Bingham fluid simulations using a physically consistent particle method

The Bingham fluid simulation model was constructed and validated using a physically consistent particle method, i.e., the Moving Particle Hydrodynamics (MPH) method. When a discrete particle system satisfies the fundamental laws of physics, the method is asserted as physically consistent. Since Bingham fluids sometimes show solid-like behaviors, linear and angular momentum conservation is especially important. These features are naturally satisfied in the MPH method. To model the Bingham feature, the viscosity of the fluid was varied to express the stress-strain rate relation. Since the solid-like part, where the stress does not exceed the yield stress, was modeled with very large viscosity, the implicit velocity calculation was introduced so as to avoid the restriction of the time step width with respect to the diffusion number. As a result, the present model could express the stopping and solid-like behaviors, which are characteristics of Bingham fluids. The proposed method was verified and validated, and its capability was demonstrated through calculations of the two-dimensional Poiseuille flow of a Bingham plastic fluid and the three-dimensional dam-break flow of a Bingham pseudoplastic fluid by comparing those computed results to theory and experiment

A fluid lubrication analysis including negative pressure using a physically consistent particle method

In recent years, particle methods, which are good for moving boundary problems, have become an effective approach to understand and predict flows in complex geometry, such as lubrication behaviors in rolling bearings. This study adopted a physically consistent particle method, i.e., the moving particle hydrodynamics for incompressible flows (MPH-I) method. For capturing the free surface flows in lubrication, a surface tension model was included. In order to maintain the physical consistency in the MPH-I method, the surface tension model expressed with the two density potentials, which are cohesive pressure potential (CPP) and density gradient potential (DGP), was adopted. The MPH-I method with the two-potential-based surface tension model enabled to handle negative pressure and nearly incompressible flow with very large bulk modulus. In fact, the MPH-I method could successfully reproduce fundamental pressure generation effects in the fluid film lubrication, i.e., the wedge film and squeeze film effects. Furthermore, the computed lubrication pressure agreed well with the experimental results and the classic prediction with Reynolds equation. This implies that the present numerical method was validated under the fluid film lubrication problems