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The full impulse response of two-dimensional jet/wake flows and implications for confinement

Published online by Cambridge University Press:  15 October 2007

MATTHEW P. JUNIPER
MATTHEW P. JUNIPER*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK
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Abstract

In this theoretical study, a linear spatio-temporal analysis is performed on unconfined and confined inviscid jet/wake flows in order to determine whether they are absolutely or convectively unstable. The impulse response is evaluated in the entire outer fluid, rather than just at the point of impulse, over a wide range of density ratios. This confirms that the dominant saddle point can validly migrate into the plane of diverging eigenfunctions. This reveals that, at certain density ratios and shear numbers, the response can grow upstream in some directions with a cross-stream component, even though it decays directly upstream of, and at, the point of impulse. This type of flow is convectively unstable when unconfined, but becomes absolutely unstable when confined. Other effects of confinement are described in a previous paper. Together, these articles have important implications for the design of fuel injectors, which often employ confined shear flows at high Reynolds number and large density ratios to generate strong mixing in combustion chambers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 163 - 185
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Barrère, M. & Jaumotte, A. & Fraeijs de Veubeke, B. & Vandenkerckhove, J. 1960 Rocket Propulsion. Elsevier.Google Scholar
Briggs, R. J. 1964 Electron-stream interaction with plasmas. M.I.T. Press.Google Scholar
Chen, J.-H., Pritchard, W. G. & Tavener, S. J. 1995 Bifurcation for flow past a cylinder between parallel planes. J. Fluid Mech. 284, 23–41.CrossRefGoogle Scholar
Delbende, I. & Chomaz, J.-M. 1998 Nonlinear convective/absolute instabilities in parallel two-dimensional wakes. Phys. Fluids 10 (11), 2724–2736.Google Scholar
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Esch, R. E. 1957 The instability of a shear layer between two parallel streams. J. Fluid Mech. 3, 289–303.Google Scholar
Garcia-Villalba, M., Fröhlich, J. & Rodi, W. 2006 Numerical simulations of isothermal flow in a swirl burner. ASME Turbo Expo GT2006-90764.Google Scholar
Healey, J. J. 2006 A new convective instability of the rotating-disk boundary layer with growth normal to the plate. J. Fluid Mech. 560, 279–310.Google Scholar
Healey, J. J. 2007 Enhancing the absolute instability of a boundary layer by adding a far-away plate. J. Fluid Mech. 579, 29–61.Google Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffat, H. K. & Worster, M. G.). Cambridge University Press.Google Scholar
Juniper, M. P. 2006 The effect of confinement on the stability of two-dimensional shear flows. J. Fluid Mech. 565, 171–195.CrossRefGoogle Scholar
Juniper, M. P. & Candel, S. M. 2003 The stability of ducted compound flows and consequences for the geometry of coaxial injectors. J. Fluid Mech. 482, 257–269.CrossRefGoogle Scholar
Shair, F. H. & Grove, A. S. & Petersen, E. E. & Acrivos, A. 1963 The effect of confining walls on the stability of the steady wake behind a circular cylinder. J. Fluid Mech. 17, 546–550.Google Scholar
Yu, M.-H. & Monkewitz, P. A. 1990 The effect of nonuniform density on the absolute instability of two-dimensional inertial jets and wakes. Phys. Fluids A 2 (7), 1175–1181.CrossRefGoogle Scholar