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Elements of Vortex Theory

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Separated and Vortical Flow in Aircraft Wing Aerodynamics

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Abstract

This chapter is devoted to a brief introduction to elements of vortex theory, which are of relevance for the topic of the book. We shortly outline each item, give basic mathematical descriptions, illustrating sketches, and provide supporting references.

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Notes

  1. 1.

    In the literature often the term “Lanchester–Prandtl-Theory” is found, in Germany it reads “Prandtl–Lanchester-Theory”, see also the remark on Sect. 1.4.

  2. 2.

    Solenoidal means source-free, or zero divergence in all points of a vector field.

  3. 3.

    The simple lifting-line model anyway does hold only for wings with large aspect ratio, say \(\varLambda \) \(\gtrapprox \) 3.

  4. 4.

    Regarding the Kutta condition in the reality of aircraft see Chap. 6.

  5. 5.

    The barotropic fluid is a fluid, whose density is only a function of pressure.

  6. 6.

    Regarding the development and the structure of the wake of a large aspect-ratio wing see the discussion of the corresponding Unit Problem in Sect. 8.4.

  7. 7.

    Regarding the reference area we note that Airbus uses the ‘Airbus Gross’ definition and Boeing the ‘Wimpress’ definition (after its inventor at Boeing), www.lissys.demon.co.uk/pug/c03.html.

  8. 8.

    Local force and moment coefficients are denoted with lower-case letter indices.

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Author information

Authors and Affiliations

  1. Institute of Aerodynamics and Gasdynamics, University Stuttgart, Zorneding, Germany

    Ernst Heinrich Hirschel

  2. Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology, Stockholm, Sweden

    Arthur Rizzi

  3. Chair of Aerodynamics and Fluid Mechanics, Technical University of Munich, Munich, Germany

    Christian Breitsamter

  4. Institute of Flightsystems, Bundeswehr University Munich, Zorneding, Germany

    Werner Staudacher

Authors
  1. Ernst Heinrich Hirschel
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  2. Arthur Rizzi
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  3. Christian Breitsamter
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  4. Werner Staudacher
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Correspondence to Ernst Heinrich Hirschel .

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Hirschel, E.H., Rizzi, A., Breitsamter, C., Staudacher, W. (2021). Elements of Vortex Theory. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_3

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  • DOI: https://doi.org/10.1007/978-3-662-61328-3_3

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