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

Abstract

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 large-amplitude sloshing. The composite equivalent modeling method suitable for large-amplitude sloshing in normal and low-gravity is proposed in this paper. By considering the change of liquid equilibrium position in sloshing, the large-amplitude 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.