Lagrangian particle tracking with new weighted fraction Monte Carlo method for studying the soot particle size distributions in premixed flames

Abstract

Purpose The purpose of this paper is to study the soot formation and evolution by using this newly developed Lagrangian particle tracking with weighted fraction Monte Carlo (LPT-WFMC) method. Design/methodology/approach The weighted soot particles are used in this MC framework and is tracked using Lagrangian approach. A detailed soot model based on the LPT-WFMC method is used to study the soot formation and evolution in ethylene laminar premixed flames. Findings The LPT-WFMC method is validated by both experimental and numerical results of the direct simulation Monte Carlo (DSMC) and Multi-Monte Carlo (MMC) methods. Compared with DSMC and MMC methods, the stochastic error analysis shows this new LPT-WFMC method could further extend the particle size distributions (PSDs) and improve the accuracy for predicting soot PSDs at larger particle size regime. Originality/value Compared with conventional weighted particle schemes, the weight distributions in LPT-WFMC method are adjustable by adopting different fraction functions. As a result, the number of numerical soot particles in each size interval could be also adjustable. The stochastic error of PSDs in larger particle size regime can also be minimized by increasing the number of numerical soot particles at larger size interval.

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

“…The computational efficiency of the new SAMWFMC method is evaluated by comparing with other studied MC methods. The computational time required for the WFMC method with the HFF in each case is regarded as the reference time because the WFMC method with the HFF has been fully tested for different cases in Jiang and Chan (2021) and also used for studying soot aerosol dynamics in Jiang and Chan (2022). Hence, the corresponding normalized computational times of different cases required for all MC methods are listed in Table 1.…”

“…In the present study, it is considered that coagulation events occur among a part of or all real particles between the i th-group and j th-group, which is characterized by a fraction function, α ij (Jiang and Chan, 2021, 2022). The mean number of coagulation events within these real particles is given by Jiang and Chan (2021): Therefore, the number of coagulation events of the real particles between the i th-group and j th-group per unit time in the computational domain can also be formulated by ΩC ij (Jiang and Chan, 2021): where C ij is the coagulation rate between numerical particles, i and j , which can be written as (Jiang and Chan, 2021): where βij′ is the new coagulation kernel function, which is used to construct the jump Markov process.…”

“…Zhou et al (2020) reported that the weight function used in the MC method has a beneficial effect on the prediction of the PSD. Jiang and Chan (2021) have innovatively introduced fraction functions for particle weight functions, and applied it to a newly developed MC method called weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021, 2022). Numerical results showed that the WFMC method can reduce the stochastic errors in high-order moments of the PSD by introducing adjustable fraction functions.…”