Prandtl's Theory Research Paper

Optimization of a Thruster Sections by Prandtl’s Theories
Abidi Essia 1; Hcini Cherif 2; Kamoun Badreddinne 3
1, 2, 3 Laboratory of Applied Physics, Faculty of Sciences of Sfax, Department of Physics, Road Soukra: km 4- BP n° 802 -Sfax- 3038
E-mail of corresponding author: [e-mail]
Phone number of corresponding author: [phone]

Abstract
Wind power is now the world’s fastest growing energy source. It is well known that energy production depends on the shape of the thruster (sail of yacht or a blade) and on the wind characteristics on a given site. In this work we try to maximize the performances of a thruster by optimizing the most important aerodynamic design parameters.
One of the most important challenges in aerodynamics

Results
3.1. Optimization of the thruster geometry
In this section, the thruster geometry optimization is based on a numerical model "PCLLT" based on Prandtl’s classic lifting line theory.
3.1.1. Validation of the numerical model "PCLLT"
We varied the angle of incidence of a rectangular thruster having an aspect ratio of between 0° and 14°, and we made a comparison with a lift experimental results [12] (Figure 1). Figure 1: Variation of the lift according to the incidence angle of a rectangular thruster ( )
For low incidences (below 10°), where the linear approximation is valid, the results of our model are close to the experimental results [12], which proves the validity of our calculation code.
3.1.2. Effect of the aspect ratio
Figure 2 shows the effect of the aspect ratio of a non-twisted rectangular thruster on its performance which is characterized by the drag polar curve: the lift according to the induced drag . Figure 2 : Effect of the aspect ratio on the drag polar
It is clear that the increase of the aspect ratio causes an increase in the lift and reduction in the induced drag and consequently the increase in the thruster efficiency.
3.1.3. Effect of the taper

Indeed, an increase of 1% of camber leads to a remarkable increase in lift, hence the appearance of acute circulation curve. This unfavorable shape is due to the sudden increase in circulation in passing from one assembly to another. However, a deviation of 1% in thickness does not greatly affect the lift, and therefore, a slight increase of the circulation is noted in passing from one assembly to another. Therefore, it is better to follow a thickness law than a camber