A joint moment projection method and maximum entropy approach for simulation of soot formation and oxidation in diesel engines

Abstract

A joint moment projection method and maximum entropy approach for treating the soot population balance equations is developed and presented in this work. The moment projection method is used to solve the population balance equations and generate moments that are supplied to the maximum entropy approach as a post-processing technique to reconstruct the soot particle size distribution. The particle size range required by the maximum entropy for particle size distribution reconstruction is determined based on the weighted particles generated in the moment projection method. The performance of the joint approach is first evaluated by solving a set of simplfied population balance equations on MatLab, then it is implemented into a Stochastic Reactor Model engine code to simulate the formation and oxidation of soot particles in a single-cylinder direct injection diesel engine. Results suggest

Stochastic population balance methods for detailed modelling of flame-made aerosol particles

“…10). This method has also been combined with a maximum entropy (ME) approach to reconstruct the PSDs from the moments, and applied to study soot formation in diesel engines (Wu et al, 2020). The MPM was shown to provide a computationally economical treatment of the soot model (with only a 20 % increase in CPU time associated with adding treatment of particles) and reasonably good agreement with experimental data given limitations in obtaining reliable estimates of model parameters.…”

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

“…Thereby, it can be guaranteed that the smallest particle class is accurately taken into account. The method has been applied recently in combination with the ME approach for numerical solution of PBEs characterizing for of soot formation in combustion engines [132,133].…”

Mechanism of the noncatalytic oxidation of soot using in situ transmission electron microscopy

“…(2) In the situation that soot samples cannot be obtained, the maturity parameter can be theoretically calculated using the number density function by quantifying the carbon atom number and C/H ratio 62 of the as-formed soot in combustion modeling. The oxidation models can be selected on that basis to calculate the reaction rate in population balance equations which has been applied in counter flow flame, diffusion flame, and premixed flame [63][64][65][66] . As soot maturation progresses, the oxidation model can be changed with maturity parameters.…”