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Thesis (M.S.)--University of Wisconsin--Madison, 1962. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 68-69).

The broad aim of the work presented in this thesis is to investigate the wake of an airfoil under the combined effects of streamwise curvature and pressure gradient. This was accomplished by an experimental investigation using hot-wire anemometry and large eddy simulation (LES). The wake was generated by placing a NACA 0012 airfoil in a uniform stream of air, which is then subjected to an abrupt 90o curvature created by a duct bend. The experimental work was conducted in a subsonic open-return type wind tunnel. The test section measured 457 mm × 457 mm in cross-section and consisted of a 90o bend with radius-to-height ratio of 1.17. The symmetrical airfoil was of chord length (c) 150 mm, and its trailing edge was located one chord length upstream of the bend entry. The effects of airfoil angle of attack and mainstream velocity on the mean velocity and turbulence quantities of the near-wake were examined. In addition, the mean velocity and turbulence intensity profiles of the boundary layer on the upper surface of the airfoil were measured. In the numerical investigation, the three-dimensional, incompressible turbulent flow in the duct was computed using the finite volume method. The effect of modelling parameters, namely, grid resolution and sub-grid scale (SGS) model were studied. Three different sub-grid scale models were employed, namely, the classical Smagorinsky, its dynamic variant (DSMG) and the dynamic kinetic energy transport. The effect of grid resolution was assessed by conducting simulations with the DSMG model on three different grids. The first two grids incorporated the full spanwise extent of the duct (3c), and the third grid comprised a reduced spanwise segment (0.5c) with periodic conditions set in the spanwise direction. A bounded central differencing scheme was employed for the discretization of the convection terms. The temporal discretization was by a second-order implicit method that incorporated a forward difference approximation. The performance of LES in depicting the experimental flow was assessed and compared with the results predicted by the Reynolds Stress Model. The experimental profiles at zero angle of attack revealed the differing effects of curvature on the mean and turbulence quantities in the inner-side and outer-side of the wake. The spanwise distributions of mean velocity and turbulence intensity, in the near-wake, indicated variations with identifiable peaks and troughs which corresponded to the presence of streamwise vortices in the wake. The spanwise variations were larger on the inner side of the wake and significantly reduced on the outer side. The results showed that close to the trailing edge, the dominant effect on the wake was from the airfoil boundary layer, whereas one chord length downstream of the trailing edge, it was the effect of curvature and pressure gradient from the duct which was dominant. The results from the numerical study showed the advantages of LES over Reynolds-averaged Navier-Stokes methods in predicting separation on the convex wall of the bend on relatively coarse grids, but also shortcomings in the prediction of the wake parameters. The dynamic variants of the SGS models were more accurate in predicting the flow in the wake. On a considerably finer grid with near-wall airfoil grid spacings of Δx+ < 80, Δy+ < 0.5, and 20 < Δz+ < 50, LES resulted in much improved comparisons with the experimental data. The improved prediction of the wake parameters was attributed to the improved simulation of the boundary layers on the upper surface of the airfoil. However, the effect of the reduced spanwise extent resulted in a lack of prediction of separation on the convex wall of the duct.

<p>The purpose of this thesis was to study the influence of manufacturing variations on gear performance. The manufacturing variations inherent in different manufacturing methods were studied to include the effect of real surfaces. Real surfaces have surface irregularities at least on some scale, which can significantly influence how loads are transmitted at the gear contact. To some extent, the lubricant design can help to prevent contact that could lead to tooth failures by forming a protective surface boundary layer. An experimental study was used to consider the compositions of these layers with a surface analysis method.</p><p>In Paper <strong>A</strong> a robust design approach was used to find out to what extent the current standard for calculation of surface durability treats manufacturing variations and the choice of lubricant. The results show that the simplest calculation method used is not enough to predict the effect of these on surface durability. Additionally, the standard quality levels are poorly incorporated in the standard calculating procedures for surface durability, and the quality of the gear tooth is restricted to include only a few parameters.</p><p>In Paper <strong>B</strong> a pin-on-disc machine was used to evaluate the tribofilm formation by the additives and the corresponding wear occurring in the boundary lubrication regime in environmentally adapted lubricants. Studies of the additive and base fluid interaction were carried out using glow discharge-optical emission spectroscopy. It was found that the chemically reacted surface boundary layers played an important role in terms of wear. More specifically, the oxide layer thickness had significant influence on wear. The findings also demonstrate the complexity of lubrication design formulations coupled to these layers. For example, it was found that the pre-existing surface boundary layer (before any lubricant had been added) played an important role in allowing the lubricant to react properly with the surfaces.</p><p>The aim of Paper <strong>C</strong> was to contribute to the knowledge of how different surface topographies, tied to manufacturing methods, influence the early life contact conditions in gears. Topographical measurements of differently manufactured tooth flanks were used as data input to a contact analysis program. The variation in surface topography inherent in the manufacturing method was found to have a strong influence on the contact area ratio.</p>

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This thesis aims to contribute to the understanding of transitional flows in the blade boundary layers of axial compressors. Two experiments are described, the first examining in detail the transitional boundary layer on a simulated controlled-diffusion blade and the second surveying the mid-height flowfield in an embedded stage of a low-speed axial compressor. The velocity distribution on the simulated blade is identical to the Velocity distribution on the suction surface of the blades in the axial compressor. At 2 Reynolds numbers and 3 levels of freestream turbulence, a single hot wire was used to conduct a boundary layer survey on a simulated controlled-diffusion blade. Integral parameters of the boundary layers are explored to dene the length and nature of transition. At low Reynolds number there is a separated or near separated region at the leading edge which does not lead to turbulence. Transition covers a length of approximately 20% of the blade chord, starting between 20% and 30% chord. The position of transition is strongly influenced by the level of freestream turbulence. Most of the transition process occurs within the decelerating flow region which exists from 20% of the chord. At high Reynolds number, a leading edge separation bubble leads to transition within 2% of the blade chord. Abu-Ghannam & Shaws correlation for the start and length of transition was found to predict the start of transition well for attached flows, but could not be relied upon for separated flows. It is apparent that the correlation was not designed for the very strong Velocity gradients in the leading edge region, and probably not for separated flow. _ Three flow conditions in the axial compressor were used: design speed, peak efficiency, low Reynolds number at peak efficiency (the machine was slowed to one-quarter speed) and design speed near the stall. Using hot wires at mid-height, axial and circumferential velocity and turbulence information was obtained. Wakes and structure within wakes are visible in the turbulence and Reynolds stress distributions. The wakes of more than one upstream blade row are visible; the region where two wakes intersect gives some information about interaction between a stator blade Wake and a rotor blade boundary layer. Some information is available about the length scale 'distribution inside and outside wakes. Secondary flow in the axial-circumferential plane shows motion within wakes and a vortex in the near-stall flowfield, shed preferentially at one point in the blade-passing cycle.

During take-off, the aerodynamic performance of a transonic engine intake is dominated by the flow-field over the nacelle lower lip, around which the flow might accelerate to supersonic speeds. A shock wave might appear and impinge on the incoming boundary layer. Flow separation may result from this interaction, leading to severe flow distortion. In order to maximise fuel efficiency by reducing aerodynamic drag, slimmer nacelle designs are currently being pursued by manufacturers. Understanding the impact of design choices on the development of shock-wave boundary layer interactions (SBLI) is crucial, as these phenomena have a severe effect on the stability of the flow inside the nacelle. The available literature is rather scarce and unable to assess the nature and severity of SBLIs, which remain to be addressed in the context of nacelles at incidence. To address this shortcoming, a novel experimental rig has been designed exclusively to assess the detrimental effects resulting from shock-induced separation for a number of intake lip shapes and inflow conditions. For the reference intake shape, the flow field around the lower lip during on-design take-off conditions was found to be relatively benign, with minimal shock-induced separation. As incidence is increased by 2◦, from the reference incidence of 23◦, this separation gets noticeably larger and unsteadiness develops. The downstream boundary layer is more distorted and reflects the losses across the interaction. This is exacerbated at even higher incidence. Increasing the mass flow rate over the lip up to 15% of the initial value had only minor effects on performance. The parametric investigation revealed a significant effect of lip shape on the position and severity of the SBLI. In particular, a slimmer nacelle performed poorly, favouring shock development very close to the lip nose and promoting large scale separation as the incidence increases. From correlation studies based on the parametric investigation, it appears that the extent of shock-induced separation is the main factor affecting the aerodynamic performance. Somewhat surprisingly, this was found to be independent of shock strength but potentially related to the severity of the diffusion downstream of the shock. Alongside delaying flow reattachment, this diffusion is also likely to have a direct detrimental effect on the boundary layer development close to the engine fan.

The main focus of this work was to investigate the nature of unsteady boundary-layer development over finite domains, with the behaviour of the boundary layer on a rotating sphere in an unbounded, rotating fluid used as a prototype. The sphere and its surrounding fluid are assumed to be initially rotating as a solid body, and the evolution of a boundary layer on the sphere is analysed in cases where the sphere has been smoothly slowed, or brought to a state of rotation in an opposite sense to its initial conditions. It may be seen that a characteristic property of this flow is that the boundary layer is bi-directional; over most of the streamwise domain for the flow, whether the flow is positive or negative in the streamwise coordinate direction depends on the transverse location being considered. This fact leads to challenges in the numerical evaluation of the flow field due to the parabolic nature of the boundary-layer equations. A further consideration is the implication that these regions of reversed flow cause the flow field to contain minima and maxima in the streamwise velocity component. This has been shown in a little-known study by Cowley et al. (1985) to cause the boundary layer to become susceptible to asymptotically short-scale perturbations with large frequencies. The unsteady boundary layer on a rotating sphere under these conditions is consequently shown to be extremely challenging to compute numerically. It is also found that using local approximations at the ends of the finite domain, which in the case of the sphere are the pole and equator, to investigate the two-dimensional boundary layer can cause difficulties, as in some cases there exist steady, spatial perturbations to a boundary-layer state which introduce short spatial scales. The instabilities and other features analysed in this work are framed largely in the context of the rotating sphere, but the causes of the phenomena are found to be sufficiently generic that they may be observed in other physical contexts. To demonstrate this, the shallow katabatic flow down a cooled slope is briefly investigated, and the above mathematical features are again uncovered.

The boundary layer problems in periodic homogenization arise naturally from the quantitative analysis of convergence rates. Formally they are second-order linear elliptic systems with periodically oscillating coefficient matrix, subject to periodically oscillating Dirichelt or Neumann boundary data. In this dissertation, for either Dirichlet problem or Neumann problem, we establish the homogenization results and obtain the nearly sharp convergence rates, provided the domain is strictly convex. Also, we show that the homogenized boundary data is in W1,p for any p ∈ (1,∞), which implies the Cα-Hölder continuity for any α ∈ (0,1).