Nowadays, the climate change issue is becoming more and more actual in our society. Increase of the average temperature on Earth in a couple of degrees could have catastrophic consequences. One of the possible solutions seems to be renewable energy sources as photovoltaics, biomass of water and wind energy. This thesis deals with the aerodynamics problems of wind energy source. Wind turbines transform kinetic energy of wind to mechanical power. The efficiency is physically limited to 59,26 %, but in reality, it is getting around 45 %. This is caused by three biggest losses inducted in wind turbines as wake losses, losses due to finite number of blades and drag losses. Based on analytical relationships and including these three losses the aerodynamics blade design is conducted. Later, the numerical simulations show higher values of drag and lower values of lift force on airfoil compared to analytical calculation. In fact, percentage deviations are acceptable and to conclude, the numerical analysis was able to relatively accurately simulate force action of free stream velocity on the blade.

Tidal energy represents a promising resource for the future energy mix. For harnessing tidal currents free stream horizontal axis turbines have been investigated for some years. The acting physics is very similar to the one of horizontal axis wind turbines, with the additional phenomenon of cavitation, which causes performance reduction, flow induced noise and severe damages to the turbine blade and downstream structures. The paper presents an enhanced semi-analytical model that allows the prediction of the performance characteristics including cavitation inception of horizontal axis tidal turbines. A central component is the well-known blade element momentum theory which is refined by various submodels for hydrofoil section lift and drag as a function Reynolds number and angle of attack, turbine thrust coefficient, blade hub and tip losses and cavitation. Moreover, the model is validated by comparison with comprehensive experimental data from two different turbines. Predicted power and thrust coefficient characteristics were found to agree well with the experimental results for a wide operational range and different inflow velocities. Discrepancies were observed only at low tip speed ratios where major parts of the blades operate under stall conditions. The predicted critical cavitation number is somewhat larger than the measured, i.e. the prediction is conservative. As an overall conclusion the semi-analytical model developed seems to be so fast, accurate and robust that it can be integrated in a future workflow for optimizing tidal turbines.

Preference for one stimulus context over another and resistance to disruption within those contexts are a function of the conditions of reinforcement arranged within those contexts. According to behavioral momentum theory, these measures are converging expressions of the concept of response strength. Most studies have found that preference in concurrent chains and resistance to change are greater in contexts presenting higher rates or larger magnitudes of reinforcement. The present series of experiments attempted to extend behavioral momentum theory by examining whether differences in reinforcer type affect relative response strength with rats lever pressing for different types of food. In Experiment 1 of Chapter 2, several nonuniform disrupter types were examined that provided free access to a food type that was the same as one reinforcer type. Responding decreased more in the context presenting the same type of reinforcer as the disrupter, suggesting that many traditional disrupters (e.g., satiation) are inappropriate for examining how reinforcer type impacts response strength. Therefore, extinction was used throughout the remainder of the experiments to more uniformly disrupt responding across contexts. In Experiment 2 of Chapter 2, resistance to extinction was assessed when food pellets and a sucrose solution maintained responding across contexts. Moreover, relative reinforcer type was manipulated by changing the sucrose concentration across conditions. Relative response rates were systematically affected by changing sucrose concentration, but relative resistance to extinction was not. In Experiment 3 of Chapter 2, qualitative difference between reinforcers was enhanced and preference also was assessed to provide a converging measure of response strength. Preference and relative response rates were systematically affected, but relative resistance to extinction again was not. Finally, in Chapter 3, relative reinforcer rate and type were manipulated while assessing preference and resistance to extinction using the matching law. Preference, but not resistance to extinction, consistently was affected by changes in reinforcer rate and type. Systematic deviations in sensitivity and bias, however, suggested that different reinforcer types interacted with reinforcer rate. Overall, these findings suggest that the overall context of reinforcement, including interactions between different reinforcer types, should be considered when assessing preference and relative resistance to change.

An experimental study on the application of Digital Image Correlation (DIC) to measure the deformation and strain of rotating blades is described. Commercial DIC software was used to obtain measurements on three different types of rotors with diameter ranging from 18 to 39 and with varying flexibility to explore applicability of the technique over a breadth of scales. The image acquisition was synchronized with the frequency of rotation such that images could be obtained at the same phase and the consistency of measurements was observed. Bending and twist distributions were extracted from the data with deformation as high as 0.4 measured with a theoretical accuracy of 0.0038 and span-wise resolution of 0.066. The technique was demonstrated to have many advantages including full-field high resolution results, non-intrusive measurement, and good accuracy over a range of scales. The span-wise deformation profiles from the DIC technique are used in conjunction with Blade Element Momentum Theory to calculate the thrust and power consumed by the rotor with rigid vi blades; results are comparable to load cell measurements albeit thrust is somewhat under-predicted and power is over-predicted. Overall, the correlation between DIC calculated thrust and BEMT approximations for comparable blades with constant pitch were within 12% through the onset of stall. Measurement of flexible blade deformation that would not have been possible with other techniques demonstrated the utility of the DIC method and helped to confirm predictions of flexible blade behavior. / text

A wind turbine needs to be controlled to ensure its safe and optimal operation, especially during high wind speeds. The most common control objectives are to limit the power and rotational speed of the wind turbine by using pitch control. Aero Energy is a company based in Potchefstroom, South Africa, that has been developing and manufacturing wind turbine blades since 2000. Their most popular product is the AE1kW blades. The blades have a tendency to over-speed in high wind speeds and the cut-in wind speed must be improved. The objective of this study was to develop an active pitch control system for wind turbines. A prototype active pitch control system had to be developed for the AE1kW blades. The objectives of the control system are to protect the wind turbine from over-speeding and to improve start-up performance. An accurate model was firstly developed to predict a wind turbine’s performance with active pitch control. The active pitch control was implemented by means of a two-stage centrifugal governor. The governor uses negative or stalling pitch control. The first linear stage uses a soft spring to provide improved start-up performance. The second non-linear stage uses a hard spring to provide over-speed protection. The governor was manufactured and then tested with the AE1kW blades. The governor achieved both the control objectives of over-speed protection and improved start-up performance. The models were validated by the results. It was established that the two-stage centrifugal governor concept can be implemented on any wind turbine, provided the blades and tower are strong enough to handle the thrust forces associated with negative pitch control. It was recommended that an active pitch control system be developed that uses positive pitching for the over-speed protection, which will eliminate the large thrust forces. Keywords: pitch control, wind turbine, centrifugal governor, over-speed protection, cut-in wind speed, blade element-momentum theory, rotor, generator, stall, feathering. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

A wind turbine needs to be controlled to ensure its safe and optimal operation, especially during high wind speeds. The most common control objectives are to limit the power and rotational speed of the wind turbine by using pitch control. Aero Energy is a company based in Potchefstroom, South Africa, that has been developing and manufacturing wind turbine blades since 2000. Their most popular product is the AE1kW blades. The blades have a tendency to over-speed in high wind speeds and the cut-in wind speed must be improved. The objective of this study was to develop an active pitch control system for wind turbines. A prototype active pitch control system had to be developed for the AE1kW blades. The objectives of the control system are to protect the wind turbine from over-speeding and to improve start-up performance. An accurate model was firstly developed to predict a wind turbine’s performance with active pitch control. The active pitch control was implemented by means of a two-stage centrifugal governor. The governor uses negative or stalling pitch control. The first linear stage uses a soft spring to provide improved start-up performance. The second non-linear stage uses a hard spring to provide over-speed protection. The governor was manufactured and then tested with the AE1kW blades. The governor achieved both the control objectives of over-speed protection and improved start-up performance. The models were validated by the results. It was established that the two-stage centrifugal governor concept can be implemented on any wind turbine, provided the blades and tower are strong enough to handle the thrust forces associated with negative pitch control. It was recommended that an active pitch control system be developed that uses positive pitching for the over-speed protection, which will eliminate the large thrust forces. Keywords: pitch control, wind turbine, centrifugal governor, over-speed protection, cut-in wind speed, blade element-momentum theory, rotor, generator, stall, feathering. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

Orientador: Prof. Dr. Rodrigo Fresneda / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , 2016. / O modelo de Ponzano-Regge é um modelo de gravitação quântica em três dimensões. O principal objetivo deste trabalho é apresentar os fundamentos para construção desse modelo. Buscamos introduzir conceitos necessários para entendê-lo, abordando a teoria de representações de grupos de Lie compactos, tais como: redutibilidade de uma representação, representações de produto direto, e representações no espaço de funções. Tratamos especialmente do caso particular do grupo SU(2). Nesse contexto particular, apresentamos os símbolos 3j e 6j e suas propriedades. O modelo de Ponzano-Regge descreve uma geometria tridimensional discretizada, dada em termos de uma triangulação por simplexos (tetraedros, em três dimensões), de tal forma que o comprimento de cada aresta corresponde a uma representação irredutível do grupo de Lie SU(2). Estes tetraedros são descritos como símbolos 6j, cuja fórmula assintótica possibilita a passagem ao limite clássico, levando a uma expressão para a função de partição que representa uma soma sobre geometrias em três dimensões. / The Ponzano-Regge model is a quantum gravity model in three dimensions. The main goal of this work is to present the foundations for the construction of this model. We aim at introducing the necessary concepts to understand it, taking into account the theory of representations of compact Lie groups, such as: reducibility of representations, direct product representations, and representations in function spaces. We treat the particular case of the SU(2) group. In this special case, we present the 3j and 6j symbols and their properties. The Ponzano-Regge model describes a discretized 3-geometry, given in terms of a triangulation through simplices (tetrahedrons, in 3 dimensions), such that the length of each edge corresponds to an irreducible representation of the Lie group SU(2). These tetrahedrons are described as 6j symbols, whose asymptotic formula allows taking the classical limit, leading to an expression of the partition function that represents a sum over 3-geometries.

Because compressibility effects arise in real applications of propellers and turbines, the Actuator Disk Theory or Froude’s Momentum Theory was established for compressible, subsonic flow using the three laws of conservation and isentropic thermodynamics. The compressible Actuator Disk Theory was established for the unducted (bare) and ducted cases in which the disk was treated as the only assembly within the flow stream in the bare case and enclosed by a duct having a constant cross-sectional area equal to the disk area in the ducted case. The primary motivation of the current thesis was to predict the ideal performance of a small ram-air turbine (microRAT), operating at high subsonic Mach numbers, that would power an autonomous Boundary Layer Data System during test flights. The compressible-flow governing equations were applied to a propeller and a turbine for both the bare and ducted cases. The solutions to the resulting system of coupled, non-linear, algebraic equations were obtained using an iterative approach. The results showed that the power extraction efficiency and the total drag coefficient of the bare turbine are slightly higher for compressible flow than for incompressible flow. As the free-stream Mach increases, the Betz limit of the compressible bare turbine slightly increases from the incompressible value of 0.593 and occurs at a velocity ratio between the far downstream and the free-stream that is lower than the incompressible value of 0.333. From incompressible to a free-stream Mach number of 0.8, the Betz limit increases by 0.021 while its corresponding velocity ratio decreases by 0.036. The Betz limit and its corresponding velocity ratio for the ducted turbine are not affected by the free-stream Mach and are the same for both incompressible and compressible flow. The total drag coefficient of the ducted turbine is also the same regardless of the free-stream Mach number and the compressibility of the flow; but, the individual contributions of the turbine drag and the lip thrust to the total drag differs between compressible and incompressible flow and between varying free-stream Mach numbers. It was concluded that overall compressibility has little influence on the ideal performance of an actuator disk.

abstract: An airborne, tethered, multi-rotor wind turbine, effectively a rotorcraft kite, provides one platform for accessing the energy in high altitude winds. The craft is maintained at altitude by its rotors operating in autorotation, and its equilibrium attitude and dynamic performance are affected by the aerodynamic rotor forces, which in turn are affected by the orientation and motion of the craft. The aerodynamic performance of such rotors can vary significantly depending on orientation, influencing the efficiency of the system. This thesis analyzes the aerodynamic performance of an autorotating rotor through a range of angles of attack covering those experienced by a typical autogyro through that of a horizontal-axis wind turbine. To study the behavior of such rotors, an analytical model using the blade element theory coupled with momentum theory was developed. The model uses a rigid-rotor assumption and is nominally limited to cases of small induced inflow angle and constant induced velocity. The model allows for linear twist. In order to validate the model, several rotors -- off-the-shelf model-aircraft propellers -- were tested in a low speed wind tunnel. Custom built mounts allowed rotor angles of attack from 0 to 90 degrees in the test section, providing data for lift, drag, thrust, horizontal force, and angular velocity. Experimental results showed increasing thrust and angular velocity with rising pitch angles, whereas the in-plane horizontal force peaked and dropped after a certain value. The analytical results revealed a disagreement with the experimental trends, especially at high pitch angles. The discrepancy was attributed to the rotor operating in turbulent wake and vortex ring states at high pitch angles, where momentum theory has proven to be invalid. Also, aerodynamic design constants, which are not precisely known for the test propellers, have an underlying effect on the analytical model. The developments of the thesis suggest that a different analytical model may be needed for high rotor angles of attack. However, adding a term for resisting torque to the model gives analytical results that are similar to the experimental values. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2019

Behavioral momentum theory (BMT) has become a prominent method of studying the effects of reinforcement on operant behavior. BMT represents a departure from the Skinnerian tradition in that it identifies the strength of responding with its resistance to change. Like in many other operant research paradigms, however, responses are considered to be momentary phenomena and so little attention has been paid to non-rate dimensions of responding. The current study takes up the question of whether or not the degree of effort defining a discriminated operant class has any meaningful effect on its resistance to change. Using a force transducer, rats responded on a two-component multiple VI 60-s VI 60-s schedule where each component was correlated with a different force requirement. Resistance to change was tested through prefeeding and extinction. Proportional declines in response rate were equal across components during all disruption tests. Differentiated response classes remained intact throughout. The negative result suggests several future research directions.