Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-22T11:47:38.548Z Has data issue: false hasContentIssue false
  • English
  • Français

An exact integral (field panel) method for the calculation of two-dimensional transonic potential flow around complex configurations

Published online by Cambridge University Press:  04 July 2016

P. M. Sinclair
P. M. Sinclair*
Affiliation:
British Aerospace, PLC Military Aircraft Division, Brough
Get access Rights & Permissions [Opens in a new window]

Summary

An exact integral formulation of the two-dimensional full potential equation is presented. The well developed standard surface panel method based on the linear Prandtl-Glauert equation is extended by means of sources in the field surrounding the configuration, allowing the calculation of transonic flows.

A major attraction of the Field Panel Method is that solutions can be obtained using standard surface panelling together with a field grid which has no special form. The surface panels are used to satisfy the boundary conditions so that the field grid does not have to be surface-fitted which is a requirement for existing field methods. Further, the grid need only be in a region close to the configuration where nonlinear compressibility effects are non-negligible and need not extend to the far field as generally required. Grid generation is therefore trivial allowing solutions for arbitrary configurations. Convergence, especially for flows with shock waves, is enhanced by use of a modified Approximate Factorisation scheme. Results for single aerofoils are compared with Garabedian-Korn solutions and show good agreement; and to demonstrate the ease of grid generation, results for multicomponent aerofoils are also presented. Finally, an outline is given of how the method can be extended to threedimensions.

The work was carried out in conjunction with the Department of Applied Mathematics, University of Leeds together with Procurement Executive, Ministry of Defence.

Type
Research Article
Information
The Aeronautical Journal , Volume 90 , Issue 896 , July 1986 , pp. 227 - 236
Copyright
Copyright © Royal Aeronautical Society 1986 

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. Hess, J. L. and Smith, A. M. O. Calculation of non-lifting potential flow about arbitrary three-dimensional bodies. Progress in Aeronautical Science, edited by Kuchemann, D., 1967, 8, 1–138.Google Scholar
2. Murman, E. M. and Cole, J. D. Calculation of plane steady transonic flows. AIAA Journal, 1971, 9.Google Scholar
3. Petrie, J. A. H. Development of an efficient and versatile panel method for aerodynamic problems. University of Leeds PhD thesis, 1979.Google Scholar
4.User Guide for SPARV Panel Program. BAe Brough Note YAD 3385, October 1985.Google Scholar
5. Jameson, A. and Caughey, D. A. A Finite Volume Method for Transonic Potential Flow Calculations. AIAA Conference, Albuquerque, New Mexico, June 1977.Google Scholar
6. Habashi, W. G. and Hafez, M. H. Finite element solutions of transonic flow problems. AIAA Journal, 20, 10, 1368–1376.Google Scholar
7. Jameson, A. Transonic Flow Calculations. VKI Lecture Series 87, Computational Fluid Dynamics, March 1976.Google Scholar
8. Baker, T. J. The computation of transonic potential flow. ARA memo No. 233, May 1981.Google Scholar
9. Brandt, A. Multigrid techniques 1984 guide with applications to fluid dynamics. VKI lecture series, 1984.Google Scholar
10. Crown, J. C. Calculation of transonic flow over thick airfoils by integral methods. AIAA Journal, 1968, 6, 413–423.Google Scholar
11. Piers, W. J. and Sloof, J. W. Calculation of transonic flow by means of a shock-capturing Field Panel Method. AIAA paper 79–1459, Williamsburg 1979.Google Scholar
12. Milne-thomson, L. M. Theoretical Hydrodynamics. Macmilland and Company Limited. 1968.Google Scholar
13. Kellog, O. D. Foundations of potential theory. Dover Publications Inc, New York, Chapter VIII.Google Scholar
14. Maskew, B. Numerical lifting surface methods for calculating the potential flow about wings and wing-bodies of arbitrary geometry. University of Loughborough PhD thesis, 1972.Google Scholar
15. Garabedian, P., Korn, D. G. and Jameson, A. Supercritical wing sections. Lecture notes in economic and mathematical systems No 66, 1972.Google Scholar
16. Williams, B. R. An exact test case for the plane potential flow about two adjacent lifting aerofoils. Ministry of Defence Aeronautical Research Council Reports and Memoranda Number 3717, 1973.Google Scholar
17. Suddoo, A. and Hall, I. M. Inviscid compressible flow past a multi-element aerofoil. AGARD Conference Proceedings No 365, 1984 Google Scholar