This paper presents a mathematical model for predicting the propagation of\ncircumferential waves (acoustic, entropy and vorticity waves) through an annular\nnozzle. Combustion chambers in modern aero-engines are typically annular, and so\na model for circumferential waves is essential for understanding and predicting both\ncombustion noise and thermoacoustic instabilities for such geometries. The linearised\nEuler equations are solved using the Magnus expansion to obtain the reflection and\ntransmission coefficients of the annular nozzle for acoustic, entropy and vorticity\nperturbations. Predictions which account for flow physics, such as a non-zero mean\nflow angle and the generation of vorticity noise, are obtained for the first time.\nResults are compared with two numerical methods, showing that the mathematical\nmodel is able to predict the transmission and reflection of waves for both compact\nand non-compact frequencies. The model is used to prove one particularly interesting\nand relevant feature of annular geometries: the generation of a vorticity wave by the\nacceleration of a circumferential entropy wave. It is shown that this phenomenon\noriginates from the baroclinic torque in the vorticity equation.
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