Modeling and quantification of acoustic damping induced by vortex shedding in non-compact thermoacoustic systems

This paper presents a methodology to compute acoustic damping rates of transversal modes due to vortexshedding. This acoustic damping rate presents one key quantity for the assessment of linear thermoacoustic stability of gas turbine combustors in the high-frequency regime. State-of-the-art network models - as employed to calculate damping rates in low-frequency, longitudinal systems - cannot fulfill this task due to the acoustic non-compactness encountered in the high-frequency regime. Furthermore, direct eigensolutions of the Linearized Euler Equations (LEE) yield incorrect results for the damping rates due to the implicit presence of acoustic as well as hydrodynamics contributions in these solutions. The proposed methodology consist of three steps: (1) The regions in which acoustic fluctuations are transformed into vortical disturbances are identified from LEE simulation results. (2) The respective regions are modeled as acoustic momentum sinks, which are suitably included in the Helmholtz Equation (HE). (3) The unknown loss coefficients are obtained by requiring equality between reflection coefficients (which is a purely acoustic quantity) of the concerned configuration obtained from LEE and HE plus sink model. The desired acoustic damping rates are then computed by solving the respective HE for the transversal eigenmodes of interest. The methodology's applicability to technically relevant systems is demonstrated by a validation test case using a lab-scale, swirl-stabilized combustion system.