# Cycle-to-Cycle Variation of a Diesel Engine Fueled with Fischer-Tropsch Fuel Synthesized from Coal
## 3 Results and Discussion
### Cyclic Variation Characteristics  
The inequality of fuels injected into the engine caused cycle-to-cycle variations, which significantly affected the combustion stability. The P\({}_{\text{max}}\) has \"easy to measure\" and \"sensitive to cyclic variations\" characteristics, so the coefficient of variation (COV) was analyzed to characterize the difference based on the published research [40; 41]. COV was defined by using Equations (3)-(5); the linear dependence of relativity on peak in-cylinder pressure and combustion parameters (R(P\({}_{\text{max}},\text{y}\))) was measured in terms of the Pearson's correlation, as presented in Equation (6), where the mean value of in-cylinder pressure is expressed in \(\overline{\text{P}_{\text{max}}}\), N is the total cycle number, i represents the cycle index, and \(\sigma_{\text{P}}\) is the standard deviation [42; 43; 44]. A significant correlation was observed among parameters when R was in the range of 0.5-1.0. \[\overline{\text{P}_{\text{max}}}=\frac{1}{\text{N}}\sum_{\text{i=1}}^{\text{N }}\text{P}_{\text{i}} \tag{3}\]  
\[\sigma_{\text{P}}=\sqrt{\frac{\sum_{\text{i=1}}^{\text{N}}(\text{P}_{\text{i} }-\overline{\text{P}_{\text{max}}})^{2}}{\text{N}-1}} \tag{4}\]  
\[\text{Cov}_{\text{P}}=\frac{\sigma_{\text{P}}}{\overline{\text{P}_{\text{max} }}}\times 100\% \tag{5}\]  
\[\text{R}(\text{P}_{\text{max}},\text{y})=\frac{\sum_{\text{i=1}}^{\text{N}}( \text{P}_{\text{i}}-\overline{\text{P}})(\text{y}_{\text{i}}-\overline{\text{ y}})}{(\text{N}-1)(\sigma_{\text{P}}\text{-}\sigma_{\text{y}})} \tag{6}\]  
P\({}_{\text{max}}\) is an important mechanical indicator in modern compression engine [34; 45]. Figure 6 demonstrates the variations of P\({}_{\text{max}}\) for 100 consecutive cycles under three speed conditions with the test fuels. Furthermore, the differences between the mean P\({}_{\text{max}}\) and COV under 100 cycles were calculated. P\({}_{\text{max}}\) changed stochastically under different speed conditions. However, the mean P\({}_{\text{max}}\) increased with the increase in the speed, and the F-T diesel showed a lower mean value than 0# diesel at the same speed, which was in line with the results presented in Section 3.1. Notably, values of COV of F-T diesel are 1.72, 1.32, and 2.02%, respectively, for the speeds of 1200, 2000, and 2800 rpm, which are lower than 2.49, 2.16, and 4.01% of 0# diesel. The F-T diesel with higher CN and lower viscosity was found to be beneficial to improve air-fuel mixture. Moreover, fuel atomization was in accordance with gas turbulence intensity during the kernel formation phase owing to its advanced combustion. Ascribed to these factors mentioned above, the F-T diesel exhibited excellent properties of combustion stability with little variation. On the other hand, cyclic variations at the speed of 2000 rpm were minimal and the maximum was obtained at the speed of 2800 rpm. This was mainly because the quality of air-fuel mixtures was further improved with a higher in-cylinder temperature and airflow motion as the engine speed increased. Thus, the combustion stability increased, and finally the COV decreased at a speed of 2000 rpm compared to that at 1200 rpm. At the speed of 2800 rpm, the time for proper combustion phasing was reduced; moreover, the residual exhaust gas was increased and therefore it was easier to cause combustion instability, so the cyclic variation sharply increased. Figure 7 displays the fluctuation intensity of 100 consecutive cycles versus ignition delay under different conditions with the test fuels. Correspondingly, the intensity of fluctuation versus combustion duration is shown in Figure 8. Notably, the intensity of fluctuation follows a trend similar to that of the COV, which acquired the minimum average value at the engine speed of 2000 rpm and the maximum value at the speed of 2800 rpm.