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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Effects of Nozzle Helmholtz Number on Indirect Combustion Noise by Compositional Perturbations

[+] Author and Article Information
Luca Magri

Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CB2 1PZ, UK
e-mail: lm547@cam.ac.uk

Jeffrey O'Brien, Matthias Ihme

Center for Turbulence Research,
Stanford University,
488 Escondido Mall,
Stanford, CA 94305

1Corresponding author.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 29, 2017; final manuscript received July 28, 2017; published online October 17, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(3), 031501 (Oct 17, 2017) (9 pages) Paper No: GTP-17-1238; doi: 10.1115/1.4037914 History: Received June 29, 2017; Revised July 28, 2017

By modeling a multicomponent gas, a new source of indirect combustion noise is identified, which is named compositional indirect noise. The advection of mixture inhomogeneities exiting the gas-turbine combustion chamber through subsonic and supersonic nozzles is shown to be an acoustic dipole source of sound. The level of mixture inhomogeneity is described by a difference in composition with the mixture fraction. An n-dodecane mixture, which is a kerosene fuel relevant to aeronautics, is used to evaluate the level of compositional noise. By relaxing the compact-nozzle assumption, the indirect noise is numerically calculated for Helmholtz numbers up to 2 in nozzles with linear velocity profile. The compact-nozzle limit is discussed. Only in this limit, it is possible to derive analytical transfer functions for (i) the noise emitted by the nozzle and (ii) the acoustics traveling back to the combustion chamber generated by accelerated compositional inhomogeneities. The former contributes to noise pollution, whereas the latter has the potential to induce thermoacoustic oscillations. It is shown that the compositional indirect noise can be at least as large as the direct noise and entropy noise in choked nozzles and lean mixtures. As the frequency with which the compositional inhomogeneities enter the nozzle increases, or as the nozzle spatial length increases, the level of compositional noise decreases, with a similar, but not equal, trend to the entropy noise. The noisiest configuration is found to be a compact supersonic nozzle.

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Figures

Grahic Jump Location
Fig. 1

Acoustic wave, π, entropy perturbation, σ, compositional inhomogeneity, ξ, decomposition in a (a) subsonic nozzle and (b) supersonic nozzle. M¯th is the Mach number at the throat. The area variation is pictorial.

Grahic Jump Location
Fig. 2

S-shaped curve of maximum temperature Tmax versus scalar dissipation rate at stoichiometric condition χst for n-dodecane-air flamelet computed at p = 1 bar with boundary conditions Tfuel=Tox=295 K. The “X” marker indicates the χst=1 s−1 condition.

Grahic Jump Location
Fig. 3

(a) Chemical potential function, Ψ, and (b) its gradient with respect to theMach number, ∂Ψ/∂M, for an n-dodecane inhomogeneity isentropically compressed/expanded in a nozzle. The results are presented as a function of the rescaled mixture-fraction coordinate. The stoichiometric condition is at 0.5, with the lean side being <0.5.

Grahic Jump Location
Fig. 4

One-dimensional diffusion flame in the mixture-fraction space. (a) Temperature T (solid-black lines), n -dodecane mass fraction YC12H26 (blue-dashed lines), oxygen mass fraction YO2 (red dotted–dashed lines), and water mass fraction YH2O (magenta-dotted lines). (b) Chemical potential function Ψ at the inlet (black-solid line) and specific Gibbs energy of the mixture (blue-dashed lines).

Grahic Jump Location
Fig. 5

(a) Nozzle cross-sectional area A(η) and (b) mean-flow Mach number M¯ versus spatial coordinate η for linear velocity profile cases. A* is the throat area, where in the supersonic nozzle, M¯=1 at η=0.652.

Grahic Jump Location
Fig. 6

Modulus of (a) downstream propagating acoustic response to entropic forcing πb+ /σa and (b) acoustic response at nozzle exit to entropic forcing πb−/σa versus Helmholtz number, He. The corresponding phases are shown in panels (c,d). The solutions reported in Ref. [28] are denoted by circles and were taken from the online version of their paper.

Grahic Jump Location
Fig. 7

Same as Fig. 6 for acoustic perturbations imposed at the inlet instead of entropy perturbations

Grahic Jump Location
Fig. 8

Same as Fig. 7 for compositional perturbations imposed at the inlet instead of acoustic perturbations

Grahic Jump Location
Fig. 9

Modulus of the ratio between indirect noise generated by accelerated compositional inhomogeneities and (a) direct noise and (b) indirect noise generated by accelerated entropy perturbations

Grahic Jump Location
Fig. 10

Spatial evolution of the response to compositional forcing in a supersonic nozzle with linear-velocity profile, M¯a=0.29, M¯b=1.5. First column shows the downstream acoustic response π+(η)/ξa, and second column shows the compositional response ξ(η)/ξa. Top row shows magnitude of response, and bottom row shows the phase. The five lines overlap each other in panel (b).

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