# Cycle-to-Cycle Variation of a Diesel Engine Fueled with Fischer-Tropsch Fuel Synthesized from Coal
## 3 Results and Discussion
### Cyclic Variation Characteristics
The F-T diesel presents a lower mean fluctuation intensity than 0# diesel; moreover, the mean intensity of fluctuation was 0.185, 0.189, and 0.205 at the speeds of 1200, 2000, and 2800 rpm during the entire test conditions, respectively. Furthermore, the mean intensity of fluctuation of 0# diesel was 0.187, 0.191, and 0.211, respectively, under the corresponding speed conditions. As mentioned above, F-T diesel showed excellent properties of combustion stability, so the mean and variance of in-cylinder pressure were small, which resulted in lower fluctuation intensity. When the engine was operated at the speed of 2800 rpm, the in-cylinder pressure increased and the intensity of fluctuation was enhanced with the increase in combustion instability. Figure 6: COV of P\({}_{\text{max}}\) under different speeds with the test fuels. (**a**) F-T diesel, (**b**) 0# diesel. Figure 7: Intensity of fluctuation versus ignition delay under different speeds with the test fuels. To explore the trend of peak in-cylinder pressure with ignition delay, the relationship between P\({}_{\max}\) and ignition delay was established as shown in Figure 9. Figure 9 shows that the P\({}_{\max}\) increases linearly with a longer ignition delay. The relationship can be described by the equation in the figure and R was 0.75, 0.78, and 0.73 when the engine was fueled with F-T diesel at the speeds of 1200, 2000, and 2800 rpm, respectively. A similar method was used to state the relationship between P\({}_{\max}\) and ignition delay under different working conditions using 0# diesel. The results are displayed in the corresponding figure and the R was 0.81, 0.86, and 0.83, respectively. It can be concluded that P\({}_{\max}\) and ignition delay were highly correlated, and a longer ignition delay was useful in increasing in-cylinder pressure. However, the cyclic variation enhanced and the tendency of combustion instability increased. The results indicated that cyclic variability rapidly increased with ignition delay under high speed, which was relatively small under lower speed conditions according to the fitting equations between P\({}_{\max}\) and ignition delay. Compared to 0# diesel, ignition delay had relatively little effect on the cyclic variation since the R of F-T diesel was smaller than that of 0# diesel at the corresponding speed conditions. The relationship between P\({}_{\max}\) and combustion duration is shown in Figure 10. In contrast to the results presented in Figure 9, the P\({}_{\max}\) decreases linearly with increased combustion duration. The relationship can be described in terms of the equations displayed in the figure and R was 0.61, 0.67, and 0.65 when the engine was fueled with F-T diesel at the speeds of 1200, 2000, and 2800 rpm, while for 0# diesel R was 0.73, 0.79, and 0.75 under the corresponding speed conditions, respectively. Similar findings are displayed under other operating conditions. This indicates that P\({}_{\max}\) increases with short combustion duration, which is correct since the higher constant volume combustion leads to a shorter combustion duration. Within a certain range, combustion stabi  
Figure 8: Intensity of fluctuation versus combustion duration under different speeds with the test fuels. \[\sigma_{\text{P}}=\sqrt{\frac{\sum_{\text{i=1}}^{\text{N}}(\text{P}_{\text{i} }-\overline{\text{P}_{\text{max}}})^{2}}{\text{N}-1}} \tag{4}\]0 The correlation between peak in-cylinder pressure and ignition delay with (**a**) F–T diesel, (**b**) 0# diesel. by decreasing the combustion duration. According to the fitting equations, the combustion duration significantly influenced the P\({}_{\max}\) under the lower speed condition. Similarly, the correlation of F-T diesel was smaller than that of 0# diesel. Moreover, combustion duration had a more obvious effect on cyclic variation when fueling with F-T diesel compared to 0# diesel, because the absolute slope of linear regression was greater than that of 0# diesel at the same speed condition due to its higher CN and shorter combustion duration.