59321 - A Non-Compact Effective Impedance Model for Can-to-Can Acoustic Communications: Analysis and Optimization of Damping Mechanisms 

Modern heavy-duty gas turbines are commonly designed with can-annular combustors, in which all flames are physically separated. Acoustically, however, the cans communicate via the upstream located compressor plenum and at the downstream gaps found at the transition to the turbine inlet. Recently, various studies have focused on modeling the acoustic communication between adjacent cans in a can-annular arrangement. Although the models available in the literature vary in complexity, they all reproduce the main feature of can-annular combustors, namely the existence of clusters of modes with different azimuthal order that are close in the complex frequency space. Dissipative effects at the connection between adjacent cans have not yet been addressed, although, as is shown in this study, they can have a significant effect on the can-to-can acoustic communication.

In a previous study (GT2020-14665), we presented a coupling boundary condition in the form of an effective impedance, which, when applied at the boundary of a single-can model, emulates the acoustic response of a corresponding can-annular arrangement. The theory behind this model is based on the Bloch-wave formalism, which can be applied if the system features a discrete rotational symmetry. The model was derived under the assumption of a negligible influence of density fluctuations, which is equivalent to an acoustic compactness assumption for the can-to-can connection element upstream of the turbine inlet. In the present study, we improve our model in two ways. First, we take density fluctuations into account to extend the model for acoustically non-compact connections. Second, we use known results from the literature to include an acoustic resistance at the cross talk section into the governing equations to include dissipative effects. Using this new effective impedance, we discuss in detail the effect of the resistance for different azimuthal orders and derive a condition for maximum damping in the low-frequency limit. We show that the damping of azimuthal modes depends on the geometry of the connection apparatus, mean flow parameters and the azimuthal order itself. These results suggest the possibility of addressing the damping of modes of certain azimuthal order by a geometric variation of the connection apparatus. We propose the idea of adding a second connection device in the form of a liner between adjacent cans, placed just upstream of the gaps found at the transition to the turbine inlet. By varying the porosity of the liner, we show how the damping of modes of certain azimuthal orders can be addressed and discuss the physical mechanisms at play.

As an exemplary application of the theory, we set up a network model of a generic industrial 12-can combustor that exhibits an unstable mode of azimuthal order one. We design a liner element to address the damping of order one modes, add it to the network model, and show that the unstable mode becomes stable. The findings of this study provide a deeper understanding of the mechanisms that drive the can-to-can acoustic communication, and open the stage for devising passive damping strategies aimed at stabilizing specific modes in the architecture of can-annular combustors.