Numerical lubrication model considering the history effect in narrow gaps under a low-resolution environment

When two particles approach each other in a fluid, significant pressure variations and energy dissipation may occur in the narrow gap in the inter-particle region. These effects are often modeled based on classical lubrication theory. However, the applicability of the classical models is limited because the theory disregards the effects of unsteady fluid behavior in the region. This study proposes an unsteady lubrication model that covers a wide range of particle Reynolds number in particle-dispersed flows , and the corresponding numerical implementation smoothly connects the lubrication model to the numerical solutions around the particles by considering the spatial similarity of the fluid dynamics. The proposed model is consists of a lubrication theory and boundary layer theory, and it gives a boundary condition for the pressure at the rim of lubrication-dominant region. The method enables analysis of the history effect due to the unsteady development of the boundary layer in the narrow gap without introducing fine grids, allowing for a significant reduction in computational costs. To establish the validity of the proposed method, the flow in a narrow space between a flat plate and a cylinder in periodic relative motion is demonstrated, and the results of comparing the numerical solution with high spatial resolution and the numerical solution of the proposed method are presented.