# Parametric Simulations on Leakage and Performance of a Miniature Free-Piston Generator (MFPG)
## 6 Conclusions  
This work centers on the influences of the system parameters on characteristics of the in-cylinder mass leakage and the corresponding system performance. The effects of scavenging pressure, ignition position, combustion duration and piston mass are investigated. A sample power flow and energy distribution are analyzed to understand the pattern of energy conversion in the MFPG prototype. (1) The leakage loss is closely related to the mass leakage during the compression \(m_{lcp}\), which increases with increased scavenging pressure \(p_{sc}\). The combustion duration \(t_{cd}\) and piston mass \(m_{p}\) have little effect on the \(m_{lcp}\). With the advancing of the onset of combustion, \(m_{lcp}\) maximizes at \(x_{ign}\) = 2 mm. The effect of leakage loss on the indicated thermal efficiency \(\Delta\eta_{i,a-b}\) can be straightforwardly inferred by the gas leakage ratio \(m_{lcp}/m_{scep}\). (2) The indicated thermal efficiency \(\eta_{i,c}\) can be improved by boosting the scavenging pressure \(p_{sc}\), whereas the increase in combustion duration \(t_{cd}\) and piston mass \(m_{p}\) deteriorates the \(\eta_{i,c}\). The optimal position of SOC for the higher \(\eta_{e,c}\) is around 3 mm. The effective thermal efficiency \(\eta_{e,c}\) decreases monotonously with the delay of SOC and the MFPG system is incapable to output power when the \(x_{ign}\) is less than 2 mm. (3) The piston mass \(m_{p}\) has the most significant effect on the operation frequency \(f_{p}\) and peak piston velocity \(v_{\max}\). The TDC and effective compression ratio \(\varepsilon_{cc}\) are most sensitive to the change of SOC. The promotion effect of \(p_{sc}\) boosting on the in-cylinder peak pressure \(p_{\max}\) and indicated thermal efficiency \(\eta_{i,c}\) has a \"saturated trend\". (4) During the entire working cycle, the powers of the MFPG system are dynamically conserved and circulate among each other. The frictional power \(P_{f}\) absorbs energy from the piston all the time. When the transient states of the two ultimate power states \(P_{ele}\) and \(P_{p}\) are not balanced, the residual power is stored temporarily in the form of \(P_{a}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Symbol** & **Value (J)** & **Ratio (\%)** & **Descriptions** \\ \hline Heat input & \(Q_{inel}\) & 11.38 & 100 & Heat input through scavenging port at the very beginning \\ Short cut loss & \(Q_{scut}\) & 4.017 & 35.30 & Heat lost by the fuel flowing away from the exhaust port \\ Leakage loss & \(Q_{lcp}\) & 1.955 & 17.18 & Heat lost by the fuel leaked through the piston–cylinder gap \\ Heat transfer loss & \(Q_{w}\) & 1.858 & 16.33 & Heat dissipated across the cylinder wall \\ Indicated work & \(W_{i}\) & 1.737 & 15.26 & Work performed by the in-cylinder gas \\ Friction loss & \(W_{f}\) & 0.311 & 2.73 & Energy lost by the frictional force \\ Gross electric power & \(W_{gen}\) & 1.426 & 12.32 & Electric energy generated by the linear motor \\ Scavenging loss & \(W_{pump}\) & 0.282 & 2.49 & Energy loss for boosting the scavenging pressure \\ Motoring energy & \(W_{consm}\) & 0.495 & 4.35 & Electric energy consumed for motoring the piston \\ Net electric power & \(W_{net}\) & 0.649 & 5.70 & Net electric energy produced in a single working cycle \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy flow distribution per cycle in the MFPG prototype. **Author Contributions:** Conceptualization, S.Y. ; methodology and software, W.W. and H.W. ; funding acquisition and writing--original draft preparation, S.Z. ; funding acquisition and conceptualization, C.Z. ; writing--review and editing, Y.L. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by The China Postdoctoral Science Foundation, grant number 2019M660484, also by The Shandong Postdoctoral Science Foundation, grant number 202003067 and The Fundamental Research Funds for the Central Universities (CHD), grant number 300102220506.