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Vortex is the dominant flow structure in hydro-energy machinery, and its swirling features are mainly determined by the rigid rotation part of vorticity. In this study, the rigid vorticity transport equation is proposed based on the vorticity decomposition. The vortex spatial evolution is described by the stretching term RST, the dilatation term RDT, the Lamb term RCT and the viscous term RVT. The shape change of a vortex tube is mainly affected by RST and RDT, while vortex production and dissipation are mainly reflected by RCT and RVT. Compared with the traditional vorticity transport equation, this new theoretical tool can distinguish between rigid rotation and shearing motion of local fluids, and it can better reveal the intuitive evolution characteristics of vortical structures. Two cases with clear engineering demands are analysed by using the transport equation, and the results show that it can provide a practical method for the analysis and control of vortical flows in hydro-energy machinery.

Vortex is the dominant flow structure in hydro-energy machinery, and its swirling features are mainly determined by the rigid rotation part of vorticity. In this study, the rigid vorticity transport equation is proposed based on the vorticity decomposition. The vortex spatial evolution is described by the stretching term RST, the dilatation term RDT, the Lamb term RCT and the viscous term RVT. The shape change of a vortex tube is mainly affected by RST and RDT, while vortex production and dissipation are mainly reflected by RCT and RVT. Compared with the traditional vorticity transport equation, this new theoretical tool can distinguish between rigid rotation and shearing motion of local fluids, and it can better reveal the intuitive evolution characteristics of vortical structures. Two cases with clear engineering demands are analysed by using the transport equation, and the results show that it can provide a practical method for the analysis and control of vortical flows in hydro-energy machinery. [ABSTRACT FROM AUTHOR]

• A modified STRUCT turbulence model (MST) is proposed. • A new URANS baseline is employed to improve the sensitivity to rotation and curvature. • A new time-scale ratio is defined to improve the adaptability of damping function to flow fields. • The normalized helicity is introduced to detect the energy backscatter phenomenon. • Efficient engineering computations of turbulence in hydro-energy machinery can be achieved. A modified STRUCT (MST) turbulence model for efficient engineering computations of turbulent flows in hydro-energy machinery is proposed in this paper. The MST model switches between URANS and LES-like modes using a new damping function to adjust the turbulent viscosity. Compared with the original STRUCT method, the modifications are as follows: (1) the BSL k-ω model with the Spalart-Shur correction is chosen as the new baseline to improve the sensitivity to rotation and curvature; (2) a new adaptive time-scale ratio is proposed to avoid the arbitrariness of geometric averaging operation in the original method; (3) the normalized helicity is introduced into the new damping function to detect the energy backscatter phenomenon. Five classical high Reynolds number flow cases are tested. The results show that the turbulent viscosity of the MST model is reasonably reduced in the massively separated regions and LES-like mode is activated, which captures more turbulent vortices and fluctuations on the URANS grids. With high efficiency and robustness, the MST model inherits the advantages of the original STRUCT method and improves the prediction accuracy of the turbulence with rotation and curvature, which enables efficient engineering computations of turbulent flows in hydro-energy machinery. [ABSTRACT FROM AUTHOR]