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Unstable jet–edge interaction. Part 1. Instantaneous pressure fields at a single frequency

Published online by Cambridge University Press:  21 April 2006

Ruhi Kaykayoglu  and
Donald Rockwell
Ruhi Kaykayoglu
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
Donald Rockwell
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

Despite its central importance, the pressure field at a leading edge has remained uncharacterized for the classical jet-edge interaction at a single predominant frequency. This investigation shows that the force, due to the integrated instantaneous pressure field on the edge, is located a distance downstream of the tip of the edge as much as one-quarter of a wavelength (λ) of the incident instability; this distance also corresponds to about one-quarter of the geometric length (L) between the nozzle and tip of the edge. Consequently, the traditional assumption that the phase-locking criterion for self-sustained oscillations can be expressed as a ratio of L/λ is inappropriate for low-speed jet flows, which have been of primary interest over the past two decades.

The edge pressure field is made up of two regions bounded by the maximum amplitude at the onset of separation from the surface of the edge: a near-tip region (0 ≤ x/λ [lsim ] 0.1) where the amplitude drops to a minimum as the tip is approached; and a downstream region (x/λ [gsim ] 0.1) where the amplitude varies as x−a. Since the drop in pressure in the near-tip region does not occur over a streamwise length commensurate with the length of the edge, imposition of a Kutta condition is inappropriate in simulations of the edge region. Moreover, in the near-tip region (0 [lsim ] x/λ [lsim ] 0.2), the pressure field is non-propagating; a wave-type representation is appropriate only downstream of this region.

At the tip of the edge, occurrence of the pressure minimum is due to the minimum in fluctuating angle of attack a of the approaching shear layer, deducible from the velocity eigenfunctions of linear theory; correspondingly, flow separation occurs downstream of, not at, the tip of the edge. When the tip is displaced off centreline, there is a rise in a, giving a rise in tip pressure amplitude; nevertheless, the overall x−a amplitude distribution persists.

This overall x−a (a ∼ ½) variation of the pressure amplitude commences downstream of the tip of the edge near the onset of flow separation, which leads to secondary-vortex formation; in turn, it is driven by development of the primary vortex in the unstable jet shear layer, having initially distributed vorticity. The role of this flow separation and subsequent secondary-vortex formation is, therefore, not to relieve a singularity at the tip of the edge; it is simply a consequence of growth of the primary vortex along the edge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 169 , August 1986 , pp. 125 - 149
Copyright
© 1986 Cambridge University Press

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References

Brown, G. B. 1937 Vortex motion causing edge tones. Proc. Phys. Soc. 49, 493–507.Google Scholar
Cerra, A. & Smith, C. 1983 Experimental observations of vortex ring interaction with the fluid adjacent to a surface. Rep. SM-4, Lehigh University, AFOSR TR-84-0130, ADA 138999.
Crighton, D. G. 1981 Acoustics as a branch of fluid mechanics. J. Fluid Mech. 106, 261–298.Google Scholar
Crighton, D. G. 1985 The Kutta condition in unsteady flow. Ann. Rev. Fluid Mech. 17, 411–445.Google Scholar
Didden, N. & Ho, C.-M. 1985 Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235–256.Google Scholar
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1980 A production mechanism for turbulent boundary-layers. In. Viscous Drag Reduction (ed. G. Gettough); Prog. Astro. Aero. 72, 47–72.
Doligalski, T. L. & Walker, J. D. A. 1984 The boundary layer induced by a convected two-dimensional vortex. J. Fluid Mech. 139, 1–28.Google Scholar
Goldstein, M. E. 1978 Characteristics of the unsteady motion on transversely sheared mean flows. J. Fluid Mech. 84, 305–329.Google Scholar
Goldstein, M. E. 1979 Scattering and distortion of the unsteady motion on transversely sheared mean flows. J. Fluid Mech. 91, 601–632.Google Scholar
Goldstein, M. E. 1981 The coupling between flow instabilities and incident disturbances at a leading edge. J. Fluid Mech. 104, 217–246.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flow field produced by trailing vortices in the vicinity of the ground. AIAA J. 9, 1659–1660.Google Scholar
Homa, J. & Rockwell, D. 1983 Vortex-body interaction. Bull. Am. Phys. Soc. 28, 1365.Google Scholar
Horne, C. & Karamcheti, K. 1979 Experimental observations of a two-dimensional planar wall jet. AIAA Paper 79–0208.
Howe, M. S. 1981 The role of displacement thickness fluctuations in hydroacoustics, and the jet-drive mechanism in the flue organ-pipe. Proc. R. Soc. Lond. A 374, 543–568.Google Scholar
Karamcheti, K., Bauer, A. B., Shields, W. L., Stegen, G. R. & Wooley, J. P. 1969 Some features of an edge-tone flow field. In Basic Aerodynamic Noise Research, NASA SP 207; conference held at NASA Headquarters, Washington, D.C., July 14–15, pp. 275–304.
Kaykayoglu, R. 1984 Interactions of unstable shear layers with leading edges and associated pressure fields. Ph.D. dissertation, Department of Mechanical Engineering and Mechanics, Lehigh University.
Kaykayoglu, R. & Rockwell, D. 1985 Vortices incident upon a leading edge: instantaneous pressure fields. J. Fluid Mech. 156, 439–461.Google Scholar
Kaykayoglu, R. & Rockwell, D. 1986 Unstable jet-edge interaction. Part 2: Multiple frequency pressure fields. J. Fluid Mech. 169, 151–172.Google Scholar
Lucas, M. & Rockwell, D. 1984 Self-excited jet: upstream modulation and multiple frequencies. J. Fluid Mech. 147, 333–352.Google Scholar
Magarvey, R. H. & McLatchy, C. S. 1964 The disintegration of vortex rings. Can. J. Phys. 42, 684–689.Google Scholar
Powell, A. 1953 On edge tones and associated phenomena. Acustica 3, 233–242.Google Scholar
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33, 395.Google Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21, 645–664.Google Scholar
Rockwell, D. & Naudascher, E. 1979 Self-sustaining oscillations of impinging free shear layers. Ann. Rev. Fluid Mech. 11, 67–94.Google Scholar
Schneider, P. E. M. 1978 Morphologisch-phänomenologische Untersuchung der Umbildung von Ringwirbeln, die Körper anströmen. Max-Planck-Institut für Strömungsforschung Bericht Nr. 14/1978, Göttingen.
Walker, J. D. A. 1978 The boundary layer due to rectilinear vortex. Proc. R. Soc. Lond. A 359, 167–188.Google Scholar