Jerson Rogério Pinheiro Vaz

An Investigation of a Mathematical Model for the Internal Velocity Profile of Conical Diffusers Applied to DAWTs

The Diffuser Augmented Wind Turbines (DAWTs) have been widely studied, since the diffusers improve the power coefficient of the wind turbine, particularly of small systems. The diffuser is a device which has the function of causing an increase on the flow velocity through the wind rotor plane due to pressure drop downstream, therefore resulting in an increase of the rotor power coefficient. This technology aids the turbine to exceed the Betz limit, which states that the maximum kinetic energy extracted from the flow is 59.26%. Thus, the present study proposes a mathematical model describing the behavior of the internal velocity for three conical diffusers, taking into account the characteristics of flow around them. The proposed model is based on the Biot-Savarts Law, in which the vortex filament induces a velocity field at an arbitrary point on the axis of symmetry of the diffusers. The results are compared with experimental data obtained for the three diffusers, and present good agreement.

Contribution to the marine propeller hydrodynamic design for small boats in the Amazon region

Na Amazonia, a navegacao e muito importante devido a extensao de rios navegaveis e a falta de redes rodoviarias alternativas. As embarcacoes geralmente trabalham em condicoes desfavoraveis, uma vez que nao ha relacao entre a hidrodinâmica dos helices, geometria e as dimensoes do casco da embarcacao. Atualmente, nao ha metodologia para otimizacao hidrodinâmica com baixo custo computacional e facil implementacao na regiao. O objetivo deste trabalho foi o desenvolvimento de uma abordagem matematica voltada para o projeto de propulsores maritimos aplicados as embarcacoes tipicamente encontradas nos rios da Amazonia. Nos desenvolvemos uma formulacao otimizada para o calculo das distribuicoes de corda e ângulo de torcao, considerando o modelo classico de Glauert. Uma analise teorica para as relacoes de empuxo e torque em um volume de controle anular foi realizado. O modelo matematico utilizado foi baseado na teoria do momento do elemento de pa (BEMT). Concluimos que a nova metodologia, proposta neste trabalho, demonstra bom comportamento fisico quando comparado com a teoria de Glauert e os dados experimentais do propulsor Wageningen B3-50.

UMA ABORDAGEM PARA O COMPORTAMENTO TRANSIENTE DE TURBINAS EÓLICAS DE EIXO HORIZONTAL (HAWT) UTILIZANDO A TEORIA DO ELEMENTO DE PÁ

In this work, an efficient mathematical model applied to transient behavior of Horizontal-Axis Wind Turbines (HAWT) was developed. The influence of the power drive on HAWT dynamic modelling was taken into account, in order to present an improved approach for the design of wind power systems. In all simulations, a rotor with 30 m diameter operating at 20 m/s wind velocity was used. The driveline comprises the mass-moment of inertia, electromagnetic torque, and the friction torque of whole system. To solve the nonlinear dynamic equation at each time step, 4th order Runge-Kutta numerical method was considered, while a Newton-Raphson scheme was applied to the steady-state regime. In addition, to calculate the aerodynamic torque, the Blade Element Theory (BET) was implemented, since such a parameter is usually obtained through approximated mathematical functions, mainly those applied to large wind turbines as described in several works available in the literature. BET is a well-known method applied to design and aerodynamic analysis of wind turbines, which presents good agreement with experimental data. To conclude, the results show the rotational speed, output power and torque dependents on time, and depict good behavior when compared with Bao and Ye (2001). An application using BET was also carried out, which yielded consistent results. Keywords: Wind turbine, Dynamic behavior of HAWT, Blade Element Theory. RESUMO Neste trabalho foi desenvolvido um modelo matematico eficiente aplicado ao comportamento transiente de Turbinas Eolicas de Eixo Horizontal (HAWT). Foi levado em consideracao a influencia da unidade de transmissao na modelagem dinâmica a fim de se obter uma abordagem melhorada para o projeto de sistemas de energia eolica. Em todas as simulacoes, um rotor de 30 m de diâmetro operando a 20 m/s de velocidade de vento foi utilizado. O sistema de transmissao compreende o momento de inercia, torque eletromagnetico e o torque de atrito de todo o sistema. Para solucionar a equacao dinâmica nao linear em cada intervalo de tempo, o metodo de Runge-Kutta de 4a ordem foi considerado, enquanto que o metodo de Newton-Raphson foi aplicado ao regime estacionario. Alem disso, para calcular o torque aerodinâmico, a teoria do elemento de pa (BET) foi implementada, uma vez que o torque do rotor e frequentemente calculado atraves de funcoes matematicas aproximadas, principalmente quando aplicados a grandes turbinas eolicas, tal como descrito em varias obras disponiveis na literatura. BET e um metodo bem conhecido aplicado ao projeto e analise aerodinâmica de turbinas eolicas, o qual apresenta boa concordância com dados experimentais. Para concluir, os resultados para a velocidade de rotacao, potencia de saida e torque dependentes do tempo mostram bom comportamento quando comparados com Bao; Ye (2001). Uma aplicacao utilizando o metodo BET tambem foi realizado, o qual produziu resultados consistentes. Palavras-chave: Turbinas eolicas, comportamento dinâmico de HAWT, teoria do elemento de pa.

Numerical Study of Wake Characteristics in a Horizontal-Axis Hydrokinetic Turbine

Over the years most studies on wake characteristics have been devoted to wind turbines, while few works are related to hydrokinetic turbines. Among studies applied to rivers, depth and width are important parameters for a suitable design. In this work, a numerical study of the wake in a horizontal-axis hydrokinetic turbine is performed, where the main objective is an investigation on the wake structure, which can be a constraining factor in rivers. The present paper uses the Reynolds Averaged Navier Stokes (RANS) flow simulation technique, in which the Shear-Stress Transport (SST) turbulent model is considered, in order to simulate a free hydrokinetic runner in a typical river flow. The NREL-PHASE VI wind turbine was used to validate the numerical approach. Simulations for a 3-bladed axial hydrokinetic turbine with 10 m diameter were carried out, depicting the expanded helical behavior of the wake. The axial velocity, in this case, is fully recovered at 12 diameters downstream in the wake. The results are compared with others available in the literature and also a study of the turbulence kinetic energy and mean axial velocity is presented so as to assess the influence of proximity of river surface from rotor in the wake geometry. Hence, even for a single turbine facility it is still necessary to consider the propagation of the wake over the spatial domain.