Limitations of simplified models to predict soot formation in laminar flames

Abstract

Soot formation and radiation are important aspects for combustion problems. In this work, numerical simulations of ethylene coflow laminar flames are used to evaluate soot formation and radiation processes under different modeling approximations. Priority was given for models that were capable of producing detailed information with reduced computational requirements. So, the objective of this work is to show and quantify the importance of heat loss by gas and soot radiation and to quantitatively show the impact of different transport models (a detailed and a simplified) in soot predictions. For soot modeling, a semiempirical two-equation model is chosen for predicting soot mass fraction and number density. The model describes particle nucleation, surface growth and oxidation. For flame radiation, the radiant heat losses (gas and soot) are modeled by using the gray-gas approximation with optically thin approximation. For the chemical kinetics, a detailed approach is employed. It is found that gas and soot components of the radiative heat loss are comparable, with the gas radiation being larger (65%). To capture 99.9% of the total heat loss, the numerical domain has to be extended to 2.4 times the flame length based on the stoichiometric mixture fraction. Radiation modeling has a large impact on soot predictions. An error of 19% in the peak soot volume fraction is found when radiation is neglected. Errors due to simplified transport properties are also around 21%.

Appendices

Appendix 1: Kinetic mechanism influence in soot modeling—1D flames

For the target flame, a variety of kinetic mechanisms have been used for predicting the gas-phase species. A comparison of kinetic mechanisms and its influence in soot prediction is done for 1D counterflow flames. Seven kinetic mechanisms were tested and are presented in Table 3. Simulations were done for ethylene counterflow flames at a stretch rate a of 20 1/s and 100 1/s, for coupled and adiabatic case, using the soot model of [22]. Only the 20 1/s are shown here since the 100 1/s have the same behavior of the 20 1/s. The values for the GRI3.0 reduced (no NOx reactions) are not shown here since it produced the same results as the original mechanism.

Table 3 Kinetic mechanisms

Fig. 15

Temperature profile; zoom at the peak

Fig. 16

C$_2$H$_2$ mass fraction profile; zoom at the peak

Fig. 17

$f_\mathrm{v}$ profile; zoom at the peak

Fig. 18

OH mass fraction profile; zoom at the peak

Fig. 19

O mass fraction profile; zoom at the peak

As can be seen from Figs. 15, 16, 17, 18 and 19, the selection of kinetic mechanism can have an influence in the flame characteristics, in the soot-related gas-phase species and therefore in soot prediction.

Figure 20 presents the two most important gas-phase species for radiative heat losses, CO$_2$ and H$_2$O mass fraction profiles, for all kinetic mechanisms used in this section.

Fig. 20

CO$_2$ and H$_2$O mass fraction profiles

The figure shows that the CO$_2$ and H$_2$O mass fraction profiles are slightly affected by the kinetic mechanisms.

Appendix 2: Soot model influence in soot predictions

In this section, a comparison between two sets of parameters for soot reactions within the same soot model is done for the 2D coflow flame. The first set of parameters is the one used in the present work, from [5], and the second is from [33]. Liu et al. [33] proposed a modified version of the two-equation model of Leung, with different sets of reaction rate constants and a special attention on the oxidation rates. This set was developed to fit the experiments of [38] for atmospheric non-smoking and smoking ethylene/air coflow diffusion flames. The comparison between both soot model parameters is presented in Table 4.

Table 4 Comparison of soot models; only the differences are shown

The comparison between the two sets of parameters is done for the exact same conditions presented in Sect. 3 for simulation a non-smoking ethylene coflow flame. The comparison is shown only for the soot volume integrated along the height of the burner in Fig. 21.

Fig. 21

$f_\mathrm{v}$ integrated comparison; symbols: experimental data [39] and [41]; solid line: present simulation with soot parameter 1—[5], parameter 2—[33]

As shown in Fig. 21, the choice of the soot reactions parameters can have an important impact on the soot predictions. While the first set of parameters reaches the same peak of soot amount as the experiment, but at a lower height, the second set of parameter did neither reach the same amount of soot not the maximum soot prediction position, even though that set was fitted to do so in the original paper [33]. The maximum soot volume fraction was $f_{\mathrm{v,max}}= 7.1$ ppm and $f_{\mathrm{v,max}}= 5.3$ ppm, for Soot Parameters 1 and 2, respectively.

Similar to the analysis of radiative heat losses for model with Soot Parameter 1 (shown in Fig. 10), Fig. 22 presents the integrated radiation source term for soot model with Parameter 2.

Fig. 22

Integrated radiation source term along the height for the each phase and the combined case with Soot Parameter 2—[33]

Similar trend was found, the gas-phase radiation is the most important contribution, being responsible for 75% of the total radiative heat loss, while soot radiation is responsible for the remaining 25%. It is important to note that using Parameter 2, the amount of soot produced is less for the same flame; therefore, the soot radiation is less than with parameter 1. This results in higher overall temperature of the flame, with peak temperature of $T_{\mathrm{max}}=2103$ K, and higher gas-phase radiation.