The later stages of separated shear layer transition within separation bubbles developing over a NACA0018 airfoil operating at a chord Reynolds number of 105 and at angles of attack of 0, 5, 8, and 10 degrees were investigated experimentally in a wind tunnel. Several experimental tools, including a rake of six boundary-layer hot-wire anemometers, were used to perform measurements over the model. Novel high-speed flow visualization performed with a smoke-wire placed within the separated shear layer showed that roll-up vortices are shed within separation bubbles forming on the suction side of the airfoil. The structures were found to convect downstream and eventually break down during laminar-to-turbulent transition. Top view visualizations revealed that, at angles of attack of 0, 5, and 8 degrees, roll-up vortices form coherently across the span and undergo significant spanwise deformations prior to breaking down. At angles of attack of 5 and 8 degrees, rows of streamwise-oriented structures were observed to form during vortex breakdown. Statistics regarding the formation and development of shear layer roll-up vortices were extracted from high-speed flow visualization sequences and compared to the results of boundary layer measurements. It was found that, on the average, roll-up vortices form following the initial exponential growth of unstable disturbances within the separated shear layer and initiate the later stages of transition. The onset of these nonlinear stages was found to occur when the amplitude of velocity disturbances reached approximately 10% of the free-stream velocity. The rate of vortex shedding was found to fall within the frequency band of the unstable disturbances and lie near the central frequency of this band. The formation of vortices has been linked to the generation of harmonics of these unstable disturbances in velocity signals acquired ahead of mean transition. Once shed, vortices were found to drift at speeds between 33% and 44% of the edge velocity. Vortex merging at an angle of attack of 5?? was investigated. It was found that the majority of roll-up vortices proceed to merge with either one or two other vortices. Vortex merging between two and three vortices was found to occur periodically in a process similar to vortex merging in plane mixing layers undergoing subharmonic forcing of the most amplified disturbance. The flapping motion of the separated shear layer was investigated by performing a cross-correlation analysis on the high-speed flow visualization sequences to extract vertical displacement signals of the smoke within the shear layer. The frequency of flapping was found to correspond to the unstable disturbance band. At an angle of attack of 5??, it was found that the separated shear layer has a low-frequency component of flapping that matches a strong peak in velocity and surface pressure spectra that lies outside the unstable disturbance frequency band. The spanwise development of disturbances was assessed in the aft portion of the separation bubbles by performing a cross-correlation analysis on signals acquired simultaneously across the span with the rake of hot-wires. The spanwise correlations between signals was found to be well-correlated ahead of shear layer roll-up, after which disturbances became rapidly uncorrelated ahead of mean reattachment. These results were found to be linked to the coherent roll-up and subsequent breakdown of roll-up vortices.

The accuracy of existing methods for estimating the drag based on experimental flow field measurements were assessed for two-dimensional bodies. The effects of control volume boundary placement and inherent simplifying assumptions were also investigated. Wind tunnel experiments were performed on a circular cylinder operating at a Reynolds number of 8,000 and 20,000, and on a NACA 0018 airfoil operating at a chord Reynolds number of 100,000 for three angles of attack (α), specifically, 5◦, 10◦, and 15◦. The circular cylinder experiments fall within the the shear layer transition flow regime. Airfoil investigations span both types of flow development common to low Reynolds number airfoil operation. For α = 5◦ and 10◦, a separation bubble forms on the upper surface of the airfoil, while, for α = 15◦, the flow separates without reattaching, resulting in a stalled airfoil. Wake velocity and pressure measurements were performed at several downstream locations to investigate the impact of control volume boundary placement. Wake profiles were measured between 3 and 40 diameters downstream from the circular cylinder axis and between 1 and 4.5 chord lengths from the trailing edge of the airfoil. In addition to wake profiles, the outer flow velocity variation was quantified to investigate the appropriate location to measure freestream flow characteristics in a test section with streamwise-varying outer flow conditions. The results show that drag estimates are strongly dependent on the streamwise position of the measured wake profile for all methods investigated. Drag estimates improved, and streamwise variation decreased, with increasing streamwise position of the flow measurements. For the pressure based method examined, wake measurements should be taken at least 10 times the projected model height downstream of the model. In the case of the circular cylinder, this is equivalent to 10 diameters and, for the airfoil investigated, it is approximately 1 chord length from the trailing edge. For the methods relying on velocity measurements, acceptable estimates of drag were possible when based on measurements taken at least 30 projected heights downstream, i.e., 30 diameters for the circular cylinder and 3 chord lengths for the airfoil model investigated. The findings highlight the importance of providing a detailed description of the methodology and experimental implementation for drag estimates based on flow field measurements. Finally the study offers guidelines for implementing momentum integral based drag calculations in future investigations.

For many decades, turbulence has been the subject of extensive numerical research and experimental work. A bottleneck problem in turbulence research has been to detect and characterize the energetic, space and time-dependent structures and give a mathematical definition to each topology. This research presents a fundamental study of coherent structures, embedded in turbulent flows, by use of Proper Orthogonal Decomposition (POD). The target is to detect dominant features which contain the largest fraction of the total kinetic energy and hence contribute more to a turbulent flow. POD is proven to be a robust methodology in multivariate analysis of non-linear problems. This method also helps to obtain a low-dimensional approximation of a high-dimensional process, like a turbulent flow. This manuscript-based dissertation consists of five chapters. The first chapter starts with a brief introduction to turbulence, available simulation techniques, limitations and practical applications. Next, POD is introduced and the step-by-step approach is explained in detail. Three submitted manuscripts are presented in the subsequent chapters. Each chapter starts with introducing the study case and explaining the contribution of the study to the whole topic and also has its topic-relevant literature review. Each article consists of two parts: flow simulation and verification of the results at the onset, followed by POD analysis and reconstruction of the turbulent flow fields. For flow simulation, Large Eddy Simulation (LES) was performed to obtain databases for POD analysis. The simulations were validated by making comparison with available experimental and numerical studies. For each case, coherent topologies are characterized and the contribution of kinetic energy for each structure is determined and compared with previous literature. The first manuscript focused on investigating the large-scale dynamics in the wake of an infinite square cylinder. This case is the first step towards the targeting study case of this research, i.e. flow over rib roughened walls. The main purpose the first step is to establish a benchmark for comparison to the more complicated cases of a square cylinder with a nearby wall and flow over a rib-roughened surface. For POD analysis, the three-dimensional velocity field is obtained from LES of the flow around an infinite square cylinder at a Reynolds number of Re = 500. The POD algorithm is examined and the total energy of the flow is found to be well captured by only a small number of eigenmodes. From the energy spectrum, it is learned that each eigenmode represents a particular flow characteristic embedded in the turbulent wake, and eigenmodes with analogous characteristics can be bundled as pairs. Qualitative analysis of the dominant modes provided insight as to the spatial distribution of dominant structures in the turbulent wake. Another outcome of this chapter is to develop physical interpretations of the energetic structures by examining the temporal coefficients and tracking their life-cycle. It was observed that the paired temporal coefficients are approximately sinusoidal with similar order of magnitude and frequency and a phase shift. Lastly, it was observed that the turbulent flow field can be approximated by a linear combination of the mean flow and a finite number of spatial modes. The second manuscript analyses the influence of a solid wall on the wake dynamics of an infinite square cylinder. Different cases have been studied by changing the distance between the cylinder and the bottom wall. From the simulation results, it is learned that the value of drag and lift coefficients can be significantly affected by a nearby solid wall. From the energy decay spectrum it is observed that the energy decay rate varies for different gap ratios and accordingly a physical explanation is developed. Visualization of coherent structures for each case shows that for larger gaps, although the structures are distorted and inclined away from the wall, the travelling wave characteristic persists. Lastly, it is observed that as the gap ratio gets smaller, energetic structures originated by the wall begin to appear in the lower index modes. The last manuscript presents a numerical study of the structures in turbulent Couette flow with roughness on one wall, which as mentioned earlier, is the targeting study case of this research. Flow over both roughened and smooth surfaces was examined in a single study. Comparison was made with experiments and other numerical studies to verify the LES results. The mean velocity distribution across the channel shows that the rib roughness on the bottom wall has a strong effect on the velocity profile on the opposite wall. The energetic coherent dynamics of turbulent flow were investigated by the use of POD. The energy decay spectrum was analysed and the influence of a roughened wall and each roughness element on formation of those structures was investigated. Coherent POD modes on a spanwise sampling plane are detected. A secondary swirling motion is visualized, for the first two modes and counter-rotating cells are observed in the lower region of the channel above the rough wall for the higher modes. At the end, a quantitative analysis of the POD temporal coefficients was performed, which characterize the life-cycle of each coherent dynamic. A motivating outcome of this analysis is to decompose the time trace curves into quasi-periodic and fluctuations curves and to detect a linkage between these life cycles and physical meaning and location of each energetic pattern. At the end, in a closuring chapter, concluding remarks of this research work are presented in more detail and some potential extensions have been proposed for future researchers.

Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

The main objective of this thesis is to develop a comprehensive model with the capability of modeling both a high Reynolds number and high magnetic Reynolds number turbulent flow for application to supersonic combustor. The development of this model can be divided into three categories: one, the development of a self-consistent MHD numerical model capable of modeling magnetic turbulence in high magnetic Reynolds number applications. Second, the development of a gas discharge model which models the interaction of externally applied fields in conductive medium. Third, the development of models necessary for studying supersonic combustion applications with plasma-assistance such the extension of chemical kinetics models to extremely high temperature and non-equilibrium phenomenon.

The evolution of column instabilities that lead to break up of a microscale liquid jet is studied experimentally using shadowgraph technique. The jet formation is investigated over a range of Reynolds number, Pressure Ratio, and Ohnesorge number which are varied by the driving pressure, observation chamber pressure, and the jet liquid. Over the range of these parameters, the jet experiences different break up mechanisms as a result of different dominant instabilities. The present investigation discusses both break up mechanisms that are similar to the break up of macroscale jets and some new microscale break up phenomena.

A weakly nonlinear stability analysis was conducted for the flow induced in an incompressible, Newtonian, viscous fluid lying between two infinite parallel plates which form a channel. The plates are oscillating synchronously in simple harmonic motion. The disturbed velocity of the flow was written in the form of a series in powers of a parameter which is a measure of the distance away from the linear theory neutral conditions. The individual terms of this series were decomposed using Floquet theory and Fourier series in time. The equations at second order and third order in were derived, and solutions for the Fourier coefficients were found using pseudospectral methods for the spatial variables. Various alternative methods of computation were applied to check the validity of the results obtained. The Landau equation for the amplitude of the disturbance was obtained, and the existence of equilibrium amplitude solutions inferred. The values of the coefficients in the Landau equation were calculated for the nondimensional channel half-widths h for the cases h = 5, 8, 10, 12, 14 and 16. It was found that equilibrium amplitude solutions exist for points in wavenumber Reynolds number space above the smooth portion of the previously determined linear stability neutral curve in all the cases examined. Similarly, Landau coefficients were calculated on a special feature of the neutral curve (called a ???finger???) for the case h = 12. Equilibrium amplitude solutions were found to exist at points inside the finger, and in a particular region outside near the top of the finger. Traces of the x-components of the disturbance velocities have been presented for a range of positions across the channel, together with the size of the equilibrium amplitude at these positions. As well, traces of the x-component of the velocity of the disturbed flow and traces of the velocity of the basic flow have been given for comparison at a particular position in the channel.

[Formulae and special characters can only be approximated here. Please see the pdf version of the Abstract for an accurate reproduction.] Since the damping functions employed by most of the low-Reynolds-number models are related to the non-dimensional distance y+[ special character ??? near-wall non-dimensional distance in y direction], which is based on local wall shear stress, these models become invalid for separated flows, because the wall shear stress is zero at the reattachment point. In addition, the pressure-velocity correlation term is neglected in most of these models, although this term is shown in this thesis to be important in the near-wall region for simple flows and large pressure gradient flows. In this thesis, two main efforts are made to improve the k ??? [special character - dissipation rate] model. First, based on Myong and Kasagi???s (1990) low-Reynolds-number model (hereafter referred to as MK model), a more general damping function [special character - turbulent viscosity damping function in LRN turbulent model] is postulated which only depends on the Reynolds numbers [formula ??? near-wall turbulence Reynolds number]. Second, a form for the pressure-velocity correlation term is postulated based on the Poisson equation for pressure fluctuations. This modified model predicts the turbulent flow over a flat plate very well. It is found that the inclusion of the pressure-velocity correlation term leads to significant improvement of the prediction of near-wall turbulence kinetic energy. When the model is applied to turbulent flow over a backward-facing step, it produces better predictions than the traditional k ??? [special character - dissipation rate] model, FLUENT???s two-layer model and the MK model. Again, the pressure-velocity correlation term improves the turbulence kinetic energy prediction in the separated region over that of other models investigated here. The studies of numerical methods concerning computational domain size and grid spacing reveal that a very large domain size is required for accurate flat plate flow computation. They also show that a fine grid distribution in the near-wall region upstream of the step is necessary for acceptable flow prediction accuracy in the downstream separated region.

Thesis (M.S.) -- Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (Ph.D.) - Carleton University, 2007. / Includes bibliographical references (p. 251-264). Also available in electronic format on the Internet.