## 2 Materials and Methods
### Engine Characteristics and Modeling
\begin{table}
\begin{tabular}{c c} Engine Code & V08 ENT \\ Power & 560 kW at 2100 rpm \\ Torque & 3200 Nm at 1400 rpm \\ Idle speed & 700 rpm \\ No. of cylinder and arrangement & 8—V90 \\ Valves & 4 per cylinder \\ Air system & Supercharged and aftercooled \\ Firing order & 1-3-7-2-6-5-4-8 \\ Bore & 145 mm \\ Stroke & 152 mm \\ Compression Ratio & 17.4:1 \\ IVO/EVC & 27.5\({}^{\circ}\) BTDC/53.5\({}^{\circ}\) ABDC \\ EVO/EVC & 60\({}^{\circ}\) BBDC/22.5\({}^{\circ}\) ATDC \\ \end{tabular}
\end{table} 
Table 3: Engine characteristics [25,26]. \[P_{c}=\dot{m}_{c}\frac{k-1}{k}RT_{int,C}\left(\beta_{c}\frac{m_{c}-1}{h_{c}}-1\right) \tag{5}\]  
where \(m_{c}\) represents the polytropic exponent. More details on the flow model and solver used in this modeling approach can be found in [28]. The combustion model is based on a predictive approach, able to predict the combustion rate and, to some extent, the associated emissions for direct-injection diesel engines with single and multi-pulse injection events. A more detailed description of the model is reported in [28]. As previously introduced, the detailed 1D model was able to run in pre-defined stationary speed-load points. To perform a transient cycle throughout the simulations, it is necessary to know the engine behavior, not only in pre-defined points but in the whole operating range. For these reasons, some changes to the original model were necessary. Firstly, due to the lack of data at partial load conditions, the information necessary to develop the engine maps was obtained via simulations, starting from the validated model. From the experimental full-load power curve, several operating points at partial loads were identified, matching the percentage of load to the percentage of power. With this approach, the partial load map was identified. This map is composed of 70 engine operating points, as shown in Figure 4.  
Figure 4: Speed-Power-Load [%] output map. Figure 3: Detailed model of HD diesel engine. In these points, the requested fuel mass was assessed by an injection controller implemented into the detailed model to reach the power target, as depicted in Figure 5. The desired amount of fuel was calculated, taking into account several physical quantities of the engine (e.g., fuel energy, engine displacement, etc. ), in addition to the instantaneous values of the engine rpm. The controller required, in addition, the instantaneous values of the intake airflow, so it could calculate the amount of fuel, having, as a limit, a minimum value of Air to-Fuel ratio. This value was set to 17. It is worth highlighting that the minimum value obtained during the simulations was 19.6 (lambda 1.36), a typical value for diesel engines. When performing the simulation, each timestep is constrained, according to the Courant condition. This condition is necessary to avoid an unstable solution. Further details have been provided in Section 3.1. At the end of the simulations in the identified operating points, once defined the target fuel mass, the operative engine maps were obtained by interpolating all points. To perform the simulation of the NRTC, all of the inputs, depending on the operating conditions, have to change using either some form of look-up or a predictive model to account for the changes. Thus, all of the input maps (injection parameters, thermodynamic conditions, actuator positions, etc.) were derived and grouped into maps in order to also complete the modelling of a \"map-based\" model able to run transient cycles. Instant by instant, the simulation software via interpolation can calculate the desired input when performing the transient cycle. The quantity of the fuel to be injected time after time was defined by a look-up table as a function of the speed and load imposed by the NRTC. The load level and the engine rpm are those imposed by the NRTC after the denormalization procedure. Finally, it was necessary to consider that the wall temperature in transient operations changes over time in pipes and flow-splits, as well as cylinders.