Sloshing analysis of a heterogeneous viscous liquid in immovable tank under pitching excitation

Abstract

The effects of the heterogeneity of liquid on the tank sloshing under pitching excitation are analyzed and discussed. The time history of the free surface elevation for tank containing a homogeneous-heterogeneous liquid are recorded and discussed. Numerical simulations are performed for various functions of density using the finite-element method. A theoretical model in the case of heterogeneous viscous liquid are developed using the variation formulation based on the Navier-Stokes equations. The effect of viscosity on the responses is also discussed for each case. In each case, the time history plots for the vertical fluid displacement at a select node, and the pressure in selected elements are presented to illustrate the results of numerical simulations. The effect of heterogeneity parameter of the amplitude of liquid sloshing in a two dimensional partially filled rectangular tank under pitch excitation is conducted to investigate the effects of excitation variable density on the liquid sloshing by a series of numerical experiments. The results are compared with existing theoretical study and the comparison shows fair agreement.