# Numerical Investigation on NOx Emission of a Hydrogen-Fuelled Dual-Cylinder Free-Piston Engine
## 3 Simulation Results
### Regulation between NOx Emission and Equivalent Ratio  
Figure 15 shows the relationship between NOx emission and the equivalent ratio (\(\varphi\)) when the ignition advance angle (time) is fixed at 10 \({}^{\circ}\)CA (0.00583 s) and the engine frequency is fixed at 5 Hz. As shown, when \(\varphi<0.5\), NOx increases with the increase of \(\varphi\), but the range is relatively small and the contribution rate of \(\varphi\) is small as well; when \(0.5<\varphi<0.88\), NOx increases with the increase of \(\varphi\), but the range is large and the contribution rate of \(\varphi\) is relatively large as well; and when \(\varphi>0.88\), NOx sharply decreases with the increase of \(\varphi\). NOx emissions reach their highest point at \(\varphi=0.88\), and this regulation is highly in agreement with what has been mentioned by [PERSON], etc. [18; 19; 20].  
Figure 14: Highest in-cylinder temperature of gasoline FPE and hydrogen FPE.  
Figure 13: NOx emission comparison between three models.  
Thermal NOx is the staple NOx emission category in a hydrogen internal combustion engine, and the formation of NOx is mainly determined by three factors: high temperature, oxygen enrichment and duration of high temperature, while temperature affects the most. The stagnation temperature of the formation of thermal NOx is 1800 K; when the temperature is higher than 1800 K, the formation of NOx increases exponentially with increasing temperature. When the in-cylinder temperature is higher than 2000 K, the contribution rate of temperature will become extremely obvious. The highest mean in-cylinder temperature in this thesis was calculated by [PERSON].  
Figure 16 illustrates the highest mean in-cylinder temperature under different equivalent ratios. It could be seen that: when \(\varphi\) is between the range of 0.33-0.5, the highest mean in-cylinder temperature increases from 1412 K to 1972 K and reaches the stagnation temperature of the formation of NOx; moreover, part of the in-cylinder temperature could be higher than 1800 K; therefore, NOx emission slightly increases with the increase of temperature, but generally, the effect of \(\varphi\) on NOx formation is small; when \(\varphi=0.52\), the highest in-cylinder temperature is 2109 K, which is obviously higher than the stagnation temperature of NOx formation, and the temperature contribution rate becomes extremely high; when \(\varphi\) increases from 0.48 to 0.52, NOx increases with temperature from 10.76 ppm to 31.82 ppm.  
In the range of \(\varphi\) from 0.52 to 1.2, the highest mean in-cylinder temperature increases with the increase of \(\varphi\), but NOx does not constantly increase but reaches its highest point at \(\varphi=0.88\) and decreases with the increase of \(\varphi\) afterwards. The reason for this phenomenon is that, in the range of \(\varphi\) from 0.52 to 0.88, there is sufficient oxygen in the mixture, which makes temperature the most important factor that affects NOx formation; the higher the in-cylinder temperature is, the more NOx is produced, and high temperature causes the formation of a large amount of NOx. When \(\varphi>0.88\), with the increase of \(\varphi\), the highest mean in-cylinder temperature increases continuously, but the amount of air in the cylinder is becoming less and less, and there's less and less oxygen to bond with nitrogen. Moreover, due to the higher burning speed of hydrogen, the retention time of high-temperature gas in the cylinder is shortened, resulting in less oxygen, and the shorter retention time restricted the formation of NOx together. When \(\varphi>1\), excess hydrogen will not only reduce some of the NO but also absorb heat in the cylinder and decrease the in-cylinder  
Figure 15: NOx emission with different equivalent ratio.  
temperature, lower in-cylinder temperature and insufficient oxygen restrict the formation of NOx simultaneously.