Numerical study of the direct pressure effect of acoustic waves in planar premixed flames

Abstract Recently the unsteady response of 1-D premixed flames to acoustic pressure waves for the range of frequencies below and above the inverse of the flame transit time was investigated experimentally using OH chemiluminescence Wangher (2008) [1] . They compared the frequency dependence of the measured response to the prediction of an analytical model proposed by Clavin et al. (1990) [2] , derived from the standard flame model (one-step Arrhenius kinetics) and to a similar model proposed by McIntosh (1991) [3] . Discrepancies between the experimental results and the model led to the conclusion that the standard model does not provide an adequate description of the unsteady response of real flames and that it is necessary to investigate more realistic chemical models. Here we follow exactly this suggestion and perform numerical studies of the response of lean methane flames using different reaction mechanisms. We find that the global flame response obtained with both detailed chemistry (GRI3.0 [4] ) and a reduced multi-step model by Peters (1996) [5] lies slightly above the predictions of the analytical model, but is close to experimental results. We additionally used an irreversible one-step Arrhenius reaction model and show the effect of the pressure dependence of the global reaction rate in the flame response. Our results suggest first that the current models have to be extended to capture the amplitude and phase results of the detailed mechanisms, and second that the correlation between the heat release and the measured OH∗ chemiluminescence should be studied deeper.

[1]  R. Klein,et al.  Flame front capturing/tracking schemes for compressible and incompressible reactive flow , 2006 .

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

[3]  P. Moin,et al.  Combustion instability due to the nonlinear interaction between sound and flame , 2003, Journal of Fluid Mechanics.

[4]  J. Daily,et al.  Low-frequency pressure oscillations in a model ramjet combustor , 1991, Journal of Fluid Mechanics.

[5]  Michael S. Howe,et al.  Stability analysis of the Rijke tube with a Green's function approach , 2007 .

[6]  A. Putnam.  Combustion-Driven Oscillations in Industry , 1971 .

[7]  G. Searby,et al.  On the shape of flames under strong acoustic forcing: a mean flow controlled by an oscillating flow , 1997, Journal of Fluid Mechanics.

[8]  S. Candel,et al.  Theoretical and experimental determinations of the transfer function of a laminar premixed flame , 2000 .

[9]  E. Gutmark,et al.  Combustion instability related to vortex shedding in dump combustors and their passive control , 1992 .

[10]  Forman A. Williams,et al.  A simple one-step chemistry model for partially premixed hydrocarbon combustion , 2006 .

[11]  Paul Clavin,et al.  Theory of Acoustic Instabilities of Planar Flames Propagating in Sprays or Particle-Laden Gases , 1991 .

[12]  Christian Oliver Paschereit,et al.  A two-way coupling for modeling thermoacoustic instabilities in a flat flame Rijke tube , 2009 .

[13]  Merrill W. Beckstead,et al.  A REVIEW OF RIJKE TUBES, RIJKE BURNERS AND RELATED DEVICES , 1993 .

[14]  A. Putnam,et al.  Organ-pipe oscillations in a flame-filled tube , 1953 .

[15]  P. Pelcé,et al.  Vibratory instability of cellular flames propagating in tubes , 1992, Journal of Fluid Mechanics.

[16]  Geoffrey Searby,et al.  Experimental investigation of the unsteady response of premixed flame fronts to acoustic pressure waves , 2008 .

[17]  P.O.A.L. Davies,et al.  The measurement and prediction of sound waves of arbitrary amplitude in practical flow ducts , 2004 .

[18]  D. Thévenin,et al.  Accurate Boundary Conditions for Multicomponent Reactive Flows , 1995 .

[19]  A. McIntosh.  Pressure disturbances of different length scales interacting with conventional flames , 1991 .

[20]  N. Peters,et al.  Fifteen Lectures on Laminar and Turbulent Combustion , 1995 .

[21]  R. Klein.  Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics , 1995 .

[22]  G. Searby.  Acoustic Instability in Premixed Flames , 1992 .

[23]  A. Kerstein,et al.  Investigation of autoignition under thermal stratification using linear eddy modeling , 2008 .

[24]  F. Nicoud,et al.  Flow forcing techniques for numerical simulation of combustion instabilities , 2002 .

[25]  A. McIntosh.  The Linearised Response of the Mass Burning Rate of a Premixed Flame to Rapid Pressure Changes , 1993 .

[26]  R. Klein,et al.  An asymptotically motivated hyrodynamic-acoustic two-way coupling for modeling thermoacoustic instabilities in a Rijke tube , 2007 .

[27]  A. McIntosh.  Deflagration fronts and compressibility , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[28]  G. Searby,et al.  A parametric acoustic instability in premixed flames , 1991, Journal of Fluid Mechanics.

[29]  P. Pelcé,et al.  One-dimensional vibratory instability of planar flames propagating in tubes , 1990, Journal of Fluid Mechanics.

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

[31]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[32]  P. Blackshear.  Driving standing waves by heat addition , 1953 .

[33]  Carol S. Woodward,et al.  Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers , 2020, ACM Trans. Math. Softw..

[34]  A. Annaswamy,et al.  Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results , 1996 .

[35]  T. Lieuwen,et al.  The role of equivalence ratio oscillations in driving combustion instabilities in low NOx gas turbines , 1998 .