A limit cycle for pressure oscillations in a gas turbine burner

Humming is a dangerous, combustion-driven acoustic oscillation phenomenon which can take place in gas-turbine burners. Any satisfactory description of humming should include both acoustic-and convective-related events. In fact, the distance crossed by a fluid "particle" during one humming period is typically of the same order of the distance between the flame and the inlet of the air-fuel mixture. Available models often postulate the Mach number to vanish, which is a scarcely justifiable hypothesis. Furthermore, the combined effect of non-normality and non-linearity might invalidate the familiar correspondence between humming onset and the growth rate of the humming mode predicted by linear stability theory. The prediction of humming amplitude, not available from linear theory, is required in order to assess the impact of the phenomenon. Thus, a non-linear-albeit simplified-description is required. We make use of a proprietary Ansaldo Energia model implemented in COMSOL Multiphysics, a finite element commercial software. Nonlinear terms are introduced into the heat release model and simulations are performed in the time domain. The initial condition in the simulations is composed by a set of random frequencies. The employed model filters both the fundamental frequency, the harmonics and the convective frequency from the initial signal; the variables in the model, such as pressure, velocity and temperature perturbations, oscillate in time without further application of external forces. The evolution scenarios of the pressure perturbation depend on the flame position and the mean velocity distribution. Three possible occurrences are observed: amplitude growth, decay and saturation.