Thermoacoustic analysis of a laminar premixed flame using a linearized reactive flow solver

Avdonin, Alexander; Meindl, Max; Polifke, Wolfgang

doi:10.1016/j.proci.2018.06.142

Cited by 28 publications

(17 citation statements)

References 19 publications

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“…This would be a flame transfer function with distributed time delays with different time delays for the different geometries. The optimization method described in this paper might potentially be applied to the linearized reactive flow solver presented in [38], where the flame transfer function is not needed a priori.…”

Section: Discussionmentioning

confidence: 99%

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Falco

Juniper

2021

Journal of Engineering for Gas Turbines and Power

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Thermoacoustic instabilities, which arise due to the interaction between flames and acoustics, are sensitive to small changes to the system parameters. In this paper, we apply adjoint-based shape optimization to a 2D finite element Helmholtz solver to find accurately and inexpensively the shape changes that most stabilise a 2D thermoacoustic system in the linear regime. We examine two cases: a Rijke tube and a turbulent swirl combustor. Both systems exhibit an unstable longitudinal mode and we suppress the instability by slightly modifying the geometry. In the case of the turbulent swirl combustor, the sensitivities are higher in the plenum and in the burner than in the combustion chamber, mainly due to the effect of the mean temperature. In the cooler regions, the local wavelength is shorter, which means that geometry changes of a given distance have more influence than they do where the local wavelength is longer. This is the first time adjoint-based shape optimization is applied to 2D Helmholtz solvers in thermoacoustics, after being previously applied to low-order thermoacoustic networks. But Helmholtz solvers have an intrinsic advantage: they can handle complex geometries. The easy scalability of this method to complex 3D geometries make this tool a strong candidate for the iterative design of thermoacoustically stable combustors.

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Section: Discussionmentioning

confidence: 99%

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Falco

Juniper

2021

Journal of Engineering for Gas Turbines and Power

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“…The compressible reactive flow equations, which are to be linearized around the base state for the following analysis, are formulated in terms of conservative variables (𝜌, 𝜌𝑢, 𝜌𝑣, 𝜌ℎ, 𝜌𝑌 𝑘 ) in Cartesian coordinates (𝑥, 𝑦), where (𝑢, 𝑣) are the streamwise and cross-stream velocity components, 𝜌 is the density, ℎ is the sensible enthalpy and 𝑌 𝑘 is the mass fraction of species 𝑘. Following the notation of Avdonin et al [31], these equations are given as…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

“…Recent work on premixed laminar flames, by Polifke and coworkers [31,32,33], is highly relevant to the present study. The objective of Avdonin et al [31] was to introduce a new approach that can accurately predict FTFs and thermoacoustic modes. The linearized reactive flow approach (LRF) that contains the set of equations of a reacting flow, was used to calculate the FTF, quantitatively validated against results obtained by nonlinear timestepping.…”

Section: Introductionmentioning

confidence: 98%

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Linear instability of a premixed slot flame: Flame transfer function and resolvent analysis

Wang

Kaiser

Meindl

et al. 2022

Combustion and Flame

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“…Several approaches to understand thermo-acoustic instabilities range from 1) understanding physical mechanisms, viz. study of flow structures, flame-velocity coupling etc [3,4,5] 2) performing high fidelity computations, whereby the entire system is solved using approaches like compressible LES [6,7], hybrid approaches [8,9] and 3) network models, whereby each subsystem is modeled separately and linked by transfer matrices [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Understanding dynamical states observed in a thermo-acoustic system from perspective of frequency-phase relationship derived from a probabilistic oscillator model

Ramanan

Ramankutty

Sreed

et al. 2022

Preprint

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We perform lab scale experiments in a swirl combustor by reducing the equivalence ratio for two cases involving slightly different inlet air flow rates. Reduction in equivalence ratio at a constant air flow results in the combustor transiting from stable to unstable combustion. The transition passes through stable, type-2 intermittency and beat oscillations. The beat oscillations are seen to fluctuate at a single frequency, and hence suggestive of a process involving spatio-temporal variations in the phase of the driver (i.e., heat release rate fluctuations). This is understood in the manner of a reduced order model, where the driver is considered to an ensemble of phase oscillators with time delays and a probabilistic distribution of natural frequencies, similar to Kuramoto oscillator. The acoustic field is modeled as a Van-der-pol Duffing system, with natural frequency equal to the duct acoustic mode. The coupling between the oscillators is varied based on the physical premise of Rayleigh criterion. The coupled system is seen to qualitatively and quantitatively match the pressure data obtained from experiments. Insights into various conditions illustrate the role of mean and fluctuating instantaneous frequency amongst the phase oscillators in determining the modeled pressure oscillations. By quantifying the extent of fluctuating frequency coupling among the phase oscillators, it is observed that beat oscillations have high correlation with lower deviation compared to intermittency and stable oscillations.

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Thermoacoustic analysis of a laminar premixed flame using a linearized reactive flow solver

Cited by 28 publications

References 19 publications

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Shape Optimization of Thermoacoustic Systems Using a Two-Dimensional Adjoint Helmholtz Solver

Linear instability of a premixed slot flame: Flame transfer function and resolvent analysis

Understanding dynamical states observed in a thermo-acoustic system from perspective of frequency-phase relationship derived from a probabilistic oscillator model

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