Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-18T02:05:37.960Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of the absolutely unstable regions in the near field of low-density jets

Published online by Cambridge University Press:  17 October 2012

Wilfried Coenen  and
Alejandro Sevilla
Wilfried Coenen*
Affiliation:
Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés, Spain
Alejandro Sevilla
Affiliation:
Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, Av. Universidad 30, 28911 Leganés, Spain
*
†Email address for correspondence: wcoenen@ing.uc3m.es
Get access Rights & Permissions [Opens in a new window]

Abstract

The viscous spatiotemporal stability properties of low-density laminar round jets emerging from circular nozzles or tubes are investigated numerically providing, for the first time, a separate treatment of the two particular cases typically studied in experiments: a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture of two gases with different molecular weight, discharging into a stagnant ambient of the heavier species. To that end, use is made of a realistic representation for the base velocity and density profiles based on boundary-layer theory, with account taken of the effect of variable transport properties. Our results show significant quantitative differences with respect to previous parametric studies, and reveal that hot jets are generically more unstable than light jets, in the sense that they have larger associated critical density ratios for values of the Reynolds number and momentum thickness typically used in experiments. In addition, for several values of the jet-to-ambient density ratio, $S$, the downstream evolution of the local stability properties of the jet is computed as a function of the two main control parameters governing the jet, namely the Reynolds number, $\mathit{Re}$, and the momentum thickness of the initial velocity profile, ${\theta }_{0} / D$. It is shown that, for a given value of $S$, the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane can be divided in three regions. In the first region, defined by low values of $\mathit{Re}$ or very thick shear layers, the flow is locally convectively unstable everywhere. In the second region, with moderately large values of $\mathit{Re}$ and thin shear layers, the jet exhibits a localized pocket of absolute instability, away from boundaries. Finally, in the third region, that prevails in most of the $(\mathit{Re}, {\theta }_{0} / D)$ parameter plane, the absolutely unstable domain is bounded by the jet outlet. All the experiments available in the literature are shown to lie in the latter region, and the global transition observed in experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large. The marginal frequency of the resulting global self-excited oscillations is shown to be fairly well described by the absolute frequency evaluated at the jet outlet, in agreement with the numerical results obtained by Lesshafft et al. (J. Fluid Mech., vol. 554, 2006, pp. 393–409) for synthetic jets.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Free shear layers Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 123 - 149
Copyright
©2012 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.Google Scholar
Bolaños-Jiménez, R., Sevilla, A., Gutiérrez-Montes, C., Sanmiguel-Rojas, E. & Martínez-Bazán, C. 2011 Bubbling and jetting regimes in planar coflowing air–water sheets. J. Fluid Mech. 682, 519–542.Google 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 Bifurcation to local and global modes in spatially developing flows. Phys. Rev. Lett. 60, 25–28.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
Coenen, W., Sevilla, A. & Sánchez, A. 2012 Viscous stability analysis of jets with discontinuous base profiles. Eur. J. Mech. (B/Fluids), 36, 128–138.Google Scholar
Couairon, A. & Chomaz, J.-M. 1999 Fully nonlinear global modes in slowly varying flows. Phys. Fluids 11, 3688–3703.Google Scholar
Deissler, R. J. 1987 The convective nature of instability in plane Poiseuille flow. Phys. Fluids 30 (8), 2303–2305.Google Scholar
Hallberg, M. P., Srinivasan, V., Gorse, P. & Strykowski, P. J. 2007 Suppression of global modes in low-density axisymmetric jets using coflow. Phys. Fluids 19 (1), 014102.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
Hirschfelder, J. O., Curtiss, C. F. & Bird, R. B. 1954 Molecular Theory of Gases and Liquids. J. Wiley.Google Scholar
Ho, C.-M. & Huerre, P. 1985 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.Google Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffatt, M. K. & Worster, M. G.), pp. 159–229. Cambridge University Press.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.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.Google 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
Meliga, P., Sipp, D. & Chomaz, J.-M. 2008 Absolute instability in axisymmetric wakes: compressible and density variation effects. J. Fluid Mech. 600, 373–401.Google Scholar
Michalke, A. 1970 A note on the spatial jet-instability of the compressible cylindrical vortex sheet. DLR Research Rep., pp. FB–70–51.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, 611–639.Google Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 28, 911–916.Google Scholar
Nichols, J. R. & Lele, S. K. 2011 Global modes and transient response of a cold supersonic jet. J. Fluid Mech. 669, 225–241.Google Scholar
Nichols, J. W. & Schmid, P. J. 2008 The effect of a lifted flame on the stability of round fuel jets. J. Fluid Mech. 609, 275–284.Google Scholar
Nichols, J. W., Schmid, P. J. & Riley, J. J. 2007 Self-sustained oscillations in variable-density round jets. J. Fluid Mech. 582, 341–376.Google Scholar
Pier, B., Huerre, P., Chomaz, J.-M. & Couairon, A. 1998 Steep nonlinear global modes in spatially developing media. Phys. Fluids 10 (10), 2433–2435.Google Scholar
Raghu, S. & Monkewitz, P. A. 1991 The bifurcation of a hot round jet to limit-cycle oscillations. Phys. Fluids A 3 (4), 501–503.Google Scholar
Raynal, L., Harion, J.-L., Favre-Marinet, M. & Binder, G. 1996 The oscillatory instability of plane variable-density jets. Phys. Fluids 8, 993–1006.Google Scholar
Sánchez-Sanz, M., Rosales, M. & Sánchez, A. L. 2010 The hydrogen laminar jet. Intl J. Hydrogen Energy 35, 3919–3927.Google Scholar
Sánchez-Sanz, M., Sánchez, A. L. & Liñán, A. 2006 Fronts in high-temperature laminar gas jets. J. Fluid Mech. 547, 257–266.Google Scholar
Sevilla, A. 2011 The effect of viscous relaxation on the spatiotemporal stability of capillary jets. J. Fluid Mech. 684, 204–226.Google Scholar
Sevilla, A., Gordillo, J. M. & Martínez-Bazán, C. 2002 The effect of the diameter ratio on the absolute and convective instability of free coflowing jets. Phys. Fluids 14, 3028–3038.Google Scholar
Sevilla, A. & Martínez-Bazán, C. 2004 Vortex shedding in high Reynolds number axisymmetric bluff-body wakes: local linear instability and global bleed control. Phys. Fluids 16, 3460–3469.Google Scholar
Srinivasan, K., Hallberg, M. P. & Strykowski, P. J. 2010 Viscous linear stability of axisymmetric low-density jets: parameters influencing absolute instability. Phys. Fluids 22, 024103.Google Scholar
Sreenivasan, K. R., Raghu, S. & Kyle, D. 1989 Absolute instability in variable density round jets. Exp. Fluids 7, 309–317.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.Google Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin Cummings.Google Scholar
Yu, M.-H. & Monkewitz, P. A. 1993 Oscillations in the near field of a heated two-dimensional jet. J. Fluid Mech. 25, 323–347.Google Scholar