A cylindrical shear layer model applied to the semi-infinite jet pipe problem

This paper presents a cylindrical shear layer model for analyzing acoustic wave propagation at the exit of a semi-infinite circular jet pipe with uniform mean flow. Building upon the Pridmore-Brown equation, the formulation is derived in cylindrical coordinates to more accurately describe the transitional region between the uniform flow inside the pipe and the quiescent outer medium by developing the coupling conditions, under low Mach number and small perturbation conditions. The proposed model improves upon earlier shear layer approaches, such as the rectangular-coordinate-based model in Yanaz Çınar, Boij, Çınar, and Nilsson [(2010). 16th AIAA/CEAS Aeroacoustics Conference], and extends beyond the classical vortex sheet model introduced in Munt [(1977). J. Fluid Mech. 83, 609-640] and Munt [(1990). J. Sound Vib. 142, 413-436]. The resulting coupling conditions are applied to the fundamental problem of areoacoustics, namely, the semi-infinite jet pipe problem. Numerical analysis carried for low-frequency range demonstrates improved agreement with experimental data, in predicting the reflection coefficient for configurations with nonzero diffuser angles. These findings confirm the enhanced fidelity of the cylindrical shear layer model and its potential applicability to a broad range of aeroacoustic engineering problems.