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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

Effects of Manufacturing Deviations on Core Compressor Blade Performance

De Losier, Clayton Ray 20 April 2009 (has links)
There has been recent incentive for understanding the possible deleterious effects that manufacturing deviations can have on compressor blade performance. This is of particular importance in today's age, as compressor designs are pushing operating limits by employing fewer stages with higher loadings and are designed to operate at ever higher altitudes. Deviations in these advanced, as well as legacy designs, could negatively affect the performance and operation of a core compressor; thus, a numerical investigation to quantify manufacturing deviations and their effects is undertaken. Data from three radial sections of every compressor blade in a single row of a production compressor is used as the basis for this investigation. Deviations from the compressor blade design intent to the as-manufactured blades are quantified with a statistical method known as principle component analysis (PCA). MISES, an Euler solver coupled with integral boundary-layer calculations, is used to analyze the effects that the aforementioned deviations have on compressor blade performance when the inlet flow conditions produce a Mach number of approximately 0.7 and a Reynolds number of approximately 6.5e5. It was found that the majority of manufacturing deviations were within a range of plus or minus 4 percent of the design intent, and deviations at the leading edge had a critical effect on performance. Of particular interest is the fact that deviations at the leading edge not only degraded performance but significantly changed the boundary-layer behavior from that of the design case. / Master of Science
32

Characterization and simulation of the mechanical forces that control the process of Dorsal Closure during Drosophila melanogaster embryogenesis / Caractérisation et Simulation des forces mécaniques contrôlant le processus de Fermeture Dorsale durant l'embryogénèse de la drosophile

Dureau, Maxime 29 June 2015 (has links)
Le travail de thèse présenté ici vise à caractériser et simuler les forces mécaniques impliquées dans le processus de fermeture dorsale chez l’organisme Drosophila melanogaster. Ce processus participe à l’acquisition par l’embryon de sa forme finale. Ainsi, l’objectif du travail présenté ici est d’approfondir nos connaissances sur la mécanique des tissus,ainsi que sur leur rôle dans l’embryogenèse.La fermeture dorsale est un processus similaire à la cicatrisation, dans lequel la fermeture du trou dorsal est réalisée par l'amnioséreuse, qui couvre le trou dorsal, et la rangée la plus dorsale des cellules de l'épiderme: les leading edge cells.Une partie du travail présenté ici étudie aussi les mouvements des cellules du leading edge,dans le but de comprendre l’effet du câble d’actine sur la dynamique de la fermeture dorsale.Un algorithme permettant de détecter les contours des cellules, leur position ainsi que celle de leurs jonctions multiples a été développé, ainsi qu'un interface utilisateur.Différents modèles dynamiques ont ensuite été construits, prenant en compte différents comportements mécaniques, selon l’approche lagrangienne. Les systèmes d’équations ont été résolus numériquement, et leurs prédictions comparées aux données biologiques selon l’approche des moindres carrés. Les résultats ont été validés par le test de la fonction d’auto corrélation.Les résultats présentés dans cette thèse nous permettent de mieux comprendre les processus mécaniques impliqués dans les oscillations des cellules de l’amnioséreuse. Ils nous donnent aussi des indices sur leurs caractéristiques biologiques. Ils nous permettent enfin de mieux appréhender le rôle du cabled’actine dans ce processus. / The work presented here aims at characterizing and simulating the mechanical forces involved in the process of Dorsal Closure in the organism Drosophila melanogaster, an embryonic process. In particular, Dorsal Closure participates in the acquisition of the final form of the embryo. Therefore, the work presented here aims at fathoming our knowledge on tissues mechanics, as well as their role in the acquisition of shape. The tissues involved in Dorsal Closure are the epidermis and the amnioserosa. At this stage of development, the epidermis surrounds almost all the embryo. Nevertheless, the amnioserosa still covers a large area of the dorsal side called dorsal hole. Hence, Dorsal Closure aims at shutting this hole and joining the lateral sides of the epidermis, in a process similar to wound healing. In order to fuse the two sides of the epidermis on the dorsal line, the epidermis must be drawn dorsalward. This movement is driven by the amnioserosa on the one hand, and by the dorsalmost row of the epidermis (called Leading Edge cells) on the other hand. The latter first form a transcellular Actin Cable around the dorsal hole. The cable, contracting, will reduce the area of the dorsal hole, covered by the amnioserosa. Second, the Leading Edge cells emit protrusions that will attach to the opposite Leading Edge and drag it toward themselves, untill the two sides of the epidermis fuse. These protrusions have a limited range, hence the dragging and fusion only take place at the ends of the dorsal hole (called canthi), where the distance between the two Leading Edges is small enough. The Amnioserosa also drags the epidermis toward the dorsal line. Its cells produce a contractile network. Interstingly, Amnioserosa cells see the area of their top side (apical side) vary in a periodic way. Although these variations have been widely studied, their role in Dorsal Closure remains unknown. This PhD aims at improving our knowledge of the mechanical concepts involved in these oscillations, and to build a physical model representing these movements. The work presented here also studies the movements of the Leading Edge cells, in order to understand the effect of the Actin Cableon the dynamics of Dorsal Closure. In order to study the cells movements and the role of the tissues involved in Dorsal Closure, an algorithm was developped, allowing to detect the cells edges, their position, as well as those of their vertices (multiple junction between three or four cells) and to track them over time. A user interface was also developped, in order to facilitate the adjustment of the parameters allowing the detection, as well as the correction of possible errors. Various dynamical models were then built following the lagrangian approach. The systems of equations deriving from the Euler-Lagrange equations were numerically solved, and their predictions compared to the biological data extracted thanks to the algorithm presented earlier, following the least square approach. The model validation was performed thanks to the autocorrelation function test. Finally, the Leading Edge dynamics was studied characterising the cellular movements at the interface between the epidermis and the amnioserosa. Wild type embryos dynamics were compared to those of mutated embryos showing specific defects in the Actin Cable formation. The results presented in this manuscript allow a better understanding of the processes involved in in Amnioserosa cells oscicllations. They also give clues on their biological characteristics. Finally, they assess the role of the actin cable in this process similar to wound healing.
33

Effects of hole pitch variation on overall and internal effectiveness in the leading edge region of a simulated turbine blade with heat flux measurements

Dyson, Thomas Earl 28 October 2010 (has links)
In this study, the cooling of a simulated blade under increasing pitch between holes was examined. The change in non-dimensional surface temperature, phi, was measured experimentally to quantify this performance loss. This critical quantification of the sensitivity of cooling to pitch between holes has not been studied previously. A range of blowing ratios and angles of attack were tested. Data are presented in terms of the laterally averaged phi, and in terms of the minimum phi, arguably more important from a design perspective. Increasing the pitch 13% produced no measureable change using either parameter. An increase of 26% in pitch produced only a 4% loss in lateral averages, while some hot points dropped by 10%. These small changes are due to compensating effects of increased internal and through-hole convective cooling. A limit to these effects was shown when increasing pitch 53%. While performance loss in the average was still relatively small at 15%, the minimum phi decreased by 27%. Heat flux gauges were used to gather data on the internal and external surface. The internal impingement used in this study represents a more accurate representation of internal cooling for an actual engine part than has been previously studied, providing a starting point for exploring the differences between engine configurations and those generally investigated in the literature. External heat flux measurements were used to measure the ratio of heat flux with and without film cooling. These results call into question the use of the net heat flux reduction parameter, which is commonly used to quantify overall film cooling performance. / text
34

The Effect of Leading-Edge Geometry on the Induced Drag of a Finite Wing

January 2019 (has links)
abstract: This study identifies the influence that leading-edge shape has on the aerodynamic characteristics of a wing using surface far-field and near-field analysis. It examines if a wake survey is the appropriate means for measuring profile drag and induced drag. The paper unveils the differences between sharp leading-edge and blunt leading-edge wings with the tools of pressure loop, chordwise pressure distribution, span load plots and with wake integral computations. The analysis was performed using Computational Fluid Dynamics (CFD), vortex lattice potential flow code (VORLAX), and a few wind-tunnels runs to acquire data for comparison. This study found that sharp leading-edge wings have less leading-edge suction and higher drag than blunt leading-edge wings. The blunt leading-edge wings have less drag because the normal vector of the surface in the front section of the airfoil develops forces at opposed skin friction. The shape of the leading edge, in conjunction with the effect of viscosity, slightly alter the span load; both the magnitude of the lift and the transverse distribution. Another goal in this study is to verify the veracity of wake survey theory; the two different leading-edge shapes reveals the shortcoming of Mclean’s equation which is only applicable to blunt leading-edge wings. / Dissertation/Thesis / Masters Thesis Aerospace Engineering 2019
35

New leading/trailing edge modulation strategies for two-stage AC/DC PFC adapters to reduce DC-link capacitor ripple current

Sun, Jing 17 September 2007 (has links)
AC/DC adapters mostly employ two-stage topology: Power Factor Correction (PFC) pre-regulation stage followed by an isolated DC/DC converter stage. Low power AC/DC adapters require a small size to be competitive. Among their components, the bulk DC-link capacitor is one of the largest because it should keep the output voltage with low ripple. Also, the size of this capacitor is penalized due to the universal line voltage application. Synchronization through employing leading edge modulation for the first PFC stage and trailing edge modulation for the second DC/DC converter stage can significantly reduce the ripple current and ripple voltage of the DC-link capacitor. Thus, a smaller DC-link capacitance can be used, lowering the cost and size of the AC/DC adapter. Benefits of the synchronous switching scheme were already demonstrated experimentally. However, no mathematical analysis was presented. In this thesis, detailed mathematical analyses in per-unit quantity are given to facilitate the calculation of the DC-link capacitor ripple current reduction with Leading/Trailing Edge Modulation strategies. One of the limitations of leading/trailing edge modulation is that the switching frequencies of the two stages need to be equal to achieve the best reduction of the DC-link capacitor ripple current. The DC-link capacitor ripple current will become larger if the switching frequency of the DC/DC converter is larger than that of the PFC pre-regulator, which blocks us to employ higher frequency for isolated DC/DC converter to reduce its transformer size. This thesis proposed a new Leading/Trailing Edge Modulation strategy to further reduce the DC-link bulk capacitor ripple current when switching frequency of DC/DC converter stage is twice the switching frequency of PFC stage. This proposed pulse width modulation scheme was verified by simulation. Experimental results obtained through digital control based on FPGA are also presented in this thesis.
36

New leading/trailing edge modulation strategies for two-stage AC/DC PFC adapters to reduce DC-link capacitor ripple current

Sun, Jing 17 September 2007 (has links)
AC/DC adapters mostly employ two-stage topology: Power Factor Correction (PFC) pre-regulation stage followed by an isolated DC/DC converter stage. Low power AC/DC adapters require a small size to be competitive. Among their components, the bulk DC-link capacitor is one of the largest because it should keep the output voltage with low ripple. Also, the size of this capacitor is penalized due to the universal line voltage application. Synchronization through employing leading edge modulation for the first PFC stage and trailing edge modulation for the second DC/DC converter stage can significantly reduce the ripple current and ripple voltage of the DC-link capacitor. Thus, a smaller DC-link capacitance can be used, lowering the cost and size of the AC/DC adapter. Benefits of the synchronous switching scheme were already demonstrated experimentally. However, no mathematical analysis was presented. In this thesis, detailed mathematical analyses in per-unit quantity are given to facilitate the calculation of the DC-link capacitor ripple current reduction with Leading/Trailing Edge Modulation strategies. One of the limitations of leading/trailing edge modulation is that the switching frequencies of the two stages need to be equal to achieve the best reduction of the DC-link capacitor ripple current. The DC-link capacitor ripple current will become larger if the switching frequency of the DC/DC converter is larger than that of the PFC pre-regulator, which blocks us to employ higher frequency for isolated DC/DC converter to reduce its transformer size. This thesis proposed a new Leading/Trailing Edge Modulation strategy to further reduce the DC-link bulk capacitor ripple current when switching frequency of DC/DC converter stage is twice the switching frequency of PFC stage. This proposed pulse width modulation scheme was verified by simulation. Experimental results obtained through digital control based on FPGA are also presented in this thesis.
37

Application of hybrid methods to high frequency aeroacoustics / Application des méthodes hybrides à l'aéroacoustique à haute fréquence

Christophe, Julien 14 September 2011 (has links)
This work proposes to address the computation of flow-generated noise, including the high frequency components in an acceptable computational time, relative to industrial applications. In this framework, hybrid methods based on aeroacoustic analogies are relevant to predict the corresponding sound, in term of computational time and easy implementation, and are separating the sources of sound computation from the sound propagation itself. Both parts of the hybrid method are then investigated.<p><p>Firstly, the sources of sound should be computed accurately, reproducing most of the energy content of the turbulent flow. The present study is mainly based on LES computations, that are a good compromise between the accuracy and the time required to obtain the sources, especially for low Mach number application, where incompressible flow computations can be used. The influence of the computational parameters is then studied through the investigation of the influence of the boundary conditions, flow solver, mesh refinement, LES subgrid-scale model and computational domain definition. <p><p>Secondly, the sound sources propagation is computed using classical analogies based most of the time on free field Green's functions. They are limited to the low frequency range of the emitted sound spectrum, where the source is compact, if incompressible acoustic sources are used. They are then proposed to be combined with Amiet's theory for airfoil noise to cover the remaining high frequency part of the sound spectrum. The limitations of Amiet's theory are analysed through the geometrical and acoustical far-field assumptions. Furthermore, an inverse strip method is proposed to extend Amiet's theory to spanwise varying flow conditions and taking correctly into account the spanwise wave number effects. <p><p>The leading-edge noise mechanism is studied through the interaction of the turbulent region of a jet with a NACA0012 airfoil. The hybrid method, consisting in an incompressible LES computation combined with Curle's analogy, showed its limitation to the low frequency range of the sound spectrum when low-order CFD are used. The Amiet's theory, based on the modelisation of the upstream velocity spectrum, provides a good sound prediction at high frequency, as far as the airfoil thickness is accounted for. <p><p>The Trailing-edge noise mechanism is studied through the flow around a mid-span cut of a blade (CD airfoil) of an automotive cooling fan. <p>Three different acoustic methods are used :Curle's analogy is using wall-pressure fluctuations over the airfoil surface, Ffowcs-Williams and Hall's analogy is using volumetric velocity informations around the trailing-edge and Amiet's theory for trailing-edge noise is using the wall-pressure spectrum around the trailing-edge and the corresponding spanwise correlation. The methods using wall-pressure informations are shown to directly transfer the informations of the wall-pressure spectrum to the sound spectrum. Differences are appearing in the higher frequency range where the airfoil starts to be non compact, invalidating the use of Curle's analogy at such frequencies compared to the other methods, taking scattering effects into account implicitly in their formulations. <p><p>Finally, in order to reduce the computational cost, Amiet's theory for trailing-edge noise is proposed to be driven from steady RANS computations. Two methods to compute the wall-pressure spectrum from boundary-layer informations are studied. Their respective robustness and reliability are analysed in an uncertainty quantification framework, in case of varying velocity profiles upstream the airfoil. Both models showed similar results and tendency compared to the wall-pressure LES spectrum, as far as the flow topology remains similar. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished
38

Prediktivt underhåll för turbinblad till vindkraftverk / Predictive maintenance of turbine blades for wind turbines

Skilje, Kristoffer January 2023 (has links)
Rapporten behandlar problemen med drift- och underhåll på vindkraftverk och hur man kan minska behovet av dessa genom övervakning av vindkraftverkens tillstånd. Målet med rapporten är att undersöka om det går att förutse när och hur ett vindkraftverk kommer behöva underhållas, samt beskriva de metoder som används för att förhindra slitage av turbinbladen. Forskningsfrågor som behandlas inkluderar tillståndsövervakning av vindturbiner och vilka metoder som används för att undvika slitage på turbinbladen. Arbetet kommer att utföras som en litteraturstudie eftersom det inte är möjligt med fältstudier av vindkraftverk. Viktiga frågor som besvaras är vilka faktorer som orsakar erosion och hur det leder till minskad effektivitet och produktionskapacitet hos vindkraftsparker. Vidare tas det upp hur underhåll utförs på vindkraftverken idag och hur det kan komma att ske i framtiden, med fokus på tillståndsövervakande system och olika skyddslösningar. Även skillnaden mellan landbaserad och havsbaserad vindkraft tas upp, samt olika stadier av erosionsutbredningen på turbinbladen och hur de påverkar energiproduktionen. Slutligen diskuteras olika lösningar för att minska sannolikheten för erosion, såsom att minska maxhastigheten under otjänligt väder. För havsbaserade vindkraftverk finns det svårigheter vad gäller byggande och underhåll, men fördelar som bättre vindförhållanden och möjlighet att bygga på djupare vatten. Flytande vindkraftverk används för att möjliggöra placering på djupare vatten och längre bort från land. Framtida vindkraftverk kommer ha större turbiner och högre torn, samtidigt som minskningar av energikostnaderna för både land- och havsbaserad vindkraft är trolig. SeaTwirl har en revolutionerande design där bladet roterar genom vertikalplanet, vilket minskar effekterna av erosionsbaserade skador som regndroppar och partiklar kan påföra. Dessa flytande vindkraftverk som är tänkta att placeras på havsytan har en relativt låg kostnad, lägre underhållsbehov och lägre materialåtgång, vilket gör dem konkurrenskraftiga. Framtida utveckling finns i form av exempelvis SR Energy som börjat dela ut "vindbonus" till de som bor nära vindkraftsparker. Ytterligare ett exempel är Modvion som använder trälaminat istället för stålkonstruktioner, vilket möjliggör enklare konstruktion, kräver färre inspektioner och material kan vid avveckling återanvändas vid husbyggen. / The report addresses the issues of operation and maintenance of wind turbines and how their need can be reduced through monitoring the condition of wind turbines. The aim of the report is to investigate whether it is possible to predict when and how a wind turbine will need to be maintained, as well as describe the methods used to prevent wear of the turbine blades. Research questions that are addressed include condition monitoring of wind turbines and the methods used to avoid wear on turbine blades. The work will be carried out as a literature study since it is not possible to do field studies of wind turbines. Important questions that are answered include what factors cause erosion and how it leads to reduced efficiency and production capacity of wind farms. Furthermore, it is discussed how maintenance is currently carried out on wind turbines and how it may be done in the future, with a focus on condition monitoring systems and various protective solutions. Also, the difference between land-based and offshore wind power is discussed, as well as different stages of blade erosion and how they affect energy production. Finally, different solutions to reduce the likelihood of erosion are discussed, such as reducing the maximum speed during inclement weather. For offshore wind turbines, there are difficulties with construction and maintenance, but advantages such as better wind conditions and the ability to build in deeper water. Floating wind turbines are used to enable placement in deeper water and farther from shore. Future wind turbines will have larger turbines and higher towers, while reducing energy costs for both land and offshore wind power is likely. SeaTwirl has a revolutionary design where the blade rotates through the vertical plane, which reduces the effects of erosion-based damage that raindrops and particles can cause. These floating wind turbines that are intended to be placed on the ocean surface have a relatively low cost, lower maintenance needs, and lower material consumption, making them competitive. Future developments include, for example, SR Energy, which has started to distribute "wind bonuses" to those who live near wind farms. Another example is Modvion, which uses wooden laminate instead of steel structures, enabling simpler construction, requiring fewer inspections, and allowing material reuse in building construction.
39

Framtagning av testrigg för att testa regnerosion på vindturbinblad / Development of a test rig for testing rain erosion on wind turbine blades

Arvidsson Lindbäck, Nils, Johansson, David January 2023 (has links)
Bakgrunden till projektet är problem med kanterosion av turbinblad inom vindkraftverks- industrin. Det är ett fenomen som uppstår när turbinblad roterar i höga hastigheter och träffar partiklar, främst vattendroppar i regn. Denna erosion skadar turbinbladen, vilket både minskar vindkraftverkens effektivitet och sprider partiklar i den lokala miljön. För att både undersöka detta fenomen och ge möjlighet att utvärdera olika materials motståndskraft mot erosion ska en testrigg tas fram. Utöver detta ska testriggen även möjliggöra uppsamling av partiklar för vidare forskning kring deras effekt på miljön. Som utgångspunkt används en tribometer med rotationsmekanism från ett föregående maskinkonstruktionsprojekt på KTH. Ombyggnationen av denna avgränsas till att endast genomföras digitalt med hjälp av CAD för att hålla mängden arbete till en rimlig nivå. Förutom CAD har arbetet även inkluderat kravspecifikationer, beräkningar i MATLAB, FEA-analyser och kostnadskalkyler. Resultatet är en digitalt styrd testrigg med tillhörande komponentlista och instruktioner för tillverkning och genomförande. Inköpskostnad för ombyggnationen uppskattas till 28 000 kr. Riggen för en cylindrisk provbit genom ett artificiellt regn i hög hastighet, vilket resulterar i en accelererad nötningsprocess. Under testets gång dokumenteras erosionen visuellt med hjälp av en kamera och efter testet kan mängden förlorat material mätas i vikt och partiklar samlas upp. Flera andra parametrar dokumenteras automatiskt under testets gång för att ge en mer detaljerad bild av processen och data för undersökningar av repeterbarhet. Slutligen konstateras att testriggen uppnår alla krav ställda på den förutom att den inte har en nödbroms. Avsaknaden av nödbroms diskuteras och det leder till slutsatsen att testriggen, även utan nödbroms, är fullt fungerande, enkel och säker att använda. / The background for this project is a problem in the wind turbine industry, namely leading edge erosion of turbine blades. This occurs when wind turbine blades rotate at high speeds and collide with particles, mainly water drops in rain. This erosion damages the turbine blades, reducing the efficiency of the wind turbines and releasing particles into the local environment. To investigate this phenomenon and evaluate the durability of different materials, a test rig is to be developed. In addition, the test rig will enable the collection of particles to facilitate further research into their environmental impact. A tribometer with a rotation mechanism from a previous project at KTH serves as the starting point. The reconstruction of this tribometer is limited to a digital implementation using CAD to keep the amount of work at an appropriate level. In addition to CAD, the work has also included requirements specifications, calculations in MATLAB, FEA, and cost estimates. The result is a digitally controlled test rig with an accompanying component list and instructions for manufacturing and implementation. The estimated purchase cost for the reconstruction is 28,000 SEK. The rig tests a cylindrical sample by propelling it at high speed through artificial rain, resulting in an accelerated wear process. The erosion is visually documented using a camera during the test. Afterwards the amount of lost material can be measured by weight and the particles collected. Several other parameters are automatically recorded during the test to provide a more detailed picture of the process and data for investigations into repeatability. Finally, it is concluded that the test rig meets all its requirements except for the absence of an emergency brake. The absence of an emergency brake is discussed, leading to the conclusion that despite missing an emergency brake, the test rig is fully functional, easy to use, and safe.
40

Investigations of Partially Immersed Spinning Spheres in a Liquid Bath and Butterfly Flight

Langley, Kenneth Roy 21 March 2013 (has links) (PDF)
This thesis examines two important problems in fluid dynamics: that of a partially immersed sphere spinning in a bath of liquid and the measurement of flow velocities around a free flying butterfly. Although the actual problems are quite different, each problem incorporates many of the same principles and techniques. When a hard-boiled egg spins through a pool of milk on the kitchen counter, the milk rises up the sides of the egg and droplets are ejected. This phenomenon occurs when any partially submerged object whose radius increases upward from the fluid surface (e.g., spheres, inverted cones, rings, etc.), spins in a shallow bath of fluid. The fluid ejects from the surface at the maximum diameter in one of three ejection modes: jets, sheets, or sheet breakup. Additionally, a surprisingly large flow rate is induced by the spinning object. Spheres are used in this study to determine the effects of experimental parameters on the induced flow rate. High-speed imaging is used to experimentally characterize the modes of ejection and measure sheet breakup distance and velocities of liquid within liquid sheets. A theoretical model is derived using an integral momentum boundary layer analysis both beneath the free surface and in the thin film attached to the sphere. Experimental results are presented in comparison with predicted behavior with good agreement. The suitability of using a spinning sphere as a pump is also discussed. Second, the use of PIV to measure flow velocities around living species is becoming more widely adopted. Current efforts are starting to measure 3D, time-resolved velocities around insects in tethered flight. This work investigates the use of Synthetic Aperture PIV (SAPIV) in obtaining 3D, time-resolved volumetric velocity fields around a painted lady butterfly in free flight. Results are presented from several time steps during both the down stroke and upstroke of the butterfly showing the development of the leading edge vortex. The velocity field results have limited spatial resolution; however, the results show that SAPIV has potential in further investigating these flow structures. The reconstructed visual hull of the butterfly is also discussed.

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