A BEM and FEM analysis of fluid–structure interaction in a double tank

Abstract

In this paper we present a fluid-structure interaction analysis of shell structures with compartments partially filled with a liquid. The compound shell was a simplified model of a fuel tank. The shell is considered to be thin and Kirghoff-Lave linear theory hypotheses are applied. The liquid is ideal and incompressible. Its properties and the filling levels may be different in each compartment. The coupled problem is solved using a coupled BEM and FEM in-house solver. The tank structure is modelled by FEM and the liquid sloshing in fluid domain is described by BEM. The method relies on determining the fluid pressure from the system of singular integral equations. For its numerical solution the boundary element method was applied. The boundary of the liquid computational domain is discretized by nine-node boundary elements. The quadratic interpolation of functions and linear interpolation of flux are involved. The natural frequencies were obtained for the cylindrical double tank with two compartments.

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

“…However, using representation (28) creates difficulties in solving the problem under consideration in corner points, because it is impossible to define correctly the normal vector in corner points in classical sense, and in vicinities of these points the potential normal derivative tends to satisfy both conditions (6) and (16). This means that the normal derivative in corner points cannot satisfy Lipschitz continuity [14] so the surface density is not continuous in these points.…”

“…In the axisymmetric case, we can calculate surface integrals as curve integrals of Green's function integrated by the angle variable [15]. Green's function and its normal derivative, integrated by the angle variable, are expressed in terms of complete elliptic integrals of the first and second kind [15], [16] using the following formulae [17]…”

Multi-Domain Boundary Element Method for Axisymmetric Problems in Potential Theory and Linear Isotropic Elasticity

“…Vassiliev [11]). The finite element method was applied by Ravnik et al in [12] to evaluate the natural frequencies k  and modes k u , 1, k N  of the shell of revolution without a liquid. After forming the global stiffness L and mass M matrices, the following equation of motion for the shell containing fluid is obtained:…”

“…2). Eqn (12) are perfect contact conditions. The ratio of cylinder and inclusion heights is H 1 /H 2 = 5, and the ratio of their radii is R 1 /R 2 = 2, elasticity moduli are E 1 = 2,11ꞏ10 6 MPa, E 2 = 2,11ꞏ10 7 MPa, and Poisson's ratios are  1 =  2 = 0.3.…”

Low Frequency Sloshing Analysis of Cylindrical Containers with Flat and Conical Baffles

“…Anti-slosh properties of baffle designs have been investigated through laboratory and numerical experiments employing small size tanks of different geometry [4][5][6][7][8][9]. The experimental investigation of sloshing processes is difficult and sometimes impossible for various reasons.…”