Self-sustained oscillations in variable-density round jets

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.

[1]  Jean-Marc Chomaz,et al.  Direct numerical simulations of round jets: Vortex induction and side jets , 1994 .

[2]  Katepalli R. Sreenivasan,et al.  The instability and breakdown of a round variable-density jet , 1993, Journal of Fluid Mechanics.

[3]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[4]  James J. Riley,et al.  Direct numerical simulations of a reacting mixing layer with chemical heat release , 1985 .

[5]  D. Durran.  Numerical methods for wave equations in geophysical fluid dynamics , 1999 .

[6]  J. Harion,et al.  The oscillatory instability of plane variable-density jets , 1996 .

[7]  R. G. Jacobs,et al.  Simulations of bypass transition , 2001, Journal of Fluid Mechanics.

[8]  D. Demare,et al.  The role of secondary instabilities in the stabilization of a nonpremixed lifted jet flame , 2001 .

[9]  Dietrich W. Bechert,et al.  Self-excited oscillations and mixing in a heated round jet , 1990, Journal of Fluid Mechanics.

[10]  H. K. Moffatt,et al.  Perspectives in Fluid Dynamics , 2002 .

[11]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[12]  E. Reshotko,et al.  The vibrating ribbon problem revisited , 1990, Journal of Fluid Mechanics.

[13]  P. S. Wyckoff,et al.  A Semi-implicit Numerical Scheme for Reacting Flow , 1998 .

[14]  石岡 圭一,et al.  「Numerical Methods for Wave Equations in Geophysical Fluid Dynamics」, Dale R. Durran 著, Springer, 1998年, 465頁, 49.95ドル, ISBN 0-387-98376-7 , 1999 .

[15]  N NajmHabib,et al.  A Semi-implicit Numerical Scheme for Reacting Flow , 1998 .

[16]  T. Takeno,et al.  A numerical analysis of the structure of a turbulent hydrogen jet lifted flame , 2002 .

[17]  M. Bahadori,et al.  Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames , 1993 .

[18]  P. Schmid,et al.  Stability and Transition in Shear Flows. By P. J. SCHMID & D. S. HENNINGSON. Springer, 2001. 556 pp. ISBN 0-387-98985-4. £ 59.50 or $79.95 , 2000, Journal of Fluid Mechanics.

[19]  Pierre Sagaut,et al.  Nonlinear global modes in hot jets , 2006, Journal of Fluid Mechanics.

[20]  M. Bahadori,et al.  The transition to turbulence of microgravity gas jet diffusion flames , 1994 .

[21]  J. Chomaz,et al.  GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS: Non-Normality and Nonlinearity , 2005 .

[22]  P. Monkewitz,et al.  Absolute instability in hot jets , 1988 .

[23]  T. Poinsot,et al.  Theoretical and numerical combustion , 2001 .

[24]  T. Papanastasiou,et al.  Viscous Fluid Flow , 1999 .

[25]  P. Moin,et al.  Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion , 2004, Journal of Fluid Mechanics.

[26]  P. Strykowski,et al.  Absolute and convective instability of axisymmetric jets with external flow , 1994 .

[27]  Sanjiva K. Lele,et al.  A highly accurate technique for the treatment of flow equations at the polar axis in cylindrical coordinates using series expansions , 2002 .

[28]  A. E. Gill,et al.  Analysis of the stability of axisymmetric jets , 1962, Journal of Fluid Mechanics.

[29]  N. Marcuvitz,et al.  Electron-stream interaction with plasmas , 1965 .

[30]  Geert Brethouwer,et al.  A numerical investigation on the effect of the inflow conditions on the self-similar region of a round jet , 1998 .

[31]  E. Oran,et al.  Stabilization mechanism of lifted jet diffusion flames , 1994 .

[32]  C. Pierce,et al.  Progress-variable approach for large-eddy simulation of turbulent combustion , 2001 .

[33]  A. Michalke.  Survey on jet instability theory , 1984 .