Interactions of azimuthal acoustic modes with an unsteady heat source in an annular duct

The interactions of azimuthal acoustic modes with an unsteady heat source in an annular duct is studied in the present paper. Based on a linear analysis, two methods are given. One is the untruncated low order method in which the linear equations with full terms are solved. Another is the truncated low order method in which terms of order O(M) or higher are neglected, where M denotes the mean flow Mach number. From investigations, the quantities of disturbances, including reflected, transmitted acoustic waves, generated entropy waves, and vorticity waves are calculated. Results show that the amplitudes of reflected and transmitted acoustic waves dramatically depend on the temperature ratio across the heat source and the non-dimensional frequencies of incident acoustic waves. Furthermore, mean flow effects are investigated. The flow Mach number has significant effects on flow disturbances, especially on vorticity waves. Based on analytical results, the energy fluxes of disturbances are investigated. It is found that the energy flux contributed from an entropy fluctuation is much higher than the acoustic energy flux. The energy flux associated with a vortical mode becomes comparable with the acoustic energy flux only when the flow Mach number is large.