## 4 Evaluation of Hydrogen Combustion with the Addition of Helium
### Thermodynamic Parameters  
The analysis of the net heat rate dQ was carried out according to the equation [25,26]:  
\[\mathrm{dQ}(\alpha)=\frac{\mathrm{dQ}_{\mathrm{net}}}{\mathrm{d}\alpha}= \frac{\gamma}{\gamma-1}\mathrm{P}(\alpha)\frac{\mathrm{dV}}{\mathrm{d}\alpha} +\frac{1}{\gamma-1}\mathrm{V}(\alpha)\frac{\mathrm{dP}}{\mathrm{d}\alpha}, \tag{2}\]  
and the Q is given by the following:  
\[\mathrm{Q}(\alpha)=\int_{\alpha=-30}^{\alpha=90}\frac{\mathrm{dQ}_{\mathrm{ net}}}{\mathrm{d}\alpha}\mathrm{d}\alpha, \tag{3}\]  
where P is the instantaneous cylinder pressure, \(\alpha\) is the crank angle, \(\gamma\) is the ratio of the specific heats (\(c_{\mathrm{P}}/c_{\mathrm{v}}\)), and V is the instantaneous cylinder volume. This last parameter was calculated from the engine geometry and crank angle values. Hence, a constant value of \(\gamma=1.35\) is considered in this study for analyzing the Q in fuel operation. The lowest cylinder pressures were obtained at low excess air ratio values (Figure 5), while the heat release rate was the highest (Figure 8). This is because the increase in compression pressure as a result of changing \(\lambda\) is greater than the increase in maximum combustion pressure in the cylinder. When \(\lambda=1.55\)-\(1.46\), a high heat release rate and short combustion time in the main chamber are observed. In the prechamber, the two-stage combustion process is clearly outlined. The first peak of the heat release rate (in the PC) occurs much earlier than in the main chamber. The next peak is synchronized with the main chamber. Each further increase in \(\lambda\) causes a reduction in the heat release rate, a prolongation of the combustion process (in the main chamber), and a limitation of the first and second phases of combustion (in the prechamber). Increasing the proportion of He in the fuel significantly reduces the heat release rate. At He proportions in the mixture of 10%/20%/30%/40%, a decrease in dQ_MC was obtained, respectively: 18%/43%/68% and 75%. This is significantly more than during the IMEP analysis. Figure 7: Map of variations in the throttle position, hydrogen content of the mixture, and resulting excess air ratio (color—resulting excess air ratio; circles— excess air ratio values; triangles—projection onto the plane of \(\lambda\)-value). The maximum value of the heat release rate in the prechamber was also reduced. The dQ_PC values were as follows: 12%/33%/54% and 66%. This means that a 20% addition of He results in a 50% reduction in the heat release rate in MC (in the PC up to 33%). The above results must be reflected in the heat release (derived from Equation (3))--Figure 9. As before, the greatest heat release was obtained at low values of \(\lambda\). An analysis of combustion with a passive prechamber shows a delay in combustion and a reduction in the total amount of heat release. Increasing the fuel dose in the PC raises the overall heat release and accelerates the combustion process (assuming that the CoC in the passive combustion chamber is between 8 and 10 deg aTDC). The analysis shows that increasing the proportion of helium in the fuel mixture reduces the maximum heat release. With the following increase in the proportion of He in the fuel, 10/20/30/40%, the decrease in heat release (in MC) was, respectively, 12/22/34/39%. This means that increasing the percentage of helium in the fuel reduces the maximum heat release by an average of 10% for every 10% of increased helium content. The analysis of heat release in the PC includes the start of combustion, but information on the fluid flows between the main chamber and the primary chamber. Therefore, the released heat is greater with a passive prechamber (qo_PC = 0 mg)--Figure 9 (variable Q_PC). Despite the higher maximum values of heat release, a delay and slowing down of the initial combustion process are observed. Considering the maximum values of fuel injected into the prechamber (qo_PC = 8 ms), it can be concluded that the addition of helium to hydrogen slightly reduces the heat release in the prechamber.