A. P. Dowling

Acoustic analysis of gas turbine combustors

Combustion instability has become a major issue for gas turbine manufacturers. Stricter emission regulations, particularly on nitrogen oxides, have led to the development of new combustion methods, such as lean premixed prevaporized(LPP)combustion,to replacethetraditionaldiffusion e ame.However,LPPcombustionismuchmore liable to generate strong oscillations, which can damage equipment and limit operating conditions. As a tutorial, methods to investigate combustion instabilities are reviewed. Theemphasis is on gas turbine applications and LPP combustion. The e ow is modeled as a one-dimensional mean with linear perturbations. Calculations are typically done in the frequency domain. The techniques described lead to predictions for the frequencies of oscillations and the susceptibility to instabilities for which linear disturbances grow expotentially in time. Appropriate boundary conditions are discussed, as is the change in the linearized e ow across zones of heat addition and/or area change. Many of the key concepts are e rst introduced by considering one-dimensional perturbations. Later higher-order modes, particularly circumferential waves, are introduced, and modal coupling is discussed. The modeling of a simplie ed combustion system, from compressor outlet to turbine inlet, is described. The approaches are simple and fast enough to be used at the design stage.

A kinematic model of a ducted flame

A premixed ducted flame, burning in the wake of a bluff-body flame-holder, is considered. For such a flame, interaction between acoustic waves and unsteady combustion can lead to self-excited oscillations. The concept of a time-invariant turbulent flame speed is used to develop a kinematic model of the response of the flame to flow disturbances. Variations in the oncoming flow velocity at the flame-holder drive perturbations in the flame initiation surface and hence in the instantaneous rate of heat release. For linear fluctuations, the transfer function between heat release and velocity can be determined analytically from the model and is in good agreement with experiment across a wide frequency range. For nonlinear fluctuations, the model reproduces the flame surface distortions seen in schlieren films. Coupling this kinematic flame model with an analysis of the acoustic waves generated in the duct by the unsteady combustion enables the time evolution of disturbances to be calculated. Self-excited oscillations occur above a critical fuel–air ratio. The frequency and amplitude of the resulting limit cycles are in satisfactory agreement with experiment. Flow reversal is predicted to occur during part of the limit-cycle oscillation and the flame then moves upstream of the flame-holder, just as in experimental visualizations. The main nonlinearity is identified in the rate of heat release, which essentially ‘saturates’ once the amplitude of the velocity fluctuation exceeds its mean. We show that, for this type of nonlinearity, describing function analysis can be used to give a good estimate of the limit-cycle frequency and amplitude from a quasi-nonlinear theory.

Nonlinear self-excited oscillations of a ducted flame

Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially ‘saturates’. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory. Active control has been successfully applied to eliminate these oscillations. We demonstrate the same effect by adding a feedback control system to our nonlinear model. This theory is used to explain why any linear controller capable of stabilizing the linear flow disturbances is also able to stabilize finite-amplitude oscillations in the nonlinear limit cycles.

Reheat buzz: an acoustically coupled combustion instability. Part 2. Theory

Reheat buzz is a low-frequency instability of afterburners. It is caused by the interaction of longitudinal acoustic waves and unsteady combustion. Similar combustion instabilities occur in laboratory rigs. A theory is developed to determine the frequency and mode shape of the instability and is tested by comparison with the experimental results described in Part1. The predicted and measured frequencies are found to be within 6 Hz (7%) of each other. The theory is able to predict the observed variation of frequency with equivalence ratio, inlet Mach number and geometry.

The absorption of axial acoustic waves by a perforated liner with bias flow

The effectiveness of a cylindrical perforated liner with mean bias flow in its absorption of planar acoustic waves in a duct is investigated. The liner converts acoustic energy into flow energy through the excitation of vorticity fluctuations at the rims of the liner apertures. A one-dimensional model that embodies this absorption mechanism is developed. It utilizes a homogeneous liner compliance adapted from the Rayleigh conductivity of a single aperture with mean flow. The model is evaluated by comparing with experimental results, with excellent agreement. We show that such a system can absorb a large fraction of incoming energy, and can prevent all of the energy produced by an upstream source in certain frequency ranges from reflecting back. Moreover, the bandwidth of this strong absorption can be increased by appropriate placement of the liner system in the duct. An analysis of the acoustic energy flux is performed, revealing that local differences in fluctuating stagnation enthalpy, distributed over a finite length of duct, are responsible for absorption, and that both liners in a double-liner system are absorbant. A reduction of the model equations in the limit of long wavelength compared to liner length reveals an important parameter grouping, enabling the optimal design of liner systems.

Active Control of Reheat Buzz

Reheat buzz is a low-frequency combustion instability involving the propagation of longitudinal pressure waves inside a duct in which a flame is anchored. Active control has been successfully applied to this instability. The controller alters the upstream acoustic boundary condition and thereby changes the energy balance in the duct. Control is found to reduce the peak in the pressure spectrum resulting from combustion instability by 20 dB. The acoustic energy in the whole 0-800-Hz bandwidth is reduced to about 10% of its uncontrolled value. A comparison with numerical calculations is presented.

The absorption of sound by perforated linings

The efficiency of a perforated screen as a sound absorber can be greatly increased when a rigid surface is placed behind the screen, essentially because the sound can then interact many times with the perforations. We consider a practical application for a backed perforated screen with a bias flow through the perforations: the ‘screech liner’. This is a perforated lining which is inserted in the afterburner section of jet engines to suppress the acoustically driven combustion instability commonly known as screech. A pressure drop across the screen ensures that a bias flow of cool air is produced; this flow protects the liner from the intense heat in the afterburner. Our analysis was developed in answer to a clear need for a theory which can predict the optimal geometry and bias flow to produce a highly absorptive liner. We show that it is theoretically possible to absorb all the sound at a particular frequency. Experimental results are presented which show encouraging agreement with the theoretical predictions. Screech is thought to be the excitation of a transverse resonant oscillation in the jet pipe, but the insertion of a liner inevitably changes the frequency of such resonances because the boundary condition at the wall is altered. We examine the effect of a liner on the resonances which occur in a cylinder and show that a well-designed liner may suppress resonances over a range of frequencies. The effect of the hot axial jet flow on the performance of a liner has not previously received attention. A simple model to account for this flow is included in our analysis.

Practical active control system for combustion oscillations

A low-frequency combustion instability of a flame burning in a duct has been successfully controlled by the unsteady addition of extra fuel. A suitably phased addition of only 3% more fuel reduces the peak in the pressure spectrum due to the combustion instability by some 12 dB. The acoustic energy in the 0-400 Hz bandwidth is reduced to 18% of its uncontrolled value. Since relatively little unsteady fuel is necessary, the mechanical power requirements of the controller are modest and the system is easy to implement.

Jet Noise: Acoustic Analogy informed by Large Eddy Simulation

A novel approach to the development of a hybrid prediction methodology for jet noise is described. Modeling details and numerical techniques are optimized for each of the three components of the model. Far-field propagation is modeled by solution of a system of adjoint linear Euler equations, capturing convective and refraction effects using a spatially developing jet mean flow provided by a Reynolds-averaged Navier―Stokes computational fluid dynamics solution. Sound generation is modeled following Goldsteins acoustic analogy, including a Gaussian function model for the two-point cross correlation of the fourth-order velocity fluctuations in the acoustic source. Parameters in this model describing turbulent length and time scales are assumed to be proportional to turbulence information also taken from the Reynolds-averaged Navier―Stokes computational fluid dynamics prediction. The constants of proportionality are, however, not determined empirically, but extracted by comparison with turbulence length and time scales obtained from a large eddy simulation prediction. The large eddy simulation results are shown to be in good agreement with experimental data for the fourth-order two-point cross-correlation functions. The large eddy simulation solution is then used to determine the amplitude parameter and also to examine which components of the cross correlation are largest, enabling inclusion of all identified dominant terms in the Gaussian source model. The acoustic source description in the present approach is therefore determined with no direct input from experimental data. This model is applied to the prediction of sound to the experimental configuration of the European Union JEAN project, and gives encouraging agreement with experimental data across a wide spectral range and for both sideline and peak noise angles. This paper also examines the accuracy of various commonly made simplifications, for example: a locally parallel mean flow approximation rather than consideration of the spatially evolving mean jet flow and scattering from the nozzle; the assumption of small radial variation in Green function over the turbulence correlation length; the application of the far-field approximation in the Green function; and the impact of isotropic assumptions made in previous acoustic source models.

Reflection of circumferential modes in a choked nozzle

Small perturbations of a choked flow through a thin annular nozzle are investigated. Two cases are considered, corresponding to a ‘choked outlet’ and a ‘choked inlet’ respectively. For the first case, either an acoustic or entropy or vorticity wave is assumed to be travelling downstream towards the nozzle contraction. An asymptotic analysis for low frequency is used to find the reflected acoustic wave that is created. The boundary condition found by Marble & Candel (1977) for a compact choked nozzle is shown to apply to first order, even for circumferentially varying waves. The next-order correction can be expressed as an ‘effective length’ dependent on the mean flow (and hence the particular geometry of the nozzle) in a quantifiable way. For the second case, an acoustic wave propagates upstream and is reflected from a convergent–divergent nozzle. A normal shock is assumed to be present. By considering the interaction of the shocks position and flow perturbations, the reflected propagating waves are found for a compact nozzle. It is shown that a significant entropy disturbance is produced even when the shock is weak, and that for circumferential modes a vorticity wave is also present. Numerical calculations are conducted using a sample geometry and good agreement with the analysis is found at low frequency in both cases, and the range of validity of the asymptotic theory is determined.