Parametric study of the effects of a Tubercle's geometry on wing performance through the use of the lifting-line theory

Abstract

Prandtl’s lifting-line theory has been implemented to determine the effects of a tubercle’s amplitude and wavelength on the lift coefficient, induced drag coefficient, and the lift-toinduced- drag ratio of a NACA 0021 wing at an angle of attack of 3°, and a Reynolds number of 120,000. In addition, a new tubercle parameter has been introduced; the point along a tubercle that a wing terminates. This parameter has been termed the phase of the tubercles. The phase of the tubercles tended to have the greatest effect on the lift coefficient, induced drag coefficient, and the lift-to-induced-drag ratio, while the wavelength had the least. However, the effects of the tubercle amplitude, wavelength, and phase on the wing performance parameters considered were inter-dependent, whereby increasing the amplitude or wavelength not only resulted in these individual parameters to be more effectual, but for the phase to be more effectual as well. Typically, a particular tubercle geometry that reduced the lift coefficient also reduced the induced drag coefficient, and the lift-to-induced-drag ratio would increase. The lift-to-induced-drag ratio was increase by as much as 7.7% for the considered tubercle geometries.