Centrifugal failure mechanism analysis for ferrofluid seals based on a bidirectional coupled multi-physics model

In this paper, we propose a bidirectional coupled multi-physics (BCM) model to study the centrifugal failure mechanism of ferrofluid seals, employing a hybrid finite volume-finite element method. In this model, the evolution of the flow field is described by the two-phase incompressible Navier-Stokes (NS) equations with Kelvin force. The volume of fluid (VOF) method is used to capture the gas-ferrofluid interface. Magnetic scalar potential is introduced to solve for the magnetostatic field. We conducted secondary development on the OpenFOAM and Elmer software packages, which are based on the finite volume method (FVM) and finite element method (FEM), respectively, to calculate the flow field and magnetic field in ferrofluid seals. By developing interpolation methods between FEM and FVM grids based on the parallel bidirectional coupler EOFLibrary[1], field information exchange between the flow field and magnetic field is achieved. The BCM model executes iterative computations on the flow and magnetic fields in an alternating way, continuously synchronizing the information of each, thus facilitating bidirectional coupling between the FVM and FEM frameworks. We employ the BCM model to investigate the failure mechanisms of ferrofluid seals under different conditions, including various load pressure and rotational velocity. The results indicate that the ferrofluid will leave the surface of the shaft along the pole teeth under the action of centrifugal forces, with the highest radial velocity occurring at the boundary of the liquid film. Under varying conditions of rotational velocity and pressure drop, the centrifugal failure modes of ferrofluid seals exhibit distinct differences. Moreover, two dimensionless numbers are proposed to quantitatively evaluate the effects of load pressure and centrifugal force, thereby augmenting the efficacy of seal design.