Yes / A problem with 1-D water hammer modelling is in the application of accurate unsteady friction. Moreover, investigating the time response of fluid dynamics and unsteady turbulence structures during the water hammer is not possible with a 1-D model. This review article provides a summary of 1-D modelling using the recent finite volume approach and the discussion extends to a quasi-2-D model and historical developments as well as recent advancements in 3-D CFD simulations of water hammer. The eddy viscosity model is excellent in capturing pressure profiles but it is computationally intensive and requires more computational time. This article reviews 3-D CFD simulations with sliding mesh, an immersed solid approach, and dynamic mesh approaches for modelling valve closures. Despite prediction accuracy, a huge computational time and high computer resources are required to execute 3-D flow simulations with advanced valve modelling techniques. Experimental validation shows that a 3-D CFD simulation with a flow rate reduction curve as a boundary condition predicted accurate pressure variation results. Finally, a brief overview of the transient flow turbulence structures for a rapidly accelerated and decelerated pipe flow using DNS (Direct numerical simulation) data sets is presented. Overall, this paper summarises past developments and future scope in the field of water hammer modelling using CFD.

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: This study investigates the implementation of the finite volume numerical method applicable to non-orthogonal control volumes and the application of the method to calculate the thermo-flow field within the collector area of a solar chimney power generating plant. The discretisation of the governing equations for the transient, Newtonian, incompressible and turbulent fluid flow, including heat transfer, is presented for a non-orthogonal coordinate frame. The standard k - E turbulence model, modified to include rough surfaces, is included and evaluated in the method. An implicit solution procedure (SIP-semi implicit procedure) as an alternative to a direct solution procedure for the calculation of the flow field on nonstaggered grids is investigated, presented and evaluated in this study. The Rhie and Chow interpolation practice was employed with the pressurecorrection equation to eliminate the presence of pressure oscillations on nonstaggered grids. The computer code for the solution of the three-dimensional thermo-flow fields is developed in FORTRAN 77. The code is evaluated against simple test cases for which analytical and experimental results exist. It is also applied to the analysis of the thermo-flow field of the air flow through a radial solar collector. KEYWORDS: NUMERICAL METHOD, FINITE VOLUME, NON-ORTHOGONAL, k+-e TURBULENCE MODEL, SIP / AFRIKAANSE OPSOMMING: Die studie ondersoek die implementering van 'n eindige volume numeriese metode van toepassing op nie-ortogonale kontrole volumes asook die toepassing van die metode om die termo-vloei veld binne die kollekteerder area van 'n sonskoorsteen krag aanleg te bereken. Die diskretisering van die behoudsvergelykings vir die tyd-afhanlike, Newtonse, onsamedrukbare en turbulente vloei, insluitende hitteoordrag, word beskryf vir 'n nie-ortogonale koordinaatstelsel. Die standaard k - E turbulensiemodel, aangepas om growwe oppervlakrandvoorwaardes te hanteer, is ingesluit en geevalueer in die studie. 'n Implisiete oplossings metode (SIP-semi implisiete prosedure) as alternatief vir 'n direkte oplossingsmetode is ondersoek en geimplimenteer vir die berekening van die vloeiveld met nie-verspringde roosters. 'n Rhie en Chow interpolasie metode is gebruik tesame met die drukkorreksie-vergelyking ten einde ossilasies in die drukveld in die nie-verspringde roosters te vermy. Die rekenaarkode vir die oplossing van die drie dimensionele termo-vloeiveld is ontwikkel in FORTRAN 77. Die kode is geevalueer teen eenvoudige toetsprobleme waarvoor analitiese en eksperimentele resultate bestaan. Die kode IS ook gebruik om die termo-vloeiveld binne 'n radiale son kollekteerder te analiseer. SLEUTELWOORDE: NUMERIESE METODE, EINDIGE VOLUME, NIE-ORTOGONAAL, k - E TURBULENSIE MODEL, SIP

This study addressed the numerical modelling of flow and diffusion in packed beds of mono-sized spheres. Comprehensive research was conducted in order to implement various numerical approaches in explicit1 and implicit2 simulations of flow through packed beds of uniform spheres. It was noted from literature that the characterization of a packed bed using porosity as the only geometrical parameter is inadequate (Van Antwerpen, 2009) and is still under much deliberation due to the lack of understanding of different flow phenomena through packed beds. Explicit simulations are not only able to give insight into this lack of understanding in fluid mechanics, but can also be used to develop different flow correlations that can be implemented in implicit type simulations. The investigation into the modelling approach using STAR-CCM+®, presented a sound modelling methodology, capable of producing accurate numerical results. A new contact treatment was developed in this study that is able to model all the aspects of the contact geometry without compromising the computational resources. This study also showed, for the first time, that the LES (large eddy simulation) turbulence model was the only model capable of accurately predicting the pressure drop for low Reynolds numbers in the transition regime. The adopted modelling approach was partly validated in an extensive mesh independency test that showed an excellent agreement between the simulation and the KTA (1981) and Eisfeld and Schnitzlein (2001) correlations' predicted pressure drop values, deviating by between 0.54% and 3.45% respectively. This study also showed that explicit simulations are able to accurately model enhanced diffusion due to turbulent mixing, through packed beds. In the tortuosity study it was found that the tortuosity calculations were independent of the Reynolds number, and that the newly developed tortuosity tests were in good agreement with techniques used by Kim en Chen (2006), deviating by between 2.65% and 0.64%. The results from the TMD (thermal mixing degree) tests showed that there appears to be no explicit link between the porosity and mixing abilities of the packed beds tested, but this could be attributed to relatively small bed sizes used and the positioning and size of the warm inlet. A multi-velocity test showed that the TMD criterion is also independent of the Reynolds number. It was concluded that the results from the TMD tests indicated that more elaborate packed beds were needed to derive applicable conclusions from these type of mixing tests. The explicit BETS (braiding effect test section) simulation results confirmed the seemingly irregular temperature trends that were observed in the experimental data, deviating by between 5.44% and 2.29%. From the detail computational fluid dynamics (CFD) results it was possible to attribute these irregularities to the positioning of the thermocouples in high temperature gradient areas. The validation results obtained in the effective thermal conductivity study were in good agreement with the results of Kgame (2011) when the same fitting techniques were used, deviating by 5.1%. The results also showed that this fitting technique is highly sensitive for values of the square of the Pearson product moment correlation coefficient (RSQ) parameter and that the exclusion of the symmetry planes improved the RSQ results. It was concluded that the introduction of the new combined coefficient (CC) parameter is more suited for this type of fitting technique than using only the RSQ parameter. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2012

Pour améliorer la conception des turbomachines, les industriels doivent appréhender des phénomènes aéroélastiques complexes présents dans les compresseurs comme les cycles limites d’interaction fluide-structure des fans. La compréhension et la modélisation de ces phénomènes impliquent de développer des modèles numériques complexes intégrant des phénomènes multi-physique et de valider ces modèles à l’aide de bancs d’essais. Le banc d’essai du compresseur CREATE est instrumenté pour étudier des instabilités aérodynamiques couplées à des vibrations, notamment sur le rotor du premier étage, et permet de valider des modèles numériques. La modélisation de l’écoulement en amont du premier étage du compresseur à l’aide du logiciel Turb’Flow, développé pour l’étude des écoulements dans les compresseurs aéronautiques, a permis de mettre en évidence l’importance des conditions limites d’entrée pour l’obtention de résultats précis. En particulier, il a été possible de modéliser correctement l’ingestion d’une alimentation non-homogène en entrée de la roue directrice d’entrée. Ce phénomène peut se produire en amont des fans et interagir avec un mode de la structure. Une stratégie de couplage partitionné fort explicite dans le domaine temporel a été introduite dans le logiciel Turb’Flow. Comme cette méthode présente un risque de décalage temporel à l’interface fluide-structure, une attention particulière a été portée à la modélisation de la conservation de l’énergie à cette interface. La conservation de l’énergie à l’interface est cruciale quand les déplacements sont importants et quand un comportement non-linéaire fort apparaît entre le fluide et la structure (onde de choc et amortissement structurel nonlinéaire). Parallèlement au développement du module aéroélastique, le schéma implicite de Runge- Kutta d’ordre 3 en temps (RKI-3) a été développé et évalué sur un cas de dynamique (vibration d’une aube de turbine transsonique) et sur un cas de propagation d’onde de choc. L’utilisation du schéma RKI-3 permet d’augmenter, à iso-précision, d’un ordre le pas de temps par rapport aux schémas de Gear et de Newmark. S’il apporte un gain en temps CPU pour l’étude de la dynamique des structures, il est pénalisant dans le cadre de simulation URANS. Cependant, le schéma RKI-3 est utilisable dans le cadre de simulations couplées fluide-structure. / To increase turbomachinery design, manufacturers have to comprehend complex aeroelastic phenomena involving compressors like fluid-structure interaction limit cycles of fans. The understanding and the modeling of these phenomena involve developing complex solvers coupling techniques and validating these techniques with bench tests. The bench test of the CREATE compressor is instrumented to study the coupling between aerodynamic instabilities and structure vibration, in particular on the first stage rotor, and allows to validate numerical techniques. The flow modeling upstream to the first stage with the Turb’Flow flow solver (targeting turbomachinery applications) shows that, to have accurate results, inlet limit conditions must take into account. The ingestion of non-homogeneous flow upstream to the inlet guide vane is accurately modeled. This phenomenon can appear upstream to fans and interact with structure Eigen-modes. Explicit partitioned strong coupling considered in time domain was implemented in a Turb’Flow flow solver. As there is a risk of time shift at the fluid-structure interface, careful attention should be paid to energy conservation at the interface. This conservation is crucial when displacements are large and when strong non-linear behaviors occur in both fluid and structure domains, namely shock waves, flow separations and non-linear structural damping. In parallel with coupling technique development, the three-order implicit Runge-Kutta scheme (RKI-3) was implemented and validated on a structure dynamic case (transonic turbine blade vibration) and on a case of shock waves propagation. The RKI-3 scheme allows increasing the time step of one order of magnitude with the same accuracy. There is a CPU time gain for structure dynamics simulations, but no for URANS simulations. However, the RKI-3 scheme can be to use for fluid-structure coupling simulations. The coupling technique was validated on a test case involving tube in which the shock wave impinges on a cross flow flexible panel, initially at rest. This case allows modeling an interaction between sonic flow and a panel movement with a tip clearance. Some numerical simulations were carried out with different temporal schemes. The RKI-3 scheme has no influence on results (compared with Gear and/or Newmark scheme) on the energy conservation at the fluid-structure interface. Compared to experimental results, pressure is in fairly good ix Liste des publications agreement. The analysis of numerical results highlighted that a vertical shock tube with up and down waves creates pressure fluctuation. Frequency is under predicted and amplitude is not in fairly good agreement. The panel root modeling might be questionable.

[pt] Neste trabalho três métodos foram utilizados para estudar o escoamento turbulento em regiões de florestas. No primeiro método, a influência da vegetação no escoamento foi modelada através da adição de termos fontes nas equações de quantidade de movimento, energia cinética turbulenta e sua taxa de dissipação. No segundo, a vegetação foi considerada um meio poroso homogêneo. Finalmente, a camada do dossel foi representada por modelos 3-D de árvores, consideradas como obstáculos individuais. As equações foram resolvidas através do modelo de turbulência k −E padrão com o programa comercial FLUENT 6.2.16. As previsões dos perfis verticais da velocidade do vento médio, da intensidade da turbulência e dos tensores de Reynolds, foram comparadas com dados de experimentos de túnel de vento. Os resultados preditos dos perfis verticais da velocidade média e intensidade da turbulência, na primeira e na segunda metodologias, apresentaram boa concordância com os valores experimentais, porém, foram observadas discrepâncias nos perfis modelados do tensor de Reynolds. Entretanto, qualitativamente, a modelagem consegue capturar o comportamento físico do tensor de Reynolds no interior de florestas. Uma possível explicação para este fato, é que o modelo considera a isotropia para a viscosidade turbulenta, implicando na incapacidade de prever qualquer forte anisotropia do campo turbulento. Na terceira metodologia, as previsões dos perfis verticais de velocidade média e intensidade da turbulência apresentaram discrepâncias em relação às medições. Porém, os perfis verticais do tensor de Reynolds apresentaram boa concordância. Todos os perfis verticais da velocidade média apresentaram um ponto de inflexão na interface vegetação-atmosfera, característico de uma camada de mistura. Nas duas primeiras metodologias, este padrão foi confirmado nos perfis de tangente hiperbólica de uma camada de mistura. / [en] This work investigates different procedures in order to study the turbulent flow over the scale model of a forest region. Initially, the canopy flow was modeled by using source terms in the momentum, turbulent kinetic energy and its dissipation rate equations. After that, the forest canopy was considered a homogeneous porous medium. In the last step, the canopy boundary layer was modeled by artificial 3-D tree models. This was done by using the standard k−E turbulence model with the FLUENT commercial program. The modeled profiles of mean velocity, turbulence intensity and Reynolds stress were compared against data from wind tunnel experiments. In the two first methodologies, the model predictions of the vertical profiles of the wind speed and turbulence intensity showed good agreement with the experimental data. It was found that predictions of the Reynolds tensor were sensitive to the parameterization scheme of the standard k −E model. However, qualitatively, the model was capable of predicting the physical behavior of the Reynolds stress tensor in the canopy flow. A possible explanation for this behavior is the omission of any anisotropic eddy-viscosity effects within the k - E modelling approach. When it was considered the tree array, the model predictions for the wind speed and turbulence intensity were less satisfactory. However, it was found that the predicted results of the Reynolds stress tensor agreed well with the measured data. All the vertical profiles of the mean velocity contained an inflection point, something which is a necessary criterion for the mixing layer flow. In the tree array, the modeled results failed to the capture this behavior of the canopy flow. In the 2-D numerical simulations, it was found the characteristic hyperbolic tangent profile of a mixing layer.

Orientador: Alcides Padilha / Banca: Ivan De Domenico Valarelli / Banca: Kamal Abdel Radi Ismail / Resumo: Neste trabalho apresenta-se uma análise teórica e experimental dos resultados comparativos entre as curvas características de um ventilador axial utilizado em um sistema de pulverização agrícola para um ângulo de ataque da pá em 32 graus nas rotações de 1500, 1750, 2600 e 3000 rpm e resultados numéricos da influência da variação do ângulo de ataque da pá em 28, 32 e 36 graus e da otimização do sistema de pulverização ambos para uma rotaç]ao de 2600 rpm. O campo médio turbulento foi obtido com a aplicação da média temporal sendo que o modelo de turbulência exigido para o fechamento do conjunto de equações foi o modelo k-ε de duas equações. A resolução de todos os fenômenos acoplados foi alcançada com o auxílio do código de fluidodinâmica computacional CFX que utiliza a técnica dos volumes finitos como método numérico. Para validação da análise teórica, realizaram-se experimentos em um túnel de vento horizontal de seção circular com diâmetro de 622 mm, usando um tubo de Pitot para as tomadas de pressão de acordo com a norma para ensaios em laboratório. Apresentam-se resultados qualitativos na forma de vetores e mapas de gradiente de velocidade e, quantitativos na forma de tabelas e gráficos para as curvas características. / Abstract: This paper presents a theoretical and experimental analysis of comparative results the characteristic curves of an axial fan used in an agricultural spraying system for a blade attack angle of 32 degrees at rotations of 1500, 1750, 2600 and 3000 rpm and numerical results for the influence of blade attack angle variation at 28, 32 and 36 degrees and optimization of the spraying system, both for a rotation of 2600 rpm. The average turbulent field was obtained from the application of time average where the turbulence model required for closing the set of equations was the k-ε model for two equations. Resolution of all connected phenomena was achieved with the help of the fluid dynamics computacional, CFX, which uses the finite volumes technique as a numerical method. In order to validate the theoretical analysis, an experiment was conducted in a circular section of a horizontal wind tunnel, 622 mm in diameter and 6220 mm in length, using a Pitot tube for pressure readings according to the norm for laboratory assays. Qualitative results are shown as vectors and gradient maps for speed and quantitative results are shown in tables and graphics for characteristic curves. / Mestre

A crescente preocupação ambiental e a necessidade de se criar produtos mais eficientes têm impulsionado os pesquisadores a realizarem estudos acerca da aerodinâmica veicular. Estes dois fatores constituem os principais motivos, pelos quais existe uma grande procura por conhecimento nesta área. Esta ciência pode ser considerada relativamente nova e ainda carece de uma base de dados. Entender como a aerodinâmica se relaciona com o consumo de combustível nos automóveis, à medida que o arrasto impõe resistência ao deslocamento dos mesmos, é algo que tem estimulado as indústrias automotivas a investirem grandes esforços na obtenção de ferramentas, que possam representar as condições de tráfego normais e, assim conseguir prever o desempenho do produto em desenvolvimento. Os túneis de vento e a simulação computacional surgem neste ambiente como as principais ferramentas de análise e predição do escoamento ao redor do veículo. Por isso seu entendimento faz-se de extrema necessidade. Ter conhecimento sobre a concepção do seu projeto, como funcionam, seus pontos fortes e suas fraquezas, são requisitos necessários para a pessoa que deseja estudar esta ciência. O presente trabalho traz uma contextualização histórica da aerodinâmica veicular nas indústrias automotiva e automobilística, além de apresentar aspectos técnicos relacionados aos túneis de vento e simulação computacional. Abordando as vantagens e desvantagens de cada ferramenta, expõe-se o fato de que estas ferramentas são complementares no estudo aerodinâmico. Para exemplificar a utilização dessas ferramentas, foi realizado um estudo aerodinâmico sobre uma geometria básica, que representa com similaridade os veículos tipo hatchback, denominada Modelo SAE em ambiente computacional. Os conceitos acerca do arrasto veicular e estabilidade veicular foram expostos para embasar este estudo. Este modelo foi submetido a diferentes geometrias traseiras e condições de escoamento simétricas e assimétricas. Este estudo demonstrou que o arrasto e a estabilidade veicular compreendem conceitos distintos e, dessa forma, é possível diminuir o arrasto de um veículo sem haver perda de estabilidade. / The growing environmental concern and the necessity to create more efficient products have motivated researchers to conduct studies about the aerodynamic vehicle. These two aspects are the main reasons which are promoting a great demand for knowledge in this theme. This science may be considered relatively new and still lacks more databases. Understand how aerodynamics is related to automobiles fuel consumption such as drag resistance imposed to their displacement, is something that has made the automotive industries invest considerable effort in obtaining tools which may represent the normal traffic conditions and thus, able to predict the performance of the product in development stage. The wind tunnels and computer simulations appear in this environment as the main tools for analysis and prediction of the flow around vehicle. The understanding about them is so of utmost necessity. Knowing how it was designed, how they work, their strengths and weaknesses are essential requirements for the person who wants to study this science. This material presents a historical development of vehicle aerodynamics in automotive and motor-racing industries, indeed technical aspects related to wind tunnels and computational fluid dynamics. Exposing the advantages and disadvantages of both tools, it is evidenced these tools complement each other during an aerodynamic study. To exemplify these tools utility an aerodynamic research was conducted using a basic form geometry known as SAE Model that represents with similarity the hatchback vehicles in the market. Drag and vehicle stability concepts were exposed to build a solid basis for this study. This model was submitted to different rear geometries, symmetric and asymmetric flow conditions. It could be demonstrated that drag and vehicle stability have distinct concepts and therefore it is possible diminish the first without damaging the later.

Dois dos principais objetivos no estudo da aerodinâmica de veículos comerciais são a redução no consumo de combustível e o aumento na eficiência da refrigeração do motor. Esses objetivos podem ser alcançados através do desenvolvimento de dispositivos que modifiquem o escoamento do ar ao redor do veículo e também através da alteração da forma das superfícies externas. A inclinação das superfícies da parte traseira de um ônibus, por exemplo, tem grande influência sobre a esteira turbulenta que se forma atrás do veículo. O uso de ferramentas computacionais permite uma redução de custo e maior flexibilidade na análise aerodinâmica de autoveículos. Ainda é preciso, no entanto, que o resultado dessas ferramentas computacionais seja verificado com o maior número possível de casos para que se possa escolher e ajustar o modelo matemático de forma adequada. O objetivo do presente trabalho é a verificação dos resultados computacionais e experimentais no desenvolvimento de metodologias que visem à redução no consumo de combustível e aumento na eficiência da refrigeração do motor. Foram comparados resultados experimentais e computacionais do escoamento sobre um modelo de um ônibus comercial em escala 1:17,5. Para a realização do experimento foi utilizado um túnel de vento de seção aberta, onde foram analisadas as distribuições de pressão nas superfícies da carroceria e o arrasto aerodinâmico. Para o teste computacional, foi utilizado um software de dinâmica dos fluidos computacional em que as equações de Navier-Stokes com média de Reynolds são resolvidas pelo método dos volumes finitos usando um modelo de turbulência RNG 'capa' - 'épsilon' / Two main objectives in the study of commercial vehicle aerodynamics are the reduction in fuel consumption and the improvement in engine refrigeration efficiency. These objectives can be achieved through development of devices which vary the flow characteristics around the vehicle and also through modification of the shape of external surfaces. The slope of rear surfaces, for instance, has large influence over the wake turbulence which forms behind the vehicle. The use of computational tools yields cost reduction and greater flexibility in automotive aerodynamic analysis. There is still a need, however, for verification of results, generated by these computational tools, with the largest possible number of test cases so that the mathematical model is adequately chosen and adjusted. The objective of the present work is the verification of experimental and computational results in the development of methodologies aiming at reduction of fuel consumption and improvement in engine refrigeration efficiency. Experimental and computational aerodynamic results were compared for a commercial bus model with a 1:17.5 scale. The experiments were conducted in an open section wind tunnel where pressure distribution and aerodynamic drag were analyzed. The numerical analysis was conducted using computational fluid dynamics software which solves the Reynolds Averaged Navier-Stokes equations using the finite volume method with a RNG 'capa' - 'épsilon' turbulence model

Dois dos principais objetivos no estudo da aerodinâmica de veículos comerciais são a redução no consumo de combustível e o aumento na eficiência da refrigeração do motor. Esses objetivos podem ser alcançados através do desenvolvimento de dispositivos que modifiquem o escoamento do ar ao redor do veículo e também através da alteração da forma das superfícies externas. A inclinação das superfícies da parte traseira de um ônibus, por exemplo, tem grande influência sobre a esteira turbulenta que se forma atrás do veículo. O uso de ferramentas computacionais permite uma redução de custo e maior flexibilidade na análise aerodinâmica de autoveículos. Ainda é preciso, no entanto, que o resultado dessas ferramentas computacionais seja verificado com o maior número possível de casos para que se possa escolher e ajustar o modelo matemático de forma adequada. O objetivo do presente trabalho é a verificação dos resultados computacionais e experimentais no desenvolvimento de metodologias que visem à redução no consumo de combustível e aumento na eficiência da refrigeração do motor. Foram comparados resultados experimentais e computacionais do escoamento sobre um modelo de um ônibus comercial em escala 1:17,5. Para a realização do experimento foi utilizado um túnel de vento de seção aberta, onde foram analisadas as distribuições de pressão nas superfícies da carroceria e o arrasto aerodinâmico. Para o teste computacional, foi utilizado um software de dinâmica dos fluidos computacional em que as equações de Navier-Stokes com média de Reynolds são resolvidas pelo método dos volumes finitos usando um modelo de turbulência RNG 'capa' - 'épsilon' / Two main objectives in the study of commercial vehicle aerodynamics are the reduction in fuel consumption and the improvement in engine refrigeration efficiency. These objectives can be achieved through development of devices which vary the flow characteristics around the vehicle and also through modification of the shape of external surfaces. The slope of rear surfaces, for instance, has large influence over the wake turbulence which forms behind the vehicle. The use of computational tools yields cost reduction and greater flexibility in automotive aerodynamic analysis. There is still a need, however, for verification of results, generated by these computational tools, with the largest possible number of test cases so that the mathematical model is adequately chosen and adjusted. The objective of the present work is the verification of experimental and computational results in the development of methodologies aiming at reduction of fuel consumption and improvement in engine refrigeration efficiency. Experimental and computational aerodynamic results were compared for a commercial bus model with a 1:17.5 scale. The experiments were conducted in an open section wind tunnel where pressure distribution and aerodynamic drag were analyzed. The numerical analysis was conducted using computational fluid dynamics software which solves the Reynolds Averaged Navier-Stokes equations using the finite volume method with a RNG 'capa' - 'épsilon' turbulence model

A inserção de ar em escoamentos de altas velocidades ao longo de estruturas hidráulicas é uma técnica bastante eficiente para prevenir a cavitação. A sua importância é majorada quando se considera os custos econômicos e as questões de segurança que estão associadas à estabilidade de uma barragem. No presente trabalho são apresentados equacionamentos para quantificar a entrada de ar em vertedores através de aeradores de fundo. Essas equações foram obtidas utilizando princípios físicos de conservação de massa, energia e quantidade de movimento nos escoamentos de ar e água que ocorrem no aerador, permitindo organizar informações advindas de cada fase. Ressalta-se que buscou-se tornar o equacionamento independente da subpressão do jato, uma vez que esta subpressão é um parâmetro de difícil determinação a priori pelo projetista. Entretanto, toda formulação é direcionada justamente para melhor representar este parâmetro utilizando os princípios físicos clássicos e as variáveis decorrentes da sua utilização. Buscou-se a validação de modelos teóricos obtidos por meio de formulações baseadas nas leis de conservação de massa, quantidade de movimento e energia para aeradores de fundo. Neste contexto, comparam-se os resultados dos equacionamentos propostos e os dados experimentais encontrados na literatura, tendo se verificado boas correlações. Este tipo de quantificação essencialmente teórica de incorporação do ar em aeradores de fundo ainda é raro e o presente trabalho visa contribuir na validação de modelos com estas características. Adicionalmente, efetua-se a comparação com as equações empíricas e semi-empíricas encontradas na literatura. A experiência adquirida na área mostra que esta é a forma mais adequada de abordar o problema. / The introduction of air in flows around bottom aerators in spillways of dams is an efficient technique to prevent cavitation. Its importance is increased when one considers the costs involved and the safety issues that are associated with the stability of a large dam. Equations are presented in this study to quantify the air inlet through bed aerators in flows along spillways. The equations were obtained using the physical principles of conservation of mass, energy and momentum in both the flows of air and water in the aerator, allowing to organize the information obtained from each phase. It was possible to show the parameters that are relevant for quantifying the induced air flow in bed aerators. In addition, a comparison was conducted between the equations resulting from this analysis and empirical and semi-empirical expressions found in the literature. It is noteworthy to mention that one of the objectives of this study was to obtain a final equation independent of the relative pressure under the jet, since this low pressure is a parameter difficult to determine a priori by the designer. However, the entire formulation was directed precisely to better represent this parameter using the principles of classical physics and the variables arising from their use. The experience acquired in this area shows that this is the most appropriate way to address this problem.