Monte Carlo simulation of polydisperse particle deposition and coagulation dynamics in enclosed chambers

Li, Hongmei; Jiang, Wei; Liu, Wenming; Liu, Xuedong; Liu, Shuyuan; Chan, Tat Leung

doi:10.1016/j.vacuum.2020.109952

Cited by 5 publications

(4 citation statements)

References 52 publications

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“…More generally, the weighted flow algorithm (WFA) proposed by DeVille et al (2011) can work with arbitrary weighting functions, especially in the power law functions of particle size. The new stochastically and differentially weighted operator splitting MC methods were first developed by the research group (Liu and Chan, 2017b, 2018b, 2019; Liu et al , 2019, 2021). Another stochastic error reduction technique is the multi-Monte Carlo (MMC) method proposed by the research group (Zhao et al , 2005, 2009), which leads the concept of “fictitious particles” where the number of fictitious particles and the simulation volume are both maintained constant.…”

Section: Introductionmentioning

confidence: 99%

A new weighted fraction Monte Carlo method for particle coagulation

Jiang

Chan

2021

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Purpose The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method. Design/methodology/approach The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme. Findings Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated. Originality Value Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

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Section: Introductionmentioning

confidence: 99%

A new weighted fraction Monte Carlo method for particle coagulation

Jiang

Chan

2021

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“…In order to reduce use of computing memory and simulation time of the MC algorithm, Zhao et al [27][28][29] put forward a differentially weighted Monte Carlo (DWMC) method to solve the particle balance equation. Based on this DWMC method, Liu et al further developed a differentially weighted operator-splitting Monte Carlo (DWOSMC) method which tends to be more efficient and precise in predicting the variation of aerosol particles [24,30,31].…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling of Droplet Aerosol Coagulation, Condensation/Evaporation and Deposition Processes

et al. 2022

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The differentially weighted operator-splitting Monte Carlo (DWOSMC) method is further developed to describe the droplet aerosol dynamic behaviors, including coagulation, deposition, condensation, and evaporation processes. It is first proposed that the droplet aerosols will experience firstly condensation and then evaporation, and this phenomenon is first implemented into the Monte Carlo method and sectional method with considering coagulation, deposition, and condensation/evaporation processes in both single-component and two-component aerosol particle systems. It is found that the calculated results of the DWOSMC method agree well with both the analytical solutions and the sectional method. The further developed DWOSMC method can predict the variation of particle number density, total particle volume, mean particle diameter, particle size distributions, and the component-related particle volume densities in both single component and two-component droplet aerosol systems considering coagulation, deposition, and condensation/evaporation processes.

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“…These existing analytical solutions are of great significance and can be used as a useful benchmark for validating different numerical methods. Different numerical approaches aiming at different problems of aerosol dynamics are developed to approximate the solution of the GDE for an aerosol system of interest, such as the sectional method (SM) (Gelbard et al , 1980; Prakash et al , 2003; Zhang et al , 2020; Wu et al , 2022), method of moments (MOMs) (Frenklach and Harris, 1987; McGraw, 1997; Yu et al , 2008; Yu and Chan, 2015; Chan et al , 2018; Li et al , 2019; Liu et al , 2019c; Shen et al , 2020; Yang et al , 2020; Jiang et al , 2021; Shen et al , 2022) and Monte Carlo (MC) method (Gillespie, 1975; Garcia et al , 1987; Liffman, 1992; Smith and Matsoukas, 1998; Kruis et al , 2000; Lin et al , 2002; Zhao et al , 2009; Xu et al , 2014; Kotalczyk and Kruis, 2017; Liu and Chan, 2017; Liu and Chan, 2018a, 2018b; Liu et al , 2019a, 2019b; Liu and Chan, 2020; Liu et al , 2021; Jiang and Chan, 2021; Liu et al , 2022). As the discrete nature of the MC method perfectly matches the stochastic properties of particle motion, it can be used to closely simulate the behaviour of particles.…”

Section: Introductionmentioning

confidence: 99%

“…In the MMC method, the number of fictitious particles and the volume of the computational domain always keep constant, and each fictitious particle is a representative of some real particles. By providing different fictitious particles with different weights (Zhao and Zheng, 2009b; Xu et al , 2014; Liu and Chan, 2017; Liu and Chan, 2018a, 2018b; Liu et al , 2021), the weights of fictitious particles are unevenly distributed in the particle size spectrum (i.e. more fictitious particles at the edge of the PSD and fewer fictitious particles at those areas where the particle number concentration is high).…”

Section: Introductionmentioning

confidence: 99%

A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics

Wang

Chan

2022

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Purpose The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency. Design/methodology/approach In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme. Findings The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost. Originality/value The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

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Monte Carlo simulation of polydisperse particle deposition and coagulation dynamics in enclosed chambers

Cited by 5 publications

References 52 publications

A new weighted fraction Monte Carlo method for particle coagulation

A new weighted fraction Monte Carlo method for particle coagulation

Numerical Modeling of Droplet Aerosol Coagulation, Condensation/Evaporation and Deposition Processes

A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics

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