Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T15:51:50.325Z Has data issue: false hasContentIssue false

The Caret Wing at Certain Off-Design Conditions

Published online by Cambridge University Press:  07 June 2016

W H Hui*
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton
Get access

Summary

A unified theory is given of hypersonic and supersonic flow over the lower surface of a caret wing at certain off-design conditions when the bow shock is attached to the leading edges of the wing and when there exists no internal shock. The flow field on the lower surface of a caret wing consists of uniform flow regions near the leading edges, where the cross-flow is supersonic, and a non-uniform flow in the central region, where the cross-flow is subsonic. The basic assumption is that the flow in the central region differs slightly from the two-dimensional supersonic flow over a flat plate at the same angle of incidence as that of the lower ridge of the wing. Based on this assumption, a first-order perturbation flow is first calculated and then strained and corrected so that it matches the uniform flow which is obtained exactly. Slope discontinuities of the pressure curve are found at the cross-flow sonic line. Numerical examples and comparisons with previous theories and experiments are included.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1972

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. Messiter, A F Lift of slender delta wings according to Newtonian theory. AIAA Journal, Vol 1, p 794, 1963.CrossRefGoogle Scholar
2. Squire, L C Calculated pressure distributions and shock shapes on thick conical wings at high supersonic speeds. Aeronautical Quarterly, Vol XVIII, p 185, 1967.CrossRefGoogle Scholar
3. Squire, L C Calculated pressure distributions and shock shapes on conical wings with attached shock waves. Aeronautical Quarterly, Vol XIX, p 31, 1968.CrossRefGoogle Scholar
4. Woods, B A Hypersonic flow with attached shock waves over delta wings. Aeronautical Quarterly, Vol XXI, p 379, 1970.CrossRefGoogle Scholar
5. Hui, W H Supersonic and hypersonic flow with attached shock waves over delta wings. Proc Roy Soc, Series A, Vol 325, part number 1561, p 251, 1971.Google Scholar
6. Nonweiler, T R F Delta wings of shapes amenable to exact shock wave theory. Journal of the Royal Aeronautical Society, Vol 67, p 625, 1963.CrossRefGoogle Scholar
7. Townend, L H Some design aspects of space shuttle orbiters. RAE Technical Report 70139, 1970.Google Scholar
8. Venn, J Flower, J W Shock patterns for simple caret wings. Journal of the Royal Aeronautical Society, Vol 74, p 339, 1970.CrossRefGoogle Scholar
9. Squire, L C Pressure distributions and flow patterns at M = 4.0 on some delta wings. ARC R&M 3373, 1964.Google Scholar
10. Squire, L C Experimental results for waveriders in certain off-design conditions. Aeronautical Quarterly, Vol XXII, p 225, 1971.CrossRefGoogle Scholar
11. Pike, J The pressure on flat and anhedral delta wings with attached shock waves. Aeronautical Quarterly, Vol XXIII, p 253, November 1972 (this issue).CrossRefGoogle Scholar
12. Lighthill, M J The diffraction of blast. Part II. Proc Roy Soc, Series A, Vol 200, p 554, 1950.Google Scholar
13. Glauert, H The Elements of Aerofoil and Airscrew Theory. Cambridge University Press, 1947.Google Scholar
14. Lighthill, M J A technique for rendering approximate solutions to physical problems uniformly valid. Philosophical Magazine, Vol 40, p 1179, 1949.Google Scholar
15. Van Dyke, M D Perturbation Methods in Fluid Mechanics. Academic Press, New York, p 99, 1964.Google Scholar
16. Clarke, J H Wallace, J Uniform second-order solution for supersonic flow over delta wings using the reverse-flow integral method. Division of Engineering Report CM-1034, Brown University, Rhode Island, 1963.Google Scholar
17. Roe, P L Private communication.Google Scholar
18. Kipke, K Experimental investigations of waveriders in the Mach number range from 8 to 15. Paper 13 in AGARD Conference Proceedings 30, 1968.Google Scholar