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Global instability of low-density jets

Published online by Cambridge University Press:  05 May 2017

W. Coenen Open the ORCID record for W. Coenen [Opens in a new window] ,
L. Lesshafft Open the ORCID record for L. Lesshafft [Opens in a new window] ,
X. Garnaud  and
A. Sevilla Open the ORCID record for A. Sevilla [Opens in a new window]
W. Coenen*
Affiliation:
Grupo de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés (Madrid), Spain Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0411, USA
L. Lesshafft
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), École polytechnique – CNRS, 91128 Palaiseau, France
X. Garnaud
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), École polytechnique – CNRS, 91128 Palaiseau, France
A. Sevilla
Affiliation:
Grupo de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés (Madrid), Spain
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Instability: Instability Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , pp. 187 - 207
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Copyright
© 2017 Cambridge University Press 

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Footnotes

‡

Present address: Safran Tech, Rue des Jeunes Bois, 78772, Magny-Les-Hameaux, France.

References

Åkervik, E., Ehrenstein, U., Gallaire, F. & Henningson, D. S. 2008 Global two-dimensional stability measures of the flat plate boundary-layer flow. Eur. J. Mech. (B/Fluids) 27 (5), 501–513.CrossRefGoogle Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
Chomaz, J.-M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 25–28.Google Scholar
Coenen, W. & Sevilla, A. 2012 The structure of the absolutely unstable regions in the near field of low-density jets. J. Fluid Mech. 713, 123–149.Google Scholar
Coenen, W., Sevilla, A. & Sánchez, A. 2008 Absolute instability of light jets emerging from circular injector tubes. Phys. Fluids 20, 074104.Google Scholar
Couairon, A. & Chomaz, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11, 3688–3703.Google Scholar
Ehrenstein, U. & Gallaire, F. 2005 On two-dimensional temporal modes in spatially evolving open flows: the flat-plate boundary layer. J. Fluid Mech. 536, 209–218.CrossRefGoogle Scholar
Ehrenstein, U. & Gallaire, F. 2008 Two-dimensional global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 614, 315–327.Google Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013a Modal and transient dynamics of jet flows. Phys. Fluids 25, 044103.CrossRefGoogle Scholar
Garnaud, X., Lesshafft, L., Schmid, P. J. & Huerre, P. 2013b The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Hallberg, M. P. & Strykowski, P. J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493–507.Google Scholar
Heaton, C. J., Nichols, J. W. & Schmid, P. J. 2009 Global linear stability of the non-parallel batchelor vortex. J. Fluid Mech. 629, 139–160.Google Scholar
Hecht, F. 2012 New development in freefem + +. J. Numer. Math. 20 (3–4), 251–265.Google Scholar
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. Wiley.Google Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics (ed. Batchelor, G., Moffatt, K. & Worster, G.), pp. 159–229. Cambridge University Press.Google Scholar
Jendoubi, S. & Strykowski, P. J. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6, 3000–3009.Google Scholar
Kyle, D. M. & Sreenivasan, K. R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mech. 249, 619–664.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 (5), 054108.Google Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.Google Scholar
Lesshafft, L. & Marquet, O. 2010 Optimal velocity and density profiles for the onset of absolute instability in jets. J. Fluid Mech. 662, 398–408.Google Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.Google Scholar
Monkewitz, P. A., Bechert, D. W., Barsikow, B. & Lehmann, B. 1990 Self-excited oscillations and mixing in a heated round jet. J. Fluid Mech. 213 (-1), 611.CrossRefGoogle Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 28, 911–916.Google Scholar
Moreno-Boza, D., Coenen, W., Sevilla, A., Sanchez, A. L. & Liñán, A. 2016 Diffusion-flame flickering as a hydrodynamic global mode. J. Fluid Mech. 798, 997–1014.Google Scholar
Nichols, J. W. & Lele, S. K.2010 Global mode analysis of turbulent high-speed jets. Annual Research Briefs 2010. Center for Turbulence Research. Stanford University.Google Scholar
Nichols, J. W. & Lele, S. K. 2011a Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.CrossRefGoogle Scholar
Nichols, J. W. & Lele, S. K. 2011b Non-normal global modes of high-speed jets. Int. J. Spray Combust 3 (4), 285–302.Google Scholar
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 609, 275–284.Google Scholar
Qadri, U. A.2014 Global stability and control of swirling jets and flames. PhD thesis, University of Cambridge.Google Scholar
Qadri, U. A., Chandler, G. J. & Juniper, M. P. 2015 Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control. J. Fluid Mech. 775, 201–222.CrossRefGoogle Scholar
Tammisola, O. 2012 Oscillatory sensitivity patterns for global modes in wakes. J. Fluid Mech. 701, 251–277.CrossRefGoogle Scholar
Trefethen, L. N. & Embree, M. 2005 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.Google Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.Google Scholar