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Introduction to Transonic Aerodynamics pp 367–426Cite as

Airfoil Aerodynamics

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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 110))

Abstract

In this chapter we present the aerodynamics about two-dimensional lift-producing wing sections (airfoils) at low transonic conditions. It is shown how various design parameters influence the velocity distribution and the shock formation over an airfoil. The development of supercritical airfoils is explained from a historic perspective. First the advantages of natural laminar flow sections are explained for subsonic conditions prior to the formation local supersonic flow. It is shown how the supercritical airfoil distinguishes itself in terms pressure distribution and drag behavior once transonic conditions are encountered. Furthermore, it is demonstrated that transonic flow limitations can play a major role in the maximum lift coefficient of (multi-element) airfoils at Mach numbers as low as 0.25. A theoretical limit of the local Mach number is derived that effectively limits the amount of suction that can be generated over the upper surface of an airfoil. Also the concept of shock-boundary layer interaction is further expanded in this chapter. It is shown how periodic separation at the shock foot and shock oscillation can interact to produce a high-frequency pressure fluctuation known as transonic buffet. This chapter contains 4 examples and 16 practice problems at the end of the chapter.

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Notes

  1. 1.

    The program that is used for this evaluation is Xfoil version 6.94. XFOIL carries out a vortex-panel analysis of subsonic isolated airfoils and has the option to include a boundary layer. More information can be found on http://web.mit.edu/drela/Public/web/xfoil/.

  2. 2.

    MSES is a viscous-inviscid analysis program that couples the numerical solution of the Von Kármán equation (6.89) in the boundary layer to the numerical solution of the steady state conservative Euler equations (2.183) outside the boundary layer. More information can be found in Refs. [10, 15].

  3. 3.

    This prediction is carried out by Xfoil 6.94 using an \(e^N\) method for transition prediction with \(N_{\text {crit}}=10\).

  4. 4.

    One drag count equals a drag coefficient variation of 0.0001.

  5. 5.

    This calculation procedure for obtaining the pressure drag is often called a “near-field analysis”.

  6. 6.

    The prediction was made by assuming the flow to be inviscid (Euler solution).

  7. 7.

    A monotonic curvature means that the Mach wave is either entirely convex or entirely concave. If Mach wave curvature is not monotonic it means an inflection point is present somewhere on the Mach wave.

  8. 8.

    The data presented in this problem is based on an experiment described in [43]. In this experiment the shock movement was introduced trough a periodic change in angle of attack around \(\alpha =3.0\) of a NLR 7301 airfoil at \(M=0.70\).

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Authors and Affiliations

  1. Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands

    Roelof Vos

  2. Department of Aerospace Engineering, The University of Kansas, Lawrence, KS, USA

    Saeed Farokhi

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  1. Roelof Vos
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Vos, R., Farokhi, S. (2015). Airfoil Aerodynamics. In: Introduction to Transonic Aerodynamics. Fluid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9747-4_7

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  • DOI: https://doi.org/10.1007/978-94-017-9747-4_7

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