Accounting for Acoustic Damping in a Helmholtz Solver

Thermoacoustic Helmholtz solvers provide a cheap and efficient way of predicting combustion instabilities. However, because they rely on the inviscid Euler equations at zero Mach number, they cannot properly describe the regions where aerodynamics may interact with acoustic waves, in the vicinity of dilution holes and injectors, for example. A methodology is presented to incorporate the effect of non-purely acoustic mechanisms into a three-dimensional thermoacoustic Helmholtz solver. The zones where these mechanisms are important are modeled as two-port acoustic elements, and the corresponding matrices, which notably contain the dissipative effects due to acoustic–hydrodynamic interactions, are used as internal boundary conditions in the Helmholtz solver. The rest of the flow domain, where dissipation is negligible, is solved by the classical Helmholtz equation. With this method, the changes in eigenfrequency and eigenmode structure introduced by the acoustic–hydrodynamic effects are captured, while keeping the simplicity and efficiency of the Helmholtz solver. The methodology is successfully applied on an academic configuration, first with a simple diaphragm, then with an industrial swirler, with matrices measured from experiments and large-eddy simulation.