A finite element method for a weakly nonlinear dynamic analysis and bifurcation tracking of thermo-acoustic instability in longitudinal and annular combustors

Laera, Davide; Campa, Giovanni; Camporeale, Sergio Mario

doi:10.1016/j.apenergy.2016.10.124

Cited by 40 publications

(16 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…2], as is customary of many other studies, e.g. [8,26,27,28,29,7]. The change of the delay affects at the same time the value and the slope of the flame phase at a certain frequency ω 0 .…”

Section: Literature Reviewmentioning

confidence: 92%

“…See e.g. [5,6,7] for a finite element approach in the frequency domain, [8] in the time domain. Low order models can be analyzed in the frequency domain [9,10,11,12,13] and both in the frequency and time domain [14,15,16,17].…”

Section: Literature Reviewmentioning

confidence: 99%

“…where here and in the following the prime denotes a time derivative and n is the azimuthal wavenumber of the mode we are studying. By substituting (8) into (7) and by projecting the equations on the two modes we obtain [44]:…”

Section: Brief Derivation Of the Modelmentioning

confidence: 99%

See 2 more Smart Citations

The effect of the flame phase on thermoacoustic instabilities

Ghirardo¹,

Juniper

Bothien³

2018

Combustion and Flame

View full text Add to dashboard Cite

This paper concerns the influence of the phase of the heat release response on thermoacoustic systems. We focus on one pair of degenerate azimuthal acoustic modes, with frequency ω 0. The same results apply for an axial acoustic mode. We show how the value φ 0 and the slope −τ of the flame phase at the frequency ω 0 affects the boundary of stability, the frequency and amplitude of oscillation, and the phase φ qp between heat release rate and acoustic pressure. This effect depends on φ 0 and on the nondimensional number τ ω 0 , which can be quickly calculated. We find for example that systems with large values of τ ω 0 are more prone to oscillate, i.e. they are more likely to have larger growth rates, and that at very large values of τ ω 0 the value φ 0 of the flame phase at ω 0 does not play a role in determining the system's stability. Moreover for a fixed flame gain, a flame whose phase changes rapidly with frequency is more likely to excite an acoustic mode. We propose ranges for typical values of nondimensional acoustic damping rates, frequency shifts and growth rates based on a literature review. We study the system in the nonlinear regime by applying the method of averaging and of multiple scales. We show how to account in the time domain for a varying frequency of oscillation as a function of amplitude, and validate these results with extensive numerical simulations for the parameters in the proposed ranges. We show that the frequency of oscillation ω B and the flame phase φ qp at the limit cycle match the respective values on the boundary of stability. We find good agreement between the model and thermoacoustic experiments, both in terms of the ratio ω B /ω 0 and of the phase φ qp , and provide an interpretation of the transition between different thermoacoustic states of an experiment. We discuss the effect of neglecting the component of heat release rate not in phase with the pressure p as assumed in previous studies. We show that this component should not be neglected when making a prediction of the system's stability and amplitudes, but we present some evidence that it may be neglected when identifying a system that is unstable and is already oscillating

show abstract

Section: Literature Reviewmentioning

confidence: 92%

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

The effect of the flame phase on thermoacoustic instabilities

Ghirardo¹,

Juniper

Bothien³

2018

Combustion and Flame

View full text Add to dashboard Cite

show abstract

“…This is achieved by linearizing the FDF by fixing a velocity fluctuation level | u / u | . The finite element discretization of this set of linearized equations along with the boundary conditions results in the following eigenvalue problem [34,35] :…”

Section: Weakly Nonlinear Stability Numerical Analysismentioning

confidence: 99%

Flame Describing Function analysis of spinning and standing modes in an annular combustor and comparison with experiments

Laera

Schuller

Prieur

et al. 2017

Combustion and Flame

View full text Add to dashboard Cite

Camporeale, et al.. Flame Describing Function analysis of spinning and standing modes in an annular combustor and comparison with experiments. Combustion and Flame, Elsevier, 2017, 184, pp.(D. Laera).merical procedure combining the Flame Describing Function (FDF) framework with a Helmholtz solver to analyze azimuthal instabilities:• Specific iterative algorithms are developed to simulate the dynamics of spinning and standing modes within the FDF framework. • This is tested first on a system represented by an ideal flame response and results of recent analytical investigations are fully retrieved validating this methodology.where ψ ( )/ ψ max is the normalized azimuthal eigenmode structure. The numerical implementation of this model in the

show abstract

“…The dominant thermoacoustic instability is experimentally shown to switch by observing a shift from a low-to a high-frequency 'tone'. When combustion instability occurs 7,8 , it can cause severe vibration, overheating, flame flashback, and decreased performance 9 . In severe cases, the engines, propellant systems and structures could be damaged.…”

mentioning

confidence: 99%

Characterizing hydrogen-fuelled pulsating combustion on thermodynamic properties of a combustor

2019

View full text Add to dashboard Cite

Unlike hydrocarbon fuel, hydrogen is 'green' and attracting more and more attentions in energy and propulsion sectors due to the zero emission of CO and CO 2 . By applying numerical simulations, we explore the physics of how a hydrogen-burnt flame can sustain pulsating combustion and its impact on the thermodynamic properties of a standing-wave combustor. We also explain how implementing a heat exchanger can mitigate such pulsating combustion. The dynamic interactions of the unsteady flow-flame-acoustics-heater are examined by varying the mass flow rate ṁ H2 and the heating bands' surface temperature T H . The frequency and amplitude of the pulsating combustion are shown to depend strongly on ṁ H2 . In addition, varying T H is shown to lead to not only the molar fraction of the combustion species being changed but also the flame-sustained pulsating oscillations being mitigated somehow. Finally, nonlinearity is observed and identified in the unsteady flow velocity and the two heat sources.

show abstract

A finite element method for a weakly nonlinear dynamic analysis and bifurcation tracking of thermo-acoustic instability in longitudinal and annular combustors

Cited by 40 publications

References 53 publications

The effect of the flame phase on thermoacoustic instabilities

The effect of the flame phase on thermoacoustic instabilities

Flame Describing Function analysis of spinning and standing modes in an annular combustor and comparison with experiments

Characterizing hydrogen-fuelled pulsating combustion on thermodynamic properties of a combustor

Contact Info

Product

Resources

About