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The current paradigm in the lens distortion characterization industry is to use simple radial distortion models with only one or two radial terms. Tangential terms and the optimal distortion centre are also seldom determined. Inherent in the models currently used is the assumption that lens distortion is radially symmetrical. The reason for the use of these models is partly due to the perceived instability of more complex lens distortion models. This dissertation shows, in the first of its three hypotheses, that higher order models are indeed beneficial, when their parameters are determined using modern numerical optimization techniques. They are both stable and provide superior characterization. Although it is true that the first two radial terms dominate the distortion characterization, this work proves superior characterization is possible for those applications that may require it. The third hypothesis challenges the assumption of the radial symmetry of lens distortion. Building on the foundation provided by the first hypothesis, a sample of lens distortion models of similar and greater complexity to those found in literature are modified to have a radial gain, allowing the distortion corrections to vary both with polar angle and distance from the distortion centre. Four angular gains are evaluated, and two provide better characterization. The elliptical gain was the only method to both consistently improve the characterization and not ‘skew’ the corrected images. This gain was shown to improve characterization by as much as 50% for simple (single radial term) models and by 7% for even the most complex models. To create an undistorted image from a distorted image captured through a lens which has had its distortion characterized, one needs to find the corresponding distorted pixel for each undistorted pixel in the corrected image. This is either done iteratively or using a simplified model typically based on the Taylor expansion of a simple (one or two radial coefficients) distortion model. The first method is accurate yet slow and the second, the opposite. The second hypothesis of this research successfully combines the advantages of both methods without any of their disadvantages. It was shown that, using the superior characterization of high order radial models (when fitted with modern numerical optimization methods) together with the ‘side-effect’ undistorted image points created in the lens distortion characterization, it is possible to fit a ‘reverse’ model from the undistorted to distorted domains. This reverse characterization is of similar complexity to the simplified models yet provides characterization equivalent to the iterative techniques. Compared to using simplified models the reverse mapping yields an improvement of more than tenfold - from the many tenths of pixels to a few hundredths. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

An increased understanding of how inlet flow distortion affects transonic fans enables improved fan design and performance prediction. Inlet distortion refers to non-uniformities in the incoming flow properties. Complex inlet ducts in high performance aircraft result in distorted flow at the fan inlet. In this thesis, two studies were performed using Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations. The first study focused on understanding how the transition abruptness between the clean and distorted sector in the inlet Pt profile as well as the circumferential extent of the distorted sector affect distortion transfer and generation through a transonic fan. Simulations on two main distortion sector sizes were carried out. For each sector size, variants with decreasing levels of transition abruptness were applied to the inlet of fan. Simulations were conducted at various operating points, ranging from choke to near-stall. Fourier-based distortion descriptors were used to quantify levels of distortion transfer and generation at various axial locations. It is shown that variations in rotor incidence occur as a result of the applied Pt distortion at the inlet. A less abrupt transition diminishes the local extrema in rotor incidence, which in turn reduces the amount of distortion transfer and generation through the rotor. The near-stall condition is affected most of all operating points considered, with a 23.4% average reduction in the amount of distortion transfer at any span. The size the inlet distorted sector affects the amount of distortion transfer and generation, particularly at the near-stall operating point. This is shown to be due to the dynamic response of the fan. The second study compared the mechanisms of stall inception for cases of both clean and distorted inlet flow. In each instance, the mechanism of stall inception is shown to be interactions between the detached bow shock and the tip clearance vortex. These interactions result in the formation of two vortices within the blade passage. The location and strength of these vortices affect the LE spillage in the adjacent blade rows. Stall inception occurs when the bow shock has moved far enough upstream to allow the resultant vortices from shock/tip clearance vortex interaction to pass in front of the leading edge. When inlet distortion is present, mass redistribution upstream of the fan results in variations in rotor incidence. Within the high incidence region, the bow shock is detached 3.9%-8.1% chord more than the clean inlet case, making LE spillage more severe. The rotating stall cell grows out of the stalled passages present at the near-stall operating point and ultimately extends 180° circumferentially and 18.7% span radially. Understanding the effects of distortion on the mechanisms of stall inception will allow appropriate steps to be taken to extend the stable operating range of modern commercial and high performance fans.

Inlet total pressure non-uniformities in axial flow fans and compressors can contribute to the loss of component structural integrity through high cycle fatigue (HCF) induced by the excitation of blade vibratory modes. As previous research has shown total pressure distortion to be the dominant HCF driver in aero engines [Manwaring et al, 1997], an understanding of its transfer through, and impact on, subsequent turbomachine stages and engine components is an important topic for assessment. Since current modeling techniques allow for total pressure distortion magnitudes to be directly related to blade vibratory response, the prediction of downstream distortion patterns from an upstream measurement would allow for the inference of the vibratory response of downstream blade rows to an inlet total pressure distortion. Nonlinear Volterra theory can be used to model any periodic nonlinear system as an infinite sum of multidimensional convolution integrals. A semi-empirical model has been developed using this theory by assuming that a distortion waveform is a periodic signal that is being presented to a nonlinear system, the compressor being the system. The use of Volterra theory in nonlinear system modeling relies on the proper identification of the Volterra kernels, which make up the transfer function that defines the system's impulse response characteristics. Once the kernels of a system are properly identified, the system's response can be calculated for any arbitrary input. This model extracts these kernels from upstream and downstream total pressure distortion measurements of a transonic rotor of modern design. The resulting transfer function is then applied to predict distortion transfer at new operating points on the same rotor and compared with the measured data. The judicious choice of distortion measurement data allows predictions of the downstream distortion content based on a measured non-uniform inlet flow at conditions different from those at which the transfer function was derived. This allows for the determination of downstream total pressure distortion that has the potential to excite blade vibratory modes that could lead to HCF under operating conditions other than those at which the data was taken, such as varying inlet distortion patterns, mass flow settings, rotational speeds, and inlet geometry. This report presents the creation of a Volterra model in order to predict distortion transfer in axial flow fans and compressors. This model, in three variations, is applied to a variety of distortions and compressor operating conditions as measured in the ADLARF tests at the Compressor Research Facility. Predictions are compared with data from the test and final results are also compared with two previous studies conducted at Virginia Tech using the same experimental data. Using the Volterra model it is shown that, with appropriate limitations, distortion transfer can be predicted for flow conditions different from those used for calibration. The model is considered useful for both performance and HCF investigations. / Master of Science

Jet engines operate by ingesting incoming air, adding momentum to it, and exhausting it through a nozzle to produce thrust. Because of their reliance on an inlet stream, jet engines are very sensitive to inlet flow nonuniformities. This makes the study of the effects of inlet nonuniformities essential to improving jet engine performance. Swirl distortion is the presence of flow angle nonuniformity in the inlet stream of a jet engine. Although several attempts have been made to accurately reproduce swirl distortion profiles in a testing environment, there has yet to be a proven method to do so. A new method capable of recreating any arbitrary swirl distortion profile is needed in order to expand the capabilities of inlet distortion testing. This will allow designers to explore how an engine would react to a particular engine airframe combination as well as methods for creating swirl distortion tolerant engines. The following material will present such a method as well as experimental validation of its effectiveness. / Master of Science

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Statement of the problem: Conventional techniques for implant framework fabrication have been shown to produce errors that are inconsistent with the passive-fit requirement for osseointegrated implant frameworks. Purpose: The aim of this study was to assess the three-dimensional distortion inherent in casting of full arch, screw-retained titanium implant frameworks. Materials and methods: A conventional commercial laboratory one-piece casting, using the lost-wax technique was used. Five wax patterns were fabricated on a die-stone cast poured from a plaster impression of a five-fixture brass analogue. A reflex microscope was used to determine the three-dimensional casting error, by measuring horizontal and vertical distances for each wax pattern and its corresponding cast titanium framework, as well as offset distances from the horizontal reference plane. Results: Significant differences were found in the amount of distortion between wax patterns and cast frameworks, with the castings being approximately 416 μm to 477 μm larger than the wax frameworks. The greatest amount of distortion occurred at the terminal implant abutments, and in the vertical dimension. However, there was inconsistency in these differences, indicating the three-dimensional nature of the overall distortion of the cast frameworks. Conclusions: It is doubtful whether any conventionally cast framework can be made to the degree of accuracy required to fit passively on its abutments because of the multiple variables inherent in this process. It is therefore recommended that all full-arch, cast titanium frameworks be cast in sections, or alternatively be sectioned, indexed and soldered before being seated intraorally.