Barragens são utilizadas há séculos para diversas finalidades. Em diversas barragens os vertedouros são constituídos de degraus com o objetivo de aumentar a dissipação de energia. A presente pesquisa objetiva a caracterização dos esforços atuantes em vertedouros em degraus, através da análise da variação das pressões atuantes ao longo da calha e suas distribuições na faces do degraus. Com esse objetivo, são realizadas análises sobre modelos de vertedouros com declividade de 1V:0,75H e degraus de 3, 6 e 9 centímetros. São analisados os campos de pressões nos degraus e comparados com os resultados disponíveis na bibliografia. Também são propostos modelos para previsão de pressões nos patamares e espelhos dos degraus bem como dos esforços resultantes. Além disso, são realizadas transposições dos resultados para a escala de protótipo, inclusive com a análise da possibilidade de cavitação na estrutura. Como constatação geral sobre as pressões nos espelhos verifica-se que os esforços de tração e compressão têm magnitudes relativamente semelhantes, sendo mais intensas as pressões negativas. Sobre as pressões máximas nos patamares, destaca-se que os valores máximos de compressão ocorreram no final da calha, percebendo-se que as menores vazões geraram maiores valores de coeficientes de pressões. As variações da compressão nas faces dos patamares apresentam crescimento, no sentido da extremidade com o espelho acima deste para o vértice com o espelho abaixo do mesmo patamar. Nas faces dos espelhos, percebe-se que os mais extremos de tração são observados na parte superior, próximo à quina com os patamares. / Dams have been used throughout the centuries for a plethora of purposes. Several designs employ steps on the spillways in order to increase the power dissipation. The present research aims to characterize the forces acting on stepped spillways by analyzing both the variation of pressures acting along the pipeline and their distributions on the faces of the steps. In order to achieve this purpose, observations and discussions regarding spillways models with slope characterized as 1V: 0.75H and steps ranging from 3 to 9 centimeters are conducted. The pressure fields measured in the steps were analyzed and compared with results available in the literature. Sub sequentially, models to predict pressures on the faces of the steps and the resulting efforts were proposed. Finally, transpositions were performed on a prototype scale. Generally, it was found that the magnitude of tensile and compressive forces on the vertical faces are relatively similar, being the negative pressure slightly higher on all cases. During the experiments, it was observed that compression forces increased thought the length of the step’s horizontal face, peaking at the edge. It was also noticed that lower flows generated higher pressure coefficients. The measured compression on the horizontal faces of the step and its variation increase towards the edge of the step. It is perceived that the maximum tensile is observed on the top of the step’s vertical faces, near the corner with the horizontal faces.

As expectativas dinâmicas de um mundo de inovações tecnológicas, consubstanciados por explorações menos agressivas ao meio ambiente, dirigidas a um mercado consumista emergente, representam desafios para soluções de problemas de engenharia dirigidos para diversos segmentos da sociedade. Com o desenvolvimento do concreto compactado com rolo (CCR), a partir dos anos 70, o emprego de vertedouros em degraus em barragens de gravidade tornou-se uma solução atrativa, visto que, proporciona, simultaneamente, o aumento da dissipação da energia do escoamento e a redução do tempo e dos custos de implantação dessas obras. Atualmente, têm-se usado como restrições ao seu emprego de vertedouros em degraus valores máximos de vazões específicas que, sem um limite consensual, vêm tolhendo suas potencialidades. A macrorugosidade da calha acelera o processo de aeração do escoamento, se comparado com um vertedouro de soleira lisa, protegendo, para a zona aerada, os degraus contra erosão por cavitação. Entretanto, para o trecho não aerado do escoamento, existem riscos desse processo se estabelecer. As descontinuidades da fronteira sólida propiciam a sucessiva separação da camada limite nos cantos externos dos degraus. Nessa região são geradas pressões muito baixas. O presente estudo, realizado no Instituto de Pesquisas Hidráulicas, objetivou, através de medições experimentais, descrever, caracterizar e modelar pressões hidrodinâmicas nas soleiras dos degraus, estabelecendo limites para incipiência à cavitação no trecho não-aerado do escoamento. Três calhas escalonadas com declividade 1V:0,75H e alturas de degraus iguais a 0,03 m; 0,06 m e 0,09 m foram projetadas e construídas para a investigação. As amostras de pressões registradas com transmissores de pressão a 50 Hz e duração de 3minutos e 12 horas possibilitaram caracterizar o campo de pressão identificando zonas críticas, bem como, avaliando o comportamento estatístico dessas solicitações. As maiores flutuações de pressões foram registradas nas extremidades externas dos degraus e na seção de afloramento da camada limite, chegando a valores negativos de 0,69 vezes a distância vertical entre a crista e a seção analisada. Determinaram-se freqüências dominantes compreendidas entre 7-18 Hz, com valores máximos situados nos patamares dosdegraus. Os números adimensionais de Strouhal, calculados com as freqüências predominantes e as profundidades equivalente do escoamento, diminuíram de 0,40 a 0,04 no sentido do fluxo. Quanto aos limites de incipiência à cavitação, as vazões especificas mais restritivas ao emprego de vertedouros em degraus ficaram na faixa entre 11,3 e 15,6 m²/s com velocidades médias da ordem de 17 m/s, obtidas para a seção de afloramento da camada limite. / Hydraulic researchers have to accomplish the technological and construction materials innovations to new security design project criteria compatible to low costs requirement. At 70’s years, with the development of the Roller Compact Concrete (RCC), the use of stepped spillways has become an attractive solution for gravity dams. In steeply sloping stepped spillways, the large step macro-roughness promotes the occurrence of negative pressures on the step cavity, particularly near the external edge of the vertical step face. Consequently one may expect the occurrence of sub-atmospheric pressure conditions capable to induce cavitation for velocities lower than those observed in smooth chute spillways. Predicting cavitation damage is more complex than predicting cavitation inception. Flow conditions leading to the onset of cavitation are generally conservative in predicting damage. The severity of damage that may be expected is related both to intensity of cavitation and time of exposure. There is still no consensus on the maximum unit discharge or flow velocity which assures cavitation safe design of stepped spillways.The study carried through in the Institute of Hydraulic Research (UFRGS - Brazil), had the main goal: described, characterized and modeled experimental measurements of hydrodynamic pressures on the faces of the steps and established limits of incipient cavitation. Three stepped chutes with declivity 1V:0.75H and 0.03 m; 0.06 m and 0.09 m steps heights were projected. The samples of pressures were registered with pressure transmitters with 50 Hz and 3 minutes duration. Long-duration test were also conducted (12 hours sample size) that permitted characterize the pressure field, identifying critical zones, as well as, evaluating its statistical behaviour. The largest fluctuating pressures had been registered in the outer corner on the steps and at the inception point of air entrainment. At this last position can be expected negative pressure values close to 0.69 times the vertical distance between the crest and the analyzed section. The dominant frequencies found varied between 7-18 Hz. The dimensionless number of Strouhal calculated with the predominant frequencies and the clear equivalent depth, had diminished of 0.40 the 0.04 in the direction of the flow. The pressure measurements indicated specific discharge between 11.3-15.6 m²/s and average velocity in order of 17 m/s to inception cavitation process near the inception point.

Barragens são utilizadas há séculos para diversas finalidades. Em diversas barragens os vertedouros são constituídos de degraus com o objetivo de aumentar a dissipação de energia. A presente pesquisa objetiva a caracterização dos esforços atuantes em vertedouros em degraus, através da análise da variação das pressões atuantes ao longo da calha e suas distribuições na faces do degraus. Com esse objetivo, são realizadas análises sobre modelos de vertedouros com declividade de 1V:0,75H e degraus de 3, 6 e 9 centímetros. São analisados os campos de pressões nos degraus e comparados com os resultados disponíveis na bibliografia. Também são propostos modelos para previsão de pressões nos patamares e espelhos dos degraus bem como dos esforços resultantes. Além disso, são realizadas transposições dos resultados para a escala de protótipo, inclusive com a análise da possibilidade de cavitação na estrutura. Como constatação geral sobre as pressões nos espelhos verifica-se que os esforços de tração e compressão têm magnitudes relativamente semelhantes, sendo mais intensas as pressões negativas. Sobre as pressões máximas nos patamares, destaca-se que os valores máximos de compressão ocorreram no final da calha, percebendo-se que as menores vazões geraram maiores valores de coeficientes de pressões. As variações da compressão nas faces dos patamares apresentam crescimento, no sentido da extremidade com o espelho acima deste para o vértice com o espelho abaixo do mesmo patamar. Nas faces dos espelhos, percebe-se que os mais extremos de tração são observados na parte superior, próximo à quina com os patamares. / Dams have been used throughout the centuries for a plethora of purposes. Several designs employ steps on the spillways in order to increase the power dissipation. The present research aims to characterize the forces acting on stepped spillways by analyzing both the variation of pressures acting along the pipeline and their distributions on the faces of the steps. In order to achieve this purpose, observations and discussions regarding spillways models with slope characterized as 1V: 0.75H and steps ranging from 3 to 9 centimeters are conducted. The pressure fields measured in the steps were analyzed and compared with results available in the literature. Sub sequentially, models to predict pressures on the faces of the steps and the resulting efforts were proposed. Finally, transpositions were performed on a prototype scale. Generally, it was found that the magnitude of tensile and compressive forces on the vertical faces are relatively similar, being the negative pressure slightly higher on all cases. During the experiments, it was observed that compression forces increased thought the length of the step’s horizontal face, peaking at the edge. It was also noticed that lower flows generated higher pressure coefficients. The measured compression on the horizontal faces of the step and its variation increase towards the edge of the step. It is perceived that the maximum tensile is observed on the top of the step’s vertical faces, near the corner with the horizontal faces.

As expectativas dinâmicas de um mundo de inovações tecnológicas, consubstanciados por explorações menos agressivas ao meio ambiente, dirigidas a um mercado consumista emergente, representam desafios para soluções de problemas de engenharia dirigidos para diversos segmentos da sociedade. Com o desenvolvimento do concreto compactado com rolo (CCR), a partir dos anos 70, o emprego de vertedouros em degraus em barragens de gravidade tornou-se uma solução atrativa, visto que, proporciona, simultaneamente, o aumento da dissipação da energia do escoamento e a redução do tempo e dos custos de implantação dessas obras. Atualmente, têm-se usado como restrições ao seu emprego de vertedouros em degraus valores máximos de vazões específicas que, sem um limite consensual, vêm tolhendo suas potencialidades. A macrorugosidade da calha acelera o processo de aeração do escoamento, se comparado com um vertedouro de soleira lisa, protegendo, para a zona aerada, os degraus contra erosão por cavitação. Entretanto, para o trecho não aerado do escoamento, existem riscos desse processo se estabelecer. As descontinuidades da fronteira sólida propiciam a sucessiva separação da camada limite nos cantos externos dos degraus. Nessa região são geradas pressões muito baixas. O presente estudo, realizado no Instituto de Pesquisas Hidráulicas, objetivou, através de medições experimentais, descrever, caracterizar e modelar pressões hidrodinâmicas nas soleiras dos degraus, estabelecendo limites para incipiência à cavitação no trecho não-aerado do escoamento. Três calhas escalonadas com declividade 1V:0,75H e alturas de degraus iguais a 0,03 m; 0,06 m e 0,09 m foram projetadas e construídas para a investigação. As amostras de pressões registradas com transmissores de pressão a 50 Hz e duração de 3minutos e 12 horas possibilitaram caracterizar o campo de pressão identificando zonas críticas, bem como, avaliando o comportamento estatístico dessas solicitações. As maiores flutuações de pressões foram registradas nas extremidades externas dos degraus e na seção de afloramento da camada limite, chegando a valores negativos de 0,69 vezes a distância vertical entre a crista e a seção analisada. Determinaram-se freqüências dominantes compreendidas entre 7-18 Hz, com valores máximos situados nos patamares dosdegraus. Os números adimensionais de Strouhal, calculados com as freqüências predominantes e as profundidades equivalente do escoamento, diminuíram de 0,40 a 0,04 no sentido do fluxo. Quanto aos limites de incipiência à cavitação, as vazões especificas mais restritivas ao emprego de vertedouros em degraus ficaram na faixa entre 11,3 e 15,6 m²/s com velocidades médias da ordem de 17 m/s, obtidas para a seção de afloramento da camada limite. / Hydraulic researchers have to accomplish the technological and construction materials innovations to new security design project criteria compatible to low costs requirement. At 70’s years, with the development of the Roller Compact Concrete (RCC), the use of stepped spillways has become an attractive solution for gravity dams. In steeply sloping stepped spillways, the large step macro-roughness promotes the occurrence of negative pressures on the step cavity, particularly near the external edge of the vertical step face. Consequently one may expect the occurrence of sub-atmospheric pressure conditions capable to induce cavitation for velocities lower than those observed in smooth chute spillways. Predicting cavitation damage is more complex than predicting cavitation inception. Flow conditions leading to the onset of cavitation are generally conservative in predicting damage. The severity of damage that may be expected is related both to intensity of cavitation and time of exposure. There is still no consensus on the maximum unit discharge or flow velocity which assures cavitation safe design of stepped spillways.The study carried through in the Institute of Hydraulic Research (UFRGS - Brazil), had the main goal: described, characterized and modeled experimental measurements of hydrodynamic pressures on the faces of the steps and established limits of incipient cavitation. Three stepped chutes with declivity 1V:0.75H and 0.03 m; 0.06 m and 0.09 m steps heights were projected. The samples of pressures were registered with pressure transmitters with 50 Hz and 3 minutes duration. Long-duration test were also conducted (12 hours sample size) that permitted characterize the pressure field, identifying critical zones, as well as, evaluating its statistical behaviour. The largest fluctuating pressures had been registered in the outer corner on the steps and at the inception point of air entrainment. At this last position can be expected negative pressure values close to 0.69 times the vertical distance between the crest and the analyzed section. The dominant frequencies found varied between 7-18 Hz. The dimensionless number of Strouhal calculated with the predominant frequencies and the clear equivalent depth, had diminished of 0.40 the 0.04 in the direction of the flow. The pressure measurements indicated specific discharge between 11.3-15.6 m²/s and average velocity in order of 17 m/s to inception cavitation process near the inception point.

As expectativas dinâmicas de um mundo de inovações tecnológicas, consubstanciados por explorações menos agressivas ao meio ambiente, dirigidas a um mercado consumista emergente, representam desafios para soluções de problemas de engenharia dirigidos para diversos segmentos da sociedade. Com o desenvolvimento do concreto compactado com rolo (CCR), a partir dos anos 70, o emprego de vertedouros em degraus em barragens de gravidade tornou-se uma solução atrativa, visto que, proporciona, simultaneamente, o aumento da dissipação da energia do escoamento e a redução do tempo e dos custos de implantação dessas obras. Atualmente, têm-se usado como restrições ao seu emprego de vertedouros em degraus valores máximos de vazões específicas que, sem um limite consensual, vêm tolhendo suas potencialidades. A macrorugosidade da calha acelera o processo de aeração do escoamento, se comparado com um vertedouro de soleira lisa, protegendo, para a zona aerada, os degraus contra erosão por cavitação. Entretanto, para o trecho não aerado do escoamento, existem riscos desse processo se estabelecer. As descontinuidades da fronteira sólida propiciam a sucessiva separação da camada limite nos cantos externos dos degraus. Nessa região são geradas pressões muito baixas. O presente estudo, realizado no Instituto de Pesquisas Hidráulicas, objetivou, através de medições experimentais, descrever, caracterizar e modelar pressões hidrodinâmicas nas soleiras dos degraus, estabelecendo limites para incipiência à cavitação no trecho não-aerado do escoamento. Três calhas escalonadas com declividade 1V:0,75H e alturas de degraus iguais a 0,03 m; 0,06 m e 0,09 m foram projetadas e construídas para a investigação. As amostras de pressões registradas com transmissores de pressão a 50 Hz e duração de 3minutos e 12 horas possibilitaram caracterizar o campo de pressão identificando zonas críticas, bem como, avaliando o comportamento estatístico dessas solicitações. As maiores flutuações de pressões foram registradas nas extremidades externas dos degraus e na seção de afloramento da camada limite, chegando a valores negativos de 0,69 vezes a distância vertical entre a crista e a seção analisada. Determinaram-se freqüências dominantes compreendidas entre 7-18 Hz, com valores máximos situados nos patamares dosdegraus. Os números adimensionais de Strouhal, calculados com as freqüências predominantes e as profundidades equivalente do escoamento, diminuíram de 0,40 a 0,04 no sentido do fluxo. Quanto aos limites de incipiência à cavitação, as vazões especificas mais restritivas ao emprego de vertedouros em degraus ficaram na faixa entre 11,3 e 15,6 m²/s com velocidades médias da ordem de 17 m/s, obtidas para a seção de afloramento da camada limite. / Hydraulic researchers have to accomplish the technological and construction materials innovations to new security design project criteria compatible to low costs requirement. At 70’s years, with the development of the Roller Compact Concrete (RCC), the use of stepped spillways has become an attractive solution for gravity dams. In steeply sloping stepped spillways, the large step macro-roughness promotes the occurrence of negative pressures on the step cavity, particularly near the external edge of the vertical step face. Consequently one may expect the occurrence of sub-atmospheric pressure conditions capable to induce cavitation for velocities lower than those observed in smooth chute spillways. Predicting cavitation damage is more complex than predicting cavitation inception. Flow conditions leading to the onset of cavitation are generally conservative in predicting damage. The severity of damage that may be expected is related both to intensity of cavitation and time of exposure. There is still no consensus on the maximum unit discharge or flow velocity which assures cavitation safe design of stepped spillways.The study carried through in the Institute of Hydraulic Research (UFRGS - Brazil), had the main goal: described, characterized and modeled experimental measurements of hydrodynamic pressures on the faces of the steps and established limits of incipient cavitation. Three stepped chutes with declivity 1V:0.75H and 0.03 m; 0.06 m and 0.09 m steps heights were projected. The samples of pressures were registered with pressure transmitters with 50 Hz and 3 minutes duration. Long-duration test were also conducted (12 hours sample size) that permitted characterize the pressure field, identifying critical zones, as well as, evaluating its statistical behaviour. The largest fluctuating pressures had been registered in the outer corner on the steps and at the inception point of air entrainment. At this last position can be expected negative pressure values close to 0.69 times the vertical distance between the crest and the analyzed section. The dominant frequencies found varied between 7-18 Hz. The dimensionless number of Strouhal calculated with the predominant frequencies and the clear equivalent depth, had diminished of 0.40 the 0.04 in the direction of the flow. The pressure measurements indicated specific discharge between 11.3-15.6 m²/s and average velocity in order of 17 m/s to inception cavitation process near the inception point.

The purpose of this research was to investigate the hydraulic performance of stepped spillways. A thorough investigation was made of all printed material on stepped spillways, and a summary of this material is presented in the text. Data from experiments in the laboratory were used to develop a design procedure for stepped spillways and hydraulic jump stilling basins. The experimental study was conducted at Utah State University - Utah Water Research Laboratory in Logan, Utah. Four models were built and tested in the laboratory under various flowrates. The crest of the model spillway was constructed in the shape of a standard USBR nappe-shaped crest. Small steps were fitted to the crest so that the envelope of their tips just intersected the crest profile. These small steps allowed a smooth transition of the flow from the nappe-shaped crest to the constant slope region. Two slopes were tested in the research: 0.7H:1.0V and 0.5H:1.0V. At each of these slopes two sizes of steps were tested. Steps did not very in size down the face of the model, although step sizes varied on the different models. The model height and steps tested were for a dam with a prototype height of over 67 feet and steps in the 1-2 foot range. Diagrams and pictures of the four models tested are included in the text and appendix. Findings from the research showed that given a ratio of step height over critical depth (0.1201.897, the energy dissipation will remain in the 90% region, although there might be problems with the flow leaping away from the structure. Data on the models were slightly scattered, but all of the data from the four models agree to one energy loss graph. Support for these data showed a nearly perfect correlation in the downstream conjugate depths on all four models at similar flowrates. By using data obtained from the models and literature, a design process with guidelines for designing a stepped spillway is presented. This process includes crest design and step displacement in the transition region, approximate step size, and approximate slope necessary for adequate operation of the stepped spillway. By taking data collected from the models, and data from USBR design manuals for smooth spillways, a spreadsheet design process was created that compared the size of stilling basins required using either a smooth spillway or a stepped one. Results showed that given a unit flowrate range of 15 cfs/ft to 140 cfs/ft and spillway height of approximately 100 ft, the stilling basin volume was reduced by 62% to 43% respectively. This size reduction can translate to a considerable cost savings in prototype construction. This study, along with data from other researchers, has proven that a stepped spillway can greatly increase the amount of energy dissipation over that achieved on a standard smooth face spillway. The stepped concept can be used as an excellent energy dissipator and in some cases can totally remove the need for any type of dissipator at the toe of the spillway.

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Stepped hull forms are hulls with a vertical step in the hull bottom to improve performance at top speed. Stepped hulls are well documented anecdotally and scientifically to improve calm water performance at high speeds, but commonly demonstrate dangerous and unexpected dynamic instabilities during initial trials. These hulls also operate practically in waves, but their performance characteristics in waves are not well understood and rarely evaluated prior to full scale trials. To expand the scientific understanding of stepped hull performance, a systematic set of experiments and Reynolds Averaged Navier Stokes (RANS) computational fluid dynamics (CFD) simulations are used to evaluate the calm water performance, dynamic stability, and regular head wave response of two stepped hull models. Calm water experiments on two stepped hull models at varying displacement, longitudinal center of gravity location and forward speed offer data which can be used in the design to interpolate hull performance throughout expected operating conditions. CFD simulations in calm water are validated using the experimental results and numerical modeling approaches for stepped hull simulations are recommended. The calm water dynamic stability of both stepped hulls is investigated experimentally and numerically and procedures to evaluate the dynamic stability using both approaches are recommended. The performance of both stepped hulls in regular head waves is studied through experiments, which are used to validate CFD simulations of the hull in regular waves. System identification is used on five calm water CFD simulations to identify a reduced order model for the prediction of stepped hull response in waves. / Doctor of Philosophy / Boats designed specifically for high-speed operations, like military patrol craft, can often achieve higher top speeds when small vertical steps are added to the bottom of the hull. When a step is introduced, the back portion of the hull bottom is raised above the forward portion of the hull bottom to allow air underneath the hull at high speeds. When designed properly, a stepped hull can be safely operated by experienced and unexperienced users at higher speeds than conventional hulls. However, when the steps are not designed well a boat can be dangerous to operate, suffering from unexpected phenomena like end swapping (where the boat violently rotates from bow to stern) when beginning a turn. Unfortunately, it is currently difficult to predict how a stepped hull will behave during the early stages of the design. Builders often rely on full-scale prototype trials to assess the performance and safety of their designs, which is an expensive process. In this work, experimental tests (on small scale models) and computer simulations were performed on two stepped hull models in calm water and in waves to establish techniques to predict performance and safety without a full-scale prototype. The experiments were used to compare the performance of two geometries and assess the accuracy of computer simulation predictions. The computer simulations were found to predict the stepped hull performance accurately enough to be used in design prior to prototyping. Procedures are recommended to evaluate the safety of a stepped hull through experiments and computer simulations. Evaluation of hull safety through computer simulations or experiments offers the opportunity to reduce danger to test personnel during full scale trials and minimize the need for expensive design modifications after construction of the first prototype. The performance of the two hull designs in waves were studied experimentally, through computer simulation, and through a simplified method informed by computer simulations. The development of a simplified method to evaluate stepped hull performance in waves offers the opportunity for designers to consider performance in waves earlier in the design for a lower cost than previously available.