## 3 Engine and DOC Response
The lower sensitivity of torque in point #B to the post-injected fuel mass rate, which is represented in Figure 8b, makes the raw HC concentration gain further dependence to this variable besides the post-injection timing. Regardless, the raw HC emission increases with the delay in the post-injection as the engine load decreases and EGR is used. Concerning soot emission, Figure 8c shows that point #A is greatly dependent on the post-injection delay, increasing as the post-injection is advanced due to the incomplete combustion of the fuel in these conditions [45]. Additionally, the increase of the temperature inside the cylinder induced by the partial combustion of post-injected fuel mass is not high enough to produce a relevant oxidation of the generated soot particles [46]. The trend in raw soot emissions completely changes in point #B, as represented in Figure 8d. A lower increase of the soot emissions compared to point #A is observed. This response is explained by the fact that the soot formation at low engine load is governed by the temperature of the gas inside the cylinder at the same time that the post-injection is performed. Being that this temperature is low, the reactions responsible of creating soot precursors are inhibited, thus avoiding the production of additional soot from the post-injection [45]. Figure 7: Effect of the post-injection timing and the post-injected fuel mass rate on the brake specific fuel consumption and the torque. The boundary conditions at the DOC inlet are completed with the gas temperature, which is shown in Figure 9a and b for points #A and #B respectively. Comparing against Figure 7c,d, the DOC inlet temperature profile is observed to be almost identical to that in torque. Settings increasing the amount of post-injected fuel burned into the cylinder lead to an increase in torque and DOC inlet temperature. Therefore, the exhaust gas temperature increases as the post-injection is closer to the TDC and, to a lesser extent, the fuel mass increases, as also discussed experimentally by [PERSON] et al. [28]. By contrast, the pattern in the DOC outlet temperature is governed by the HC oxidation due to its high concentration, as plotted in Figure 9c,d. It is possible to observe how higher post-injected fuel mass rate produces the highest temperature increase across the DOC. The delay in the post-injection also favours the increase of the DOC outlet temperature. However, this effect is much more relevant in point #A than in point #B since it is intimately related to the amount of post-injected fuel mass burned into the cylinder. In fact, it can be noticed how in point #A the region with the highest DOC outlet temperature corresponds to the lowest inlet one. The same conclusions are obtained from the analysis of point #B. Nevertheless, the dependence of the DOC outlet temperature on the post-injection timing is lower due to the lower torque variation as a function of this parameter. This response evidences that the increase in the DOC inlet temperature is caused by the oxidation of the post-injected fuel into the cylinders. This contributes to increase the torque and leads to a final lower temperature at the DOC outlet for the same post-injected fuel mass rate. In fact, Figure 9e,f indicate that the O\({}_{2}\) concentration is only dependent on the post-injected fuel mass rate. In fact, it demonstrates that all the post-injected fuel is oxidised in the cylinder and/or the DOC. Figure 8: Effect of the post-injection timing and the post-injected fuel mass rate on the raw HC and soot emissions. Taking into account the effects of the different post-injection settings on the temperature field, it is possible to quantify how efficiently the invested energy is converted into an increase of the temperature at the DOC outlet.