The shape of the fundamental sloshing mode in axisymmetric containers

Abstract

ABSTRACT. In the paper we numerically study positions of high spots (extrema) of the fundamental sloshing mode of a liquid in an axisymmetric tank. Our approach is based on a linear model reducing the problem to appropriate Steklov eigenvalue problem. We propose a numerical scheme for calculating sloshing modes and a novel method of making images of oscillating fluid. We also describe the relation of the high spot problem to the celebrated hot spots conjecture.

Coupled BEM and FEM analysis of fluid-structure interaction in dual compartment tanks

“…The value h 1 /R 1 = 1.99 corresponds to the ice-fishing problem. The results of Faltinsen and Timokha [13], and Kulczycki et al [14] are very close. Both Refs.…”

“…We approximate this infinite case using the spherical tank with the small round hole on its top. It allows us to compare our numerical results with those obtained in the papers [12][13][14].…”

“…Both Refs. [13][14] and [12] results analytically approximate the sloshing eigenvalues of the spherical tank.…”

“…In Tables 1 and 2 we compare our results obtained by using SBEM and MBEM with those obtained in Refs. [12][13][14] for axisymmetric (a = 0) and non-axisymmetric (a = 1) modes. Four first frequencies (m = 1 4 , ) are evaluated for each a.…”

“…where w is an own frequency, C k and D k are unknown constants. Using (14) we obtain the eigenvalue problem for evaluating natural frequencies and modes of the fluid-filled cylindrical-spherical tank [9]. The filling levels are h 1 =1 m and h 2 = 1.5 m. The lowest frequencies of the double tank are presented in Table 4.…”