Damping due to the acoustic boundary layer in high-frequency transverse modes

In gas turbine combustors, thermoacoustic instabilities arise when the flame's unsteady heat release couples to the combustor acoustics and the resulting feedback loop transfers more energy to the acoustic field than it is dissipated by the damping mechanisms. One of these damping mechanisms are the viscous losses within the acoustic boundary layer. This paper presents a model that describes these losses, which can be implemented as a boundary condition in the acoustic governing equations, capturing the dampening effect of the acoustic viscous boundary layer without numerically resolving it. This allows to determine damping rates of generic three-dimensional geometries and mode shapes, including the transverse modes that appear beyond the cut-off frequency. The derived model is tested for the first transverse mode against damping rates measured in an experimental test rig. For that purpose, the eigenvalue problem of the Helmholtz equation-including the boundary layer boundary condition-is numerically solved and the damping rate is obtained from the imaginary part of the complex eigenfrequency.