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2020 | OriginalPaper | Buchkapitel

6. Application of Vortex Theory

verfasst von : A. P. Schaffarczyk

Erschienen in: Introduction to Wind Turbine Aerodynamics

Verlag: Springer International Publishing

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Abstract

It was already mentioned in Chap. 3 that Saffman (Vortex dynamics, 1992, [27]) quoted Küchemann, who said that

vortices are the sinews and muscles of fluid motion.

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Vorheriges Kapitel Momentum Theories

Nächstes Kapitel Application of Computational Fluid Mechanics

In fact this is a distribution (sometimes also called a generalized function) with the property that

$$\begin{aligned} \forall f \in {\mathscr {S}}: \int \delta (x) f(x) \; dx = f(0)\qquad \qquad \qquad {(6.2)} \end{aligned}$$

f(x) is called a test function. ${\mathscr {S}}$ is the set of test functions named after Laurent Schwartz, Field’s medal winner of 1950.

Von Kuik [15], [20] in Chap. 5 recently pointed out how to combine non-conservative forces with the conventional lifting-line Helmholtz–Kelvin approach.

The most famous outcome was a quantitative description of the phenomenon of induced drag $c_{D,ind} = c_L^2/ (\pi AR)$ which is minimized by an elliptical distribution of lift only. Corten [8] shows similarities and differences in the case of wind turbines. He found an AOA correction of $c_L /(8 \pi ) \cdot (B c/r) \cdot \lambda _r.$

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Titel: Application of Vortex Theory
verfasst von: A. P. Schaffarczyk
Verlag: Springer International Publishing
Buch: Introduction to Wind Turbine Aerodynamics
Print ISBN: 978-3-030-41027-8

Electronic ISBN: 978-3-030-41028-5

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-41028-5_6