摘要
Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational(e.g.,pitching)excitations.To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks,a variational domain-decomposition scheme is proposed.This scheme includes three steps:(i)dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles(i.e.,using the baffle as part of the boundaries of the sub-domain)by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces;(ii)expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients,and expressing the auxiliary normal fluid velocity functions on the artificial in terfaces as Fourier-type series with undetermined coefficients;(iii)solving the undetermined coefficients by the Trefftz method and the proposed variational formulations.The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method(FEM),and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation.The present semi-analytical result is compared with that given by computational fluid dynamics(CFD)software or literature.
液体晃动引起的力和力矩会影响贮箱及其相关结构的动力学行为.为了能够使用解析方法研究旋转(例如俯仰)激励下贮箱中液体晃动,往往需要已知解析表达的液体线性Stokes-Joukowski势.本文提出了一种变分区域剖分技术,用以获得带隔板刚性贮箱中液体的解析近似线性Stokes-Joukowski势.该技术包括3步:(1)根据隔板位置(例如使用隔板作为子域的部分边界)引入人工界商,将静流体区域剖分为简单子域.同时引入不同子域中流体的人工密度或人工界面上的辅助法向速度函数;(2)将每个子域的线性Stokes-Joukowski势解表示为一类系数待定的调和函数的线性组合,并将人工界面上的辅助法向流体速度函数表示为系数待定的Fourier级数;(3)用Trefftz方法和提出的变分公式求解待定系数.本文得到的半解析线性Stokes-Joukowski势与文献或有限元法(FEM)给出的结果吻合良好.为了验证其在非线性液体晃动问题研究中的适用性,将其应用于俯仰激励下的二维部分充液带T形隔板矩形贮箱.本文得到的半解析结果与CFD(计算流体动力学)软件或文献给出的结果符合良好.
基金
the National Natural Science Foundation of China(Grant Nos.11572018 and 11772020).
