## 4 Results  
### Comparison of In-Cylinder Temperature and Pressure  
We measured the critical parameters, namely, temperature and pressure, of gasoline and found them to be 550 K and 3.092 MPa, respectively [15]. In this simulation, the alternative fuel for gasoline is isooctane. Many researchers use n-heptane instead of diesel in their numerical simulations when the diesel supercritical parameters are unknown. The temperature and pressure of n-heptane are 540.3 K and 2.74 MPa [33]. The heat of combustion per unit of isooctane and n-heptane are \(-\)537.9705 KJ/Kg and \(-\)1536.5545 KJ/Kg, respectively. In this study, the initial temperature of fuel was set to 350 K/400 K to simulate the subcritical fuel injection condition. The initial fuel temperature was set to 600-650 K/700 K for the supercritical fuel injector condition. As shown in Figure 4a, the times of temperature mutation and temperature peak appearance in the supercritical condition are shorter than those in the subcritical condition. Compared with the situation in the subcritical condition, the rise rate of temperature in the supercritical condition is higher, and the peak temperature is slightly increased. This phenomenon is caused by the supercritical fuel's low density, high flow velocity, and high diffusion rate when the fuel flows into the cylinder, resulting in rapid mixing of fuel and air and fast fuel ignition. As shown in Figure 4b, compared with the situation in the subcritical condition, the pressure rise rate and average pressure in the supercritical fuel injection condition increase significantly. The pressure peak appears at 730\({}^{\circ}\) crank angle (CA), at which the piston has passed through the top dead center and is moving toward the bottom of the cylinder. According to the perfect gas equation, the pressure is proportional to the temperature in the enclosed volume. At 730\({}^{\circ}\) CA, the average temperature in the supercritical fuel injection condition is higher than that in the subcritical condition. Hence, pressure is higher in the supercritical condition than that in the subcritical condition. Moreover, the supercritical state fuel is close to the gaseous phase. According to the relationship between mass and density, the same mass of fuel flows into the cylinder. Supercritical fuel accounts for a large volume, and liquid fuel has a small volume only, resulting in an increase in in-cylinder density and pressure. Figure 5a shows the distribution of fuel at 350, 400, 600, 650, and 700 K in the cylinder when the fuel begins to catch fire. The distribution of fuel in supercritical and subcritical fuel injection conditions was compared at 718\({}^{\circ}\) and 720\({}^{\circ}\) CA. At 718\({}^{\circ}\) CA, the fuel is evenly distributed in the cylinder under three supercritical conditions. Then, the fuel is sprayed to the wall of the combustion chamber. The jet flow remains relatively small in the two cases of subcritical conditions, and the subcritical fuel lacks sufficient contact with air and is mixed. At this point, the supercritical state fuel begins to burn, which makes the combustion time of the supercritical condition shorter than that of the subcritical  
Figure 4: Change curve of parameters in cylinder at different time. (**a**) average temperature; (**b**) average pressure. condition. At 720\({}^{\circ}\) CA, the subcritical state fuel begins to burn, but the supercritical fuel has been burned already. As shown in Figure 3a, the in-cylinder peak temperature was immediately reached in the supercritical condition. Figure 5b shows that the diffusion rate of the fuel in the supercritical fuel injection condition is higher than that in the subcritical condition, which is beneficial to the mixing of fuel and air, increases the mixing speed of fuel and air, and makes the mixture uniform. The combustion reaction is rapid in the supercritical condition. Hence, the average in-cylinder temperature increases faster, and the temperature reaches the peak earlier than in the subcritical conditions.