Acoustic absorption and generation in ducts of smoothly varying area sustaining a mean flow and a mean temperature gradient

In ducts with varying cross-sectional area and sustaining a subsonic non-isentropic mean flow, the axially flow conditions affect acoustic energy balance of system. This is significant in understanding controlling thermo-acoustic phenomena, particularly combustors. work aims at quantifying change such configurations, using absorption coefficient, $\Delta$. The response duct to forcing determined an analytical model, neglecting effect entropy fluctuations on field, subsequently, $\Delta$ estimated. model predictions are validated linearised Euler equations (LEEs) solver. was found be accurate for Mach numbers below $0.25$, provided lower frequency limit set by solution satisfied. For conically linear temperature gradient, it observed that showed very little dependence frequency, absolute value tended maximised when upstream boundary anechoic rather than non-anechoic. More importantly, also show stronger gradient variation configurations. Further parametric optimisation studies revealed crucial finding positive representing heated caused absorption. Similarly, negative cooled generation -- key result this analysis. behaviour shown consistent simplified analysis balance. Based finding, linearly proportional reduction achieved changing gradient.