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The turbulent flow through a 90o pipe bend is complex with secondary flow that can affect pressure drop and heat/mass transfer. The mean and unsteady flow is studied using refractive index matched two-dimensional two-component (2D2C) Particle Image Velocimetry in a single 90o bend with Rc/D = 1.5 and at Re = 34800. The measurements were performed in a closed loop using a 1-inch diameter test section that was machined out of acrylic. The flow is imaged in the symmetric plane parallel to the axial flow and at different cross sectional planes including 0.25D and 1D upstream, 10o, 20o, 70o, 80o from the bend inlet and 0.25D and 1D downstream of the bend. The axial flow accelerates on the inner wall at the inlet and then moves towards the outer wall at 40o-50o. A shear layer is formed between high velocity fluid near the outer wall and the slower moving fluid at the inner wall side in the second half of the bend. The axial turbulent kinetic energy ((u^2 ) ̅+(v^2 ) ̅) is found to be high in regions corresponding to high velocity gradient regions: (i) at the outer wall near the inlet that extends up to the outlet, (ii) near the inner wall at 40o-50o, and (iii) at the shear layer formed near the inner wall. In the cross sectional planes, two vortices are formed and have a maximum strength at 80o from the bend inlet. The cross sectional turbulent kinetic energy ((v^2 ) ̅+(w^2 ) ̅) is found to be highest on the inner wall at the 80o plane. The snapshot Proper Orthogonal Decomposition (POD) technique is used to study the unsteady flow structures within the flow. There are long and short flow structures in the upstream pipe which can be related to Very Large Scale and Large Scale Motions. The secondary flow at 20o and further downstream cross sectional planes show evidence of unsteadiness as two vortices oscillate about the symmetry axis with low frequencies of St ~ 0.07, 0.13 and higher frequency at St ~ 0.3-0.6. The low frequency oscillations can be related to Very Large Scale Motions while high frequency oscillations are related to separation of the flow on the inner wall side. Evidence of swirl switching in the high frequency range (St ~ 0.3-0.5) is found at cross sectional plane 1D downstream. / Thesis / Master of Applied Science (MASc)

Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed. / Ph. D.

Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, reduced order control design is vital for practical controllers. The main contribution of this research is a method of control order reduction that uses a newly developed low order basis. The low order basis is obtained by applying Proper Orthogonal Decomposition (POD) to a set of functional gains, and is referred to as the functional gain POD basis. Low order controllers resulting from the functional gain POD basis are compared with low order controllers resulting from more commonly used time snapshot POD bases, with the two dimensional heat equation as a test problem. The functional gain POD basis avoids subjective criteria associated with the time snapshot POD basis and provides an equally effective low order controller with larger stability radii. An efficient and effective methodology is introduced for using a low order basis in reduced order compensator design. This method combines "design-then-reduce" and "reduce-then-design" philosophies. The desirable qualities of the resulting reduced order compensator are verified by application to Burgers' equation in numerical experiments. / Ph. D.

Cavitation can be defined as the breakdown of a liquid (either static or in motion) medium under very low pressure. The hydrodynamic happened in high-speed flow, where local pressure in liquid falls under the saturating pressure thus the liquid vaporizes to form the cavity. During the evolution and collapsing of cavitation bubbles, extreme physical conditions like high-temperature, high-pressure, shock-wave, and high-speed micro-jets can be generated. Such a phenomenon shall be prevented in hydraulic or astronautical machinery due to the induced erosion and noise, while it can be utilized to intensify some treatment processes of chemical, food, and pharmaceutical industries, to shorten sterilization times and lower energy consumption. Advances in the understanding of the physical processes of cavitating flows are challenging, mainly due to the lack of quantitative experimental data on the two-phase structures and dynamics inside the opaque cavitation areas. This dissertation is aimed at finding out the physical mechanisms governing the cavitation instabilities and making contributions in controlling hydraulic cavitation for engineering applications. In this thesis, cavitation developed in various convergent-divergent (Venturi) channels was studied experimentally using the ultra-fast synchrotron X-ray imaging, LIF Particle Image Velocimetry, and high-speed photography techniques, to (1) investigate the internal structures and evolution of bubble dynamics in cavitating flows, with velocity information obtained for two phases; (2) measure the slip velocity between the liquid and the vapor to provide the validation data for the numerical cavitation models; (3) consider the thermodynamic effects of cavitation to establish the relation between the cavitation extent and the fluid temperature, then and optimize the cavitation working condition in water; (4) seek the coherent structures of the complicated high-turbulent cavitating flow to reduce its randomness using data-driven methods. / Doctor of Philosophy / When the pressure of a liquid is below its saturation pressure, the liquid will be vaporized into vapor bubbles which can be called cavitation. In many hydraulic machines like pumps, propulsion systems, internal combustion engines, and rocket engines, this phenomenon is quite common and could induce damages to the mechanical systems. To understand the mechanisms and further control cavitation, investigation of the bubble inception, deformation, collapse, and flow regime change is mandatory. Here, we performed the fluid mechanics experiment to study the unsteady cavitating flow underlying physics as it occurs past the throat of a Venturi nozzle. Due to the opaqueness of this two-phase flow, an X-ray imaging technique is applied to visualize the internal flow structures in micrometer scales with minor beam scattering. Finally, we provided the latest physical model to explain the different regimes that appear in cavitation. The relationship between the cavitation length and its shedding regimes, and the dominant mechanism governing the transition of regimes are described. A combined suppression parameter is developed and can be used to enhance or suppress the cavitation intensity considering the influence of temperature.

This thesis presents the implementation and validation of a new methodology developed by Glegg et al. (2004) for solving the trailing edge noise problem. This method is based on the premises that the noise produced by a surface can be computed by the integral of the cross product between the velocity and vorticity fields, of the boundary layer and shed vorticity (Howe (1978)). To extract the source terms, proper orthogonal decomposition is applied to the velocity cross spectrum to extract modes of the unsteady velocity and vorticity. The new formulation of the trailing edge noise problem by Glegg et al. (2004) is attractive because it applies to the high frequencies of interest but does not require an excessive computational effort. Also, the nature of the formulation permits the identification of the modes producing the noise and their associated velocity fluctuations as well as the regions of the boundary layer responsible for the noise production. The source terms were obtained using the direct numerical simulation of a turbulent channel flow by Moser et al. (1998). Two-point velocity and vorticity statistics of this data set were obtained by averaging 41 instantaneous fields. For comparisons purposes, experimental boundary layer data by Adrian et al. (2000) was chosen. Statistical reduction of 50 velocity fields obtained by particle image velocimetry was performed and analysis of the two-point correlation function showed features similar to the DNS data case. Also, proper orthogonal decomposition revealed identical dominant modes and eddy structures in the flow, therefore justifying considering the channel flow as an external boundary layer for noise calculations. Comparison of noise predictions with experimental data from Brooks et al. (1989) showed realistic results with the largest discrepancies, on the order of 5 dB, occurring at the lowest frequencies. The DNS results are least applicable at these frequencies, since these correspond to the longest streamwise lengthscales, which are the most affected by the periodicity conditions used in the DNS and also are the least representative of the turbulence in an external boundary layer flow. Most of the noise was shown to be produced by low-frequency streamwise velocity modes in the bottom 10% of the boundary layer and locations closest to the wall. Only 6 modes were required to obtain noise levels within 1 dB of the total noise. Finally, the method for predicting spatial velocity correlation from Reynolds stress data in wake flows, originally developed by Devenport et al. (1999, 2001) and Devenport and Glegg (2001), was adapted to boundary-layer type flows. This method, using Reynolds stresses and the prescription of a lengthscale to extrapolate the full two-point correlation, was shown to produce best results for a lengthscale prescribed as proportional to the turbulent macroscale. Noise predictions using modeled two-point statistics showed good agreement with the DNS inferred data in all but frequency magnitude, a probable consequence of the modeling of the correlation function in the streamwise direction. Other quantities associated to noise were seen to be similar to the ones obtained using the DNS. / Master of Science

The aim of this work was to understand the physical requirements as well as to develop methodology required to employ Time Resolved Digital Particle Image Velocimetry (TRDPIV) for measuring high speed, high magnification, near wall flow fields. Previous attempts to perform measurements such as this have been unsuccessful because of both limitations in equipment as well as proper methodology for processing of the data. This work addresses those issues and successfully demonstrates a test inside of a transonic turbine cascade as well as a high speed high magnification wall jet. From previous studies it was established that flow tracer delivery is not a trivial task in a high speed high back pressure environment. Any TRDPIV measurement requires uniform spatial seeding density, but time-resolved measurements require uniform temporal seeding density as well. To this end, a high pressure particle generator was developed. This advancement enhanced current capability beyond what was previously attainable. Unfortunately, this was not sufficient to resolve the issue of seeding all together, and an advanced data reconstruction methodology was developed to reconstruct areas of the flow field that where lost do to inhomogeneous seeding. This reconstruction methodology, based on Proper Orthogonal Decomposition (POD), has been shown to produce errors in corrected velocities below tradition spatial techniques alone. The combination of both particle generator and reconstruction methodology was instrumental for successfully acquiring TRDPIV measurements in a high speed high pressure environment such as a transonic wind tunnel facility. This work also investigates the development of a turbulent wall jet. This experiment helped in demonstrating the capability of taking high speed high magnification TRDPIV measurements. This experiment was very unique in that it is one of only a few experiments that studied the developing region of these jets. The Reynolds number ranged for this experiment from 150 – 10,000 which corresponded to velocities of 1 - 80 m/s. The results from this experiment showed good agreement with currently published time averaged data. Using scaling laws for fully developed jets a new scaling law was found for the developing region of the jet that could be applied to all Reynolds numbers in this study. A temporal investigation was also carried out using the temporal coefficients from POD. A vortex identification scheme was also applied to all of the Reynolds numbers showing clear trends as Reynolds number increased. / Master of Science

In this study the complete four dimensional space time correlation function was measured in the wake of an untripped circular cylinder at a Reynolds number of 60 000. This correlation serves as the complete inflow boundary condition for an open rotor ingesting inhomogeneous turbulence. An important aspect of the turbulence ingestion problem is understanding how different inflow boundary conditions effect the sound produced by a rotor. In the present study the turbulence structure of two plane wakes were compared. Measurements completed by a previous study in the wake of a NACA 0012 airfoil were compared with the measurements completed by the present study in the wake of a cylinder. The mean flows of both plane wakes were found to be very similar, however the Reynolds stress profiles show that the cylinder wake is substantially more turbulent. The structures of the two-point correlation function in each wake are also similar, although the cylinder wake had greater maximum correlation values and was correlated at greater separations. The two-point correlation was used along with proper orthogonal decomposition to compute the average instantaneous velocity fields of both wake flows. These velocity fields represent the average eddy structures present in each wake flow. The eddy structure comparisons show that the structures in the cylinder wake are larger and better correlated at longer time delays. / Master of Science / Any fan or propeller that ingests any unsteady flow will produce noise. This is especially important in propeller aircraft and marine vehicles where turbulence is generated from appendages on the vehicle’s body. This self-generated turbulence travels downstream and is eventually drawn into the propeller and produces noise. The broad study that the present work is a part of is concerned with understanding this ingestion noise problem so that the interaction can be better modeled and the sound produced can be predicted. To predict the sound produced by a fan or propeller ingesting turbulence, detailed information about the inflow condition is needed. In the present study the turbulence structure of the wake shed by a circular cylinder at 20 meters per second. The two-point velocity correlation in the wake serves as the complete inflow condition for the turbulence ingestion problem. The structure of the cylinder wake inflow condition was compared with the structure of an airfoil wake to evaluate how the differences in the two flows would influence the sound produced by a rotor ingesting the two conditions. The two flows were found to be quite similar in the mean flow. The cylinder wake was found to be significantly more turbulent than the airfoil wake and was correlated over greater distances. This suggests that the structures in the cylinder wake are larger and remain coherent longer than those in the airfoil wake. The average instantaneous velocity fields were estimated in both wake flows and showed that the structures in the cylinder wake were significantly different from the structures in the airfoil wake. These flow structure comparisons show why the differences seen in the turbulence profiles and two-point correlations exist.

Time varying flow structures are involved in a large percentage of fluid flows although there is still much unknown regarding their behavior. With the development of high spatiotemporal resolution measurement systems it is becoming more feasible to measure these complex flow structures, which in turn will lead to a better understanding of their impact. One method that has been developed for studying these flow structures is finite time Lyapunov exponents (FTLEs). These exponents can reveal regions in the fluid, referred to as Lagragnian coherent structures (LCSs), where fluid elements diverge or attract. Better knowledge of how these time varying structures behave can greatly impact a wide range of applications, from aircraft design and performance, to an improved understanding of mixing and transport in the human body. This work provides the development of new methodologies for measuring and studying three-dimensional time varying structures. Provided herein is a method to improve replacement of erroneous measurements in particle image velocimetry data, which leads to increased accuracy in the data. Also, a method for directly measuring the finite time Lyapunov exponents from particle images is developed, as well as an experimental demonstration in a three-dimensional flow field. This method takes advantage of the information inherently contained in these images to improve accuracy and reduce computational requirements. Lastly, this work provides an in depth look at the flow field for developing wall jets across a wide range of Reynolds numbers investigating the mechanisms that contribute to their development. / Ph. D.