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Basic Fluid Mechanics

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Introduction to Wind Turbine Aerodynamics

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Abstract

Air regarded as an ideal gas may be described by its mass–density \(\rho = dm/dV\). To adjust its standard value of \(\rho _0 = 1.225\;\mathrm{kg/m}^3\) to other temperatures (\(\vartheta \)) and elevations (H) we may use \( \rho (p,T) = \frac{p}{R_i \cdot T} T = 273.15 + \vartheta R_i = 287 p(z) = p_0 \cdot e^{-z/z_{ref}} p_0 = 1015 \;\mathrm{hPa} z_{ref} = 8400 \;\mathrm{m}.\)

Ich behaupte aber, daß in jeder besonderen Naturlehre nur so viel eigentliche Wissenschaft angetroffen werden könne, als darin Mathematik anzutreffen ist (Immanuel Kant, 1786) [32]. (However, I claim that in every special doctrine of nature there can be only as much proper science as there is mathematics therein. (Ref Stanford Encyclopedia of Philosophy)).

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Notes

  1. 1.

    A tensor may be represented by a n \(\times \) n matrix. However, like scalars and vectors it is defined by its transformation rules under change of coordinates.

  2. 2.

    Heinrich Blasius, \(\star \) 08.09.1883, \(\dagger \) 04.24.1970, was one of L. Prandtl’s first Ph.D. students. His work on forces and Boundary Layer flat plate theory is discussed in almost every textbook of fluid mechanics even today. Less known is that he taught over 50 years (1912–1970) at Ingenieuerschule (Polytechnic—now University of Applied Sciences) Hamburg.

  3. 3.

    It may be of interest to note that here the essential argument is to avoid singularities in terms of infinite velocities, whereas in other applications this does not apply, for example, the infinite pressure at an inclined flat plate.

  4. 4.

    Sometimes called chaos theory.

  5. 5.

    By random we mean that there exist only probabilities for the field quantities, at least in the sense of classical statistical physics.

  6. 6.

    Many well-known physicists worked on turbulence: W. Heisenberg, L. Onsager, Carl-Friedrich von Weizsäcker, to name a few of them. An often repeated quote is that of Richard Feynman, that turbulence is the most important unresolved problem in classical physics.

  7. 7.

    Especially on 2D turbulence for which he was awarded the Dirac Medal in 2003.

  8. 8.

    It is well known from the theory of linear partial differential equations that a number of problems are simplified if formulated by Fourier transform into wavenumber–frequency co-space. The NSE equation then reads as

    figure a
  9. 9.

    Taylor’s frozen turbulence hypothesis has been used here. It states that time series may be used instead of spatially varying values.

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  1. Mechanical Engineering Department, University of Applied Sciences, Kiel, Germany

    A. P. Schaffarczyk

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Schaffarczyk, A.P. (2020). Basic Fluid Mechanics. In: Introduction to Wind Turbine Aerodynamics. Green Energy and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-41028-5_3

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  • DOI: https://doi.org/10.1007/978-3-030-41028-5_3

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