Mean Temperature Effect on a Thermoacoustic System Stability and Non-Normality

Abstract

The stability and non-normality of an open-ended thermoacoustic system with three different mean temperature configurations are considered. An acoustically-compact heat source is confined and modeled by using a modified form of King's Law. Coupling the heat release model with a Galerkin series expansion of the acoustic waves enables the time evolution of flow disturbances to be calculated, thus providing a platform on which to gain insights on the thermoacoustic system stability and non-normality behaviors. The three mean temperature configurations are a). the mean temperature in pre- and after-heater regions is assumed to be same, i.e. T̄2 / T̄1 = 1. b). the mean temperature in the after-heater region is undergoing a sudden jump, i.e. T̄2 / T̄1 > 1. c). the mean temperature in pre and after-heater regions is undergoing linear variation with axial location, i.e. T̄ = T0 + ax. First the mechanism of combustion oscillations in the modeled thermoacoustic system with the third mean temperature configuration is verified. Then the mean temperature effects on the thermoacoustic eigenfrequency and eigenmode are investigated. Compared with the experimental measurements, the predicted eigenfrequencies with the third configuration agree better with the experimental measured ones. Furthermore, the differences in the mean temperature configurations result in a variation in combustion modes. Last the mean temperature effects on the transient growth of acoustical energy are studied. The transient energy growth analysis of acoustic disturbances is performed by linearizing the heat source model and recasting it into the classical time-lag N – τ formulation. Comparison is then made between the predicted transient growths from the thermoacoustic systems with different mean temperature configurations. It is shown that the mean temperature distribution plays an important role on determining the thermoacoustic system stability. It is also found that different mean temperature configuration leads to different maximum transient growth rate.