Time-mean equation and multi-field coupling numerical method for low-Reynolds-number turbulent flow in ferrofluid

Significant breakthroughs in the theory and applications of ferrofluid have broadened their usage in areas such as sealing and actuation. However, the development of numerical ferrofluid dynamics has been slow owing to inadequate multi-field coupling techniques and incomplete equations for turbulence in ferrofluid flow. The understanding of low-Reynolds-number turbulent flow mechanisms in ferrofluid at small scales, particularly in sealing and actuation applications, remains limited, therefore hindering further advancements. This article delves into the turbulent flow equations for general fluid and discusses the influence of different-scale vortices on the average fluid motion. An anisotropic turbulence model was introduced and verified using fluid flow around a cylinder. Magnetic and flow fields data were coupled through node ranking and interpolation methods. By introducing the interaction force of magnetic dipoles, the turbulent equations were refined within Euler grids, thereby establishing a numerical model for the turbulent motion of ferrofluids influenced by multiple fields. This model was applied to study the deformation and migration processes of ferrofluid under an external magnetic field. The variations in ferrofluid motion under magnetic forces were encapsulated, and macroscopic flow comparisons were made through experiments, which demonstrated good consistency. This research provides new methods and ideas for use in ferrofluid numerical studies. Additionally, it offers valuable technical support that can aid in developing industrial products such as sealing and driving devices based on ferrofluids.