A hybrid stochastic/fixed-sectional method for solving the population balance equation

Bouaniche, Alexandre; Domingo, Pascale

doi:10.1016/j.ces.2019.115198

Cited by 16 publications

(24 citation statements)

References 52 publications

(76 reference statements)

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“…The population balance equation followed by n(v * ; x, t) may be written in the limit of dv * → 0 [6,46,47,54],…”

Section: Balance Equationsmentioning

confidence: 99%

“…A systematic analysis of this hybrid stochastic/fixed-sectional method for solving the population balance equation, along with comparisons against analytical solutions of canonical PSD evolutions may be found in [6].…”

Section: Stochastic/fixed-sectional Algorithmmentioning

confidence: 99%

“…This initial distribution is only necessary to start the calculation but it is largely negligible as compared to N T levels reached during the calculation (see Figure 2(a)). This approach has been validated elsewhere against analytical test cases featuring simultaneous nucleation and growth [6].…”

Section: Flow Configuration and Model Parametersmentioning

confidence: 99%

“…The main objective is to propose an efficient and accurate numerical scheme for solving the Population Balance Equation in the context of sooting flames. The performance of this method has been previously assessed against a series of analytical test cases in [6]. In the present work, the applicability of the hybrid method to sooting flames is demonstrated.…”

Section: Introductionmentioning

confidence: 98%

“…This approach features a fixed number of numerical particles to build the PDF at the location (x, t) and it is organised to facilitate its coupling with large eddy simulation (LES). This novel approach, combining stochastic Monte Carlo (numerical particles) and fixed-sectional methods, has been found to minimise the discretisation errors when solving the surface growth/loss term of the population balance equation for reference canonical problems [6]. The solution method relies on a fixed number of stochastic particles and sections, with a numerical algorithm organised to minimise errors even for a moderate number of stochastic particles and sections.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Soot Particle Size Distribution in a Laminar Premixed Flame: A Hybrid Stochastic/Fixed-Sectional Approach

Bouaniche

Yon

Domingo

2020

Flow Turbulence Combust

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The numerical simulation of the soot particle size distribution in flames is addressed by solving the balance equations for total number density and the probability density function (PDF) of particle sizes, leading to a hybrid stochastic/fixed-sectional method for solving soot population balance equation. Well established models are introduced in these equations for the chemistry of PAH in ethylene combustion, for particle nucleation, growth, agglomeration and oxidation. These closures are combined with a stochastic approach, which drives the evolution of a fixed number of computational particles used to solve for the particle size distribution with a control of agglomeration and numerical roundoff error through a fixed sectional discretisation. A laminar sooting flame is simulated to compare the results against measurements and previous numerical simulations, confirming the validity of the novel approach in terms of accuracy and CPU efficiency. The relation between the mobility diameter, measured in the experiments, and the equivalent sphere diameter, introduced in the modeling, is discussed under this novel numerical framework. The influence of the fractal particle shape on the simulated particle size distribution is explored. Finally, Particle Size Distributions obtained from the hybrid method are compared to the ones obtained with a representative fixed-sectional method.

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“…The population balance equation followed by n(v * ; x, t) may be written in the limit of dv * → 0 [6,46,47,54],…”

Section: Balance Equationsmentioning

confidence: 99%

Section: Stochastic/fixed-sectional Algorithmmentioning

confidence: 99%

Section: Flow Configuration and Model Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of the Soot Particle Size Distribution in a Laminar Premixed Flame: A Hybrid Stochastic/Fixed-Sectional Approach

Bouaniche

Yon

Domingo

2020

Flow Turbulence Combust

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Soot modeling in turbulent diffusion flames: review and prospects

Valencia

Ruiz

Manrique

et al. 2021

J Braz. Soc. Mech. Sci. Eng.

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This work reviews the state-of-the-art of the main soot modeling approaches used in turbulent diffusion flames. Accordingly, after a short introduction about the subject addressed here, the main soot formation mechanisms are described next. This description provides the basis for the discussions about the different soot modeling techniques employed nowadays for soot predictions. Since combustion and radiation models have a significant impact on soot predictions, as a consequence of the strong coupling between chemistry, turbulence and soot formation, a general overview about these models is also provided. For the sake of clarity, the main soot formation models reviewed in this work are classified as semi-empirical soot precursor models and detailed ones. Both advantages and disadvantages of the referred soot modeling approaches are properly discussed. In the last part of this review, comparative results obtained using some of the main soot models currently available are presented along with a discussion about the prospects for soot modeling in turbulent flames. Finally, some conclusions and references are provided.Overall, based on the literature reviewed, it is concluded that there is yet a long path to be followed before understanding first and having then a soot model able to properly describe the formation of this critical pollutant for a variety of situations of industrial interest.

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Study of industrial titania synthesis using a hybrid particle-number and detailed particle model

Boje

Akroyd

Sutcliffe³

et al. 2020

Chemical Engineering Science

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A hybrid stochastic/fixed-sectional method for solving the population balance equation

Cited by 16 publications

References 52 publications

Analysis of the Soot Particle Size Distribution in a Laminar Premixed Flame: A Hybrid Stochastic/Fixed-Sectional Approach

Analysis of the Soot Particle Size Distribution in a Laminar Premixed Flame: A Hybrid Stochastic/Fixed-Sectional Approach

Soot modeling in turbulent diffusion flames: review and prospects

Study of industrial titania synthesis using a hybrid particle-number and detailed particle model

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