Modal analysis of vortex rope and cavitation surge in a diffuser at different swirl and cavitation conditions

This study investigates cavitating swirling flow in a diffuser, i.e., a simplified model of a Francis turbine draft tube, using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) applied to velocity and pressure field data. The interaction between vortex rope precession and cavitation surge under varying swirl and cavitation numbers is analyzed. The modal analysis results depicted the coherent structures correlated to the vortex rope precession near the diffuser inlet and the diffuser outlet, and cavitation surge in the diffuser. The POD analysis accurately revealed the flow features in the diffuser: The conical structure represents the flow diffusion with vortex rope precession and the reverse core indicates the backflow in the diffuser for the averaged flow, and the double helical structure near the diffuser inlet for the representative flow oscillation. The typical coherent structures obtained by the DMD for the cavitating swirling flow in the diffuser are the double helical structure concentrated near the diffuser inlet. The double helical structure also appears near the diffuser outlet where the breakdown of vortex rope occurs and the flow oscillation slows down. Once cavitation occurs, the mode induced by cavitation surge and its corresponding coherent structure may change according to the operating condition. The flow oscillation can be changed from the double helical mode to the axial oscillation caused by cavitation surge named breathing mode if cavitation surge becomes strong enough at a small cavitation number or large swirl number.