# Exact regularized point particle (ERPP) method for particle-laden wall-bounded flows in the two-way coupling regime

## TL;DR

The paper extends the ERPP method to accurately simulate particle-fluid interactions near walls in turbulent flows, capturing vorticity effects and enabling detailed analysis of turbulence modulation and drag behavior.

## Contribution

It introduces an enhanced ERPP method that accounts for wall-induced vorticity, allowing comprehensive simulations of particle-laden flows with uneven distributions and various parameters.

## Key findings

- Particles near walls generate significant vorticity affecting flow dynamics.
- No drag reduction observed; particles can increase drag depending on conditions.
- The momentum stress budget explains the influence of particles on wall shear stress.

## Abstract

The Exact Regularized Point Particle (ERPP) method is extended to treat the interphase momentum coupling between particles and fluid in the presence of walls by accounting for the vorticity generation due to the particles close to solid boundaries. The ERPP method overcomes the limitations of other methods by allowing the simulation of an extensive parameter space (Stokes number, mass loading, particle-to-fluid density ratio and Reynolds number) and of particle spatial distributions that are uneven (few particles per computational cell). The enhanced ERPP method is explained in detail and validated by considering the global impulse balance. In conditions when particles are located close to the wall, a common scenario in wall-bounded turbulent flows, the main contribution to the total impulse arises from the particle-induced vorticity at the solid boundary. The method is applied to direct numerical simulations of particle-laden turbulent pipe flow in the two-way coupling regime to address the turbulence modulation. The effects of the mass loading, the Stokes number and the particle-to-fluid density ratio are investigated. The drag is either unaltered or increased by the particles with respect to the uncoupled case. No drag reduction is found in the parameter space considered. The momentum stress budget, which includes an extra stress contribution by the particles, provides the rationale behind the drag behaviour. The extra stress produces a momentum flux towards the wall that strongly modifies the viscous stress, the culprit of drag at solid boundaries.