abstract: Structural features of canonical wall-bounded turbulent flows are described using several techniques, including proper orthogonal decomposition (POD). The canonical wall-bounded turbulent flows of channels, pipes, and flat-plate boundary layers include physics important to a wide variety of practical fluid flows with a minimum of geometric complications. Yet, significant questions remain for their turbulent motions' form, organization to compose very long motions, and relationship to vortical structures. POD extracts highly energetic structures from flow fields and is one tool to further understand the turbulence physics. A variety of direct numerical simulations provide velocity fields suitable for detailed analysis. Since POD modes require significant interpretation, this study begins with wall-normal, one-dimensional POD for a set of turbulent channel flows. Important features of the modes and their scaling are interpreted in light of flow physics, also leading to a method of synthesizing one-dimensional POD modes. Properties of a pipe flow simulation are then studied via several methods. The presence of very long streamwise motions is assessed using a number of statistical quantities, including energy spectra, which are compared to experiments. Further properties of energy spectra, including their relation to fictitious forces associated with mean Reynolds stress, are considered in depth. After reviewing salient features of turbulent structures previously observed in relevant experiments, structures in the pipe flow are examined in greater detail. A variety of methods reveal organization patterns of structures in instantaneous fields and their associated vortical structures. Properties of POD modes for a boundary layer flow are considered. Finally, very wide modes that occur when computing POD modes in all three canonical flows are compared. The results demonstrate that POD extracts structures relevant to characterizing wall-bounded turbulent flows. However, significant care is necessary in interpreting POD results, for which modes can be categorized according to their self-similarity. Additional analysis techniques reveal the organization of smaller motions in characteristic patterns to compose very long motions in pipe flows. The very large scale motions are observed to contribute large fractions of turbulent kinetic energy and Reynolds stress. The associated vortical structures possess characteristics of hairpins, but are commonly distorted from pristine hairpin geometries. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2012

High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs. It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry. Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling. Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra. This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. / Doctor of Philosophy / Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers. This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.

Increased efficiency and durability of gas turbine components is driven by demands for reduced fuel consumption and increased reliability in aircraft and power generation applications. The complex flow near the endwall of an axial gas turbine has been identified as a significant contributing factor to aerodynamic loss and increased part temperatures. Three-dimensional (non-axisymmetric) contouring of the endwall surface has been shown to reduce aerodynamic losses, but the effect of the contouring on endwall heat transfer is not well understood. This research focused on understanding the general flow physics of contouring and the sensitivity of the contouring to perturbations arising from leakage features present in an engine. Two scaled low-speed cascades were designed for spatially-resolved measurements of endwall heat transfer and film cooling. One cascade was intended for flat and contoured endwall studies without considering typical engine leakage features. The other cascade modeled the gaps present between a stator and rotor and between adjacent blades on a wheel, in addition to the non-axisymmetric endwall contouring. Comparisons between a flat and contoured endwall showed that the contour increased endwall heat transfer and increased turbulence in the forward portion of the passage due to displacement of the horseshoe vortex. However, the contour decreased heat transfer further into the passage, particularly in regions of high heat transfer, due to delayed development of the passage vortex and reduced boundary layer skew. Realistic leakage features such as the stator-rotor rim seal had a significant effect on the endwall heat transfer, although leakage flow from the rim seal only affected the horseshoe vortex. The contours studied were not effective at reducing the impact of secondary flows on endwall heat transfer and loss when realistic leakage features were also considered. The most significant factor in loss generation and high levels of endwall heat transfer was the presence of a platform gap between adjacent airfoils. / Ph. D.

Trailing edge noise is a common noise source in aerodynamic applications, such as wind turbines, duct fan blades, and propellers. As sound is a nuisance for people near this machinery, methods of reducing trailing edge noise are being investigated. A proven method of trailing edge noise reduction is using a serrated trailing edge. Many prior experiments have shown that a trailing edge with sawtooth serrations can reduce trailing edge noise compared to a straight trailing edge, but the mechanism by which sawtooth serrations reduce noise is not fully understood. Previous theoretical models have assumed that the turbulence field convecting past a serrated trailing edge is unchanged by the presence of the serrations, but experiments have shown that this is not the case in reality. This work attempts to further explore the mechanisms behind why trailing edge serrations reduce trailing edge noise. Additionally, it evaluates the usefulness of a wall jet wind tunnel for use in the study of serrated trailing edges. Experiments were conducted in an anechoic wall jet wind tunnel using a straight trailing edge configuration and a serrated trailing edge configuration. It was found that there may be differences in the unsteady surface pressure over serrated edges in one-sided flows as compared to two-sided flows, like on that of an airfoil, most notably in relation to the magnitude of the unsteady pressure on the serrations. In the wall jet and in agreement with other studies, it was found that the unsteady pressure fluctuations increase towards the tip of the serration in one-sided flows. This is counter to what is found in some studies of two-sided flows. Good agreement was found between some models of the wavenumber-frequency wall pressure spectrum of a turbulent boundary layer and the measured wall pressure spectrum on the straight trailing edge, and these models also produced good predictions of the noise produced by this trailing edge using Amiet's equation. A surface pressure microphone array was used to estimate the zero spanwise wavenumber surface pressure spectrum. This spectrum was used in Amiet's method to predict the measured trailing edge noise. Predictions using the wavenumber-filtered measurement tended to overpredict the measured far field noise most likely due to the inclusion of broader wavenumber content through the array's side lobe response and the breadth of the main lobe. The serrated trailing edge was found to increase coherence between two points on the same serration while reducing coherence between two points on different serrations. It was concluded that the presence of the serrations decorrelates small-scale turbulent eddies. Additionally, it was found that while the serrated trailing edge did reduce the noise produced, its destructive effect on the geometry-based resonance of the straight trailing edge configuration may have amplified the magnitude of the reduction. Finally, it was concluded that the serrations do indeed affect the hydrodynamic field near the trailing edge, and the theoretical models which make the assumption otherwise must be refined. / Master of Science / Trailing edge noise is a common noise source in aerodynamic applications, such as wind turbines, duct fan blades, and propellers. As sound is a nuisance for people near this machinery, methods of reducing trailing edge noise are being investigated. A proven method of trailing edge noise reduction is using a serrated trailing edge. Many prior experiments have shown that a trailing edge with sawtooth serrations can reduce trailing edge noise compared to a straight trailing edge, but the mechanism by which sawtooth serrations reduce noise is not fully understood. This work attempts to further explore the mechanisms behind why trailing edge serrations reduce noise. Experiments were conducted in an anechoic wind tunnel facility. It was found that a one-sided flow over a serrated trailing edge may be significantly different from that over a two-sided flow. Good agreement was found between prediction models and measurements of trailing edge noise. The serrated trailing edge was effective at reducing the coherence of turbulent eddies across the roots of the sawtooth serrations. It was concluded that the serrated trailing edge is effective at reducing noise, and that one means of doing so is decreasing the correlation of small-scale turbulent eddies, and that current models of the flow over serrations may need to be refined.

The focus of the present licentiate thesis is on the effect of suction and pressure gradients on turbulent boundary-layer flows, which are investigated separately through performing numerical simulations.The first part aims at assessing history and development effects on adverse pressure-gradient (APG) turbulent boundary layers (TBL). A suitable set-up was developed to study near-equilibrium conditions for a boundary layer developingon a flat plate by setting the free-stream velocity at the top of the domain following a power law. The computational box size and the correct definition of the top-boundary condition were systematically tested. Well-resolved large-eddy simulations were performed to keep computational costs low. By varying the free-stream velocity distribution parameters, e.g. power-law exponent and virtual origin, pressure gradients of different strength and development were obtained. The magnitude of the pressure gradient is quantified in terms of the Clauser pressure-gradient parameter β. The effect of the APG is closely related to its streamwise development, hence, TBLs with non-constant and constant β were investigated. The effect was manifested in the mean flow through a much more pronounced wake region and in the Reynolds stresses through the existence of an outer peak. The terms of the turbulent kinetic energy budgets indicate the influence of the APG on the distribution of the transfer mechanism across the boundary layer. Stronger and more energetic structures were identified in boundary layers with relatively stronger pressure gradients in their development history. Due to the difficulty of determining the boundary-layer thickness in flows with strong pressure gradients or over a curvedsurface, a new method based on the diagnostic-plot concept was introduced to obtain a robust estimation of the edge of a turbulent boundary layer. In the second part, large-eddy simulations were performed on temporally developing turbulent asymptotic suction boundary layers (TASBLs). Findings from previous studies about the effect of suction could be confirmed, e.g. the reduction of the fluctuation levels and Reynolds shear stresses. Furthermore, the importance of the size of the computational domain and the time development were investigated. Both parameters were found to have a large impact on the results even on low-order statistics. While the mean velocity profile collapses in the inner layer irrespective of box size and development time, a wake region occurs for too small box sizes or early development time and vanishes once sufficiently large domains and/or integration times are chosen. The asymptotic state is charactersized by surprisingly thick boundary layers even for moderateReynolds numbers Re (based on free-stream velocity and laminar displacement thickness); for instance, Re = 333 gives rise to a friction Reynolds number Reτ = 2000. Similarly, the flow gives rise to very large structures in the outer region. These findings have important ramifications for experiments, since very large facilities are required to reach the asymptotic state even for low Reynolds numbers. / <p>QC 20160418</p>

The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, based on the element height (k) and the friction velocity, range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount depending on the height of the roughness element, showing that this amount is a function of roughness Reynolds number and the wall geometry. For the 3-D flows, the data show that the surface pressure gradient is not strongly influenced by the roughness elements. In general, for both 2-D and 3-D rough-wall TBL, the differences between the two roughness patterns (straight and diagonal), as regards the mean velocities and the Reynolds stresses, are limited to about 3 roughness element heights from the wall. The study on single elements revealed that the separated shear layers emanating from the top of the elements form a pair of counter rotating vortices that dominate the downstream flow structure. These vortices, termed as the roughness top vortex structure (RTVS), in conjunction with mean flow, forced over and around the elements, are responsible for the production of large Reynolds stresses in the neighborhood of the element height aft of the elements. When these elements are placed in a distribution, the effects of RTVS are not apparent. The roughness elements create a large region of back flow behind them which is continuously replenished by faster moving fluid flowing through the gaps in the rough-wall. The fluid in the back flow region moves upward as low speed ejections where it collides with the inrushing high speed flow, thus, leading to a strong mixing of shear layers. This is responsible for the generation of large levels of turbulent kinetic energy (TKE) in the vicinity of the element height which is transported, primarily, by turbulent diffusion. As regards the 3-D rough-wall TBL, the effect of flow three-dimensionality is seen in the large skewing of the distributions of mean velocities, Reynolds stresses and TKE, aft of the elements. In general, the regions of large TKE production-rates seem to propagate in the direction of the local velocity vector at the element height. The data-sets also enable the extraction of the turbulent flow structure to better describe the flow physics of these rough-wall turbulent boundary layers. / Ph. D.

An overview of unsteady incompressible jet flows is presented, with the primary interest being radially developing jets in cylindrical polar coordinates. The radial free jet emanates from some orifice, being axisymmetric about the transverse (z) axis and possessing reflectional symmetry across its z=0 centreline. The radial wall jet is also axisymmetric about the transverse axis, however in this case impermeability and no-slip conditions are imposed at the wall, which is situated at z=0. The numerical solution of a linear perturbation superposed on the free jet, whose temporal form is assumed to be driven by a periodic source pulsation, gives rise to a wave-like disturbance whose amplitude grows downstream as its local wavelength decreases. An asymptotic analysis of this linear perturbation, which applies to the wall jet as well with some minor changes, captures the exact nature of the exponential spatial growth, and also algebraic attenuation of the growth. The linear theory is only valid for a small amplitude pulsation (|ε| << 1, where ε is the perturbation amplitude). When a nonlinear pulsation (ε = O(1)) is applied to the radial free jet, any linear theory must be dropped. Solving the full nonlinear system of equations reveals singular behaviour at a critical downstream location, which corresponds to the presence of an infinitely steep downstream gradient. The replacement of molecular diffusivity with a larger-scale eddy viscosity does little to affect the qualitative growth of the linear perturbation. In order for an experimental study to reproduce any of the discussed boundary-layer results, we must consider the behaviour of jet-type flows at finite Reynolds number. This involves solving the full Navier-Stokes equations numerically, to determine the Reynolds number at which we should expect to qualitatively recover boundary-layer behaviour. The steady solution for the radial free jet and its linear pulsation are studied in this way, as is the linear pulsatile planar free jet. We may enhance the streamwise velocity of a radial jet by applying swirl around the z axis. Modulating this swirl is looked at as a possible mechanism to induce the previously discussed pulsation, which then motivates the introduction of a finite spinning disk problem. In this case the system may be completely confined within an enclosed cylinder, making a hypothetical experimental approach somewhat more approachable.

The delivery of nutrients to the surface of marine algae can be controlled by the local hydrodynamic regime: in higher flow velocities, the Diffusive Boundary Layer (DBL) at the uptake surface is thinner, which can increase the flux of dissolved chemicals to the algal surface. If the primary productivity of an alga is controlled by the availability of a dissolved chemical, increased water flow should result in greater primary productivity due to increased chemical flux. To test the hypothesis that increased water flow will increase Photosystem II kinematics (PSII) in the green alga Caulerpa we used a Diving Pam Fluorometer to measure the maximum relative electron transport rate (Pmax), Saturation Irradiance (Ik), Non-photochemical quenching (NPQ), the light limited slope of photosynthesis vs. irradiance curve (α) and photo-chemical quenching (qP) and compared these measured values among treatments of varying flow speeds in a portable laboratory flume. We also measured the influence of water flow on values of Pmax, Ik, α , qP and NPQ in the field. Results showed that in C. racemosa collected from Tampa bay, and tested in a laboratory flume, values of Pmax and Ik were positively correlated to increase water flow, possibly indicating mass-transfer limitation. C. mexicana, collected from the Florida Keys, showed a decrease in values of Pmax, and Ik with increasing water velocity in flume experiments, indicating that the increased flow was resulting in physiological stress. This result was supported with field measurements for C. sertularioides, which showed a negative correlation between Pmax and flow velocity and Ik and flow velocity.

<p>The boundary layer is the part of the atmosphere that is in direct contact with the ground via turbulent motion. At mid-latitudes the boundary layer is usually one or a few kilometers deep, while in the Arctic it is much more shallow, typically a few hundred meters or less. The reason is that here the absolute temperature increases in the lowest kilometer, making the boundary layer semi-permanently stably stratified. The exchange of heat, momentum and tracers between the atmosphere, ocean and ground under stable stratification is discussed from an observational, modeling and climate-change point of view. A compilation of six observational datasets, ordered by the Richardson number (rather than the widely used Monin-Obukhov length) reveals new information about turbulence in the very stably stratified regime. An essentially new turbulence closure model, based on the total turbulent energy concept and these observational datasets, is developed and tested against large-eddy simulations with promising results. The role of mesoscale motion in the exchange between the atmosphere and surface is investigated both for observations and in idealized model simulations. Finally, it is found that the stably stratified boundary layer is more sensitive to external surface forcing than its neutral and convective counterparts. It is speculated that this could be part of the explanation for the observed Arctic amplification of climate change.</p>

<p>A new large eddy simulation (LES) code is developed and used to investigate non-local features of turbulent planetary boundary layers (PBLs). The LES code is based on filtered Navier-Stokes equations, which describe motions of incompressible, Boussinesq fluid at high Reynolds numbers. The code computes directly large-scale, non-universal turbulence in the PBL whereas small-scale, universal turbulence is parameterized by a dynamic mixed subgrid closure. The LES code is thoroughly tested against high quality laboratory and field data. </p><p>This study addresses non-local properties of turbulence which emphasis on the stable stratification. Its basic results are as follows. The flow stability in PBLs is generally caused by two mechanisms: the negative buoyancy force (in the stable density stratification) and the Coriolis force (in the rotating system). The latter stabilizes the flow if the earth’s vorticity and the turbulent vorticity are anti-parallel. The Coriolis force stability suppresses large-scale turbulence and makes large eddies asymmetric. The density stratification suppresses vertical scales of turbulence. Joint actions of the Coriolis and the buoyancy forces result in a more complex behavior of turbulence. Particularly, the layers of vigorous turbulence may appear in the course of development of low-level jets in baroclinic atmosphere. </p><p>Non-local effects determine integral measures of PBLs, first of all the PBL depth. This study clearly demonstrates its pronounced dependences on the Coriolis parameter, the Kazanski-Monin internal stability parameter, and newly introduced imposed-stability and baroclinicity parameters. An LES database is created and used to validate an advanced PBL-depth formulation. LES support the idea that PBLs interact with the stably stratified free flow through the radiation of gravity waves, excited by large turbulent eddies at the interface. </p>