Theoretical analysis of sound propagation and entropy generation across a distributed steady heat source

Acoustic and entropy waves interacting in a duct with steady heat source mean flow are analysed using an asymptotic expansion (AE) for low frequencies. The analytical AE solutions obtained by taking advantage of invariants applying multi-step strategy. proposed provide first-order corrections to the compact model form integrals variables. An eigenvalue system is then built predict thermoacoustic modes containing distributed or sink. Predictions from agree well numerical results linearised Euler equations both frequencies growth rates, as long low-frequency condition satisfied. able accurately reconstruct acoustic correct significant errors predicted wave associated model. analysis illustrates that needs account generated interaction source, especially when density- entropy-dependent boundary conditions prescribed at ends. Furthermore, combination method modified WKB approximation discussed cooling case. remedy disadvantage solution very domain facilitate full-frequency theoretical analyses sound propagation generation inhomogeneous fields.