A Strategy to Tune Acoustic Terminations of Single-Can Test-Rigs to Mimic Thermoacoustic Behavior of a Full Engine

Large-scale land-based gas turbines are commonly equipped with can-annular combustion systems. The individual cans of such a combustor are coupled acoustically via the compressor exit plenum and annular gaps in front of the first turbine stage. This coupling gives rise to azimuthal modes, which extend over the entire circumference of the combustor. In order to investigate the thermoacoustic properties of such combustors, e.g. regarding their stability limits and limit cycles, the experiments or numerical models have to account for acoustic interaction of the individual cans.

Thermoacoustics of a can-annular combustor are typically investigated by means of single-can test-rigs. To mimic the effect of can-can interaction present in the full combustor the test-rig is extended at the up- and downstream side with simple acoustic elements. However, this test-rig adaption lacks a solid theoretical foundation, thus the transferability of measurements to the full combustor is dubious.

In the present study we utilize Bloch-wave theory to theoretically derive the reflection coefficient that has to be imposed at the up- and downstream side of a single-can test-rig in order to account for can-can interaction at a given azimuthal mode order. If this reflection coefficient is imposed at the up- and downstream side of a single can, this can will have the same thermoacoustic properties as the full combustor for a given azimuthal mode order. However, due to its complicated frequency dependency, this reflection coefficient cannot be directly imposed in the experiment. Instead, we propose an iterative approach, where simple acoustic elements extending the single-can test-rig at the up- and downstream side are successively adapted to approximate the correct reflection coefficient for the observed frequency.

The proposed method is developed and tested using a network model of a generic can-annular combustor. The corresponding single-can model is extended by straight ducts at the up- and downstream side to mimic can-can interaction. The length of the extensions are corrected iteratively based on the eigenfrequency of the single-can model. Within few iterations, the eigenfrequency of the single-can model approaches the eigenfrequency of the full can-annular combustor for the considered azimuthal mode order.

The presented method is validated using a numerical model of an applied single-can test-rig. For a given azimuthal mode order, thermoacoustic properties of the single-can test-rig model with matched extensions and the full can-annular combustor are in good agreement. Results show that for realistic configurations upstream coupling via the compressor exit plenum is negligible compared to coupling via the annular gap in front of the first turbine stage.