Iterative approach for optimising coefficient of power, coefficient of lift and drag of wind turbine rotor

Abstract

This paper presents an approach for the determination of aerodynamic performance characteristics of horizontal-axis wind turbines. The optimum twist of a windmill blade is examined on the basis of elementary blade-element theory. For a given wind speed and blade angular velocity, it is shown that the maximum power efficiency is achieved when the blade is twisted according to a program that depends upon the variation of the sectional lift and drag coefficients with angle of attack. Results for a typical airfoil cross-section show that the optimum angle of attack and optimum twist angle of the blade improves the performance of the wind turbine. Based on Glauert’s solution of an ideal windmill along with an exact trigonometric function method, analytical closed-form equations are derived and given for preliminary determination of the optimum chord and twist distributions. The variation of the angle of attack of the relative wind along blade span is then obtained directly from a unique equation for a known rotor size and refined blade geometry. Particular attention was paid to the axial flow and tangential flow induction factors and to the models for the representation of the lift and drag coefficients. A comparison was also made between the mathematical model presented in the paper and those considered in the literature. The mathematical code produced a power coefficient curve which showed that notwithstanding further increases in rotational velocity a constant maximum power value was reached even as wind velocity increased. This means that as wind velocity varies there will always be a rotational velocity of the turbine which maximizes its coefficient. It would be sufficient therefore to formulate the law governing the variation in rotational velocity as it varied with wind velocity to arrive at a power coefficient that is always the same and its maximum. A case study including the design of wind turbine, performance analysis with various assumption and CFD analysis of airfoils. The airfoils NACA 4410 and NACA 2415 are taken into consideration for evaluating this proposed approach. The results are discussed and compared with those obtained by other investigators. It is shown that the approach used in this study is efficient and saves much of the computational time as compared with the commonly used iterative procedures.