No description available.

A preliminary investigation of the added properties called added mass, added damping and added stiffness have been performed for a Kaplan turbine. The magnitude of dimensionless numbers have been used in order to classify the interaction of the fluid and the solid. The classification is done to bring clarity in which of the added properties are of importance for the system. The diameter of the runner and the hub have been calculated using the power output and the head for a Kaplan turbine. These dimensions have been used to determine the magnitude of the dimensionless numbers along with the velocity of the fluid. It turned out that all added properties affect the turbine, however, the magnitude of them are quite different. The magnitude of the added mass and the added damping are greater than the added stiffness, which often is neglected. The added mass can be determined if the natural frequencies of the structure in air and in water are known. The difference in natural frequencies can be used to determine the added mass factor and thereby the added mass of the system. The added damping can be determined by the change in damping ratio for different surrounding fluids. This was done using the simulation software ANSYS Workbench v.17.1, where two different types of simulation were used, ”acoustic coupled simulation” and ”two way coupled simulation”. The complexity of the geometry of the Kaplan turbine was simplified to a disc and a shaft. The result for the added mass was validated using results from an experiment [1]. The added damping could be determined, but not validated. The different types of simulation have been compared and it turned out that the added mass could be determined using ”acoustic coupled simulation” and ”two way coupled simulation”, but the added damping could only be determined using the ”two way coupled simulation”. / En preliminär undersökning av de adderade egenskaperna kallade, adderad massa, adderad dämpning och adderad styvhet har utförts för en Kaplan turbin. Magnituden av dimensionslösa tal har använts för att klassificera interaktionen av fluiden och soliden. Klassificeringen görs för att bringa klarhet i vilka av de adderade egenskaperna är av betydelse för systemet. Diametrarna för löphjulet och navet har beräknats utifrån effekt och fallhöjd för en Kaplan turbin. Dessa längder har använts för att bestämma magnituden av de dimensionslösa talen tillsammans med fluidens hastighet. Det visade sig att alla adderade egenskaper påverkar turbinen, men omfattningen av dem är helt annorlunda. Magnituden av den adderade massan och den adderade dämpningen är större än den adderade styvheten, som ofta försummas. Den adderade massan kan bestämmas om de naturliga frekvenserna av strukturen i luft och vatten är kända. Skillnaden i egenfrekvenser kan användas för att bestämma faktorn av den adderade massan och därigenom den adderade massan. Den adderade dämpningen kan bestämmas genom ändringen i dämpningsförhållande för olika omgivande fluider. Detta gjordes med hjälp av simuleringsprogrammet ANSYS Workbench v.17.1, där två olika typer av simulering användes, ”acoustic coupled simulation” och ”two way coupled simulation”. Komplexiteten i geometrin för en Kaplan turbin förenklades till en skiva och en axel. Resultatet för den adderade massan validerades med resultat från ett experiment [1]. Den adderade dämpningen kunde bestämmas, men inte valideras. De olika typerna av simulering har jämförts och det visade sig att den adderade massan kan bestämmas med hjälp av både ”acoustic coupled simulation” och ”two way coupled simulation”, men den adderade dämpningen kunde endast bestämmas med hjälp av ”two way coupled simulation”.

Kite energy systems are an emerging renewable energy technology. Unlike conventional turbines, kite energy systems extract wind power using tethered kites which can move freely in the wind or underwater in an ocean current. Due to the mobility, kite power systems can harvest power from regions with higher and steadier power density by moving in high-speed cross flow motion. An airborne kite energy system harnesses wind power at an altitude higher than the conventional wind turbines, while an undersea kite energy system extracts power close to the ocean surface. In this dissertation, the physical limitation, mathematical modeling, and control system design of the kite energy systems are studied. First, three major physical effects that are acting on the kite energy systems are investigated, including potential force, steady aero-/hydro-dynamic force and added mass effects. Furthermore, the dissipativity of the steady aero-/hydro-dynamic forces with respect to the apparent velocity is established. Based on this analysis, the power generation limit of the kite energy systems is studied. A power limit formulation is given which generalize the two-dimensional result to three-dimensional case. The different physical phenomenon is modeled in different coordinate systems, the difference of the density, viscosity between air and water are significant, and the kite energy system can operate in two distinct modes. To combine different physical effects into a single simulation framework, the equivalences of the kite model in different coordinate systems are established through kinematic analysis. Using these equivalent relations, a unified simulation model for airborne and undersea kite energy systems are derived. The control system design of kite energy systems is also investigated. The resulting equations of motion of kite energy systems are highly nonlinear. Therefore, Lyapunov methods are used to analyze the system behavior. Three different techniques are reviewed, including Lyapunov analysis for autonomous and non-autonomous systems, the ultimate boundedness and input-to-state stability and passivity methods. For the fixed tether length kite energy systems, the ultimate boundedness of the kite translation is established through the dissipativity of the steady aero-/hydro-dynamic force. For the variable tether length kite energy system, the input-to-state analysis is used to design the tether tension that guaranteed the boundedness of the kite translation. In both cases, the Lyapunov based methods are used to design kite rotational control systems which result in PD type control signals. Although this control scheme generates consecutive power cycles for kite energy systems. It is shown that the kite aero-/hydro-dynamical performance is unstable in the simulation which could result in unsteady power generation. To provide a steadier performance in kite translation and power output, the relative dynamics of the kite translation is first proposed. In this model, the kite apparent speed and attitudes, the angle of attack and side-slip angle, are used to describe the kite translation. A nonlinear control scheme is designed to regulate the angle of attack and side-slip angle using back-stepping methods by using the kite angular velocity and control inputs. However, due to the magnitude limit of the angular velocity, the residual error of the apparent attitude tracking remain large for the large desired angle of attack and side-slip angle. To achieve a better power harvesting and aero-/hydro-dynamics performance, the geometric properties of kite angle of attack and side-slip angle are studied. A geometric attitudes trajectory is constructed to track given apparent attitudes. A rotational control system is designed based on the back-stepping and sliding mode methods for the desired geometric attitude, and the high gain observer is applied to acquire the information needed for the rotational control signal. Through the geometric apparent attitudes tracking control algorithm, the angle of attack and side-slip angle act as direct control inputs to the kite translational motion. The kite translational dynamics under the geometric apparent attitude tracking is studied. These dynamics give the possibility of controlling the kite translational motion only through the rotational control scheme.

The concept of added hydrodynamic properties such as added mass is of importance in modern hydropower development, mainly for rotor dynamic calculations. Added mass could result in reduced natural frequencies and altered mode compared to existing simulation models. It is of importance to quantify added mass but also added damping to make the simulation models more accurate. Experiments are conducted on a model Kaplan turbine, D = 0,5 m, and a steel cube, S = 0,2 m, for linear vibrations in still water confined in a cylindrical tank. The experiments are conducted in air and water for evaluation of added forces. The vibrations are generated with an electrodynamic vibration exciter with a frequency range of approximately 1-10 Hz with amplitudes 0,5-3 mm. The experiments were repeated to check test rig reliability. Each individual working point [frequency, amplitude] were in total tested 40 times in 15 s intervals. The added mass was found to be function of acceleration for the model Kaplan with an increase in added mass from 10 % at 4 m/s2 to 35 % at 0,5 m/s2. The damping forces was at best measured at ±30 %, making added damping calculations unreliable. The cube experiments resulted in small differences between water and air. Cube results must be interpreted with caution due to test rig uncertainties.

No description available.

Um corpo imerso em movimento arbitrário interage com o fluido ao redor. As partículas fluidas próximas ao corpo exercem certa resistência inercial quando o corpo acelera ou desacelera, devido ao acoplamento dinâmico entre corpo e fluido. Este trabalho resolve as equações de Navier-Stokes, discretizadas pelo método dos elementos finitos, usando o programa de código aberto (LGPL) FreeFem++, e avalia as forças do escoamento que agem sobre um cilindro circular, o qual oscila harmonicamente em um fluido em repouso para números de Keulegan-Carpenter (KC) entre 0,5 e 10, mantendo o parâmetro da frequência constante e igual a 35. Os números de KC selecionados visam entender os conceitos de inércia adicional em fluido viscoso, desde em escoamentos simples até em escoamento mais complexos. O escoamento é bidimensional, laminar e não estacionário. A força em linha com o movimento é então decomposta, conforme equação de Morison, como a soma de uma força inercial e outra de arrasto. Os resultados possuem boa aderência com trabalhos analíticos, experimentais e numéricos anteriores disponíveis na literatura. A dinâmica do escoamento induzido pelo cilindro em movimento harmônico é rica. Para baixo KC, o escoamento é simétrico e estável. Para valores intermediários de KC, a camada limite descola da superfície do cilindro e vórtices são emitidos a cada meio-ciclo. Para elevado KC, certa assimetria se desenvolve e vórtices são emitidos obliquamente a cada meio-ciclo. / An immersed body in arbitrary motion interacts with the surrounding fluid. The fluid particles close to the body impart their inertial resistance when the body accelerates or decelerates, due to the dynamic coupling between body and fluid. This work solves the incompressible Navier-Stokes equation, discretized by the finite element method, using the open source (LGPL) software FreeFem++, and evaluates the flow forces that act on a circular cylinder which oscillates harmonically in a resting fluid for Keulegan- Carpenter (KC) number between 0.5 and 10, with a constant frequency parameter equal to 35. The selected KC numbers aims to understand the concepts of added inertia in viscous fluid, from simpler to more complex flows. The flow is two dimensional, laminar and unsteady. The in-line force is then decomposed, according to Morison equation, as a sum of an inertial force and a drag force. The results agree with former analytical, experimental and numerical works available in the literature. The dynamics of the flow induced by the harmonically moving cylinder is rich. For low KC, the flow is symmetric and stable. For intermediate KC, the boundary layer detaches from the cylinder surface and vortices are shed at each half cycle. For higher KC, certain asymmetry develops and vortices are shed obliquely at each half cycle.

The concept of using aluminum as the primary construction material for high speed ships and the hydroelastic behavior of the structure is widely gaining importance as a significant research topic in naval architecture. Aluminum is lighter than steel and hence can be predominantly used in high speed crafts which experiences significant slamming. This thesis work is focused on wedge shaped models. Free fall wedge impact is studied and a FORTRAN 90 computer program is developed to estimate the structural response of the wedge experiencing slamming by the use of matrix methods, finite element techniques and Newmark-Beta numerical time integration methods. The numerical solution is validated by comparison with the static solution. The theoretical hydrodynamic pressures which are used as input for this work was originally developed by using a flat cylinder theory [26]. The wedge drop at 0.6096 m (24 inch) drop height with an impact veloc- ity of v=3.05 m/s is based as the premise and the experimental pressure distributions measured by the pressure-transducers and the theoretical pressure predictions are used as inputs and the structural response is derived. Additionally, the response is compared for three different plate thicknesses and the results are compared against each other. The maximum deflection is comparable to the deflection evaluated from the experiment and tends to attain convergence as well. As the plate thickness reduces there tends to be a significant rise in the deflection values for the wedge plate, in the manner that when the plate thickness is halved there is a deviation of more than 75% in the deflection values as such.

Um corpo imerso em movimento arbitrário interage com o fluido ao redor. As partículas fluidas próximas ao corpo exercem certa resistência inercial quando o corpo acelera ou desacelera, devido ao acoplamento dinâmico entre corpo e fluido. Este trabalho resolve as equações de Navier-Stokes, discretizadas pelo método dos elementos finitos, usando o programa de código aberto (LGPL) FreeFem++, e avalia as forças do escoamento que agem sobre um cilindro circular, o qual oscila harmonicamente em um fluido em repouso para números de Keulegan-Carpenter (KC) entre 0,5 e 10, mantendo o parâmetro da frequência constante e igual a 35. Os números de KC selecionados visam entender os conceitos de inércia adicional em fluido viscoso, desde em escoamentos simples até em escoamento mais complexos. O escoamento é bidimensional, laminar e não estacionário. A força em linha com o movimento é então decomposta, conforme equação de Morison, como a soma de uma força inercial e outra de arrasto. Os resultados possuem boa aderência com trabalhos analíticos, experimentais e numéricos anteriores disponíveis na literatura. A dinâmica do escoamento induzido pelo cilindro em movimento harmônico é rica. Para baixo KC, o escoamento é simétrico e estável. Para valores intermediários de KC, a camada limite descola da superfície do cilindro e vórtices são emitidos a cada meio-ciclo. Para elevado KC, certa assimetria se desenvolve e vórtices são emitidos obliquamente a cada meio-ciclo. / An immersed body in arbitrary motion interacts with the surrounding fluid. The fluid particles close to the body impart their inertial resistance when the body accelerates or decelerates, due to the dynamic coupling between body and fluid. This work solves the incompressible Navier-Stokes equation, discretized by the finite element method, using the open source (LGPL) software FreeFem++, and evaluates the flow forces that act on a circular cylinder which oscillates harmonically in a resting fluid for Keulegan- Carpenter (KC) number between 0.5 and 10, with a constant frequency parameter equal to 35. The selected KC numbers aims to understand the concepts of added inertia in viscous fluid, from simpler to more complex flows. The flow is two dimensional, laminar and unsteady. The in-line force is then decomposed, according to Morison equation, as a sum of an inertial force and a drag force. The results agree with former analytical, experimental and numerical works available in the literature. The dynamics of the flow induced by the harmonically moving cylinder is rich. For low KC, the flow is symmetric and stable. For intermediate KC, the boundary layer detaches from the cylinder surface and vortices are shed at each half cycle. For higher KC, certain asymmetry develops and vortices are shed obliquely at each half cycle.

An experimental investigation of a vibrating Kaplan turbine runner was performed in order to understand the hydrodynamic effects and to obtain or confirm the mass and damping coefficients used for dimensioning at the design stage. Improved design can lead to increased efficiency and lifetime of hydropower stations. The method was based on the 90◦ phase shift between acceleration and velocity and their relationship with mass and damping respectively. The experiment examined frequencies between 1–9 Hz at displacements between 0.25–2.00 mm. Results showed a frequency dependent added mass which varied between 1.2 and 1.5 (neglecting the highest and lowest frequencies) and an added damping between 0.8 and 1.2 which became of importance at low frequencies. A mathematical interpretation of the fluid solid interactions (based on the constitutive equation for stresses in a Newtonian fluid) has been derived and connected to the obtained experimental data.

Cette thèse vise à analyser expérimentalement une structure flexible et légère dans différents régimes d’écoulement, dont le régime cavitant. Un protocole expérimental a donc été mis en place afin de caractériser le comportement hydroélastique d’un profil NACA 0015 en polyoxyméthylène (POM) et de le comparer à un profil en acier inoxydable considéré comme « rigide ». Des mesures en écoulement subcavitant ont été réalisées : chargement hydrodynamique, contraintes, déformées statiques, réponse vibratoire et champ de vitesse ont été mesurés pour les deux matériaux. Enfin, une analyse vibratoire a été menée en écoulement cavitant. Ces mesures nous ont permis de constater que les déformées statiques du profil flexible sont similaires aux déformations observées sur une poutre encastrée : la flexion est la déformation principale et la torsion est faible. Toutefois les performances du profil flexible sont moins bonnes que pour un profil rigide : la portance diminue tandis que la traînée augmente. D’autre part, il apparaît que la dynamique du profil est contrôlée par l’écoulement. En effet, lorsque l’incidence du profil est proche de l’angle de décrochage, une fréquence liée au détachement tourbillonnaire apparaît sur les spectres de vibration des profils. Elle conduit à une réduction des fréquences propres liées à la flexion : si l’influence de cette fréquence sur le profil rigide reste faible à basse vitesse, sa proximité avec la fréquence propre du profil flexible conduit à un lock-in. Celui-ci se produit également en écoulement cavitant : lorsque la poche de cavitation devient instable, sa fréquence d’oscillation devient très énergétique et prend le contrôle de la dynamique du profil flexible. Le lock-in prend fin quand une supercavitation se développe autour du profil. Il conduit à une augmentation de la masse ajoutée au profil alors qu’elle devrait diminuer en présence de vapeur d’eau. / This work deals with an experimental analysis of a flexible and light lifting profile for various flow conditions, including cavitation. An experimental protocol was set up to study a flexible NACA 0015 made of polyoxymethylene (POM) and compare its behaviour with a foil made of steel, which is considered as rigid. The forces, strains, stresses and vibrations of the foils were measured, as well as the velocity field. Moreover, a vibratory analysis was performed in cavitating flow. The flexible foil behaves like a built-in beam : the deformations corresponds to predictions from the beam theory, with high bending and low twisting. These deformations imply lower lift and higher drag compared to the rigid foil. The vortex shedding frequency appears on the vibration spectra near stall. It increases with flow velocity and leads to a decrease of the natural bending frequency. But flexibility involves lower natural frequencies : the first bending frequency of the flexible foil is 3.5 times lower than the rigid one. This allows lock-in between the first bending frequency of the flexible foil and the vortex shedding frequency. Lock-in occurs in cavitating flows too : when cavitation becomes unstable, it oscillates with a frequency close to the bending natural frequency of the flexible foil. This lock-in ends when the cavitation number is low enough, what leads to a decrease of the cavitation oscillation frequency. In those conditions, the added mass of the flexible foil does not decrease with the cavitation number as the added mass of the rigid foil.