Particle size distribution functions in laminar and turbulent flames

Fabian Mauss, Karl Netzell, Caroline Marchal, Gladys Moréac

Abstract

The formation of soot in flames results from a number of complex physical and chemical
processes. Several of these processes are still not fully understood and modelling soot
formation still relies on empirical assumptions. In addition to the complexity of the problem
the modeller was in the past confronted to the fact that the experimental data were limited to
measurements of global quantities; i.e. number density and soot volume fraction, namely the
first and second moment of the particle size distribution function (PSDF) [1,2]. Information
about the PSDF or the shape and consistency of soot particles have been very rare [3]. For the
latter, probes from particulates through thermophoretic sampling in flames were taken. Today,
measurements of particle size distribution functions are available for simple flame
configurations [4,5]. Until the late nineties modelling soot formation was directed towards understanding the most sensitive processes only. Model validation was performed by comparing calculated profiles of soot volume fraction against experimental data. This caused, that most mathematical methods describing the soot PSDF included the first and second moment of the PSDF only [6,7]. These developments have been consolidated through the formulation of the method of moments with interpolative closure (MoM) for soot particles and the soot precursors, rigorously deriving the governing equations for any moment of the PSDF. At the same time the hydrogen abstraction carbon addition mechanism was introduced as the major chemical growth mechanism for soot particles [8,9,10]. In [11] it was shown that the HACA mechanism can explain the sensitivity of soot formation on varying H and H2 concentration in the flame. In [11,12] the method of moments was formulated including convection, size dependent diffusion and thermophorezes. The absolute amount for the soot volume fraction was often adjusted by optimizing the active site coefficient, as in ref. [13], where it was made temperature dependent to cover a full regime of experimental data. This limited the validation of the models to validating the general trends, i.e. pressure dependence, fuel dependence etc. . Comparison of calculated and measured soot number densities suffered often from the fact, that the numerical models include particles down to sizes of 1 nm, while the experimental data were limited to certain sizes. Measurements of particle size distribution functions as presented in [6,7] offer additional information on the processes of soot formation in flames. The ratio, of particle inception, surface reactions and coagulation decide on the modality of the PSDF, the gradient of Particle concentration with size in the nucleation mode, the valley between nucleation mode and the coagulation mode, and the width of the distribution in the coagulation mode. In this study a sectional method is chosen to model the PSDF in laminar premixed flames [5]. The sectional method – as the method of moments – has the advantage, that transport equations can be formulated without any further approximations. This allows applying the method in turbulent diffusion flames using the interactive flamelet model. First calculations with this model show that particles with large sizes can break through the reaction layer of turbulent diffusion flames [14].