Mechanical Engineering - Theses
Permanent URI for this collection
Search Results
1 - 2 of 2
-
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.
-
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.