Vórtices helicoidais : modelo, aplicação e o problema do fator de ponta em hélices e turbinas eólicas

Abstract

The helical vortex method has been research topic mainly due to the growth in the use of clean energy, especially wind energy, as it reliably and robustly represents the wake downstream of wind turbines. The model originated in aeronautics in the 1930s, having been little used in propeller design. In this work, revisiting this method, as well as a reviewing research on the subject was made, contributing to the methods evaluation for calculating the performance of propellers and wind turbines. The work sought to validate the hypothesis that it is possible to mitigate performance prediction errors by replacing the use of tip correction factors with the effective calculation of aerodynamic conditions at each position along the blade through the use of the helical vortex technique, removing the consideration of independent elements, such as those used in traditional methods based on Blade Element-Momentum (BEM). An application methodology was detailed and validated by determining the circulation distribution for optimal efficiency in cases of a rotor with an infinite number of blades and zero drag; infinite number of blades in the presence of drag; finite number of blades and zero drag; and, finite number of blades in the presence of drag. Still in the method validation stage, the performance of a previously tested rotor was calculated and results from the optimization of the blade’s geometric parameters were presented to maximize the efficiency of this same rotor. A total of 27 cases for propellers were evaluated, as well as 9 cases for wind turbines. The present method was compared with traditional aerodynamic methods as well as with computational fluid mechanics results, using κ − ω SST RANS models. The present method proved capable of predicting the values of the coefficients and their distributions in a satisfactory manner, with advantages over other methods, as it avoids errors and inconsistencies related to the use of tip correction functions. The values of the thrust and power coefficients were estimated with good precision, with errors between the range of -2.5% and 6% for propellers and 0.9% and 14.9% for wind turbines. The results showed a large divergence in the prediction of induced velocities between the BEM and MVH methods due to the deviations between the tip effect correction functions predictions and the values calculated for the potential field due to the helical wake. The results obtained confirm the physical tip correction models inconsistency, reinforcing the hypothesis that the field calculation using MVH is a viable alternative for the design and analysis of propellers and wind turbines.