On the characteristics of thermoacoustic instabilities in ducted swirling flows with radially dependent velocities

This paper is devoted to revealing the effects of swirling flows with radially dependent velocity profiles on thermoacoustic instability. By reformulating the three-dimensional linearized Euler equations in cylindrical coordinates under standing-wave assumptions according to inlet/outlet boundary reflections, and integrating flame response dynamics, we develop a dispersion relation framework for thermoacoustic instability analysis. In so doing, the model generalizes prior network-based approaches for thermoacoustic instabilities (with axial and circumferential flow) to incorporate radial velocity gradients. Validation against analytical and numerical solutions for benchmark cases spanning thermoacoustic instabilities and aeroacoustic phenomena demonstrates quantitative agreement across configurations. Subsequent parametric studies further indicate that both radially dependent azimuthal and axial velocity components exert a considerable influence on the prediction of azimuthal thermoacoustic instability in an annular duct. This finding suggests that the assumption of uniform velocities in existing models may lead to inaccurate estimations of instability. Additionally, acoustic energy analysis indicates that axial flow components (perpendicular to inlet/outlet cross-sections) exhibit higher acoustic energy efflux at the combustor outlet than the circumferential components of swirling flows. Meanwhile, in comparison with burner-induced acoustic energy variations at the combustor inlet, an increase in the circumferential flow component reduces acoustic energy transmission at the combustor outlet for counter-propagating waves while amplifying it for copropagating waves. These effects are further enhanced by a stronger axial component of swirling flows. Overall, the proposed framework provides a foundational tool for elucidating thermoacoustic mechanisms and advancing instability mitigation strategies in a swirling flow configuration within confined spaces.