Method of discrete singularities in problems of filler vibrations in fuel tanks under overloads and at low gravity

Abstract

The paper is about free vibration problems in fuel tanks with different levels of fillers both under overloads and low gravity. The fuel tanks are considered as rigid shells of revolution. The liquid, contained in the tanks, is supposed to be an ideal and incompressible one, and its flow, induced by external excitations, is irrotational. The problem of free axisymmetric harmonic oscillations of the fluid-filled rigid compound shell is considered. The mixed boundary value problem is formulated, and boundary conditions are received on the boundaries of the fluid domain. The non-penetration conditions is formulated on the rigid shell boundaries, and on the free liquid surface there are kinematic and dynamic boundary conditions. The flow fluctuations are described by using the velocity potential that for ideal and incompressible liquids satisfies the Laplace equation. For its solution, the integral representation is in use. But there are two unknown functions, the velocity potential and the function describing the shape and position of the free surface during time. The transformation of the boundary conditions leads to eliminating one of these unknown functions. So, the system of boundary singular integral equations is obtained to determine the velocity potential. The discrete singularity method and the boundary element method are applied for its numerical solution. The problem of determining own modes and frequencies is solved by using the techniques, where the surface tension effects are neglected. Then these modes are considered as basic functions to determine the modes and frequencies of the liquid taking into account the surface tension. Thus, in this work the method is developed which takes into account the surface tension effect on the frequency of fluid fluctuations in the rigid tank under low gravity conditions. The surface of the interaction between liquid media and gas is considered as a thin membrane, whose thickness is neglected. The fluid pressure on this surface is determined by the Laplace-Young equation. The developed method is useful for the investigation of free and forced fluid oscillations in rigid compound shells with arbitrary meridians.