## 2 Numerical Simulations  
A 0-D thermodynamic model, described in [22], properly calibrated using experimental data coming from a spark-ignition engine fueled with both gasoline and gaseous fuels [22; 23], was used in the present work to obtain BTE maps of the engine when fueled with both gasoline and hydrogen. Table 1 shows the ICE specifications. The main model inputs are the engine speed, engine load (Manifold Absolute Pressure or MAP), air/fuel mass ratio and spark advance (SA); the main model outputs are the engine indicated and brake mean effective pressures (IMEP and BMEP), the engine indicated and brake thermal efficiencies (ITE and BTE) and the engine torque and power. With respect to the previous simulation version [22], which was able to evaluate only the in-cylinder pressure during the whole engine cycle and then the IMEP, an engine friction model was added in order to evaluate the friction mean effective pressure (FMEP) and, in turn, both the BMEP and BTE. The Chen and Flynn friction model [24] was implemented; according to this model, the engine FMEP can be evaluated using the following equation:  
\[\text{FMEP}=\text{A}+\text{B}\cdot p_{\text{max}}+\text{C}\cdot n+\text{D} \cdot n^{2} \tag{1}\]  
where \(p_{\text{max}}\) is the maximum in-cylinder pressure; \(n\) is the engine speed; and A, B, C and D are calibration coefficients that were tuned by means of experimental data in [15]. To identify the air/fuel (A/F) ratio of a mixture, the coefficient of excess air \(\lambda\) is defined, it is the fraction between the actual A/F ratio and the stoichiometric one. In order to avoid dangerous combustion phenomena, such as pre-ignition and knocking, the hydrogen-fueled ICE must be operated with a lean A/F mixture [5; 6; 7; 8] (i.e., with \(\lambda>1\)), and this (together with the lower specific power of hydrogen) reduces the engine performance with respect to the gasoline operation mode; to fill this gap, one of the most used techniques is supercharging. In the literature, many combinations of supercharging pressure and \(\lambda\) values can be found that lead to knock-safe operation and allow obtaining the same performance as gasoline-fueled engine [5; 25; 26; 27]. The only pollutant emitted by a hydrogen-fueled engine, with a stoichiometric A/F ratio, is nitrova oxides (NOx); however, as soon as the A/F mixture is doubled (i.e., \(\lambda=2\)) a drastic drop in NOx emissions is found [5; 25; 26]. Even supercharged engines do not emit NOx as long as the maximum combustion temperature remains below 1800 K [5], and in all the simulations presented in this work, the maximum combustion temperature remains below 1700 K.  
Resuming the literature findings, one can roughly say that, with \(\lambda=2\) and a supercharging pressure of 2 bar absolute, the hydrogen-fueled engine is able to restore the gasoline engine performances and almost eliminate the NOx emissions. Regarding the combustion speed, hydrogen exhibits a laminar flame velocity one order of magnitude greater than gasoline for the stoichiometric A/F ratio and around 60% greater than gasoline for \(\lambda=2\)[27; 28]. Considering the same engine and operating conditions, the turbulence inside the combustion chamber should be the same for both gasoline and hydrogen fuels, and then the ratio between the laminar flame velocities of the two fuels can be roughly considered the same between the turbulent flame velocities. This conclusion was confirmed by some preliminary experimental tests performed by the author on an ICE test bench. Resuming all the above-mentioned considerations, in order to simulate a hydrogen-fueled engine that should produce the same performance of the gasoline counterpart (i.e., the maximum power), that should not produce abnormal combustion phenomena and that should not emit NOx, the combustion duration must be