Figure 6 — (A) ε calculated with the frozen equilibrium assumption using a single zone approach compared with the equilibrium ε from the multi-zone parcel model. (B) Temperature in the single zone model (dashed line).

Effect of sulfur content In order to investigate the effect of the fuel sulfur content on the resulting conversion fraction, a number of simulations with different sulfur content has been conducted. The results from the 75% load case are depicted in Figure 7. The simulations have been conducted with all other parameters including the applied mixing rate fixed for all sulfur contents.As seen from Figure 7 the conversion fraction decreases with increasing sulfur content. Taking the relatively large range in sulfur content into account the decrease in ε is modest. Nevertheless, the result is in qualitative agreement with the literature [1, 4].

Figure 7 — Conversion fraction, ε, as a function of  fuel sulfur content. Results from simulations of the 75% load case

Reactions controlling conversion fraction The reaction mechanism applied in the present work has provided valuable insight as already discussed. Nevertheless the models investigated are still coarse with many simplifying assumption. In order to take the analysis to the next level it would be desirable to use the applied reaction mechanism coupled to a full CFD code. However due to the high number of reaction steps this approach will be expensive in terms of the time required for simulating a single combustion cycle. This cost can be significantly reduced if a reduced mechanism, still capturing the most important reaction paths, can be formulated. In fact it often turns out that even large reaction mechanisms contain a few steps which govern the overall rate

[38, 39]. It is not the purpose of the present paper to propose a reduced mechanism. Nevertheless, some hints and guidelines can be found in the literature pin pointing the most important reactions. These will be briefly summarized below. Previous studies by Cerru et al. [40, 41] have been devoted to the formulation of a reduced mechanism for sulfur oxidation. Although a two step mechanism is formulated for SO2 oxidation a number of reaction rates (used in linear combinations) are required. Tremmel and Schumann [18] conducted a sensitivity analysis study, and concluded that the rate constant of the reaction showed the highest impact on the conversion

SO2 + OH(+M) = HOSO2(+M) (10)

fraction for conditions relevant for aviation turbine conditions. At some conditions the rate constant of the following reaction was found to also control the conversion fraction

SO2 + O(+M) = SO3(+M) (11)

Reaction Eq. 11 is highlighted to be of major importance by Glarborg [28], especially at high temperatures. Reaction Eq. 10 in combination with the reaction

HOSO2 + O2 = SO3 + HO2 (12)

is proposed to be important mainly at lower temperatures i.e. when the burned gases are

cooled. In another study Glarborg and co-workers [24] also point out the importance of the reactions

SO2 + OH = SO3 + H (13)

and

SO2 + HO2 = SO3 + OH (14)

through a rate of production and sensitivity analysis. Since the importance of the above reactions has been proven at conditions not exactly matching those in a large two-stroke diesel engines a future sensitivity study should be devoted to the formulation of a reduced mechanism.

CONCLUSIONS

In this paper the in-cylinder formation of SO3 and H2SO4 of a large two-stroke diesel engine has been studied. A detailed kinetic mechanism has been used in combination with measured incylinder pressure in order to calculate the concentration of sulfur containing species using a multi zone approach with the rate of mixing of fresh gas into the burned parcels as the main adjustable parameter. By combining the multizone model with a NO formation model (Zeldovich) the mixing rate has been adjusted in order for the calculated NO to match the measured value. Applying the fitted mixing rates values of ε lying in a range from 2.6 to 6.7% is found. The results are comparable with previous measurements of the SO2 conversion fraction in heavy duty diesel engines [4]. The presented model gives valuable information about the process of in-cylinder formation of SO3 and H2SO4 on a qualitative scale. Nevertheless, in order to improve the predictive reliability of the model on a more quantitative scale, a number of recommended actions remain to be taken.