Self-excited Acoustic Oscillations Research Articles

Incompressible versus compressible large eddy simulation for the identification of premixed flame dynamics

The present work compares the respective advantages and disadvantages of compressible and incompressible computational fluid dynamics (CFD) formulations when used for the estimation of the acoustic flame response. The flame transfer function of a turbulent premixed swirl-stabilized burner is determined by applying system identification (SI) to time series data extracted from large eddy simulation (LES). By analyzing the quality of the results, the present study shows that incompressible simulations exhibit several advantages over their compressible counterpart with equal prediction of the flame dynamics. On the one hand, the forcing signals can be designed in such a way that desired statistical properties can be enhanced, while maintaining optimal values in the amplitude. On the other hand, computational costs are reduced and the implementation is fundamentally simpler due to the absence of acoustic wave propagation and corresponding resonances in the flame response or even self-excited acoustic oscillations. Such an increase in efficiency makes the incompressible CFD/SI modeling approach very appealing for the study of a wide variety of systems that rely on premixed combustion. In conclusion, the present study reveals that both methodologies predict the same flame dynamics, which confirms that incompressible simulation can be used for thermoacoustic analyses of acoustically compact velocity-sensitive flames.

Mutual synchronization of self-excited acoustic oscillations in coupled thermoacoustic oscillators

Synchronization refers to the adjustment of rhythms of two nonidentical oscillators due to interaction. In this study, we report for the first time on the ability of computational fluid dynamics (CFD) to simulate the synchronization of self-sustained acoustic oscillations in two coupled thermoacoustic (TA) oscillators that interfere with each other through acoustic radiation. A bifurcation diagram containing both asynchronous and synchronous states is first mapped out by changing the end-to-end distance and the resonator length difference. It is found that the two TA oscillators are analogous to mutually coupled van der Pol oscillators with reactive coupling. Then, the dynamic characteristics of beating and periodic oscillations in asynchronous and synchronous states are analysed separately to facilitate the comprehension of the synchronization process. This research demonstrates that the CFD methodology provides a valuable numerical tool for studying the synchronization of thermally induced acoustic oscillations in TA systems.

Linear and nonlinear modeling of self-excited acoustic oscillations in a T-shaped thermoacoustic engine

Branch tubes are often used in thermoacoustic engines (TAEs) for acoustic power extraction or acoustic field adjustment. Their roles, although critical for the performance of the thermoacoustic system, are not fully understood yet. To address this issue, this study investigates the self-excited acoustic oscillations inside a T-shaped TAE where a branch tube is connected to a classical standing-wave TAE. First, system-level theoretical models based on the linear acoustic and thermoacoustic theories in the frequency domain were established to study the acoustic modes and their stability. System-wide computational fluid dynamics (CFD) simulations were carried out to simulate the evolution of the unstable acoustic modes from the initial start-up to the steady state in the time domain. Second, parametric studies on the coupling position of the branch tube and its length were conducted. The effects of the coupling position and branch length on the natural frequencies and mode shapes of the T-shaped TAE were determined by theoretical derivations and substantiated by CFD simulations. The growth/attenuation rate of each acoustic mode was also examined. The CFD results show that bifurcation in steady-state dynamics occurs when the coupling position is altered or the branch length is increased. The steady-state behavior of the T-shaped TAE can transit from limit-cycle oscillations to quasi-periodic oscillations, or vice versa. The theoretical and CFD methodologies in this work are valuable in comprehending the acoustic/dynamic characteristics of the T-shaped standing-wave TAE, providing useful guidelines for studying the coupling of external loads in traveling-wave thermoacoustic systems that usually have more complex structures but are inherently more efficient.

Underlying physics of limit-cycle, beating and quasi-periodic oscillations in thermoacoustic devices

Under certain circumstances, self-excited acoustic oscillations inside thermoacoustic systems exhibit beating and quasi-periodic patterns, in contrast to constant-amplitude limit-cycle oscillations regularly studied in the literature. This paper explores the underlying physics of limit cycles, beating and quasi-periodicity in thermoacoustic devices from acoustic/vibrational and thermodynamic/hydrodynamic perspectives. Firstly, the acousto-mechanical coupling between the thermoacoustic engine and external load is investigated using a lumped element model, which is verified against a distributed parameter model. The effect of external load on the natural frequencies and mode shapes of intrinsic oscillation modes is inspected. Secondly, the thermo-acoustic coupling between the temperature and acoustic fields is analysed using a reduced-order network model based on the linear thermoacoustic theory. The effect of thermoacoustic core on stability of oscillation modes is studied. Finally, the steady-state behaviour of the device is examined by considering the unsteady linear decay/growth and nonlinear saturation processes. This study demonstrates that the linear mode selection decides whether the steady state is static (quiescent) or dynamic. Apart from linear mode selection, the dynamic steady-state responses are also affected by nonlinear mode competition during the saturation process. Simultaneous excitement of oscillation modes at different external loads may lead to distinctively different steady-state waveforms including beating and quasi-periodicity. Discussions on the steady-state energy transition/conversion indicate that, to improve the performance of the thermoacoustic device, excitation of the oscillation mode whose frequency is close to that of the external load is encouraged. It is suggested that ultra-compliant transducers should be employed for better acoustic power extraction.

Acoustic Response of Multiple Shallow Cavities and Prediction of Self-Excited Acoustic Oscillations

Self-sustaining oscillations of flow over ducted cavities and in corrugated pipes are a known source of tonal noise and excessive vibration in industrial applications. Corrugated pipes can be modeled as a series of axisymmetric cavities. In the current study, the aero-acoustic sources generated by one-, two-, and three-cavity configurations have been experimentally investigated by means of the standing wave method (SWM) for a wide range of Strouhal numbers and acoustic excitation levels. The source strength is found to increase in a nonlinear manner with increasing the number of cavities. Moreover, the self-excited acoustic resonances of the same cavity combinations are investigated. The source characteristics are compared with the observed lock-in range from the self-excited experiments. A prediction model is also developed to utilize the measured source characteristics for estimating the amplitude of the cavities self-sustained oscillations. The self-excited experimental data are used to assess the effect of acoustic absorption at the cavity edges. This absorption is found to be substantial and must be accounted for in the prediction model. When the model is supplemented with appropriate loss coefficients, it predicts fairly well the pulsation amplitude within the resonance lock-in range of the studied multiple cavity configurations.

Nonlinear Interactions Between Forced and Self-Excited Acoustic Oscillations in Premixed Combustor

This paper describes an experimental investigation of the nonlinear interactions between self-excited and driven oscillations in a premixed swirl-stabilized combustor. This interaction is studied by externally forcing oscillations at some frequency, fdrive , in an unstable combustor oscillating at a frequency, fins . Above a certain amplitude of forcing, the self-excited oscillation amplitude decreases. In some cases, the self-excited oscillations can be eliminated almost completely, but in others the effect is slight. As such, in the former case, open-loop forcing is very effective in reducing the overall acoustic power. This paper characterizes a variety of features of these oscillations, such as the quenching amplitude, its dependence upon frequency spacing between the driven and natural modes, and the frequency shift of the unstable mode. Although not understood, it is observed that the key difference between cases where open loop forcing is and is not effective in reducing the overall acoustic power, is that the instability frequency stays roughly constant and changes with forcing amplitude, respectively.

A MODEL FOR THE THERMOACOUSTIC RESPONSE OF A PREMIXED SWIRL BURNER, PART I: ACOUSTIC ASPECTS

Results from previous measurements on a small laboratory swirl burner undergoing self-excited acoustic oscillations with premixtures of either CH4 or C3H8 are summarized. The measurements of acoustic pressure and the distribution of chemiluminescent emission were used to deduce semi-empirical descriptions of the flame response functions, and these are used here in conjunction with a validated model for the acoustics of the premixture supply system, burner, and combustion chamber to reproduce the excitation frequencies and to deduce the required amplitudes of the flame response function. Variations of the burner flow rate and the equivalence ratio are examined, as is the sensitivity of the results to the acoustic and flame parameters. The results are of considerable relevance to the response of industrial gas-turbine combustion systems, and the calculations lay the foundations for the fundamental model of the flame response that is derived in Part II.

Jet forking driven by pipe tone.

The present work deals with an experimental investigation of flow of air through a square-edged circular orifice at the downstream end of a circular duct. Self-excited acoustic oscillations at the natural duct modes are observed for certain flow velocities when the orifice is sufficiently thick. For a specific Reynolds number based on the orifice diameter and the mean jet velocity (9150 < Re < 9850), the jet forks into two trains, with the alternating vortices falling into the same branch of the forked train. Whereas this phenomenon has been reported earlier to have occurred when the density ratio of the jet is less than 0.72, the present results show that it is possible for a jet having the same density as the ambient atmosphere. The jet forking is coincident with jump in the acoustic frequency from one natural acoustic mode to another with comparable amplitudes of both the modes.

INTERACTION OF THE ACOUSTIC PROPERTIES OF A COMBUSTION CHAMBER WITH THOSE OF PREMIXTURE SUPPLY

If the response of a flame to acoustic waves is not known, it must be deduced from measurements in a system for which the acoustic impedances can be inferred. Measurements have been made on a simple combustion system in which gaseous propane is mixed with air in a cylindrical chamber of variable length before flowing up a burner tube. At the end of the tube, the premixture flows around a centre-body, behind which a flame is stabilized. When placed in cylindrical combustion chambers of two different lengths, the flame generates self-excited acoustic oscillations. These have been measured with pressure transducers at three different points and with a system for collecting the UV radiation from the whole flame at a wavelength of chemiluminescent emission. The data demonstrate that the acoustic transmission through the premixture supply system and through the combustion chamber can be described by standard one-dimensional acoustic theory, provided an appropriate choice of mean speed of sound in the combustion chamber is made. This then allows the jump in the volumetric acoustic fluxes across the flame to be calculated, and it is shown, by examination of the magnitude and phase of the transfer function, that this jump is proportional to the UV emission over a range of frequencies up to 800 Hz (a frequency corresponding to wavelengths of the order of the combustion chamber length). This relationship is in accordance with thermo-acoustic theory for a “thin” flame, if the UV emission can be taken as proportional to the instantaneous rate of heat release. The observations therefore validate both the experimental technique and the applicability of the theoretical assumptions, and lay the foundation for a more detailed study of the structural response of the flame.

Non-linear self-excited acoustic oscillations in cavities

Non-linear acoustic oscillations in covered cavities, excited by a jet which is wall-bounded on one side, are discussed on the basis of a second-order theory. With the shear layer at the free edge of the jet considered as a simple (stable) vortex sheet the matching conditions between the acoustic wave fields in the jet and the cavity are introduced in a general second-order equation for wave fields in rectangular resonators. This procedure leads to a second-order wave equation containing a time lag. Solutions are computed with the help of an evolution scheme and compared with experiments. Based upon a simple impedance model it is suggested that the wave equation may change its character when the shear layer at the free edge of the jet is strongly disturbed, with the interesting consequence that the oscillation amplitudes in the cavity are reduced significantly.

Nonlinear self-excited acoustic oscillations within fixed boundaries

In §1 a brief discussion of the general problem of self-excited acoustic oscillations within fixed boundaries is given. I n §2 a second-order analysis is developed for the special case of rectangular cavities. A nonlinear wave equation is derived for essentially arbitrary boundary conditions. The analysis can be extended to other cavity geometries provided that the first-order solutions can be expressed in closed form. Various applications of the analysis are discussed in §3. It turns out that two-dimensional problems of self-excited oscillations generally lead to nonlinear equations containing terms with a time lag. It is anticipated that the time lag (rather than viscous effects or sound radiation) represents the key to a fundamental understanding of the character of the oscillations and the variety of modes appearing in self-excited resonators.

Non-linear self-excited acoustic oscillations

The response of a gas column contained in a tube to a destabilizing boundary condition is investigated. For the special case where the particle velocity at an end wall of the tube is proportional to the pressure disturbance, a non-linear analysis is given for closed and open tubes (with and without mean flow). The inviscid solutions for closed tubes are sawtooth waves, for open tubes without mean flow they turn out to be essentially square waves and for open tubes with mean flow the tops and bottoms of the square waves become ramp-like.

Closure to "Discussions of 'Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations'" (1977, ASME J. Fluids Eng., 99, pp. 788–789)

Closure to "Discussions of 'Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations'" (1977, ASME J. Fluids Eng., 99, pp. 788–789)

Discussion: "Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations" (Hill, W. G., and Greene, P. R., 1977, ASME J. Fluids Eng., 99, pp. 520–525)

Discussion: "Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations" (Hill, W. G., and Greene, P. R., 1977, ASME J. Fluids Eng., 99, pp. 520–525)

Discussion: "Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations" (Hill, W. G., and Greene, P. R., 1977, ASME J. Fluids Eng., 99, pp. 520–525)

Discussion: "Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations" (Hill, W. G., and Greene, P. R., 1977, ASME J. Fluids Eng., 99, pp. 520–525)

Increased Turbulent Jet Mixing Rates Obtained by Self-Excited Acoustic Oscillations

A new device, capable of greatly increasing subsonic jet mixing rates, has been discovered. This device, which we have named the “whistler nozzle,” consists of a convergent nozzle section, a constant area section, and a step change to an exit section with a larger constant area. The exit section excites a standing acoustic wave in the constant area section, in a way similar to the action of an organ pipe. The result of this resonance is a loud pure tone and a greatly increased rate of jet mixing. The increased mixing rates appear related to the acoustically stimulated vortex shedding character (large scale structure or superturbulence) observed by Crow and Champagne [1] in their pioneering study of jets excited by a loudspeaker, and others utilizing upstream valves and pistons, except that the whistler nozzle is self-excited. The standing wave and the resulting increased mixing rates occur for a wide range of exit plane configurations and jet parameters.

Acoustical oscillation in a combustion system with a flat flame

Self-excited acoustic oscillations in a laboratory combustion system containing a premixed flat flame are investigated. The flat flame is stabilized by a copper matrix burner with about 700 deep ports and burns in a resonator tube (diameter 30 nm) of the same area. The system may therefore be treated one-dimensionally. The perturbing mechanisms under consideration are the oscillating reactant input and the oscillating heat transport from the flame to the burner matrix due to the particle displacement (which can be derived by integrating the particle velocity of the standing soundwave). No oscillations are found if the velocity of the reactants is equal to or larger than the laminar flame speed. The experiments show an instability range in the plane of equivalence ratio φ and oscillation period T similar to other studies using premixed gas-fired rocket chambers. However, in our system there is a definite limit with a minimum oscillation period of 1.2 ms; no oscillations with smaller periods are found. Acoustic measurement of the burner impedance shows a change of sign (±) of the reactance (imaginary part of impedance) exactly at this limiting oscillation period. By analogy to electric line theory an “inductive” and a “capacitive” burner reactance can be defined. Oscillations were only observed at an inductive burner reactance. Under the acoustical condition the heat (or temperature) oscillation is exactly in phase with the pressure oscillation if there is a negligible combustion time lag. The criterion set up by Rayleigh is fulfilled.