## 3 Results and Discussions
### Compression Ratio
Figure 3: Combustion pressures and heat release rates at different compression ratios: 1—CR 12.4 (purple); 2—CR 14.1 (black); 3—CR 16.5 (green); 4—CR 19.9 (yellow); 5—CR 25.2 (red). Figure 4 shows the cyclic variations in p\({}_{\rm mi}\) over 200 consecutive test cycles at compression ratios of 14.1, 16.5, 19.9, and 25.2. At the compression ratio of 14.1, p\({}_{\rm mi}\) varies from  
Figure 4: p\({}_{\rm mi}\) at different compression ratios. Figure 5: CA10, CA50, and CA90 at different compression ratios. 0.23 to 0.28 MPa with a mean value of 0.251 MPa, and the cyclic variation coefficient in p\({}_{\text{mi}}\) (COV\({}_{\text{pmi}}\)) is 3.39%. At a compression ratio 16.5, p\({}_{\text{mi}}\) ranges from 0.16 to 0.23 MPa with a mean value of 0.192 MPa, and COV\({}_{\text{pmi}}\) is 6.30%. At the compression ratio 19.9, p\({}_{\text{mi}}\) goes from 0.10 to 0.16 MPa with a mean value of 0.130 MPa, and COV\({}_{\text{pmi}}\) is 7.82%. At the compression ratio of 25.2, p\({}_{\text{mi}}\) varies from \(-\)0.01 to 0.10 MPa with a mean value of 0.036 MPa, and COV\({}_{\text{pmi}}\) is 58.6%; at this moment, misfire and partial burning cycles are present in large numbers (if p\({}_{\text{mi}}\) of an individual cycle is less than one-third of the average p\({}_{\text{mi}}\) of successively sampled test cycles, the individual cycle is considered a partial burning or misfire cycle [33]). As shown in the figure, p\({}_{\text{mi}}\) drops unexpectedly as the compression ratio increases. Thermodynamically, the optimal combustion phase should end the combustion exothermic process with an isovolumic heating process at the TDC. Correspondingly, the recommended value of A\({}_{\text{pmx}}\) is generally from 10 to 15 deg ATC for modern reciprocating piston internal combustion engines. As seen in Figure 3a, A\({}_{\text{pmx}}\) is within the recommended range only at the compression ratio 14.1. In contrast, the combustion phase is excessively advanced at the other compression ratios and significantly decreases thermal efficiency. Figure 5 shows the cyclic variations in CA10, CA50, and CA90 over 200 consecutive test cycles for 14.1, 16.5, 19.9, and 25.2 compression ratios. CA10 is the crank angle at which 10% fuel heat has been released, CA50 is the crank angle at which 50% fuel heat has been released, and CA90 is the crank angle at which 90% fuel heat has been released. In Figure 5a, CA10 slightly advances as the compression ratio increases from 14.1 to 16.5 to 19.9; however, the cyclic variations in CA10 are more significant, reflecting the relative instability of the low-temperature exothermic reaction. At the compression ratio 25.2, because of the heat absorbing process with a negative exothermic rate in the pre-combustion stage, CA10 calculated from the thermodynamic zero-dimensional model is relatively reversed. In Figure 5b, CA50 varies from 2.5 to 11.5 deg ATC at the compression ratio of 14.1, from \(-\)1.6 to 6.5 deg ATC at the compression ratio of 16.5, and from \(-\)5 to \(-\)1.4 deg ATC at the compression ratio of 19.9. Only at the compression ratio 14.1 is CA50 close to the thermodynamically recommended value of a range from 5 to 10 deg ATC. At the compression ratio of 25.2, CA50 no longer continues to advance. In Figure 5c, CA90 moves ahead as the compression ratio increases from 14.1 to 16.5 to 19.9 but is no longer advanced at the compression ratio 25.2. At the compression ratio of 19.9, most test cycles have CA90 at a point before the TDC, which denotes a highly unreasonable heat release time. In addition, the combustion duration identified by the interval between CA10 and CA90 decreases dramatically from 23.5 deg CA at the compression ratio of 14.1 to 10.5 deg CA at the compression ratio of 19.9; meanwhile, the cyclic variations in CA50 and CA90 decrease obviously. However, the improvement in combustion duration and stability does not compensate for the harmful effects of the heat release time being too far ahead at the compression ratio 19.9.