Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T07:32:14.678Z Has data issue: false hasContentIssue false
  • English
  • Français

The Evaluation of an Integral Equation Method for Two-Dimensional Shock-Free Flows

Published online by Cambridge University Press:  07 June 2016

D Nixon  and
J Patel
D Nixon
Affiliation:
Queen Mary College, University of London
J Patel
Affiliation:
Queen Mary College, University of London
Get access

Summary

The numerical aspects of the integral equation method developed by Nixon and Hancock for two-dimensional steady shock-free flow have been rationalised; this numerically refined method is evaluated by calculating the pressure distribution around a wide range of aerofoils. These test cases include aerofoils in supercritical shock-free flow as well as subcritical flow and exact solutions are available for comparison. The computational time in the present method is significantly less than that required by the exact methods. The present results compare satisfactorily with the exact results.

Type
Research Article
Information
Aeronautical Quarterly , Volume 26 , Issue 1 , February 1975 , pp. 59 - 70
Copyright
Copyright © Royal Aeronautical Society. 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Sells, C C L Plane subcritical flow past a lifting aerofoil. Proc Roy Soc, A, 308, 1968.Google Scholar
2 Steger, J L Lomax, H Numerical calculation of transonic flow about two-dimensional airfoils by relaxation procedures. AIAA Journal, Vol 10, pp 49–54, 1972.CrossRefGoogle Scholar
3 A Jameson Transonic calculations for airfoils and bodies of revolution. Grumman Aerospace Corporation, Aerodynamics Report 390-71-1, 1971.Google Scholar
4 Garabedian, P Korn, D Analysis of transonic airfoils. Communications on Pure and Applied Mathematics, Vol XXIV, pp 841–851, 1971.CrossRefGoogle Scholar
5 Nieuwland, G Y Transonic potential flow around a family of quasi-elliptic aerofoil sections. NLR-TRT172, 1967.Google Scholar
6 Boerstel, J W Uijlenhoet, R Lifting aerofoils with supercritical shock-free flow. Proceedings of ICAS Conference, 1970.Google Scholar
7 Garabedian, P Korn, D Numerical design of transonic airfoils. In Numerical Solution of Partial Differential Equations, Vol II, Academic Press, 1971.Google Scholar
8 Lock, R C Test cases for numerical methods in two-dimensional transonic flows. AGARD Report R-575-70, 1970.Google Scholar
9 Oswatitsch, K Die Geschwindigkeitsverteilung auf symmetrischen Profilen beim aufreten lokaler Uberschallgebiete. Acta Physica Austriaca, Vol 4, pp 228–271, 1950.Google Scholar
10 Gullstrand, T R The flow over symmetric aerofoils without incidence at sonic speed. KTH Aero TN 24, Royal Institute of Technology, Stockholm, 1952.Google Scholar
11 Spreiter, J R Alksne, A Y Theoretical prediction of pressure distributions on non-lifting aerofoils at high subsonic speeds. NACA Report 1217, 1955.Google Scholar
12 Nixon, D Hancock, G J High subsonic flow past a steady two-dimensional aerofoil. ARC Current Paper 1280, 1974.Google Scholar
13 Weber, J The calculation of the pressure distribution on the surface of thick cambered wings and the design of wings with given pressure distributions. ARC R & M 3026, 1955.Google Scholar
14 Hancock, G J Padfield, G Numerical solution for a steady two-dimensional aerofoil in incompressible flow. Queen Mary College Report QMC EP 1003, 1973.Google Scholar
15 Hewitt, B L Marland, D Surface velocity solutions of the Prandtl-Glauert equation for thick lifting aerofoils and wings using small perturbation techniques. To be published as British Aircraft Corporation Report BAC (MAD) Report Ae/354.Google Scholar
16 Kacprzynski, J J Ohman, L H Garabedian, P Korn, D Analysis of the flow past a shockless lifting airfoil in design and off-design conditions. National Research Council of Canada (Ottawa) Aero Report LR-554, 1971.Google Scholar
17 Nixon, D Extended integral equation method for transonic flows. To be published in the AIAA Journal.Google Scholar
18 Nixon, D An extended integral equation method for the steady transonic flow past a two-dimensional aerofoil. To be published in the Proceedings of the I.M.A. Conference of Computational Methods in Aeronautical Fluid Dynamics.Google Scholar