Three-dimensional (3D) turbulent boundary layers (TBLs) are ubiquitous in most engineering applications, but most turbulence models used to simulate these flows are built on two-dimensional turbulence theory, limiting the accuracy of simulation results. To improve the accuracy of turbulence modeling capabilities, a better understanding of 3DTBL physics is required. This dissertation outlines the experimental investigation of the attached 3D TBL flow over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel. The mean flow and turbulence behavior of the boundary layer are studied and compared with turbulence theories to identify the validity of these assumptions in the BeVERLI Hill flow. It is shown that the pressure gradients and curvature of the hill have a significant effect on the turbulence behavior, including significant history effects at all stations due to the changing pressure gradient impact through the height of the boundary layer. Supplementing the experimental results with analysis from rapid distortion theory and simulations, it is shown that the stations lower on the hill are significantly affected by the non-linear history effects due to the varying upstream origins of the flow passing through those stations. Stations closer to the hill apex pass through a region of extremely strong favorable pressure gradient and hill constriction, resulting in behavior that matches qualitatively with the results from rapid distortion theory and provides insights into the physical mechanisms taking place in these regions of the flow. Despite the misalignment of the mean flow angle (γ_FGA) and turbulent shear stress angle (γ_SSA) throughout all of the profiles, the proposed 3D law of the wall of van den Berg (1975), which incorporates pressure gradient and inertial effects and relies on the assumption that γ_FGA=γ_SSA, is able to predict the flow behavior at more mildly non-equilibrium stations. This suggests that models that currently rely on assumptions founded on the two-dimensional law of the wall could be improved by incorporating van den Berg's model instead. The total shear stress distribution at selected stations on the BeVERLI Hill are all significantly reduced below equilibrium two-dimensional (2D) levels, indicating that turbulence models built on this assumptions will not be able to accurately simulate the 3D turbulence behavior. / Doctor of Philosophy / As an object moves through a fluid or a fluid moves past an obstacle, fluid sticks to the solid boundary of the object because of the fluid's viscosity, resulting in zero velocity on the surface (known as the "no-slip" condition). There then exists a region where the flow velocity increases from zero to the freestream velocity - this region is known as the boundary layer. The nature of the boundary layer developing around a body significantly influences how the body and fluid interact and is critical to practical items of engineering interest, such as estimating how much drag a vehicle will experience. Most bodies of engineering interest are three-dimensional (3D), like an aircraft or a car, and thus induce a three-dimensional boundary layer, but many turbulence theories used in computational fluid dynamics simulations are based on simplified two-dimensional (2D) flow behavior studied in laboratories. To further improve the accuracy of simulations, a better understanding of three-dimensional turbulent boundary layer flows is required. This dissertation outlines a study of three-dimensional turbulent flows by analyzing the three-dimensional turbulent boundary layer over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry (LDV) in the Virginia Tech Stability Wind Tunnel. LDV uses the Doppler shift principle to measure the fluid velocity and turbulence at different points in the flow. Through analysis of the fluid velocity and turbulence in the flow, it is shown that the turbulence and flow behavior at certain stations are heavily influenced on the upstream flow history. Stations closer to the bottom of the hill are more influenced by the upstream flow history, while stations closer to the top of the hill experience such strong acceleration due to the local favorable pressure gradient and hill curvature that the upstream history has a more linear influence. In general, the turbulence on the hill is reduced due to the acceleration over the surface below 2D levels and does not match with the 2D fundamental relationships often used in turbulence theories for simulations. Thus, simulations that rely on these assumptions will not be able to accurately predict the details of the 3D flow. A proposed 3D model for the mean velocity behavior by van den Berg (1975) will perform better in simulations than the typical 2D law used in some turbulence model assumptions.

M. S.

Acoustic metamaterials have been shown to support acoustic surface waves when excited by a broadband signal in a quiescent environment and these waves could be manipulated by varying the geometry of the structure making up the metamaterial. The study presented here demonstrates the generation of trapped acoustic surface waves when excited by a turbulent flow source. The metamaterial and flow were interfaced using a Kevlar covered single cavity whose Kevlar side faced the flow to ensure no significant disturbance to the flow and the other side was open to a quiescent (stationary) environment housing the metamaterial. Acoustic measurements were performed very close to the surface of the metamaterial in the Anechoic Wall Jet Facility at Virginia Tech using two probe-tip microphones and correlation analysis yielded the structure of the surface waves. Two different metamaterials; slotted array and meander array were tested and characterized by their dispersion relations, temporal correlations, and spatial-temporal structure. The measurements proved the existence of surface waves with propagating speeds of a tenth of the speed of sound, when excited by a turbulent boundary layer flow. These waves were much weaker than the overlying flow exciting them but showcased excellent attenuation properties away from the source of excitation. Measurements along the length of the unit-cell geometry of the metamaterial demonstrated high coherence over a range of frequencies limited by the dimension of the cell. This was a surprising behavior provided the cavity was excited by a fully developed turbulent flow over a flat plate and indicated to an area averaging phenomenon. A wall normal two-dimensional particle image velocimetry (2D-PIV) measurement was performed over the Kevlar covered cavity and a smooth surface to study the effects of the cavity on the flow. The field of view was the same for both cases which made direct flow comparison possible. Flow characteristics such as the boundary layer profiles, Reynolds stress profiles and fluctuating velocity spectrum were studied over the cavity and at downstream locations to quantify the differences in the flows. The boundary layer profiles collapsed in the inner region of the boundary layer but there were small differences in the outer region. The Reynolds stress profiles were also very similar with differences within the uncertainties of processing the images and it reflected similar average behavior of the flow over a smooth wall and a Kevlar covered cavity. The fluctuating velocity spectrum studied over the cavity location showed some differences at low frequencies for all wall normal locations while at higher frequencies the differences were within ±3 dB. These measurements showcased the underlying physics behind the interaction of acoustic metamaterials and turbulent boundary layer flows creating possibilities of using these devices for flow control although further analysis/optimization is needed to fully understand the capabilities of these systems. The demonstration of no significant effect on flow by the Kevlar covered cavity stimulated development of sensors which can average over a region of the wall pressure spectrum. / M.S. / In the field of physics, acoustic metamaterials have gained popularity due to their ability to exhibit certain properties such as sound manipulation which cannot be seen in regular materials. These materials have a key feature which is the periodic arrangement of geometric elements in any dimension. These materials can support a phenomenon termed as acoustic surface waves which are essentially pressure disturbances in the medium which behave differently than some known phenomenon such as sound waves when excited by a broadband pressure signal in a stationary medium. Also, it has been shown that these materials can change the nature of the acoustic surface waves if their geometry is changed. Here a successful attempt has been made to link two different fields in physics: acoustic metamaterials (acoustics) and turbulent flows (fluid dynamics). The study here uses turbulent boundary layer flows to excite these metamaterials to show the existence of acoustic surface waves. This is done by creating an interface between the flow and the metamaterial using a Kevlar covered through cavity which is essentially a through hole connecting to different sides: flow side and the stationary air/quiescent side. This cavity acted as the source of excitation for the metamaterial. The Kevlar covering ensures that the flow does not get disturbed due to the cavity which was also proved in this study using a visualization technique: Particle Image Velocity (PIV). Two microphones were used to study the pressure field very close to two metamaterials; one was referred to as the slotted array comprised of slot cavities arranged in one dimension (along the direction of the flow), while the other was termed as the meander array and it comprised of a meandering channel. The pressure field was well characterized for both the acoustic metamaterials and it was proved that these metamaterials could support acoustic surface waves even when excited by a turbulent flow. The idea here was to fundamentally understand the interaction of acoustic metamaterials and turbulent flows, possibly finding use in applications such as trailing edge noise reduction. The use of these metamaterials in direct applications needs further investigation. A finding from the pressure field study showed that the pressure measured along the length of the Kevlar covered cavity was uniform. The flow visualization study looked at the turbulent flow on a smooth wall and over a Kevlar covered cavity. This was done by injecting tiny particles in air and shooting a laser sheet over these to illuminate the flow. Images were recorded using a high-speed camera to track the movement of these particles. It was found that the flow was unaffected with or without the presence of a Kevlar covered cavity. This result coupled with the pressure field uniformity could have some wide applications in the field of pressure sensing.

Three new computational procedures are presented for the simulation of incompressible wall-bounded turbulent flows. First, an integral method based on the strip integral method has been developed for the solution of three-dimensional turbulent boundary-layer flows. The integral equations written in a general form using non-orthogonal streamline coordinates include the turbulent shear stress at the upper limit of an inner strip inside the boundary-layer. The shear stress components are modeled using the Boussinesq assumption, and the eddy viscosity is defined explicitly as in differential methods. The turbulence modeling is not hidden in opaque empirical correlations as in conventional integral methods. A practical four-parameter velocity profile has been established based on the Johnston Law of the Wall using a triangular model for the crosswise velocity. Two strips are used to solve for the four unknowns: skin friction coefficient, wall crossflow angle, boundary-layer thickness, and location of maximum crosswise velocity. The location of maximum crosswise velocity proves to be a natural and adequate parameter in the formulation, but it is numerically sensitive and has a strong influence on the wall crossflow angle. Good results were obtained when compared to predictions of other integral or differential methods. Secondly, two computational procedures solving the Reynolds Averaged Navier-Stokes equations for 20 and 3D flows respectively have also been developed using a new treatment of the near-wall region. The flow is solved down to the wall with a slip velocity based on Clauser's idea of a pseudolaminar velocity profile. The present idea is different from the wall-function methods and does not require a multi-layer eddy viscosity model. The solution of the equations of motion is obtained by the Finite Element Method using the wall shear stress as a boundary condition along solid surfaces, and using the Clauser outer region model for the eddy viscosity. The wall shear stress distribution is updated by solving integral equations obtained from the enforcement of conservation of mass and momentum over an inner strip in the near-wall region. The Navier-Stokes solution provides the necessary information to the inner strip integral formulation in order to evaluate the skin friction coefficient for 2D flows, or the skin friction coefficient and the wall crossflow angle for 3D flows. The procedures converge to the numerically "exact" solution in a few iterations depending on the accuracy of the initial guess for the wall shear stress. A small number of nodes is required in the boundary-layer to represent adequately the physics of the flow, which proves especially useful for 3D calculations. Excellent results were obtained for the 2D simulations with a simple eddy viscosity model. 3D calculations gave good results for the turbulent boundary-layer flows considered here. The present methods were validated using well-known experiments chosen for the STANFORD conferences and EUROVISC workshop. The 2D numerical predictions are compared with the experimental measurements obtained by Wieghardt-Tillmann, Samuel-Joubert, and Schubauer-Klebanoff. For the 3D analyses, the numerical predictions obtained by the strip-integral method and the Finite Element Navier-Stokes Integral Equation procedure are validated using the Van den Berg-Elsenaar and Müller-Krause experiments. / Ph. D.

The transition from laminar to turbulent flow in boundary-layers occurs in three stages: onset of two-dimensional TS waves, onset of three-dimensional secondary disturbances of fundamental or subharmonic type, and onset of the turbulent regime. In free flight conditions, subharmonic disturbances are the most amplified. Recent modeling of the subharmonic disturbance as a parametric instability arising from the presence of a finite amplitude TS wave has given results in quantitative agreement with experiments conducted in a Blasius boundary-layer. The present work extends the analysis to the Falkner-Skan family of profiles, and develops a formulation for spatially growing disturbances to exactly match the experimental observations. Results show that subharmonic disturbances in Falkner-Skan flows behave similarly to those in a Blasius flow. The most noticeable effect of the pressure gradient is a decrease (favorable) or an increase (adverse) of the disturbance's growth rate. Due to the lack of experimental data, a comparison of subharmonic growth rates from theory and experiment is limited to the Blasius boundary-layer. A comparison of results from the spatial formulation with those previously obtained from a temporal formulation shows the difference to be small. A connection between disturbance growth in a separating boundary-layer profile and a free shear layer is presented. A modification of Caster's transformation from temporal to spatial growth rates for secondary disturbances is given. / M.S.

The presence of roughness on a surface subject to high Reynolds number flows promotes the formation of a turbulent boundary layer and the generation of a fluctuating pressure field imposed on the surface. While numerous studies have investigated the wall pressure fluctuations over zero-pressure gradient smooth walls, few studies have examined the effects of surface roughness on the wall pressure field. Additionally, due to the difficulties in obtaining high Reynolds number flows over fully rough surfaces in laboratory settings, an even fewer number of studies have investigated this phenomenon under flow conditions predicted to be fully free of transitional effects that would ensure similarity laws could be observed. This study presents the efforts to scale and describe the wall pressure spectrum of a rough wall, high Reynolds number turbulent boundary layer free of transitional effects. Measurements were taken in the Virginia Tech Stability Wind Tunnel for both smooth and rough walls. A deterministic roughness fetch composed of 3-mm hemispheres arranged in a 16.5-mm square array was used for the rough surface. Smooth and rough wall flows were examined achieving Reynolds numbers up to Re_θ = 68700 and Re_θ = 80200 respectively, with the rough wall flows reaching roughness based Reynolds numbers up to k_g⁺ = 507 with a simultaneous blockage ratio of δ/k_g = 76. A new roughness based inner variable scaling is proposed that provides a much more complete collapse of the rough wall pressure spectra than previous scales had provided over a large range of Reynolds numbers and roughness configurations. This scaling implies the presence of two separate time scales associated with the near wall turbulence structure generation. A clearly defined overlap region was observed for the rough wall surface pressure spectra displaying a frequency dependence of Ï ^-1.33, believed to be a function of the surface roughness configuration and its associated transport of turbulent energy. The rough wall pressure spectra were shown to decay more rapidly, but based on the same function as what defined the smooth wall decay. / Master of Science

An oscillating-hot-wire system is developed to allow mean-flow velocity measurements in separated flows. Disturbance velocities can also be measured in regions of interest. An oscillating-arm assembly provides a directional bias to the hot-wire probe, and a linear-step assembly steps the probe through the boundary layer. These assemblies are mounted to a positioning plate which allows profiles to be taken at a discrete number of chord locations. Data sampling is computer regulated using a trigger pulse from an exterior source. A distance proximity probe gives the distance of the hot-wire probe from the model. Series of mean-velocity profiles over an airfoil are measured for R_C 150,000, 200,000, 250,000, and 300,000 with a= 14° and for R_C = 200,000 and 250,000 with α= 12°. / M.S.

This thesis presents measurements of the three-dimensional flow due to the horseshoe vortex formed at the junction of a flat wall and the leading edge of a Rankine half body. The half body is located between the parallel end walls of a duct to model the situation in turbomachinery where struts and vanes, which generate performance losses due to horseshoe vortices and other secondary flow mechanisms, extend over the total flow passage height. The boundary layer on the duct end wall is artificially thickened to produce a large horseshoe vortex. Flow measurements are presented showing the inlet flow and the three-dimensional flow just downstream of the leading edge of the body. Sufficient data is presented to provide a means for testing the validity of three-dimensional viscous flow calculations. A three-dimensional flow measurement technique using a single slanted hotwire anemometer is evaluated. The hotwire anemometer measurements are compared with measurements of the same flow made with a five-hole pressure probe. A two-dimensional laminar and turbulent boundary layer analysis is performed at mid-height on the body. / M.S.

A rotor immersed in a thick turbulent boundary layer produces unsteady loading on the blades which generates unwanted noise and vibration. Two point velocity fluctuations were measured in detail to determine the full four-dimensional correlation function of a boundary layer generated over a smooth wall in the Virginia Tech Stability Wind Tunnel. The correlation function reveals anisotropy in the flow dominated by a large scale correlation structure elongated in the streamwise direction and inclined relative to the wall. This correlation function was then evaluated in the blade frame of reference of an idealized 10 bladed rotor partially immersed in the flow. Blade to blade upwash coherence shows significant asymmetry which is a direct result of the anisotropy of the flow. Using a newly developed theory, the correlation function was used to predict the far-field radiated noise from the rotor at various operating and flow conditions. Predictions show the sound field is dominated by the effects of "haystacking" which is further increased with the inclusion of the presence of the wall. Directivity predictions suggest the far-field sound field acts like a monopole/dipole combination. / Master of Science

An expression for the static temperature-velocity distribution for a zero pressure gradient turbulent boundary layer is derived based on the differential equations for local heat transfer and shear. The present theoretical method of computation is found to give results that correspond well with available experimental temperature velocity distributions. / Master of Science