## 4 Experimental Results  
As discussed in the introduction section, experiments carried out on the examined engine have highlighted significant differences in the combustion evolution between cylinders, mainly ascribed to a non-uniform effective in-cylinder air/fuel (A/F) ratio [15]. Cylinder-by-cylinder variations are apparent in Figure 2a which shows the experimental incylinder pressure trace and the rate of heat release (ROHR) for two representative operating points (3000@9 and 3000@13, 0% EGR). As aforementioned, the pressure data refer to the ensemble average over 270 consecutive cycles. For both operating conditions, the pressure curves of two cylinders are overlapped in the compression stage, denoting the same air volumetric efficiency, while Cyl #2 provides higher pressure peak and combustion rate than Cyl #1. The same behavior is found at each investigated operating point, suggesting a systematic difference in pressure cycles. Further experimental tests on the adopted fuel injection system have highlighted a different fuel supply to cylinders, resulting from a variation in port injectors fuel rates (Figure 2b). The results plotted in Figure 2b were collected through injection tests realized at am-bent air pressure with fuel injection system removed from the engine. A drive signal to injectors was used to simulate the injection timing; a certain number of injection timings were considered to measure the gasoline mass per stroke delivered by injectors. In particular, consistently with the in-cylinder pressure traces shown in Figure 2a, the injector corresponding to Cyl #2 provides a higher fuel mass flow rate. Interestingly, no difference was found also when the relative position of two injectors was switched, indicating the fuel rail geometry as responsible of the cylinder-by-cylinder variation. Indeed, the gasoline rail mounted on the examined engine at test bench represents a non-optimized prototype geometry. The optimized version of rail, mounted on the commercial SI engine, does not exhibit differences in the gasoline mass flow rates between port injectors. All the previous considerations underline that rail geometry is main responsible for the experimental cylinder-by-cylinder variation analyzed in this research activity. Figure 2: Comparison of experimental in-cylinder pressure traces and burn rates profiles at 3000 rpm, two IMEP levels (9 and 13 bar) and EGR = 0% (**a**). Differences of the injected gasoline mass per stroke between port injectors (**b**). Figure 3 shows the relative air-fuel ratio (\(\lambda\)) in Cyl #1, Cyl #2 and the engine exhaust at different engine operating points and EGR rates. \(\lambda\) of Cyl #1 was estimated from the composition of the exhaust gases of that cylinder through the carbon balance of species. Similarly, the overall engine \(\lambda\) was verified from the overall exhaust gas composition. This allows to indirectly evaluate the \(\lambda\) value of Cyl #2 under the hypothesis of an equal volumetric efficiency for both cylinders, as suggested by the comparison of pressure traces in the compression stage. Even though the engine conditions are close to stoichiometric, lean (\(\lambda\) between 1.03 and 1.08) and rich (\(\lambda\) between 0.96 and 0.98) mixtures are obtained in Cyl #1 and Cyl #2, respectively. Considering that the engine does not provide an individual set of injection and combustion phasing for each cylinder, the same spark advance and injection parameters are chosen for both cylinders, optimizing the engine load. As a consequence, a difference in the single cylinder load is found at each operating condition. The individual IMEP levels for both cylinders at different operating points are shown in Figure 4 as a function of the EGR rate. As expected, the larger fuel amount introduced in the Cyl #2 results in a higher IMEP at each investigated condition. Furthermore, the adoption of the same spark advance for both cylinders penalizes the combustion phasing of Cyl #1 which results slightly late compared to the MBT.