Uma abordagem matemática aplicada ao projeto de turbinas hidrocinéticas e eólicas com difusor utilizando a teoria do elemento de pá

Abstract

It is known surrounding a turbine with diffuser may significantly increase its power. This effect has attained considerable attention as it shows theoretically the possibility of achieving a power coefficient about 2 times greater than an ordinary turbine. However, the effect of the diffuser efficiency has not been implemented into blade element momentum yet, as well as the use of minimum pressure coefficient criterion to avoid cavitation during the optimization of the hydrokinetic chord along the blade. Hence, this work presents a novel approach to design diffuser-augmented hydro turbines considering the diffuser efficiency. Based on the blade element momentum, new expressions for the axial induction factor and thrust are obtained. In addition, both efficiency and load generated on a diffuser are considered to the extension of existing formulation to determine power coefficient in cases where diffuser losses are taken into account through efficiency (ηd) and area ratio (β). To assess the proposed model, a comparative evaluation of two different diffusers (flanged conical diffuser and flanged lens diffuser) is performed. Numerical and theoretical results are compared for a shrouded turbine equipped with 83% efficiency diffuser. The relative difference observed for the maximum power coefficient between the proposed model and an actuator disk model with diffuser is about 5.3%. For the hydro turbine with flanged conical diffuser, the mass flow rate is about 20% higher than for a bare turbine, while for the turbine with flanged lens diffuser the increase is only 2.4%. Also, for the flanged conical diffuser the power is increased by 53%. Furthermore, it is observed that the proposed blade element momentum with diffuser achieved good agreement with the numerical model, providing improved results compared to other models available in the literature. The optimization model of hydrokinetic chord shows relevant results in relation to the prevention of cavitation.