Mechanical Engineering - Theses
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ItemSensor and actuator selection for feedback control of fluid flows( 2019)The present thesis regards linear estimation and control for two fluid flows, with a particular focus on the placement of sensors and actuators. In the first part of the thesis, we study the complex Ginzburg-Landau equation, a simple model for spatially developing flows such as jets, wakes and cavities. (This equation can be seen as a low-dimensional substitute for the Navier-Stokes equations.) The specific focus is on the extent to which estimation and control are (i) fundamentally difficult and (ii) limited by having only a single sensor and a single actuator. To answer these questions, we study three problems. First, we consider the optimal estimation problem in which a single sensor is used to estimate the entire flow field (without any control). Second, we consider the full information control problem in which the whole flow field is known, but only a single actuator is available for control. Third, we consider the overall input-output control problem in which only a single sensor is available for measurements; and only a single actuator is available for control. By considering the optimal sensor placement, optimal actuator placement or both while varying the stability of the system, fundamental placement trade-offs are made clear. We discuss implications for effective feedback control with a single sensor and a single actuator and compare the results to previous placement studies. In the second part of this thesis, we look at an incompressible turbulent channel flow at a friction Reynolds number of Re$_\tau = 2000$. A linear Navier-Stokes operator is formed about the turbulent mean and augmented with an eddy viscosity. Velocity perturbations are then generated by stochastically forcing the linear Navier- Stokes operator. The objective is to estimate and control these perturbations. The estimation and control problems perform best for the largest scales that (i) are high in energy when stochastically forced, (ii) exhibit large transient growth and (iii) are coherent over large wall-normal distances. We determine the locations of sensors and actuators for which estimation and control are most effective by looking at two arrangements: (i) placing them at the wall; and (ii) placing them some distance off the wall. Finally, it is shown that a control arrangement with a well-placed sensor and actuator performs comparably to either measuring the flow everywhere (while actuating it at a single wall height) or actuating it everywhere (while measuring it at a single wall height). In this way, we gain insight (at low computational cost) into how specific scales of turbulence are most effectively estimated and controlled.
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ItemExperimental investigation of velocity and vorticity in turbulent wall flows( 2019)This thesis details the results of a research effort both to acquire sufficiently-resolved velocity and vorticity vector time-series in turbulent wall-bounded flows, as well as to use the acquired data to juxtapose two canonical wall-bounded flows: the zero-pressure-gradient boundary layer and the fully-developed pipe. Towards these ends, a novel configuration of measurement sensors has been designed, evaluated, and deployed in three of the largest canonical wall-flow facilities in existence: the Flow Physics Facility (FPF) at the University of New Hampshire, the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT) at the University of Melbourne, and the Centre for International Cooperation in Long Pipe Experiments (CICLoPE) at the University of Bologna. The datasets presented herein are the first to contain simultaneously-acquired velocity and vorticity statistics in both pipe and boundary layer flows under matched conditions. The capacity of the measurement probe to resolve the velocity and vorticity vectors under idealised conditions is evaluated via `synthetic experiments', whereby the response of the probe to a simulated turbulent flow is modeled, and the resulting aggregate statistics compared to those of the known input. The synthetic experimental results are then compared to statistics obtained from physical experiments, and show close agreement for most quantities despite differences in Reynolds number. Disagreement between the physical and synthetic experimental results in several quantities is used to diagnose a limitation of the present sensor system. An awareness of the measurement capabilities (and limitations) afforded by the comparison between the synthetic and physical experiments pervades the ensuing analysis and discussion of additional physical experimental results. Normalised statistical moments (up to the kurtosis) of velocity and vorticity are presented for both pipe and boundary layer cases. The two flows are shown to exhibit virtually no differences from one another wallward of the wake region aside from the transverse velocity component variances. The boundary layer wake is characterised by higher turbulence enstrophy and turbulence kinetic energy (TKE) than the pipe, despite containing both turbulent and non-turbulent states. Although there is no `free-stream' in the fully-developed pipe, a significant time-fraction of the flow can be described as `quasi-irrotational' near the centreline. This results in a departure of the velocity and vorticity kurtosis (and, when not identically zero, skewness) from Gaussian behaviour in the outer region of the pipe, as is known to occur in the boundary layer (owing to turbulent/non-turbulent intermittency). Spectral properties of the velocity and vorticity signals acquired in both flows are examined, both for their own content as well as to compare the two flows. Despite very little difference in the observed streamwise turbulence kinetic energy, the contributions to the total differ considerably by scale between the two flows. The pipe is observed to contain more streamwise TKE than the boundary layer in scales longer than 10 times the outer length scale $\delta$, while the opposite is true for scales shorter than $10\delta$. This `crossover' scale also applies to the spectra of the transverse velocity components and Reynolds shear stress. The measured enstrophy spectrum is shown to be approximately invariant under Kolmogorov normalisation for wall-distances greater than about 200 viscous-lengths. Finally, local isotropy and axisymmetry in the velocity components are evaluated. Local isotropy is observed to be satisfied over a range of scales for which the characteristic timescale of inertial energy transfer is expected to be small relative to the timescale of the mean strain rate. The relationship between the transverse velocities and the streamwise velocity, however, does not appear to approach isotropy along the pipe centreline, suggesting that the bounding wall also plays a role in imposing a sense of direction on the turbulence. Indeed, the aforementioned timescale criterion is shown to identify a cutoff scale that increases proportionally with wall-distance, confounding a conclusive statement regarding the primary source of anisotropy away from the centreline.
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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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ItemNumerical methods and turbulence modelling for large-eddy simulations( 2015)Turbulence is of interest in many engineering applications, ranging from aerospace design to naval architecture. The inherent complexities of turbulence make it difficult to measure experimentally, and, to simulate numerically. The focus of this dissertation is the simulation of turbulent flow with the computational methodology known as large-eddy simulation (LES). LES uses a filter to partition a flow-field into large- (or resolved) and small- (or subgrid) scales and solves only for the large-scales. This method provides more accuracy when compared to other computational methods, such as those based on the Reynolds-averaged Navier--Stokes equations. The increased accuracy, however, comes with an associated increase in computational cost. Indeed, the computational cost of LES can often be prohibitive, especially for cases involving wall-bounded flow over complex geometries at high Reynolds numbers. This high computational expense is one of the primary limitations of LES. Methods to reduce the cost of LES form the focus of this dissertation. The high cost of LES is in great part due to the near-wall resolution requirement. To accurately represent a flow-field with LES, it is necessary to sufficiently resolve all of the dynamically important scales of motion. This is relatively inexpensive in free-shear flows, where the large-scales are the most energetic, but it is more difficult in wall-bounded flows, where the energy-containing scales get increasingly small near a wall. These near-wall small-scales make it impractical to resolve all of the energy containing scales. Therefore, models that mimic the effect of the near-wall turbulent structures on the wall and on the core of the flow are often used. These models are known as wall-models, and, if accurate, they are able to significantly reduce the computational cost of a large-eddy simulation. At present there is no wall-modelling approach that has been shown to be apposite in a broad range of applications. In particular, current wall-models are often inaccurate when applied to separating wall-bounded flow and are limited by their inability to predict fluctuations of wall-shear-stress and the near-wall velocity. Because of this, a key focus of this dissertation is the proposal and investigation of a new wall-model that aims to overcome these two limitations. In addition, the new model aims to reduce the computational cost of LES by significantly reducing the near-wall resolution requirement. Before introducing this new wall-model, flow over a circular cylinder is investigated in order to gain familiarity with the large-eddy simulation methodology and to assess the effect of some key computational parameters in LES. In this investigation, the effects of mesh resolution, discretisation schemes, SGS-models, and wall-models on prediction of the flow-field are assessed. One of the primary outcomes of this study is the finding that `standard' wall-models are inadequate for turbulent separating flows. This motivated the investigation of the new wall-model. The new wall-model is able to predict the fluctuating wall-shear-stress from a large-scale velocity input. The model is based on the spectral structure of the turbulent boundary layer and the interaction between large-scale events in the logarithmic layer and small-scale events near the wall. Importantly, the model includes many important parameters that are able to preserve the structure of the boundary layer while remaining relatively straightforward to implement in a solver. Further, the model does not increase the computational cost of a simulation compared to current wall-modelling approaches. The model is implemented in large-eddy simulations of channel flow to assess its efficacy compared to a standard wall-model. The influence of two subgrid-scale models on the large-scale velocity input is also investigated. Results show that the new wall-model is able to resolve more of the wall-shear-stress variance when compared to a standard wall-model, and it has a small effect in the outer-regions of the boundary layer.
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ItemEvolution of zero pressure gradient turbulent boundary layers from different initial conditions( 2012)Turbulent boundary layers developing under zero pressure gradient (ZPG) condition are investigated experimentally with the overall aim of learning more about the streamwise evolution of these wall-bounded flows close to the quasi-equilibrium state (The definition of a quasi-equilibrium boundary layer is from Perry et al. [1994] where the wake parameter II is allowed to vary with streamwise distance but it is assumed that the wake gradient is sufficiently small so as to have negligible effect on the shear stress profiles). Scaling of the streamwise broadband turbulence intensity is also investigated. A key aspect of this study is obtaining high fidelity measurements at high Reynolds numbers over a large range of streamwise locations. This has required a novel hot-wire calibration technique. The research work also represents an effort to acquire very high quality ZPG turbulent boundary layer data ranging from Reт = δ Uт/ v ≈2740—22884 (here δ is boundary layer thickness, Uт is friction velocity and v is kinematic viscosity). The inner-normalized wire length l+ ≈ 23 ± 2 is maintained for Reynolds numbers Reт = 2740 —13320. This length increases to 29 and 38 for Reт = 17777 and 22884 respectively. To minimize the effect of changes in boundary conditions for different freestream velocities, the entire set of experiments were performed at three freestream velocities of 20m/s, 30m/s and 40m/s to maintain constant unit Reynolds number U∞/v ≈ 1.295 x 106, 1.91 x 106 and 2/50 x 106 m-1 respectively. Different Reynolds numbers were achieved at 10 different streamwise stations over a 27m long tunnel floor. Mean flow and higher order statistics such as broadband turbulence intensity, skewness, flatness as well as spectral measurements were made for all the Reynolds numbers. The logarithmic law of the wall provides a universal behaviour for the mean velocity profile in the inner region. Universal behaviour in the outer region is provided by the law of the wake. A new scaling is proposed for the streamwise Reynolds stress and energy spectra covering the inner, logarithmic and outer region. Comparisons are made with results from other experiments and numerical simulations. The research work also represents an effort to acquire very high quality ZPG turbulent boundary layer data ranging from Reт = δ Uт/ ѵ ≈2740—22884 (here δ is boundary layer thickness, Uт is friction velocity and ѵ is kinematic viscosity). The inner-normalized wire length l+ ≈ 23 ± 2 is maintained for Reynolds numbers Reт = 2740 —13320. This length increases to 29 and 38 for Reт = 17777 and 22884 respectively. To minimize the effect of changes in boundary conditions for different freestream velocities, the entire set of experiments were performed at three freestream velocities of 20m/s, 30m/s and 40m/s to maintain constant unit Reynolds number U∞/ѵ ≈ 1.295 x 106, 1.91 x 106 and 2/50 x 106 m-1 respectively. Different Reynolds numbers were achieved at 10 different streamwise stations over a 27m long tunnel floor. Mean flow and higher order statistics such as broadband turbulence intensity, skewness, flatness as well as spectral measurements were made for all the Reynolds numbers. The logarithmic law of the wall provides a universal behaviour for the mean velocity profile in the inner region. Universal behaviour in the outer region is provided by the law of the wake. A new scaling is proposed for the streamwise Reynolds stress and energy spectra covering the inner, logarithmic and outer region. Comparisons are made with results from other experiments and numerical simulations.