Comparison of Lagrange-based CFD methods with Euler-based methods for two-dimensional simulation of sloshing in tanks and evaluation of three-dimensional effects for selected test cases

Abstract

Sloshing is a key phenomena, which has an influence in the stability and performance of spacecraft guidance systems. With CFD methods it is possible to study the effects that sloshing has on the spacecraft. Usually CFD calculations can take a lot of time to complete, therefore the study of different CFD methods to see their advantages and disadvantages is of interest. Long simulation times are not compatible with the requirements of fast design loops during preliminary development of launch vehicles. Another way to reduce simulation time is to perform 3D physical phenomena in a two dimensional basis, this is not always possible, due to the disappear of important effects. If computational costs or time consumed are reduced by either of these two methods, the efficiency while performing these type of studies can be increased. The focus of this work was the evaluation of alternative CFD methods such as the Smooth Particle Hydrodynamics (SPH). The other purpose of this work was to investigate and evaluate the possibility of replacing 3D simulations by 2D. Here an evaluation of the influence that a dimension reduction has on the results for a selected application case was done. Without a proper interpretation of the simulation results a comparison is not possible, therefore a dimensionless parameter was introduced for the correct analysis of the force and momentum generated by the fluid. The dimensionless parameter correspond to the relation between the inertial force and the force on the tank walls generated by the fluid. The comparison showed that the amplitude of both cases correspond with one another. Also, they showed a phase shift, which was expected due to the change in geometry, which is directly correlated with the system’s natural frequency. The time reduction from three dimensional to two dimensional analysis is considerable. There was a time reduction from up to 22 times for the worst case scenario. The simulations done with the Smooth Particle Hydrodynamics method showed a strong damping effect for the different parameters investigated. Despite the strong damp on the results, the Lagrangian simulations showed a good behavior and trace of the results in comparison with the Eulerian results, which can give an idea of the sloshing effect behavior on the forces applied to the tank walls and the variation of the system’s center of mass.