(130f) Mathematical Modelling of Nano-Particle Formation and Evolution in Combustion Processes

Mathematical modelling of particle formation in combustion processes is a very interesting and complex problem with very different final applications.

In fact, it can be used to design and develop combustors characterised by low soot emissions. Soot formation is a common issue for all combustion systems and it is caused by incomplete oxidation of the species that constitute the fuel. This problem has gained in recent years rising importance, because of the well-known impact of particulate matter on human health.

On the other end the interest in developing such mathematical models is also due to the possibility of applying them to design, optimize and scale-up reactors for the production of particles with given characteristics (i.e., particle size distribution, fractal dimension, morphology) through the so-called flame aerosol synthesis process.

Reliable mathematical models must be based on Computational Fluid Dynamics (CFD), which represents a very useful modelling tool for the description of turbulent reacting flows, such as turbulent combustion. CFD must be coupled with detailed kinetics expressions for the very fast gas-phase reactions and their interactions with turbulent fluctuations must be taken into account by resorting to micro-mixing models. Moreover, the population balance equation describing nucleation of the first solid particles and their evolution as a consequence of growth, oxidation and aggregation must be implemented in the CFD code and solved.

Our work has focused on the development of turbulent-chemistry models, such as presumed probability density (PDF) methods and in the development of population balance models suitable for implementation in CFD codes. In particular the approach known as finite-mode PDF [1] has been coupled with a simplified kinetic scheme which has allowed us to describe the combustion process overcoming the hypothesis of instantaneous equilibrium. A significant improvement of the agreement with experimental data was found when comparing predictions obtained with the developed approach and with standard approaches in commercial CFD codes such as flamelets and beta-PDF [2]. The description of the evolution of the solid particles has been described by using a macroscopic approach based on the population balance equation. In order to solve this equation within the CFD code a novel method for the solution of bivariate population balance equations has been proposed, namely the Direct Quadrature Method of Moments (DQMOM) [3], validated and implemented in the commercial CFD code FLUENT 6.2.

The overall modelling approach has been validated by comparison with experimental data found in literature regarding soot nano-particles formation in ethylene-air turbulent flames [4,5]. In this flame a turbulent jet of ethylene is burned in still air. The use of this fuel, which assures a relevant amount of soot formed, is very common in experimental works on soot formation.

In Fig. 1 a sketch of the experimental set-up used by Hu, Yang and Koylu [5] is reported along with the temperature contour plot calculated with the standard k-ε turbulence model and the β-PDF available within Fluent 6.2. Comparison of the soot volume fraction profiles along the flame axis predicted by the CFD code with experimental data showed good agreement as well as comparison for the mean particle size and particle number density. It is important to highlight here that because a bivariate population balance was implemented and solved in the CFD code two independent properties of the population of particles can be tracked (e.g., particle size and fractal dimension, or particle size and number of primary particles per aggregate), conferring great flexibility and accuracy to the model.

[1] Fox, R.O., 1998. On the relationship between Lagrangian micromixing models and computational fluid dynamics. Chemical Engineering and Processing 37 (6), 521?535.

[2] Fox, R.O., 2003. Computational models for turbulent reacting flows. Cambridge University Press, Cambridge, UK.

[3] Marchisio, D.L., Fox, R.O., 2005. Solution of population balance equations using the direct quadrature method of moments. Journal of Aerosol Science 36 (1), 43?73.

[4] Kent, J.H., Honnery, D., 1987. Soot and mixture fraction in turbulent diffusion flames. Combustion Science and Technology 54, 383?397.

[5] Hu, B., Yang, B., Koylu, U., 2003 Soot measurements at the axis of an ethylene/air non-premixed turbulent jet flame. Combustion and Flame, 134 (1-2), 93-106.