Trajectory prediction of underwater launch equipment based on varying flow coefficient. (1st April 2023) - Yuan, Jingxin; Zhu, Junjie; Xu, Jin; Sun, Xingfa; Zhang, Xiaoping; Zheng, Xinliang
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. Highlights: A physical model for the underwater launch was proposed to predict the motion state of the equipment during launch. The pressure-flow coupling relationship is clearly described to model the control body's emission motion. On this basis, the fixed flow coefficient's flaws are thoroughly examined, and a prediction model based on the time-varying flow coefficient is proposed. The following are the main conclusions: The pressure-flow equation of motion of each control body of the launch system is deduced, and the influence of the variable coupling relationship of the pressure-flow equation on the movement trajectory of the equipment is further investigated. The influence of the flow coefficient on the movement state of the equipment is investigated using aspects of energy transfer and conversion as well as a mathematical model. The fixed flow coefficient cannot simultaneously reflect the characteristics of energy transfer peak and inertial delay because it acts in the same direction on pressure and pressure acceleration, as shown by an analysis of the flow coefficient action law on pressure. A variable flow coefficient-based equipment motion prediction model is proposed, which addresses the problem that fixed flow coefficients cannot be applied to compressible and strong transient fluids. The mutual coupling relationship between multiple control bodies such as fluid, pipeline structure, and equipment motion is established by incorporating the motion state of the equipment into the flow coefficient. The multi-physical quantity motion law of the launch system is expounded on this basis. The proposed prediction model can accurately predict equipment motion by simultaneously reflecting the motion law of energy transfer peak value and flow inertial delay.