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A numerical method for second order thin airfoil theory

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Sommario

In questa nota si presenta un veloce algoritmo per il calcolo dell’integrale di Cauchy che è stato applicato al calcolo di flussi simmetrici incomprimibili in base ad una teoria quadratica delle piccole perturbazioni. La velocità calcolata nell’intorno del bordo di attacco è stata corretta con la regola di Lighthill. Si presentano alcuni risultati relativi a profili alari isolati ed a schiere di profili.

Summary

In this note a fast Cauchy integral solver and its application to the solution of symmetric incompressible flows, based on a quadratic thin airfoil theory, are presented. The computed velocity near the leading edge has been corrected with the Lighthill rule. Some results relative to airfoils and to cascade are reported.

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Abbreviations

h :

cascade spacing

l e :

leading edge

q :

velocity

q c :

corrected velocity

\(\bar q\) :

source strength

s :

axial distance from leading edge

t e :

trailing edge

T :

body shape

T n :

function defined in [4]

U ∞ :

undisturbed velocity

x, y :

cartesian coordinates

x I :

axial coordinate of leading edge

x F :

axial coordinate of trailing edge

W :

complex potential

z :

complex coordinate (x+iy)

Δx :

step size

ε:

maximum body thickness

φ n (n=1,2..):

disturbance potential components

References

  1. Hess J.L. andSmith A.M.O.,Calculation of potential flow about arbitrary bodies, Progress in Aeronautical Sciences, Vol. 8, Pergamon Press, 1966.

  2. Bristow D.R.,Recent improvements in surface singularity methods for the flow field analysis about two-dimensional airfoils, AIAA 3rd Computational Fluid Dynamics Conference, a collection of technical papers, 1977.

  3. Karamchety K.,Principles of ideal-fluids aerodynamics, Krieger Publishing Company.

  4. Van Dyke M.,Perturbation methods in fluid mechanics, The Parabolic Press.

  5. Napolitano M., andVacca G.,A thin airfoil spline panel method, Meccanica, pp. 30–32, March 1981.

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Authors and Affiliations

  1. Istituto di Macchine, Via Re David 200, 70125, Bari

    Bernardo Fortunato (Associate Professor)

Authors
  1. Bernardo Fortunato
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Fortunato, B. A numerical method for second order thin airfoil theory. Meccanica 20, 171–175 (1985). https://doi.org/10.1007/BF02337637

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  • DOI: https://doi.org/10.1007/BF02337637

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