Dynamics of entropy wave generation in a simplified model of gas turbine combustor: A theoretical investigation

Entropy noise remains as a largely unexplored mechanism of combustion generated noise. Currently, little is known about the production sources of entropy waves in flames. To address this issue, the present work puts forward a theoretical investigation of the generation of entropy waves in a one-dimensional, ducted flow. A linear theory is developed for the dynamic responses of different sources of unsteady entropy generation including thermal, hydrodynamic, pressure, and chemical irreversibility. For the first time in the literature, dynamics of chemical sources of unsteady entropy generation are investigated extensively. It is found that the mixture fraction fluctuations are responsible for the production of almost all unsteady chemical entropy and the effect of chemical potential is negligibly small. For the Strouhal numbers less than unity, fluctuations in pressure are the most significant source of the overall generation of unsteady entropy. However, at higher frequencies, mixture fraction fluctuations dominate the generation of entropy wave. The cut-off frequency for the generation of entropy wave is shown to depend not only on the thermal and hydrodynamic characteristics of the flame but also on the chemical properties of the downstream gases. It is further argued that the transfer function of entropy generation for a thin flame may feature an unrealistically high amplitude. This study shows that neglecting the chemical sources of an entropy wave can result in wrong predictions of the combustor acoustics and impede the suppression of combustion instabilities and noise.