Population balance modelling of soot formation in laminar and turbulent flames

Abstract

The reduction of soot emissions in combustion processes is a primary concern of combustion engineers due to the severe health impact of soot, and the prediction of the soot particle size distribution (PSD) has become important. The evolution of the PSD can be predicted by solving the population balance equation (PBE), and several approaches have been proposed for introducing soot morphology in the PBE. Furthermore, the PBE must be coupled with fluid dynamics, species transport and chemical kinetics in order to predict soot properties in laminar and turbulent flames. Finally, accurate and computationally efficient methods must be employed for solving the CFD-PBE approach.

In the first part of this thesis, the recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) is extended to a two-PBE approach for modelling soot formation that distinguishes between coalescence and aggregation and accounts for finite-rate fusing of primary particles within aggregates, while providing a numerically accurate description of primary particle surface growth and oxidation within aggregates. The validation of the method is conducted by reproducing the self-preserving distributions of aggregates with varying fractal dimension. Subsequently, the one-PBE and two-PBE approaches are coupled with CFD and applied to the application of the Santoro laminar non-premixed co-flow sooting flame. By using a comprehensive soot kinetic model, the deficiencies of the one-PBE approach are analysed, and the two-PBE approach is shown to provide a significant improvement in the description of soot morphology using a properly adjusted particle fusing rate. At present, the model parameters for the fusing of soot primary particles are based on sintering models from silica and titania nanoparticles due to the lack of experimental data for soot. Therefore, a comprehensive sensitivity analysis of the model parameters is conducted. The results show the predictive potential of both the one-PBE and two-PBE approaches. With the presently available experimental measurements, the results suggest that one-PBE method is a reasonable choice for the applications associated with turbulent flame.

Subsequently in the second part, the one-PBE method is incorporated into the LES-PBE-PDF approach developed within the group for modelling soot formation in turbulent flames. For the first time, the LES-PBE-PDF approach provides a comprehensive physicochemical model accounting for nucleation, surface growth, oxidation, condensation, coalescence and aggregation. The interaction between chemistry, turbulence and soot particles are accounted for by resolving an evolution equation for the LES-filtered one-point, one-time, joint scalar-number density probability density function (PDF). The Eulerian stochastic field method is used for the solution of the joint-scalar-number density PDF. By using the same kinetics and model parameters as tested in the laminar flame case, the LES-PBE-PDF approach is applied to model soot formation in the Sandia turbulent non-premixed sooting flame. The predicted thermochemical conditions and soot volume fraction are in reasonably good agreement with experimental measurements. The analysis and findings demonstrate good predictive capability and computational feasibility of the complete LES-PBE-PDF approach.

In summary, this thesis presents a systematic study for soot formation in the laminar and turbulent flames. In particular, the key adjustable model parameters, surface reactivity $\alpha$ and cut-off point $d_c$, are calibrated in the laminar flame and employed in the turbulent flame. Yet, some limitations should be pointed out. For soot study, the current methodology does not capture the composition of soot during its formation and growth, thus the surface reactivity model applied is rather primitive and needs some adjustments, and the work assumes a constant fractal dimension, whose impact should be further investigated. For turbulent sooting flame, future investigation regarding the micromixing model is warranted.