Theoretical and computational investigations of the optimal tip-speed ratio of horizontal-axis wind turbines

Abstract

An important factor in the optimization of the geometry of a horizontal-axis wind turbine (HAWT) is the design tip-speed ratio (DTSR). Previous research has suggested that DTSR values between 6 and 8 are desirable. However, a different approach was used in this study. Two standard airfoils with aerodynamic properties that are specified in the wind turbine airfoil catalog were selected and six different HAWT geometries were generated using the Schmitz formula for three DTSR values. These geometries were investigated theoretically based on the blade-element momentum (BEM) theory and numerically by using computational fluid dynamics (CFD) to calculate the rotor power efficiency and the optimal tip-speed ratio (OTSR). The six HAWTs had an average maximum power coefficient of 0.54 and an OTSR of 8.2 when the airfoil properties given in the airfoil catalog were used; these values were 0.43 and 6.7, respectively, when the airfoil properties were calculated using CFD and 0.41 and 7.3 when the HAWTs were simulated using three-dimensional CFD. To determine the power coefficient and OTSR values based on the BEM theory, the maximum value of CL/CD should be carefully selected considering factors such as the Reynolds numbers. Based on these findings, it was concluded that the CFD results validated the BEM theorem; the differences between the results obtained by these methods were likely due to the assumptions used when applying the BEM theory. Keywords: Design and optimum tip-speed ratio, Wind turbines, Reynolds number, Computational fluid dynamics, Blade element momentum theory