ACCIONES MÁS BENEFICIOSAS VALOR DE AGREGACIÓN
7.6 DISCUSION Y VALORACION DE IMPACTOS AMBIENTALES 1 Impacto sobre el medio físico
at a High pressure
Due to the increased computation cost of the high-pressure EOS-VLE calculations in addition to the original cost to calculate the changes in composition of droplets in the evaporation subroutine, it is decided not to use the high-pressure EOS-VLE approach for spray combustion calculation in StarCD. As partial justification of the present choice, the comparisons of spray simulation results using the low-pressure evaporation model along with the modified pyrolysis model for HFO with the experiment results are shown in section 7.3. The low-pressure evaporation model is tested for two representative fuel samples, one with the good combustion quality and the other with poor and for two sets of experimental results. Good qualitative agreement is shown between the computer simulations and the measured experimental data, without the use of the high-pressure EOS-VLE model.
The only aspect that has not been explored in the present study is the difference in the HFO fuel spray prediction calculation using the low-pressure model (Raoult’s law) and the high-pressure EOS-VLE model. A literature study by Siebers [131] has noted that the use of EOS-VLE calculation in the spray only has a second-order effect. Siebers [131] mentioned that more realistic VLE analysis have very little impact on the spray calculations. Moreover, Kim & Sung [73] investigated the effect of low-pressure and high- pressure models on evaporating spray. Their results showed that the fraction of evaporated fuel predicted by the low-pressure model is only about 5% less than the high-pressure model. However, in the present section efforts are made to compare the low and high- pressure VLE (with interaction coefficients) models along with modified pyrolysis model of a 30-micron single droplet (which is representative size for a droplet in developed spray) at a very high pressure.
In the present case, simulation is carried out for a 30-micron initial diameter droplet which is exposed to the 1200 K surroundings temperature and 100 atm pressure. The overall results of the simulation are the same as what is observed in previous sections. However, as expected, the effect of high pressure on a small droplet is reflected. Some distinctive
results obtained using the low-pressure model and high-pressure model are given in Figure 5-30 and Figure 5-31. In both figures, sub-figure (a) shows composition history of the pure hydrocarbons along with the droplet temperature, (b) shows liquid mole fractions of components along with normalised droplet size history, (c) shows compositions expressed as percentage of initial droplet mass, (d) shows vapour phase mole fraction at the droplet surface, (e) shows evaporating molar flux and (f) shows the overall mass balance of a droplet along with the droplet temperature.
Figure 5-30: Predicted results of a 30-micron HFO droplet using the low-pressure evaporation model and modified pyrolysis model.
(Ambient condition:T∞ = 1200 K and P∞ = 100 atm). Sub-figure (a) shows composition history of the pure hydrocarbons along with the
droplet temperature, (b) shows liquid mole fractions of components along with normalised droplet size history, (c) shows compositions expressed as percentage of initial droplet mass, (d) shows vapour phase mole fraction at the droplet surface, (e) shows evaporating molar flux and (f) shows the overall mass balance of a droplet along with the droplet temperature.
d e
c
f
Figure 5-31: Predicted results of a 30-micron HFO droplet using the high-pressure evaporation model with interaction coefficients and
modified pyrolysis model. (Ambient condition: T∞= 1200 K and P∞ = 100 atm). Sub-figure (a) shows composition history of the pure
hydrocarbons along with the droplet temperature, figure (b) shows liquid mole fractions of components along with normalised droplet size history, figure (c) shows compositions expressed as percentage of initial droplet mass, figure (d) shows vapour phase mole fraction at the droplet surface, figure (e) shows evaporating molar flux and figure (f) shows the overall mass balance of a droplet along with the droplet temperature.
b c
a
As shown in Figure 5-30 and Figure 5-31, the droplet temperature for a small droplet (30- micron) at 100 atm pressure, increases at a faster rate than is observed for a big droplet (see Figure 5-17 of a 100 micron droplet which is exposed to 1200 K and 50 atm pressure). The reason behind this sharp increase in the droplet temperature is its smaller surface area to volume ratio. Baert [14] demonstrated that the heating rate of a single droplet is almost inversely proportional to its size. Noticeably, a high heating rate to the droplet helps in the evaporation of the light components from the surface quickly.
The mole fractions and molar fluxes obtained at the droplet surface showed that evaporation of a 30-micron droplet is a very rapid process compared to the pyrolysis. The pyrolysis of the droplet continues here at a slow rate until the end of droplet lifetime. In the present case, the droplet temperature only increases up to the initial chamber temperature. However, in reality, where the combustion of fuel occurs, the droplet temperature would increase more than the initial chamber temperature which would help to pyrolise the heavy molecules at a faster rate.
By comparison of Figure 5-30 with Figure 5-31, it is clear that overall results obtained from both models including the droplet lifetime, pyrolysis products (polymer and gas) are essentially same, except the evaporation of light components occurs at a faster rate in the high-pressure model compared to low-pressure model. The evaporation of the light components for the high-pressure model finishes in 2 ms, whereas the evaporation of the light components in the low-pressure model requires 3 ms. This faster evaporation rate does not affect the already high heating rate. Therefore, at the end, overall droplet lifetime remains the same. The choice made to avoid the complex high-pressure model implementation for spray combustion in StarCD is reasonable because the low-pressure model and high-pressure model give similar results, except the vapour concentration, at a high pressure and temperature for a small single droplet. However, where cutter stock proportion is higher than the present model, early evaporation rate for the high-pressure model could influence the early vapour concentration and composition which will affect the ignition reactions and ultimately the ignition delay.
5.7
Summary
In summary, Baert’s pyrolysis model based on chemical kinetics for thermal cracking and polymerisation rate is developed. Results of this pyrolysis model show that polymer formation within a droplet is dependent on droplet heating rate and composition. Moreover, it is observed in Baert’s pyrolysis model results that the process of polymerisation starts prior to the thermal cracking. This order of thermal cracking and polymerisation is contradictory to the experimental evidence. Subsequently, Baert’s pyrolysis model parameters are modified. Results of the modified pyrolysis model did not show any significant dependency of polymer formation on droplet heating rate and in addition it showed thermal cracking beginning earlier than the polymerisation.
A comparison of the low-pressure model with the high-pressure model for a 30 micron droplet at high pressure show that evaporation of the volatile hydrocarbons (n-paraffins, aromatics, naphthenes) from HFO occurs at a faster rate for the high-pressure model. However, this faster evaporation does not significantly affect the droplet lifetime because modelled HFO contains only 30% volatile hydrocarbons (cutter stock) by mass. Therefore, droplet lifetime is found to be similar for both models. Thus in sprays where droplets are generally small, the VLE calculation can be obtained with sufficient accuracy by the low- pressure model avoiding the use of the complex high-pressure EOS model. However, where cutter stock proportion is higher than the present model, early evaporation rate for the high-pressure model could influence the early vapour concentration and composition which is important for ignition. An additional reason to study the high-pressure model is to inspect the effect of interaction coefficients on the evaporation rate of heavy component, the analysis showed that interaction coefficients does not significantly affect the evaporation of heavy component.