Theoretical prediction of the onset of thermoacoustic instability from the experimental transfer matrix of a thermoacoustic core

Guédra, Matthieu; Pénelet, Guillaume; Lotton, Pierrick; Dalmont, Jean‐Pierre

doi:10.1121/1.3592227

Cited by 31 publications

(31 citation statements)

References 31 publications

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“…Thermoacoustic pumping is well described analytically for simple pore shapes [9], or with hybrid analytic/experimental approaches for more complex materials [10,11]. Acoustic streaming is accounted for in models by higher-order developments of the basic equations [12,13], and experimental solutions are implemented to limit its effects [14,15].…”

Section: Introductionmentioning

confidence: 99%

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

Olivier¹,

Pénelet²,

Poignand³

et al. 2015

Acta Acustica united with Acustica

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Though thermoacoustic engines usually operate at high acoustic amplitude, they rarely exhibit strong deformation of the wavefront due to nonlinear propagation. It has however been demonstrated experimentally that obtaining shock waves in thermoacoustic engines is possible under specific conditions. This paper aims at presenting a simple description of the periodic steady-state operation of thermoacoustic engines describing the wave steepening process leading to shock wave formation. Results of numerical simulations are compared to experimental data in different engine configurations, and model improvements are proposed to reach a realistic description of the weakly nonlinear propagation in thermoacoustic engines.

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Section: Introductionmentioning

confidence: 99%

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

Olivier¹,

Pénelet²,

Poignand³

et al. 2015

Acta Acustica united with Acustica

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“…In the following, we give a brief description of this element and of the experimental procedure used for measuring its transfer matrix (for a complete description of the measurements methods, the reader can find more details in Refs. [28,29] The acoustic properties of the TAC can be characterized by means of the so-called transfer matrix [30] (T-matrix), which gives a relationship between the complex amplitudes of acoustic pressure and acoustic velocity at both sides of the TAC. More precisely,…”

Section: Description Of the Thermoacoustic Core And T-matrix Measuremmentioning

confidence: 99%

“…Therefore, acoustic propagation through the TAC is only characterized by the four complex elements T ij of its matrix, which depend on the frequency of acoustic oscillations, on the geometrical and thermophysical properties of the stack and heat exchangers, and on the assigned temperature distribution along the TAC. In previous works, we performed the measurements of the T-matrices of various TAC by means of two different methods, namely a classical two-load method [28] and another method based on the use of an acoustic impedance sensor [29]. As a result, experimental data for different kinds of TAC equipped with different stack materials (ceramic catalyst, stainless steel grids, RVC and NiCr foams) are now available, which are obtained for different values of heat power supply in the frequency range 30 Hz-500 Hz.…”

Section: Description Of the Thermoacoustic Core And T-matrix Measuremmentioning

confidence: 99%

“…In previous studies [28,29], we presented an experimental setup for the measurements of the acoustical transfer matrix of a TAC under various heating conditions, and we used the experimental data to predict the onset of self-sustained oscillations of any thermoacoustic device equipped with the TAC characterized beforehand. However, such a black box approach does not provide information about the inside of the thermoacoustic core, and therefore the main objective of this study is to evaluate an inverse method approach to get information about the acoustical and thermal properties of the stack/regenerator.…”

Section: Introductionmentioning

confidence: 99%

“…However, such a black box approach does not provide information about the inside of the thermoacoustic core, and therefore the main objective of this study is to evaluate an inverse method approach to get information about the acoustical and thermal properties of the stack/regenerator. More precisely, the purpose of the present paper is (1) to propose a theoretical description of the TAC and (2) to make use of the experimental results from [28,29] so as to adjust parameters which are generally hard to evaluate (tortuosity, heat exchange coefficient . .…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation for the characterization of thermoacoustic stacks and regenerators

Guédra¹,

Bannwart²,

Pénelet³

et al. 2015

Applied Thermal Engineering

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Highlights• A model for the propagation of acoustic waves in a thermoacoustic core is proposed • Geometrical and thermal parameters are adjusted by using an inverse method • Parameters are estimated for a ceramic catalyst, a stack of grids and a carbon foam• The values for geometrical parameters are close to manufacturers' data • The heat diffusion length is higher for the stainless-steel grids stack Abstract This paper deals with the in-situ characterization of open-cell porous materials that might be used as a so-called stack (or regenerator) in a thermoacoustic engine. More precisely, the manuscript presents an inverse method aiming at estimating geometrical and thermal properties of various samples of porous media surrounded by heat exchangers and connected to a thermal buffer tube to form a ThermoAcoustic Core (TAC). This estimation is realized from acoustic measurements, and it is expressed as a minimization problem applied to the squared norm of the difference between experimental and theoretical transfer matrices of the TAC. Experimental data, obtained for different stacks (ceramic catalyst, pile of stainless steel wire meshes, carbon and metallic foams) under various heating conditions, are used in order to fit the theoretical forward model by adjusting geometrical properties of the sample and heat exchange coefficients. Common geometrical properties (porosity and average pore's radius) obtained with the present method are consistent with available data from manufacturers. Moreover, this method allows to estimate the tortuosity of the material which is not given by manufacturers. Estimation of heat coefficients (and their variations with heating) provides global in-formation about anisotropic heat diffusion through the porous material employed as a thermoacoustic stack submitted to a temperature gradient. Among the four characterized samples, it appears that the carbon foam allows to get the highest temperature gradients

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Impact of the Acoustic Forcing Level on the Transfer Matrix of a Turbulent Swirling Combustor with and Without Flame

Gaudron

Gatti

Mirat

et al. 2019

Flow Turbulence Combust

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Thermoacoustic instabilities are a major issue for industrial and domestic burners. One possible framework to study these instabilities is to represent the system by a network of Dimensionless Acoustic Transfer Matrices (DATM) that link pressure and velocity fluctuations upstream and downstream each element of the network. In this article, the DATM coefficients of a turbulent swirling combustor are determined for a thermoacoustically stable configuration using harmonic acoustic forcing. Since the dynamics of the whole system is controlled by nonlinearities, the impact of the forcing level needs to be considered. The four DATM coefficients are thus measured for reactive operating conditions (premixed flame) and cold flow conditions for increasing acoustic excitation levels. The velocity level is controlled by a hot wire located inside the injector, in a region with a laminar top-hat velocity profile. The upstream and downstream specific acoustic impedances are also measured. Results for the acoustic response under cold flow conditions are first presented. In this case, the DATM coefficients are found to be independent of the forcing level except for the modulus of the coefficients linking the downstream velocity fluctuations to the upstream pressure and velocity fluctuations. This behavior is linked to the nonlinear response of the injector but is not entirely captured by the acoustic network model developed in this work. For reactive operating conditions, measurements indicate that all DATM coefficients depend on the forcing level to a certain extent. The Flame Describing Function, linking heat release rate fluctuations to velocity fluctuations, is used to reconstruct the transfer matrix through an acoustic network model. This network model accurately predicts the trend of the measured coefficients but the impact of the forcing level is not reproduced. Saturation for reactive operating conditions is shown to be not only related to the nonlinear flame response but also to the nonlinear injector dynamics. Finally, a data-driven reconstruction of the FDF using the acoustic network model along with the hot wire and microphone measurements is performed. This data-driven acoustic reconstruction is subsequently compared with the FDF determined with an optical technique.

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Theoretical prediction of the onset of thermoacoustic instability from the experimental transfer matrix of a thermoacoustic core

Cited by 31 publications

References 31 publications

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

Weakly Nonlinear Propagation in Thermoacoustic Engines: A Numerical Study of Higher Harmonics Generation up to the Appearance of Shock Waves

Parameter estimation for the characterization of thermoacoustic stacks and regenerators

Impact of the Acoustic Forcing Level on the Transfer Matrix of a Turbulent Swirling Combustor with and Without Flame

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