0
Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

# Reduced-Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Noncompact Gas Turbine Combustors

[+] Author and Article Information
Tobias Hummel

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany;
Technische Universität München,
Garching D-85748, Germany
e-mail: hummel@td.mw.tum.de

Constanze Temmler

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany
e-mail: temmler@td.mw.tum.de

Bruno Schuermans

Technische Universität München,
Garching D-85748, Germany;
Alstom Power,
e-mail: bruno.schuermans@power.alstom.com

Thomas Sattelmayer

Lehrstuhl für Thermodynamik,
Technische Universität München,
Garching D-85748, Germany
e-mail: sattelmayer@td.mw.tum.de

1Corresponding author.

Contributed by the Coal, Biomass and Alternate Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 17, 2015; final manuscript received August 28, 2015; published online October 27, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(5), 051502 (Oct 27, 2015) (11 pages) Paper No: GTP-15-1342; doi: 10.1115/1.4031542 History: Received July 17, 2015; Revised August 28, 2015

## Abstract

A methodology is presented to model noncompact thermoacoustic phenomena using reduced-order models (ROMs) based on the linearized Navier–Stokes equations (LNSEs). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSEs, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow and are hence capable of describing propagation and (e.g., vortical) damping of the acoustic fluctuations within the considered volume. Such an ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools and is conceptually based on three core features: First, the multidimensional and volumetric nature of the ROM establishes access to account spatial variability and noncompact effects on heat-release fluctuations. As a result, it is particularly useful for high-frequency phenomena such as screech. Second, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Third, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, nonlinear saturation mechanisms can be included, which reproduce the nonlinear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM's underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain and discretized via the finite element method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order ($N∼$ 200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: $Nr∼$ 100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE–FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of noncompact thermoacoustic systems using the herein presented ROMs.

<>

## Figures

Fig. 1

Orifice-tube configuration

Fig. 2

Mesh refinement at orifice

Fig. 3

Numerical setup of the orifice tube

Fig. 4

Scattering matrix

Fig. 5

Pressure responses: (a) upstream response–upstream excitation, (b) downstream response–upstream excitation, (c) upstream response–downstream excitation, and (d) downstream response–downstream excitation

Fig. 6

Scattering matrix coefficients: (a) amplitudes and (b) phase angles

Fig. 7

Temperature field (K) and excitation information

Fig. 8

ROM verification responses: (a) L-excitation, (b) T1-excitation, and (c) T2-excitation

Fig. 9

Schematic—flame subregions

Fig. 10

Schematic—MIMO feedback

Fig. 11

Growth rates

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections

• TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
• EMAIL: asmedigitalcollection@asme.org