# Parametric Simulations on Leakage and Performance of a Miniature Free-Piston Generator (MFPG)
## 4 Parametric Study on Leakage and Performance
### Effect of the Start of Combustion  
In reality, the ignition time is controlled by adjusting the temperature of the glow plug and the SOC is characterized by the ignition position \(x_{ign}\). In the simulation, the value of \(x_{ign}\) is varied from 1-4 mm, while all the other parameters remain unchanged. The increase in \(x_{ign}\) indicates the advancing of SOC and the decrease in \(x_{ign}\) means the delay of SOC. According to Figure 8a, when the \(x_{ign}\) varies, the in-cylinder gas mass at EPC \(m_{gspc}\) shows little difference, while the in-cylinder gas mass at SOC \(m_{gspc}\) varies largely. When the combustion takes place between 2-4 mm, \(m_{gspc}\) increases with the advance of SOC, whereas \(m_{gvac}\) decreases with the advancing of SOC after the piston is compressed less than 2 mm. The reason is that the piston frequency \(f_{p}\) increases sharply with the delay of SOC, reduces the time of leakage and offsets the effect of the increase in pressure difference at this range. The corresponding leakage characteristics are presented in Figure 8b. In most cases, the mass leaked during the expansion stroke is more than that during the compression stroke. As seen from the mass leakage ratio curve, the leakage peaks at \(x_{ign}\) = 2 mm indicate that the worst sealing performance occurs there. Better sealing could be achieved either by advancing ignition time or postponing the ignition until the piston passes 2 mm. Figure 8: The influence of ignition position on leakage and system performance. (**a**) Mass variations of in-cylinder gas in function of stroke; (**b**) Mass leakage; (**c**) Pressure variations of in-cylinder gas in function of stroke; (**d**) Piston dynamic characteristics; (**e**) Thermal efficiencies; (**f**) Indicated thermal efficiency drops. Figure (**a,c,d**) apply the same legend displayed in figure (**c**). The blue, green, red and black solid lines stand for the ignition positions at 1.0, 2.0, 3.0 and 4.0 mm, respectively. The values in figure (**a**) show the exact amount of the in-cylinder gas mass at the corresponding positions. The symbol \(f_{p}\) in figure (**d**) stands for piston frequency, Hz. The delay of SOC is realized by controlling the combustion that takes place closer to the cylinder head, so the effective compression ratio \(\varepsilon_{cc}\) monotonically increases with the delay of SOC. The in-cylinder peak pressure \(p_{\text{max}}\), on the other hand, varies more complexly, as shown in Figure 8c. When \(x_{ign}\) is in the range of 3-4 mm, \(p_{\text{max}}\) increases with the delay of SOC, as being straightforwardly influenced by the increased \(\varepsilon_{cc}\). When \(x_{ign}\) decreases to the range of 2-3 mm, the mass leakage exacerbates and overtakes the promoting effect of \(\varepsilon_{cc}\) increase. Thus, the \(p_{\text{max}}\) decreases with a delay of SOC in this range. As \(x_{ign}\) further decreases to the range of 1-2 mm, \(p_{\text{max}}\) increases with the delay of SOC, again due to the combined effects of the increased \(\varepsilon_{cc}\) and the aforementioned slight increase in \(m_{goc}\) in this range. As shown in Figure 8d, the more advanced the SOC, the farther the piston trajectory form the cylinder head. This means that the TDC and BDC deviate from the cylinder head further at the same time with the advancing of SOC. However, compared to the given range of SOC, the position difference of the BDC is little. Therefore, the geometric compression ratio \(\varepsilon_{c}\) decreases with the advancing of SOC. The variation of piston stroke \(S\) and peak piston velocity \(v_{\text{max}}\) show the same trend as \(p_{\text{max}}\). Since the effect of \(p_{\text{max}}\) enhancement on system dynamic stiffness is partly counteracted by the effect of piston stroke \(S\) elongation, the piston frequency \(f_{p}\) decreases with the advance of SOC, in general. Figure 8e displays the predicted indicated and effective thermal efficiencies of the MFPG prototype.