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Nondegenerate eigenvalues in annular gas turbines

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Presentation on theme: "Nondegenerate eigenvalues in annular gas turbines"โ€” Presentation transcript:

1 Nondegenerate eigenvalues in annular gas turbines
Driek Rouwenhorst 6th TANGO Meeting Ansaldo, Genoa September 14th 2015

2 Overview Low-order TA model for annular combustion systems Results
Monitoring strategy for annular gas turbines Example: Analysis of simulated data Potential work for Tango2

3 Traveling wave solution through an annulus
Black box: Unknown effects can alter ๐Ž and ๐œถ ๐‘ญ ๐œฝ,๐’• = ๐‘ญ ๐ŸŽ ๐’† ๐’Š( ๐Ž ๐‘ญ ๐’•โˆ’๐œฝ/๐’Ž)โˆ’ ๐œถ ๐‘ญ ๐’• ๐‘ฎ ๐œฝ,๐’• = ๐‘ฎ ๐ŸŽ ๐’† ๐’Š( ๐Ž ๐‘ฎ ๐’•+๐œฝ/๐’Ž)โˆ’ ๐œถ ๐‘ฎ ๐’• ๐’‘ ๐œฝ,๐’• =๐‘ญ+๐‘ฎ Different frequencies and decay rates Azimuthal bulk flow Temperature gradients Reflections Swirl etc. Difference in damping possibly caused by dispersion (for example velocity gradient in annulus)

4 Heat release couples the traveling waves
Heat release: continuous ๐’โˆ’๐‰ model ๐‘ธ ๐’•,๐œฝ โˆ ๐‘ต ๐œฝ ๐’‘ ๐’•โˆ’๐‰,๐œฝ Thermoacoustic coupling: Rayleigh ๐‘ซ๐‘ฌ ๐‘ซ๐’• = ๐œธโˆ’๐Ÿ ๐‘ธ ๐’•,๐œฝ ๐’‘ ๐’•,๐œฝ Simplification: ๐‘ฌ=๐’‘ ๐’‘ โ‹† โ†’ Feedback only on acoustic pressure, ๐’–(๐’‘) ๐‘ซ๐‘ญ ๐‘ซ๐’• =โˆ’ ๐œถ ๐‘ญ ๐‘ญ+ ๐‘ต ๐’…๐’‘ ๐’…๐‘ญ โ‹† ๐’‘(๐’•โˆ’๐‰,๐œฝ) ๐‘ซ๐‘ฎ ๐‘ซ๐’• =โˆ’ ๐œถ ๐‘ฎ ๐‘ญ+ ๐‘ต ๐’…๐’‘ ๐’…๐‘ฎ โ‹† ๐’‘(๐’•โˆ’๐‰,๐œฝ)

5 Results very similar to simplified network model approach of Bauerheim et al.
๐’… ๐’…๐’• ๐‘ญ ๐‘ฎ =๐Œ ๐‘ญ ๐‘ฎ ๐Œ(๐Ž, ๐œถ,๐’Ž, ๐ ,๐‰)

6 Azimuthally traveling wave spectra observed in gas turbine data
Stochastic differential equation: ๐‘ญ ๐‘ฎ ๐’Š+๐Ÿ = ๐ˆ+๐Œ๐šซ๐’• ๐‘ญ ๐‘ฎ ๐’Š + ๐ˆ ๐Ÿ ๐šซ๐’• ๐’˜ ๐’Š Sensor readings: ๐’” ๐Ÿ ๐’” ๐Ÿ โ€ฆ ๐’” ๐’Œ ๐’Š =๐‘จ ๐‘ญ ๐‘ฎ ๐’Š

7 Better damping estimation and more physical information after decomposition

8 Conclusions Low-order TA-model for annular combustion systems
Takes into account azimuthal effects Azimuthal modes split Traveling, standing and mixed modes Decomposition in azimuthal modes Improved stability margin determination

9 Future challenges? Measurement options in industrial gas turbines
Heat release, inlet velocity Excitation possibilities Better identification Passive control strategies Specific action to stabilize identified system

10


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