An open‐source population balance modeling framework for the simulation of polydisperse multiphase flows

Abstract

Polydispersity is a challenging feature of many industrial and environmental multiphase flows, influencing all related transfer and transport processes. Besides their size, the fluid or solid particles may be distributed with respect to other properties such as their velocity or shape. Here, a population balance model based on the method of classes is combined with a multifluid solver within the open source computational fluid dynamics library OpenFOAM. The model allows for tracking the evolution of one or more size-conditioned secondary properties. It is applied to two different problems, the first being bubbly flow of air and water in a vertical pipe, where considering the velocity as a secondary property allows to resolve the sizedependent radial segregation. The second application is the gas phase synthesis of titania powder, where non-spherical particle aggregates appear whose shape is modeled through a collision diameter, leading to an improved prediction of the size distribution.

A computational fluid dynamics—Population balance equation approach for evaporating cough droplets transport

“…For the former case, Eq. (22) for a volume-based DSD, , can be written in the th interval as ( Lehnigk et al, 2022 ): where is the size class fraction and is the volume fraction for the th size class; is the velocity of all droplets and is independent of the internal coordinate ; is the pivotal volume of ; is the volume change rate. The third term in the left hand side (LHS) of Eq.…”

“…The group velocity can be obtained from the MFM. More details can be found in Lehnigk et al (2022) . Our MUSIG-based simulations will group the size classes of the PBE into only two disperse phases, small and large droplets, and each moves with its own velocity.…”

“…The PBE is a continuity statement written in terms of the droplet number density function (NDF), and is able to provide a detailed description of the disperse phase ( Marchisio and Fox, 2013 ). In recent year, the PBE has been coupled with TFM and applied in polydisperse bubble flows with ( Lehnigk et al, 2022 ) or without ( Heylmun et al, 2019 ) interphase mass transfer. Satisfactory performances are observed.…”

Dynamic computational resource allocation for CFD simulations based on pareto front optimization

“…Bubble size distribution can be tracked with population balance equation [21], which incorporates the effects of coalescence (particles agglomerate into bigger ones) and breakup (particles split into smaller ones). The method of classes [13] models the distribution of bubbles by discretizing the bubble population into a finite number of size groups (visualised in Figure 1). All of the interactions between bubble size groups are then aggregated by source term assembly and used to produce a new updated distribution.…”

Heavy and light inertial particle aggregates in homogeneous isotropic turbulence: A study on breakup and stress statistics

“…On the macro-scale (i.e., the scale of the equipment), where flow field heterogeneities and boundary layer phenomena affect the evolution of the dispersed phase, so called Eulerian-Eulerian approaches, especially when coupled with population balance models (Marchisio et al, 2006), are of particular interest, as they can be conveniently used to promptly compute the breakup dynamics and the particle size distribution. By such an approach a number of systems of practical relevance have been investigated, such as emulsions (Lebaz et al, 2021), bubbly flows (Syed et al, 2018;Zhang et al, 2021;Maluta et al, 2021;Lehnigk et al, 2022) and particle synthesis processes (Schikarski et al, 2022). However, despite the wide range of applications, such approaches still rely on empirical correlations, generally assuming a single phenomenon (e.g.…”