轴对称贮箱内液体大幅晃动的复合等效力学模型

Composite equivalent mechanical models for large-amplitude liquid sloshing in axisymmetrical tanks

航天工程中普遍使用等效力学模型描述液体晃动动力学,但基于线性理论的传统等效力学模型在大幅晃动中的适用性较差、精度较低.为此本文提出适用于常/低重力环境下液体大幅晃动的复合等效建模方法.以轴对称贮箱为例,提出了大幅晃动下跟随等效重力的液体动平衡位置确定方法,建立了球面摆形式的复合等效力学模型,并推导了等效系统动力学方程.为验证该建模方法有效性和模型准确性,对大幅平动和转动激励下三维圆柱形贮箱和Cassini贮箱内液体的晃动力和力矩、质心位置等进行了计算,并将复合等效力学模型、传统等效力学模型及计算流体动力学软件的计算结果进行了对比分析.结果表明,该复合等效力学模型可对液体大幅晃动的动力学响应进行较为准确的预测.

Equivalent mechanical models are widely used to describe the dynamics of liquid sloshing in aerospace engineering,but the traditional equivalent mechanical models based on linear theory have poor applicability and accuracy in largeamplitude sloshing.The composite equivalent modeling method suitable for large-amplitude sloshing in normal and lowgravity is proposed in this paper.By considering the change of liquid equilibrium position in sloshing,the largeamplitude motion of the liquid relative to the tank is decomposed into bulk motion following the equivalent gravity and additional small-amplitude sloshing,thus greatly expands the application scope of the linear equivalent mechanical model.Taking the axisymmetrical tanks as examples,the liquid dynamic equilibrium position following the equivalent gravity under large-amplitude sloshing is determined,and the composite equivalent mechanical model in the form of a spherical pendulum is established.For spherical tanks,all liquid is assumed to be involved in bulk motion and the model parameters are found constant during sloshing.For non-spherical tanks such as cylindrical and Cassini tanks,liquid near the tank wall is assumed motionless relative to the tank,and the time-dependent model parameters are approximated by linear interpolation based on equivalent gravity and inclination of the liquid surface.Based on the spherical pendulum model,the dynamic equation of the equivalent system is derived,thus the slosh forces,moments and positions of the liquid center of mass under large translational and rotational excitations are calculated in 3D axisymmetrical tanks.To verify the validity of the modeling method and the accuracy of the composite model,the results of the composite equivalent mechanical model,the traditional equivalent mechanical model as well as the computational fluid dynamics(CFD)software are compared and analyzed.As shown by the results,the composite equivalent mechanical model proposed can accurately predict the dynamic responses of large-amplitude liquid sloshing in axisymmetrical tanks.