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Self-sustained oscillations in variable-density round jets

Published online by Cambridge University Press:  14 June 2007

JOSEPH W. NICHOLS ,
PETER J. SCHMID  and
JAMES J. RILEY
JOSEPH W. NICHOLS
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
PETER J. SCHMID
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS–École Polytechnique, 91128 Palaiseau, France
JAMES J. RILEY
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
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Abstract

The stability properties of round variable-density low-Mach-number jets are studied by means of direct numerical simulation (DNS) and linear stability analysis. Fully three-dimensional DNS of variable-density jets, with and without gravity, demonstrate that the presence of buoyancy causes a more abrupt transition to turbulence. This effect helps to explain differences between normal gravity and microgravity jet diffusion flames observed in the laboratory.

The complete spectrum of spatial eigenmodes of the linearized low-Mach-number equations is calculated using a global matrix method. Also, an analytic form for the continuous portion of this spectrum is derived, and used to verify the numerical method. The absolute instability of variable-density jets is confirmed using Brigg's method, and a comprehensive parametric study of the strength and frequency of this instability is performed. Effects of Reynolds number, the density ratio of ambient-to-jet fluid (S1), shear-layer thickness and Froude number are considered. Finally, a region of local absolute instability is shown to exist in the near field of the jet by applying linear stability analysis to mean profiles measured from DNS.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 341 - 376
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Ashpis, D. E. & Reshotko, E. 1990 The vibrating ribbon problem revisited. J. Fluid Mech. 213, 531–547.CrossRefGoogle Scholar
Bahadori, M. Y., Stocker, D. P., Vaughan, D. F., Zhou, L. & Edelman, R. B. 1992 Effects of buoyancy on laminar, transitional, and turbulent gas jet diffusion flames. In Second International Workshop on Combustion Science in Microgravity. Cleveland, Ohio.CrossRefGoogle Scholar
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.CrossRefGoogle Scholar
Bird, R. W., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.Google Scholar
Boersma, B. J., Brethouwer, G. & Nieuwstadt, F. T. M. 1998 A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet. Phys. of Fluids 10 (4), 899–909.CrossRefGoogle Scholar
Brancher, P., Chomaz, J. M. & Huerre, P. 1994 Direct numerical simulations of round jets: vortex induction and side jets. Phys. Fluids 6, 1768–1774.CrossRefGoogle Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. MIT Press.CrossRefGoogle Scholar
Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and non-linearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
Chorin, A. J. 1967 A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2, 12–26.Google Scholar
Constantinescu, G. S. & Lele, S. K. 2002 A highly accurate technique for the treatment of flow equations at the polar axis in cylindrical coordinates using series expansions. J. Comput. Phys. 183, 165–186.CrossRefGoogle Scholar
Demare, D. & Baillot, F. 2001 The role of secondary instabilities in the stabilization of a nonpremixed lifted jet flame. Phys. Fluids 13 (9), 2662–2670.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge: University Press.Google Scholar
Durran, D. R. 1999 Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer.CrossRefGoogle Scholar
Hegde, U., Zhou, L. & Bahadori, M. Y. 1994 The transition to turbulence of microgravity gas jet diffusion flames. Combust. Sci. Technol. 102, 95–113.CrossRefGoogle Scholar
Huerre, P. 2000 Open shear flow instabilities. In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 159–229. Cambridge University Press.Google Scholar
Idicheria, C. A., Boxx, I. G. & Clemens, N. T. 2003 Characteristics of turbulent nonpremixed jet flames in different gravity levels. In Third Joint Meeting of the US Sections of the Combustion Institute. Chicago, IL.Google Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jendoubi, S. & Strykowski, P. J. 1994 Absolute and convective instability of axisymmetric jets with external flow. Phys. Fluids 6, 3000–3009.Google Scholar
Kaplan, C. R., Oran, E. S. & Baek, S. W. 1994 Stabilization mechanism of lifted jet diffusion flames. In Twenty-Fifth Symp. (Int. on Combustion, pp. 1183–1189. The Combustion Institute, Pittsburgh.CrossRefGoogle Scholar
Kyle, D. M. & Sreenivasan, K. R. 1993 The instability and breakdown of a round variable-density jet. J. Fluid Mach. 249, 619–664.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Lesshafft, L., Huerre, P., Sagaut, P. & Terracol, M. 2006 Nonlinear global modes in hot jets. J. Fluid Mech. 554, 393–409.Google Scholar
McMurtry, P. A. 1987 Direct numerical simulations of a reacting mixing layer with chemical heat release. PhD thesis, University of Washington.Google Scholar
McMurtry, P. A., Jou, W. H., Riley, J. J. & Metcalfe, R. W. 1986 Direct numerical simulations of mixing layers with heat release. AIAA J. 24, 962.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerospace Sci. 21, 159–199.Google Scholar
Mizobuchi, Y., Tachibana, S., Shinjo, J., Ogawa, S. & Takeno, T. 2002 A numerical analysis of the structure of a turbulent hydrogen jet lifted flame. In Proc. Combustion Institute, pp. 2009–2015, Part 2. The Combustion Institute, Pittsburgh.CrossRefGoogle Scholar
Monkewitz, P. A. & Sohn, K. D. 1988 Absolute instability in hot jets. AIAA J. 26, 911–916.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
Najm, H. N., Wyckoff, P. S. & Knio, O. M. 1998 A semi-implicit numerical scheme for reacting flow. I. Stiff chemistry. J. Comput. Phys. 143, 381–402.CrossRefGoogle Scholar
Nichols, J. W. 2005 Simulation and stability analysis of jet diffusion flames. PhD thesis, University of Washington.Google Scholar
Pierce, C. D. & Moin, P. 2001 Progress-variable approach for large-eddy simulation of turbulent combustion. Tech. Rep. Stanford University.Google Scholar
Poinsot, T. & Veynante, D. 2001 Theoretical and Numerical Combustion. Edwards, Flourtown, PA.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.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
White, F. M. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.Google Scholar