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.

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

Proper Orthogonal Decomposition (POD), combined with the Method of Snapshots and Galerkin projection, is a popular method for the model order reduction of nonlinear PDEs. The POD requires the left singular vectors from the singular value decomposition (SVD) of an n-by-m "snapshot matrix" S, each column of which represents the computed state of the system at a given time. However, the direct computation of this decomposition can be computationally expensive, particularly for snapshot matrices that are too large to fit in memory. Hierarchical Approximate POD (HAPOD) (Himpe 2016) is a recent method for the approximate truncated SVD that requires only a single pass over S, is easily parallelizable, and can be computationally cheaper than direct SVD, all while guaranteeing the requested accuracy for the resulting basis. This method processes the columns of S in blocks based on a predefined rooted tree of processors, concatenating the outputs from each stage to form the inputs for the next. However, depending on the selected parameter values and the properties of S, the performance of HAPOD may be no better than that of direct SVD. In this work, we numerically explore the parameter values and snapshot matrix properties for which HAPOD is computationally advantageous over the full SVD and compare its performance to that of a parallelized incremental SVD method (Brand 2002, Brand 2003, and Arrighi2015). In particular, in addition to the two major processor tree structures detailed in the initial publication of HAPOD (Himpe2016), we explore the viability of a new structure designed with an MPI implementation in mind. / Master of Science / Singular Value Decomposition (SVD) provides a way to represent numeric data that breaks the data up into its most important components, as well as measuring how significant each part is. This decomposition is widely used to assist in finding patterns in data and making decisions accordingly, or to obtain simple, yet accurate, representations of complex physical processes. Examples of useful data to decompose include the velocity of water flowing past an obstacle in a river, a large collection of images, or user ratings for a large number of movies. However, computing the SVD directly can be computationally expensive, and usually requires repeated access to the entire dataset. As these data sets can be very large, up to hundreds of gigabytes or even several terabytes, storing all of the data in memory at once may be infeasible. Thus, repeated access to the entire dataset requires that the files be read repeatedly from the hard disk, which can make the required computations exceptionally slow. Fortunately, for many applications, only the most important parts of the data are needed, and the rest can be discarded. As a result, several methods have surfaced that can pick out the most important parts of the data while accessing the original data only once, piece by piece, and can be much faster than computing the SVD directly. In addition, the recent bottleneck in individual computer processor speeds has motivated a need for methods that can efficiently run on a large number of processors in parallel. Hierarchical Approximate POD (HAPOD) [1] is a recently-developed method that can efficiently pick out the most important parts of the data while only accessing the original data once, and which is very easy to run in parallel. However, depending on a user-defined algorithm parameter (weight), HAPOD may return more information than is needed to satisfy the requested accuracy, which determines how much data can be discarded. It turns out that the input weights that result in less extra data also result in slower computations and the eventual need for more data to be stored in memory at once. This thesis explores how to choose this input weight to best balance the amount of extra information used with the speed of the method, and also explores how the properties of the data, such as the size of the data or the distribution of levels of significance of each part, impact the effectiveness of HAPOD.

With the maturity of conventional industrial robots, there has been increasing interest in designing robots that emulate realistic animal motions. This discipline requires careful and systematic investigation of a wide range of animal motions from biped, to quadruped, and even to serpentine motion of centipedes, millipedes, and snakes. Collecting optical motion capture data of such complex animal motions can be complicated for several reasons. Often there is the need to use many high-quality cameras for detailed subject tracking, and self-occlusion, loss of focus, and contrast variations challenge any imaging experiment. The problem of self-occlusion is especially pronounced for animals. In this thesis, we walk through the process of collecting motion capture data of a running lizard. In our collected raw video footage, it is difficult to make temporal correspondences using interpolation methods because of prolonged blurriness, occlusion, or the limited field of vision of our cameras. To work around this, we first make a model data set by making our best guess of the points' locations through these corruptions. Then, we randomly eclipse the data, use Gappy POD to repair the data and then see how closely it resembles the initial set, culminating in a test case where we simulate the actual corruptions we see in the raw video footage. / Master of Science / There has been increasing interest over the past few years in designing robots that emulate realistic animal motions. To make these designs as accurate as possible requires thorough analysis of animal motion. This is done by recording video and then converting it into numerical data, which can be analyzed in a rigorous way. But this conversion cannot be made when the raw video footage is ambiguous, for instance, when the footage is blurry, the shot is too dark or too light, the subject (or parts of the subject) are out of view of the camera, etc. In this thesis, we walk through the process of collecting video footage of a lizard running and then converting it into data. Ambiguities in the video footage result in an incomplete translation into numerical data and we use a mathematical technique called the Gappy Proper Orthogonal Decomposition to fill in this incompleteness in an intelligible way. And in the process, we lay your hands on the fundamental drivers of the animal’s motion.

Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still encumbered by lengthy processing times. Accurate models can be produced quickly by utilizing projection Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated into a ROM. Additional sources of nonlinearities such as radiation boundary conditions, temperature dependent source heating terms, and complex geometry were also integrated. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model. / Ph. D. / Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still limited by the time it takes to compute meaningful results. Accurate models can be produced quickly by utilizing some mathematical techniques whereby the original problem is projected into a smaller sub-space and solved with fewer variables. The full space results are then determined by undoing the projection on the results. This is one approach from a larger knowledge base called Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated using the projection approach, tailored to treat the specific material property nonlinearity as well as radiation boundary conditions, temperature dependent source heating terms, and complex geometry. While the approach presented here is specific to the heat transfer application, other problems of a similar form can be handled in the same manner. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model.

Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Prior work has shown that total temperature non-uniformity is a noise reduction technique which introduces a stream of cold flow into the heated jet. This method has been shown to cause changes in the exhaust plume and result in a 2±0.5 dB reduction of peak sound pressure levels. The goal of this work is to reveal underlying changes in the spatial-temporal structure of plume instability and turbulence caused by non-uniform total temperature distributions. Studies have demonstrated several methods of jet noise reduction by modifying the turbulent mixing in the exhaust plume. Large-scale turbulent structures have been shown to be the dominant source of noise in heated supersonic jets, especially over long, streamwise distances. Therefore, a large field-of-view measurement is desirable for studying these structures. Time-Resolved Doppler Global Velocimetry (TR-DGV) with a sampling frequency of 50 kHz is used to collect flow velocity data that is resolved in both time and space. The experiments for data collection were performed on a heated supersonic jet at the Virginia Tech Advanced Propulsion and Power Laboratory. A converging-diverging nozzle with a diameter Reynolds number of 850,000 was used to generate a perfectly expanded, heated flow of Mach 1.5 and a nozzle pressure ratio (NPR) of 3.67. The unheated plume was introduced at the center of the nozzle, with a total temperature ratio (TTR) of 2. Comparison of the mean velocity fields shows that the introduction of the cooler temperature flow in the thermally non-uniform case results in a velocity deficit of about 10% compared to the thermally uniform case. The method of spectral proper orthogonal decomposition (SPOD) was used to reveal the large-scale, coherent noise producing mechanisms. SPOD results indicate that the thermally non-uniform case showed a decrease in turbulent kinetic energy compared to the uniform case at all frequencies. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise. / Master of Science / Supersonic jet exhaust plumes produce noise in jet engines, which has been a problem in the aerospace field. Researchers are working on ways to reduce this turbulent mixing noise, with little modification to the engine and nozzle. Traditionally, nozzles produce a single stream of uniform temperature flow. This work identifies a method of reducing jet noise, known as thermal non-uniformity. A stream of cold flow is introduced at the center of the nozzle. Applying this method to jet engines can result in quieter aircraft. Large-scale turbulent structures are the dominant noise producing source in supersonic free jets. To further understand the relationship between coherent structures and acoustic jet noise, spectral analysis is used to educe these structures from the flow. This study uses velocity data collected using Time-Resolved Doppler Global Velocimetry (TR-DGV). The study compares the results of a thermally uniform and a thermally non-uniform heated supersonic jet of Mach 1.5. The goal of this study is to determine the effects of thermal non-uniformity on large-scale coherent structures using a modal decomposition analysis known as spectral proper orthogonal decomposition (SPOD). The results from this study show that the thermally non-uniform cases contained less turbulent kinetic energy compared to the thermally uniform cases. Coherent fluctuations start developing further upstream in the thermally non-uniform case. The addition of the unheated plume results in a disruption in the propagation of the Mach waves from the shear layer into the ambient. The results indicate that the total temperature non-uniformity results in a modified exhaust plume and mean flow distribution at the nozzle exit, compared to that of a thermally uniform flow, which past studies have indicated is a method to reduce jet noise.

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.