On sloshing modes in a circular tank

  title={On sloshing modes in a circular tank},
  author={Odd Magnus Faltinsen and Alexander N. Timokha},
  journal={Journal of Fluid Mechanics},
  pages={467 - 477}
Abstract Employing the multipole-type functions given by Faltinsen & Timokha (J. Fluid Mech., vol. 665, 2010, pp. 457–479), we derive a Trefftz-type representation of the velocity potential for the liquid sloshing problem in a two-dimensional circular tank. This representation defines a continuation of the velocity potential into the ‘air’ area confined by the ‘dry’ tank surface. Its usage facilitates an effective approximation of the natural sloshing modes for all tank fillings. 

Analytical studies of sloshing in half-cylindrical tanks

The technically important problem of two-dimensional inviscid standing-wave motion of a fluid in a semi-cylindrical vessel is examined using a variety of the Boussinesq wave equation as well as the

Analytically approximate natural sloshing modes for a spherical tank shape

Abstract The multimodal method requires analytical (exact or approximate) natural sloshing modes that exactly satisfy the Laplace equation and boundary condition on the wetted tank surface. When

Some aspects of the eigenfrequency computation in a two-dimensional tank filled with two non miscible fluids

Determining the natural frequencies of the sloshing modes in a two-dimensional tank is a well-known problem in potential theory (see Ibrahim, 2005, or Faltinsen and Timokha, 2009, among recent

The Narimanov–Moiseev Multimodal Analysis of Nonlinear Sloshing in Circular Conical Tanks

The chapter reports mathematical aspects of the Narimanov–Moiseev multimodal modelling for the liquid sloshing in rigid circular conical tanks, which perform small-magnitude oscillatory motions with

Multimodal Method in Sloshing

The multimodal method reduces the sloshing problem with free surface to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic

Damping of liquid sloshing by foams

When a container is set in motion, the free surface of the liquid starts to oscillate or slosh. Such effects can be observed when a glass of water is handled carelessly and the fluid sloshes or even



Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth

  • P. Mciver
  • Engineering
    Journal of Fluid Mechanics
  • 1989
The two-dimensional sloshing of a fluid in a horizontal circular cylindrical container and the three-dimensional sloshing of a fluid in a spherical container are considered. The linearized theory of

A multimodal method for liquid sloshing in a two-dimensional circular tank

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank.

Analytical velocity potentials in cells with a rigid spherical wall

By using Kelvin's inversion, we construct analytical harmonic functions satisfying the zero‐Neumann condition on the inner spherical wall everywhere except a single point where the velocity is

On liquid motion in a circular cylinder with horizontal axis

SummaryThe flow pattern of the slosh motion of a homogeneous, nonviscous (inviscid) and incompressible fluid with a free surface, contained in a rigid circular canal, has been dealt with analytically

On the eigenvalue problem for fluid sloshing in a half-space

SummaryThe boundary-value problem for free oscillations of a liquid in a half-space, which is bounded above by a rigid plane that contains a circular aperture, is transformed to a homogeneous,

A Nyström method for boundary integral equations in domains with corners

SummaryWe give a convergence and error analysis for a Nyström method on a graded mesh for the numerical solution of boundary integral equations for the harmonic Dirichlet problem in plane domains

Handbook of Linear Partial Differential Equations for Engineers and Scientists

INTRODUCTION: SOME DEFINITIONS, FORMULAS, METHODS, AND SOLUTIONS Classification of Second Order Partial Differential Equations Basic Problems of Mathematical Physics Properties and Particular

Sloshing 현상과 제어

최근 다루어지고 있는 sloshing에 관한 연구에 대하여 고찰하여 보았다. 탱크내의 유체운동의 추정에 관해서는 수치해석법에 의한 추정에 대하여는 어느 정도의 가능성을 제시하게 되었다. 그러나 구조강도상 중요한 유체충격에 의한 충격압의 추정에 대해서는 새로운 정량적 검토가 필요하다. 즉 수치계산법으로는 한계가 있기 때문에 이를 극복하기 위해서는 경험이나

Mixed boundary value problems in plane domains with corners