Investigation of vortex turbulent structures and multiscale energy transfer characteristics in the draft-tube vortex of a pump-as-turbine based on flow field model reduction and energy cascade analysis

To investigate the turbulent characteristics and energy transfer mechanisms of the draft-tube vortex rope under pump-as-turbine operation (PAT-DTV), this paper develops a multidimensional analysis framework integrating turbulence characterization, energy cascade analysis, and coherent-structure modal decomposition. This framework enables a systematic examination of vortex occurrence, turbulence features, and energy injection and dissipation pathways. Results indicate that the PAT-DTV is primarily distributed within 0–0.556 D0 downstream of the guide cone, driven jointly by geometric confinement and impeller-induced unsteady disturbances. The turbulence in the vortex generation region approaches isotropy, whereas turbulence anisotropy is significantly intensified in the downstream vortex region. Energy cascade spectra show that the kinetic energy at four times the BPF at cross-section P1 is only 10.67% of that at the BPF, while the BPF energy at cross-section P4 decreases to 15.30% of that at P1, indicating attenuation of kinetic energy in both frequency and spatial domains. Energy injection at the BPF and its harmonics induces redistribution of kinetic energy across scales. SPOD modal analysis indicates that the primary effect of impeller rotation is to enhance the intensity of the vorticity response, while the spatial response patterns of vorticity and kinetic energy exhibit pronounced differences. Moreover, the strong correspondence between entropy production dissipation and vorticity SPOD modes confirms that the shear layer at the vortex periphery is the dominant source of irreversible energy loss. These analyses provide an important theoretical basis for investigating PAT-DTV turbulence and the mechanisms of energy loss.