Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-08T01:26:37.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform second-order solution for supersonic flow over delta wing using reverse-flow integral method

Published online by Cambridge University Press:  28 March 2006

Joseph H. Clarke  and
James Wallace
Joseph H. Clarke
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
James Wallace
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem of supersonic flow over an inclined flat-plate delta wing with supersonic edges is solved to second order in incidence. This solution for surface pressure is uniform and fully analytic. The approach utilizes a reverse-flow integral method previously developed for second-order problems. This method is augmented by a number of techniques appropriate to its framework. The simplification over standard techniques achieved by using these reverse-flow methods is quite substantial and makes the problem tractable.

Reverse-flow procedures give a volume-surface integral relation that connects the second-order forward flow over the body of interest with the linearized reverse-flow over a related body. A singular integral equation is generated from the integral relation by introducing the edge sweep of the reverse-flow wing as a free parameter. An inversion is available which gives the second-order solution on the surface of the wing. The solution is then made uniformly valid using techniques previously developed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 225 - 238
Copyright
© 1964 Cambridge University Press

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

Clarke, J. H. 1959 Reverse flow and supersonic interference. J. Fluid Mech. 6, 272.Google Scholar
Clarke, J. H. 1962 A supersonic-hypersonic small-disturbance theory. Brown Univ., Div. of Engrg, Rep. no. CM-1007.Google Scholar
Clarke, J. H. 1963 Reverse-flow integral methods for second-order supersonic flow theory. Brown Univ. Div. of Engrg, Rep. no. CM-1033; also J. Fluid Mech. 18, 177.Google Scholar
Fowell, L. R. 1956 Exact and approximate solutions for the supersonic delta wing. J. Aero. Sci. 23, 709.Google Scholar
Lagerstrom, P.A. 1950 Linearized supersonic theory of conical wings. NACA TN no. 1685.Google Scholar
Lighthill, M. J. 1949 The shock strength in supersonic ‘conical fields’. Phil. Mag. 17, 1202.Google Scholar
Lighthill, M. J. 1954 High Speed Aerodynamics and Jet Propulsion, Vol. VI, sec. E, p. 345. Princeton University Press.
Moore, F. K. 1950 Second approximation to supersonic conical flows. J. Aero. Sci. 17, 328.Google Scholar
Reyn, J. W. 1960 Differential-geometric considerations on the hodograph transformation for irrotational conical flow. Arch. Rat. Mech. Anal. 6, 299.Google Scholar
Tricomi, F. G. 1957 Integral Equations. New York: Interscience.
Van Dyke, M. D. 1952 A study of second-order supersonic flow theory. NACA Rep. no. 1081.Google Scholar
Wallace, J. & Clarke, J. H. 1963 Uniformly valid second-order solution for supersonic flow over cruciform surfaces. AIAA J. 1, 179.Google Scholar
Ward, G. N. 1955 Linearized Theory of Steady High-Speed Flow. Cambridge University Press.
Widder, D. V. 1940 The Laplace Transform. Princeton University Press.