Numerical Investigations of a Partitioned FSI Algorithm for Tetra Pak's Filling Tube

Abstract: Numerical simulations of fluid-structure interaction of a water-filled tube with a free surface are conducted using an implicit partitioned coupling scheme. Abaqus and STAR-CCM+ are used for the solid- and fluid domains respectively. This application has stability issues, with the most severe turning out to be the added mass effect. Rayleigh β damping and grid flux under-relaxation has been used to keep simulations stable and these parameters’ effect on the solution and stability are investigated. A model problem consisting of a completely filled tube of a linear elastic material and a potential flow is analysed with respect to stability, considering the HHT time integration scheme used in Abaqus. A criterion for the displacement under-relaxation factor ω is found, depending on the geometry, material parameters, β and time step. The impact on stability of changing these parameters is discussed and the stability criterion is validated against simulations. An effort is made to provide suitable settings and recommendations for future simulations. It is found that β damping is very effective in stabilising the algorithm, but changes the solu- tion significantly. Grid flux under-relaxation also helps stabilise the solution, but the mechanism is not clear and its effect on the solution is erratic. It turns out that smaller time steps have a destabilising effect on the partitioned algorithm, and so do long tubes, thin, weak structures and heavy fluids. The added mass effect can be mitigated by lowering ω, but at the cost of com- putation time. The results of numerical experiments are in good agreement with the criterion established by the model problem. Some additional factors influencing stability are discussed, including viscosity, the effect of an obstructed flow, boundary conditions, a nonlinear finite ele- ment formulation and a higher order time discretisation scheme.