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

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.

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.

This thesis uses Proper Orthogonal Decomposition to model parametric and coupled systems. First, Proper Orthogonal Decomposition and its properties are introduced as well as how to numerically compute the decomposition. Next, a test case was used to show how well POD can be used to simulate and control a system. Finally, techniques for modeling a parametric system over a given range and a coupled system split into subdomains were explored, as well as numerical results. / Master of Science

The thesis deals with the flow in pipe bends and radial turbines geometries that are commonly found in an Internal Combustion Engine (ICE). The development phase of internal combustion engines relies more and more on simulations as an important complement to experiments. This is partly because of the reduction in development cost and the shortening of the development time. This is one of the reasons for the need of more accurate and predictive simulations. By using more complex computational methods the accuracy and predictive capabilities are increased. The disadvantage of using more sophisticated tools is that the computational time is increasing, making such tools less attractive for standard design purposes. Hence, one of the goals of the work has been to contribute to assess and improve the predictive capability of the simpler methods used by the industry. By comparing results from experiments, Reynolds Averaged Navier-Stokes (RANS) computations, and Large Eddy Simulations (LES) the accuracy of the different computational methods can be established. The advantages of using LES over RANS for the flows under consideration stems from the unsteadiness of the flow in the engine manifold. When such unsteadiness overlaps the natural turbulence the model lacks a rational foundation. The thesis considers the effect of the cyclic flow on the chosen numerical models. The LES calculations have proven to be able to predict the mean field and the fluctuations very well when compared to the experimental data. Also the effects of pulsatile exhaust flow on the performance of the turbine of a turbocharging system is assessed. Both steady and pulsating inlet conditions are considered for the turbine case, where the latter is a more realistic representation of the real flow situation inside the exhaust manifold and turbine. The results have been analysed using different methods: single point Fast Fourier Transforms (FFT), probe line means and statistics, area and volume based Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). / Denna avhandling behandlar flödet i rörkrökar och radiella turbiner som vanligtvis återfinns i en förbränningsmotor. Utvecklingsfasen av förbränningsmotorer bygger mer och mer på att simuleringar är ett viktigt komplement till experiment. Detta beror delvis på minskade utvecklingskostnader men även på kortare utevklningstider. Detta är en av anledningarna till att man behöver mer exakta och prediktiva simuleringsmetoder. Genom att använda mer komplexa beräkningsmetoder så kan både nogrannheten och prediktiviteten öka. Nackdelen med att använda mer sofistikerade metoder är att beräkningstiden ökar, vilket medför att sådana verktyg är mindre attraktiva för standardiserade design ändamål. Härav, ett av målen med projektet har varit att bidra med att bedöma och förbättra de enklare metodernas prediktionsförmåga som används utav industrin. Genom att jämföra resultat från experiment, Reynolds Averaged Navier-Stokes (RANS) och Large Eddy Simulations (LES) så kan nogrannheten hos de olika simuleringsmetoderna fastställas. Fördelarna med att använda LES istället för RANS när det gäller de undersökta flödena kommer ifrån det instationära flödet i grenröret. När denna instationäritet överlappar den naturligt förekommande turbulensen så saknar modellen en rationell grund. Denna avhandling behandlar effekten av de cykliska flöderna på de valda numeriska modellerna. LES beräkningarna har bevisats kunna förutsäga medelfältet och fluktuationerna väldigt väl när man jämför med experimentell data. Effekterna som den pulserande avgasströmning har på turboladdarens turbin prestanda har också kunnat fastställas. Både konstant och pulserande inlopps randvillkor har används för turbinfallet, där det senare är ett mer realistiskt representation av den riktiga strömningsbilden innuti avgasgrenröret och turbinen. Resultaten har analyserats på flera olika sätt: snabba Fourier transformer (FFT) i enskilda punkter, medelvärden och statistik på problinjer, area och volumsbaserade metoder så som Proper Orthogonal Decomposition (POD) samt Dynamic Mode Decomposition (DMD). / <p>QC 20140919</p>

In many areas of aerodynamics the technique of Large Eddy Simulation (LES) has proved a practical way of modelling the unsteady phenomena in numerical simulations. Few applications are as dependent on such an approach as the prediction of flow within a gas turbine combustor. Like any form of Computational Fluid Dynamics (CFD), LES requires specification of the velocity field at the inflow boundary, with much evidence suggesting the specification of inlet turbulence can be critical to the resultant accuracy of the prediction. While a database of time-resolved velocity data may be obtained from a precursor LES calculation, this technique is prohibitively expensive for complex geometries. An alternative is to use synthetic inlet conditions obtained from experimental data High-speed Particle Image Velocimetry (PIV) is used here to provide planar velocity data at up to 1kHz temporal resolution in two test cases representative of gas turbine combustor flows (a vortex generator in a duct and an idealised combustor). As the data sampling rate is approaching a typical LES time-step it introduces the possibility of applying instantaneous experimental data directly as an inlet condition. However, as typical solution domain inlet regions for gas turbine combustor geometries cannot be adequately captured in a single field of PIV data, it is necessary to consider a method by which a synchronous velocity field may be obtained from multiple PIV fields that were not captured concurrently. A method is proposed that attempts to achieve this by a combined process of Linear Stochastic Estimation and high-pass filtering. The method developed can be generally applied without a priori assumptions of the flow and is demonstrated to produce a velocity field that matches very closely that of the original PIV, with no discontinuities in the velocity correlations. The fidelity and computational cost of the method compares favourably to several existing inlet condition generation methods. Finally, the proposed and existing methods for synthetic inlet condition generation are applied to LES predictions of the two test cases. There is shown to be significant differences in the resulting flow, with the proposed method showing a marked ii reduction in the adjustment period that is required to establish turbulent equilibrium downstream of the inlet. However, it is noted the presence of downstream turbulence generating features can mask any differences in the inlet condition, to the extent that the flow in the core of the combustor test case is found to be insensitive to the inlet condition applied at the entry to the feed annulus for the test conditions applied here.

Assessing the impact of inlet flow distortion in turbomachinery is desired early in the design cycle. This thesis introduces and validates the use of methods based on the Proper Orthogonal Decomposition (POD) to analyze clean and 1/rev static pressure distortion simulation results at design and near stall operating condition. The value of POD comes in its ability to efficiently extract both quantitative and qualitative information about dominant spatial flow structures as well as information about temporal fluctuations in flow properties. Observation of the modes allowed qualitative identification of shock waves as well as quantification of their location and range of motion. Modal coefficients revealed the location of the passage shock at a given angular location. Distortion amplification and attenuation between rotors was also identified. A relationship was identified between how distortion manifests itself based on downstream conditions. POD provides an efficient means for extracting the most meaningful information from large CFD simulation data. Static pressure and axial velocity were analyzed to explore the flow physics of 3 rotors of a compressor with a distorted inlet. Based on the results of the analysis of static pressure using the POD modes, it was concluded that there was a decreased range of motion in passage shock oscillation. Analysis of axial velocity POD modes revealed the presence of a separated region on the low pressure surface of the blade which was most dynamic in rotor 1. The thickness of this structure decreased in the near stall operating condition. The general conclusion is made that as the fan approaches stall the apparent effects of distortion are lessened which leads to less variation in the operating condition. This is due to the change in operating condition placing the fan at a different position on the speedline such that distortion effects are less pronounced. POD modes of entropy flux were used to identify three distinct levels of entropy flux in the blade row passage. The separated region was the region with the highest entropy due to the irreversibilities associated with separation.

Three methods were developed to better understand and characterize the near-field dynamic processes of rotary bell atomization. The methods were developed with the goal of possible integration into industry to identify equipment changes through changes in the primary atomization of the bell. The first technique utilized high-speed imaging to capture qualitative ligament breakup and, in combination with a developed image processing technique and PIV software, was able to gain statistical size and velocity information about both ligaments and droplets in the image data. A second technique, using an Nd:YAG laser with an optical filter, was used to capture size statistics at even higher rotational speeds than the first technique, and was utilized to find differences between serrated and unserrated bell ligament and droplet data. The final technique was incorporating proper orthogonal decomposition (POD) into image data of a side-profile view of a damaged and undamaged bell during operation. This was done to capture differences between the data sets to come up with a characterization for identifying if a bell is damaged or not for future industrial integration.