This work presents an experimental and theoretical investigation into the influence of a passive, off-resonance flexible plate on a dual-mode thermoacoustic instability. Simultaneous measurements of acoustic pressure, heat release, and plate velocity (via Laser Doppler Vibrometry) are used to characterize the coupled fluid–structure dynamics. In the rigid-wall baseline, the combustor exhibits a limit cycle dominated by a single acoustic mode. Introducing the flexible plate fundamentally alters this behavior, inducing modal competition in which the dominance intermittently shifts between two closely spaced acoustic modes. A low-order model, consisting of two coupled delayed oscillators, is developed and calibrated against the experimental data to probe the underlying mechanism. The analysis shows that, although the plate acts as an energy sink, this additional damping alone cannot account for the emergence of the secondary mode. Instead, the model indicates that modal competition arises from an alteration of the thermoacoustic feedback loop, driven by an induced frequency shift and a modification of the effective flame driving strengths. This demonstrates that the compliant boundary does not merely introduce damping but reshapes the competitive stability balance between modes, revealing a non-intuitive mechanism with direct relevance for passive control strategies. Novelty and significance statement This work provides new insight into the complex dynamics of a multi-mode unstable thermoacoustic system interacting with a compliant boundary. The study combines simultaneous acoustic, heat release and vibrometry measurements to characterize such an interaction in-situ. We experimentally investigate a phenomenon of modal competition triggered by this passive, off-resonance structural element, which alters the dynamics of the thermoacoustic modes. The findings provide a valuable benchmark for the development and validation of descriptive low-order models.

This paper utilizes Cauchy's argument principle in the frequency domain to develop novel stability maps, providing guidelines for measures which can be taken to mitigate thermoacoustic instabilities in combustion appliances. The existing approaches mainly concentrate on identifying the onset of thermoacoustic instabilities by calculating unstable frequencies and growth rates. However, they provide limited practical guidance for modifying system characteristics, especially those dependent on frequency, to achieve flame stabilization. In the present contribution, several thermoacoustic stability criteria are introduced that leverage the Cauchy's argument principle and direct evaluation of the dispersion relation's argument. These criteria offer deeper insights and facilitate a systematic flame stabilization process by enabling modifications to both the (passive) acoustic subsystems and/or the (active) subsystem containing the combustion processes. This approach allows for a construction and comprehensive understanding of the stability map for a given thermoacoustic system, leading to more effective guidelines to elaborate and implement the combustion system stabilization strategies. To demonstrate the practical application of this framework, two illustrative thermoacoustic systems are discussed. Novelty and significance statement This study introduces a novel framework for assessing thermoacoustic stability.

• It provides a method for detecting the onset of thermoacoustic instability and offers valuable insights into critical frequency ranges. This approach facilitates the identification of necessary modifications in flame and acoustic subsystems across different frequencies to achieve system stabilization.

• This framework allows for the selection of the most suitable stability criterion based on the available combustion system's characteristics. For example, by knowing acoustic properties in both upstream and downstream components, either the DDS or DCS criterion can generate a comprehensive, frequency-dependent stability map for flame transfer function values. This approach eliminates the need for iterative integration, differential equations, or direct solutions to dispersion relations.

A novel approach to perform linear stability analysis using a spectral element-based reduced order model is proposed, thereby facilitating the comprehensive study of (thermo)acoustic (in)stability across complex waveguide configurations. Providing a generalization of a wave-based method (e.g. spectral element method) to the Laplace domain, this study is offering not only a new methodology for analyzing thermoacoustic systems but also expanding the application of the spectral element method and other wave-based techniques to a broader class of problems. By solving the wave equation in the Laplace domain, spectral elementary matrices can be defined in the complex plane in both wavenumber and frequency domains, allowing for an examination of system stability. This technique supports a wide range of waveguide investigations, whether using an analytical description to get the spectral matrix or a numerical method to determine the dispersion curves and eigenvectors in the cross-section. Additionally, the proposed method simplifies the implementation of parametric optimization procedures due to its low computational cost, thus offering significant advancements in the study of waveguide behavior of thermoacoustic systems.

In this paper, we propose a data-driven nonlinear modeling approach to describe the dynamics of smart surfaces composed of electroactive liquid crystal networks (LCNs). LCNs are among the top candidates for materials to be employed in smart surfaces such as haptic displays. To realize such applications, the ability to predict an accurate LCN surface response as a function of the input signal is crucial. In this paper, we propose a data-driven modeling approach to identify the parameters of a dynamic model based on experimental data. The resulting model is used for feedforward control to compute the appropriate excitation parameters that ensure a certain desired surface deformation. This feedforward control approach is validated in a simulation study.

A generalization of the Wave Finite Element Method is proposed for the linear stability analysis of thermoacoustic systems, incorporating high-order modes associated with cross-sectional wave propagation and fluid–structure interaction. Formulated in the Laplace domain, this methodology enables the estimation of transfer matrices that integrate into network models for stability predictions. By extending beyond the classical plane wave assumption in network modeling, the framework accurately captures wave propagation in complex geometries where high-order acoustic modes play a crucial role. Additionally, it accounts for fluid–structure interaction, demonstrating how coupling between the fluid and structure modifies wave propagation and influences the system stability. The approach is validated through case studies of increasing complexity and the results confirm the importance of incorporating high-order modes and fluid–structure interaction effects into predictive models. By providing a computationally efficient alternative to full-domain numerical simulations, the proposed wave-based framework enhances the accuracy of reduced-order models, improving their predictive capabilities for thermoacoustic stability analysis and enabling design-oriented studies such as the optimization of flexible wall configurations for passive instability control.

Thermoacoustic instability poses a significant challenge in the development of combustion appliances, where the lack of specific information on upstream and downstream acoustic terminations during the research and development phase is common. This knowledge gap often necessitates extensive trial-and-error approaches, emphasizing the need for a reliable indicator to assess thermoacoustic quality in advance. Traditionally, a burner and its associated flame are characterized as an acoustically active two-port block, coupled with passive acoustic terminations upstream and downstream. In this paper, we investigate the application of the direct conservative stability criterion in the frequency domain to introduce a suitable indicator, termed the S factor, as a figure-of-merit for thermoacoustic quality. We explore various scenarios that may arise during the research and development phase of thermoacoustically stable combustion systems. Additionally, we address the limitations associated with using Monte Carlo simulations to determine the probability of instability as a potential figure-of-merit. Our findings highlight potential misinterpretations and misrepresentations when employing the Monte Carlo approach to evaluate and compare the thermoacoustic quality of different burners and flames. Finally, the applicability of the S factor is demonstrated and experimentally validated in the lab-scale thermoacoustic system to rank two different burners at the same thermal power.

Assessing the thermoacoustic performance of designed combustors, with a focus on the stability quality factor, is crucial. Thermoacoustic instability in combustion appliances arises from intricate interactions among unsteady combustion, heat transfer, and (maybe) acoustic modes within the system. Accurate prediction of system stability requires modeling all components, including the burner with flame. Traditionally, the burner in the presence of combustion is represented as an acoustically (active) two-port block with passive upstream and downstream acoustic terminations. The dispersion relation of the thermoacoustic system is commonly used for anticipating eigen-frequencies and assessing stability. However, practical scenarios often lack specific information about upstream and downstream terminations during development. This raises a critical question: How can the thermoacoustic performance of burners and their associated flames be evaluated without specified acoustics? This article addresses this question by exploring the concept of unconditional stability in a generic two-port thermoacoustic system. The unconditional stability criteria have been used as quality indicators in designing electrical devices. This rich toolbox has been introduced in thermoacoustics. We first scrutinize assumptions underlying two most known unconditional stability-based criteria called mu and k factors, connecting them to the general thermoacoustic problems. Then, the application of these criteria in assessing the thermoacoustic quality of burners with flames are discussed. This investigation revealed that while they are able to accurately predict the histogram of unstable frequencies and critical frequency bands, their use as reliable indicators to assess thermoacoustic quality in burners are not recommended due to their mathematical limitations and high level of conservatism of these factors.

Experimental measurement methods and theoretical evaluations based on low-order modeling approaches for both the growth rate and frequency at the onset of thermo-acoustic combustion instability are proposed, and their performance is evaluated. The developed techniques are demonstrated through a systematic measurement of the linear growth rate and frequency of evolving oscillations in the laboratory setup and also applied for the thermo-acoustic qualification of an industrial domestic boiler and a heat cell unit (combination of a burner with a heat-exchanger). Generic measurements have been done for a burner deck with premixed surface-stabilized Bunsen-type flames. The industrial domestic boiler and the heat cell unit are equipped with burners of a similar type but differ by their perforation pattern. They have been tested at different conditions and the experimental and theoretical results are compared. Two modeling strategies are tested: 1- in Laplace domain, with estimating a rational function in the complex domain to fit the measured frequency response, 2- exclusively in frequency domain, without estimating a rational function. Both methods include measurement of the frequency response of two reflection coefficients from i) the upstream part of the system, Rup, and ii) burner with flame completed by the downstream part of the appliance, Rin. Within the first approach, a procedure for an analytic continuation of the measured frequency response to the complex domain is applied and complex eigenfrequencies are calculated by solving the corresponding dispersion equation. An alternative approach was proposed by Kopitz and Polifke and allows estimating both the frequency of oscillation and the growth rate from the analysis of the polar plot of the system's characteristic equation in the frequency domain. The comparison shows that the unstable frequencies can be predicted accurately by both tested modeling strategies. This conclusion holds also for the tested industrial applications. The prediction of the instability growth rates is closer to the measured one when the modeling method in the complex domain is used. However, the frequency domain analysis provides less accurate, but still reasonable estimates of the growth rates and frequencies. Moreover, a good overview of thermo-acoustic performance of each industrial boiler/burner at different conditions is obtained via Rin measurements.

This study introduces an innovative approach to assess the thermoacoustic characteristics of components downstream of a flame, employing two sets of distinct Single-Input-Single-Output (SISO) acoustic measurements. Conventional direct assessments of downstream reflection coefficients face challenges due to the need for measurements in the high-temperature downstream region and complexities arising from heat inflow from the flame. To address these challenges, we leverage the widely adopted dispersion relation format from the theory of radio-frequency circuits. In the current methodology, the flame transfer function (TF) technique, as a well-established tool in thermoacoustics, is used. The second method utilizes a standard impedance tube test based on a one-port acoustic reflection test, conducted on the upstream/cold side with a flame present. To demonstrate the effectiveness of our approach, we applied the method to a ducted premixed burner-stabilized Bunsen-type flame. The straightforward reconstruction of downstream reflection coefficients revealed strong sensitivity to noise and uncertainty, particularly in higher frequencies, necessitating specialized data treatment. To mitigate this sensitivity, we conducted multiple tests with slight changes in operating conditions, creating a dataset expected to yield nearly identical downstream reflection coefficients. We then formulated an over-determined system of linear equations, employing the least-squares method to minimize errors and sensitivity. This work showcases a significant reduction in sensitivity through the use of multiple tests and data treatment techniques. The reconstructed downstream acoustics were employed to construct the reflection coefficient measured at upstream side of active subsystem and flame TF at a thermal power close to that corresponding to the reconstructed downstream acoustics, demonstrating substantial improvements in accuracy and reliability.

Thermoacoustic instability within combustion systems is heavily influenced by the thermoacoustic characteristics of the burner in conjunction with its flame. A promising strategy to mitigate these instabilities involves targeting the thermoacoustic properties of the burner itself. One innovative approach for modifying or designing the burner with its corresponding flame is grounded in the heuristic notion that the acoustic response of one flame (with burner) can be counterbalanced by the appropriately tuned response of other flames. In the case of premixed gaseous multiple Bunsen-type flames anchored to the burner deck with perforations, this concept suggests the integration of various sizes and shapes of perforations in burners. However, without prior knowledge, this approach often necessitates extensive trial and error, leading to excessive costs in the Research and Development (R&D) process. Achieving a burner design and its corresponding flame that operate thermo-acoustically stable within the combustion system, while also meeting additional requirements such as emissions, operational durability, mechanical resilience, modulation rate, and others, poses a significant challenge. In this study, we initially articulate the concept of the burner transfer matrix (TM) composition to allows us to predict the TM of complex composite burners on basis of TM of its constituting parts. Then, we establish the complete framework of burner-flame TM composition based on a tabulated library of elemental burners’ pressure drop (PD), elemental burners TM, and elemental flame Transfer Functions (TF). To illustrate this design methodology, we analyze a duct-flame-duct case study. Finally, we present a stability chart that delineates thermo-acoustically safe and unsafe combinations of segments/partitions, offering valuable insights into the R&D process of burner development. By leveraging such a stability chart and considering other operational constraints, designers can systematically achieve optimized designs.