论文部分内容阅读
针对在求解液化天然气连续泄漏到水面上的扩展蒸发模型过程中遇到的难以求得解析解的问题,在恒定泄漏速率时,采用摄动法对模型方程中的参数进行无量纲化,求解出液池质量、液池半径、液池蒸发速率、液池厚度的近似解析解。摄动法的应用简化了数学求解问题和求解过程,得出清晰的解析结构,避开了计算机数值求解中解的精度、稳定性与收敛性等问题。结合具体泄漏情况对求解出的高阶摄动解,用龙格-库塔法求解出的数值解进行验证,结果表明两者几乎一致。
Aiming at the difficult problem of solving analytic solution for solving the extended evaporating model of continuous LNG leaking to the water surface, the parameters in the model equation are dimensionlessly solved by the perturbation method at a constant leakage rate Liquid pool quality, liquid pool radius, liquid pool evaporation rate, liquid pool approximate analytical solution The application of perturbation method simplifies the problem of mathematical solution and the process of solving, obtains a clear analytic structure, and avoids the problems of accuracy, stability and convergence of solution in numerical computer numerical solution. Combined with the specific leakage case, the solution of the higher-order perturbation solution is validated by the numerical solution of Runge-Kutta method. The results show that the two solutions are almost the same.