Implementing a hybrid immersed boundary/fictitious domain (HFD-IB) method coupled with the Discrete Element Method (DEM) to consider lubrication effects between the particles in the fluid domain

Suspensions of particles in a fluid domain could be seen in different natural and industrial applications, ranging from food production to blood flow. For this reason, many researchers studied this topic to get a better insight into the physics of the problem. One of the main topics in this field is to understand the inter-particle forces. In which, particles in the fluid domain face three main forces, which are hydrodynamic long-range interaction, a collision between particles, and lubrication forces. [1] Treatment of first and second forces is straightforward because they could be modeled accurately with the computational fluid dynamics (CFD) method coupled with the Discrete Element Method (CFD-DEM). However, this strategy becomes less accurate for calculating lubrication force when two particles approach each other in a gap distance smaller than the grid size. This is because the grid resolution is not fine enough to capture the correct hydrodynamic interaction.
Among different CFD methods that could be implemented to consider the physics of the suspensions of particles, Immersed Boundary (IB) method has provided a better description of the nature of the topic since it could be used to provide fully resolved CFD simulation. However, the results of the previous researchers also have shown the IB methods also face difficulty in correctly capturing the lubrication effects. Although some researchers have proposed to add a corrective force term in the IB method, this strategy faces a stability problem when there are many particles inside the simulation domain. For this reason, Naoki Hori et al [2] proposed a new strategy to use IB without considering any correction term. In their work, the C dt parameter is defined as a function of time step size, fluid viscosity, and mesh resolution. By keeping this parameter in a specific range, IB could simulate lubrication force with high accuracy, meaning that the grid resolution and time step size are the key parameters in determining the lubrication force. [2]
In the present work, a variant of the IB method named the hybrid immersed-boundary/fictitious domain (HFD-IB) method was selected as the CFD solver. [3] Then, it was coupled with the XDEM code to consider the collision forces between the particles. After successful validation of this CFD-DEM solver, the problem of falling two inline spherical particles in the fluid domain is considered. Our solver could get the interaction forces between two-particle correctly by keeping the C dt in a specific range mentioned by the reference articles. As seen in Figure 1, drafting, kissing, and tumbling of particles are illustrated.
References
[1] Kroupa, M., Vonka, M., Soos, M. and Kosek, J., 2016. Utilizing the discrete element method for the modeling of
viscosity in concentrated suspensions. Langmuir, 32(33), pp.8451-8460.
[2]Hori, N., Rosti, M.E. and Takagi, S., 2022. An Eulerian-based immersed boundary method for particle suspensions
with implicit lubrica
[3] Municchi, F. and Radl, S., 2017. Consistent closures for Euler-Lagrange models of bi-disperse gas-particle
suspensions derived from particle-resolved direct numerical simulations. International Journal of Heat and Mass
Transfer, 111, pp.171-190.