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

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.

Near-wall turbulence modulation by small inertial particles

“…2015; Horwitz & Mani 2016; Ireland & Desjardins 2017; Battista et al. 2019; Pakseresht, Esmaily & Apte 2020). Moreover, results in the literature for integral observables show qualitatively different trends.…”

“…For instance, while Vreman (2007) and Zhao, Andersson & Gillissen (2010) have observed a drag-reducing behaviour in two-way coupled particle-laden turbulent channel flow, other studies have measured a drag increase (Battista et al. 2019). These opposite trends suggest the presence of different regimes of momentum transfer in wall-bounded particle-laden turbulence.…”

The discrete Green's function paradigm for two-way coupled Euler–Lagrange simulation

“…In other words, we have verified that the DGF model can accurately predict the undisturbed fluid velocity of a moving particle at low Reynolds number in wall-bounded settings, regardless of the form of force model, which may change based on various physical considerations. We speculate that Gaussian based schemes which estimate the undisturbed fluid velocity assuming unbounded settings (Gualtieri et al 2015;Ireland & Desjardins 2017;Balachandar et al 2019) would perform qualitatively like the Esmaily & Horwitz (2018) method, while the scheme developed by Battista et al (2019) would likely exhibit qualitatively similar performance to the DGF results presented here.…”

“…The extension of the DGF method to finite Reynolds number makes it an attractive approach compared with the extended ERPP approach, which is based on analytical solutions to the unsteady Stokes equations (Battista et al 2019). However, the ERPP approach may be more advantageous in regimes where the density ratio is not exceptionally large, such as liquid-solid flow.…”

“…We will also demonstrate explicitly how discretization of the field equations (via finite differences or finite elements for example) is connected to the discrete disturbance flow and ultimately the computation of the undisturbed fluid velocity. It is worth mentioning that the exact regularized point-particle method (ERPP) (Gualtieri et al 2015) was recently extended to the wall-bounded flow regime (Battista et al 2019). This approach is particularly attractive in its incorporation of unsteady effects, however, ERPP is presently limited to low particle Reynolds number, which will not be a general limitation of the method presented in this work.…”