Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T04:58:12.719Z Has data issue: false hasContentIssue false
  • English
  • Français

An expression for the dynamic stability of blunt slender elliptic bodies in hypersonic flow

Published online by Cambridge University Press:  27 January 2016

M. Khalid  and
K. A. Juhany
M. Khalid*
Affiliation:
King Abdul Aziz University, Jeddah, Saudi Arabia
K. A. Juhany
Affiliation:
King Abdul Aziz University, Jeddah, Saudi Arabia
*
mkholid@kau.edu.sa
Get access Rights & Permissions [Opens in a new window]

Abstract

Dynamic stability data on axially symmetric pointed and blunt cones, parabolic profiles and other ogive and blunt cylindrical shapes is readily available in literature; the dynamic stability on elliptic blunt paraboloids has not been studied at any great lengths in the past. Both numerical and experimental results are scarce. The present paper uses the shock expansion method to obtain the unsteady pressure distribution on blunt elliptic conical bodies at small angles-of-attack. The resulting unsteady pressure distribution is suitably integrated over the surface of the elliptic body to obtain appropriate analytic expressions for static and dynamic stability. Owing to scarcity of meaningful numerical or measured data for elliptic bodies, the results are compared in qualitative terms against published dynamic stability data on pointed elliptical cones or other axisymmetric blunt cones.

Type
Research Article
Information
The Aeronautical Journal , Volume 118 , Issue 1207 , September 2014 , pp. 1079 - 1089
Copyright
Copyright © Royal Aeronautical Society 2014 

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. Hui, W.H. Stability of oscillating wedges and caret wings in hypersonic and supersonic flows, AIAA J, 1969, 7, 1524–1530.Google Scholar
2. Hui, W.H. Interaction of a strong shock with Mach waves in unsteady flow, AIAA J, 1969, 7, 1605–1607.Google Scholar
3. Hui, W.H. Large-amplitude slow-oscillation of wedges in inviscid hypersonic and supersonic flows, AIAA J, 1970, 8, 1530–1532.Google Scholar
4. Hemdan, H. Similarity solutions for oscillating pointed-nosed slender axisymmetric bodies – Part II: Curved bodies, Acta Astonautica, 2001, 49, No. 11, pp. 611–626.Google Scholar
5. Hobbs, R.B. Results of experimental studies on the hypersonic dynamic stability characteristics of a 10° cone at M - 20, May 1964, General Electric ATDM 1:37.Google Scholar
6. Welsh, C.J., Winchenbach, G.L. and Madagan, A.N. Free-fight investigation of the aerodynamic characteristics of a cone at high Mach numbers, AIAA J, 1970, 8, No. 2., pp. 294–300.Google Scholar
7. Brong, E.A. The flow field about a right circular cone in unsteady fight, 1965, AIAA Paper 65-398, San Francisco, CA, USA.Google Scholar
8. Rie, H., Linkiewicz, B.A. and Bosworth, F.D. Hypersonic Dynamic Stability, Part III, Unsteady Flow Field Program, Jan 1967, FDL-TDR-64-149, Air Force Flight Dynamics Lab., Wright-Patterson Air Force Base.Google Scholar
9. Van Dyke, M.D. A study of hypersonic small disturbance theory, 1954, NACA Report 1194.Google Scholar
10. Busemann, A. Flussigkeits –und Gasbewegund, handworterbuch der Naturwissenschaften, Zweite Aufage (Gustav Fischer, Jena), 1933, pp 257–277.Google Scholar
11. Probstein, R.F. and Bray, K.N.C.A. Hypersonic similarity and the tangent cone approximation for the un yawed bodies of revolution, J Aeronaut Sci, Jan 1958, 22, no. 1, pp 66–68.Google Scholar
12. Lighthill, M. Oscillating airfoils at high Mach number, J Aeronaut Sci, 1953, 20, No. 6,, pp. 402–406.Google Scholar
13. Ashley, H. and Zartarian, G. Piston theory - A new aerodynamic tool for the aeroelastician, J Aeronaut Sci, 1956, pp 1109–1118.Google Scholar
14. Khalid, M. and East, R.A. Stability derivatives of blunt cones at high Mach Numbers, Aeronautical Q, Nov 1979, 30, pp-559–590.Google Scholar
15. Taylor, G.I. The formulation of a blast wave by a very intense explosion, Proc Roy Soc (a), 1952, 201, 159–186.Google Scholar
16. Chernyi, G.G. Introduction to Hypersonic Flow, (translated from Russian by Probstein, R.F.), 1961.Google Scholar
17. Khalid, M. and East, R.A. High Mach number dynamic stability of pointed cones at angles of attack, AAIA J, October 1980, 18.Google Scholar
18 Khalid, M. Stability derivatives of blunt cones at high Mach numbers, Aeronaut J, 1992, 30, pp 559–570.Google Scholar
19. Khalid, M. Viscous contribution to the high Mach number damping in pitch of blunt slender cones at small angles of attack, Aeronaut J, February 1995, pp 69–74.Google Scholar
20. Ramussen, M.L. and Lee, H.M. Approximation for hypersonic flow past slender elliptic cone, 1979, AIAA Paper 79-0364, 17th AIAA Aerospace Meeting, New Orleans, January 1979.Google Scholar
21. Ericsson, L.E. Technical evaluation report on the Fluid Dynamics Panel Symposium on Dynamic Stability Parameters, 1979, AGARD AR-137.Google Scholar
22. Hayes, W.D. and Probstein, R.F. Hypersonic Flow Theory, 1955, Academic Press, New York, USA.Google Scholar
23. Bertram, M.H. Boundary-layer displacement effects in air at Mach numbers of 0.8 and 9.6, 1957, NACA Technical Note no. 4133 ()Google Scholar
24. Kendall, J.M. An experimental investigation of leading edge shock wave – boundary layer interaction at Mach 5.8, J Aeronaut Sci, 1957, 24, pp 47–56.Google Scholar
25. Lees, L. Hypersoic Flow, June 1955, IAS Reprint No. 554.Google Scholar
26. Kussoy, M. Local pressure distribution on a blunt delta wing for angles of attack up to 35° at Mach Numbers 3.4 to 7, NASA Technical Note D-1554.Google Scholar
27. Eggers, A.J. On the calculation of flow about objects travelling at high supersonic speeds, 1952, NACA TN 2811.Google Scholar
28. Zartarian, G., Hsu, P.T. and Ashley, H. Dynamic air loads and aero elastic problems at reentry Mach numbers, J Aeronaut Sci, March 1961, 28, (3).Google Scholar
29. Ericsson, L.E., α effects are negligible in hypersonic flow - fact or fiction, 1968, 19th International Congress of the Aeronautical Federation, New York, USA.Google Scholar
30. Devan, L. Non-axisymmetric body supersonic inviscid dynamic derivative prediction, 1989, NSWC TR 89-99, Naval Surface Warfare Centre.Google Scholar