Three-dimensional dynamic liquid slosh in partially-filled horizontal tanks subject to simultaneous longitudinal and lateral excitations

Abstract

Three-dimensional liquid slosh in a horizontal cylindrical tank is analyzed assuming inviscid, incompressible and irrotational flows under simultaneous application of longitudinal and lateral accelerations, idealizing a braking-in-a-turn maneuver in a road tanker. The spectral problem of liquid slosh within the partially-filled tank of arbitrary cross-section and finite length is initially formulated using the higher order boundary element method (BEM). The three-dimensional Laplace equation is subsequently reduced to a two-dimensional Helmholtz equation using the separation of variables, which significantly reduces the computing demand. The computing time is further reduced by reducing the generalized eigenvalue problem to a standard one considering only the velocity potential on the half free-surface length. The resulting natural slosh frequencies and modes are implemented in a linear multimodal method to obtain generalized coordinates of the free-surface in a partly-filled circular cross-section tank. The slosh forces and moments are subsequently formulated in terms of generalized coordinates and hydrodynamic coefficients considering the damping due to liquid viscosity in the boundary layer. It is shown that the proposed BEM integrating the multimodal method yields computationally efficient solution of the three-dimensional liquid slosh within moving horizontal tanks. The validity of the model is demonstrated using reported analytical and experimental results. The range of applicability of the linear theory for predicting three-dimensional transient slosh is further discussed through comparisons with nonlinear simulation results obtained from a commercial CFD code. The results suggest that the linear theory can predict the slosh forces and moments with reasonably good accuracy when the steady-magnitudes of the lateral and longitudinal accelerations are less than 0.3 g and 0.2 g, respectively, for a tank with aspect ratio in the order of 2.4.