Noise generated in aircraft engines is usually suppressed by acoustically treating the engine ducts. The optimization of this treatment requires an understanding of the transmission and attenuation of the acoustic waves. A critical review is presented of the state of the art regarding methods of determining the transmission and attenuation parameters and the effect on these parameters of (1) acoustic properties of liners, (2) the mean velocity, including uniform and shear profiles and nonparallel flow, (3) axial and transverse temperature gradients, (4) slowly and abruptly varying cross sections, and (5) finite-amplitude waves and nonlinear duct liners.

Acoustics of Aircraft Engine-Duct Systems

The propagation and attenuation of sound in lined ducts containing uniform or “plug” flow

In this work, the influence of azimuthal staging concepts on the thermoacoustic behavior of annular combustion chambers is assessed theoretically and numerically. Staging is a well-known and effective method to abate thermoacoustic pulsations in combustion chambers. However, in the case of, for example, fuel staging the associated inhomogeneity of equivalence ratio may result in increased levels of NOx emissions. In order to minimize this unwanted effect a staging concept is required in which the transfer functions of the burners are changed while affecting the equivalence ratio as little as possible. In order to achieve this goal, a theoretical framework for predicting the influence of staging concepts on pulsations has been developed. Both linear and nonlinear analytical approaches are presented and it is shown that the dynamics of azimuthal modes can be described by coupled Van der Pol oscillators. A criterion based on the thermoacoustic coupling strength and on the asymmetry degree provides the modal ...

Investigation of azimuthal staging concepts in annular gas turbines

Thermoacoustic instability can appear in thermal devices when unsteady heat release is coupled with pressure perturbations. This effect results in excitation of eigen acoustic modes of the system. These instabilities are important in various technical applications, for instance, in rocket motors and thermoacoustic engines. 

A Rijke tube, representing a resonator with a mean flow and a concentrated heat source, is a convenient system for studying the fundamental physics of thermoacoustic instabilities. At certain values of the main system parameters, a loud sound is generated through a process similar to that in real-world devices prone to thermoacoustic instability. Rijke devices have been extensively employed for research purposes. The current work is intended to overcome the serious deficiencies of previous investigations with regard to estimating experimental errors and the influence of parameter variation on the results. Also, part of the objective here is to account for temperature field non-uniformity and to interpret nonlinear phenomena. The major goals of this study are to deliver accurate experimental results for the transition to instability and the scope and nature of the excited regimes, and to develop a theory that explains and predicts the effects observed.

An electrically heated, horizontally oriented, Rijke tube is used for the experimental study of transition to instability. The stability boundary is quantified as a function of major system parameters with measured uncertainties for the data collected. Hysteresis in the stability boundary is observed for certain operating regimes of the Rijke tube. 

An innovative theory is developed for modeling the Rijke oscillations. First, linear theory, incorporating thermal analysis that accurately determines the properties of the modes responsible for the transition to instability, is used to predict the stability boundary. Then, a nonlinear extension of the theory is derived by introducing a hypothesis for a special form of the nonlinear heat transfer function. This nonlinear modeling is shown to predict the hysteresis phenomenon and the limit cycles observed during the tests. 

A new, reduced-order modeling approach for combustion instabilities in systems with vortex shedding is derived using the developed analytical framework. A hypothesis for the vortex detachment criterion is introduced, and a kicked oscillator model is applied to produce nonlinear results characteristic for unstable combustion systems.

The experimental system and the mathematical model, developed in this work for the Rijke tube, are recommended for preliminary design and analysis of real-world thermal devices, where thermoacoustic instability is a concern.

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Thermoacoustic instabilities in the Rijke tube: experiments and modeling

This paper presents an analytical/numerical study of the effects of the mean flow on thermoacoustic instabilities. Simple quasi-1D configurations such as a 1D premixed flame in a duct connected to a nozzle are considered in order to investigate to what extent the frequency of oscillation and growth rate are modified when the Mach number is not zero. It is demonstrated that the zero Mach number assumption for the mean flow can lead to significant errors, especially when the mean flow is not isentropic, a condition which is always met in combustion applications. The analysis confirms that terms involving the mean velocity may contribute to the disturbance energy equation as much as the flame forcing ('Rayleigh') term. Besides, the net effect of the non zero Mach number terms on the stability of the modes strongly depends on both the boundary conditions and the flame response. For moderate Mach number values of order 0.05, the errors made by assuming that the mean flow is at rest are large enough to change the stability of the frequencies of interest in an academic combustor.

https://journals.sagepub.com/doi/pdf/10.1260/175682709788083335

A. Cummings

Papers

Sound propagation in a combustion can with axial temperature and density gradients

Acoustics of a wine bottle

Sound transmission in 180o duct bends of rectangular section