Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T13:26:59.087Z Has data issue: false hasContentIssue false
  • English
  • Français

Tuning the axial singularity method for accurate calculation of potential flow around axisymmetric bodies

Published online by Cambridge University Press:  04 July 2016

M. F. Zedan
M. F. Zedan*
Affiliation:
Mechanical Engineering Department College of Engineering, King Saud University, Riyadh, Saudi Arabia
Get access Rights & Permissions [Opens in a new window]

Abstract

The performance of axial line singularity methods has been investigated systematically for various solution parameters using carefully chosen test cases. The results indicate that increasing the number of elements and using stretched node distribution improves the solution accuracy until the matrix becomes near-singular. The matrix condition number increases with these parameters as well as with the order of intensity variation and profile thickness. For moderate fineness ratios, the linear methods outperform zero-order methods. The linear doublet method performs best with control points at the x-locations of nodes while the source methods perform best with control points mid-way between nodes. The doublet method has a condition number an order of magnitude lower than the source method and generally provides more accurate results and handles a wider range of bodies. With appropriate solution parameters, the method provides excellent accuracy for bodies without slope discontinuity. The smoothing technique proposed recently by Hemsch has been shown to reduce the condition number of the matrix; however it should be used with caution. It is recommended to use it only when the solution is highly oscillatory with a near-singular matrix. A criterion for the optimum value of the smoothing parameter is proposed.

Type
Research Article
Information
The Aeronautical Journal , Volume 98 , Issue 976 , July 1994 , pp. 215 - 226
Copyright
Copyright © Royal Aeronautical Society 1994 

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. Oberkampf, W.L. and Watson, L.E., Incompressible potential flow solutions for arbitrary bodies of revolution. AIAA J, 12, (3), 1974, pp 409–411.Google Scholar
2. Zedan, M.F. and Dalton, C, Higher order axial singularity distributions for potential flow about bodies of revolution, Comput Methods Appl Mech Eng, 21, 1980, pp 295–314.Google Scholar
3. Jones, D.J., On the representation of axisymmetric bodies at zero angles of attack by sources along the axis, Canadian Aeronaut Space J, 27, (2), 1981, pp 135–143.Google Scholar
4. Campell, G.S., Calculation of potential flow past simple bodies using axial sources and a least squares method, J Aircr, 21, (6), 1984, pp 437–438.Google Scholar
5. Hemsch, M.J., Improved, robust, axial line singularity method forbodies of revolution, J Aircr, 27, (6), 1990, pp 551–557.Google Scholar
6. Handelsman, R.A. and Keller, J.B., Axially symmetric potential flow around a slender body, J Fluid Mech, 28, part 1, 1967, pp 131–147.Google Scholar
7. Hess, J., The unsuitability of ellipsoids as test cases for line-source methods, J Aircr, 22, (4), 1985, pp 346–347.Google Scholar
8. Von karman, T., Calculation of pressure distribution on airship hulls, 1927, translated as NACA TM 574, 1930.Google Scholar
9. Zedan, M.F. and Dalton, C, Potential flow around axisymmetric bodies: direct and inverse problems, AIAA J, 16, (3), 1978, pp 242–250.Google Scholar
10. Wolfe, W.P. and Oberkampf, W.L., A design method for the flow field and drag of bodies of revolution in incompressible flow, AIAA Paper 82-1359, Aug 1982.Google Scholar
11. Kuhlman, J.M. and Shu, J.-Y., Potential flow past axisymmetric bodies at angle of attack, J Aircr, 21, (3), 1984, pp 218–220.Google Scholar
12. Shu, J.-Y., and Kuhlman, J.M., Calculation of potential flow pastnon-lifting bodies at angle of attack using axial and surface singularity methods, NASA CR 166058, Feb 1983.Google Scholar
13. D'sa, J.M. and Dalton, C, Body of revolution comparisons for axial — and surface — singularity distributions, J Aircr, 23, (8), 1986, pp 669–672.Google Scholar
14. Phillips, D.L., A technique for the numerical solution of certain integral equations of the first kind, J Assoc Comput Much, 9, 1962, pp 84–97.Google Scholar
15. Twomey, S., On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature, J Assoc Comput Mach, 10, 1963, pp 97–101.Google Scholar
16. Wong, T.-C, Liu, C.H., and Geer, J., Comparison of uniform perturbation and numerical solutions for some potential flows past slender bodies, Comput Fluids, 13, (3), 1985, pp.271–283.Google Scholar
17. Vallantine, H.R., Applied Hydrodynamics, Butterworth, London, 1967.Google Scholar
18. Forsythe, G.E., Malcolm, M.A. and Moler, C.B., Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs, NJ, 1977.Google Scholar
19. Moran, J.P., Line source distributions and slender-body theory, J Fluid Mech, 17, 1963, pp 285–304.Google Scholar