Abstract
This chapter is devoted to an introduction to some of the concepts used when dealing with separated and vortical flow.
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.
Regarding the geometry of actual trailing and leading edges see Chap. 6.
- 2.
This momentum thickness concept does not hold for three-dimensional boundary layers. There the momentum-flow displacement thickness is the physically meaningful concept [5]. Nevertheless, the two-dimensional momentum thickness concept suffices for our considerations, as long as the treated flow is not too strongly three-dimensional.
- 3.
If locally the inverse of the boundary-layer thickness \(\delta \) is of the order of magnitude of the largest of the principal surface curvatures radii \(R_{i}\), the pressure gradient is no more small due to the centrifugal forces induced by the surface curvature [5]. This is the best known boundary-layer higher-order effect. It can be treated with second-order boundary-layer theory.
- 4.
External means at the outer edge of the boundary layer.
- 5.
This contradicts van Dykes statement that a wake exerts a first-order influence even in the flow upstream [16]. Of course, the integral forces and moments, which the flow exerts on the body, are affected by separation.
- 6.
When in the late 1930s the potential of airbreathing jet propulsion emerged—recognized at that time predominantly in Germany [17]—the drag divergence was a matter of very high concern.
In Germany up to 1945 frantic work at research organizations and in aircraft industry was conducted in order to shift in particular the drag divergence to as high as possible (sub-sonic) flight Mach numbers. Connected to the supercritical airfoil are the names K.H. Kawalki and B. Göthert, to the swept wing the names A. Busemann, H. Ludwieg, A. Betz, to the delta wing A. Lippisch, and to the area rule O. Frenzl. The area rule later was confirmed with the equivalence theorem by F. Keune and K. Oswatitsch (1953). An overview of the work is given in [17] and a very detailed account in [18].
When the war ended, the outcome of this work, which in Germany barely came to an application, found its way to the Allies. In [17] a short section “Transfer of the German Aeronautical Knowledge After 1945” is included, details regarding the American acquisition of data are given in [19]. Large research and development efforts in a short time then changed the geometrical appearance of all kind of aircraft. For the USA see in this respect the publication of J.D. Anderson, Jr., “The Airplane: A History of Its Technology” [20].
- 7.
The zero-lift drag is the drag of the aircraft without the induced drag.
- 8.
The shock wave terminates orthogonally to the airfoil’s surface, although at the boundary-layer edge particular phenomena can be present. For all pre-shock Mach numbers this leads to a reduction of the unit Reynolds number and hence to a thickening of the boundary layer.
- 9.
In the literature often the lower critical Mach number \(M^{*}_{\infty ,l}\) is distinguished from the upper critical Mach number \(M^{*}_{\infty ,u}\). At \(M^{*}_{\infty ,l}\) supersonic flow begins to appear at the body, at \(M^{*}_{\infty ,u}\) the flow past the body is fully supersonic, at a blunt-nosed body except for the subsonic region at the nose.
References
Shapiro, A.H.: Basic equations of fluid flow. In: Streeter, V.L. (ed.) Handbook of Fluid Dynamics. McGraw-Hill Book Company, New York, pp. 2-1–2-19 (1961)
Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, 2nd edn. Wiley, New York (2002)
Anderson Jr., J.D.: Fundamentals of Aerodynamics, 5th edn. McGraw-Hill Book Company, New York (2011)
Schlichting, H., Gersten, K.: Boundary Layer Theory, 8th edn. Springer, Berlin (2000)
Hirschel, E.H., Cousteix, J., Kordulla, W.: Three-Dimensional Attached Viscous Flow. Springer, Berlin (2014)
Hirschel, E.H.: Basics of Aerothermodynamics, 2nd edn, revised. Springer, Cham (2015)
N.N.: Boundary-layer simulation and control in wind tunnels. AGARD-AR-224 (1988)
Cebeci, T., Cousteix, J.: Modeling and Computation of Boundary-Layer Flows, 2nd edn. Horizons Publishing, Long Beach and Springer, Berlin (2005)
Knopp, T., Eisfeld, B., Calvo, J.B.: A new extension for k-\(\omega \) turbulence models to account for wall roughness. Int. J. Heat Fluid Flow 30, 54–65 (2009)
Thwaites, B.: Approximate calculation of the laminar boundary layer. Aeronaut. Q. 1(3), 245–280 (1949)
Stratford, B.S.: The prediction of separation of the turbulent boundary layer. J. Fluid Mech. 5(1), 1–16 (1959)
Cebeci, T., Mosinskis, G.J., Smith, A.M.O.: Calculation of separation points in incompressible turbulent flow. J. Aircr. 9(9), 618–624 (1972)
Délery, J.: Transonic shock-wave boundary-layer interactions. In: Babinsky, H., Harvey, J.K. (eds.) Shock-Wave Boundary-Layer Interactions, pp. 5–86. Cambridge Universtity Press, Cambridge (2011)
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)
Dallmann, U., Herberg, T., Gebing, H., Su, W.-H., Zhang, H.-Q.: Flow-field diagnostics: topological flow changes and spatio-temporal flow structure. AIAA Paper 95–0791, (1995)
Van Dyke, M.: Perturbation Methods in Fluid Mechanics. Academic, New York (1964)
Hirschel, E.H., Prem, H., Madelung, G. (eds.): Aeronautical Research in Germany–from Lilienthal until Today. Springer, Berlin (2004)
Meier, H.U. (ed.): German Development of the Swept Wing–1935–1945. Library of Flight. AIAA, Reston (2010)
Samuel, W.W.E.: American Raiders: The Race to Capture the Luftwaffe’s Secrets. University Press of Mississippi, Jackson (2004)
Anderson Jr., J.D.: The Airplane: A History of Its Technology. AIAA, Reston (2002)
Schlichting, H., Truckenbrodt, E.: Aerodynamik des Flugzeuges, vol. 1 and 2, Springer, Berlin (1959), also: Aerodynamics of the Aeroplane, 2nd edn (revised). McGraw Hill Higher Education, New York (1979)
Göthert, B.: Hochgeschwindigkeitsuntersuchungen an symmetrischen Profilen mit verschiedenen Dickenverhältnissen im DVL-Hochgeschwindigkeits-Windkanal (2.7 m \(\emptyset \)) und Vergleich mit Messungen in anderen Windkanälen. ZWB/FB 1506 (1941)
Vos, R., Farokhi, S.: Introduction to Transonic Aerodynamics. Springer Science+Business Media, Dordrecht (2015)
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). Separation: Some Relevant Boundary-Layer Properties, Interaction Issues, and Drag. In: Separated and Vortical Flow in Aircraft Wing Aerodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61328-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-61328-3_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-61326-9
Online ISBN: 978-3-662-61328-3
eBook Packages: EngineeringEngineering (R0)