Computer modeling of liquid sloshing in tanks with baffles

Abstract

Research Objective. The objective of this study is to develop numerical methods for analyzing the stability of fluid motion in tanks equipped with various types of internal baffles.Relevance. The investigation of fluid motion stability in tanks with horizontal and vertical baffles is of significant theoretical and practical importance for many fields — from aerospace and aviation to marine and ground-based liquid storage (e.g., fuels, process fluids, chemical reagents). The presence of baffles substantially alters the sloshing behavior: they affect the frequency spectrum of the free surface, vortex structures, energy localization, and the emergence of resonant modes. Improper consideration of these effects may lead to reduced safety, increased dynamic loads on the structure, and degraded performance of the overall system. Experimental studies of such processes are often technically complex, costly, and potentially hazardous. Testing real liquid volumes requires large-scale facilities, high material and equipment expenses, as well as rigorous safety measures when dealing with flammable, aggressive, or explosive substances. Therefore, the development of accurate mathematical models, numerical algorithms, and simulation methods for fluid motion in baffled tanks is of particular relevance. Computer-based modeling provides a safe and relatively low-cost means to explore a wide range of fluid behavior regimes.

Research Methods. The study employs methods from potential theory and singular integral equations, the boundary element method (BEM), the subdomain method, and the method of prescribed normal forms.

Results. Systems of one-dimensional singular integral equations were derived to determine the velocity potential. Basis functions were obtained, specifically the free surface oscillation modes, which were then used to solve the problem of forced oscillations. The influence of combined horizontal and vertical excitations was analyzed for tanks of various designs — both without baffles and with vertical or horizontal baffles. Regions of stable and unstable fluid motion were identified. It was found that the presence of baffles significantly reduces the amplitude of free surface oscillations.

Conclusions. The obtained results demonstrated that the use of horizontal and vertical baffles has a significant impact on the stability of fluid motion in tanks, specifically by considerably reducing the amplitude of free surface oscillations. The data obtained may be applied to improve the reliability and safety of tank systems across various engineering domains, particularly in aviation, space, marine, and energy industries.