On Sloshing Modes in Equilateral-Polygonal-Section Containers

Abstract

Vertical sloshing is the liquid surface motion in a container forced to oscillate in the vertical direction. The present paper concerns the vertical sloshing in various equilateral-polygonal-section containers such as octagonal-, heptagonal-, hexagonal-, pentagonal-, square- and triangular-section containers together with a circular-section container, in order to generalise their sloshing modes. As a result, the authors classify the sloshing modes on the basis of the conventional circular-section-container sloshing modes. It is revealed that this modal classification has some advantages over that based on the conventional square-section-container sloshing modes. Furthermore, the stability diagrams for all the equilateral-polygonal-section containers are investigated by both experiments and computations. The present computation is based on a discrete singularity method. The proposed modal classification is useful to predict the eigen frequencies. Specifically speaking, it is found that the equivalent diameter de1 based on the hydraulic mean depth is the most adequate as a characteristic length scale to classify all the sloshing modes. The authors show a unified formula to predict the eigen frequencies, using de1 together with the proposed modal classification.

Keywords

• sloshing
• vibration
• polygonal-section container
• faraday resonance
• free surface
• two-phase flow
• regular polygon