Sloshing Forces on a Tank With Two Compartments, Application of the Pendulum Model and CFD

Abstract

Two different methods, pendulum model and computational fluid dynamics (CFD), to predict the forces on the ship caused by the flooded water are compared against the model test results. Calculations were performed for a tank in forced motions at different frequencies, for which experimental results were available. The tank had a dividing wall with an opening. The overall behaviour of the force time history was well captured with the pendulum model. In particular at lower frequency the agreement of the force range is very good. Some small force peaks due to the sloshing were predicted in a good correspondence with the CFD simulations. At a higher frequency slight discrepancy is shown also in the CFD calculations. The free surface behaviour is captured in detailed level by the CFD calculations, but the overall motion of the water is captured also with the pendulum model with plane surface model. Comparison to the model tests shows the applicability of the pendulum model in simulating sloshing case with the exchange of water between the compartments. These comparisons show that the pendulum model is a sufficiently accurate and calculation time wise efficient method. It provides a tool to perform a great amount of simulations in order to study the impact of different parameters and the statistical probabilities of ship survival under different accident scenarios.

A Fast Simulation Method for Damaged Ship Dynamics

“…Damaged ship roll is affected by flooding water exchange. This is implemented in the numerical simulation by means of the flooding law (9,10), where Q is the flow rate:…”

“…Among these, the most accurate are computational fluid dynamics (CFD) approaches, such as the mesh-less technique named smoothed-particle hydrodynamic (SPH) [3,4] and volume of fluid methods (VOF) [5][6][7]. In general, CFD is used intensively for studying sloshing phenomena [8][9][10] and many efforts are made to couple them with the dynamics of a damaged ship in waves [7,11,12].…”

Hydrodynamic Analysis of Partially Filled Liquid Tanks Subject to 3D Vehicular Manoeuvring

“…where β m is the modal displacement, sloshing force F m is written in 5 × 5 matrix form, and M is the liquid mass matrix considered as solid. Q m is the transfer function between modal response β and the sloshing forces in 5 × 1 matrix form, which can be summarized from equations (15)- (20):…”

“…On the other hand, it has been observed that if the sloshing is relatively mild, the free surface does not break and the sloshing motion is not chaotic [16], and its motion pattern is analogous to a mechanical system. erefore, many past studies simplify the sloshing liquid into a spring-mass [17,18] or a pendulum [19,20] system. e complication encountered in this approach is that since the mechanical analogy is not based on the fluid theory, it is hard to derive the parameters (mass, stiffness, damping, and natural frequency) of the analogical model directly, unless the tank geometry is simple such as a rectangular tank.…”

A study on the coupling effect between sloshing and motion of FLNG with partially filled tanks

“…Mitra et al [18,19] developed a coupled algorithm using a hybrid marine control system for ship-motion simulation and a finite element method for nonlinear sloshing. Nakashima et al [20] and Manderbacka et al [21] applied pendulum models to obtain sloshing forces with low computational load. These simplified models, although application may be restricted to some specific limits, can give benchmark data to CFD computations.…”