Coupling between entropy and unsteady heat release in a thermoacoustic system with a mean flow

In this work, the coupling between entropy and unsteady heat release in a one dimensional duct in the presence of a mean flow is considered. As acoustic disturbances impinge on a compact heat source enclosed in the duct, entropy disturbances are generated. The transfer function between the generated entropy waves and oncoming flow velocity fluctuations is deduced by conducting order analysis of the linearized governing equations. The effects of the mean flow are emphasized for different forms of unsteady heat release model. It is shown that there is a strong coupling between entropy, heat release, mean flow and acoustic impedance at the heat source. To validate our theoretical analysis, numerical investigation is conducted by using a low order model. Comparing the theoretical and the low order model׳s results reveals that a good agreement is observed. It is found that when the mean flow Mach number is not negligible, the term of O(M1) in the identified entropy transfer function is as important as that of O(M0). Neglecting the term of O(M1) may lead to wrong prediction of the entropy waves produced in the system.