In order to improve the velocity of torpedoes, the transient calculation model of a torpedo launching propulsion pump during rapid start-up process was established based on the Reynolds average N-S equation and SST k-ω turbulence model in present paper. The hydraulic characteristics and the flow field evolution of the propulsion pump under three start-up time conditions were studied by numerical method. The results show that the flow rate and the thrust continue to increase with time. The head, the axial force, the axial moment and the power increase at first and then decrease. The efficiency firstly increases and then remains stable. The maximum values of the head, the axial force, the axial moment and the power appear at the end of acceleration, and the maximum values decrease with the increase of start-up time. At the beginning of start-up, there are serious inflow impact, flow separation and vortex structure in the impeller area, and the flow field tends to be stable gradually with time. Start-up time has a significant effect on the flow field evolution of the propulsion pump. The smaller the start-up time is, the faster the flow field reaches stable state. In order to ensure that the propulsion pump has no cavity and the internal flow field runs to stable state in a relatively short time during star-up process, it is recommended to start propulsion pump by 0.2 seconds start-up time.

Developing a reliable potential flow solver is necessary for the ship CAE software. The method on the three-dimensional time-domain Green function of ships with forward speed in infinite depth was studied. Firstly, a three-dimensional transient free-surface Green function was introduced, and its Rankine part was calculated by Hess & Smith’s method, and its free-surface memory part was calculated by the method of Beck team from the University of Michigan, US. Secondly, the memory part of the Green function and its derivatives were obtained in the mathematical expressions for making the program in five regions. Thirdly, the source method was used to calculate the source and the radiation potential, and then the radiation force was obtained by integrating the pressure around the floating body. Finally, the radiation force of the Wigley I ship was calculated, and compared with the published experimental and numerical results. The reliability of the method and the code in this paper is confirmed.