Modelling of soot coalescence and aggregation with a two-population balance equation model and a conservative finite volume method

Sun, Binxuan; Rigopoulos, Stelios; Liu, Anxiong

doi:10.1016/j.combustflame.2021.02.028

Cited by 24 publications

(9 citation statements)

References 74 publications

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“…Pantarhei has been used extensively to simulate transitional and turbulent flows in boundary layers, around airfoils, behind fractal grids and inside stirred vessels (Thomareis & Papadakis 2017, 2018; Xiao & Papadakis 2017, 2019; Başbuğ, Papadakis & Vassilicos 2018; Paul, Papadakis & Vassilicos 2018; Mikhaylov, Rigopoulos & Papadakis 2021). The code CPMOD has been employed for various population balance problems, including aerosol synthesis and soot formation (Sewerin & Rigopoulos 2017 a , 2018; Liu & Rigopoulos 2019; Sun, Rigopoulos & Liu 2021).…”

Section: Methodsmentioning

confidence: 99%

On the interaction of turbulence with nucleation and growth in reaction crystallisation

2022

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The objective of this work is to investigate the interaction of turbulence with the nonlinear processes of particle nucleation and growth that occur in reaction crystallisation, also known as precipitation. A validated methodology for coupling the population balance equation with direct numerical simulation of turbulent flows is employed for simulating an experiment conducted by Schwarzer et al. (Chem. Engng Sci., vol. 61, no. 1, 2006, pp. 167–181), where barium sulphate nanoparticles are formed by mixing and reaction of barium chloride and sulphate acid in a T-mixer, with the spatial resolution resolved down to the Kolmogorov scale. A unity Schmidt number is assumed, since at present it is not possible to resolve the Batchelor scale for realistic Schmidt numbers (order of 1000 or more). The probability density function, filtered averages and spatial distribution of time and length scales are all examined in order to shed light on the interplay of turbulence and precipitation. Separate Damköhler numbers are defined for nucleation and growth and both are found to be close to unity, indicating that the process is neither mixing nor kinetics controlled. The nucleation length scales are also evaluated and compared with the Kolmogorov scale to show the importance of resolving nucleation bursts. In addition, zones of different rate-determining mechanisms are identified. The ultimate aim of precipitation is to obtain control over the product particle size distribution, and the present study elucidates the synergistic or competing roles of mixing, nucleation and growth on the process outcome and discusses the implications for modelling.

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Section: Methodsmentioning

confidence: 99%

On the interaction of turbulence with nucleation and growth in reaction crystallisation

2022

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“…The soot models applied in benchmark flames, generally include detailed gaseous chemical mechanisms with PAHs pathways, detailed soot processes and aerosol dynamics. Soot processes usually include nucleation (the dimerisation of PAHs [36,37]), surface growth (HACA mechanism [38] or ARS aromatic site model [39], adsorption of PAHs), multi-regime coagulation/agglomeration [40] and sintering [41], and also the morphology of soot particles. Numerical approaches, including methods of moment, discretisation methods, and Monte Carlos methods, have been implemented to solve properties of soot particles, i.e.…”

Section: Introductionmentioning

confidence: 99%

Modelling of laminar diffusion flames with biodiesel blends and soot formation

Liu

Gao

Rigopoulos

et al. 2022

Fuel

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“…The agglomerate structure, quantified by the relation between

and

[ 10 ], changes depending on the number [ 11 ], diameter and polydispersity of their constituent primary particles [ 12 ]. Accounting for the evolving agglomerate structure with SPBM is not trivial, as multiple equations per section need to be solved [ 13 , 14 ]. Therefore, models for the combustion synthesis of nanomaterials assume that

, based on a constant fractal dimension,

[ 15 , 16 ] often with a constant value for

[ 17 , 18 ].…”

Section: Introductionmentioning

confidence: 99%

“…Sectional models have been interfaced with computational fluid dynamics (CFD) in order to explain soot formation in diffusion flames [ 13 , 14 ] or predict agglomeration of soot nanoparticles from diesel engine exhausts [ 7 , 25 ]. Finite element methods have also been coupled with SPBMs to simulate coagulation of spheres [ 26 ], fractal-like agglomerates [ 27 ] and linear stacks (rouleaux) [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

A Monodisperse Population Balance Model for Nanoparticle Agglomeration in the Transition Regime

Kelesidis

Kholghy

2021

Materials

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Nanoparticle agglomeration in the transition regime (e.g. at high pressures or low temperatures) is commonly simulated by population balance models for volume-equivalent spheres or agglomerates with a constant fractal-like structure. However, neglecting the fractal-like morphology of agglomerates or their evolving structure during coagulation results in an underestimation or overestimation of the mean mobility diameter, dm, by up to 93 or 49%, repectively. Here, a monodisperse population balance model (MPBM) is interfaced with robust relations derived by mesoscale discrete element modeling (DEM) that account for the realistic agglomerate structure and size distribution during coagulation in the transition regime. For example, the DEM-derived collision frequency, β, for polydisperse agglomerates is 82 ± 35% larger than that of monodisperse ones and in excellent agreement with measurements of flame-made TiO2 nanoparticles. Therefore, the number density, NAg, mean, dm, and volume-equivalent diameter, dv, estimated here by coupling the MPBM with this β and power laws for the evolving agglomerate morphology are on par with those obtained by DEM during the coagulation of monodisperse and polydisperse primary particles at pressures between 1 and 5 bar. Most importantly, the MPBM-derived NAg, dm, and dv are in excellent agreement with the data for soot coagulation during low temperature sampling. As a result, the computationally affordable MPBM derived here accounting for the realistic nanoparticle agglomerate structure can be readily interfaced with computational fluid dynamics in order to accurately simulate nanoparticle agglomeration at high pressures or low temperatures that are present in engines or during sampling and atmospheric aging.

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Modelling of soot coalescence and aggregation with a two-population balance equation model and a conservative finite volume method

Cited by 24 publications

References 74 publications

On the interaction of turbulence with nucleation and growth in reaction crystallisation

On the interaction of turbulence with nucleation and growth in reaction crystallisation

Modelling of laminar diffusion flames with biodiesel blends and soot formation

A Monodisperse Population Balance Model for Nanoparticle Agglomeration in the Transition Regime

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