This thesis presents results of computations of supersonic flow over finite cylinders with varying geometries at the cylinder-wall juncture. The flow domain and geometries were modeled after experiments conducted at University of Tennessee Space Institute (UTSI). CREATE Kestrel (KCFD) was used to perform improved-delayed detached simulations (IDDES) of the unsteady flow. Time-accurate data were collected via taps along the centerline partially on the surface of the cylinder geometries and on the wall upstream of the cylinder. Spectra of the pressure signals and two-point correlations were computed to compare the flow between the different cases consisting of a baseline cylinder, the cylinder with a smaller gap, and the cylinder with a wider fairing. Properties on the cylinder surface for the gap case had the greatest difference compared to the others. In addition, the spectral content showed higher frequency activity for the gap case on the surface in front of the cylinder. <br>

The variance of the Taylor factor due to variations in the microstructure and window size is explored using both a random sampling method and a previously developed statistical relationship. The results from the random sampling method correlated well with the statistical variance relationship when the magnitude of the variance was greater than that of the numerical errors observed in the statistical calculation. An empirical relation was developed to model the results and the constants for this relationship were determined for pseudo-three dimensional Fe-3%Si. Implementation of the statistical variance relationship in true 3D microstructures is not limited by material opacity, since it depends only upon the 2-point pair correlation functions. The connection between the variance of the R-value and variance of the Taylor factor is considered. Although only a weak connection was found, it was observed that relatively small variations in the Taylor factor yield large variances in the R-value.

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

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.

An experimental study was designed to investigate the effect of different parameters on the development and structure of turbulent 3D offset jets. The present investigation considered the effects of offset height ratio, expansion ratio, surface roughness and rib placement on the flow dynamics of a turbulent 3D offset jet. The velocity measurements were performed using an acoustic Doppler velocimetry (ADV) and particle image velocimetry (PIV). Measurements were conducted within the symmetry and lateral planes. For the PIV technique, the measurements in the symmetry and lateral planes were conducted over a streamwise range of 0 ≤ x/bo ≤ 80 and 12 ≤ x/bo ≤ 60, respectively (where bo is the nozzle height). Likewise, velocity measurements using the ADV technique were conducted over a range of 4 ≤ x/bo ≤ 45 in both the symmetry and lateral planes. The velocity measurements were analyzed using both one-point and multi-point statistics. The one-point statistics included profiles of the mean velocities, Reynolds stresses and some of the budget terms in the turbulent kinetic energy transport equation. The quadrant analysis technique was used to investigate the dominant events that contribute towards the Reynolds shear stress. The two-point correlation analysis was used to investigate how the turbulence quantities are correlated. Information obtained from the two-point correlation analysis was also used to investigate the inclination of vortical structures within the inner and outer shear layers of the 3D offset jet. The direction of the positive mean shear gradient played an active role in the inclination of these vortical structures within the inner and outer shear layers. The reattachment process resulted in the breakdown of these structures within the developing region. Similarly, various length scales were estimated from these structures. The proper orthogonal decomposition was used to examine the distribution of the turbulent kinetic energy within the offset jet flow. Also, the dynamic role of the large scale structures towards the turbulent intensities, turbulent kinetic energy and Reynolds shear stress was investigated. / October 2016

Tidal bores are surge waves propagating upstream rivers as the tide rushes into estuaries. They induce large turbulences and mixing of the river and estuary flow of which effects remain scarcely studied. Herein, tidal bores are investigated experimentally and numerically with an idealised model of positive surges propagating upstream an initially steady flow. The experimental work estimated flow changes and typical turbulent length scale evolution induced by undular bores with and without breaking roller. The bore passage was associated with large free surface and flow velocity fluctuations, together with some variations of the integral turbulent scales. Coherent turbulent structures appeared in the wake of leading wave near the bed and moved upward into the water column during the bore propagation. The numerical simulations were based on previous experimental work on undular bores. Some test cases were realised to verify the accuracy of the numerical methods. The results gave access to the detailed flow evolution during the bore propagation. Large velocity reversals were observed close to the no-slip boundaries. In some configurations, coherent turbulent structures appeared against the walls in the wake of the bore front.

Design space exploration (DSE) is used to improve and understand engineering designs. Such designs must meet objectives and structural requirements. Design improvement is non-trivial and requires new DSE methods. Turbomachinery manufacturers must continue to improve existing engines to keep up with global demand. Two challenges of turbomachinery DSE are: the time required to evaluate designs, and knowing which designs to evaluate. This research addressed these challenges by developing novel surrogate and principal component analysis (PCA) based DSE methods. Node and PCA-based surrogates were created to allow faster DSE of turbomachinery blades. The surrogates provided static stress estimation within 10% error. Surrogate error was related to the number of sampled finite element (FE) models used to train the surrogate and the variables used to change the designs. Surrogates were able to provide structural evaluations three to five orders of magnitude faster than FEA evaluations. The PCA-based surrogates were then used to create a PCA-based design workflow to help designers know which designs to evaluate. The workflow used either two-point correlation or stress and geometry coupling to relate the design variables to principal component (PC) scores. These scores were projections of the FE models onto the PCs obtained from PCA. Analysis showed that this workflow could be used in DSE to better explore and improve designs. The surrogate methods were then applied to vibratory stress. A computationally simplified analysis workflow was developed to allow for enough fluid and structural analyses to create a surrogate model. The simplified analysis workflow introduced 10% error but decreased the computational cost by 90%. The surrogate methods could not directly be applied to emulation of vibration due to the large spikes which occur near resonance. A novel, indirect emulation method was developed to better estimate vibratory responses Surrogates were used to estimate the inputs to calculate the vibratory responses. During DSE these estimations were used to calculate the vibratory responses. This method reduced the error between the surrogate and FEA from 85% to 17%. Lastly, a PCA-based multi-fidelity surrogate method was developed. This assumed the PCs of the high and low-fidelities were similar. The high-fidelity FE models had tens of thousands of nodes and the low-fidelity FE models had a few hundred nodes. The computational cost to create the surrogate was decreased by 75% for the same errors. For the same computational cost, the error was reduced by 50%. Together, the methods developed in this research were shown to decrease the cost of evaluating the structural responses of turbomachinery blade designs. They also provided a method to help the designer understand which designs to explore. This research paves the way for better, and more thoroughly understood turbomachinery blade designs.

Un mascaret est une vague remontant contre le courant d’un fleuve lorsque la marée se propage dans un estuaire. À son passage, le mascaret induit une forte turbulence et un fort mélange dont les effets sur la vie de l’estuaire sont encore mal quantifiés. Ici, le phénomène est étudié expérimentalement et numériquement en utilisant un modèle d’onde positive se propageant contre un courant permanent.L’étude en laboratoire a permis de mesurer les variations de la surface libre, de la vitesse de l’écoulement ainsi que des échelles de turbulence. Lors de son passage, des fluctuations importantes de la surface libre et de la vitesse de l’écoulement sont observées, ainsi que des variations des échelles de turbulences. Des structures turbulentes semblent se former près du fond sous le front de l’onde et montent dans la colonne d’eau après le passage du front.La simulation numérique fut réalisée à partir de données expérimentales d’onde positive ondulée sur fond lisse. Une validation des méthodes numériques a été réalisée pour différente configuration. Les résultats des simulations d’onde positives donnent une cartographie détaillée de l’écoulement dans tout le canal. De plus, la simulation a permis d’identifier une inversion de la vitesse près des parois lors du passage des crêtes des ondes générant dans certaines configurations des structures turbulentes. / Tidal bores are surge waves propagating upstream rivers as the tide rushes into estuaries. They induce large turbulences and mixing of the river and estuary flow of which effects remain scarcely studied. Herein, tidal bores are investigated experimentally and numerically with an idealised model of positive surges propagating upstream an initially steady flow. The experimental work estimated flow changes and typical turbulent length scale evolution induced by undular bores with and without breaking roller. The bore passage was associated with large free surface and flow velocity fluctuations, together with some variations of the integral turbulent scales. Coherent turbulent structures appeared in the wake of leading wave near the bed and moved upward into the water column during the bore propagation. The numerical simulations were based on previous experimental work on undular bores. Some test cases were realised to verify the accuracy of the numerical methods. The results gave access to the detailed flow evolution during the bore propagation. Large velocity reversals were observed close to the no-slip boundaries. In some configurations, coherent turbulent structures appeared against the walls in the wake of the bore front.