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Research Papers: Gas Turbines: Turbomachinery

# Analysis and Modeling of Entropy Modes in a Realistic Aeronautical Gas Turbine

[+] Author and Article Information
Emmanuel Motheau

CERFACS-CFD Team,
42 av. Gaspard Coriolis, Toulouse 31057, France
e-mail: emmanuel.motheau@cerfacs.fr

Yoann Mery

Safran Snecma,
Rond Point René Ravaud,
Moissy Cramayel 77550, France
e-mail: yoann.mery@snecma.fr

Franck Nicoud

CNRS UMR 5149,
University Montpellier II,
Montpellier 34095, France
e-mail: franck.nicoud@univ-montp2.fr

Thierry Poinsot

CNRS-Institut de Mécanique des Fluides,
1 Allée du Professeur Camille Soula,
Toulouse 31000, France
e-mail: thierry.poinsot@cerfacs.fr

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received June 27, 2013; final manuscript received June 27, 2013; published online August 21, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(9), 092602 (Aug 21, 2013) (7 pages) Paper No: GTP-13-1190; doi: 10.1115/1.4024953 History: Received June 27, 2013; Revised June 27, 2013

## Abstract

A combustion instability in a combustor typical of aero-engines is analyzed and modeled thanks to a low order Helmholtz solver. A dynamic mode decomposition (DMD) is first applied to the large eddy simulation (LES) database. The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 350 Hz) and it shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. With the lowest purely acoustic mode being in the range 650–700 Hz, it is postulated that the instability observed around 350 Hz stems from a mixed entropy/acoustic mode where the acoustic generation associated with the entropy spots being convected throughout the choked nozzle plays a key role. A delayed entropy coupled boundary condition is then derived in order to account for this interaction in the framework of a Helmholtz solver where the baseline flow is assumed to be at rest. When fed with the appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz solver proves able to predict the presence of an unstable mode around $350$ Hz, which is in agreement with both the LES and the experiments. This finding supports the idea that the instability observed in the combustor is indeed driven by the entropy/acoustic coupling.

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## Figures

Fig. 1

Description of the configuration of interest. One sector of the azimuthal SAFRAN combustor is represented.

Fig. 2

Typical snapshot from the LES of the SAFRAN combustor and time evolution of pressure within the chamber

Fig. 3

Fluctuating pressure (left) and temperature (right) from the DMD mode at 331 Hz. From top to bottom, the four rows correspond to phases 0, π/2, π, and 3π/2.

Fig. 4

Schematic view of the modeling strategy: instead of solving for the LEEs over the whole domain, the Helmholtz equation is solved over the combustion chamber only, with the acoustic environment from the compressor and turbine being accounted for by imposing proper impedances, which take into account the mean flow

Fig. 5

Frequency of the oscillation (upper graph) and growth rate (bottom graph) corresponding to a 1D combustor mounted on a compact choked nozzle. Solid line (—): analytical result at finite Mach number [19]. Symbols: Helmholtz equation at zero Mach number and Eq. (9) as the boundary condition, without (+, Gus=0) or with (×, Gus from Eq. (8)) entropy coupling.

Fig. 6

Computational domain for the Helmholtz analysis. The point of reference and the zone of averaging used for the entropy generation modeling (see Eq. (10)) are displayed along with the exit section where the entropy-acoustic boundary condition (see Eq. (5)) is applied.

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