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 intake duct is one of the main components of a waterjet, and the hydraulic loss in the intake duct is an important part of the total loss of the waterjet. The geometry structure of the intake duct induces non-uniform inflow of the propulsion pump, which has adverse effects on the hydraulic efficiency and dynamic excitation of the waterjet. The intake duct of the waterjet is numerically simulated by using the adjoint method, the flow equations are first solved in the forward direction, then followed by the reverse solution of the adjoint equations. The flow region most related to the inflow is obtained based on the field of the adjoint operator. The method to capture the inflow surface of the waterjet duct based on the adjoint method is then established and verified. The duct geometry is optimized through the adjoint method by taking the boundary of the intake duct as the design input variable and the non-uniformity of the outflow as the objective. After 8 iterations, the non-uniformity of the outflow relatively decreases 18.7%, which validates that the adjoint method can effectively optimize the geometry of the intake duct.

This paper systematically discusses the basic theoretical research on the control volume, thrust characterization, waterjet propulsion and their interaction of the waterjet propulsion system, and the key design methods, relevant simulation evaluation and test verification methods of the waterjet propulsion system of the waterjet propulsion pump, inlet duct, steering and reversing mechanism and low-noise propulsion system. It also discusses the current status of the typical applications of waterjet propulsion devices in the three major fields of high-speed military vessels, civilian ships and amphibious vehicles. According to the characteristics of waterjet propulsion technology and its integration with the development of modern technology, the development trends of the waterjet propulsion technology are proposed, including the integrated system design of the waterjet propulsion and the ship, the hydrodynamic design from macro to micro, the digital and intelligent technology of the waterjet propulsion, the integrated electric-driven waterjet propulsion system, and the coordination design of the waterjet propulsion for stealthiness.