*4.2. Cyclic NOx–RoHRmax Correlation*

As has been widely reported in the literature [27,35], one of the main challenges with adapting dual-fuel combustion for the entire speed–load range production engines is related to the control of the combustion. Despite the fact that Gaussian RoHR shape at advanced SOIs is accompanied by very low NOx and high efficiency, its high sensitivity to in-cylinder thermodynamic conditions and the SOI position significantly reduces the operating range of the engine. As a result, to increase the combustion controllability avoiding knock or misfire, previous efforts proposed retarded SOI operation for a certain number of engine cycles [17,26,35]. By using such SOI actuation, the engine can instantaneously recover from anomalous combustion events, preventing failures or damage to other components, such as the turbocharger, exhaust line, auxiliaries, etc.

Even though retarding the SOI can be considered an effective way to mitigate the wellknown dual-fuel combustion, especially knock, moving from a single-stage Gaussian RoHR to a two-stage RoHR increases the NOx emission. As reported in Figure 3a and confirmed by pollutants emissions shown in Figure 4, the two-stage combustion (SOI from −10 to −30 deg aTDC) is characterized by a very sharp first combustion stage and high NOx production. As mentioned before, such behavior is generated by the very short ignition delay of the HRF when injected close to TDC (pressure, temperature and the stratification of the air–fuel mixture are high) which ignites the amount of charge in the stratified zone.

Since NOx formation is driven by local temperatures potentially caused by the local air–fuel ratio stratification in dual-fuel combustion, RoHR calculated using a global combustion model is not directly referable to NOx emissions. This is made even more difficult especially when the nature of combustion changes significantly (i.e., from two-stage to single-stage Gaussian RoHR).

However, because the NOx production is promoted when a significant amount of energy is released in a short time, the link between the combustion behavior and the measured NOx can be obtained by examining combustion indices related to knock. Typically, such information can be easily obtained by the analysis of the RoHR, and in particular its maximum value.

From Figure 3a, it is evident that for combustion characterized by two-stage RoHR (SOI from −10 to −30 deg aTDC), the maximum value of the RoHR (RoHRmax), typically occurring in the first stage, is significantly and consistently higher with respect to the more advanced SOIs (SOI from −40 to −50 deg aTDC). Figure 11 shows the steady-state (slow-speed) NOx emissions measured with the Richmond bench and the RoHRmax (300 cycles) during the SOI sweep. It is evident that both NOx and RoHRmax follow the same trend, demonstrating a potential link between the identified combustion parameter and NOx production.

Focusing the attention on the SOI range characterized by two-stage combustion (SOI from −10 to −30 deg aTDC), because the first combustion stage progressively becomes more intense (Figure 2a), both NOx and RoHRmax increase. The reported trend is generated by the decreasing HRF ignition delay, which promotes local air–fuel ratio stratification and higher local temperatures inside the combustion chamber. A further advancement in SOI (from −35 to −50 deg aTDC) modifies the RoHR shape, characterized by a smoother energy release (Gaussian profile). Such behavior is mainly related to the HRF ignition delay increment because of the unfavorable thermodynamic conditions in the combustion chamber when the HRF is injected [28,29]. The very low NOx emissions shown by Figure 11 at advanced SOIs confirms a potential link between the combustion shape (i.e., the existence of a distinct first stage of RoHR) and NOx emissions. It is important to highlight that the RoHRmax tends to increase when SOI is advanced because the center of combustion moves to MBT (Figure 2). A further confirmation of this trend can be found by the information shown in Figure 4, where ISFC and pollutants are reported.

Upon identification of the link between RoHRmax and NOx emissions using the ensemble-averaged RoHR data and slow-speed NOx measurements, cycle-to-cycle analysis was performed.

**Figure 11.** Average NOx-RoHRmax correlation obtained through slow speed pollutant measurement (Richmond measurement system) running a SOI sweep in dual-fuel mode at low-load.

Following the same approach described in the previous section for identifying the HC–IMEP correlation, the fast NOx signal was acquired and synchronized with the EVO (after compensating for time-delay as discussed above). By phasing the instantaneous NOx emissions with the exhaust stroke, it was possible to clearly identify the NOx emissions associated with each engine cycle. Since the signal output characteristics of the CAMBUS-TION CLD500 have the same features as the fast HC analyzer, the same signal processing (acquisition and filtering) was adopted. Figure 12 shows the CAMBUSTION CLD500 signal (red line) and in-cylinder pressure signal (blue line) of an engine cycle characterized by high NOx emission (retarded SOI −20 deg aTDC).

Figure 12 clearly shows the peak of NOx emissions placed at the end of expansion stroke (EVC −355 deg aTDC) which can be assumed as the cyclic NOx production. Such behavior can be related to the delay of the Fast NOx before starting to measure the exhaust gases of the actual cycle. As documented by Peckham et al. [37] and Schurov et al. [38], the evident instantaneous NOx signal drop reported in Figure 12, around EVO, is related to the residence time of the exhaust gases behind the valve. The first portion of the gas sampled will be that which was released at the end of the previous exhaust stroke and then stayed in the port throughout the entire exhaust valve closed period resulting in a low NOx concentration. Moreover, since fast NOx and fast FID data have the same characteristics in term of signal output, the cycle resolved data have a crank angle resolution of 16 degrees that contributes retarding the rise of NOx signal.

With the aim of confirming the NOx-RoHRmax correlation identified through the analysis of the average data in Figure 11, the two stage RoHR combustion region (SOI from −10 to −30 deg aTDC) was considered. As clearly shown in Figure 13, where a cycle-to-cycle comparison (300 consecutive engine cycles) between the maximum value of the instantaneous NOx and the calculated RoHRmax was performed, the same trend reported in Figure 11 can be noticed. As discussed before, by advancing the SOI, the magnitude of the first RoHR stage initially increases and subsequently decreases, with obvious consequences in terms of NOx production. A further advancement in SOI generates near-zero NOx production because of the different combustion behavior (Gaussian RoHR shape), confirming the link between the combustion RoHR shape and NOx production. This strong linear correlation (R<sup>2</sup> = 0.82) between NOx emissions and the transformation of the RoHR shape in dual-fuel combustion has been previously observed by several researchers, most recently by Partridge et al. [32], who attributed the RoHR shape transformation to local air–fuel ratio stratification.

**Figure 12.** In-cylinder pressure signal and Instantaneous NOx production for a dual-fuel engine operating condition at SOI −20 deg aTDC.

**Figure 13.** Cycle-to-cycle NOx-RoHRmax correlation obtained through high-frequency pollutant measurement (CAMBUSTION measurement system) running a SOI sweep in dual-fuel mode at low load.
