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Generation of axi-symmetric body shapes in subsonic flow by means of polynomial distributions of sources and doublets along the axis of symmetry

Published online by Cambridge University Press:  04 July 2016

P. A. T. Christopher  and
C. T. Shaw
P. A. T. Christopher
Affiliation:
College of Aeronautics, Cranfield Institute of Technology
C. T. Shaw
Affiliation:
College of Aeronautics, Cranfield Institute of Technology
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Summary

A method is presented for determining the potential flow around bodies of revolution, at incidence, in uniform, incompressible, flow. This method utilises polynomial distributions of both sources and doublets, in the manner of Fuhrmann, and gives considerable advantage over existing techniques. In particular, when compared with the method of Nielsen, in a typical case, the computer storage requirement is reduced by a factor of eleven. Compared with panel methods the saving is very much greater.

Unlike the method of Landweber, both body surface and flow field conditions are obtainable and it would appear that the new method is ideally suited to the ‘store trajectory’ application in place of the existing discrete source method.

Type
Research Article
Information
The Aeronautical Journal , Volume 91 , Issue 904 , April 1987 , pp. 155 - 169
Copyright
Copyright © Royal Aeronautical Society 1987 

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References

1. Goldstein, S. (ED) Modern developments in fluid dynamics, 2 volumes, Dover, 1965.Google Scholar
2. Myring, D. F. The profile drag of bodies of revolution in subsonic axisymmetric flow. RAE TR 72234, 1972.Google Scholar
3. Thomson, K. D. Calculatibn of subsonic normal force and centre of pressure position of bodies of revolution using a slender body theory-boundary layer method. Aeronautical Quarterly, February 1980, 1–25.Google Scholar
4. Thwaites, B. (ED) Incompressible Aerodynamics, Oxford University Press, 1960.Google Scholar
5. Lamb, H. Hydrodynamics. 6th Ed. Cambridge University Press, 1932.Google Scholar
6. Kaplan, C. Potential flow about elongated bodies of revolution. NACA Report 516, 1935.Google Scholar
7. Kaplan, C. On a new method for calculating the potential flow past a body of revolution. NACA Report 752, 1943.Google Scholar
8. James, R. M. A general analytical method for axi-symmetric incompressible potential flow about bodies of revolution. Computer methods in applied mechanics and engineering, 12, 1977, 47–67.Google Scholar
9. Rankine, W. J. M. On the mathematical theory of streamlines, especially those with four foci and upwards. Phil Trans 161, 267, 1871.Google Scholar
10. Fuhrmann, G. Theoretische und experimentelle untersuchungen an ballon modellen. Zeitschrift fur Flugtechnik und Motorluftschiffart. 11, 1911.Google Scholar
11. Karman, T. Von. Calculation of pressure distribution on airship hulls. NACA TM 574, 1930.Google Scholar
12. Laitone, E. V. The subsonic flow about a body of revolution. Quarterly of Applied Mathematics, 5, 2 July 1947, 227–231.Google Scholar
13. Laitone, E. V. The linearised subsonic and supersonic flow about inclined slender bodies of revolution. Journal of the Aeronautical Sciences 14, 11 November 1947, 631–642.Google Scholar
14. Lotz, I. The calculation of the potential flow past airship bodies in yaw. NACA TM 675, 1931.Google Scholar
15. Weinstein, A. On axially symmetric flows. Quarterly of Applied Mathematics, 5, 1948, 379.Google Scholar
16. Tuyl, A. Van. Axially symmetric flow around a new family of half-bodies. Quarterly of Applied Mathematics, 7, 1950, 399.Google Scholar
17. Vandrey, F. A method for calculating the pressure distribution of a body of revolution moving in a circular path through a perfect incompressible fluid. ARC R&M 3139, 1953.Google Scholar
18. Hess, J. L. and Smith, A. M. O. Calculation of potential flow about arbitrary bodies. Progress in Aeronautical Sciences, 8, Pergamon, 1967.Google Scholar
19. AGARD. Drag and other aerodynamic effects of external stores. AGARD, AR 107, 1977.Google Scholar
20. Nielsen Engineering & Research Inc. Prediction of six-degree-of-freedom store separation trajectories at speeds up to the critical speed. AFFDL-TR-72-83, 1&2, 1974.Google Scholar
21. Zedan, M. F. and Dalton, C. Higher-order axial singularity distributions for potential flow about bodies of revolution. Computer Methods in Applied Mechanics & Engineering, 21, 1980, 295–314.Google Scholar
22. Karamcheti, K. Principles of Ideal Fluid Aerodynamics. Wiley, 1966.Google Scholar
23. Jones, D. J. On the representation of axisymmetric bodies by sources along the axis. National Aeronautical Establishment, Ottawa, Canada, LTR-HA-53.Google Scholar
24. Oberkampf, W. L. and Watson, L. E. Incompressible potential flow solutions for arbitrary bodies of revolution. AIAA Journal, 12, March 1974, 409–411.Google Scholar
25. Albone, C. M. Fortran programmes for axisymmetric potential flow about closed and semi-finite bodies. ARC CP 1216, 1972.Google Scholar
26. Landweber, L. The axially symmetric potential flow past elongated bodies of revolution. David W. Taylor Model Basin Report 761, 1951.Google Scholar
27. Jones, R. The distribution of pressures on a prolate spheroid. ARC R&M 1061, 1925.Google Scholar
28. Gradstein, I. S. and Ryshik, I. M. Tables of Series, Products and Integrals. Academic Press, 1965.Google Scholar