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Published Articles

The Volume 6, No 3, September 2001

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Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor with a Choked Exit

Wolfgang Polifke, Christian Oliver Paschereit and Klaus Doebbeling


Thermoacoustic instabilities are a cause for concern in combustion applications as diverse as small household burners, gas turbines and rocket engines. In this work, a feedback mechanism is analysed, which couples combustion chamber acoustics with convectively transported fluctuations of entropy (entropy waves) generated within a premixed flame. Essential elements of this thermo-acoustic feedback loop are: 1) fluctuations in fuel concentration, induced by acoustic disturbances at the location of fuel injection, 2) convective transport of fuel inhomogeneities through the premixing section of the burner, 3) modulations in heat release rate and hot gas entropy resulting from the consumption of fuel/air mixture with varying fuel concentration by the flame, and 4) the generation of sound through entropy non-uniformities at the turbine inlet. From a qualitative analysis based on relative phases, it is concluded that, depending on the various convective and acoustic time lags involved, entropy waves may couple constructively as well as destructively with combustor acoustics. However, such qualitative analysis does not indicate whether the coupling between entropy and acoustic waves is strong enough to significantly influence thermo-acoustic stability. Therefore, a linear model has been constructed to estimate the effect of entropy waves on the thermo-acoustic response and stability of a combustor with a choked exit nozzle, as it might be found in a gas turbine. Note that phenomena like dispersion of convective waves, distributed heat release, vortical velocities, etc., have not been taken into account, as they would burden the presentation with unnecessary complexity. Results obtained indicate that the interaction between combustor acoustics and entropy waves can be significant, especially for the lowest non-axisymmetric modes, and even at frequencies higher than those usually associated with convective waves. As expected, it was observed that the coupling between pressure and entropy waves at the exit nozzle can enhance as well as reduce the thermo-acoustic stability of a combustor, or the responsiveness to an external or internal fluid-mechanic excitation mechanism. It is concluded that a comprehensive thermo-acoustic analysis of a premixed combustor with a choked exit must in general include the generation and propagation of entropy waves and the coupling with combustor acoustics.

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Covariance Control of Turbomachinery Vibrations

ElSayed M. ElBeheiry


Two contrasting controller designs are proposed and investigated in this study. The goal is to suppress random vibrations of a high speed, flexible rotor-bearing system undergoing random base excitation. This turborotor is supported by two hydrodynamically lubricated fluid film bearings and carries three non-identical, heavy disks. It has been modelled by a Finite Element (FE) method that accounts for gyroscopic moments, rotary inertia, internal viscous and hysteretic damping and shear deformations. The application of the Extended Modal Reduction (EMR) method, that leaves the retained eigenfrequencies and mode shapes unaltered from their original values, provided a significant model truncation for reduced-order controller design. The first controller applies the active control forces directly to the rotor while the second one introduces these forces to either the bearing housing or the pedestal mass. The base excitations are modelled as stationary and Gaussian random processes in both the vertical and the horizontal direction. The two controllers are designed by using the State Covariance Assignment (SCA) theory that allows the achievement of prescribed variances by state or output feedback control. The results show that the two controllers marginally reduce vibrations due to random base excitations, when compared to the uncontrolled system.

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Theoretical and Experimental Study of the Propagation and Divergence of Bounded Acoustic Beams

Jeroen Vandeputte, Oswald Leroy, Abdellatif Bey Temsamani, Steve Vandenplas and Leo Van Biesen


In this paper, propagation and divergence effects of ultrasonic fields are studied. Four theoretical models are considered. Experiments were conducted in order to validate the results. The characteristics of the propagation and divergence of Gaussian acoustic beam are handled theoretically. It is shown that the propagation behaviour strongly depends on the material parameters and the initial halfwidth of the Gaussian beam. An experimentally measured profile at a distance z from the emitter is used as boundary condition in the SDM-model and as a tool to estimate the parameters of the CHW-model and the GBS-model by an inversion procedure. Comparison is made with experimental results.

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Investigation of Methods Based on International Standards to Determine Sound Power of Machinery Noise Sources Under Hemi-anechoic Conditions

Stephen Keith, G. Krishnappa


Sound power standards using sound pressure and sound intensity measurements, developed by the International Organisation for Standardisation, were compared on the basis of accuracy and speed. Measurements were carried out under hemi-anechoic conditions on three sources, a reference source, a vacuum cleaner and a circular saw. Both hemispherical and box measurement surfaces were employed in the investigations as prescribed in the standards. The measurement accuracy of the results was examined in two different ways. In the first method the accuracy was assumed to be related to the measurement grade, which was determined by the criteria given in the associated standards. The other method was to find the largest discrepancy between the measured values and the best available estimate. The results for all three sources showed similar trends. The minimum time to obtain a given measurement grade was found for pressure measurements at points distributed over a hemispherical surface, or scanning intensity measurements over a box surface. To obtain the same measurement grade, point intensity measurements over a hemisphere took up to twice the time required by the corresponding pressure measurements. Intensity measurements for points over a box surface took at least twice the time needed for pressure measurements for points on a hemisphere. The investigations also suggested that intensity scanning measurements could be employed to achieve precision grade.

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Experimental Investigation on the Occurrence of Internal Resonances in a Clamped-Clamped Beam

P. Ribeiro, L. Alves and J. Marinho


The geometrically non-linear vibration of an aluminium beam clamped at both ends was investigated experimentally, with the goal of verifying the occurrence of internal resonances. The beam was excited transversely with a harmonic excitation and the deflections of the first and higher harmonics were analysed in order to detect the mode shapes involved. One to three and one to five internal resonances between the first and higher order modes and between the second and higher order modes were found.

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