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The far field of an oscillating airfoil in supersonic flow

  • A. F. Messiter (a1) and S. L. Woodruff (a1)


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.



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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, 751773.
Lighthill, M. J. 1954 Higher Approximations. In General Theory of High-Speed Aerodynamics, pp. 345489. Princeton University Press.
Luke, J. C. 1966 A perturbation method for nonlinear dispersive wave problems. Proc. R. Soc. Lond. A 292, 403412.
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.
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