Study on the effects of winglets: wind turbine blades having circular arc blade section profile

Abstract

Performance enhancement of horizontal axis wind turbine with circular arc blade section has been investigated both experimentally and computationally using upstream and downstream winglet configurations. A computational study is performed for a three-blade rotor of 0.5-m-diameter in ANSYS Fluent to identify the optimum values for cant angle and twist angle. Findings from the numerical analysis are then utilized as inputs for the experimental study. The height of the winglet is selected as 6% of the rotor radius while cant angle and twist angle are 55° and 0°, respectively. Power and thrust coefficient are measured for both the upstream and downstream winglet orientations at different pitch angles ($\varphi$) and tip speed ratios (λ). Results show that upstream winglet provides 9.79% extra power in comparison with reference model at design tip speed ratio (TSR = 5) and zero pitch angle. Improved performance is obtained with downstream winglet achieving almost 15% additional power. Conversely, for all the pitch angles, power decreases as λ^0.1 beyond the design tip speed.

Appendix A

The level of uncertainty can be obtained using the following equation

$$\delta R = \sqrt {\left( {\delta x_{1} \frac{\partial R}{{\partial x_{1} }}} \right)^{2} + \left( {\delta x_{2} \frac{\partial R}{{\partial x_{2} }}} \right)^{2} + \cdots + \left( {x_{n} \frac{\partial R}{{\partial x_{n} }}} \right)^{2} }$$

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Coefficient of power equation in simplified form:

$$C_{{\text{P}}} = \frac{{(F_{1} - F_{2} )R * \frac{2\pi r}{{60}}}}{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}\rho \pi r^{2} V_{\infty }^{3} }}$$

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The uncertainty equation becomes:

$$\delta_{{C_{{\text{p}}} }} = \sqrt {\left( {\delta F_{1} \frac{{\partial C_{{\text{P}}} }}{{\partial F_{1} }}} \right)^{2} + \left( {\delta F_{2} \frac{{\partial C_{{\text{P}}} }}{{\partial F_{2} }}} \right)^{2} + \left( {\delta R\frac{{\partial C_{{\text{P}}} }}{\partial R}} \right)^{2} + \left( {\delta N\frac{{\partial C_{{\text{P}}} }}{\partial N}} \right)^{2} + \left( {\delta \rho \frac{{\partial C_{{\text{P}}} }}{\partial \rho }} \right)^{2} + \left( {\delta r\frac{{\partial C_{{\text{P}}} }}{\partial r}} \right)^{2} + \left( {\delta V_{\infty } \frac{{\partial C_{{\text{P}}} }}{{\partial V_{\infty } }}} \right)^{2} }$$

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$$\delta_{{C_{{\text{p}}} }} = \pm 0.0129$$

$${\text{Experimental}}\,{\text{Uncertainty}}\,{\text{at}}\,{\text{design}}\,{\text{TSR}} = \, 0.329 \pm 0.0129$$

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$$\begin{aligned} {\text{Percentage}}\,{\text{of}}\,{\text{error}} & = \frac{0.0129}{{0.329}}*100\% \\ & = 3.92\% \\ \end{aligned}$$

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