Shear flow instabilities in swirl-stabilized combustors and their impact on the amplitude dependent flame response: a linear stability analysis

Abstract The hydrodynamic instabilities in the flow field of a swirl-stabilized combustor are investigated theoretically. These instabilities give rise to large-scale flow structures that interact with the flame front causing unsteady heat release rate fluctuations. The streamwise growth of these coherent structures depends on the receptivity of the shear layer, which can be predicted numerically by means of linear stability analysis. This analysis is applied to the reacting flow field of a perfectly premixed swirl-stabilized combustor that is subjected to strong axial forcing mimicking thermoacoustic oscillations. The linear stability analysis reveals a clear correlation between the shear layer receptivity and the measured amplitude dependent flame transfer function. The stability analysis based on the natural flow predicts the distinctive frequency dependent flame response to low amplitude forcing. At these conditions, the flow reveals strong spatial amplification near the nozzle, causing the inlet perturbations to be significantly amplified before they reach the flame. At higher forcing amplitudes, the flow instabilities saturate, which manifests in a saturation of the flame response. The saturation of the shear layers predicted from the linear stability analysis is compared to phase-locked measurements of the forced flow field revealing good qualitative agreement. The analysis of the mean flow stability offers a powerful analytical tool to investigate the impact of shear flow instabilities on the flame describing function.

[1]  Robert L. Ash,et al.  Application of spectral collocation techniques to the stability of swirling flows , 1989 .

[2]  L. Lourenço.  Particle Image Velocimetry , 1989 .

[3]  Chih-Ming Ho,et al.  Perturbed Free Shear Layers , 1984 .

[4]  T. Lieuwen,et al.  Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances , 2008 .

[5]  Jinhee Jeong,et al.  On the identification of a vortex , 1995, Journal of Fluid Mechanics.

[6]  S. Candel,et al.  Acoustically perturbed turbulent premixed swirling flames , 2011 .

[7]  P. Monkewitz,et al.  LOCAL AND GLOBAL INSTABILITIES IN SPATIALLY DEVELOPING FLOWS , 1990 .

[8]  W. Meier,et al.  Phase-resolved characterization of vortex–flame interaction in a turbulent swirl flame , 2011 .

[9]  Tim Lieuwen,et al.  Density ratio effects on reacting bluff-body flow field characteristics , 2012, Journal of Fluid Mechanics.

[10]  R. Mankbadi,et al.  A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet , 1981, Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences.

[11]  V. Theofilis.  Global Linear Instability , 2011 .

[12]  François Gallaire,et al.  Spiral vortex breakdown as a global mode , 2006, Journal of Fluid Mechanics.

[13]  S. Candel,et al.  Modeling tools for the prediction of premixed flame transfer functions , 2002 .

[14]  S. Candel,et al.  Vortex-driven acoustically coupled combustion instabilities , 1987, Journal of Fluid Mechanics.

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

[16]  C. O. Paschereit,et al.  Why Nonuniform Density Suppresses the Precessing Vortex Core , 2013 .

[17]  D. G. Crighton,et al.  Stability of slowly diverging jet flow , 1976, Journal of Fluid Mechanics.

[18]  S. Candel,et al.  Experimental analysis of nonlinear flame transfer functions for different flame geometries , 2009 .

[19]  Felix Güthe,et al.  Phase-locking in post-processing for pulsating flames , 2007 .

[20]  Sébastien Candel,et al.  Combustion dynamics and control: Progress and challenges , 2002 .

[21]  S. Candel,et al.  Combustion dynamics of inverted conical flames , 2005 .

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

[23]  Benoît Pier,et al.  On the frequency selection of finite-amplitude vortex shedding in the cylinder wake , 2002, Journal of Fluid Mechanics.

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

[25]  A. Dowling.  Nonlinear self-excited oscillations of a ducted flame , 1997, Journal of Fluid Mechanics.

[26]  Israel J Wygnanski,et al.  The evolution of instabilities in the axisymmetric jet. I - The linear growth of disturbances near the nozzle. II - The flow resulting from the interaction between two waves , 1987 .

[27]  A. Hussain,et al.  The mechanics of an organized wave in turbulent shear flow , 1970, Journal of Fluid Mechanics.

[28]  Eliezer Kit,et al.  Large-scale structures in a forced turbulent mixing layer , 1985, Journal of Fluid Mechanics.

[29]  Jean-François Bourgouin,et al.  Nonlinear interaction between a precessing vortex core and acoustic oscillations in a turbulent swirling flame , 2012 .

[30]  L. Rayleigh,et al.  The theory of sound , 1894 .

[31]  Tim Lieuwen,et al.  Characterization of acoustically forced swirl flame dynamics , 2009 .

[32]  Jürgen Kompenhans,et al.  Particle Image Velocimetry - A Practical Guide (2nd Edition) , 2007 .

[33]  Peter Freymuth,et al.  On transition in a separated laminar boundary layer , 1966, Journal of Fluid Mechanics.

[34]  V. Yang,et al.  Dynamics and stability of lean-premixed swirl-stabilized combustion , 2009 .

[35]  Tim Colonius,et al.  Instability wave models for the near-field fluctuations of turbulent jets , 2011, Journal of Fluid Mechanics.

[36]  S. Candel,et al.  The combined dynamics of swirler and turbulent premixed swirling flames , 2010 .

[37]  C. A. Armitage,et al.  Investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations , 2006 .

[38]  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.

[39]  Mujeeb R. Malik,et al.  A spectral collocation method for the Navier-Stokes equations , 1985 .

[40]  Hans-Christian Hege,et al.  Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction , 2011, Journal of Fluid Mechanics.

[41]  S. Candel,et al.  A unified framework for nonlinear combustion instability analysis based on the flame describing function , 2008, Journal of Fluid Mechanics.

[42]  Tim Lieuwen,et al.  Modeling Premixed Combustion-Acoustic Wave Interactions: A Review , 2003 .

[43]  Campbell D. Carter,et al.  Experimental study of vortex-flame interaction in a gas turbine model combustor , 2012 .

[44]  C. O. Paschereit,et al.  On the impact of swirl on the growth of coherent structures , 2014, Journal of Fluid Mechanics.

[45]  Xiaolong Yang,et al.  Absolute and convective instability of a cylinder wake , 1989 .

[46]  A. Dowling,et al.  Experimental investigation of the nonlinear response of turbulent premixed flames to imposed inlet velocity oscillations , 2005 .

[47]  Tim Lieuwen,et al.  Further Characterization of the Disturbance Field in a Transversely Excited Swirl-Stabilized Flame , 2011 .

[48]  A. Michalke.  On spatially growing disturbances in an inviscid shear layer , 1965, Journal of Fluid Mechanics.

[49]  Peter A. Monkewitz,et al.  The absolute and convective nature of instability in two-dimensional wakes at low Reynolds numbers , 1988 .

[50]  D. Barkley.  Linear analysis of the cylinder wake mean flow , 2006 .

[51]  Christian Oliver Paschereit,et al.  Key parameters governing the precessing vortex core in reacting flows: An experimental and analytical study , 2015 .

[52]  B. R. Noack,et al.  A hierarchy of low-dimensional models for the transient and post-transient cylinder wake , 2003, Journal of Fluid Mechanics.