Consideram-se neste trabalho seções bidimensionais oscilando em balanço. Adotam-se modelos representativos do movimento segundo este único grau de liberdade. Estimam-se os parâmetros de inércia e de amortecimento hidrodinâmicos por meio de experimentos de decaimento. Simulações numéricas incorporando os parâmetros estimados experimentalmente, bem como previsões empíricas de resultados da literatura, são confrontadas à registros experimentais para verificação da adequação das previsões, e para avaliação da adequação dos modelos à representação da dinâmica da oscilação. Com a metodologia de análise escolhida, avalia-se a influência de determinados parâmetros sobre as propriedades hidrodinâmicas; consideram-se variações: de proporções da seção, de posição vertical do centro de massa, de inércia própria em balanço, de forma do bojo, e quanto a presença de bolina e suas proporções. Também é considerada a influência do ângulo inicial de banda nas propriedades hidrodinâmicas, bem como a participação da energia irradiada pela onda na energia acumulada pelo sistema anterior ao início do movimento. Os elementos anteriores levam à proposição de orientações para avaliação da influência das propriedades geométricas e inerciais no comportamento do casco em balanço. / The scope of this work is the verification of hydrodynamic properties of two dimensional rolling sections. Analytical models of a single degree-of-freedom movement are adopted. The added inertia and damping are estimated by free decay tests. Numerical simulations with the obtained experimental parameters as well as empirical literature results are compared to the data tests in order to verify the adequacy of the procedures. With the chosen method of analysis, the influence of the hydrodynamic parameters are verified. The following parameters are considered: the beam draft ratio, vertical position of center of gravity, moment inertia, bilge shape and the addition or not of bilge keels. The initial angle of roll is also considered as well as the transport of the energy accumulated before the decay by the wave generated by the movement of the model. These elements lead to the proposition of orientations for the verification of the influence of geometric and inertial properties in the behave of rolling two-dimensional sections.

Consideram-se neste trabalho seções bidimensionais oscilando em balanço. Adotam-se modelos representativos do movimento segundo este único grau de liberdade. Estimam-se os parâmetros de inércia e de amortecimento hidrodinâmicos por meio de experimentos de decaimento. Simulações numéricas incorporando os parâmetros estimados experimentalmente, bem como previsões empíricas de resultados da literatura, são confrontadas à registros experimentais para verificação da adequação das previsões, e para avaliação da adequação dos modelos à representação da dinâmica da oscilação. Com a metodologia de análise escolhida, avalia-se a influência de determinados parâmetros sobre as propriedades hidrodinâmicas; consideram-se variações: de proporções da seção, de posição vertical do centro de massa, de inércia própria em balanço, de forma do bojo, e quanto a presença de bolina e suas proporções. Também é considerada a influência do ângulo inicial de banda nas propriedades hidrodinâmicas, bem como a participação da energia irradiada pela onda na energia acumulada pelo sistema anterior ao início do movimento. Os elementos anteriores levam à proposição de orientações para avaliação da influência das propriedades geométricas e inerciais no comportamento do casco em balanço. / The scope of this work is the verification of hydrodynamic properties of two dimensional rolling sections. Analytical models of a single degree-of-freedom movement are adopted. The added inertia and damping are estimated by free decay tests. Numerical simulations with the obtained experimental parameters as well as empirical literature results are compared to the data tests in order to verify the adequacy of the procedures. With the chosen method of analysis, the influence of the hydrodynamic parameters are verified. The following parameters are considered: the beam draft ratio, vertical position of center of gravity, moment inertia, bilge shape and the addition or not of bilge keels. The initial angle of roll is also considered as well as the transport of the energy accumulated before the decay by the wave generated by the movement of the model. These elements lead to the proposition of orientations for the verification of the influence of geometric and inertial properties in the behave of rolling two-dimensional sections.

In order to reach climate and environmental goals, Sweden is increasing the implementation of intermittent renewable energy sources such as wind and solar power to the electricity grid. The increase of intermittent energy sources is rising power regulation requirement towards hydropower, which increasingly exposes the hydraulic turbines to high loads and fluctuating hydraulic forces. These conditions affect the turbine’s structural and rotor dynamic behavior, leading to fatigue in turbine components. Identifying the parameters that affect the dynamics of the water turbine is an essential part of analyzing and, if possible, avoiding these situations. Furthermore, accurate rotor dynamic models are necessary to design for a robust hydropower unit and improve the estimate of wear on turbine components. Added parameters (added mass, polar moment of inertia, and damping) are hydrodynamic effects occurring due to interaction between structural vibrations and surrounding fluid. Added parameters can modify the turbine’s natural frequencies and consequently its dynamic behavior. Therefore, it is of interest to study and quantify the impact of these parameters on the turbine for accurate rotor dynamic modeling and turbine design. The added parameters have been investigated by conducting experiments on a model Kaplan runner, for which the project has been divided into two consecutive parts. First, experiments were performed in a test rig, in which the runner was excited in a lateral movement to determine added mass and linear damping. Secondly, experiments were performed in a test rig similar to the first, except the runner was excited in a torsional movement to determine added polar moment of inertia and torsional damping. Force and displacement have been measured during both movements, with the runner placed in air and thereafter in quiescent water. The added parameters were quantified by comparing measurements conducted with the runner in air against those conducted in water. By varying the excitation frequency and amplitude, added parameters have been analyzed against excitation frequency, velocity, and acceleration to determine dependent variables. The dimensionless added mass ratio, γma, was investigated within a range of acceleration of 0.07m/s2 to 5.00 m/s2 and in an excitation frequency of 2-9 Hz. Results exhibited a frequency-dependent added mass ratio, leading to a mass addition variation of 1.00-1.49 times the test rig mass with a mean γma of 1.22. Similarly, the dimensionless added polar moment of inertia, γIp, was investigated within a range of angular acceleration between 2.4 rad/s2 to 29.6 rad/s2 and in an excitation frequency range of 2-10 Hz. The mean added polar inertia ratio, γIp, was obtained as 1.09 times the polar moment of inertia of the test rig, corresponding to an increase in polar inertia of about 9%, compared to the total dry polar inertia of the test rig. Results showed that the added polar inertia ratio varied by approximately 1.8% within the studied frequency range. Thus, no frequency dependence could be determined. Due to measurement uncertainties and limitations of the test rigs, added linear damping and torsional damping could not be determined in either of the existing test rigs (lateral and torsional movement).

Ship roll motion has been the subject of many studies, because of the complexities associated with this mode of ship motion, and its impact on operability, safety, and survivability. Estimation and prediction of the energy transfer and dissipation of the hydrodynamic components, added inertia and damping, is essential to accurately describe the roll motions of a ship. This is especially true for ship operations in moderate to extreme sea conditions. In these conditions, a complex process of energy transfer occurs, which alters the physical behavior of the hydrodynamic components, and ultimately affects the amplitude of ship roll motion. Bilge keels have been used on ships for nearly two centuries, to increase damping and reduce the severity of roll motions experienced by a ship in waves. Because ship motions are more severe in extreme sea conditions, large roll angles may occur. With the possibility of crew injury, cargo damage, or even capsize, it is important to understand the behavior of the roll added inertia and damping for these conditions. Dead ship conditions, where ships may experience excitation from beam, or near beam, seas present a worst case scenario in heavy weather. The behavior of a ship in this condition should be considered in both the design and assessment of seakeeping performance. In this study, hydrodynamic component models of roll added inertia and roll damping were examined and assessed to be unsuitable for accurate prediction of ship motions in heavy weather. A series of model experiments and numerical studies were carried out and analyzed to provide improved understanding of the essential physical phenomena which affect the hydrodynamic components and occur during large amplitude roll motion. These observations served to confirm the hypothesis that the existing models for roll added inertia and damping in large amplitude motions are not sufficient. The change in added inertia and damping behavior for large roll motion is largely due to the effects of hull form geometry, including the bilge keels and topside geometry, and their interactions with the free surface. Therefore, the changes in added inertia and damping must be considered in models to describe and predict roll motions in severe wave environments. Based on the observations and analysis from both experimental and numerical methods, several time-domain model formulations were proposed and examined to model hydrodynamic components of large amplitude roll motions. These time-domain formulations included an analytical model with memory effects, a piecewise formulation, and several possibilities for a bilge keel force model. Although a piecewise model for roll damping was proposed, which can improve the applicability of traditional formulations for roll damping to heavy weather conditions, a further attempt was undertaken to develop a more detailed model specifically for the bilge keel force. This model was based on the consideration of large amplitude effects on the hydrodynamic components of the bilge keel force. Both the piecewise and bilge keel force models have the possibility to enable improved accuracy of potential flow-based numerical prediction of ship roll motion in heavy weather. However, additional development remains to address issues for further practical implementation. / Ph. D.

This thesis documents the studies conducted in deriving a mathematical model representing the dynamics of a maneuvering ship to be implemented as part of an interactive real-time simulation system, as well as the details and results of the implementation process itself. Different effects on the dynamics of ship motions are discussed separately, meaning that the effects are considered to be applied to the system one at a time and they are included in the model simply by the principle of superposition. The model is intended to include the hydrodynamic interactions between the ship hull and the ocean via added mass (added inertia), damping and restoring force concepts. In addition to these effects, which are derived considering no incident waves are present on the ocean, the environmental disturbances, such as wind, wave and ocean current are also taken into account for proposing a mathematical model governing the dynamics of the ship. Since the ultimate product of this thesis work is a running computer code that can be integrated into an available simulation software, the algorithm development and code implementation processes are also covered. Improvements made on the implementation to achieve &ldquo / better&rdquo / real-time performance are evaluated comparatively in reference to original runs conducted before the application of improvement under consideration. A new method to the computation of the wave model that allows faster calculation in real-time is presented. A modular programming approach is followed in the overall algorithm development process in order to make the integration of new program components into the software, such as a new hull or propulsion model or a different integrator type possible, easily and quickly.