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Introduction

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Separated and Vortical Flow in Aircraft Wing Aerodynamics

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Abstract

Vortex layers and vortices, although not occupying much space in the flow field around and behind an aircraft, can be seen as “the sinews and muscles of the fluid motion”, as D. Küchemann was putting it [1].

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Notes

  1. 1.

    In the context of flow singularities the singularity of the Blasius solution at the “leading edge” (\(x = 0\)) of the flat plate with zero thickness should be mentioned. In the hypothetical reality of such a flat plate—the zero thickness of course cannot be realized in an experiment—no singularity exists. However, a very small initial region is present, where the assumption of continuum flow is not valid. We point in this regard to the discussion of—although hypersonic—leading-edge flow in [32].

  2. 2.

    In Chap. 2 we consider some relevant properties of boundary layers, because they are what separates from a body surface.

  3. 3.

    In these two kinds of separation always two boundary layers are involved in the separation process. This situation is the rule, but there are singular points at the body surface where the situation is different, Chap. 7.

  4. 4.

    The case of a single separation bubble—example in Fig. 7.2a in Sect. 7.1.4—is found, if a suction peak is present shortly behind the airfoil’s nose (peaky pressure distribution) and laminar-turbulent transition happens across this bubble (bubble transition) [14].

  5. 5.

    Trailing vortices and tip vortices often are mixed up. They are separate phenomena. They only in a sense fall together in Prandtl’s lifting-line model.

  6. 6.

    The appearance of the lee-side vortex pair depends not only on the angle of attack, but also on the leading-edge sweep and the free-stream Mach number, Sect. 10.2.

  7. 7.

    The reader should note that we do not treat fuselage-flow problems in this book.

  8. 8.

    This is one of three criteria discussed, for instance, by E.A. Eichelbrenner [38].

  9. 9.

    We give only a very brief sketch of the developments. The interested reader will find detailed material in, for instance, [39, 40].

  10. 10.

    Below we will see that also compressible potential flow is possible.

  11. 11.

    The reader should note that we do not use the term strength for the vorticity integral as Lighthill does. We call that integral the intensity of the boundary layer or vortex layer, and more generally, the local vorticity content of a shear layer.

  12. 12.

    The drag of the airfoil then is a purely viscous drag, composed of the skin-friction drag and the viscosity-effects induced pressure or form drag due to the displacement properties of the boundary layers at the upper and the lower side of the airfoil, Sect. 2.4. In supercritical compressible flow other effects come into play, also Sect. 2.4.

  13. 13.

    Actually this equation is derived from the continuity equation. For a generalized derivation see, e.g., [49].

  14. 14.

    An ideal discrete modeled Euler solution (Model 7) would not have such diffusive properties.

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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

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  1. Ernst Heinrich Hirschel
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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). Introduction. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_1

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