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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ItemNumerical simulation of turbulent flows over rough surfaces( 2017)Turbulent flows over roughness are ubiquitous in engineering and geophysical applications, however their study is limited by the expense of laboratory experiments and conventional direct numerical simulations (DNS). In this thesis, we develop a framework in which fully resolved numerical simulations of rough-wall flows can be conducted at a reduced cost compared to conventional DNS. The framework utilises the minimal-span channel technique previously used to study smooth-wall turbulent flows. This technique only captures the near-wall flow while the outer layer is explicitly not captured. Roughness primarily alters the near-wall flow, while the outer layer remains similar with respect to the wall shear stress, making it a prime candidate for minimal-span channels. The streamwise domain length of the channel is investigated with the minimum length found to be three times the spanwise domain width or 1000 viscous units, whichever is longer. The outer layer of the minimal channel is inherently unphysical and as such alterations to it can be performed so long as the near-wall flow, which is the same as in a full-span channel, remains unchanged. Firstly, a half-height (open) channel with slip wall is shown to reproduce the near-wall behaviour seen in a standard channel, but with half the number of grid points. Next, a forcing model is introduced into the outer layer of a half-height channel. This reduces the high streamwise velocity associated with the minimal channel and allows for a larger computational time step. An empirical costing argument is developed to determine the cost in terms of CPU hours of minimal-span channel simulations a priori. This argument involves counting the number of eddy lifespans in the channel, which is then related to the statistical uncertainty of the streamwise velocity. For a given statistical uncertainty in the roughness function, this can then be used to determine the simulation run time. The minimal-span channel is then used to investigate turbulent flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at k+ = 10, where k is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity (frontal area divided by plan area) ranging from 0.05 to 0.54. In the sparse regime of roughness (solidity less than approximately 0.15) the roughness function increases with increasing solidity, while in the dense regime the roughness function decreases with increasing solidity. It was found that the dense regime begins when the solidity is greater than approximately 0.15-0.18, in agreement with the literature. A model is proposed for the limit of solidity approaching infinity, which is a smooth wall located at the crest of the roughness elements. This model assists with interpreting the asymptotic behaviour of the roughness, and the rough-wall data show that the near-wall flow is tending towards this modelled limit. The peak streamwise turbulence intensity, which is associated with the turbulent near-wall cycle, is seen to move increasingly further away from the wall with increasing solidity. In the sparse regime, increasing the solidity reduces streamwise turbulent energy associated with the near-wall cycle, while increasing the solidity in the dense regime increases turbulent energy. An analysis of the difference of the integrated mean-momentum balance between smooth- and rough-wall flows reveals that the roughness function decreases in the dense regime due to a reduction in the Reynolds shear stress. This is predominantly due to the near-wall cycle being pushed away from the roughness elements, which leads to a reduction in turbulent energy in the region previously occupied by these events. Finally, we conduct simulations of turbulent flow over two-dimensional rectangular bars aligned in the spanwise direction. This roughness has been often described as d-type, as the roughness function is thought to depend only on the outer-layer length scale (pipe diameter, channel half height or boundary-layer thickness). This is in contrast to conventional engineering rough surfaces, named k-type, for which the roughness function depends on the roughness height, k. The present results show that increasing the trough-to-crest height, k, of the roughness while keeping the width between roughness bars, w, fixed in wall units, results in non-k-type behaviour. The roughness function appears to scale linearly with w+, suggesting that this is the only relevant parameter for very deep rough surfaces with k/w greater than approximately 3. In these situations, the flow no longer has any information about how deep the roughness is and instead can only `see' the width of the fluid gap between the bars.
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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.