Abstract
In the mid 1980s computer speed and storage had developed to a degree that Euler methods (Model 8 in Table 1.3) became a viable tool for aerodynamic design work. At that time very much discussed was the fact that at delta wings with sharp leading edges lee-side vortices resulted in the relevant angle of attack and Mach number regime. The question was, where is the apparent vorticity coming from, and accordingly the associated entropy rise.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See also the introductory discussion in Sect. 1.4.
- 2.
Regarding the definition of the boundary-layer thickness see Appendix A.5.4.
- 3.
A discussion of the flow at the trailing edges of real airfoils and wings is given in Chap. 6.
- 4.
The amount of vorticity which must be canceled is small compared to the amount of vorticity of each of the involved boundary layers, usually only a few per cent.
- 5.
These properties are important, because behind a straight shock wave with constant pre-shock Mach number, a total pressure loss is present, but no vorticity. See in this regard Crocco’s theorem, Sect. 3.5.
- 6.
Note that a discrete (Model 8) Euler solution close to a solid surface always exhibits a thin total-pressure loss layer, casually called Euler boundary layer. That is an artifact due to the finite discretization of the computation domain and the flow variables used.
- 7.
- 8.
See the examples in Chap. 8.
- 9.
- 10.
Trailing edge properties as well as the Kutta condition in reality are treated in Chap. 6.
- 11.
Lighthill calls the trailing vorticity also residual vorticity.
References
Hirschel, E.H.: Considerations of the vorticity field on wings. In: Haase, W. (ed.) Recent Contributions to Fluid Mechanics, pp. 129–137. Springer, Berlin (1982)
Hirschel, E.H., Fornasier, L.: Flowfield and vorticity distribution near wing trailing edges. AIAA-Paper, 1984–0421 (1984)
Hirschel, E.H.: On the creation of vorticity and entropy in the solution of the Euler equations for lifting wings. MBB-LKE122-AERO-MT-716, Ottobrunn, Germany (1985)
Hirschel, E.H., Rizzi, A.: The mechanisms of vorticity creation in Euler solutions for lifting wings. In: Elsenaar, A., Eriksson, G. (eds.) International Vortex-Flow Experiment on Euler Code Validation. FFA, Bromma (1987)
Eberle, A., Rizzi, A., Hirschel, E.H.: Numerical Solutions of the Euler Equations for Steady Flow Problems. Notes on Numerical Fluid Mechanics, Vol. 34. Vieweg, Braunschweig Wiesbaden (1992)
Hirschel, E.H.: Vortex flows: some general properties, and modelling. Configurational and manipulation aspects. AIAA-Paper, 96–2514 (1996)
Hirschel, E.H., Cousteix, J., Kordulla, W.: Three-Dimensional Attached Viscous Flow. Springer, Berlin (2014)
Fischer, J.: Selbstadaptive, lokale Netzverfeinerung für die numerische Simulation kompressibler, reibungsbehafteter Strömungen (Self-Adaptive Local Grid Refinement for the Numerical Simulation of Compressible Viscous Flows). Doctoral Thesis, University Stuttgart, Germany (1993)
Stanewsky, E., Puffert, W., Müller, R., Batemann, T.E.B.: Supercritical Airfoil CAST 7—Surface Pressure, Wake and Boundary Layer Measurements. AGARD AR-138, A3-1–A3-35 (1979)
Zierep, J.: Der senkrechte Verdichtungsstoß am gekrömmten Profil. ZAMP, vol. IXb, pp. 764–776 (1958)
Lighthill, J.: An Informal Introduction to Theoretical Fluid Mechanics. Clarendon Press, Oxford (1986)
Mangler, K.W., Smith, J.H.B.: Behaviour of the vortex sheet at the trailing edge of a lifting wing. Aeronaut. J. R. Aeronaut. Soc. 74, 906–908 (1970)
Anderson Jr., J.D.: Fundamentals of Aerodynamics, 5th edn. McGraw Hill, New York (2011)
Schwamborn, D.: Laminare Grenzschichten in der Nähe der Anlegelinie an Flügeln und flügelänlichen Körpern mit Anstellung (Laminar Boundary Layers in the Vicinity of the Attachment Line at Wings and Wing-Like Bodies at Angle of Attack). Doctoral thesis, RWTH Aachen, Germany, 1981, also DFVLR-FB 81-31 (1981)
Zahm, A.F.: Flow and force equations for a body revolving in a fluid. NACA Rep. No. 323 (1930)
Maruhn, K.: Druckverteilung an elliptischen Rümpfen und in ihrem Außenraum. Deutsche Luftfahrtforchung, Jahrbuch 1941, SI, pp. 135–147 (1941)
Schlichting, H., Truckenbrodt, E.: Aerodynamik des Flugzeuges, vol. 1 and 2, Springer, Berlin/Göttingen/Heidelberg, 1959, also: Aerodynamics of the Aeroplane, 2nd edn (revised). McGraw Hill Higher Education, New York (1979)
Prandtl, L.: Tragflügeltheorie, I. und II. Mitteilung. Nachrichten der Kgl. Ges. Wiss. Göttingen, Math.-Phys. Klasse, 451–477 (1918) und 107–137 (1919)
Spreiter, J.R., Sacks, A.H.: The rolling up of the trailing vortex sheet and its effect on the downwash behind wings. J. Aeronaut. Sci. 18, 21–32 (1951)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer-Verlag GmbH Germany, part of Springer Nature
About this chapter
Cite this chapter
Hirschel, E.H., Rizzi, A., Breitsamter, C., Staudacher, W. (2021). The Local Vorticity Content of a Shear Layer. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-61328-3_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-61326-9
Online ISBN: 978-3-662-61328-3
eBook Packages: EngineeringEngineering (R0)