Exact regularized point particle method for multiphase flows in the two-way coupling regime

Abstract

Particulate flows have mainly been studied under the simplifying assumption of a one-way coupling regime where the disperse phase does not modify the carrier fluid. A more complete view of multiphase flows can be gained calling into play two-way coupling effects, i.e. by accounting for the inter-phase momentum exchange, which is certainly relevant at increasing mass loading. In this paper we present a new methodology rigorously designed to capture the inter-phase momentum exchange for particles smaller than the smallest hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. The momentum coupling mechanism exploits the unsteady Stokes flow around a small rigid sphere, where the transient disturbance produced by each particle is evaluated in a closed form. The particles are described as lumped point masses, which would lead to the appearance of singularities. A rigorous regularization procedure is conceived to extract the physically relevant interactions between the particles and the fluid which avoids any 'ad hoc' assumption. The approach is suited for high-efficiency implementation on massively parallel machines since the transient disturbance produced by the particles is strongly localized in space. We will show that hundreds of thousands of particles can be handled at an affordable computational cost, as demonstrated by a preliminary application to a particle-laden turbulent shear flow.

A numerical approach for particle-vortex interactions based on volume-averaged equations

“…For the history force at a finite Reynolds number, a reliable model for general flows is not available so far. However, as discussed by Gualtieri et al (2015), the history effect can be partly reproduced in accurate two-way coupling simulations without any specific model. Therefore, in the present model, we will numerically solve the following equation…”

“…Thus, the turbulence attenuation by particles of D ∼ η is not reasonably reproduced by traditional two-way coupling simulations (Eaton, 2009;Schneiders et al, 2017). On the other hand, fully-resolved simulations like those in Kempe and Fröhlich (2014), Picano et al (2015), Fornari et al (2016) and Santarelli and Fröhlich (2016) are still too expensive for configurations of practical interest, which justifies the need for better models.…”

A correction scheme for two-way coupled point-particle simulations on anisotropic grids

“…the velocity at the location of particle according to Eq. (11), which in combination with Eq. (13) yields…”

Experimental study of inertial particles clustering and settling in homogeneous turbulence

“…Moreover, modeling the backreaction of the dispersed phase by point-particle methods present technical issues associated with the application of the point-wise forcing on the fluid computational grid (Balachandar 2009;Eaton 2009;Gualtieri et al 2013). To overcome these shortcomings, advanced methods have recently been proposed (Gualtieri et al 2015;Horwitz & Mani 2016;Ireland & Desjardins 2017) whose merits need to be fully appreciated in future comparisons with well-controlled experiments. Setting up the turbulent flow in two-way coupled simulations is also a critical issue: forcing steady-state homogeneous turbulence in either Fourier or physical space leads to artificial energy transfers hardly discernible from the actual interphase dynamics (Lucci et al 2010).…”