2.2.1. Combustion Kinetic Scheme

The fuel was treated as n-heptane. The kinetic scheme of Ra and Reitz [42], based on 131 reactions and 41 species, was employed for combustion. Another common approach to treat combustion in CFD is to assume that the kinetics is so fast that chemical species remain at equilibrium due to the high temperatures. Nevertheless, previous works [43,44] indicated that a kinetic scheme is more accurate than the equilibrium hypothesis, since the cooling during the expansion process and dilution with the excess air elongates the time needed to achieve equilibrium. Indeed, several studies about diesel engines verified that the measured CO emissions are higher than those provided by the equilibrium concentrations. The reason is that one of the sources of CO in diesel engines are lean regions which are not able to burn properly [45,46]. This happens when the local turbulent and diffusion time scales are much smaller than the time required to achieve equilibrium. In these cases, the chemical equilibrium hypothesis leads us to overestimate the levels of the minor species. For these reasons, another procedure developed in the present work was the implementation of a chemical kinetic model. Figure 3 represents the CO and HC emissions experimentally and numerically obtained using chemical equilibrium and the kinetic model. As can be seen, the kinetic model improves the results. Regarding CO2 emissions, these remain practically inalterable so are not included in the figure. According to the improvement obtained using the kinetic model compared to the equilibrium assumption, the kinetic model developed by Ra and Reitz [42] was employed in the remainder of the present work.

**Figure 3.** HC and CO emissions experimentally and numerically obtained.

### 2.2.2. NOx Formation Kinetic Scheme

The numerical model employs the kinetic scheme of Yang et al. [47], based on 43 reactions and 20 species. In CFD, it is common to employ the so called extended Zeldovich mechanism [48,49], based on 3 reactions and 7 species. Nevertheless, previous works [44,50] compared several kinetic schemes using experimental results and concluded that the model of Yang et al. provides satisfactorily accurate results.

### 2.2.3. NOx Reduction Kinetic Scheme

The kinetic scheme chosen for NOx reduction is the one proposed by Miller and Glarborg [51], based on 134 reactions and 24 species. The accuracy of this and other kinetic schemes was also compared with experimental measurements elsewhere [43,52], concluding that the model of Miller and Glarborg [51] provides satisfactorily accurate results.

### *2.3. Validation of the Overall Numerical Model*

The overall numerical model, summarized in Table 3, was validated using experimental measurements. The emissions and consumption obtained experimentally and numerically at several loads are shown in Figure 4. This figure includes CO, CO2, NOx, HC, and SFC. As can be seen, a reasonable correspondence between numerical and experimental resultswas obtained. Thein-cylinder pressure obtained experimentally and numerically at 100% load is shown in Figure 5. This figure also indicates a satisfactory correspondence between experimental and numerical results. Other loads also provided satisfactory concordance between experimental and numerical results, and thus are not represented again.


**Table 3.** Numerical models.

**Figure 4.** NOx, HC, CO and CO2 emissions as well as BSFC experimentally and numerically obtained.

**Figure 5.** In-cylinder pressure experimentally and numerically obtained at 100% load.
