水平激励下带竖向隔板的二维矩形储箱中流体晃动研究

Analysis of liquid sloshing in a 2D rectangular container with vertical baffle under horizontal excitation

研究了水平激励下二维矩形储箱中流体的晃动,抑制晃动的装置为竖向的刚性隔板,建立了隔板在储箱自由液面处的解析模型。首先通过引入人工界面的方式,将流体域划分成若干个流体子域,使每个流体子域对应的速度势函数满足C1连续性条件。基于叠加原理,使用分离变量法求得每个流体子域的速度势的形式解,将形式解代入子域间界面与自由液面条件可得含有待定系数的级数方程,通过加权积分消去方程中的空间坐标,截断方程可得特征方程,由此可得晃动频率与模态。将水平激励下的速度势函数分解为摄动速度势与刚体速度势,将摄动速度势和刚体速度势代入自由液面的波动方程即可求得含广义坐标的动力响应方程,求解该方程可得储箱中流体的晃动响应。

The sloshing of liquid in a 2D rectangular container under horizontal excitation was investigated.A rigid vertical baffle was installed as the sloshing control device.The analytical models of the baffle at free surfaces were established,respectively.Firstly,the liquid domain was divided into several liquid subdomains which satisfied the continuous boundary conditions of class C1 by introducing artificial interfaces・Based on the superposition principle,the formal solution of the velocity potential of each liquid subdomain was obtained using the method of variables separation.The formal solution was substituted into the condition of interfaces between the subdomains and the free liquid surface,giving a series equation with the undetermind coefficients・The spatial coordinates in the equation were eliminated by weighted integration,and the characteristic equation was obtained by truncating the equation.The sloshing frequency and mode were then achieved by the characteristic equation.The total velocity potential function under lateral excitation was decomposed into the container potential function and the liquid perturbed potential function.The dynamic response equation with generalized coordinates was thereby obtained by substituting the perturbation velocity potential and rigid body velocity potential into the wave equation of liquid surface.The sloshing response of liquid in the container was finally obtained by solving the equation.