Construction of 3D Mandelbrot Set and Julia Set

Negi, Ashish; Garg, Ankit; Agrawal, Akshat

doi:10.5120/14920-3514

Cited by 1 publication

(1 citation statement)

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“…Lin (1996) 3) stated that symmetry represents the state of orderliness in a pattern configuration. Naturally reoccurring patterns exhibit similarity at different level and scale such as Mandelbrot set 4) . It means that patterns are set of shapes that repeat in identical manner without being in random configuration 5) .…”

Section: Introductionmentioning

confidence: 99%

Study of √2 Conjecture in the Construction of Drag Induced Wind Turbine Blade Morphology

Ashwindran¹,

Aziz²,

Oumer³

2021

Evergreen

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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 √2 conjecture found in the construction of circles, Fibonacci and Pythagoras spiral in relations to √2, √2 + 1 and √2 + 2. It is found that √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 (Cm) of the constructed wind turbine shape via the proposed conjecture. Results shows that the proposed shape constructed based on the conjecture has improved Cm by 7.2 % at λ = 0.59 and 4 % at λ = 0.94 compared to conventional SWT.

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Section: Introductionmentioning

confidence: 99%