Abstract
This chapter is devoted to the discussion of the flow—mainly the trailing vortex layer and the pair of trailing vortices—past lifting large aspect-ratio wings in view mostly of the results and insights gained in Chap. 4. Considered always is the clean-wing situation, selected topics of the real-wing situation (high-lift system, integrated engines etc.) are presented in Chap. 9.
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Notes
- 1.
Regarding differentiation aspects of large and low aspect-ratio wings see Sect. 8.4.4.
- 2.
This kink near the wing root is called a Yehudi break after its inventor at Boeing [2].
- 3.
These vortices sometimes are called necklace vortices.
- 4.
The decades old concept of in-flight camber changes now seems to approach reality thanks to the potential of carbon-fiber structures.
- 5.
HISSS method = Higher-Order Subsonic-Supersonic Singularity method.
- 6.
The large leading-edge sweep of the wing combined with a large angle of attack—see below—makes it necessary to investigate whether leading-edge separation can be present.
- 7.
For the definition of the trailing-edge flow shear angle \(\psi _{e}\) and the vortex-line angle \(\varepsilon \) see Fig. 4.11.
- 8.
This deflection is the reason for the well observed unwelcome accumulation of boundary-layer material at the wing root (and the fuselage) of forward swept wings. This can lead to adverse separation phenomena and, with rear-mounted engines at the aft end of the fuselage, makes special measures necessary regarding the position of the engines. The general deflection of course is also a property of the trailing vortex layer which leaves the wing’s trailing edge.
- 9.
In the mid-section of the wing, the Euler solution shows an irregularity, which seems to be due to the sharp apex of the wing.
- 10.
The 1-g shape is the shape of the elastic wing due to the aerodynamic load at nominal level flight, see, e.g., [7].
- 11.
In [27] this situation is called flow obstacle, although there the swept obstacle is not a topic.
- 12.
Note that at the leading edge the vortex separation is beginning at the rear and then moves forward with increasing angle of attack.
- 13.
Note that along the attachment line the flow velocity does not change much. This is indicated, too, by the pressure distribution along it, see the figure of the attachment line’s end, Fig. 8.31, left side. Hence the consideration of the local chord properties—without regard to their spanwise location—is permitted, though not in an exact quantitative sense.
- 14.
Note that the upper indices ’2’ of the velocity components do not indicate that they are squared velocities. They simple indicate the lateral direction in the local wake coordinate system, t in Fig. 4.11.
- 15.
This observation assumes a more or less two-dimensional behavior of the wing’s boundary layers. The justification is twofold: (1) the thickness of the boundary layer along the attachment line is more or less constant, and with this the initial conditions for the chordwise flow, (2) a larger three-dimensionality is present only in the immediate vicinity of the attachment line. Hence for qualitative considerations and also for crude estimations the assumption of two-dimensionality is permissible.
- 16.
The superscript index notation does not mean that the velocity components are contravariant ones as they are defined for instance in [26].
- 17.
The WRP was chosen as initial position, which, however, is a makeshift, because the actual flow situation at that location is highly complex, Fig. 8.33.
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Hirschel, E.H., Rizzi, A., Breitsamter, C., Staudacher, W. (2021). Large Aspect-Ratio Wing Flow. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_8
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