConvective methods of pumping and drag reduction( 2013)It is the convection of the velocity field by itself that renders many fluid mechanics problems mathematically challenging, and produces complicated, and often non-intuitive flow phenomena. Pumping and drag reduction are effectively related concepts, in that they both involve increasing the volume flux of the fluid. In this work, we consider three different methods of pumping and drag reduction, all of which result, partially or entirely, from the effect of convection. The first of these methods is the drag reduction obtained by the addition of elastic polymers to a turbulently flowing liquid. This effect is not well understood, and a complete physical explanation of the phenomenon remains to be made. However, it is clear that the polymer has the capacity to transport energy and momentum within the fluid, and energy may also dissipate within the polymer itself. In this work, it is proved that the addition of elastic polymers to a turbulent flow cannot reduce the drag to a level below that of the equivalent laminar flow. This proof can also be applied to similar methods of drag reduction, such as the presence of surfactant micelles within a turbulently flowing liquid and the presence of sand particles within high winds and water droplets within cyclones. The second method is known as "transpiration", and consists of a dynamic regime of blowing and suction at the wall of the pipe or channel which imparts no net volume flux upon the flow. Using a perturbation analysis, the pumping effect of transpiration has been quantified in this work. It is shown that this pumping results from convection, and relies on the presence of large velocity gradients within the flow. The third method consists of oscillating waves in the wall of the pipe or channel. This has particular relevance to the valveless impedance pump, which consists of a thin tube, one section of which is elastic and is subjected to rhythmic pinching at some point offset from its centre. This pinching induces oscillating waves within the wall of the tube, which in turn induce a flow. The flow induced by small-amplitude oscillations, in the wall, has been derived through a perturbation analysis. In this way, we are able to separate the effect of convection from the more readily intuitive dragging effect that the wave has upon the fluid, and thereby quantify the importance of convection in such systems. It is found that even within small tubes, the effect of convection remains generally of the same order of magnitude as the dragging effect, and that no effective model of the valveless impedance pump could safely neglect the effect of convection.
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ItemNumerical study of internal wall-bounded turbulent flows( 2011)Direct numerical simulation (DNS) of turbulent pipe flow has been performed at Reynolds numbers ranging from Reτ ≈ 170 to 2000. A literature review highlights a need for higher Reynolds number pipe flow DNS data. There have been many numerical studies for internal geometry (pipe and channel) wall-bounded turbulent flows. Many of the numerical data for both pipe and channel flows, which are now readily accessible are at lower Reynolds numbers. At higher Reynolds numbers, there is a lack of pipe flow DNS data as compared to channel flow DNS data. As the highest Reynolds numbers in numerical simulations are starting to overlap the lower region of experiments, validation of both experimental and numerical results is now possible. Moreover, numerical simulations are extremely useful in complementing experimental results in the near-wall region where accurate experimental data are often difficult to obtain. However, available DNS data of internal wall-bounded turbulent flows are performed with different grid resolutions and computational domain sizes, making it difficult to directly compare between them. An undertaking of this thesis involves a systematic study (using constant grid resolutions) of the domain length effect on the convergence of turbulence statistics. Investigations carried out using numerical data from fully developed pipe flow simulations indicate a recommended computational length of 8π pipe radius or half channel height for turbulence statistics to converge. It is hoped that this will serve as a benchmark computational domain length for future numerical simulations performed. A study is also carried out to better understand the similarities and differences of the flow physics between turbulent channel and pipe flows. This is performed using the newly obtained pipe flow DNS data and channel flow DNS data of del ´ Alamo et al. (2004) at a comparable Reynolds number of Reτ ≈ 1000. Different turbulence statistics investigated including mean flow, turbulence intensities, correlations and energy spectra. Comparison of both wall-bounded channel and pipe flows shows little discrepancies in the near-wall region but differences are observed in the outer-region. Although there is abundant literature for both experimental and numerical wall bounded turbulent flows, further analysis reveals discrepancies in the open literature. One of the primary contributing factors that plagues reported results are spatial resolution issues. In this thesis, the numerical data is used to investigate the effects of insufficient spatial resolution in wall-bounded turbulence by averaging the streamwise velocity component in the spanwise direction. A correction scheme is proposed to correct experimental results suffering from insufficient spatial resolution. The correction scheme is applied to attenuated experimental results such as streamwise turbulence intensity and one-dimensional energy spectra and is shown to be effective. The method of using DNS data to analysis and correct experimental results can be extended to other experimental techniques such as particle image velocimetry and laser doppler velocimetry.
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ItemRecovery of fluid mechanical modes in unsteady separated flows( 2010)This study is concerned with the recovery of fluid mechanical modes that can be used to describe the physical properties of unsteady separated flows. The flow configuration of interest is a spanwise homogeneous NACA 0015 airfoil with leading edge laminar separation and turbulent recirculation. An in-depth understanding of the unsteady flow dynamics and fluid mechanical stability properties, can assist in the future development of more efficient separation control strategies. In order to provide a richer understanding of the physics, the flow fields are numerically generated, and characterised at various key Reynolds numbers leading up to the target turbulent case. Proper Orthogonal Decomposition modes are recovered to most efficiently represent the unsteady scales of motion, and linear stability modes are sought to identify how a perturbation will evolve in this unsteady environment. The generation of the Proper Orthogonal Decomposition modes can require very large amounts of data, and the current study presents a means of recovering these modes using parallel computation. To enable the stability analysis, a means of performing the calculation in steady two-dimensional flows of semi-complex geometry has been developed. The corrections required to perform the stability analysis in unsteady turbulent flows has also been identified by using a non-linear eddy viscosity model to close the triple decomposition stability equations. It is intended that the means of recovering these fluid mechanical modes can assist in the future development of reduced order models necessary for the control of unsteady separated flows.