Selected topics in the Hydrodynamics of floating offshore wind turbines: heave damping and second order surge motions

La Energía eléctrica producida mediante tecnología eólica flotante es uno de los recursos más prometedores para reducir la dependencia de energía proveniente de combustibles fósiles. Esta tecnología es de especial interés en países como España, donde la plataforma continental es estrecha y existen pocas áreas para el desarrollo de estructuras fijas. Entre los diferentes conceptos flotantes, esta tesis se ha ocupado de la tipología semisumergible. Estas plataformas pueden experimentar movimientos resonantes en largada y arfada. En largada, dado que el periodo de resonancia es largo estos puede ser inducidos por efectos de segundo orden de deriva lenta que pueden tener una influencia muy significativa en las cargas en los fondeos. En arfada las fuerzas de primer orden pueden inducir grandes movimientos y por tanto la correcta determinación del amortiguamiento es esencial para la analizar la operatividad de la plataforma. Esta tesis ha investigado estos dos efectos, para ello se ha usado como caso base el diseño de una plataforma desarrollada en el proyecto Europeo Hiprwind. La plataforma se compone de 3 columnas cilíndricas unidas mediante montantes estructurales horizontales y diagonales, Los cilindros proporcionan flotabilidad y momentos adrizante. A la base de cada columna se le ha añadido un gran “Heave Plate” o placa de cierre. El diseño es similar a otros diseños previos (Windfloat). Se ha fabricado un modelo a escala de una de las columnas para el estudio detallado del amortiguamiento mediante oscilaciones forzadas. Las dimensiones del modelo (1m diámetro en la placa de cierre) lo hacen, de los conocidos por el candidato, el mayor para el que se han publicado datos. El diseño del cilindro se ha realizado de tal manera que permite la fijación de placas de cierre planas o con refuerzo, ambos modelos se han fabricado y analizado. El modelo con refuerzos es una reproducción exacta del diseño a escala real incluyendo detalles distintivos del mismo, siendo el más importante la placa vertical perimetral. Los ensayos de oscilaciones forzadas se han realizado para un rango de frecuencias, tanto para el disco plano como el reforzado. Se han medido las fuerzas durante los ensayos y se han calculado los coeficientes de amortiguamiento y de masa añadida. Estos coeficientes son necesarios para el cálculo del fondeo mediante simulaciones en el dominio del tiempo. Los coeficientes calculados se han comparado con la literatura existente, con cálculos potenciales y por ultimo con cálculos CFD. Para disponer de información relevante para el diseño estructural de la plataforma se han medido y analizado experimentalmente las presiones en la parte superior e inferior de cada placa de cierre. Para la correcta estimación numérica de las fuerzas de deriva lenta en la plataforma se ha realizado una campaña experimental que incluye ensayos con modelo cautivo de la plataforma completa en olas bicromaticas. Pese a que estos experimentos no reproducen un escenario de oleaje realista, los mismos permiten una verificación del modelo numérico mediante la comparación de fuerzas medidas en el modelo físico y el numérico. Como resultados de esta tesis podemos enumerar las siguientes conclusiones. 1. El amortiguamiento y la masa añadida muestran una pequeña dependencia con la frecuencia pero una gran dependencia con la amplitud del movimiento. siendo coherente con investigaciones existentes. 2. Las medidas con la placa de cierre reforzada con cierre vertical en el borde, muestra un amortiguamiento significativamente menor comparada con la placa plana. Esto implica que para ensayos de canal es necesario incluir estos detalles en el modelo. 3. La masa añadida no muestra grandes variaciones comparando placa plana y placa con refuerzos. 4. Un coeficiente de amortiguamiento del 6% del crítico se puede considerar conservador para el cálculo en el dominio de la frecuencia. Este amortiguamiento es equivalente a un coeficiente de “drag” de 4 en elementos de Morison cuadráticos en las placas de cierre usadas en simulaciones en el dominio del tiempo. 5. Se han encontrado discrepancias en algunos valores de masa añadida y amortiguamiento de la placa plana al comparar con datos publicados. Se han propuesto algunas explicaciones basadas en las diferencias en la relación de espesores, en la distancia a la superficie libre y también relacionadas con efectos de escala. 6. La presión en la placa con refuerzos son similares a las de la placa plana, excepto en la zona del borde donde la placa con refuerzo vertical induce una gran diferencias de presiones entre la cara superior e inferior. 7. La máxima diferencia de presión escala coherentemente con la fuerza equivalente a la aceleración de la masa añadida distribuida sobre la placa. 8. Las masas añadidas calculadas con el código potencial (WADAM) no son suficientemente precisas, Este software no contempla el modelado de placas de pequeño espesor con dipolos, la poca precisión de los resultados aumenta la importancia de este tipo de elementos al realizar simulaciones con códigos potenciales para este tipo de plataformas que incluyen elementos de poco espesor. 9. Respecto al código CFD (Ansys CFX) la precisión de los cálculos es razonable para la placa plana, esta precisión disminuye para la placa con refuerzo vertical en el borde, como era de esperar dado la mayor complejidad del flujo. 10. Respecto al segundo orden, los resultados, en general, muestran que, aunque la tendencia en las fuerzas de segundo orden se captura bien con los códigos numéricos, se observan algunas reducciones en comparación con los datos experimentales. Las diferencias entre simulaciones y datos experimentales son mayores al usar la aproximación de Newman, que usa únicamente resultados de primer orden para el cálculo de las fuerzas de deriva media. 11. Es importante remarcar que las tendencias observadas en los resultados con modelo fijo cambiarn cuando el modelo este libre, el impacto que los errores en las estimaciones de fuerzas segundo orden tienen en el sistema de fondeo dependen de las condiciones ambientales que imponen las cargas ultimas en dichas líneas. En cualquier caso los resultados que se han obtenido en esta investigación confirman que es necesaria y deseable una detallada investigación de los métodos usados en la estimación de las fuerzas no lineales en las turbinas flotantes para que pueda servir de guía en futuros diseños de estos sistemas. Finalmente, el candidato espera que esta investigación pueda beneficiar a la industria eólica offshore en mejorar el diseño hidrodinámico del concepto semisumergible. ABSTRACT Electrical power obtained from floating offshore wind turbines is one of the promising resources which can reduce the fossil fuel energy consumption and cover worldwide energy demands. The concept is the most competitive in countries, such as Spain, where the continental shelf is narrow and does not provide space for fixed structures. Among the different floating structures concepts, this thesis has dealt with the semisubmersible one. Platforms of this kind may experience resonant motions both in surge and heave directions. In surge, since the platform natural period is long, such resonance can be excited with second order slow drift forces and may have substantial influence on mooring loads. In heave, first order forces can induce significant motion, whose damping is a crucial factor for the platform downtime. These two topics have been investigated in this thesis. To this aim, a design developed during HiPRWind EU project, has been selected as reference case study. The platform is composed of three cylindrical legs, linked together by a set of structural braces. The cylinders provide buoyancy and restoring forces and moments. Large circular heave plates have been attached to their bases. The design is similar to other documented in literature (e.g. Windfloat), which implies outcomes could have a general value. A large scale model of one of the legs has been built in order to study heave damping through forced oscillations. The final dimensions of the specimen (one meter diameter discs) make it, to the candidate’s knowledge, the largest for which data has been published. The model design allows for the fitting of either a plain solid heave plate or a flapped reinforced one; both have been built. The latter is a model scale reproduction of the prototype heave plate and includes some distinctive features, the most important being the inclusion of a vertical flap on its perimeter. The forced oscillation tests have been conducted for a range of frequencies and amplitudes, with both the solid plain model and the vertical flap one. Forces have been measured, from which added mass and damping coefficients have been obtained. These are necessary to accurately compute time-domain simulations of mooring design. The coefficients have been compared with literature, and potential flow and CFD predictions. In order to provide information for the structural design of the platform, pressure measurements on the top and bottom side of the heave discs have been recorded and pressure differences analyzed. In addition, in order to conduct a detailed investigation on the numerical estimations of the slow-drift forces of the HiPRWind platform, an experimental campaign involving captive (fixed) model tests of a model of the whole platform in bichromatic waves has been carried out. Although not reproducing the more realistic scenario, these tests allowed a preliminary verification of the numerical model based directly on the forces measured on the structure. The following outcomes can be enumerated: 1. Damping and added mass coefficients show, on one hand, a small dependence with frequency and, on the other hand, a large dependence with the motion amplitude, which is coherent with previously published research. 2. Measurements with the prototype plate, equipped with the vertical flap, show that damping drops significantly when comparing this to the plain one. This implies that, for tank tests of the whole floater and turbine, the prototype plate, equipped with the flap, should be incorporated to the model. 3. Added mass values do not suffer large alterations when comparing the plain plate and the one equipped with a vertical flap. 4. A conservative damping coefficient equal to 6% of the critical damping can be considered adequate for the prototype heave plate for frequency domain analysis. A corresponding drag coefficient equal to 4.0 can be used in time domain simulations to define Morison elements. 5. When comparing to published data, some discrepancies in added mass and damping coefficients for the solid plain plate have been found. Explanations have been suggested, focusing mainly on differences in thickness ratio and distance to the free surface, and eventual scale effects. 6. Pressures on the plate equipped with the vertical flap are similar in magnitude to those of the plain plate, even though substantial differences are present close to the edge, where the flap induces a larger pressure difference in the reinforced case. 7. The maximum pressure difference scales coherently with the force equivalent to the acceleration of the added mass, distributed over the disc surface. 8. Added mass coefficient values predicted with the potential solver (WADAM) are not accurate enough. The used solver does not contemplate modeling thin plates with doublets. The relatively low accuracy of the results highlights the importance of these elements when performing potential flow simulations of offshore platforms which include thin plates. 9. For the full CFD solver (Ansys CFX), the accuracy of the computations is found reasonable for the plain plate. Such accuracy diminishes for the disc equipped with a vertical flap, an expected result considering the greater complexity of the flow. 10. In regards to second order effects, in general, the results showed that, although the main trend in the behavior of the second-order forces is well captured by the numerical predictions, some under prediction of the experimental values is visible. The gap between experimental and numerical results is more pronounced when Newman’s approximation is considered, making use exclusively of the mean drift forces calculated in the first-order solution. 11. It should be observed that the trends observed in the fixed model test may change when the body is free to float, and the impact that eventual errors in the estimation of the second-order forces may have on the mooring system depends on the characteristics of the sea conditions that will ultimately impose the maximum loads on the mooring lines. Nevertheless, the preliminary results obtained in this research do confirm that a more detailed investigation of the methods adopted for the estimation of the nonlinear wave forces on the FOWT would be welcome and may provide some further guidance for the design of such systems. As a final remark, the candidate hopes this research can benefit the offshore wind industry in improving the hydrodynamic design of the semi-submersible concept.

Ash layers, hyaloclastite, and alteration of basaltic glass at DSDP Leg 65 Holes

Three types of tephra deposits were recovered on Leg 65 of the Deep Sea Drilling Project (DSDP) from three drill sites at the mouth of the Gulf of California: (1) a series of white ash layers at Sites 483, 484, and 485; (2) a layer of plagioclase- phyric sideromelane shards at Site 483; and (3) an indurated, cross-bedded hyaloclastite in Hole 483B. The ash layers in (1) are composed of colorless, fresh rhyolitic glass shards with minor dacitic and rare basaltic shards. These are thought to be derived from explosive volcanoes on the Mexican mainland. Most of the shards in (2) are fresh, but some show marginal to complete alteration to palagonite. The composition of the glass is that of a MORB-type tholeiite, low in Fe and moderately high in Ti, and possibly erupted from off-axis seamounts. Basaltic glass shards occurring in silt about 45 meters above the basement at Site 484 A in the Tamayo Fracture Zone show a distinctly alkalic composition similar to that of the single basement basalt specimen drilled at this site. The hyaloclastite in (3) is made up chiefly of angular sideromelane shards altered to smectite and zeolites (mainly phillipsite) and minor admixtures of terrigenous silt. A very high K and Ba content indicates significant uptake of at least these elements from seawater. Nevertheless, the unusual chemical composition of the underlying massive basalt flow is believed to be reflected in that of the hyaloclastite. This is a powerful argument for interpreting the massive basalt as a surface flow rather than an intrusion. Glass alteration is different in the glassy margins of flows than in thicker glassy pillow rinds. Also, it appears to proceed faster in coarse- than fine-grained sediments.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

Hydraulics of skimming flows on stepped chutes: The effects of inflow conditions?

Modern stepped spillways are typically designed for large discharge capacities corresponding to a skimming flow regime for which flow resistance is predominantly form drag. The writer demonstrates that the inflow conditions have some effect on the skimming flow properties. Boundary layer calculations show that the flow properties at inception of free-surface aeration are substantially different with pressurized intake. The re-analysis of experimental results highlights that the equivalent Darcy friction factor is f similar to 0.2 in average on uncontrolled stepped Chute and f similar to 0.1 on stepped chute with pressurized intake. A simple design chart is presented to estimate the residual flow velocity, and the agreement of the calculations with experimental results is deemed satisfactory for preliminary design.

Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone

Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within +/- 0.001, or 1/20th -1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05-0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly Suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler's equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., delta u/delta t > 0 similar to delta p/delta x < 0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone.

Simulations of pendant drop formation of a viscoelastic liquid

A modified Volume-of-Fluid (VOF) numerical method is used to predict the dynamics of a liquid drop of a low viscosity dilute polymer solution, forming in air from a circular nozzle. Viscoelastic effects are represented using an Oldroyd-B model. Predicted drop shapes are compared with experimental observations. The main features, including the timing of the shape evolution and the bead-on-a-string effect, are well reproduced by the simulations. The results confirm published conclusions of the third author, that the deformation is effectively Newtonian until near the time of Newtonian pinch-off and that the elastic stress becomes large in the pinch region due to the higher extensional flow there.

Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

Discrete element modelling of a rotating drum and drum granulation

This thesis reports the results of DEM (Discrete Element Method) simulations of rotating drums operated in a number of different flow regimes. DEM simulations of drum granulation have also been conducted. The aim was to demonstrate that a realistic simulation is possible, and further understanding of the particle motion and granulation processes in a rotating drum. The simulation model has shown good qualitative and quantitative agreement with other published experimental results. A two-dimensional bed of 5000 disc particles, with properties similar to glass has been simulated in the rolling mode (Froude number 0.0076) with a fractional drum fill of approximately 30%. Particle velocity fields in the cascading layer, bed cross-section, and at the drum wall have shown good agreement with experimental PEPT data. Particle avalanches in the cascading layer have been shown to be consistent with single layers of particles cascading down the free surface towards the drum wall. Particle slip at the drum wall has been shown to depend on angular position, and ranged from 20% at the toe and shoulder, to less than 1% at the mid-point. Three-dimensional DEM simulations of a moderately cascading bed of 50,000 spherical elastic particles (Froude number 0.83) with a fractional fill of approximately 30% have also been performed. The drum axis was inclined by 50 to the horizontal with periodic boundaries at the ends of the drum. The mean period of bed circulation was found to be 0.28s. A liquid binder was added to the system using a spray model based on the concept of a wet surface energy. Granule formation and breakage processes have been demonstrated in the system.

Characteristics of surface-water flows in the ridge and slough landscape of Everglades National Park: implications for particulate transport

Over the last one hundred years, compartmentalization and water management activities have reduced water flow to the ridge and slough landscape of the Everglades. As a result, the once corrugated landscape has become topographically and vegetationally uniform. The focus of this study was to quantify variation in surface flow in the ridge and slough landscape and to relate flow conditions to particulate transport and deposition. Over the 2002–2003 and 2003–2004 wet seasons, surface velocities and particulate accumulation were measured in upper Shark River Slough in Everglades National Park. Landscape characteristics such as elevation, plant density and biomass also were examined to determine their impact on flow characteristics and material transport. The results of this study demonstrate that the release of water during the wet season not only increases water levels, but also increased flow speeds and particulate transport and availability. Further, flow speeds were positively and significantly correlated with water level thereby enhancing particulate transport in sloughs relative to ridges especially during peak flow periods. Our results also indicate that the distribution of biomass in the water column, including floating plants and periphyton, affects velocity magnitude and shape of vertical profiles, especially in the sloughs where Utricularia spp. and periphyton mats are more abundant. Plot clearing experiments suggest that the presence of surface periphyton and Utricularia exert greater control over flow characteristics than the identity (i.e., sawgrass or spike rush) or density of emergent macrophytes, two parameters frequently incorporated into models describing flow through vegetated canopies. Based on these results, we suggest that future modeling efforts must take the presence of floating biomass, such as Utricularia, and presence of periphyton into consideration when describing particulate transport.

A tidal creek water budget: Estimation of groundwater discharge and overland flow using hydrologic modeling in the Southern Everglades

Taylor Slough is one of the natural freshwater contributors to Florida Bay through a network of microtidal creeks crossing the Everglades Mangrove Ecotone Region (EMER). The EMER ecological function is critical since it mediates freshwater and nutrient inputs and controls the water quality in Eastern Florida Bay. Furthermore, this region is vulnerable to changing hydrodynamics and nutrient loadings as a result of upstream freshwater management practices proposed by the Comprehensive Everglades Restoration Program (CERP), currently the largest wetland restoration project in the USA. Despite the hydrological importance of Taylor Slough in the water budget of Florida Bay, there are no fine scale (∼1 km2) hydrodynamic models of this system that can be utilized as a tool to evaluate potential changes in water flow, salinity, and water quality. Taylor River is one of the major creeks draining Taylor Slough freshwater into Florida Bay. We performed a water budget analysis for the Taylor River area, based on long-term hydrologic data (1999–2007) and supplemented by hydrodynamic modeling using a MIKE FLOOD (DHI,http://dhigroup.com/) model to evaluate groundwater and overland water discharges. The seasonal hydrologic characteristics are very distinctive (average Taylor River wet vs. dry season outflow was 6 to 1 during 1999–2006) with a pronounced interannual variability of flow. The water budget shows a net dominance of through flow in the tidal mixing zone, while local precipitation and evapotranspiration play only a secondary role, at least in the wet season. During the dry season, the tidal flood reaches the upstream boundary of the study area during approximately 80 days per year on average. The groundwater field measurements indicate a mostly upwards-oriented leakage, which possibly equals the evapotranspiration term. The model results suggest a high importance of groundwater contribution to the water salinity in the EMER. The model performance is satisfactory during the dry season where surface flow in the area is confined to the Taylor River channel. The model also provided guidance on the importance of capturing the overland flow component, which enters the area as sheet flow during the rainy season. Overall, the modeling approach is suitable to reach better understanding of the water budget in the mangrove region. However, more detailed field data is needed to ascertain model predictions by further calibrating overland flow parameters.

Dynamics of an axisymmetric electromagnetic 'crucible' melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

Automatic dynamic mask extraction for PIV images containing an unsteady interface, bubbles, and a moving structure

When performing Particle Image Velocimetry (PIV) measurements in complex fluid flows with moving interfaces and a two-phase flow, it is necessary to develop a mask to remove non-physical measurements. This is the case when studying, for example, the complex bubble sweep-down phenomenon observed in oceanographic research vessels. Indeed, in such a configuration, the presence of an unsteady free surface, of a solid–liquid interface and of bubbles in the PIV frame, leads to generate numerous laser reflections and therefore spurious velocity vectors. In this note, an image masking process is developed to successively identify the boundaries of the ship and the free surface interface. As the presence of the solid hull surface induces laser reflections, the hull edge contours are simply detected in the first PIV frame and dynamically estimated for consecutive ones. As for the unsteady surface determination, a specific process is implemented like the following: i) the edge detection of the gradient magnitude in the PIV frame, ii) the extraction of the particles by filtering high-intensity large areas related to the bubbles and/or hull reflections, iii) the extraction of the rough region containing these particles and their reflections, iv) the removal of these reflections. The unsteady surface is finally obtained with a fifth-order polynomial interpolation. The resulted free surface is successfully validated from the Fourier analysis and by visualizing selected PIV images containing numerous spurious high intensity areas. This paper demonstrates how this data analysis process leads to PIV images database without reflections and an automatic detection of both the free surface and the rigid body. An application of this new mask is finally detailed, allowing a preliminary analysis of the hydrodynamic flow.

Air Entrainment in the Turbulent Ship Hull Boundary Layer

Turbulent fluctuations in the vicinity of the water free surface along a flat, vertically oriented surface-piercing plate are studied experimentally using a laboratory-scale experiment. In this experiment, a meter-wide stainless steel belt travels horizontally in a loop around two rollers with vertically oriented axes, which are separated by 7.5 meters. This belt device is mounted inside a large water tank with the water level set just below the top edge of the belt. The belt, rollers, and supporting frame are contained within a sheet metal box to keep the device dry except for one 6-meter-long straight test section between rollers. The belt is launched from rest with an acceleration of up to 3-g in order to quickly reach steady state velocity. This creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer created along a flat-sided ship moving at the same velocity, with a length equivalent to the length of belt that has passed the measurement region since the belt motion began. Surface profile measurements in planes normal to the belt surface are conducted using cinematic Laser Induced Fluorescence and quantitative surface profiles are extracted at each instant in time. Using these measurements, free surface fluctuations are examined and the propagation behavior of these free surface ripples is studied. It is found that free surface fluctuations are generated in a region close to the belt surface, where sub-surface velocity fluctuations influence the behavior of these free surface features. These rapidly-changing surface features close to the belt appear to lead to the generation of freely-propagating waves far from the belt, outside the influence of the boundary layer. Sub-surface PIV measurements are performed in order to study the modification of the boundary layer flow field due to the effects of the water free surface. Cinematic planar PIV measurements are performed in horizontal planes parallel to the free surface by imaging the flow from underneath the tank, providing streamwise and wall-normal velocity fields. Additional planar PIV experiments are performed in vertical planes parallel to the belt surface in order to study the bahvior of streamwise and vertical velocity fields. It is found that the boundary layer grows rapidly near the free surface, leading to an overall thicker boundary layer close to the surface. This rapid boundary layer growth appears to be linked to a process of free surface bursting, the sudden onset of free surface fluctuations. Cinematic white light movies are recorded from beneath the water surface in order to determine the onset location of air entrainment. In addition, qualitative observations of these processes are made in order to determine the mechanisms leading to air entrainment present in this flow.

Bow and stern flows with constant vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

Private equity bids in Australia : an exploratory study

In this study, we provide an insight into how private equity players choose their targets and the bid arrangements they prefer. We test our expectations of the unique features of private equity targets using a sample of 23 listed private equity target firms during 2001–2007. We find, relative to a benchmark sample of 81 corporate targets matched by year and industry, the private equity target firms to be larger, more profitable, use their assets more efficiently, more highly levered and have greater cash flow. Multivariate testing indicates that private equity targets have relatively greater financial slack, greater financial stability, greater free cash flow and lower measurable growth prospects. All conclusions are found to be robust to a control sample of 502 takeover bids during 2001–2007.