Damping of liquid sloshing in the tanks subjected to vertical acceleration by using the boundary element method

  • Maria Myronenko Institute of Mechanical Engineering Problems A. N. Podgorny NASU, 2/10 Pozharsky Street, Kharkiv, 61046, Ukraine; O. M. Beketov National University of Urban Economy in Kharkiv, 17, Marshala Bazhanova Street, Kharkiv, 61002, Ukraine http://orcid.org/0000-0002-0266-4463
Keywords: mathematical modeling, sloshing, boundary element method, free surface, gravitational waves, capillarity waves


The paper presents numerical simulations of liquid sloshing in the partially filled fuel tanks subjected to vertical acceleration. The tanks are considered to be shells of revolution, and a liquid inside the tank is supposed to be incompressible with viscosity effects being accounted for. The liquid motion is irrotational, and a velocity potential can be introduced. The boundary value problem is formulated for the Laplace’s equation to obtain the velocity potential and the free surface level. Non-penetration boundary conditions are used at the wetted surface of a shell. The kinematic and dynamic boundary conditions are given on the free liquid surface. Effects of a surface tension are included into the Bernoulli equation as an additional pressure that is proportional to the mean curvature of the free surface. It allows considering coupled effects of both gravitational and capillarity waves. The boundary value problem is solved by using boundary element method. The system of the Mathieu equations is obtained and modified according to the damping effects. These effects are estimated, and stability regions on Ince-Strutt diagram are specified.


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How to Cite
Myronenko, M. (1). Damping of liquid sloshing in the tanks subjected to vertical acceleration by using the boundary element method. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 52, 43-51. https://doi.org/10.26565/2304-6201-2021-52-06