The secondary flow is the concomitant flow of the mainstream, which generally exists in nature and turbomachinery, most typically in the turbomachinery. The secondary flow in the turbomachinery not only changes the motion of the mainstream, deteriorates the flow field, induces the boundary layer separation, intensifies the jet wake at the exit, but also generates flow losses and noise. It is therefore of increasing concern of scholars and has risen to the same research level as the potential flow theory. Since 1950s, scholars at home and abroad have studied the phenomenon of the secondary flow from the perspectives of theoretical analysis, experimental research and numerical simulation, gradually understanding the flow mechanism and structure of the secondary flow in turbomachinery and establishing a continuously improving mathematical model, loss assessment and experimental methods for the secondary flow. Starting from the phenomenon of the secondary flow, the flow structure, mathematical model, and loss calculation and test methods of the secondary flow of the turbomachinery are reviewed and summarized. It is pointed out that the classical theoretical model of the secondary flow based on streamwise vortex built by ZANGENEH has some limitations. The key directions for future research are proposed based on the S3 flow surface theory of the secondary flow. It can provide references for the improvement of the flow field quality and the hydrodynamic performance of various types of turbomachinery, including waterjet pumps.

The matching optimization design of the blade geometry of the existing hydraulic model of the impeller and guide vane is carried out in order to improve the hydraulic performance of the waterjet pump. The Latin Hypercube sampling method is used for the space sampling of parameters that affect the performance of the waterjet pumps, such as the impeller blade load, the guide vane blade load and the stacking position. The performance parameters of the pump is obtained through steady numerical simulation of each sample by using the RANS equations. The mapping response model is built between the pump design parameters and the calculated performance parameters based on the artificial neural network. The genetic algorithm is adopted to optimize the waterjet pump hydraulic model with the aim of the maximum hydraulic efficiency. The iterative cycling of the optimization process is automatically completed, which can shorten the design and development period of the hydraulic model. The results show that after optimization, the internal flow field is significantly improved with the same head of the pump, and the efficiency of the calculation design point reaches 91.8%, while the efficiency validated by model test reaches 88.9%, as well as the range of the flow rate in high efficiency region is widened by 15%.

Submerged water-jet propulsion is a new development of traditional water-jet propulsion technology. The current study systematically analyzes the propulsion efficiency, the interaction between the hull and the water-jet and the specific speed of the propulsion pump based on the concept of this type of water-jet propulsion. It firstly establishes the mathematical modelling of the specific speed and the advance coefficient of the waterjet-propelled ship that are described by principal parameters of the hull and the propulsion system. The range of the speed and the specific speed of the propulsion pump for the submerged propulsion system has been demonstrated to reveal the mechanism of high efficiency. The variation of the main parameters of the propulsion system with the speed ratio and speed of revolution has been validated through case studies. It can provide a theoretical basis for the development and application of the submerged water-jet propulsion system.

A mixed-flow pump equipped on a high-speed ship has been studied by using the Reynolds-Averaged Navier-Stokes (RANS) method combined with the Lighthill acoustic analogy equation based on the STAR-CCM+ software. The jet wake field and the noise characteristics corresponding to different immersion depths are studied by adjusting the ship draught. The numerical simulation method of the integrated flow field of the ship and pump and the noise calculation method of the jet wake field are established for the mooring condition. The influence of the jet immersion depth on the wake is investigated by the simulation of the flow field. It is concluded that the underwater jet has less energy dissipation and weaker wake flow characteristics than the surface jet, and reduced hydrodynamic noise with the increase of the immersion depth after complete immersion. It can provide significant references for the development of the water-jet propulsion and even the comprehensive ship stealth technology.