# Volume 8 Issue 3 ( September 2021 )

Pages_574-585

## Study of $\sqrt{2}$ Conjecture in the Construction of Drag Induced
Wind Turbine Blade Morphology

### S.N. Ashwindran, A.A. Azizuddin, A.N. Oumer

#### [ABSTRACT ]

In wind engineering, the morphology of the turbine blade system governs the effectiveness in harvesting wind energy. The flow
field response is the result of the turbine blade shape interaction with flow. Hence, mathematically interpreting the shape of the
blade will help to understand the principals and properties of the utilized geometry for the blade construction. In this study,
semicircle geometry of Savonius wind turbine blade is mathematically analyzed in order to understand its fundamental building
block. We provide discussion on $\sqrt{2}$ conjecture found in the construction of circles, Fibonacci and Pythagoras spiral in relations to $\sqrt{2}$,
$\sqrt{2}$+1 and $\sqrt{2}$+2. It is found that $\sqrt{2}$ conjecture can be utilized in determining the geometrical properties of circle and spiral. We also
performed thorough assessment of the proposed conjecture to prove its robustness and reliability. The proposed conjecture is
adapted to construct the blade morphology of drag induced wind turbine. CFD analysis is carried out to investigate the
aerodynamic properties namely moment coefficient (C_{m} ) of the constructed wind turbine shape via the proposed conjecture.
Results shows that the proposed shape constructed based on the conjecture has improved C_{m} by 7.2 % at λ = 0.59 and 4 % at λ =
0.94 compared to conventional SWT.

**Keywords: Savonius wind turbine; blade morphology; irrational number**