Abstract
The topological analysis of velocity and skin-friction fields potentially is a useful tool for flow-field interpretations and also for problem diagnosis. In practice, however, normally not much use is made of topological analysis, maybe because it is often treated in a rather formalistic way. In view of the topic of this book we intend to accentuate the practical rather than the theoretical side of the field of topology. Even this will be made only in a rather sketchy way.
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Notes
- 1.
Note, however, that more than one primary attachment point can be present, depending on the overall shape of the aircraft.
- 2.
A very detailed discussion of the distinction between attached and separated flows is given in [1].
- 3.
See also Sect. 4.3.2.
- 4.
H. J. Lugt differentiates between vorticity lines and vortex lines [12]. What is called here vortex lines is in his nomenclature vorticity lines.
- 5.
We do not always mention detachment points and lines. It is self-evident what also holds for them in the following discussion.
- 6.
In [14] these are called “phase portraits” of the surface shear-stress vector field.
- 7.
- 8.
Experimental evidence of separation usually is given by changes of the wall-pressure distribution compared to that of the unseparated case. A pressure plateau may be formed, or at the aft of a two-dimensional body the recompression is severely suppressed.
- 9.
We keep the coordinate convention of the preceding sections.
- 10.
The Orr-Sommerfeld equation describes when a two-dimensional laminar boundary layer becomes unstable, triggering laminar-turbulent transition, see, e.g., [6].
- 11.
We neglect possible forward stagnation points at the propulsion units and at antennas and the like.
- 12.
This surface generator is a geodesic, the boundary layer is a quasi-two-dimensional one [6].
- 13.
For the meaning and the definition of the characteristic thickness \(\triangle _{c}\) see Appendix A.5.4.
- 14.
Time-dependent flow can be treated by applying the rules to the instantaneous flow field [5].
- 15.
- 16.
Note that with the attachment lines—the two primary lines, and also (!) with the two secondary lines and the tertiary line—inviscid flow attaches. However, the attachment-line flows themselves are viscous, i.e. the viscous layers or boundary layers at those lines have finite thicknesses, Sect. 7.3.
- 17.
We gratefully acknowledge that the following figures were provided by C. Weiland [26].
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Hirschel, E.H., Rizzi, A., Breitsamter, C., Staudacher, W. (2021). Topology of Skin-Friction and Velocity Fields. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_7
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