A conservative method for numerical solution of the population balance equation, and application to soot formation

Liu, Anxiong; Rigopoulos, Stelios

doi:10.1016/j.combustflame.2019.04.019

Cited by 41 publications

(31 citation statements)

References 58 publications

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“…A recent approach by Liu and Rigopoulos [140] is based on a piecewise constant approximation of the distribution in the context of a finite volume scheme, applicable to an arbitrary grid. The resulting equations are akin to the formulation in [104,106], which however employ geometric grids.…”

Section: (Sections 32 and 33)mentioning

confidence: 99%

“…The extension to an arbitrary grid, suggested in [106], involves many different cases for the boundaries of the double integrals approximating the coagulation integral terms. The method described in [140] identifies the boundaries for all cases in an arbitrary grid and results in a compilation of formulas for their geometric evaluation. As the boundaries are pre-computed, there is no overhead in the CPU time.…”

Section: (Sections 32 and 33)mentioning

confidence: 99%

“…With the combination of detailed models for both chemical kinetics and aerosol dynamics, good agreement can be obtained. Figure 3 shows some results from [140], where the original Santoro experiments were employed to demonstrate the applicability of the conservative finite volume PBE discretisation method to soot.…”

Section: Coupling Of Fluid and Aerosol Dynamicsmentioning

confidence: 99%

“…This also means that the soot model need not be comprehensive, but only commensurate with the level of detail of the overall simulation. RANS simulations [140] have been conducted on laboratory flames, IC engine combustion chambers and gas turbine combustors. Most of the studies on laboratory flames have been conducted with kmodel variants, such as the standard kwith a modification for the spreading rate (e.g.…”

Section: Overview Of the Closure Problem For Soot In Turbulent Flowsmentioning

confidence: 99%

“…Simulation of the Santoro et al[157,158] laminar co-flow non-premixed ethylene-air flame with the conservative finite volume PBE discretisation method[140]. Clockwise from top to bottom: a) representation of the computational domain, b) prediction of integrated soot volume fraction at different heights above burner with different PBE grids, c) temperature profile at the centreline, and d) radial temperature profiles at various cross-sections.…”

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confidence: 99%

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Modelling of Soot Aerosol Dynamics in Turbulent Flow

Rigopoulos

2019

Flow Turbulence Combust

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Aerosol dynamics plays an important role in the modelling of soot formation in combustion processes, as it is responsible for predicting the distribution of size and shape of soot particles. The distribution is required for the correct prediction of the rates of surface processes, such as growth and oxidation, and furthermore it is important on its own because new regulations on particulate emissions require control of the number of smaller particles. Soot formation is strongly dependent on the local chemical composition and thermodynamic conditions and is therefore coupled with fluid dynamics, chemical kinetics and transport phenomena. Comprehensive modelling of soot formation in combustion processes requires coupling of the population balance equation, which is the fundamental equation governing aerosol dynamics, with the equations of fluid dynamics. The presence of turbulence poses an additional challenge, due to the non-linear interactions between fluctuating velocity, temperature, concentrations and soot properties. The purpose of this work is to review the progress made in aerosol dynamics models, their integration with fluid dynamics and the models for addressing the turbulence-soot interaction.

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Section: (Sections 32 and 33)mentioning

confidence: 99%

Section: (Sections 32 and 33)mentioning

confidence: 99%

Section: Coupling Of Fluid and Aerosol Dynamicsmentioning

confidence: 99%

Section: Overview Of the Closure Problem For Soot In Turbulent Flowsmentioning

confidence: 99%

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confidence: 99%

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Modelling of Soot Aerosol Dynamics in Turbulent Flow

Rigopoulos

2019

Flow Turbulence Combust

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An efficient method for spatiotemporally resolved aerosol flow modeling: Discrete migration and GPU acceleration

Shang

et al. 2023

AIChE Journal

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Describing spatiotemporal evolution and characteristics of dispersed systems using the population balance equation (PBE), examples including sectional and moment methods are fraught with numerous issues. Hence, this study develops an accurate method by combining computational fluid dynamics and population balance‐Monte Carlo method (CFD‐PBMC) with a moderate computational cost. An efficient sub‐model for particle migration was proposed to simulate the convection and diffusion processes of particulate flows. A graphics processing unit (GPU)‐based parallel computation was performed to accelerate the high‐dimensional CFD‐PBMC. Several classical cases with analytical or benchmark solutions were simulated, and a comprehensive comparison was made using the classical weighted random walk method. Good agreements were obtained, except in the case of radial migration, the reasons for which are explained in detail. The measured speedups on the GPU showed a factor of ~450 for pure migration and ~50 for the CFD‐PBMC method when compared with a standard high‐performance computer.

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Large Eddy Simulation of Turbulent Flame Synthesis of Silica Nanoparticles with an Extended Population Balance Model

Tsagkaridis,

Papadakis,

Jones

et al. 2023

Flow Turbulence Combust

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In the present study, a recently proposed extended population balance equation (PBE) model for aggregation and sintering is incorporated into a large eddy simulation-probability density function (LES-PDF) modelling framework to investigate synthesis of silica nanoparticles in a turbulent diffusion flame. The stochastic field method is employed to solve the LES-PBE-PDF equations, characterising the influence of the unresolved sub-grid scale motions and accounting for the interactions between turbulence, chemistry and particle dynamics. The models for gas-phase chemistry and aerosol dynamics are the same as those recently used by the authors to simulate silica synthesis in a laminar flame (Tsagkaridis et al. in Aerosol Sci Technol 57(4):296–317, 2023). Thus, by retaining the same kinetics without any adjustments in parameters, we focus on the modelling issues arising in silica flame synthesis. The LES results are compared with experimental in-situ small-angle X-ray scattering (SAXS) data from the literature. Good agreement is found between numerical predictions and experimental data for temperature. However, the LES model underestimates the SAXS data for the primary particle diameter by a factor of two. Possible reasons for this discrepancy are discussed in view of the previous laminar flame simulations.

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A conservative method for numerical solution of the population balance equation, and application to soot formation

Cited by 41 publications

References 58 publications

Modelling of Soot Aerosol Dynamics in Turbulent Flow

Modelling of Soot Aerosol Dynamics in Turbulent Flow

An efficient method for spatiotemporally resolved aerosol flow modeling: Discrete migration and GPU acceleration

Large Eddy Simulation of Turbulent Flame Synthesis of Silica Nanoparticles with an Extended Population Balance Model

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