Trajectory prediction of underwater launch equipment based on varying flow coefficient

Abstract

In the underwater launch systems, a real-time prediction of the trajectory of the equipment out of the tube can provide accurate motion feedback for the closed-loop control. In this paper, using an analytical approach, a hydrodynamic mathematical model is developed for the open pipeline underwater launch system, along with an analysis of the coupling of pressure-flow variables influence mechanism on the trajectory. A time-varying coefficient-based prediction model for the equipment trajectory of the underwater launch process is developed for the compressible fluid and the strong transient characteristics of the fluid during the underwater launch process. Through the incorporation of the time-varying component of inertia into the flow coefficient, the interlinking relationship between the fluid, the pipe structure, and the equipment motion is clarified. This addresses the problem that the traditional steady-state hydrodynamic pipeline model cannot accurately describe the strong transient launch process. The experimental results show that, under typical firing conditions, the maximum error between the equipment motion velocity predicted by the mathematical model based on the time-varying flow coefficient and the measured velocity is 8.48%, with an error root mean square of 0.3035, proving the accuracy of the model based on the time-varying flow coefficient.