# Particle-Fluid modelling

At present, a lot of phenomena in the particle-fluid system has not been well understood yet. The essential reason is the lack of understanding of the interaction mechanism between the fluid and solid phase as well as the inter-particle collisions.

Due to the stochastic nature of the solid particle behaviors, the particle-fluid interaction problems are often too complex to be solved analytically or observed by physical experiments. Therefore, they have to be analyzed by means of numerical simulations.

We focuse on the numerical investigation of the particle-fluid systems based on the Discrete Element Method (DEM). Firstly, we have coupled the DEM with Direct Numerical Simulation (DNS) to study the particle-laden turbulent flow. Then, we have coupled DEM with Lattice Boltzmann Method (LBM) to study the particle sedimentation in Newtonian laminar flow.

## Particle-laden turbulent square duct flows

Particle-laden turbulent square duct flows are commonly encountered in both engineering and environmental applications as shown in Fig.1.

This configuration is of high interest because the behavior of the solid particles can be affected by the secondary vortexes that are known as the secondary flow of Prandtlâ€™s second kind as shown in Fig.2a. Statistically, these eight vortexes distribute symmetrically about the bisectors of the walls and the diagonals of the square cross-sections. However, the instantaneous flow fields could show fairly stronger vortexes and more complex patterns due to the chaotic changes in the turbulent structure as shown in Fig.2b.

The secondary flow in a square duct has the effect of enhancing the lateral mixing and advective transport of solid particles. When the wall-normal gravitational force is considered, the secondary flow plays an important role in the resuspension process as a balance force to gravity.

The resuspension is dominant especially close to the central plane and the sidewalls in the lower half of the duct where the flow velocities are upwards. Finally, the lateral secondary flows close to the duct bottom also play an important role to transport particles from the corners to the center.

We investigated the dispersion of solid particles during transportation as shown in Fig.3 and final deposition as shown in Fig.4.

## LBM-IBM-DEM modeling

Particle collisions play a very important role in determining the fluid-particle multiphase flow, and thus it is crucial to treat the particle-particle interaction using a felicitous method in numerical simulations.

A novel combined LBM – IBM – DEM scheme was presented in this chapter with its application to model the sedimentation of two-dimensional circular particles in incompressible Newtonian flows.

The hydrodynamic model of the incompressible Newtonian flow was based on the Bhatnagar-Gross-Krook LBM, and a momentum exchange-based IBM was adopted to calculate the fluid-solid interaction force.

The kinematics and trajectory of the discrete particles were evaluated by DEM, in which the particle-particle interaction rules were governed by theoretical contact mechanics to enable the direct use of real particle properties.

This eliminated the need of artificial parameters and also improves the reliability of the numerical results. By using a more accurate and physical description of particle interaction, a â€™safe zoneâ€™ or threshold was also no longer required.

Firstly, case studies of two particles settling in a channel were carried out, the velocity characteristics of the particle during settling and near the bottom were examined.

Then, in order to examine the LBM-IBM-DEM scheme for handling system containing large number of inter-particle collisions as well as particle-wall collisions, a simulation of sedimentation of 504 circular particles in a cavity was conducted.

## PIBM: Particulate Immersed Boundary Method

The LBM-IBM-DEM scheme is attractive because no artificial parameters are required in the calculation of both fluid-particle and particle-particle interaction force.

However, the computational cost of this coupling scheme not only lies on the grid resolutions in LBM and the solid particle number NP , but also highly depends on the number of the Lagrangian points NLP distributed on the solid particle boundaries.

Since NLP on each particle should be large enough to ensure the accurate calculation of the fluid-particle interaction force and torque, the actual point number considered in the numerical interpolation is NPÃ—NLP which makes the main calculation effort in the LBM-IBM-DEM modeling highly related to the IBM part.

To conquer this drawback, we proposed the PIBM. Unlike the aforementioned treatments in which the Lagrangian points were linked by stable solid bonds, or flexible filaments, the constraints between the Lagrangian points are thoroughly removed.

By doing so, the free floating of the Lagrangian points is allowed and the driving force on them is simply based on the momentum exchange of the fluid particles.

Compared with the conventional IBM, dozens of times speedup in two-dimensional simulation and hundreds of times in three-dimensional simulation can be expected under the same particle and mesh number.

Numerical simulations of particle sedimentation in Newtonian flows were conducted based on a combined LBM – PIBM – DEM scheme, showing that the PIBM can capture the feature of particulate flows in fluid and is indeed a promising scheme for the solution of the fluid-particle interaction problems.

## Publications

H. Zhang, F.X. Trias, A. Gorobets, A. Oliva, D. Yang, Y. Tan, Y. Sheng. Effect of collisions on the particle behavior in a turbulent square duct flow.Â **Powder Technology**. 269(2015), 320-336.

H. Zhang, F.X. Trias, A. Oliva, D. Yang, Y. Tan, Y. Sheng. PIBM: Particulate immersed boundary method for fluid-particle interaction problems. ArXiv preprint arXiv:1407.6704

H. Zhang, Y. Tan, S. Shu, X. Niu, F.X. Trias, D. Yang, H. Li, Y. Sheng. Numerical investigation on the role of discrete element method in combined LBM-IBM-DEM modeling.Â **Computers & Fluids**, 94(2014), 37-48.

H. Zhang, Y. Tan, D. Yang, F.X. Trias, S. Jiang, Y. Sheng. Numerical investigation of the location of maximum erosive wear damage in elbow: effect of slurry velocity, bend orientation and angle of elbow.Â Â **Powder Technology**. 217(2012), 467-476.

H. Zhang, F.X. Trias, A. Gorobets, A. Oliva, D. Yang, Y. Tan, Y. Sheng. Numerical investigation on particle resuspension in turbulent duct flow via DNS-DEM: Effect of collisions. 11th World Congress on Computational Mechanics (WCCM XI). 2014. Barcelona, Spain.