The calculation of thermoacoustic oscillations

Dowling, Ann P.

doi:10.1006/jsvi.1995.0100

Cited by 368 publications

(255 citation statements)

References 0 publications

Supporting

Mentioning

235

Contrasting

Unclassified

Order By: Relevance

“…The amplitudes of these planar waves in the injection and combustion ducts are coupled via jump relations to account for the crosssection area change and the combustion source term at x = 0, using the assumption that the flame is compact with regards to the acoustic wave lengths. These are known as the acoustical Rankine-Hugoniot jump relations, expressed here in the limit of zero Mach number [9][10][11][12][13]:…”

Section: Theoretical Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

DNS of Intrinsic ThermoAcoustic modes in laminar premixed flames

Courtine

Selle

Poinsot

2015

Combustion and Flame

View full text Add to dashboard Cite

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. , Emmert et al. 2015 suggest that thermoacoustic modes can appear in combustors with anechoic terminations, which have no acoustic eigenmodes. These modes, called here Intrinsic ThermoAcoustic (ITA), can be predicted with simple theoretical arguments, but have been ignored for a long time. They are reproduced in this paper using Direct Numerical Simulation (DNS) of a laminar premixed Bunsen type flame. DNS results and theory are compared showing very good agreement in terms of both frequency and mode structure. DNS confirms that the frequency of ITA modes does not depend on any acoustic characteristic of the burner. Based on a numerical evaluation of the Flame Transfer Function, stability limits of ITA modes predicted by theory are also recovered in the DNS with reasonable accuracy. Finally, DNS is used to analyze the mechanisms of ITA modes.

show abstract

Section: Theoretical Backgroundmentioning

confidence: 99%

“…(4)), the acoustic emission is due to dilatation induced by the unsteady reaction rate. This relation is expressed in terms of volumetric flow rate, as effects of mean flow on the acoustics are ignored 3 [10,13].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

DNS of Intrinsic ThermoAcoustic modes in laminar premixed flames

Courtine

Selle

Poinsot

2015

Combustion and Flame

View full text Add to dashboard Cite

show abstract

“…This may lead to thermoacoustic instabilities if the energy gain exceeds the losses through the boundaries and other dissipation mechanisms (Gullaud et al 2009). The instability mechanism depends strongly on the boundary conditions of the combustion chamber: the phase of the reflection coefficient will influence the resonance frequency at which the instability occurs, and the modulus will control the rate at which the energy of the instability is lost through the boundaries, determining whether the mode is stable or unstable (Williams 1985;Candel & Poinsot 1988;Culick 1988;Dowling 1995). The propagation of waves through nozzles was first studied by Tsien (1952), who analysed the propagation of acoustic waves through a quasi-one-dimensional nozzle with a spatially linear velocity profile.…”

Section: Introductionmentioning

confidence: 99%

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

2013

View full text Add to dashboard Cite

The acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (1977) and the effective nozzle length proposed by Stow et al. (2002) and by Goh & Morgans (2011a) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewiselinear approximation of the velocity profile in the nozzle proposed by Moase et al. (2007) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

show abstract

“…Proof: by application of rules (2) and (3) on the expression (24), one finds easily the result of K-B approximation described in lemma (4).…”

Section: And the Results (24) The Application Of K-b Approximation Givesmentioning

confidence: 99%

“…Recent important research programs oriented on this topic are conducted in some countries with industrial collaboration (inter alia USA, France and UK). The papers [2,3,4,5] give an overview of this activity. These phenomena are extremely complex and hard to predict, but in most cases it can be explained by an unsteady flame generating pressure waves which are reflected by physical boundaries into the combustion process.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

Landau¹,

Bouziani²,

Bitmead

Analysis and Design of Nonlinear Control Systems

View full text Add to dashboard Cite

PreludeIt is a great pleasure for us to contribute to this book dedicated to Alberto Isidori on the occasion of his sixty fifth birthday. It is also, for the first author, the occasion to acknowledge a very long period of useful and pleasant exchange which started in 1973 (bilinear systems) and has continued through the years on various specific subjects.The important contributions of Albereto Isidori in the control of nonlinear systems have had a tremendous impact in the control community. Feedback linearization was one of the important subjects developed by Alberto. While the oscillatory nonlinear system considered in this contribution requires specific techniques for its analysis, still a feedback linearization is used for quenching the oscillations.

show abstract

The calculation of thermoacoustic oscillations

Cited by 368 publications

References 0 publications

DNS of Intrinsic ThermoAcoustic modes in laminar premixed flames

DNS of Intrinsic ThermoAcoustic modes in laminar premixed flames

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

Contact Info

Product

Resources

About