The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.

This document addresses problems encountered when establishing the very low air-flow speeds required for experimental investigations of the mechanisms of low-Reynolds-number boundary-layer turbulence. Small-scale motions in the near-wall region are important features of turbulent boundary-layer dynamics, and, if these features are to be resolved by measurements in air with conventionally-sized hot-wire probes, a well-behaved canonical turbulent boundary layer must be developed at free stream flow speeds no higher than 4 m/s. However, at such low speeds, the turbulent boundary layers developed on the walls of a wind tunnel are very susceptible to perturbation by non-turbulent time-dependent flow structures which originate upstream from the test section in the laminar flow at the inlet and in the contraction. Four different non-turbulent flow structures have been identified. The first is a result of quasi-two-dimensional separation of the laminar boundary-layer from the surfaces of the wind-tunnel contraction. Potential flow simulations show that susceptibility to this form of separation is reduced by increasing the degree of axisymmetry in the cross-section geometry and by decreasing the streamwise curvature of the concave surfaces. The second source of time-dependence in the laminar boundary-layer flow is an array of weak streamwise vortices produced by Goertler instability. The Goertler vortices can be removed by boundary-layer suction at the contraction exit. The third form of flow perturbation, revealed by visualisation experiments with streamers, is a weak large-scale forced-vortex swirl produced by random spatial fluctuations of temperature at the wind-tunnel inlet. This can be prevented by thorough mixing of the inlet flow; for example, a centrifugal blower installed at the inlet reduces the amplitude of temperature nonuniformity by a factor of about forty and so prevents buoyancy-driven swirl. When subjected to weak pressure gradients near the start of a wind-tunnel contraction, Goertler vortices in laminar wall layers can develop into three-dimensional separations with strong counter-rotating trailing vortices. These trailing vortices are the fourth source of unsteady flow in the test-section. They can be suppressed by a series of appropriately located screens which remove the low-speed-streak precursors of the three-dimensional separations. Elimination of the above four contaminating secondary flows permits the development of a steady uniform downstream flow and well-behaved turbulent wall layers. Measurements of velocity in the turbulent boundary layer of the test-section have been obtained by hot-wire anemometry. When a hot-wire probe is located within the viscous sublayer, heat transfer from the hot-wire filament to the wall produces significant errors in the measurements of both the mean and the fluctuating velocity components. This error is known as wall-proximity effect and two successful methods are developed for removing it from the hot-wire signal. The first method is based on the observation that, if all experimental parameters except flow speed and distance from the wall are fixed, the velocity error may be expressed nondimensionally as a function of only one parameter, in the form DeltaU^+=f(y^+). The second method, which also accommodates the effect of changing the hot-wire overheat ratio, is based on a dimensional analyis of heat transfer to the wall. Velocity measurements in the turbulent boundary layer at the mid-plane of a nearly square test-section duct have established that, when the boundary-layer thickness is less than one quarter of the duct height, mean-velocity characteristics are indistinguishable from those of a two-dimensional flat-plate boundary layer. In thicker mid-plane boundary layers, the mean-velocity characteristics are affected by stress-induced secondary flow and by lateral constriction of the boundary-layer wake region. A significant difference between flat-plate and duct boundary layers is also observed in momentum-balance calculations. The momentum-integral equation for a duct requires definitions of momentumd and displacement thickness which are different from those given for flat-plate boundary layers. Momentum-thickness growth rates predicted by the momentum-integral equation for a duct agree closely with measurements of the newly defined duct momentum thickness. Such agreement cannot be obtained in terms of standard flat-plate momentum thickness. In duct boundary layers with Reynolds numbers Re_theta between 400 and 2600, similarity in the wake-region distributions of streamwise turbulence statistics has been obtained by normalising distance from the wall with the flat-plate momentum thickness, theta_2. This result indicates that, in contrast with the mean velocity characteristics, the structure of mid-plane turbulence does not depend on the proportion of duct cross-section occupied by boundary layers and is essentially the same as in a flat-plate boundary layer. For Reynolds numbers less than 400, both wall-region and wake-region similarity fail because near-wall turbulence events interact strongly with the free stream flow and because large scale turbulence motions are directly influenced by the wall. In these conditions, which exist in both duct and flat-plate turbulent boundary layers, there is no distinct near-wall or wake region, and the behaviour of turbulence throughout the boundary layer depends on both wall variables and on outer region variables simultaneously. / Thesis (Ph.D.)--School of Mechanical Engineering, 1998.

An experimental study was conducted to explore the possible application of dynamically actuated nanowires to effectively disturb the wall layer in fully developed, turbulent channel flow. Actuated nanowires have the potential to be used for the mixing and filtering of chemicals, enhancing convective heat transfer and reducing drag. The first experimental evidence is presented suggesting it is possible to manipulate and subsequently control turbulent flow structures with active nanowires. An array of rigid, ultra-long (40 μm) TiO2 nanowires was fabricated and installed in the bounding wall of turbulent channel flow then oscillated using an attached piezoelectric actuator. Flow velocity and variance measurements were taken using a single sensor hot-wire with results indicating the nanowire array significantly influenced the flow by increasing the turbulent kinetic energy through the entire wall layer.

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This document addresses problems encountered when establishing the very low air-flow speeds required for experimental investigations of the mechanisms of low-Reynolds-number boundary-layer turbulence. Small-scale motions in the near-wall region are important features of turbulent boundary-layer dynamics, and, if these features are to be resolved by measurements in air with conventionally-sized hot-wire probes, a well-behaved canonical turbulent boundary layer must be developed at free stream flow speeds no higher than 4 m/s. However, at such low speeds, the turbulent boundary layers developed on the walls of a wind tunnel are very susceptible to perturbation by non-turbulent time-dependent flow structures which originate upstream from the test section in the laminar flow at the inlet and in the contraction. Four different non-turbulent flow structures have been identified. The first is a result of quasi-two-dimensional separation of the laminar boundary-layer from the surfaces of the wind-tunnel contraction. Potential flow simulations show that susceptibility to this form of separation is reduced by increasing the degree of axisymmetry in the cross-section geometry and by decreasing the streamwise curvature of the concave surfaces. The second source of time-dependence in the laminar boundary-layer flow is an array of weak streamwise vortices produced by Goertler instability. The Goertler vortices can be removed by boundary-layer suction at the contraction exit. The third form of flow perturbation, revealed by visualisation experiments with streamers, is a weak large-scale forced-vortex swirl produced by random spatial fluctuations of temperature at the wind-tunnel inlet. This can be prevented by thorough mixing of the inlet flow; for example, a centrifugal blower installed at the inlet reduces the amplitude of temperature nonuniformity by a factor of about forty and so prevents buoyancy-driven swirl. When subjected to weak pressure gradients near the start of a wind-tunnel contraction, Goertler vortices in laminar wall layers can develop into three-dimensional separations with strong counter-rotating trailing vortices. These trailing vortices are the fourth source of unsteady flow in the test-section. They can be suppressed by a series of appropriately located screens which remove the low-speed-streak precursors of the three-dimensional separations. Elimination of the above four contaminating secondary flows permits the development of a steady uniform downstream flow and well-behaved turbulent wall layers. Measurements of velocity in the turbulent boundary layer of the test-section have been obtained by hot-wire anemometry. When a hot-wire probe is located within the viscous sublayer, heat transfer from the hot-wire filament to the wall produces significant errors in the measurements of both the mean and the fluctuating velocity components. This error is known as wall-proximity effect and two successful methods are developed for removing it from the hot-wire signal. The first method is based on the observation that, if all experimental parameters except flow speed and distance from the wall are fixed, the velocity error may be expressed nondimensionally as a function of only one parameter, in the form DeltaU^+=f(y^+). The second method, which also accommodates the effect of changing the hot-wire overheat ratio, is based on a dimensional analyis of heat transfer to the wall. Velocity measurements in the turbulent boundary layer at the mid-plane of a nearly square test-section duct have established that, when the boundary-layer thickness is less than one quarter of the duct height, mean-velocity characteristics are indistinguishable from those of a two-dimensional flat-plate boundary layer. In thicker mid-plane boundary layers, the mean-velocity characteristics are affected by stress-induced secondary flow and by lateral constriction of the boundary-layer wake region. A significant difference between flat-plate and duct boundary layers is also observed in momentum-balance calculations. The momentum-integral equation for a duct requires definitions of momentumd and displacement thickness which are different from those given for flat-plate boundary layers. Momentum-thickness growth rates predicted by the momentum-integral equation for a duct agree closely with measurements of the newly defined duct momentum thickness. Such agreement cannot be obtained in terms of standard flat-plate momentum thickness. In duct boundary layers with Reynolds numbers Re_theta between 400 and 2600, similarity in the wake-region distributions of streamwise turbulence statistics has been obtained by normalising distance from the wall with the flat-plate momentum thickness, theta_2. This result indicates that, in contrast with the mean velocity characteristics, the structure of mid-plane turbulence does not depend on the proportion of duct cross-section occupied by boundary layers and is essentially the same as in a flat-plate boundary layer. For Reynolds numbers less than 400, both wall-region and wake-region similarity fail because near-wall turbulence events interact strongly with the free stream flow and because large scale turbulence motions are directly influenced by the wall. In these conditions, which exist in both duct and flat-plate turbulent boundary layers, there is no distinct near-wall or wake region, and the behaviour of turbulence throughout the boundary layer depends on both wall variables and on outer region variables simultaneously. / Thesis (Ph.D.)--School of Mechanical Engineering, 1998.

The paper is concerned with the Nitsche mortaring in the framework of domain decomposition where non-matching meshes and weak continuity of the finite element approximation at the interface are admitted. The approach is applied to singularly perturbed reaction-diffusion problems in 2D. Non-matching meshes of triangles being anisotropic in the boundary layers are applied. Some properties as well as error estimates of the Nitsche mortar finite element schemes are proved. In particular, using a suitable degree of anisotropy of triangles in the boundary layers of a rectangle, we derive convergence rates as known for the conforming finite element method in presence of regular solutions. Numerical examples illustrate the approach and the results.

<div>Hypersonic flows consist of harsh environments where chemistry effects are relevant and low speed assumptions such as the ideal gas law and the continuum hypothesis</div><div>begin to break down. Because of these processes, computer models do a poor job of predicting behavior of vehicles in hypersonic flight. High fi?delity ground test</div><div>measurements are necessary to anchor and extrapolate CFD simulations so that flight vehicle designs can continue to improve. Due to the harsh conditions and complexities</div><div>of test facilities, implementing experimental measurements can prove challenging. Molecular tagging methods such as Femtosecond Laser Electronic Excitation Tagging</div><div>(FLEET) are attractive for use in hypersonic ground test facilities for many reasons. They are generally considered non-intrusive, since they require no physical probes or seed particles to be placed in the flow. This both keeps the facility safe from damage and minimizes the disturbance imparted on the flowfi?eld by the measurement. Since the tracer is comprised of molecules already present in the flow, the measurement is reliable and can track velocities over a wide dynamic range. The optical arrangement for FLEET is rather simple, requiring only a focused laser beam and a camera to capture the signal. The method can even be applied as a one-sided measurement requiring only one direction of optical access. The current state-of-the-art for the FLEET method is point-wise measurements made at 1 kHz with a</div><div>commercially available laser system. The basis for this thesis is to identify and address current limitations in the implementation of FLEET to relevant flow facilities in terms of the useful aerodynamic information that can be extracted. Fundamental advances to the spatial extent and temporal resolution of FLEET are investigated, and novel applied measurements in high speed flow facilities are presented. Considerations of the precision, spatial resolution and ability to implement fundamental advances to harsh and more complex environments are discussed. A custom-built burst-mode femtosecond laser system is used to enable FLEET measurements at 1 MHz, an improvement of three orders</div><div>of magnitude in measurement rate. New optical arrangements including microlens arrays and holographic beamsplitters are developed to allow multi-dimensional grids</div><div>to be tracked to instantaneously measure velocity gradients. Shock wave and shear measurements in a supersonic bladeless turbine and boundary layer measurements</div><div>on a Mach 6 cone-cylinder-flare are demonstrated. Additionally, an adapted method, Femtosecond Laser Activation and Sensing of Hydroxyl (FLASH) is developed and applied to measure velocity in reacting environments such as a Rotating Detonation Engine (RDE). These innovations provide a path forward for improving the spatiotemproal fi?delity of velocity measurements and extending the capability for investigation high-speed reacting and non-reacting flows in hypersonic ground test facilities.</div><div><br></div>

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.

The focus of this thesis is on the numerical study of subcritical transition to turbulence in the asymptotic suction boundary layer (ASBL). Applying constant homogeneous suction prevents the spatial growth of the boundary layer, granting access to the asymptotic dynamics. This enables research approaches which are not feasible in the spatially growing case. In a first part, the laminar–turbulent separatrix of the ASBL is investigated numerically by means of an edge-tracking algorithm. The consideration of spanwise-extended domains allows for the robust localisation of the attracting flow structures on this separatrix. The active part of the identified edge states consists of a pair of low- and high-speed streaks, which experience calm phases followed by high energy bursts. During these bursts the structure is destroyed and re-created with a shift in the spanwise direction. Depending on the streamwise extent of the domain, these shifts are either regular in direction and distance, and periodic in time, or irregular in space and erratic in time. In all cases, the same clear regeneration mechanism of streaks and vor- tices is identified, bearing strong similarities with the classical self-sustaining cycle in near-wall turbulence. Bifurcations from periodic to chaotic regimes are studied by varying the streamwise length of the (periodic) domain. The resulting bifurcation diagram contains a number of phenomena, e.g. multistability, intermittency and period doubling, usually investigated in the context of low-dimensional systems. The second part is concerned with spatio–temporal aspects of turbulent ASBL in large domains near the onset of sustained turbulence. Adiabatically decreasing the Reynolds number, starting from a fully turbulent state, we study low-Re turbulence and events leading to laminarisation. Furthermore, a robust quantitative estimate for the lowest Reynolds number at which turbulence is sustained is obtained at Re <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Capprox" /> 270. / <p>QC 20140213</p>

This thesis project aims to advance the modelling of pressure gradient turbulent boundary layers (PG TBLs) and offer new insights into TBLs modelling. Previous analytical studies have explored various mathematical models, but this research introduces an extended unstacked Deep Operator Networks (DeepONets) architecture with double outputs and five branch parameters. The objective is to capture the mean velocity and Reynolds stress of turbulent boundary layers under pressure gradients. Numerical and experimental datasets of PG TBLs were accessed and utilized to train the DeepONets models. These models successfully predicted the mean velocity and Reynolds stress profiles using outer-scaled parameters. The DeepONets effectively learned the operator that describes the desired profiles based on input parameters, which correspond to the development of boundary layer thickness and pressure gradients. To identify the model with the best prediction performance, error statistics and distribution were examined across different configurations and dimensions. Furthermore, the individual and global sensitivity analyses revealed the relationship between input parameters and their influence on modelling PG TBLs with DeepONets.