Circular cylinders in cross-flow have been extensively studied in the last century. However, there are still many unsolved problems in this area, one of which is the flow structure around two staggered finite circular cylinders. This thesis mainly focuses on an experimental investigation of the vortex shedding characteristics of two staggered finite circular cylinders of equal diameter in cross-flow. Wind tunnel experiments were conducted to measure the vortex shedding frequency at the mid-height of the two cylinders and along the height of the two cylinders. Two identical circular cylinders of aspect ratio AR = 9 were partially immersed in a flat-plate turbulent boundary layer, where the boundary layer thickness to cylinder height ratio at the location of the cylinders was δ/H = 0.4. The Reynolds number based on the cylinder diameter was Re<i>D</i> = 2.4z_x~104. Centre-to-centre pitch ratios of <i>P/D</i> = 1.125, 1.25, 1.5, 2, 2.5, 3, 4 and 5 were examined and the incidence angle was incremented in small steps from á = 0° to 180°. For each configuration of the cylinders, the vortex shedding frequency, represented in dimensionless form as the Strouhal number, St, was measured with a single-component hot-wire anemometer. Also, a seven-hole pressure probe was used to measure the time-averaged wake velocity field behind the cylinders at selected configurations in order to get a better understanding of the wake structure.<p>The vortex shedding frequencies measured at the mid-height of the cylinders clearly showed the similarities and differences of vortex shedding between two staggered finite and infinite circular cylinders. The Strouhal number behavior of the two finite circular cylinders is generally similar to that of two infinite circular cylinders, but the values of St for the two finite cylinders were found for most cases to be smaller than the case of the infinite cylinders.<p>The measurements of vortex shedding frequency along the heights of each finite cylinder revealed that, for most incidence angles, the value of the Strouhal number remains constant along the height of the cylinder, but a notable variation in the shape and strength of the vortex shedding peak along the heights of the cylinders is observed. Sharp and strong peaks in the power spectra are measured around the mid-height of the cylinder. Broader and weaker peaks are found both at the base of the cylinder and near the free end. At several particular configurations, the vortex shedding frequency changes along the height of the cylinder, caused by the varying flow pattern in the vertical direction.<p>Wake measurements showed the velocity field behind the two finite circular cylinders arranged in tandem configurations of P/D = 1.125, 2 and 5. The experimental data revealed that the flow structure behind two finite circular cylinders arranged in a tandem configuration is much more complicated than that of the single finite circular cylinder. The downwash flow from the tip of the downstream cylinder is weaker due to the flow interaction between the free ends of two cylinders, and this downwash flow becomes stronger with increasing P/D. A similar trend happens to the vorticity of the tip vortex structures. However, the upwash flow behind the downstream cylinder is not strongly affected by the existence of the upstream cylinder.

Circular cylinders in cross-flow have been extensively studied in the last century. However, there are still many unsolved problems in this area, one of which is the flow structure around two staggered finite circular cylinders. This thesis mainly focuses on an experimental investigation of the vortex shedding characteristics of two staggered finite circular cylinders of equal diameter in cross-flow. Wind tunnel experiments were conducted to measure the vortex shedding frequency at the mid-height of the two cylinders and along the height of the two cylinders. Two identical circular cylinders of aspect ratio AR = 9 were partially immersed in a flat-plate turbulent boundary layer, where the boundary layer thickness to cylinder height ratio at the location of the cylinders was δ/H = 0.4. The Reynolds number based on the cylinder diameter was Re<i>D</i> = 2.4z_x~104. Centre-to-centre pitch ratios of <i>P/D</i> = 1.125, 1.25, 1.5, 2, 2.5, 3, 4 and 5 were examined and the incidence angle was incremented in small steps from á = 0° to 180°. For each configuration of the cylinders, the vortex shedding frequency, represented in dimensionless form as the Strouhal number, St, was measured with a single-component hot-wire anemometer. Also, a seven-hole pressure probe was used to measure the time-averaged wake velocity field behind the cylinders at selected configurations in order to get a better understanding of the wake structure.<p>The vortex shedding frequencies measured at the mid-height of the cylinders clearly showed the similarities and differences of vortex shedding between two staggered finite and infinite circular cylinders. The Strouhal number behavior of the two finite circular cylinders is generally similar to that of two infinite circular cylinders, but the values of St for the two finite cylinders were found for most cases to be smaller than the case of the infinite cylinders.<p>The measurements of vortex shedding frequency along the heights of each finite cylinder revealed that, for most incidence angles, the value of the Strouhal number remains constant along the height of the cylinder, but a notable variation in the shape and strength of the vortex shedding peak along the heights of the cylinders is observed. Sharp and strong peaks in the power spectra are measured around the mid-height of the cylinder. Broader and weaker peaks are found both at the base of the cylinder and near the free end. At several particular configurations, the vortex shedding frequency changes along the height of the cylinder, caused by the varying flow pattern in the vertical direction.<p>Wake measurements showed the velocity field behind the two finite circular cylinders arranged in tandem configurations of P/D = 1.125, 2 and 5. The experimental data revealed that the flow structure behind two finite circular cylinders arranged in a tandem configuration is much more complicated than that of the single finite circular cylinder. The downwash flow from the tip of the downstream cylinder is weaker due to the flow interaction between the free ends of two cylinders, and this downwash flow becomes stronger with increasing P/D. A similar trend happens to the vorticity of the tip vortex structures. However, the upwash flow behind the downstream cylinder is not strongly affected by the existence of the upstream cylinder.

The present study aims to explore dynamical behavior of the fluid- elastic vibration of a single cylinder and three cylinders in shear flow by numerical simulations. This paper investigates the effects of the shear parameter, mass ratio, and spacing(P/D) on fluid-elastic vibration of the cylinders. Continuity equation and momentum equations are solved alternatively using a CFD package, Fluent 6.3.26. Dynamic meshing techniques together with the cylinder motion equations are employed in the simulation. Under different flow conditions, flow types, and cylinder motion models, lock-in and fluid-elastic vibration are studied. The results show that motion and flow types of a single cylinder in uniform flow are in agreement with the previous studies in literatures. In shear flow, however, as the shear parameter increases, the fluid-elastic vibration of the cylinder is induced, and thus amplitude of the cylinder increases considerably. Further, three cylinders in the shear flow are studied. Three cylinders arrangements (classified as side-by-side, tandem ,and stagger) and the distance between cylinders are the factors to cause fluid-elastic vibration. Compared with the single cylinder motion, three cylinders motion¡¦s critical flow velocity is smaller than that of the single cylinder motion, which means two cylinders motion are more subject to fluid-elastic vibration.

This research is aimed to investigate the fluid-elastic instability of the motion simulation using a single cylinder and two cylinders within the context of shear flows. T/D, shear parameter and mass ratio are parameters to be investigated. Besides, cylindrical motion treks and the amplitude are also analyzed. Continuity equation and momentum equations are solved alternatively using a CFD package, Fluent 6.3.26. The force caused by the flow interacts with the cylindrical motion. Thus Motion meshing techniques together with the cylindrical motion equations are employed in the simulation. Under different flow conditions, flow types and cylindrical motion models, lock-in and fluid-elastic instability are studied. The results show that motion and flow types of a single cylinder within the context of the uniform flow have a general agreement with the related literatures. In terms of the shear flow, however, as the shear parameter increases, the fluid-elastic instability is caused, and thus amplitude of the cylinder augments considerably. Further, double cylinders in the shear flow are studied. Double cylinder arrangements( classified as side-by-side and tandem) and the distance between cylinders are the factors to cause fluid-elastic instability. Compared with the single cylindrical motion, double cylindrical motion¡¦s critical flow velocity is smaller than the single cylindrical motion, which means double cylindrical motion are more subject to fluid-elastic instability.

The challenge of tackling global climate change and our increasing reliance on power means that new and diverse renewable energy generation technologies are a necessity for the future. From a number of technologies reviewed at the outset, the cross-flow tidal turbine was chosen as the focus of the research. The numerical investigation begins by choosing to model flow around a circular cylinder as a challenging benchmarking and evaluation case to compare two potential solvers for the ongoing research, ANSYS CFX and OpenFOAM. A number of meshing strategies and solver limitations are extracted, forming a detailed guide on the topic of cylinder lift, drag and Strouhal frequency prediction in its own right. An introduction to cross-flow turbines follows, setting out turbine performance coefficients and a strategy to develop a robust numerical modelling environment with which to capture and evaluate hydrodynamic phenomena. The validation of a numerical model is undertaken by comparison with an experimentally tested lab scale turbine. The resultant numerical model is used to explore turbine performance with varying Reynolds number, concluding with a recommended minimum value for development purposes of Re = 350 × 103 to avoid scalability errors. Based on this limit a large scale numerical simulation of the turbine isconducted and evaluated in detail, in particular, a local flow sampling method is proposed and presented. The method captures flow conditions ahead of the turbine blade at all positions of motion allowing local velocities and angles of attack to be interrogated. The sampled flow conditions are used in the final chapter to construct a novel blade pitching strategy. The result is a highly effective optimisation method which increases peak turbine power coefficient by 20% for only two further case iterations of the numerical solution.

Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

Analytic solutions to the static and stationary boundary value field problems relative to an arbitrary configuration of parallel cylinders are obtained by using translational addition theorems for scalar Laplacian polar functions, to express the field due to one cylinder in terms of the polar coordinates of the other cylinders such that the boundary conditions can be imposed at all the cylinder surfaces. The constants of integration in the field expressions of all the cylinders are obtained from a truncated infinite matrix equation. Translational addition theorems are available for scalar cylindrical and spherical wave functions but such theorems are not directly available for the general solution of the Laplace equation in polar coordinates. The purpose of deriving these addition theorems and applying them to field problems involving systems of cylinders is to obtain exact analytic solutions with controllable accuracies, thereby, yielding benchmark solutions to validate other approximate numerical methods.

O problema das vibrações induzidas por vórtices em cilindros flexíveis inclinados em relação ao perfil de correnteza incidente é estudado através de uma abordagem experimental. Este tema se mostra de grande importância e aplicação na Engenharia Naval e Oceânica uma vez que são diversas as estruturas que se encaixam nesta descrição, como são o casos dos risers e linhas de amarração. Apesar de extensa, a literatura técnica especializada no assunto é focada em simplificações, tais como os estudos de cilindros rígidos fixos, cilindros rígidos montados em base elástica e cilindros flexíveis verticais ou lançados em catenária livre. A questão da inclinação é abordada em termos do Principio da Independência que diz que as forças e a frequência de emissão de vórtices em um cilindro inclinado são iguais as de um cilindro vertical se considerada apenas a parcela da correnteza normal à direção de inclinação. Estudos anteriores mostraram que este princípio é válido somente em algumas condições específicas e poucos deles apresentam resultados para cilindros flexíveis. Com base nisso, um ensaio em escala reduzida em tanque de reboque foi realizado com um modelo de linha composto por um tubo de silicone preenchido com microesferas de aço e condições de contorno articuladas em suas extremidades, o que conferiu características inerciais e geométricas ideais para a obtenção do fenômeno. Além da configuração vertical (? = 0°), que é o caso de referência, o modelo foi estudado em outras quatro inclinações com a vertical: ? = 10°, 20°, 30° e 45°. Estas inclinações foram ensaiadas para cinco diferentes azimute: ? = 0°, 45°, 90°, 135° e 180°, resultando em vinte e uma configurações de inclinação. Os resultados são analisados em termos da decomposição modal da vibração da linha, ou seja, são apresentadas amplitudes e frequências de oscilação ocorridas em cada um dos modos de vibrar. Além disso são realizadas análises espectrais, gráficos de evolução espaço-temporal, trajetórias de pontos ao longo do modelo flexível, entre outros. Frequências naturais, coeficientes de amortecimento e trações no topo são apresentados, complementarmente, como resultados de caracterização do modelo. Os estudos apontaram para uma validade do PI com algumas ressalvas, principalmente influenciadas pela diferença nas frequências do primeiro e segundo modo que é crescente com o aumento da inclinação. Além disso conclusões importantes sobre a coexistência modal, em regiões de ressonância e/ou de transição da dominância modal, foram obtidas. / The vortex-induced vibration problem in flexible cylinders yawed in relation to the incident current profile is studied through an experimental approach. This topic has great importance and application on Naval and Oceanic Engineering once there are multiple structures that fit into this description, such as risers and mooring lines. Though extensive, technical literature specialized on this topic is focused on simplifications such as the study of fixed rigid cylinders, elastic base rigid cylinders and flexible cylinders assembled vertically or launched in free hanging catenary. The inclination issue is addressed in the terms of the Principle of Independence which states that the forces and frequency shedding in an inclined cylinder are equal to those of a vertical cylinder if only considered the current component normal to the inclination plane. Previous studies showed that this principle is valid only on some specific conditions and few of them showed results to flexible systems. Based on this, a scaled tow tank test was performed with a line model composed of a silicone tube filled with steel microspheres and articulated end conditions, which offered the ideal inertial and geometrical conditions to obtaining the phenomenon. Besides the vertical configuration (? = 0°), which is the reference case, the model was studied in other four inclinations with the vertical: ? = 10°,20°, 30° and 45°. These inclinations were tested for five different azimuth directions: ? = 0°, 45°, 90°, 135° and 180°, resulting in 21 configurations. The results are analyzed on terms of the modal decomposition of the line motions, that is, amplitudes and oscillation frequencies are presented for each one of the vibration modes. Furthermore other analyzes are made, as spectral graphs, spatio-temporal evolution graphs, line points trajectories, among others. Natural frequencies, damping coefficients and tensions at the top are presented, complementarly, as results of the model characterization. The studies pointed to a validity of the IP with some reservations, mainly influenced by the difference in of the first and second mode frequencies that is increasing with the yaw increase. In addition, important conclusions about modal coexistence in regions of resonance and / or transition of modal dominance were obtained.

The hydrodynamic effects of long-line mussel farms are studied through a two-pronged approach. Large-scale hydrodynamic effects are investigated through the use of field measurements, primarily at a large mussel farm in Golden Bay, New Zealand (230 long-lines, covering an area of 2.45 km by 0.65 km). The research focuses on three areas: the effect of the farm on currents, mixing and stratification, and the dissipation of wave energy. Measurements are also made of the forces on long-line anchor ropes, and a limited investigation is made of phytoplankton depletion. The second approach is the use of laboratory drag measurements and Particle Tracking Velocimetry (PTV) to study the effect of mussel dropper (vertical lengths of mussel-encrusted crop rope) roughness and spacing on flow at small scales. These experiments provide data on very rough cylinders, and on cylinder arrays. The field measurements show that the local effects of mussel farms on currents are significant, but that magnitudes of the effects depend on dropper density, mussel sizes, orientation of the long-lines to the flow, and other parameters that are necessary to characterise the complex interactions between a farm and the flow. The drag on the submerged structures reduces water velocities within the Golden Bay farm by between 47% and 67%. Mussel farms present a porous obstacle to the flow, and flow that does not pass through the farm must be directed around or beneath it. The field measurements indicate that at the study site, most of the flow is diverted around the farm despite its large horizontal dimensions. The droppers at the study site extend over most of the water column (average dropper length ~ 8 m, average water depth ~ 11 m), providing a restriction to the flow beneath the farm. The strength of the density stratification may also favour a horizontal diversion. The flow around the farm is essentially two-dimensional. This suggests that two-dimensional numerical models should be sufficient to obtain reasonable predictions of the velocity drop within, and the diversion around, mussel farms. A simple two-dimensional pipe-network model gives reasonable estimates of the velocity within the farm, demonstrating that the drag of the farm may be adequately parameterised through local increases of bed friction. A wake in the form of reduced velocities extends downstream of the farm, and a mixing layer analogy suggests that this wake spreads slowly. The downstream extent of the wake cannot be determined, although it is likely to be limited by the tidal excursion. The degree of vertical mixing caused by the flow through a mussel farm cannot be quantified, although there are clear interactions between the stratification and the farm. Two mixing mechanisms are considered. A shear layer is generated beneath the farm due to the difference in velocities between the retarded flow within the farm and the flow beneath. Shear layers beneath mussel farms are likely to be weak unless the ambient currents are strong. It will be necessary for stratification to be weak or non-existent for this mechanism to generate significant mixing. The second mechanism is smaller-scale turbulence generated by the mussel droppers. Although the efficiency of this form of mixing is likely to be low, the large number of mussel droppers suggests that there will be some enhancement of vertical mixing. Frequency-dependent wave attenuation is recorded, and is predicted with some success by an analytical model. Both the model and the field data show that wave dissipation increases as the wave period decreases. Wave energy dissipation at the study site averages approximately 10%, although the measurements are made during a period of low wave heights (Hs < 0.25 m). Measurements of long-line anchor rope tension at two study sites indicate that the loadings are induced by the tide, currents, and waves. Dynamic wave loadings may be significant, and higher wave forces are measured at the offshore end of a long-line. The issue of seston or phytoplankton depletion is considered briefly through the examination of fluorescence, turbidity, and acoustic backscatter data. Although the results are consistent with a reduction of seston within the farm, differences between the inside and outside of the farm are not statistically significant. Mussel droppers resemble extremely rough circular cylinders, with the mussel shells forming the surface roughness elements. Drag measurements and PTV flow visualisation are used to investigate the importance of the large surface roughness, and the influence of dropper spacing and long-line orientation on flow. Drag measurements conducted with smooth and rough cylinders show that high surface roughness (ks/D ~ 0.092) has little effect on the drag coefficient of single cylinders in the range 4,000 < Re < 13,000, yet increases the drag coefficient of a row of cylinders normal to the flow. High surface roughness on single cylinders has the effect of shortening the near-wake region, increasing the peak turbulent kinetic energy (TKE) behind the cylinder, and decreasing the Strouhal number (St = 0.21, 0.19, 0.17 for ks/D = 0, 0.048, and 0.094 respectively). Arrays of rough cylinders (ks/D = 0.094) demonstrate similar flow characteristics to those of smooth cylinders. At cylinder spacings of S/D < 2.2, the surface roughness acts to favour the formation of a particular metastable wake pattern, whereas different metastable wake patterns are formed each run behind the smooth cylinders. The experiments show that the drag on single row arrays of cylinders are related to the cylinder spacing (increasing drag with decreasing spacing), and the drag also varies with the sine of the angle to the flow, except where the array is at low angles to the flow. The PTV measurements provide new data regarding the two-dimensional distributions of velocity, TKE, and turbulence statistics behind the cylinder arrays.

O problema das vibrações induzidas por vórtices em cilindros flexíveis inclinados em relação ao perfil de correnteza incidente é estudado através de uma abordagem experimental. Este tema se mostra de grande importância e aplicação na Engenharia Naval e Oceânica uma vez que são diversas as estruturas que se encaixam nesta descrição, como são o casos dos risers e linhas de amarração. Apesar de extensa, a literatura técnica especializada no assunto é focada em simplificações, tais como os estudos de cilindros rígidos fixos, cilindros rígidos montados em base elástica e cilindros flexíveis verticais ou lançados em catenária livre. A questão da inclinação é abordada em termos do Principio da Independência que diz que as forças e a frequência de emissão de vórtices em um cilindro inclinado são iguais as de um cilindro vertical se considerada apenas a parcela da correnteza normal à direção de inclinação. Estudos anteriores mostraram que este princípio é válido somente em algumas condições específicas e poucos deles apresentam resultados para cilindros flexíveis. Com base nisso, um ensaio em escala reduzida em tanque de reboque foi realizado com um modelo de linha composto por um tubo de silicone preenchido com microesferas de aço e condições de contorno articuladas em suas extremidades, o que conferiu características inerciais e geométricas ideais para a obtenção do fenômeno. Além da configuração vertical (? = 0°), que é o caso de referência, o modelo foi estudado em outras quatro inclinações com a vertical: ? = 10°, 20°, 30° e 45°. Estas inclinações foram ensaiadas para cinco diferentes azimute: ? = 0°, 45°, 90°, 135° e 180°, resultando em vinte e uma configurações de inclinação. Os resultados são analisados em termos da decomposição modal da vibração da linha, ou seja, são apresentadas amplitudes e frequências de oscilação ocorridas em cada um dos modos de vibrar. Além disso são realizadas análises espectrais, gráficos de evolução espaço-temporal, trajetórias de pontos ao longo do modelo flexível, entre outros. Frequências naturais, coeficientes de amortecimento e trações no topo são apresentados, complementarmente, como resultados de caracterização do modelo. Os estudos apontaram para uma validade do PI com algumas ressalvas, principalmente influenciadas pela diferença nas frequências do primeiro e segundo modo que é crescente com o aumento da inclinação. Além disso conclusões importantes sobre a coexistência modal, em regiões de ressonância e/ou de transição da dominância modal, foram obtidas. / The vortex-induced vibration problem in flexible cylinders yawed in relation to the incident current profile is studied through an experimental approach. This topic has great importance and application on Naval and Oceanic Engineering once there are multiple structures that fit into this description, such as risers and mooring lines. Though extensive, technical literature specialized on this topic is focused on simplifications such as the study of fixed rigid cylinders, elastic base rigid cylinders and flexible cylinders assembled vertically or launched in free hanging catenary. The inclination issue is addressed in the terms of the Principle of Independence which states that the forces and frequency shedding in an inclined cylinder are equal to those of a vertical cylinder if only considered the current component normal to the inclination plane. Previous studies showed that this principle is valid only on some specific conditions and few of them showed results to flexible systems. Based on this, a scaled tow tank test was performed with a line model composed of a silicone tube filled with steel microspheres and articulated end conditions, which offered the ideal inertial and geometrical conditions to obtaining the phenomenon. Besides the vertical configuration (? = 0°), which is the reference case, the model was studied in other four inclinations with the vertical: ? = 10°,20°, 30° and 45°. These inclinations were tested for five different azimuth directions: ? = 0°, 45°, 90°, 135° and 180°, resulting in 21 configurations. The results are analyzed on terms of the modal decomposition of the line motions, that is, amplitudes and oscillation frequencies are presented for each one of the vibration modes. Furthermore other analyzes are made, as spectral graphs, spatio-temporal evolution graphs, line points trajectories, among others. Natural frequencies, damping coefficients and tensions at the top are presented, complementarly, as results of the model characterization. The studies pointed to a validity of the IP with some reservations, mainly influenced by the difference in of the first and second mode frequencies that is increasing with the yaw increase. In addition, important conclusions about modal coexistence in regions of resonance and / or transition of modal dominance were obtained.