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Global instability of low-density jets

  • W. Coenen (a1) (a2), L. Lesshafft (a3), X. Garnaud (a3) and A. Sevilla (a1)
Abstract

The global stability of laminar axisymmetric low-density jets is investigated in the low Mach number approximation. The linear modal dynamics is found to be characterised by two features: a stable arc branch of eigenmodes and an isolated eigenmode. Both features are studied in detail, revealing that, whereas the former is highly sensitive to numerical domain size and its existence can be linked to spurious feedback from the outflow boundary, the latter is the physical eigenmode that is responsible for the appearance of self-sustained oscillations in low-density jets observed in experiments at low Mach numbers. In contrast to previous local spatio-temporal stability analyses, the present global analysis permits, for the first time, the determination of the critical conditions for the onset of global instability, as well the frequency of the associated oscillations, without additional hypotheses, yielding predictions in fair agreement with previous experimental observations. It is shown that under the conditions of those experiments, viscosity variation with composition, as well as buoyancy, only have a small effect on the onset of instability.

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Email address for correspondence: wicoenen@ucsd.edu
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Present address: Safran Tech, Rue des Jeunes Bois, 78772, Magny-Les-Hameaux, France.

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E. Åkervik , U. Ehrenstein , F. Gallaire  & D. S. Henningson 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. (B/Fluids) 27 (5), 501513.

J.-M. Chomaz 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.

J.-M. Chomaz , P. Huerre  & L. G. Redekopp 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 2528.

W. Coenen  & A. Sevilla 2012 The structure of the absolutely unstable regions in the near field of low-density jets. J. Fluid Mech. 713, 123149.

W. Coenen , A. Sevilla  & A. Sánchez 2008 Absolute instability of light jets emerging from circular injector tubes. Phys. Fluids 20, 074104.

A. Couairon  & J.-M. Chomaz 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11, 36883703.

U. Ehrenstein  & F. Gallaire 2005 On two-dimensional temporal modes in spatially evolving open flows: the flat-plate boundary layer. J. Fluid Mech. 536, 209218.

U. Ehrenstein  & F. Gallaire 2008 Two-dimensional global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 614, 315327.

X. Garnaud , L. Lesshafft , P. J. Schmid  & P. Huerre 2013a Modal and transient dynamics of jet flows. Phys. Fluids 25, 044103.

X. Garnaud , L. Lesshafft , P. J. Schmid  & P. Huerre 2013b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189202.

F. Giannetti  & P. Luchini 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167197.

M. P. Hallberg  & P. J. Strykowski 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493507.

C. J. Heaton , J. W. Nichols  & P. J. Schmid 2009 Global linear stability of the non-parallel batchelor vortex. J. Fluid Mech. 629, 139160.

F. Hecht 2012 New development in freefem + +. J. Numer. Math. 20 (3–4), 251265.

S. Jendoubi  & P. J. Strykowski 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6, 30003009.

D. M. Kyle  & K. R. Sreenivasan 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619664.

L. Lesshafft  & P. Huerre 2007 Linear impulse response in hot round jets. Phys. Fluids 19, 024102.

L. Lesshafft , P. Huerre  & P. Sagaut 2007 Frequency selection in globally unstable round jets. Phys. Fluids 19 (5), 054108.

L. Lesshafft , P. Huerre , P. Sagaut  & M. Terracol 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393409.

L. Lesshafft  & O. Marquet 2010 Optimal velocity and density profiles for the onset of absolute instability in jets. J. Fluid Mech. 662, 398408.

O. Marquet , D. Sipp  & L. Jacquin 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221252.

P. A. Monkewitz , D. W. Bechert , B. Barsikow  & B. Lehmann 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213 (-1), 611.

D. Moreno-Boza , W. Coenen , A. Sevilla , A. L. Sanchez  & A. Liñán 2016 Diffusion-flame flickering as a hydrodynamic global mode. J. Fluid Mech. 798, 9971014.

J. W. Nichols  & S. K. Lele 2011a Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225241.

J. W. Nichols  & S. K. Lele 2011b Non-normal global modes of high-speed jets. Int. J. Spray Combust 3 (4), 285302.

U. A. Qadri , G. J. Chandler  & M. P. Juniper 2015 Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control. J. Fluid Mech. 775, 201222.

O. Tammisola 2012 Oscillatory sensitivity patterns for global modes in wakes. J. Fluid Mech. 701, 251277.

F. A. Williams 1985 Combustion Theory, 2nd edn. Benjamin Cummings.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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