Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T04:06:27.960Z Has data issue: false hasContentIssue false
  • English
  • Français

The far field of an oscillating airfoil in supersonic flow

Published online by Cambridge University Press:  21 April 2006

A. F. Messiter  and
S. L. Woodruff
A. F. Messiter
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140, USA
S. L. Woodruff
Affiliation:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An approach utilizing multiple scales and matched asymptotic expansions is developed for the description of small perturbations at large distances from a thin airfoil oscillating harmonically in a uniform supersonic flow. The problem of determining the unsteady perturbation potential is formulated in general, and an analytical solution is derived for an airfoil with parabolic or flat surfaces. The results describe the flow ahead of the region influenced by the trailing edge. The variation in the pressure jump across an attached leading-edge shock wave is also obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 175 - 183
Copyright
© 1987 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

Garrick, I. E. & Rubinow, S. I. 1946 Flutter and oscillating air-force calculations for an airfoil in a two-dimensional supersonic flow. NACA Rep. 846.
Kevorkian, J. & Cole, J. D. 1981 Perturbation Methods in Applied Mathematics. Springer.
Kurosaka, M. 1977 Cumulative nonlinear distortion of an acoustic wave propagating through non-uniform flow. J. Fluid Mech. 83, 751–773.Google Scholar
Lighthill, M. J. 1954 Higher Approximations. In General Theory of High-Speed Aerodynamics, pp. 345–489. Princeton University Press.
Luke, J. C. 1966 A perturbation method for nonlinear dispersive wave problems. Proc. R. Soc. Lond. A 292, 403–412.Google Scholar
Van Dyke, M. D. 1954 Supersonic flow past oscillating airfoils including nonlinear thickness effects. NACA Rep. 1183.
Van Dyke, M. D. 1975 Perturbation Methods in Fluid Mechanics. Parabolic Press.