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Published byMargaret Barker Modified over 6 years ago
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Nondegenerate eigenvalues in annular gas turbines
Driek Rouwenhorst 6th TANGO Meeting Ansaldo, Genoa September 14th 2015
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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
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Traveling wave solution through an annulus
Black box: Unknown effects can alter ๐ and ๐ถ ๐ญ ๐ฝ,๐ = ๐ญ ๐ ๐ ๐( ๐ ๐ญ ๐โ๐ฝ/๐)โ ๐ถ ๐ญ ๐ ๐ฎ ๐ฝ,๐ = ๐ฎ ๐ ๐ ๐( ๐ ๐ฎ ๐+๐ฝ/๐)โ ๐ถ ๐ฎ ๐ ๐ ๐ฝ,๐ =๐ญ+๐ฎ 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)
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Heat release couples the traveling waves
Heat release: continuous ๐โ๐ model ๐ธ ๐,๐ฝ โ ๐ต ๐ฝ ๐ ๐โ๐,๐ฝ Thermoacoustic coupling: Rayleigh ๐ซ๐ฌ ๐ซ๐ = ๐ธโ๐ ๐ธ ๐,๐ฝ ๐ ๐,๐ฝ Simplification: ๐ฌ=๐ ๐ โ โ Feedback only on acoustic pressure, ๐(๐) ๐ซ๐ญ ๐ซ๐ =โ ๐ถ ๐ญ ๐ญ+ ๐ต ๐
๐ ๐
๐ญ โ ๐(๐โ๐,๐ฝ) ๐ซ๐ฎ ๐ซ๐ =โ ๐ถ ๐ฎ ๐ญ+ ๐ต ๐
๐ ๐
๐ฎ โ ๐(๐โ๐,๐ฝ)
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Results very similar to simplified network model approach of Bauerheim et al.
๐
๐
๐ ๐ญ ๐ฎ =๐ ๐ญ ๐ฎ ๐(๐, ๐ถ,๐, ๐ ,๐)
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Azimuthally traveling wave spectra observed in gas turbine data
Stochastic differential equation: ๐ญ ๐ฎ ๐+๐ = ๐+๐๐ซ๐ ๐ญ ๐ฎ ๐ + ๐ ๐ ๐ซ๐ ๐ ๐ Sensor readings: ๐ ๐ ๐ ๐ โฆ ๐ ๐ ๐ =๐จ ๐ญ ๐ฎ ๐
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Better damping estimation and more physical information after decomposition
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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
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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
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