Modeling shape deformation of ferrofluid ring section and secondary flow in ferrofluid seals with rectangular polar teeth using BEM and FVM

Abstract

The focus of this study is on modeling the shape deformation of ferrofluid ring sections and secondary flows in ferrofluid seals with a rectangular polar tooth. These factors determine the sealing capability and homogenization of particles in ferrofluids. The model consists of governing equations for ferrofluid flows, the balance equation of normal stresses on ferrofluid free surfaces, the magnetic field equations and the ferrofluid volume equation. To solve the mathematical model, a method utilizing a combination of boundary element method and finite volume method is proposed. Discretizing the azimuthal velocity equation with boundary element method enables efficient determination of ferrofluid-ring section shape deformation. Furthermore, a discretely fitting method is proposed to solve the issue of lack of analytic expressions for the magnetic field distribution in sealing structures with rectangular polar teeth. Numerical tests of the magnetic field and azimuthal velocity distribution verify the validity and accuracy of the proposed solution method. Numerical experiments conducted on an actual ferrofluid sealing structure show that increasing the rotational speed of the shaft, in conjunction with effect of the centrifugal force, leads to deformation of the ferrofluid-ring section shape and reduces the contact area between the ferrofluid ring and shaft. This results in a decrease in pressure resistance. Typically, at a speed of 10 m/s, the pressure resistance falls by around 20%. The maximum value of secondary-flow velocity is significantly affected by the rotational speed of the shaft, although it does not exceed 0.8% of the linear velocity on the shaft surface in our study.