Analysis of Damping of Fluid Oscillations in Spherical Tanks Using the Boundary Element Method

Abstract

The aim of this study is to develop numerical methods for analyzing the stability of fluid motion in spherical tanks with horizontal baffles. Partially filled spherical tanks are important components of modern engineering systems. They are widely used as storage vessels for drinking water and hazardous liquids, as well as structural elements of launch vehicle fuel tanks. Experimental testing of such tanks for strength and dynamic stability is generally expensive and not always safe. This necessitates the development of virtual testing methods based on efficient computational algorithms. In this context, the development of new numerical methods for analyzing fluid oscillations and motion stability in tanks, where the radius of the free surface depends on the filling level, is a relevant problem. The study employs methods of potential theory, the boundary element method, the method of prescribed normal modes, and numerical techniques for solving systems of differential equations. Spectral boundary value problems are solved to determine the natural frequencies and mode shapes of fluid oscillations in spherical tanks without baffles and in tanks with horizontal baffles containing openings of various diameters. These problems are reduced to systems of one-dimensional singular integral equations. The obtained natural modes are used as basis functions for solving the problem of forced fluid oscillations in spherical tanks subjected to simultaneous vertical and horizontal excitations. Expressions for the velocity potential and the free surface elevation function are derived in the form of infinite series, and the convergence of these series is analyzed. The problem of determining the dynamic characteristics of the fluid is reduced to solving a system of ordinary differential equations of the Mathieu type, which makes it possible to study the stability of fluid motion in a spherical tank under combined horizontal and vertical loading. An efficient numerical approach for studying fluid oscillations and motion stability in partially filled spherical tanks has been developed and implemented. The proposed approach can be used for virtual testing of spherical tanks and for analyzing fluid behavior in the design and operation of tanks and fuel systems in aerospace engineering.