Thermoacoustic Oscillations Research Articles

Експериментальні дослідження термоакустичних двигунів з двофазним робочим тілом

A distinguishing feature of these days is the general tendency to decrease the temperature level of the waste heat of engines for power plants in industry, transport, and energy. These circumstances complicate the usage of traditional energy-saving technologies designed to transform this heat into mechanical work. Given the lack of effective technologies, large volumes of such heat emissions are lost. As an example, we can consider ship power engineering. On ships that are equipped with dual-fuel medium and low-speed engines, the thermal emissions of the cooling systems have a temperature of 355…365 K. Given the small exegetical potential, the use of such low-temperature waste energy sources by any heat engines is a difficult problem. Therefore, the task of improving existing energy-saving technologies or developing new ones remains relevant. Thermoacoustic technologies can be useful in solving this problem. A significant advantage of thermoacoustic heat machines is the ability to use any external heat source, in this case low-temperature sources, and produce mechanical work. There are known cases of thermoacoustic oscillations at small temperature differences between heat sources under conditions of high humidity of the working environment. This phenomenon can be used to create low-temperature energy-saving systems based on thermoacoustic engines (TAE) with a wet two-phase working environment. The practical use of thermoacoustic systems as part of ship power plants requires additional research to solve low-level issues, in particular, increasing the specific power of the TAE. This work provides a description of the experimental equipment, design of experimental TAE with a wet working body and research methods. The results of the experiments showed that in experimental TAEs with a two-component (moist) working environment, the temperature of spontaneous thermoacoustic oscillations was 355…359 K, while the longitudinal temperature gradient in the matrix was 1.19…1.30 K/m. The specific power of TAE with a moist environment increased by 1.7…7 times, and the acoustic pressure increased by 2…4.7 times compared to the operation in dry air. It is shown that in the existing TAEs, the condensation of water vapor in the ceramic matrix and on the surfaces of the heat exchangers can lead to a loss of power, roughly up to 25 %, while maintaining the operational capacity.

Prediction of Thermoacoustic Instability and Fluid–Structure Interactions for Gas Turbine Combustor

Abstract This work simulates a laboratory-scale three-dimensional methane/air burner, which features a bluff body stabilized, lean partially premixed flame experiencing strong limit cycle oscillations. A thin steel liner is installed around the combustion chamber, which heavily interacts with the flow field and produces large amplitude structural deformation via fluid–structure interaction (FSI). An unsteady Reynolds averaged Navier–Stokes (URANS) approach uses the shear stress transport (SST) turbulence model and a flamelet generated manifold (FGM) combustion model to predict the thermoacoustic oscillations in the turbulent reacting flow. The solver also has a built-in finite element structure model, which solves the structural governing equations simultaneously with the computational fluid dynamics (CFD)-computed, finite volume flow equations. This way, a fully coupled, two-way FSI simulation can be performed to predict the thermoacoustic instabilities and the associated solid deformations in the burner. Overall, the predicted strongest pressure oscillation and wall displacement modes (frequency and amplitude) are all in good agreement with the experimental data across different operating conditions. The established workflow may support realistic gas turbine combustor design and prognosis.

Dynamical states and bifurcations in coupled thermoacoustic oscillators.

The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a comprehensive theoretical study on the manifestation of these exquisite phenomena in a reduced-order model of two coupled Rijke tube oscillators, which are prototypical thermoacoustic oscillators. We characterize the dynamical behaviors of two such identical and non-identical oscillators by varying both system parameters (such as the uncoupled amplitudes and the natural frequencies of the oscillators) and coupling parameters (such as the coupling strength and the coupling delay). The present model captures all the dynamical phenomena-namely, synchronization, phase-flip bifurcation, amplitude death, and partial amplitude death-observed previously in experiments on coupled Rijke tubes. By performing numerical simulations and deriving approximate analytical solutions, we systematically decipher the conditions and the bifurcations underlying the aforementioned phenomena. The insights provided by this study can be used to understand the interactions between multiple cans in gas turbine combustors and develop control strategies to avert undesirable thermoacoustic oscillations in them.

Dynamic behavior and driving region of thermoacoustic combustion oscillations in a swirl-stabilized turbulent combustor

We attempt to identify the driving region of combustion oscillations by methodologies based on symbolic dynamics, synchronization, and complex networks. As the equivalence ratio is increased, the dynamic behavior of pressure fluctuations transitions from a stable combustion state to high-amplitude combustion oscillations via type-II intermittent combustion oscillations and the subsequent low-amplitude combustion oscillations. Rayleigh index-based transition network entropy is a useful indicator for determining the driving region of low-amplitude combustion oscillations. We clearly observe that a critical slowing down begins to appear in the combustion state close to the formation region of type-II intermittent combustion oscillations with temporally increasing equivalence ratio.

Rijke tube: A nonlinear oscillator.

Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.

Spontaneous and explicit symmetry breaking of thermoacoustic eigenmodes in imperfect annular geometries

This article deals with the symmetry breaking of azimuthal thermoacoustic modes in annular combustors. Using a nominally symmetric annular combustor, we present experimental evidence of a predicted spontaneous reflectional symmetry breaking, and also an unexpected explicit rotational symmetry breaking in the neighbourhood of the Hopf bifurcation which separates linearly stable azimuthal thermoacoustic modes from self-oscillating modes. We derive and solve a multidimensional Fokker–Planck equation to unravel a unified picture of the phase space topology. We demonstrate that symmetric probability density functions of the thermoacoustic state vector are elusive, because the effect of asymmetries, even imperceptible ones, is magnified close to the bifurcation. This conclusion implies that the thermoacoustic oscillations of azimuthal modes in real combustors will systematically exhibit a statistically dominant orientation of the mode in the vicinity of the Hopf bifurcation.

Quenching and amplification of thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling.

We numerically explore the quenching and amplification of self-excited thermoacoustic oscillations in two nonidentical Rijke tubes interacting via time-delay and dissipative coupling. On applying either type of coupling separately, we find that the presence of nonidentical heater powers can shrink the regions of amplitude death in both oscillators, while producing new regions of amplitude amplification in the weaker oscillator. We find that the magnitude of amplitude amplification grows with the heater power mismatch and with the total power input. These effects are also present when both types of coupling are applied simultaneously. This study highlights the critical role that nonidentical thermal loads can play in determining the amplitude response of coupled thermoacoustic systems, facilitating the design of control strategies for coupled oscillatorlike devices such as gas turbines.

Cryogenic thermoacoustics in the SPIRAL2 LINAC

SPIRAL2 is a superconducting LINAC subject to cryogenic thermoacoustic oscillations occurring in its valves boxes. 4 years of monitoring and experimental investigations with thousands of datasets turned these unwanted effects into an opportunity to study and understand thermoacoustics in a complex environment such as a real life accelerator. Without digging deep into Rott’s thermoacoustics theory, thoroughly shown in other works, this paper describes the instrumentation and the methods that prepare more advanced modeling of these phenomena either to damp or to harness the energy of cryogenic thermoacoustics.

Numerical simulation of nonlinear phenomena in a standing-wave thermoacoustic engine with gas-liquid coupling oscillation

• A CFD model of gas-liquid standing-wave thermoacoustic engine is developed and experimentally verified. • Time-domain impedance boundary condition is employed to truncate the modelling of liquid column. • Entire transient evolution of self-excited thermoacoustic oscillation from onset to saturation is captured. • Three different acoustic streamings are observed through inspecting the time-averaged mass flux field. A computational fluid dynamics (CFD) model based on the compressible, nonlinear Navier-Stokes equations is developed to simulate the nonlinear phenomena in a gas-liquid standing-wave thermoacoustic engine, which employs gas as the working fluid and liquid as the phase-matching element. The CFD model is well validated when comparing the simulated onset and steady-state performances with those measured from a real experimental system. Based on the CFD model, the nonlinear phenomena of the engine are analyzed from three aspects. Firstly, the nonlinear dynamic phenomena of self-excited thermoacoustic oscillation from onset to saturation are investigated, focusing on onset temperature difference and steady-state pressure amplitude. Then, the nonlinear acoustic phenomena of the engine operating at steady state are analyzed. The steady-state fluctuating pressure is decomposed into a superimposition of the acoustic modes with different frequencies, which reveals the existence of high-order harmonics. Finally, the nonlinear hydrodynamic phenomena including multi-dimensional flow effect and mass streaming are observed by examining the steady-state flow fields in the engine. The proposed CFD model provides an effective approach to comprehending the mechanism of nonlinear phenomena in gas-liquid coupling thermoacoustic engines.

On the impact of H[formula omitted]-enrichment on flame structure and combustion dynamics of a lean partially-premixed turbulent swirling flame

Large Eddy Simulation (LES) with Conjugate Heat Transfer (CHT) is used to analyze the impact of H2-enrichment on the flame structure and combustion dynamics of a lean partially-premixed turbulent CH4/Air swirling flame. Experimentally, the combustor is operated at atmospheric pressure with H2 fuel fractions of up to 50%, by volume. LES-CHT results are compared and validated against time-resolved stereo PIV, OH* chemiluminescence, OH-PLIF imaging and acoustic pressure measurements. In terms of dynamics, for the pure CH4 and 20% of H2 enrichment cases, no thermoacoustic oscillation is observed in either the experimental or numerical data. As the fuel fraction of hydrogen is increased, the flame length reduces due to the increase in laminar flame speed and the heat release rate distribution becomes more compact. CHT simulations reveal that H2-enrichment leads to higher temperatures at the centerbody tip. At 50% H2, in agreement with experiments, LES predicts a bi-modal thermoacoustic oscillation, with two main frequencies corresponding to the quarter and chamber modes of the system. Dynamic Mode Decomposition is performed on the measured OH-PLIF images and LES 3D fields to extract each mode contribution to the overall flame dynamics. It is observed that both modes are characterized by local variations of equivalence ratio, while only the higher frequency (chamber) mode is characterized by vortices periodically detaching from the backplane and the centerbody walls causing a strong periodic wrinkling of the flame front during the thermoacoustic oscillation.

Assessment of thrust chamber stability margins to high-frequency oscillations based on mathematical modeling of coupled ‘injector – rocket combustion chamber’ dynamic system

High-frequency instability of a liquid-propellant rocket engine (LRE) during static firing tests is often accompanied by a significant increase in dynamic loads on the combustion chamber structure, often leading to a chamber destruction. This dynamic phenomenon can also be extremely dangerous for the dynamic strength of a liquid-propellant rocket engine. The calculation of acoustic combustion product oscillation parameters is important in the design and static firing tests of such rocket engines. The determination of the oscillation parameters (natural frequencies and stability margins such as oscillation decrement) is one of the problems solved in the LRE design period as part of the development of measures to ensure the engine stability. The main aim of the paper is to develop a numerical approach to determining the parameters of acoustic oscillations of combustion products in liquid-propellant rocket engines combustion chambers taking into account the features of combustion space configuration and the variability of gaseous medium physical properties depending on the axial length of the chamber, acoustic impedance in critical throat and dissipation effects (damping experimental values) in the shell structure and the gas media in the chamber. The approach is based on mathematical modeling of the coupled ‘chamber shell structure – gas’ dynamic system by using the finite element method and the CAE (Computer Aided Engineering) system. The developed approach testing and further analysis of the results for the RD 253 engine using nitrogen tetroxide and unsymmetrical dimethylhydrazine as a propellant pair were carried out. The dynamic system shapes and frequencies of longitudinal, tangential and radial modes are determined. The results of mathematical modeling of the dynamic system indicate a satisfactory agreement of the calculated decrements of the first longitudinal oscillation mode and third tangential oscillation mode with the experimental decrements obtained by hot-fire tests data. From system harmonic analysis of the thrust chamber, it follows that the dynamic pressure gain factor of the gas media in the chamber at the first longitudinal mode frequency is 1.6 times greater than the system dynamic gain in the tangential mode. At the same time, the oscillation decrement for the system tangential mode is 2 times smaller than that of the first longitudinal mode. This means that the thrust chamber tangential mode is more dangerous and can lead to rocket engine combustion instability. The effect of the injector on the high-frequency stability of the combustion chamber and the possibility of partial suppression of combustion chamber thermoacoustic oscillations by adjusting the high-frequency dynamics of the injector are shown theoretically.

Optimizing combustion systems to mitigate thermoacoustic instabilities

Simulations capture thermoacoustic oscillations to reduce greenhouse gases, improve operation of combustors under lean fuel-air premixed conditions

Determination of the heat conduction transfer function within the thermoacoustic instability limit cycle in a Rijke tube

In this work, experimental measurements of the heat conduction transfer function (HCTF) within the limit cycle of thermoacoustic instabilities were conducted associated with a feedback controller. The responses of the heat conduction from the heater to the air in the vicinity to the oncoming flow disturbance can be described as the HCTF. When self-excited thermoacoustic instability occurs, it is not possible to measure the HCTF. The measurement experiment is twofold. Firstly, the active feedback control is applied to suppress the self-excited thermoacoustic oscillation in the Rijke tube. Secondly, the two-microphone method is applied to achieve the measurement of the HCTF at different working conditions. Experimental results show that the mean air flow velocity has an effect on the attenuation time of the thermoacoustic oscillation. Both of the mean air flow velocity and the electric-heating power have a significant effect on HCTFs.

Numerical investigation on oscillations characteristics of self-excited thermoacoustic system forced by acoustic wave

Self-excited thermoacoustic oscillations usually occur in many practical systems such as rocket motors, gas turbines and cryogenic distribution systems. We study the dynamics of a self-excited cryogenic thermoacoustic system subjected to acoustic forcing. The effect of the driving phase on the amplitude of the coupled oscillation is analyzed and the results present two states. To provide a guide for the selection of driving signal, the dynamics of a self-excited cryogenic thermoacoustic system subjected to acoustic forcing are investigated. When ϕ=30°, the radius of the limit cycle gradually shrinks, and self-oscillation amplitude is suppressed by 99.5%. For small driving phase, the self-oscillation can be suppressed, while for large driving phase, the phase portraits depict period-1 limit cycle oscillations. The results show that excessive driving phase has unfavorable effect on self-excited oscillation, and small drive phase can achieve oscillation suppression better. To reveal the coupling mechanism of externally forced oscillation and system self-excited oscillation, the phase relationships between self-excited oscillations and coupling pressure fluctuation waves in different periods are analyzed. Hence, the work indicates that under low-frequency disturbances, the system oscillation will have a phase delay, which will cause the hysteresis dissipation and restrain the system oscillation.

Numerical simulation of thermo-acoustic gas oscillation for nuclear application

Numerical simulations are performed to study the characteristics of thermo-acoustic oscillation of a gas confined in a loop-type pipe with the section of short and narrow channels. In order to simulate the irreversible heat exchange between the gas and the pipe wall, the compressible mass, momentum and energy conservation equations are solved in the loop pipe as well as the heat conduction equations in the pipe wall. Spontaneous oscillations are obtained when the temperature gradient along the narrow channel becomes large. It is found that the onset temperature of simulated thermo-acoustic oscillation agrees with that of the stability analysis and increases when the effect of gravity is not taken into account.

Synchronization and chimeras in a network of four ring-coupled thermoacoustic oscillators

We take a complex systems approach to investigating experimentally the collective dynamics of a network of four self-excited thermoacoustic oscillators coupled in a ring. Using synchronization metrics, we find a wide variety of emergent multi-scale behaviour, such as (i) a transition from intermittent frequency locking on a $\mathbb {T}^{3}$ quasiperiodic attractor to a breathing chimera, (ii) a two-cluster state of anti-phase synchronization on a periodic limit cycle, and (iii) a weak anti-phase chimera. We then compute the cross-transitivity from recurrence networks to identify the dominant direction of the coupling between the heat-release-rate ($q^{\prime }_{\mathbb {X}}$) and pressure ($p^{\prime }_{\mathbb {X}}$) fluctuations in each individual oscillator, as well as that between the pressure ($p^{\prime }_{\mathbb {X}}$ and $p^{\prime }_{\mathbb {Y}}$) fluctuations in each pair of coupled oscillators. We find that networks of non-identical oscillators exhibit circumferentially biased $p^{\prime }_{\mathbb {X}}$–$p^{\prime }_{\mathbb {Y}}$ coupling, leading to mode localization, whereas networks of identical oscillators exhibit globally symmetric $p^{\prime }_{\mathbb {X}}$–$p^{\prime }_{\mathbb {Y}}$ coupling. In both types of networks, we find that the $p^{\prime }_{\mathbb {X}}$–$q^{\prime }_{\mathbb {X}}$ coupling can be symmetric or asymmetric, but that the asymmetry is always such that $q^{\prime }_{\mathbb {X}}$ exerts a greater influence on $p^{\prime }_{\mathbb {X}}$ than vice versa. Finally, we show through a cluster analysis that the $p^{\prime }_{\mathbb {X}}$–$p^{\prime }_{\mathbb {Y}}$ interactions play a more critical role than the $p^{\prime }_{\mathbb {X}}$–$q^{\prime }_{\mathbb {X}}$ interactions in defining the collective dynamics of the system. As well as providing new insight into the interplay between the $p^\prime_{\mathbb{X}}\text{--}p^\prime_{\mathbb{Y}}$ and $p^\prime_{\mathbb{X}}\text{--}q^\prime_{\mathbb{X}}$ coupling, this study shows that even a small network of four ring-coupled thermoacoustic oscillators can exhibit a wide variety of collective dynamics. In particular, we present the first evidence of chimera states in a minimal network of coupled thermoacoustic oscillators, paving the way for the application of oscillation quenching strategies based on chimera control.

Observation of reactive shear layer modulation associated with high-frequency transverse thermoacoustic oscillations in a gas turbine reheat combustor experiment

This paper presents the investigation of high-frequency thermoacoustic oscillations and associated flame dynamics in an experimental gas turbine reheat combustor at atmospheric pressure. Examination of dynamic pressure measurements reveals bursts of high-frequency periodic oscillations which appear randomly amidst stochastic fluctuations in the reheat combustor. Analysis of the flame dynamics during these bursts of periodic behaviour reveals that increased heat release in the reactive shear layers of the reheat flame is associated with greater thermoacoustic driving potential. This redistribution of heat release is likely due to the stochastic nature of auto-ignition kernel formation. To determine the underlying flame-acoustic coupling mechanism behind the driving potential, phase-resolved flame dynamics over the acoustic cycle are investigated which reveal the presence of an oscillatory heat release pattern associated with the first transverse eigenmode. An in-phase interaction between the acoustic field and these heat release oscillations in the shear layer regions indicates that this phenomenon likely constitutes a thermoacoustic driving mechanism. This is an important step towards the development of models for high-frequency thermoacoustic driving mechanisms relevant to reheat combustion systems, which will allow accurate prediction and mitigation of thermoacoustic instabilities in future designs.

Hybrid CFD/low-order modeling of thermoacoustic limit cycle oscillations in can-annular configurations

We propose a hybrid strategy for modeling non-linear thermoacoustic phenomena, e.g. limit-cycle (LC) oscillations, in can-annular combustion systems. The suggested model structure comprises a compressible CFD simulation limited to the burner/flame zone of one single can, coupled to a low-order model (LOM) representing the remaining combustor. In order to employ the suggested strategy for modeling non-linear phenomena like LC oscillations, the LOM must capture non-linear flame dynamics in the cans, which are not resolved by CFD. Instead of identifying such non-linear flame models in preliminary simulations, we aim at learning the non-linear dynamics “on-the-fly”, while simulating the self-excited system under consideration. Based on the observation of flame dynamics in the CFD domain, the parameters of the employed non-linear models are estimated during run time. The present study reveals that block-oriented models, which comprise a linear dynamic part followed by a static non-linear function, are well suited for this purpose. The proposed hybrid model is applied to a laminar can-annular combustor. Results agree well with the monolithic CFD simulation of the entire combustor, while the computational cost is drastically reduced. The employed flame models, whose parameters are identified during the simulation of the self-excited LC oscillation, represent well the relevant non-linear dynamics of the considered flame.

Coupling-induced instability in a ring of thermoacoustic oscillators.

Thermoacoustic instabilities in can-annular combus-tors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multiscale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillators model of an idealized can-annular combustor. The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighbouring cans. Using a Bloch-wave ansatz, the resulting system is reduced to a single equation for the frequency spectrum. A linear stability analysis is then performed to study the perturbation of the spectrum by the can-to-can interaction. It is observed that the acoustic coupling can suppress or amplify thermoacoustic instabilities, raising the potential for instabilities in nominally stable systems.

Effects of Intrinsic Flame Instabilities on Thermoacoustic Oscillations in Lean Premixed Gas Turbines

Abstract Thermoacoustic instabilities are commonly encountered in the development of aeroengines and rocket motors. Research on the fundamental mechanism of thermoacoustic instabilities is beneficial for the optimal design of these engine systems. In the present study, a thermoacoustic instability model based on the lean premixed gas turbines (LPGT) combustion system was established. The longitudinal distribution of heat release caused by the intrinsic instability of flame front was considered in the model. Effects of different heat release distributions and characteristic parameters (Lewis number Le, Zeldovich Number β, and Prandtl number Pr) of the premixed gas on thermoacoustic instability behaviors of the LPGT system were investigated based on the established model. Results show that the LPGT system features have two kinds of unstable thermoacoustic modes. The first one corresponds to the natural acoustic mode of the plenum and the second one corresponds to that of the combustion chamber. The characteristic parameters of the premixed gases have a large impact on the stability of the system and can even change the system from stable to unstable state.