考虑非线性效应的浅水亚临界航速船舶水压场数值计算与分析

Numerical Calculation and Analysis of Nonlinear Pressure Field Induced by Ship Motion at Subcritical Speed in Shallow Water

基于浅水波动势流理论和薄船假定,建立了考虑非线性效应和色散效应影响的浅水船舶水压场理论模型。采用有限差分方法对浅水亚临界航速船舶水压场进行了数值计算,为了保证非线性方程计算过程的稳定性,在船体和上下游边界条件中添加了人工粘性项,通过与试验结果比对,验证了所建立的船舶水压场理论模型和计算方法的准确性,并分析了不同航道宽度、不同水深及不同水深弗劳德数下非线性效应对船舶水压场的影响。结果表明,航道宽度越窄,水深越浅,非线性效应对船舶水压场影响越大,而当船舶以近临界速度在不同宽度的航道内航行时,非线性效应的影响均不容忽视。

Based on the shallow water wave potential flow theory and the slender ship assumption, a mathematical model for pressure field considering nonlinear effects and the dispersive effects induced by ship motion at subcritical speed in shallow water was established. The pressure field was calculated by using finite difference method. In order to overcome the instability of the nonlinear equation, artificial viscous effects were added in radiation condition and ship boundary conditions. Computation results were compared with experimental results, by which both the mathematical model and calculation method were validated. The nonlinear effects on the ship hydrodynamic pressure field in different width of channel, different depth water and Froude numbers at different depth were analyzed. The results show that the nonlinear effects on the hydrodynamic pressure field became greater, with the width and the depth getting narrow and shallow respectively. If a ship is moving at near-critical speed, then the nonlinear effects must be considered in any channel.