Linear sloshing in a 2D rectangular tank with a flexible sidewall

Abstract

A 2D rectangular sloshing tank with a flexible sidewall have been studied analytically and numerically, with a focus on the coupling between sloshing and the flexible wall. This analysis introduces new knowledge of the effect of internal motions and flow in a membrane structure with a free surface, such as closed flexible fish cages. A framework for analyzing coupled fluid-membrane interaction in the time, and frequency domain in 2D have been developed. The analytical solution gives new knowledge about the effect of the deformations on the linear pressure inside the tank. Coupled eigenfrequencies and the transfer functions for two different membrane lengths due to sway excitation have been found both analytically and numerically. The analytical and numerical results agree. The eigenfrequencies of the system are highly dependent on both the tension and the 2D membrane length. If we consider a given value of tension, then the eigenfrequency of the coupled system is smaller than the sloshing frequency of the rigid tank for any given . If the tension is small, and we consider a given sloshing frequency of the rigid tank, then there can be more than eigenfrequencies of the coupled system that is lower than the sloshing frequency of the rigid tank. For large tensions, the eigenfrequencies of the system become the sloshing frequency of a rigid tank. For low tensions, numerical challenges for the direct numerical solution for frequencies close to the natural sloshing frequencies were pointed out.

Revisiting the experiment of a free-surface resonance of a liquid in a vibration tank using a nonlinear fluid–structure computational model

“…The effects of the geometrical nonlinearities of structures containing liquids have been studied in order to quantify the influence of a fluid on the large amplitude motion of the structure (Dowell, 1998;Amabili, 2008;Strand and Faltinsen, 2017;Alijani and Amabili, 2014). For example, many experimental studies are available for large amplitude vibrations of thin shells partially filled with liquids such as the ones proposed by (Olson, 1965;Leissa, 1973;Chen and Babcock, 1975;Chiba, 1992;Koval'chuk and Lakiza, 1995) and also by (Carra et al, 2013) in which the experimental study that is presented could be used as a test case for future nonlinear fluid-structure interaction problem.…”

Wave and Current Effects on Floating Fish Farms

“…10. Structural elastic membrane effects for flexible cages (Strand and Faltinsen 2017) will influence the natural sloshing frequencies.…”

Developments in Modeling Techniques for Reliability Design of Aquaculture Cages: A Review

“…Severe sloshing originates from the lowest sloshing mode with nonlinear energy transfer [159]. Furthermore, the sloshing response is predicted to be infinite at the eigenfrequencies of the cage system through the linear potential flow theory instead of the finite amplitude in reality; thus, viscous damping and nonlinear free water surface effects should be included [162]. Especially, the viscous boundary layer damping is nonnegligible when wave breaking occurs [125].…”