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sulfuric acid is favored. At a temperature of 1273 K the fraction of SO3 relative to SO2 +SO3 equals 14 and 35 % at 10 and 100 bar, respectively. Upon cooling from high temperatures, the amount of SO3and H2SO4 will increase from a thermodynamic point of view. However, due to potential kinetic limitations the SO3 and H2SO4 concentration may
be frozen by quenching the gas. The exact concentration of sulfur containing species is thus a complex function of temperature, pressure, initial concentrations, cooling rate, and residence time.The effect of kinetics on the formation ofSO3/H2SO4 is investigated in the next section.Figure 3 — Concentration of SO2, SO3, and H2SO4as a function of temperature at (upper) a pressure of 10 bar and at (lower) a pressure of 100 bar.Initial concentration is xO2 = 0.15, xH2O = 0.05, xS =0.01, no other components other than Argon
present.Simulations of in cylinder formation of sulfur species
Adjustment of mixing rate. The main tuneable parameter in the model applied in this study is the mixing rate at which fresh air is mixed into each parcel. The limits of the mixing rate is zero, at the low end, corresponding to fuel being burned at stoichiometric conditions i.e. λ = 1 and cooling is only due to the expansion of cylinder gas. The higher limit corresponds to an infinite mixing rate i.e air is mixed into each parcel increasing the local lambda from 1 towards the global lambda very fast.Both limits are unrealistic for modelling real mixing controlled diesel spray combustion and emission formation. The former limit will result in too high parcel temperatures and too low oxygen concentration and for the latter limit the opposite is the case. In reality the mixing rate is somewhere in
between the two. Thus the temperature (cooling by fresh gas) and oxygen concentration in each parcel is closely linked to the applied mixing rate. In order to investigate the effect of applied mixing rate on the calculated conversion fraction, ε, a number of simulations have been performed in which the mixing rate is varied. The results are depicted in Figure 4. Figure 4 — Conversion fraction, ε, resulting air excess ratio in the burned zones at exhaust valve opening, and calculated NO concentration as a function of applied mixing rate. Results are calculated for the 75 % load case In addition to the calculated ε and the resulting average air excess ratio in the burned zones, the results of a NO model have been included as well. The NO model used is the extended Zeldovich
mechanism [2, 14]
N2 + O = NO + N (7)
N + O2 = NO + O (8)
N + OH = NO + H (9)
The kinetic parameters are taken from [14]. Since NO has been measured for the tests investigated in the present study comparison between measured and calculated NO concentrations allows a tuning of the mixing ratio in order to give satisfactory
Agreement. As seen from the figure the conversion fraction, ε, increases due to increased mixing. The resulting average air excess ratio in the burned zones increase up to the global air excess ratio at a mixing rate of 10. Both the lowest and highest mixing rates applied may seem unrealistic,nevertheless they provide a rough range for ε of approx. 1-12%. The measured NO concentration is 1266 vol. ppm. In order for the calculated NO concentration to equal this, a mixing rate of 3.29 is required, as found by interpolation. The corresponding ε is 4.43 %. Using the same approach in order to match the experimental NO concentration for the remaining load cases of 1119,
1236, and 1320 vol ppm for 100, 50, and 25% load,respectively, the corresponding values of ε are 2.59, 4.25, and 6.72 %. Thus, for a wide range of engine loads ε apparently lies in a relatively narrow range of 2.5-6.7%. From these results as well as
from Figure 4 it is interesting to note the similar effect of varying mixing rate on both NO and ε. Engel et al. measured the conversion of SO2 to SO3 on a number of heavy duty diesel engines operated at different load, different fuel quality, different sulfur content etc. In their study they found a conversion fraction ranging from 2–8%. Clearly our results agree very well with these findings. In the following the 75% load case with a mixing rate of 3.29 will be investigated in more detail.