求Cassini贮箱内液体小幅晃动频率的解析方法

为得到航天器上燃料晃动频率,针对Cassini贮箱内液体小幅晃动,将贮箱的柱段近似为非常扁长的椭球,建立了原点位于与箱内静液面接触线处相切的圆锥顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,采用伽辽金方法将变分方程转变为一个标准的特征值问题形式的频率方程,求解了不同尺寸比例的旋转椭球形贮箱和Cassini贮箱在不同的充液比和不同的Bond数情况下液体小幅晃动的基频,并与已有的理论和实验结果进行对照.结果表明,本文方法用于求解旋转椭球形贮箱和Cassini贮箱内液体小幅晃动频率是可行的.

Analytical Method of Solving the Small Amplitude Sloshing Eigenfrequencies of Liquid in Cassini Tanks

In order to get the small amplitude sloshing eigenfrequency of liquid in spacecraft, for Cassini tanks, the cylindrical part of the tank is considered to be a part of a very prolate ellipsoid approximately. Spherical coordinates is built, whose origin is at the top of the cone that is tangent to the tank at the contact line of the hydrostatic surface with the tank wall. The velocity potential and the liquid surface displacement were determined analytically in terms of the Gauss hypergeometric series. The variation function was transformed into a frequency equation in the form of a standard eigenvalue problem by Galerkin method. The achieved first eigenfrequencies of liquid in spheroidal tanks and Cassini tanks with different dimension, different liquid filling level and different Bond number were compared with those from other theoretical and experimental methods. Large calculations prove that this analytical method is practicable to find the solution of small amplitude sloshing eigenfrequencies of liquid in spheroidal tanks and Cassini tanks.