Research Papers: Gas Turbines: Turbomachinery

Thermoacoustic Shape Optimization of a Subsonic Nozzle

[+] Author and Article Information
Alexis Giauque

e-mail: alexis.giauque@onera.fr

Franck Clero

Department of Computational Fluid
Dynamics and Aeroacoustics,
Onera–The French Aerospace Lab,
Châtillon 92322, France

Franck Richecoeur

CNRS, UPR 288,
Laboratoire EM2C,
Ecole Centrale Paris,
Grande Voie des Vignes,
Chatenay-Malabry 92230, France

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 3, 2013; final manuscript received July 8, 2013; published online August 27, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(10), 102601 (Aug 27, 2013) (9 pages) Paper No: GTP-13-1224; doi: 10.1115/1.4025038 History: Received July 03, 2013; Revised July 08, 2013

Indirect combustion noise originates from the acceleration of nonuniform temperature or high vorticity regions when convected through a nozzle or a turbine. In a recent contribution (Giauque et al., 2012, “Analytical Analysis of Indirect Combustion Noise in Subcritical Nozzles,” ASME J. Eng. Gas Turbies Power, 134(11), p. 111202) the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrarily shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in detail. The evolution of the cross-section changes are introduced using Bezier's splines, which provide the necessary freedom to actually achieve arbitrary shapes. Bezier's polar coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (Bloy, 1979, “The Pressure Waves Produced by the Convection of Temperature Disturbances in High Subsonic Nozzle Flows,” J. Fluid Mech., 94(3), pp. 465–475), the results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections, leading to a square evolution of the cross-section area. Providing insight into the underlying physical reason leading to the difference in the noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an acoustic emission factor, which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This acoustic emission factor, which is much faster to compute, only involves the knowledge of the evolution of the cross-section area and the inlet thermodynamic and velocity characteristics to be computed.

Copyright © 2013 by ASME
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Fig. 1

Schematic view of the combustor designed at EM2C to investigate indirect combustion noise. The combustor will be equipped to measure and control acoustics in harsh environments.

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Fig. 2

Comparison of two different individuals, a and b, based on the integral of their indirect combustion noise transfer function (objective function)

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Fig. 3

Bezier's spline representation of the nozzle geometry: P1 to P7 represent the pole positions

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Fig. 4

Schematic view of the stochastic reproduction process

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Fig. 5

The general optimization algorithm. Parallel processing is used to fasten the convergence.

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Fig. 6

The low noise emission optimization; the evolution of the objective function with respect to the individual number

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Fig. 7

Optimal 3D shape of the most silent individual

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Fig. 8

Forward indirect combustion noise transfer function for the silent nozzle: (a) amplitude, and (b) phase (—, analytical solution (MarCan); ○, numerical solution (SUNDAY))

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Fig. 9

The high noise emission optimization; the evolution of the objective function with respect to the individual number

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Fig. 10

Optimal 3D shape of the most noisy individual

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Fig. 11

Forward indirect combustion noise transfer function for the noisy nozzle: (a) amplitude, and (b) phase (—, analytical solution (MarCan); ○, numerical solution (SUNDAY))

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Fig. 12

Superposition of the two extreme individuals of the study: silent nozzle (most external shape), and noisy nozzle (most internal shape)

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Fig. 13

Evolution of the source term with respect to the frequency in: ▪, the converging part of the nozzle; ●, the diverging part; ▲, the entire nozzle; (a) silent individual, and (b) noisy individual. Circles of amplitude 400 and 100 are represented to provide a sense of scale to the reader.

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Fig. 14

Evolution of the AEF (see Eq. (12)) with respect to the objective function for the 224,000 individuals considered in this study

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Fig. 15

Evolution of the AEF* (see Eq. (13)) at f0 = 400 Hz with respect to the objective function for the 224,000 individuals considered in this study




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