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Optimal velocity and density profiles for the onset of absolute instability in jets

Published online by Cambridge University Press:  27 September 2010

LUTZ LESSHAFFT  and
OLIVIER MARQUET
LUTZ LESSHAFFT*
Affiliation:
Laboratoire d'Hydrodynamique, CNRS – École Polytechnique, 91128 Palaiseau, France
OLIVIER MARQUET
Affiliation:
ONERA DAFE, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: lutz.lesshafft@ladhyx.polytechnique.fr
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Abstract

The absolute/convective character of the linear instability of axisymmetric jets is investigated for a wide range of parallel velocity and density profiles. An adjoint-based sensitivity analysis is carried out in order to maximize the absolute growth rate of jet profiles with and without density variations. It is demonstrated that jets without counterflow may display absolute instability at density ratios well above the previously assumed threshold ρjet/ρ∞ = 0.72, and even in homogeneous settings. Absolute instability is promoted by a strong velocity gradient in the low-velocity region of the shear layer, as well as by a step-like density variation near the location of maximum shear. A new efficient algorithm for the computation of the absolute instability mode is presented.

JFM classification

Instability: Absolute/convective instability Instability: Instability Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 398 - 408
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Bottaro, A., Corbett, P. & Luchini, P. 2003 The effect of base flow variation on flow stability. J. Fluid Mech. 476, 293–302.Google Scholar
Coenen, W., Sevilla, A. & Sánchez, A. 2008 Absolute instability of light jets emerging from circular injector tubes. Phys. Fluids 20, 074104.CrossRefGoogle Scholar
Gallaire, F. & Chomaz, J.-M. 2003 Mode selection in swirling jet experiments: a linear stability analysis. J. Fluid Mech. 494, 223–253.CrossRefGoogle Scholar
Hallberg, M., Srinivasan, V., Gorse, P. & Strykowski, P. 2007 Suppression of global modes in low-density axisymmetric jets using coflow. Phys. Fluids 19, 014102.Google Scholar
Huerre, P. & Monkewitz, P. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.Google Scholar
Hwang, Y. & Choi, H. 2006 Control of absolute instability by basic-flow modification in a parallel wake at low Reynolds number. J. Fluid Mech. 560, 465–475.Google Scholar
Jendoubi, S. & Strykowski, P. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6, 3000–3009.CrossRefGoogle Scholar
Lesshafft, L. & Huerre, P. 2007 Linear impulse response in hot round jets. Phys. Fluids 19, 024102.Google Scholar
Lesshafft, L., Huerre, P. & Sagaut, P. 2007 Frequency selection in globally unstable round jets. Phys. Fluids 19, 054108.Google Scholar
Michalke, A. 1971 Instabilität eines kompressiblen runden Freistrahls unter Berücksichtigung des Einflusses der Strahlgrenzschichtdicke. Z. Flugwiss. 19, 319–328.Google Scholar
Monkewitz, P., Bechert, D., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213, 611–639.Google Scholar
Monkewitz, P. & Sohn, K. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.Google Scholar
Srinivasan, V., Hallberg, M. P. & Strykowski, P. J. 2010 Viscous linear stability of axisymmetric low-density jets: parameters influencing absolute instability. Phys. Fluids 22 (2), 024103.Google Scholar