Numerical Simulation of the Interaction of A Membrane with Water with A Free Surface

Abstract

In order to collect validation data for the study of the mechanism of fluid-structure interaction (FSI), an lab experiment was conducted by L. Rizos in the towing tank, 3ME,TUDelft in 2016. The concept of the experiment is shown in the figure 1. A cylindrical container is partially filled with water. A small cylindrical oscillator with flexible bottom is placed in the container. The oscillator is driven harmonically by a motor. During the experiment, the deflection of the flexible bottom, the motion of the free surface and the driven force were monitored and recorded. The figure 2 is the photo of the experiment. In order to better understand Rizos’ experiment, a series of researches are conducted in the Section Ship Hydromechanics, which includes analytical simulation and several numerical simulations with different methods. A linear algorithm is developed in this thesis, which applies implicit, monolithic (solving the fluid domain and structure domain simultaneously) and one-step (without iteration) methods. The model of the numerical simulation is shown in the figure 3, a small cylinder with flexible bottom is placed in the big cylindrical container. The two cylinders are partially filled with water and the still water levels are the same. The inner cylinder does not moves up and down as a whole. The oscillation of the whole system is the result of the initial wave elevation in the fluid domain and/or the initial deflection in the structure domain. The result of the numerical simulation is shown in the figure 4. The effect of added mass for a structure submerged in water results in that smaller eigen frequency of the structural vibration. The structure interacts with the ambient fluid, especially the free surface. For a pre-defined initial condition, the influence of the free surface results in the mode dispersion. The numerical periods of this FSI system agrees with the analytical periods. Significant numerical dissipation exists in the 1st order time integration techniques. Thus, the second order implicit Adam Moulton method, i.e., the trapezoidal rule, is implemented to improve the algorithm. in this way, the numerical dissipation is decreased drastically (5% less dissipation after 10 periods) without increasing the computational costs.