This thesis presents a modern approach to two Integral Boundary Layer methods implemented in the Python programming language. This work is based on two 2D boundary layer methods: Thwaites' method for laminar boundary layer flows and Head's method for turbulent boundary layer flows. Several novel enhancements improve the quality and usability of the results. These improvements include: a common ordinary differential equation (ODE) integration framework that generalizes computational implementations of Integral Boundary Layer methods; the use of a dense output Runge-Kutta ODE solver that allows for querying of simulation results at any point with accuracy to the same order as that of the solver; and an edge velocity treatment method using cubic spline interpolation that improves the simulation performance using only points from an inviscid edge velocity distribution. Both the laminar and turbulent methods are shown to benefit from smoothing of the edge velocity distribution. The choice of ODE solver alleviates the need to artificially limit step sizes. Comparisons against analytic solutions, experimental data and XFOIL results provide a wide varity of verification and validation cases with which to compare. The implementation of Thwaites' method in this thesis avoids simplifications made in other implementations of this method, which results in more robust results. The implementation of Head's method produces high-quality results typically found in other implementations while utilizing the common ODE integration framework. Utilizing the common ODE framework results in significantly less code needed to implement Thwaites' and Head's methods. In addition, the boundary layer solvers produce results in seconds for all results presented here. Boundary layer transition and separation criteria are implemented as a proof of concept, but require future work.

The extension of the theory for two dimensional turbulent boundary layers into three dimensional flows has met with limited success. The failure of the extended models is attributed to the anisotropy of the turbulence. This is seen by the turbulent shear stress angle lagging the flow gradient angle and by the behavior of the Reynolds shear stresses lagging that of the mean flow. Transport equations for the turbulent shear stresses were proposed to be included in a modeling effort capable of accounting for the lags seen in the flow. This study is aimed at developing algebraic relationships between the various Reynolds-averaged terms in these modeling equations. Particular emphasis was placed on the triple products that appear in the transport equations. Eleven existing experimental data sets were acquired from the original authors and re-examined with respect to developed and existing parameters. A variety of flow geometries were collected for comparison. Emphasis was placed on experiments that included all six components of the Reynolds stress tensor and triple products. Parameters involving the triple products are presented that appear to maintain a relatively constant value across regions of the boundary layer. The variation of these parameters from station to station and from flow to flow is discussed. Part of this study was dedicated to parameters that were previously introduced, but never examined with respect to the data that was collected. Results of these parameters are presented and discussed with respect to agreement or disagreement with the previous results. The parameters presented will aid in the modeling of three dimensional turbulent boundary layers especially with models that employ the transport equations for the Reynolds stresses. / Master of Science

This report documents the measurements of turbulence quantities resulting from vortices embedded in a zero pressure gradient turbulent boundary layer. Turbulent boundary layers are found in most flow regimes over large scale vehicles and have been studied for many years. Various systems to control separation of boundary layers have been proposed, but vortex generators have proven to be an economical choice as they are often used to fix deficiencies in a flow field after large scale production of a vehicle has commenced. In order to better understand the interaction between vortex generators and the boundary layer in which they are embedded, an experiment has been performed using through non-invasive Comprehensive Laser Doppler Velocimeter. The results show that normalization on edge velocity is appropriate for comparison with previous work. The 1/S parameter and vq^2 parameter were found to be most appropriate to correlate the Reynolds stresses and triple products, respectively. The higher inflow edge velocity and greater momentum thickness, creating a lower vortex generator to boundary layer height ratio, result in a more diffuse vortex as compared to previous work conducted in the same wind tunnel, with the same geometry, but with different inflow conditions. / Master of Science

No description available.

The development of aerodynamic boundary layers on wind turbine blades is an important consideration in their performance. It can be quite challenging to replicate full scale conditions in laboratory experiments, and advanced diagnostics become valuable in providing data not available from traditional means. A new variant of Doppler global velocimetry (DGV) known as cross-correlation DGV is developed to measure boundary layer profiles on a wind turbine blade airfoil in the large scale Virginia Tech Stability Wind Tunnel. The instrument provides mean velocity vectors with reduced sensitivity to external conditions, a velocity measurement range from 0ms^-1 to over 3000ms^-1, and an absolute uncertainty. Monte Carlo simulations with synthetic signals reveal that the processing routine approaches the Cramér-Rao lower bound in optimized conditions. A custom probe-beam technique is implanted to eliminate laser flare for measuring boundary layer profiles on a DU96-W-180 wind turbine airfoil model. Agreement is seen with laser Doppler velocimetry data within the uncertainty estimated for the DGV profile. Lessons learned from the near-wall flow diagnostics development were applied to a novel benchmark model problem incorporating the relevant physical mechanisms of the high amplitude periodic turbulent flow experienced by turbine blades in the field. The model problem is developed for experimentally motivated computational model development. A circular cylinder generates a periodic turbulent wake, in which a NACA 63215b airfoil with a chord Reynolds number Re_c = 170, 000 is embedded for a reduced frequency k = (pi)fc/V = 1.53. Measurements are performed with particle image velocimetry on the airfoil suction side and in highly magnified planes within the boundary layer. Outside of the viscous region, the Reynolds stress profile is consistent with the prediction of Rapid Distortion Theory (RDT), confirming that the redistribution of normal stresses is an inviscid effect. The fluctuating component of the phase- averaged turbulent boundary layer profiles is described using the exact solution to laminar Stokes flow. A phase lag similar to that in laminar flow is observed with an additional constant phase layer in the buffer region. The phase lag is relevant for modeling the intermittent transition and separation expected at full scale. / Ph. D.

It is demonstrated that the method for locating a velocity profile origin, or plane of zero velocity, by fitting log profiles to streamwise velocity measurements is applicable to a larger range of roughness scales than previously expected. Five different sets of detailed, experimental velocity measurements were analyzed encompassing sediment-scale roughness elements, roughness caused by rigid vegetation, and large-scale roughness elements comprised of mobile bedforms. The method resulted in similar values of normalized zero-plane displacement for all roughness types considered. The ratios of zero-plane displacement, dh, to roughness height, ks, were 0.20 and 0.26 for the sediment- and vegetation-scale experiments, respectively. The results for the two experiments with bedform dominated roughness were 0.34 and 0.41. An estimate of dh/ks ranging from 0.2 to 0.4 is therefore recommended for a range of roughness types with the higher end of the range being more appropriate for the larger, bedform-scale roughness elements, and the lower end for the sediment-scale roughness elements. In addition, it is demonstrated that the location of the plane of zero velocity is temporally constant even when the bed height is not. The effects of roughness element packing density were also examined with the identification of a possible threshold at 4%, above which zero-plane displacement is independent of packing density. The findings can be applied to field velocity measurements under mobile bed conditions, facilitating the calculation of turbulence parameters such as shear velocity, by using point measurements and providing guidelines for the estimation of an appropriate value for zero-plane displacement. / Master of Science

Experimental investigations were conducted with and without the presence of the surface-mounted obstacle to quantify its effects on the far wake. The obstacle chosen for this study was a 3:2 elliptical nose NACA 0020 tail wing-body (Rood body), approximately of height equal to the boundary layer thickness at one of the measurement locations of the flow. The experiments were performed by varying the Reynolds number of the flow and manipulating the pressure gradient distributions using a NACA 0012 airfoil placed within the wind tunnel test section. The measurements were acquired utilizing a spanwise traversing boundary layer rake and a point pressure sensing microphone array. The findings reveal that the presence of the obstacle introduces disruptions in the flow, such as vortex and jet regions in the wake. However, the overall flow behavior remains consistent with that of an undisturbed turbulent boundary layer, for varying Reynolds numbers and pressure gradients. Notably, an adverse pressure gradient and lower Reynolds number both accentuate the prominence of the jet and vortex region within the wake, with the trend reversing towards the other end of the spectrum. This behavior is akin to the larger turbulent boundary layer under adverse pressure gradients and lower Reynolds numbers. Furthermore, the presence of obstacles induces an increase in the overall level of the wall pressure spectrum by approximately 2 dB, regardless of the flow condition. Additionally, it leads to a deviation in the slope of the mid-frequency range of the autospectra compared to the smooth wall case. Specifically, the mid-slope frequency of an undisturbed turbulent boundary layer is steeper than that observed in the disturbed wake flow caused by the obstacle. / Master of Science / The interaction between turbulence and aerodynamic surfaces gives rise to wall-pressure fluctuations, which in turn induce structural vibrations and acoustic noise. On surfaces turbulent flows meet, antennae, flaps, and other frequently mounted measuring devices. The flow in their wake is impacted by the coherence of a turbulent boundary layer being disrupted by these impediments mounted on aerodynamic surfaces. They also alter the nature of the pressure fluctuations that are generated on the surface of interest. The far wake of a Rood Body obstacle was studied using a point pressure sensing microphone array and a spanwise traversing boundary layer rake. Experimental measurements were taken for a range of Reynolds numbers and pressure gradient environments at the Virginia Tech Stability Wind Tunnel. Results show that the boundary layer rake measurements resolve the presence of the obstacle wake successfully, by characterizing the wake structures and confirming the presence of jet and vortex regions in the wake of the obstacle. Surface pressure measurements reveal that the presence of the obstacle causes the low-frequency content of the wall pressure to be less dominant than the no obstacle case, while the high-frequency content becomes more dominant in the presence of the obstacle. The presence of obstacles also increases the overall levels of the wall pressure spectrum by approximately 2 dB.

Surface flow noise results from fluid-surface interactions, manifesting as surface vibrations or far-field noise. Decomposing the surface pressure field reveals distinct components, with the sub-convective component being particularly critical due to its coupling with structural modes, inducing vibrations. This component, characterized by wavenumbers lower than convective wavenumbers, is significantly weaker than its convective counterpart, making it difficult to measure and model accurately. Existing studies rely on limited measurements, constrained by instrumentation and facility capabilities, leading to empirical wall pressure models with restricted accuracy and applicability. This study presents the first high-resolution measurements of sub-convective pressure fluctuations, enabling validation of wall pressure spectrum models. A novel measurement approach inspired by acoustic metamaterials was developed, employing sub-resonant cavity sensors that integrate seamlessly into existing geometries. These sensors, leveraging off-the-shelf pressure transducers, operate effectively in grazing flow environments without disturbing the flow. Their dynamic response, determined by geometry, can be optimized for specific flow conditions, offering versatility across applications. To minimize aliasing effects at low wavenumbers, an optimized sensor array with spanwise-elongated geometries was deployed linearly along the flow direction. Wind tunnel experiments across varying Reynolds numbers and pressure gradients provided crucial insights. Long statistical averages ($mathcal{O}(10^6delta/U_e)$) revealed the statistical characteristics of large-scale turbulent motions. Results showed an asymmetric convective ridge about the convective line, a sharp transition into the sub-convective domain, and sub-convective levels 30–35 dB below convective levels. Comparisons with existing models revealed discrepancies, with all models overpredicting measured levels. While the Chase model aligned over certain ranges, deviations highlight the need for improved wall pressure models. This study lays the groundwork for enhanced vibroacoustic analysis and model refinement through innovative measurement techniques. Overall, these measurements provide a refined insight into the nature of sub-convective pressure fluctuations and will aid in the development of more accurate wall pressure models, crucial for fluid-structure interaction analysis. / Doctor of Philosophy / Imagine traveling in a car or flying in a plane, tuning out conversations or music to focus on the background noise. What you'd mostly hear is a whooshing sound, a symphony of the vehicle's HVAC system, engines, and other mechanical components. But there's another significant, often overlooked, contributor to this noise: the fluid flowing around the vehicle. This phenomenon is not limited to cars and planes—it's also true for underwater vehicles. As air or water flows around a vehicle, it interacts with its surface through a thin layer called the boundary layer, whether it's the fuselage of an aircraft or the body of a car. This interaction generates fluctuating pressure forces on the surface, causing the structure to vibrate and produce noise. Unlike sticking your head out of a moving vehicle, which creates its own kind of noise, this source involves a complex interplay between the fluid flow and the structural dynamics of the vehicle. The vibrations generated from this interaction manifest as structural waves that travel much faster than the fluid itself. These waves, characterized by large spatial scales or low wavenumbers, depend on specific pressure fluctuations in the boundary layer to excite them. These particular fluctuations, called sub-convective or low-wavenumber pressure fluctuations, are much weaker—about 10,000 times less intense—than the turbulence carried by the flow. However, their overlap with the structural wave's characteristics allows for coupling, making them a crucial but elusive noise source. Measuring these weak fluctuations is incredibly challenging. Classical techniques often struggle because stronger noises, such as flow self-noise or external disturbances, can easily overwhelm the data. While some progress has been made using spatial filtering methods, these approaches often lack resolution and provide inconsistent results across studies, signaling the need for better techniques. This study introduces an innovative method inspired by acoustic metamaterials to measure these elusive pressure fluctuations with greater precision and reliability. By designing custom sensors based on multi-neck Helmholtz resonators, capable of filtering out unwanted noise, this approach offers a breakthrough in the field. The sensor design, working principle, and testing process under various flow conditions are detailed, providing insights into how flow speed impacts the fluctuations. Comparisons with existing models and measurements validate the findings, and updates to current models are proposed, paving the way for more accurate noise prediction and mitigation strategies in vehicles of all kinds.

<p>The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.</p>

Direct Numerical Simulations (DNS) are performed to investigate laminar-turbulent transition in a boundary layer on a sharp cone at Mach 6. The main objective of this dissertation research is to explore which nonlinear breakdown mechanisms may be dominant in a broad--band "natural" disturbance environment and then use this knowledge to perform controlled transition simulations to investigate these mechanisms in great detail. Towards this end, a "natural" transition scenario was modeled and investigated by generating wave packet disturbances. The evolution of a three-dimensional wave packet in a boundary layer has typically been used as an idealized model for "natural" transition to turbulence, since it represents the impulse response of the boundary layer and, thus, includes the interactions between all frequencies and wave numbers. These wave packet simulations provided strong evidence for a possible presence of fundamental and subharmonic resonance mechanisms in the nonlinear transition regime. However, the fundamental resonance was much stronger than the subharmonic. In addition to these two resonance mechanisms, the wave packet simulations also indicated the possible presence of oblique breakdown mechanism. To gain more insight into the nonlinear mechanisms, controlled transition simulations were performed of these mechanisms. Several small and medium scale simulations were performed to scan the parameter space for fundamental and subharmonic resonance. These simulations confirmed the findings of the wave packet simulations, namely that, fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently a set of highly resolved fundamental and oblique breakdown simulations were performed. In these DNS, remarkable streamwise arranged "hot'' streaks were observed for both fundamental and oblique breakdown. The streaks were a consequence of the large amplitude steady longitudinal vortex modes in the nonlinear régime. These simulations demonstrated that both second--mode fundamental breakdown and oblique breakdown may indeed be viable paths to complete breakdown to turbulence in hypersonic boundary layers at Mach 6.