Thermoacoustic Oscillations Research Articles

Fast and Unbiased Determination of Dominant Frequencies and Amplitude of Thermoacoustic Oscillations

Reported is a three-step procedure (also referred to as the observer) for fast and unbiased determination of the dominant frequencies and amplitude of thermoacoustic oscillations. The first step is to determine the rang of the dominant frequency by computing the amplitude at frequency bins uniformly distributed from the lowest possible frequency to the Nyquist frequency (i.e., one-half of the sampling frequency) with a strategically specified, widely spaced frequency-bin separation. The other steps are to refine the estimation. The frequency estimation becomes unbiased after step 2, and the error (or uncertainty) is insensitive to the signal-to-noise ratio. The computational complexity can be orders-of-magnitude lower than the discrete Fourier transform and the fast Fourier transform, and the accuracy is no longer limited by , where and refer to the sampling frequency and the data length, respectively. This Paper recommends that the frequencies and amplitude be estimated every two pressure cycles. Cycle-to-cycle (or short-term) variations in the frequencies and amplitude are well resolved for thermoacoustic oscillations in three different real devices exhibiting quasi-steady oscillations before the onset of combustion instabilities and spontaneous instabilities (i.e., linearly unstable oscillations) with different levels of nonlinearities, respectively.

Combustion modes and driving mechanisms of pressure fluctuation in a novel vortex-tube combustor with quasi-steady and stratified properties

The operating limit and pressure fluctuations of a localized stratified vortex-tube combustor (LSVC) are investigated experimentally by taking methane as fuel at the inlet temperature of 300 K and the combustor pressure of 1 atm over a range of equivalence ratios (0.1–1.0). The combustion modes are distinguished according to the properties of pressure fluctuations and the driving mechanisms of each combustion mode are explored in combination with numerical simulation. The results show that the LSVC can realize stable combustion with pressure fluctuation amplitudes always less than 4 kPa in a large operating range, and the flame front is always continuous. The operating flammability limit experimental range can be divided into five regimes with different combustion modes. The first and fifth combustion modes are steady combustion with pressure fluctuation amplitudes less than 1 kPa, and the second to fourth ones are quasi-steady combustion with pressure fluctuation amplitudes between 1–4 kPa. The spectrum analyses of pressure fluctuations show that there are one low-frequency peak around 300 Hz and one high-frequency peak around 1500 Hz, which are dominated by the first and third axial natural acoustic modes of resonant oscillation combustion, respectively. In the first and fifth combustion modes, the resonances are both weak due to the influences of low flow rate and laminarization respectively. In the second mode, the thermo-acoustic coupling oscillation and the resonance are excited simultaneously, yielding the highest pressure fluctuation amplitude in the entire operating range. The high-frequency resonance causes the high-frequency pressure fluctuation of the third mode. Both the unsteady heat release and flow field affect the pressure fluctuation in the fourth mode. The former produces the low-frequency fluctuation, which can resonate with the natural frequency and excite a weak thermal-acoustic coupling.

Amplitude death phenomenon and modulation of thermoacoustic oscillation in cryogenic systems

In this paper, an innovative method of adopting a piping insert with an abrupt contraction or expansion structure has been proposed to eliminate undesirable thermally driven gas oscillations in cryogenic systems. In addition, the influences of the piping inserts’ geometrical parameters and position on the performance of thermoacoustic oscillation in cryogenic systems have been investigated. A series of simulations has been conducted, and simulation bifurcation diagrams show that thermoacoustic oscillation can be completely stopped, which, in other words, is called the amplitude death (AD) phenomenon. When the pipeline inserts are equipped in the cold part, AD can be achieved regardless of the pipeline inserts’ radius. When the pipeline inserts are located in the warm part, AD can be realized by the pipe inserts with an abrupt contraction. The identification of nonlinear characteristics of different state transitions with different insert geometries is further conducted by unfolding these original time series in an embedding space. The nonlinear change process of thermoacoustic oscillation is demonstrated in the phase space diagrams. As the insert radius increases, the system transforms from a periodic state to a quasi-periodic state and then from a quasi-periodic state to an AD state. This work will have practical impacts on the design of oscillation-free piping systems.

Erratum: “Experiments on Self-excited Thermoacoustic Oscillations in an Air-filled Looped Tube with a Pair of Stacks” [J. Phys. Soc. Jpn. 87, 104401 (2018)

Erratum: “Experiments on Self-excited Thermoacoustic Oscillations in an Air-filled Looped Tube with a Pair of Stacks” [J. Phys. Soc. Jpn. 87, 104401 (2018)

Characteristics of thermoacoustic conversion and coupling effect at different temperature gradients

The thermoacoustic engine that can convert heat into sound offers a promising methodology of energy usage. However, the low energy conversion rate limited the exploitation of this technology. To obtain high acoustic power and energy outputs, effects of temperature gradients on thermoacoustic characteristics were numerically investigated in this study. The results indicated that temperature gradients had significant impacts on the output sound pressure and heat flux. Meanwhile, complicated coupling effects among the temperature, fluid velocity and sound pressure were observed during the thermoacoustic oscillations. Deep insight into the phase changes implied that the temperature difference would initiate the oscillations of the fluid movement and induce the sound pressure afterwards. The study also demonstrated that large temperature differences and abrupt temperature changes were favorable for the acoustic power output.

Characterizing nonlinear dynamic features of self-sustained thermoacoustic oscillations in a premixed swirling combustor

To meet stringent NOx emission requirements, lean premixed swirling combustion technology is widely applied in power generation and propulsion systems. However, such combustion systems are more susceptible to nonlinear combustion instability due to the fluid flow-acoustics-combustion interaction. It is typically self-exited and characterized by large-amplitude pulsating oscillations. By applying experimental measurements and theoretical modelling, we explore the rich physics of how a methane-burnt swirling flame sustains periodic pulsating combustion oscillations, and its nonlinear dynamics features via recurrence plots (RP) and 0–1 chaotic test. The effects of (1) the equivalence ratio Φ, (2) the volume flow rate Va of inlet air and (3) the swirling number SN are examined. Hopf Supercritical and period-doubling bifurcation behaviours are experimentally observed with increased Φ from lean to rich combustion. Same nonlinear features are theoretically modelled by using ‘kick-oscillator’ model representing combustion pulses and to capture periodic limit cycle behaviours followed by period-doubling bifurcation and transition to chaos. The deterministic or chaotic nature of the swirling combustor could be experimentally identified using classical approaches such as probability density functions (PDFs) and acoustics power spectrum in presence of combustion-sustained periodic fluctuations and 0–1 chaotic test method. When the combustor is experimentally operated under either lean (Φ ≤ 0.6) or rich (Φ ≥ 1.1) conditions, no self-sustained periodic acoustic fluctuations are generated. Furthermore the combustor is found to be more chaotic. The flame shapes (M- or V-shaped), colour, brightness and volumes are found to depend on SN strongly. The present findings are physically insightful on understanding nonlinear features of swirling flow-acoustics-flame interaction.

Solution of Thermoacoustic Eigenvalue Problems With a Noniterative Method

Abstract Gas turbine combustors are prone to undesirable combustion dynamics in the form of thermoacoustic oscillations. Analysis of the stability of thermoacoustic systems in the frequency domain leads to nonlinear eigenvalue problems (NLEVP); here, “nonlinear” refers to the fact that the eigenvalue, the complex oscillation frequency, appears in a nonlinear fashion. In this paper, we employ a noniterative strategy based on contour integration in the complex eigenvalue plane, which returns all eigenvalues inside the contour. An introduction to the technique is given, and is complemented with guidelines for the specific application to thermoacoustic problems. Two prototypical nonlinear eigenvalue problems are considered: a network model of the classical Rijke tube with an analytic flame response model and a finite element discretization of an annular model combustor with an experimental flame transfer function (FTF). Computation of all eigenvalues in a domain of interest is vital to assess stability of these systems. We demonstrate that this is generally challenging for iterative strategies. An eigenvalue solver based on contour integration, in contrast, provides a reliable, noniterative method to achieve this goal.

Mutual synchronization of two flame-driven thermoacoustic oscillators: Dissipative and time-delayed coupling effects.

Low-emissions can-annular gas turbines are prone to develop low-frequency self-excited thermoacoustic oscillations. Such oscillations arise from the coupling between adjacent combustors and can increase wear and thermal stresses. In this experimental study, we explore the mutual synchronization of two thermoacoustic oscillators (i.e., two model combustors) interacting via dissipative and time-delayed coupling, as introduced via a cross-talk section. Unlike most previous studies, our study makes use of a turbulent lean-premixed flame in each combustor, bringing the system configuration closer to that of practical gas turbines. Using stationary and transient measurements, we examine the effect of the cross-talk diameter and length so as to gain insight into the effect of dissipative and time-delayed coupling. We find that strengthening the dissipative coupling promotes mutual synchronization, but that weakening the dissipative coupling leads to weakly coupled or desynchronized oscillations. On operating the two combustors at different conditions, we find a significant reduction in their overall oscillation amplitude for some coupling conditions. On varying the combustor length and examining the transient response, we find elaborate changes in the pressure-heat-release-rate coupling, spontaneous mode transitions between coupled thermoacoustic modes, and the emergence of a rhomboid structure in the phase plane owing to the coexistence of in-phase and out-of-phase synchronization. In the combustion community, these two types of synchronization are known to be associated with push-push modes and push-pull modes. These findings offer new insight into the mutual synchronization of low-frequency, self-excited thermoacoustic oscillations in can-annular gas turbines, paving the way for the development of improved control strategies.

The thermoacoustic instability in a stratified swirl burner and its passive control by using a slope confinement

•Mechanisms of thermoacoustic oscillations in the dump confinement are elucidated.•A passive control method is proposed by using the slope confinement.•This method suppresses the flame front wrinkling and flame root angle fluctuation.•The slope confinement reduces the gain of the flame transfer function.•This reduction of the gain enhances the system thermoacoustic stability.

Active control of thermoacoustic instability using microsecond plasma discharge

The thermoacoustic instability produced in a simple heat-driven-acoustic-oscillation device (so-called Rijke tube) has been controlled by the periodic plasma discharge. A perforated plate is placed at the upstream of the tube as the heater. Due to the interaction between the heat and acoustic waves, thermoacoustic instabilities occur. The high-voltage microsecond pulsed plasma is generated within pin-to-pin electrodes that are used as an actuator since the pressure wave generated by the plasma is quite strong and able to attenuate the thermoacoustic sound wave in the Rijke tube. However, since the pressure waveform generated by the plasma discharge is different from the sinusoidal signal that is generated by a loudspeaker and widely used as a control actuator, it is necessary to derive the new model from the simplified Rijke tube. The time domain oscillation simulation is conducted, and the phase shift method is used to find appropriate control strategy. The discharge pressure waveform is subsequently fitted with an eighth-order Fourier series, and the overall Fourier signal is adjusted so that the first-order waveform in the discharge was similar to the analog sinusoidal control signal; the control is quite effective. It is known that when the sinusoidal control waveform of same frequency as thermoacoustic instability can meet control requirements, the non-sinusoidal signal can also control the thermoacoustic instability. Finally, according to the simulation results, the high-voltage microsecond plasma discharge is adjusted to the suitable amplitude and phase used for closed-loop control on the thermoacoustic oscillation, which significantly suppressed the instability.

Input-output system identification of a thermoacoustic oscillator near a Hopf bifurcation using only fixed-point data.

We present a framework for performing input-output system identification near a Hopf bifurcation using data from only the fixed-point branch, prior to the Hopf point itself. The framework models the system with a van der Pol-type equation perturbed by additive noise, and identifies the system parameters via the corresponding Fokker-Planck equation. We demonstrate the framework on a prototypical thermoacoustic oscillator (a flame-driven Rijke tube) undergoing a supercritical Hopf bifurcation. We find that the framework can accurately predict the properties of the Hopf bifurcation and the limit cycle beyond it. This study constitutes an experimental demonstration of system identification on a reacting flow using only prebifurcation data, opening up pathways to the development of early warning indicators for nonlinear dynamical systems near a Hopf bifurcation.

A Backstepping-based observer for estimation of thermoacoustic oscillations in a Rijke tube with in-domain measurements

This paper presents an observer design for estimation of thermoacoustic instabilities in a Rijke tube. To study this problem, we consider that the acoustic dynamics is represented by the wave equation with a point source term representing the heat release. In turn, the heat release dynamics is given by a first-order ordinary differential equation (ODEs). The observer, whose design is based on the backstepping methodology, relies on measurements of acoustic pressure and velocity at an arbitrary point of the domain. The design employs a folding transformation (with two folds) around the measurements and the heat release point, allowing to write the system into a form with more states but boundary measurements and ODE couplings. Then, we formulate a well-posed and invertible integral transformation with both triangular and full terms that maps the observer error dynamics into an exponentially stable target system. The theoretical results were tested through numerical simulations in order to show the effectiveness of the design.

Rijke Organ: Modeling and Control of Array of Rijke Tubes

Rijke tube is a popular physical experiment demonstrating a spontaneous generation of sound in an open vertical pipe with a heat source. This laboratory instance of thermoacoustic instability has been researched due to its significance in practical thermoacoustic systems. We revisit the experiment, focusing on the possible use of the Rijke tube as a musical instrument. The novelty presented in this paper consists in shifting the goal from sound suppression to active sound generation. This called for modifying the previously investigated methods for stabilization of thermoacoustic oscillations into their excitation and control of their amplitude. On our way towards this goal, we developed a time-domain mathematical model that considers the nonlinear and time-varying aspects of the Rijke tube. The model extends the existing modeling and analysis approaches, which are mainly based in frequency domain. We also present an extension of the basic laboratory setup in the form of an array of Rijke tubes equipped with a single speaker used to control multiple Rijke tubes with different natural frequencies simultaneously.

Procedure for calculating the thermoacoustic pressure fluctuations at boiling subcooled liquid

This paper reports a study of the thermoacoustic phenomena in steam-generating channels of the cooling system of heat-loaded devices. The examined cooling modes are characterized by surface boiling of the heat carrier, which occurs due to high heat flows at the cooled surface and large underheating of the flow core to the saturation temperature. Under such conditions, high-frequency pulsations of acoustic pressure may occur in cooling channels. It has been established that the emergence of thermoacoustic oscillations could lead to the formation of a standing wave in the channel, one of the conditions for whose formation is the presence of a wave reflection boundary. We have proposed a mathematical model describing the generation of thermoacoustic vibrations in a cooling channel. It was assumed that fluctuations with a high amplitude arise due to the resonance observed when the frequency of forced vibrations of steam bubbles coincides with the vapor-liquid column's natural frequency of vibrations or their harmonics. To calculate the amplitude of pressure fluctuations in the channel, the dependence has been derived, which takes into consideration the viscous dissipation of energy and energy losses at the ends of the channel. It has been shown that when approaching the resonance, the contribution of volumetric viscosity to the viscosity absorption factor increases. It has been established that for the examined conditions the losses of energy on the walls of the channel and losses in the boundary layer could be neglected. We have calculated the amplitude of thermoacoustic pressure fluctuations for conditions corresponding to actual processes in surface-boiling cooling channels. The reported procedure is proposed to be used in the design of liquid cooling systems for heat-loaded devices for which cooling modes imply a significant underheating of the heat carrier to a saturation temperature, as well as surface boiling

Study of Dynamic Behaviors of Thermoacoustic Oscillations by Using Laser Absorption Spectroscopy

The present work demonstrates the feasibility of dynamic characterization of thermoacoustic oscillations using temperature-based method. Experiment was conducted in a typical thermoacoustic system using a line-of-sight laser absorption measurement system. The unexpected laser beam steering and water vapor condensation encountered in the experiment were eliminated via adopting the optical integrating sphere and gas heating device, respectively. The measured temperature signals were compared and validated by the synchronous pressure signals obtained by a pressure transducer. Comparison results indicate that the dominant characteristic contained in temperature and pressure signals are consistent, but the temperature signals catch more detailed information than the pressure signals. To further extract transient features from the temperature signals, the multi-cycle average-based method and the time-frequency analysis based on the Hilbert-Huang transform were then conducted. The underlying mechanism responsible for the temperature characteristics were analyzed based on the multi-cycle averaged signals and HHT spectrum. Results show that the proposed temperature measurement method is effective in characterizing the transient temperature in the thermoacoustic oscillations. The temperature oscillations catch abundant information (e.g., obvious second harmonic component), which can provide comprehensive reference data for in-depth understanding of mechanism of the thermoacoustic oscillations.

Experimental Investigation on the Route to Vortex-acoustic Lock-In Phenomenon in Bluff Body Stabilized Combustors

ABSTRACT We investigate the phenomenon of vortex-acoustic lock-in in a bluff body stabilized Rijke type combustor, which experiences self-excited thermoacoustic oscillations. The focus is to identify and understand the various regions (in airflow rate) occurring during the transition to lock-in. In this regard, an axisymmetric bluff body stabilized burner is used, which sheds Benard–Von Karman vortices. The dynamics of the combustor is monitored through the measurement of unsteady pressure and heat release rate fluctuations. At low airflow rates, peaks associated with both vortex shedding and acoustic modes are observed in the measured spectra. These peaks are far apart. As the airflow rate is increased, vortex shedding frequency increases. At a certain flow rate, it reaches the acoustic frequency. Beyond this flow rate, large amplitude oscillations occur and only one common peak is observed in the spectra. This common peak has the frequency close to the acoustic mode of the duct. Vortex shedding process locks in to this common frequency and the phenomenon is termed as vortex-acoustic lock-in. We observe a series of well-defined regions that appear as the system progresses toward lock-in. In this paper, we made an attempt to understand the characteristics of these regions in a systematic manner. The study will help in developing lower-order models, which capture the essential dynamics of lock-in observed in vortex shedding combustors.

A reduced-order model of thermoacoustic instability in solid rocket motors

A finite-dimensional dynamical system is derived from a coupled system of partial differential equations modeling the thermoacoustic oscillations inside a solid rocket motor. The governing equations for the coupling between the chamber acoustics and combustion of the solid propellant are derived from conservation laws and existing combustion models. Model reduction is carried out for the unsteady burning rate model based on a pseudo-spectral truncation, leading to a three-dimensional dynamical system. The resulting low-dimensional dynamical system is shown to be able to capture the main bifurcation behavior of the original infinite-dimensional system. The reduced-order model can be used to predict the nonlinear thermoacoustic behavior of a solid rocket motor at reduced computation costs.

Time–frequency localisation of intermittent dynamics in a bistable turbulent swirl flame

This work examines the complex flow field in a bistable turbulent swirl flame, where the flame alternates irregularly between a lifted-off M-shape and an attached V-shape. The flow field consists of various types of intermittent dynamics due to flame-shape switching that occur on different time scales. In order to properly identify, separate and temporally resolve these dynamic components, a novel method of multiresolution proper orthogonal decomposition (MRPOD) is developed by interfacing the maximum overlap discrete wavelet packet transform (MODWPT) of multidimensional data series with the conventional snapshot POD. Specific care is taken to select the wavelet filter, decomposition level and reconstruction bandwidth to achieve variable spectral bandpasses and adequate temporal resolutions. When applied to data series from high-speed three-component velocity field measurements in the bistable swirl flame, MRPOD is capable of isolating frequency components that are usually lumped into a single POD mode, with enhanced spatial/temporal coherence for even weak and highly intermittent dynamics. Owing to the improved spectral purity, a series of previously unknown dynamics is uncovered alongside well-characterised instabilities such as the precessing vortex core (PVC) and thermoacoustic (TA) instabilities. In particular, a non-periodic switch mode is found to couple with the previously identified shift mode only during flame-shape transitions, with pronounced modifications on the backflow and near the inlet of the combustor, a region known to influence the growth rate of PVC. TA oscillations are seen to drive repetitive flame reattachment during M–V transitions that eventually settles into a V-flame. But sustained high TA amplitudes alone do not appear to necessarily presage the onset of such a transition. Additional higher-order harmonics of PVC and evidence of TA modulations on PVC dynamics are uncovered, which also exhibit bi-modal behaviours: while maintaining their characteristic frequencies, these instabilities could attain either a single or double helical structure and are only active during either V- or M-flame periods.

Stability, sensitivity and optimisation of chaotic acoustic oscillations

In an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic oscillations, also known as thermoacoustic instabilities, can cause large vibrations up to structural failure. Numerical and experimental studies showed that thermoacoustic oscillations can be chaotic. It is not yet known, however, how to minimise such chaotic oscillations. We propose a strategy to analyse and minimise chaotic acoustic oscillations, for which traditional stability and sensitivity methods break down. We investigate the acoustics of a nonlinear heat source in an acoustic resonator. First, we propose covariant Lyapunov analysis as a tool to calculate the stability of chaotic acoustics making connections with eigenvalue and Floquet analyses. We show that covariant Lyapunov analysis is the most general flow stability tool. Second, covariant Lyapunov vector analysis is applied to a chaotic system. The time-averaged acoustic energy is investigated by varying the heat-source parameters. Thermoacoustic systems can display both hyperbolic and non-hyperbolic chaos, as well as discontinuities in the time-averaged acoustic energy. Third, we embed sensitivities of the time-averaged acoustic energy in an optimisation routine. This procedure achieves a significant reduction in acoustic energy and identifies the bifurcations to chaos. The analysis and methods proposed enable the reduction of chaotic oscillations in thermoacoustic systems by optimal passive control. The techniques presented can be used in other unsteady fluid-dynamics problems with virtually no modification.

Analysis of degenerate mechanisms triggering finite-amplitude thermo-acoustic oscillations in annular combustors

A simplified model is introduced to study finite-amplitude thermo-acoustic oscillations in $N$-periodic annular combustion devices. Such oscillations yield undesirable effects and can be triggered by a positive feedback between heat-release and pressure fluctuations. The proposed model, comprising the governing equations linearized in the acoustic limit, and with each burner modelled as a one-dimensional system with acoustic damping and a compact heat source, is used to study the instability caused by cross-sector coupling. The coupling between the sectors is included by solving the one-dimensional acoustic jump conditions at the locations where the burners are coupled to the annular chambers of the combustion device. The analysis takes advantage of the block-circulant structure of the underlying stability equations to develop an efficient methodology to describe the onset of azimuthally synchronized motion. A modal analysis reveals the dominance of global instabilities (encompassing the large-scale dynamics of the entire system), while a non-modal analysis reveals a strong response to harmonic excitation at forcing frequencies far from the eigenfrequencies, when the overall system is linearly stable. In all presented cases, large-scale, azimuthally synchronized (coupled) motion is observed. The relevance of the non-modal response is further emphasized by demonstrating the subcritical nature of the system’s Hopf point via an asymptotic expansion of a nonlinear model representing the compact heat source within each burner.