# Parametric Simulations on Leakage and Performance of a Miniature Free-Piston Generator (MFPG)
## 4 Parametric Study on Leakage and Performance
### Effect of the Scavenging Pressure  
The scavenging pressure \(p_{sc}\) influences the scavenging efficiency \(\varphi_{s}\) and the mass of gas sealed in the cylinder at the exhaust port closing, thus affecting the mass of fuel supplied per cycle \(m_{fuel}\). Figure 7 shows the simulation results as \(p_{sc}\) increases from 1.05 to 1.20 bar. It is seen from Figure 7a that the mass of the charge decreases nonlinearly as the piston moves towards the cylinder head in all the cases. For instance, when the scavenging pressure is 1.2 bar, the gas mass at the scavenging port closing (SPC) is around 3 mg. As the piston moves to the exhaust port closing (EPC), it decreases to 2.73 mg and further to 2.08 mg at the start of combustion (SOC), respectively. As suggested in Equation (7), the difference between 2.73 mg at EPC and 2.08 mg at SOC is the mass leakage during the compression stroke, \(m_{lcp}\). It is about 0.65 mg.  
Figure 7: The influence of scavenging pressure 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 scavenging pressures at 1.05, 1.10, 1.15 and 1.20 bar, 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. After the onset of the combustion, the piston moves backward from SOC to the exhaust port opening position (EPO), due to the high-pressure produce by the burning fuel. The in-cylinder gas still leaks nonlinearly during this period and the mass leakage is the \(m_{lexp}\). It can be calculated according to Equation (8). The value of mass leakages during the compression and expansion strokes is displayed in Figure 7b. It shows that the \(m_{lexp}\) is greater than the \(m_{lexp}\), indicating a more serious mass leakage at the expansion stroke. This is because that the in-cylinder pressure rises rapidly due to the fuel combustion, as inferred in in Figure 7c, compared to the almost unchanged pressure on the other side of the piston. Therefore, the pressure difference between the two sides of the piston rod increases enormously, which deteriorates the mass leakage as can be inferred from Equation (7). Thus, the mass leaks asymmetrically with respect to the SOC. The boosting of \(p_{sc}\) increases the mass flow at both scavenging and exhaust port simultaneously, but the increment decreases gradually. This observation means that there is a limit to the promoting effect of the scavenging pressure on the mass trapped in the cylinder, which is referred as a \"saturated trend\" here. The in-cylinder gas mass at SOC \(m_{gaco}\) shows a similar saturation trend, which explains the phenomenon of increment saturation of the in-cylinder peak pressure \(p_{\max}\) shown in Figure 7c. In terms of the mass leakage during the compression \(m_{lexp}\), as described in Equation (7), is the mass difference between the EPC and SOC. It increases from 0.61 mg to 0.65 mg as \(p_{sc}\) increases from 1.05 to 1.20 bar, as shown in Figure 7b. The reason is that the time consumed during the compression increases, which prolongs the time of leakage, and the elevated in-cylinder gas pressure, which increases the pressure difference between the two piston ends. However, the mass leak ratio \(m_{lep}/m_{gpc}\) decreases, indicating a better sealing performance under higher the scavenging pressure condition. As to the top dead centre (TDC), it increases slightly with the increase in \(p_{sc}\), as shown in Figure 7d. This results in a gentle increase in the effective compression ratio \(\epsilon_{cc}\), and therefore, a relatively higher combustion pressure to be compensated by the piston movement.