带环形隔板圆柱形储液罐中液体晃动的解析研究
王佳栋; 周 叮;刘伟庆
ANALYTICAL STUDY OF SMALL AMPLITUDE SLOSHING OF LIQUID IN A CYLINDRICAL TANK WITH AN ANNUAL BAFFLE
研究带有环形刚性隔板的部分充液刚性圆柱罐中液体的微幅晃动特性。将复杂的液体域分割为若干个形状简单的子域,分别研究各子域内液体运动的势函数。利用叠加原理和分离变量法,可得到每个子域内液体所对应的振型函数的一般解。由液体子域界面处的连续条件以及自由表面处的表面波条件,得到含有待定系数的级数方程。对方程作Fourier和Bessel展开,即可求得液体的固有晃动频率和振型函数。数值结果与基于变分原理的Galerkin法以及有限元法的结果分别进行了比较,显示出很好的一致性。
The small amplitude sloshing of ideal fluid in a partially fluid-filled cylindrical rigid tank with a rigid annular baffle was studied. Separating the complicated fluid domain into several simple subdomains, the velocity potential functions corresponding to every fluid subdomains were solved. By introducing the modal expansion method, the general expressions of the modal shapes functions of each subdomains were analytically deduced by using the method of separation of variables based on the superposition principle. According to the continuous conditions among the subdomain interfaces and the free fluid surface wave conditions, the velocity potential equations with unknown coefficients have been obtained. The unknown coefficients in the solutions and the natural sloshing frequencies were determined by using the Fourier series expansion and the Bessel series expansion. The convergence study shows the high accuracy. The numerical results were compared with those obtained by the Galerkin method based on the variational principle and those obtained by the finite element method. Excellent agreement has been achieved.
环形隔板 / 圆柱形储液罐 / 液体子域 / 函数展开 / 固有频率 / 振型函数 {{custom_keyword}} /
annual baffle / cylindrical tank / fluid subdomain / function expansion / natural frequency / modal shape functions {{custom_keyword}} /
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