Erosion and deposition in gas turbine engines are functions of particle/wall interactions and the Coefficient of Restitution (COR) is a fundamental property of these interactions. COR depends on impact velocity, angle of impact, temperature, particle composition, and wall material. In the first study, a novel Particle Tracking Velocimetry (PTV) / Computational Fluid Dynamics (CFD) hybrid method for measuring COR has been developed which is simple, cost-effective, and robust. A Laser-Camera system is used in the Virginia Tech Aerothermal Rig to measure microparticles velocity. The method solves for particle impact velocity at the surface by numerical methods. The methodology presented here characterizes a difficult problem by a combination of established techniques, PTV and CFD, which have not been used in this capacity before. The current study characterizes the fundamental behavior of sand at different impact angles. Two sizes of Arizona Road Dust (ARD) and one size of Glass beads are impacted on to 304-Stainless Steel. The particles are entrained into a free jet of 27m/s at room temperature. Mean results compare favorably with trends established in literature. This technique to measure COR of microparticle sand will help develop a computational model and serve as a baseline for further measurements at elevated, engine representative air and wall temperatures. In the second study, ARD is injected into a hot flow field at temperatures of 533oK, 866oK, and 1073oK to measure the effects of high temperature on particle rebound. The results are compared with baseline measurements at ambient temperature made in the VT Aerothermal Rig, as well as previously published literature. The effects of increasing temperature and velocity led to a 12% average reduction in total COR at 533oK (47m/s), a 15% average reduction at 866oK (77m/s), and a 16% average reduction at 1073oK (102m/s) compared with ambient results. From these results it is shown that a power law relationship may not conclusively fit the COR vs temperature/velocity trend at oblique angles of impact. The decrease in COR appeared to be almost entirely a result of increased velocity that resulted from heating the flow. / Ph. D.

Previous work has systematically and numerically demonstrated feasibility and performance benefits of the tension-element concept in golf club heads; however, higher fidelity models needed to be created and validated for this concept. There is a need for more accurate models for this concept to further investigate its performance benefits. Performance is measured in terms of impact efficiency of the ball and head and is referred to as coefficient of restitution (COR). COR is affected by the dynamic effective face stiffness and mass properties of the club. This thesis creates and validates high-fidelity, non-linear, dynamic finite element models for the tension-element golf club concept. These models predicted COR with less than one percent error when compared to dynamic experimentation results.

When a gas turbine operates in a particle laden environment, such as a desert, small solid particles are ingested into the engine. The ingested sand particles can cause damage to engine components and reduce the service life of the engine. Particle ingestion causes the erosion of metal blades and vanes, and, if the firing temperature is hot enough, deposition of molten particles in the hot sections of the engine. Both deposition and erosion phenomena can severely reduce overall engine performance. The Coefficient of Restitution (COR) is a measure of the particle-wall interaction, and has been widely used to quantify particle rebound characteristics in past particle impact studies. This work investigates the effects of temperature on sand particle impact characteristics by measuring the COR and other deposition related impact parameters. The first study presented as part of the dissertation contains a description of a novel method used to measure COR using a Particle Tracking Velocimetry (PTV) method. This is combined with Computational Fluid Dynamics (CFD) flow field to allow for an accurate determination of the particle impact velocity. The methodology described in this paper allows for measurement of the COR in a wide range of test conditions in a relatively simple manner. The COR data for two different sizes of Arizona Road Dust (ARD) and one size of glass beads are presented in this paper. Target material was stainless steel 304 and the impact angle was varied from 25 to 85 degrees. The second study details the first quantification of the COR of san particles at elevated temperatures. Temperatures used in this study were 533 K, 866 K, and 1073 K. In this study the mass flow rate through the experimental setup was fixed. This meant that velocity and temperature were coupled. Target material for this study was stainless steel 304 and the impact angle was varied from 30° to 80°. The COR was found to decrease substantially at the temperatures and velocity increased. It was determined that the decrease in COR was almost certainly caused by the increase in velocity, and not the decrease in temperature. The third study contains COR results at elevated temperatures. Significant improvements from the method used to calculate COR in the first paper are described. The particle used for these tests was an ARD sand of 20-40 μm size. Target materials used were stainless steel 304 and Hastelloy X. The particles impinged on the target coupon at a velocity of 28m/s. Tests were performed at three different temperatures, 300 K (ambient), 873 K, and 1073 K to simulate temperatures seen in gas turbine cooling flows. The angle of impingement of the bulk flow sand on the coupon was varied between 30° and 80°. A substantial decrease in COR was discovered at the elevated temperatures of this experiment. Hastelloy X exhibited a much larger decrease in COR than does stainless steel 304. The results were compared to previously published literature. The final study also used the ARD size of 20-40 μm. The target material was a nickel alloy Hastelloy X. Experiments for this study were performed at a constant velocity of 70m/s. Various temperatures ranging from 1073 K up to and including 1323 K were studied. Particle angle of impact was varied between 30° and 80°. Significant deposition was observed and quantified at the highest two temperatures. The COR of the ARD sand at the highest temperatures was found not to change despite the occurrence of deposition. At elevated temperatures, many of the particles are not molten due to sand's non-homogenous and crystalline nature. These particles rebound from the target with little if any change in COR. / Ph. D.

Many gas turbine engines operate in harsh environments where the engine can ingest solid particles. Particles can accelerate the deterioration of an engine and reduce the engine’s service life. Understanding particle interactions with the materials used in gas turbines, at representative engine conditions, can improve the design and development of turbomachinery operating in particle laden environments. Coefficient of Restitution (COR) is a measure of the particle/wall interactions and is used to study erosion and deposition. This study presents data taken using the Virginia Tech Aerothermal Rig. Arizona Road Dust (ARD) of 20-40 μm is injected into a flow field to measure the effects of temperature and velocity on particle rebound from a polished high temperature material coupon. The high temperature coupon was tested at different temperatures of ambient (300K), 873K, 1073K, 1173 K, 1223 K, 1273 K, and 1323 K while the velocity of the flow field was held constant at 28 m/s or 70 m/s. The impingement angle of the coupon was varied from 30° to 80° for each temperature tested. The results show an increase in deposition as the temperature approaches the melting temperature of sand. The results have also been compared to previously published literature. / Master of Science

Granular media continue to be among the most manipulated materials found in various industries. Particle interactions in granular flow has fundamental importance in analyzing the performance of a wide range of key engineering applications such as hoppers, tumblers, and mixers etc. In spite of such ubiquitous presence, till date, our understanding of the granular flow is very limited. This restricts our ability to design efficient and optimal granular processing equipment. Additionally, the existing design abilities are also constrained by the number of particles to be analyzed, where, a typical industrial application involves millions of particles. This motivated the current research where investigations on the above limitations are pursued from three different angles: experimental, theoretical, and simulation. More specifically, this work aims to study particle-wall interaction and developing a computationally efficient cellular automata simulation framework for industrial granular applications. Towards this end, the current research is divided into two part: (I) energy dissipation during particle-wall interaction (II) cellular automata modeling. In part I, detailed experiments are performed on various sphere-thin plate combinations to measure the coefficient of restitution (COR) which is a measure of energy dissipation and it is one of the most important input parameters in any granular simulation. Alternatively, the energy dissipation measure also used to evaluate the elastic impact performance of superelastic Nitinol 60 material. Explicit finite element simulations are performed to gain detail understanding of the contact process and underlying parameters such as contact forces, stress-strain fields, and energy dissipation modes. A parametric study reveals a critical value of plate thickness above which the effect of plate thickness on the energy dissipation can be eliminated in the equipment design. It is found that the existing analytical expressions has limited applicability in predicting the above experimental and numerical results. Therefore, a new theoretical model for the coefficient of restitution is proposed which combines the effect of plastic deformation and plate thickness (i.e. flexural vibrations). In part II, in order to advance the existing granular flow modeling capabilities for the industry (dry and slurry flows) a cellular automata (CA) modeling framework is developed which can supplement the physically rigorous but computationally demanding discrete element method (DEM). These include a three-dimensional model which takes into account particle friction and spin during collision processing, which provides the ability to handle flows beyond solely the kinetic regime, and a multiphase framework which combines computational fluid dynamics (CFD) with CA to model multi-million particle count applications such as particle-laden flows and slurry flows.

The design of structures and mechanisms subject to impact loading has historically involved designing in such a way as to minimize damage induced by the impact. This has historically been accomplished by absorbing and dissipating the energy of the impact. However, in some applications it is desirable to harness the energy and return it to the impacting object to maximize the coefficient of restitution (COR), resulting in large rebound velocities. The use of traditional rigid-body mechanisms to achieve high-COR mechanisms is limited by issues of friction, durability, poor strain-energy distribution and others. Compliant mechanisms do not possess the same limitations and are well-suited to these types of applications. The principles needed to realize these types of designs are found in existing literature but are confined to very specific applications such as hollow-body golf club heads. The contribution of this thesis is an approach to the generation and evaluation of compliant mechanism concepts for use in impact applications where a high COR is required. This approach is based loosely on common general concept development processes found in literature. This thesis describes the process of including the use of lumped mass or mechanical models, the categorization of strain-energy storage, the use of both closed-form and finite-element static models and the use of dynamic finite-element models to determine if a configuration is eligible to be used in a final design process. This thesis also contributes a case study in the development of configurations for metalwood golf club driver heads.

Rockfalls is a major problem around the world, if they occur in populated areas, they can cause major damage to infrastructure, injure or kill people. For this reason, it is important to be able to predict where the risk of rockfalls and how to prevent and protect populated areas from them. However, it is no easy task to predict rockfalls. Although if an area with potential area for rockfall is localized it may seem easy to construct protective meshing or bolting potential blocks down. But in many cases this is not easy to do due to practical issues or economic reasons, for example in rock cuts on older railways in Sweden. Fall heights from rock cuts like that are not particularly high but the risk of damage to the trains and infrastructure in the track area is high, however, it is unknown how extensive the damage may be. Trafikverket, the Swedish authority responsible for Sweden's roads and railways, has for some years investigated a new method for classifying and minimize the risk of rockfalls from rock cuts next to the railways. This study include aims to include the potential maximum distance of a block from the rockfall can travel to the existing method. This master's work is part of the investigation and will include full scale field test where the rockfalls are examined by filming them and then evaluate the “bounce coefficient”, coefficient of restitution, from the individual rockfalls using photogrammetric methods. During the field study, a geotechnical testing equipment, DCP test rig, to be evaluated for its ability of an easy way in the field to produce an estimated value on the coefficient of restitution. During the evaluation, two rockfall simulating software be used to investigate how well the results from them match the true blocks movements. / Stenras är ett stort problem runtom i världen, om de inträffar i bebyggda områden kan de leda till stora skador på infrastruktur, skador eller dödsfall. Av den anledningen är det viktigt att kunna förutse vart det finns risk för stenras och hur man kan förebygga dem och skydda bebyggda områden från dem. Dock är det ingen lätt uppgift att förutse stenras. Även om det finns ett potentiellt område för stenras kan det tyckas lätt att placera ut skyddsnät eller bulta fast potentiella block. Men i många fall är detta inte praktiskt, eller ekonomiskt, till exempel i bergsskärningar på äldre järnvägar i Sverige. Fallhöjderna här är inte speciellt höga men risken för skador på tåg och infrastruktur i spårområdet är hög, dock är det okänt hur omfattande skadorna kan bli. Trafikverket, den svenska myndigheten som ansvarar för Sveriges vägar och järnvägar, har under flera år utrett en ny metod för att klassificera och minimera riskerna för stenras från bergskärningar bredvid järnvägar. Denna utredning syftar bland annat till att till att väga in det potentiella maximalt avstånd ett block från stenras kan färdas i den befintliga modellen. Det här mastersarbetet är en del i den utredningen och kommer att innefatta ett fullskaligt fältförsök där stenras undersöks genom att de filmas och sedan utvärderas studskoefficienten, coefficient of restitution, från de enskilda rasen i stereo. Under fältstudien kommer en geoteknisk testutrustning, DCP test rigg, att utvärderas för sin förmåga att lätt i fält få fram ett uppskattat värde på studskoefficienten. Under utvärderingen kommer två stenrassimuleringsprogram att användas för att undersöka hur väl de stämmer med de verkliga blockens rörelser.

Solid Energy New Zealand plans to mine a 6 to 10m thick coal seam below the Mt. Augustus and Mt. Fredrick ridgeline at Stockton Mine near Westport, NZ. The coal is covered by up to 30m of overburden, which requires removal to access 4 million tones of high quality coal. However, the Coal Mining Lease boundary (CML) is located just below the basal coal measures and the neighbouring land is owned by the Department of Conservation (DoC). In addition, the neighbouring DoC estate is Powelliphanta Augustus snail habitat. It is necessary to remove the overburden without releasing any material above natural discharge levels onto the DoC land. In order to control the rockfall risk at the site, the largest design-build rockfall protection project in the southern hemisphere was constructed using a high-capacity dynamic rockfall barrier installed along the length of the ridgeline. During the design phase of the project, it was evident that current methods to determine the coefficient of restitution (normal and tangential) are subjectively based on the designer's judgement. Currently, there is limited quantitative information available for the determination of dampening coefficients (restitution coefficients) for use in rockfall computer simulation programs. Accurate parameters are necessary for the design and dimensioning of rockfall protection structures. This project investigates an objective method to calculate these parameters for use in rockfall modelling based on field measurements of the slope. The first stage of the project is a review of current rockfall simulation programs and rockfall mechanics. This is followed by a review of the design of the rockfall protection measures installed at Stockton Mine. The site is revisited and detailed investigations are performed to further classify the slope conditions and observe current ridgeline mining methodology and effectiveness. Included in this are detailed geotechnical investigations of the slope (soil and rock) materials. The majority of the slopes below the ridgeline mining are heavily vegetated. This project investigates the interrelation of rockfall and vegetation. A series of laboratory tests are conducted using rock and soil samples from the ridgeline-mining project. Overburden samples were cut into spheres and cubes to investigate the influence of shape and rockfall trajectory. A rockfall simulation device was fabricated to drop samples of various shapes onto rock slabs and soil beds. The drop test trajectories were filmed using high-speed video recordings and used for rebound calculations. The purpose of these tests was to observe the effect of impact angle (slope angle) and shape on the coefficients of restitution. Also investigated was the influence of soil moisture and density on rockfall impacts. Observations from the field investigations and laboratory experiments were then used to calibrate the original rockfall design parameters at the site. This included comparing several common commercially available rockfall simulation programs for trajectory analysis. Recent rockfall events that have occurred during the ridgeline mining were compared to original estimates of volume and block-size to actual rockfall events (both natural and mining-induced).

Solid Energy New Zealand plans to mine a 6 to 10m thick coal seam below the Mt. Augustus and Mt. Fredrick ridgeline at Stockton Mine near Westport, NZ. The coal is covered by up to 30m of overburden, which requires removal to access 4 million tones of high quality coal. However, the Coal Mining Lease boundary (CML) is located just below the basal coal measures and the neighbouring land is owned by the Department of Conservation (DoC). In addition, the neighbouring DoC estate is Powelliphanta Augustus snail habitat. It is necessary to remove the overburden without releasing any material above natural discharge levels onto the DoC land. In order to control the rockfall risk at the site, the largest design-build rockfall protection project in the southern hemisphere was constructed using a high-capacity dynamic rockfall barrier installed along the length of the ridgeline. During the design phase of the project, it was evident that current methods to determine the coefficient of restitution (normal and tangential) are subjectively based on the designer's judgement. Currently, there is limited quantitative information available for the determination of dampening coefficients (restitution coefficients) for use in rockfall computer simulation programs. Accurate parameters are necessary for the design and dimensioning of rockfall protection structures. This project investigates an objective method to calculate these parameters for use in rockfall modelling based on field measurements of the slope. The first stage of the project is a review of current rockfall simulation programs and rockfall mechanics. This is followed by a review of the design of the rockfall protection measures installed at Stockton Mine. The site is revisited and detailed investigations are performed to further classify the slope conditions and observe current ridgeline mining methodology and effectiveness. Included in this are detailed geotechnical investigations of the slope (soil and rock) materials. The majority of the slopes below the ridgeline mining are heavily vegetated. This project investigates the interrelation of rockfall and vegetation. A series of laboratory tests are conducted using rock and soil samples from the ridgeline-mining project. Overburden samples were cut into spheres and cubes to investigate the influence of shape and rockfall trajectory. A rockfall simulation device was fabricated to drop samples of various shapes onto rock slabs and soil beds. The drop test trajectories were filmed using high-speed video recordings and used for rebound calculations. The purpose of these tests was to observe the effect of impact angle (slope angle) and shape on the coefficients of restitution. Also investigated was the influence of soil moisture and density on rockfall impacts. Observations from the field investigations and laboratory experiments were then used to calibrate the original rockfall design parameters at the site. This included comparing several common commercially available rockfall simulation programs for trajectory analysis. Recent rockfall events that have occurred during the ridgeline mining were compared to original estimates of volume and block-size to actual rockfall events (both natural and mining-induced).

The development of current golf club designs has followed an evolutionary process starting with the original wooden heads of a hundred years ago, to the thin-walled, hollow body titanium heads of today. Current designs utilize what has become known as the trampoline effect to increase the efficiency of the ball-club impact, which has a number of limiting factors that restrict clubhead performance. These limitations provided the motivation for this research to explore new mechanisms by which the efficiency of the ball club impact could be increased. In particular this research focuses on the development of compliant mechanisms to increase club performance. The results of this research, from concept development to initial prototype plans, are included in this study. A discussion of past and current research in the area of golf club design is presented. A new list of performance metrics for golf clubs and a number of new golf club concepts is also presented. This is followed by a static and dynamic analysis of the most promising golf club configuration. The study is concluded with a concept validation analysis and a presentation of possible prototype configurations for a new golf club design.