Effect of choked outlet on transient energy growth analysis of a thermoacoustic system

Thermoacoustic instability occurs in many practical combustion systems. These systems are non-normal and associated with transient growth of acoustic disturbances. If the transient growth is large enough, then thermoacoustic instability may be triggered. In this work, transient energy growth analysis of a thermoacoustic system with a choked outlet is conducted. The effect of the choked boundary is studied by using an analytical and a linearized Euler equation (LEE) method. To quantify the transient growth, two energy measures are defined and calculated. One is associated with the acoustical energy. The other is the total energy of both entropy and acoustic fluctuations. Comparison is made between the transient growth results obtained from the analytical method and those from the LEE method. It is found that the transient growth analysis of the total energy by using the analytical model with the expression of the choked outlet is consistent with that by using the LEE method. However, when only acoustical energy is considered, the analytical model may leads to a wrong prediction of transient growth. The present work opens up new applicable way to predict transient stability behaviors of a practical engine system ended with a choked outlet.

[1]  Christian Troger,et al.  Prediction and control of combustion instabilities in industrial gas turbines , 2004 .

[2]  Dan Zhao,et al.  Transient growth of flow disturbances in triggering a Rijke tube combustion instability , 2012 .

[3]  A. Dowling.  A kinematic model of a ducted flame , 1999, Journal of Fluid Mechanics.

[4]  Franck Nicoud,et al.  About the Zero Mach Number Assumption in the Calculation of Thermoacoustic Instabilities , 2009 .

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

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

[7]  Tom Hynes,et al.  Reflection of circumferential modes in a choked nozzle , 2002, Journal of Fluid Mechanics.

[8]  H. Pitsch,et al.  An experimental study on MILD combustion of prevaporised liquid fuels , 2015 .

[9]  M. K. Myers,et al.  Transport of energy by disturbances in arbitrary steady flows , 1991, Journal of Fluid Mechanics.

[10]  M. Juniper.  Triggering in the horizontal Rijke tube: non-normality, transient growth and bypass transition , 2010, Journal of Fluid Mechanics.

[11]  Wenming Yang,et al.  Numerical investigation of the effect of distributed heat sources on heat-to-sound conversion in a T-shaped thermoacoustic system , 2015 .

[12]  Raman Sujith,et al.  Thermoacoustic instability in a Rijke tube: non-normality and nonlinearity , 2007 .

[13]  Ann P. Dowling,et al.  Sound and Sources of Sound , 1983 .

[14]  R. Sujith,et al.  Non-normality and nonlinearity in combustion–acoustic interaction in diffusion flames , 2007, Journal of Fluid Mechanics.

[15]  Ahmed F. Ghoniem,et al.  Fuel flexibility, stability and emissions in premixed hydrogen-rich gas turbine combustion: Technology, fundamentals, and numerical simulations , 2015 .

[16]  Ercang Luo,et al.  Investigation on the thermoacoustic conversion characteristic of regenerator , 2015 .

[17]  F. E. Marble,et al.  Acoustic disturbance from gas non-uniformities convected through a nozzle , 1977 .

[18]  Tim Lieuwen,et al.  Combustion Instabilities In Gas Turbine Engines: Operational Experience, Fundamental Mechanisms, and Modeling , 2006 .

[19]  A. Pagano,et al.  Monitoring combustion unstable dynamics by means of control charts , 2009 .

[20]  Alberto Fichera,et al.  Neural prediction of combustion instability , 2002 .

[21]  Dan Zhao,et al.  Nonorthogonality analysis of a thermoacoustic system with a premixed V-shaped flame , 2014 .

[22]  Aimee S. Morgans,et al.  The Influence of Entropy Waves on the Thermoacoustic Stability of a Model Combustor , 2013 .

[23]  Andrea Toffolo,et al.  Low computational cost CFD analysis of thermoacoustic oscillations , 2010 .

[24]  Aimee S. Morgans,et al.  Phase prediction of the response of choked nozzles to entropy and acoustic disturbances , 2011 .

[25]  S. Hochgreb,et al.  Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor , 2012 .

[26]  Xiaofeng Sun,et al.  Effect of vorticity waves on azimuthal instabilities in annular chambers , 2015 .

[27]  Stéphane Moreau,et al.  Boundary Conditions for the Computation of Thermoacoustic Modes in Combustion Chambers , 2014 .

[28]  Wenming Yang,et al.  Theoretical and experimental investigation of thermoacoustics transfer function , 2015 .

[29]  Ann P. Dowling,et al.  Acoustic Analysis of Gas Turbine Combustors , 2003 .

[30]  B. Chu.  On the energy transfer to small disturbances in fluid flow (Part I) , 1965 .

[31]  Franck Nicoud,et al.  Using Boundary Conditions to Account for Mean Flow Effects in a Zero Mach Number Acoustic Solver , 2012 .

[32]  Dan Zhao,et al.  Effect of heat source on transient energy growth analysis of a thermoacoustic system , 2015 .

[33]  L. Kovasznay,et al.  Non-linear interactions in a viscous heat-conducting compressible gas , 1958, Journal of Fluid Mechanics.

[34]  A. Dowling.  THE CALCULATION OF THERMOACOUSTIC OSCILLATIONS , 1995 .

[35]  Franck Nicoud,et al.  Accounting for convective effects in zero-Mach-number thermoacoustic models , 2014 .

[36]  Claude Sensiau,et al.  Assessing non-normal effects in thermoacoustic systems with mean flow , 2011 .

[37]  I. Duran,et al.  Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion , 2013, Journal of Fluid Mechanics.

[38]  Xiaofeng Sun,et al.  Effect of distributed heat source on low frequency thermoacoustic instabilities , 2013 .

[39]  Franck Nicoud,et al.  Analysis and Modelling of Entropy Modes in a Realistic Aeronautical Gas Turbine , 2013 .

[40]  Xiaotao Wang,et al.  Study on energy conversion characteristics of a high frequency standing-wave thermoacoustic heat engine , 2013 .

[41]  Miao Yu,et al.  Thermo-acoustic behavior of a swirl stabilized diffusion flame with heterogeneous sensors , 2013 .

[42]  Dan Zhao,et al.  Transient energy growth of acoustic disturbances in triggering self-sustained thermoacoustic oscillations , 2015 .

[43]  Scott Backhaus,et al.  Travelling-wave thermoacoustic electricity generator using an ultra-compliant alternator for utilization of low-grade thermal energy , 2012 .

[44]  Ghislain Lartigue,et al.  Experimental and numerical investigation of self-excited combustion oscillations in a scaled gas turbine combustor , 2004 .

[45]  A. Fichera,et al.  Experimental analysis of thermo-acoustic combustion instability , 2001 .

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

[47]  F. E. Marble,et al.  The interaction of entropy fluctuations with turbine blade rows; a mechanism of turbojet engine noise , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.