# Parametric Simulations on Leakage and Performance of a Miniature Free-Piston Generator (MFPG)
## 1 Introduction  
The design and manufacture of micro/small scale heat engines have drawn wide attention in all the works due to the relatively low energy density of chemical batteries [1, 2, 3]. The energy density of hydrocarbon fuels is 75 times higher than that of an ordinary lithium battery [4, 5]. A heat engine with an energy conversion efficiency of no less than 2.5% can achieve a higher energy density than all the existing chemical batteries [6]. The experimental investigation of a 20 mm ultra-micro scale gas turbine obtained 15 W at 60,000 rpm. Thermal cyclic efficiency of 18.6% was attained [7]. A micro linear power generation system was proven to reach an energy density of 180 Whr/kg [8], which is on the upper limit of rechargeable lithium batteries [9]. A variety of small-scale heat engine prototypes havebeen developed and investigated in the form of micro gas turbines [7; 10; 11; 12; 13], micro rotor engines [14; 15; 16], micro internal combustion swing engines [17; 18; 19], micro free-piston generators [20; 21; 22; 23], micro steam turbine [24; 25; 26] and micro P\({}^{3}\) (Personal Power Pack) external combustion engines [27; 28]. Free-piston heat engines do not involve the conventional rod-crankshaft mechanism, so its piston motion is determined by the resultant force of external forces acting on the piston. Compared to other micro heat engines, the free-piston configuration has advantages of a simple structure, better sealing and controllable compression ratio [29; 30]. Although the operation frequency is relatively low, it also degrades the requirements on materials and bearings. In addition, the wider fuel adaptability and flexible piston trajectory provide a new way to improve the thermal efficiency of the system [31; 32]. [PERSON] et al. [33; 34] carried out a fundamental study of the combustion process of a free-piston combustor as small as 3 mm in diameter and 0.3 mm in length. They stated that to generate 10-20 W power in \(10^{3}\) mm\({}^{3}\), the time scale of compression and expansion stroke must be much smaller than that of thermal diffusion, indicating a completely adiabatic combustion process. Therefore, a small-scale free-piston engine with ultra-high frequency could achieve higher theoretical thermal efficiency. However, with the reduction in the scale, the heat loss caused by the resulting enormous area-to-volume ratio and the leakage caused by the sealing problem between the piston and cylinder both increase severely, which limits the improvement of engine efficiency. [PERSON] et al. [20] proposed a small-scale high-aspect-ratio free-piston engine. They applied two different sealing methods. Their experiment demonstrated that the better sealing resulted in a longer stroke, 6.35 mm, compared to a 3.175 mm stroke obtained by the worse sealing method. A significant improvement in power generation is obtained with the better sealing method. [PERSON] et al. [35] manufactured a 0.0095 cc miniature free-piston generator on a silicon wafer. Single ignition combustion was successfully realized with an output power of 29.1 mW. However, the in-cylinder peak pressure was only 142.6 kPa, whereas the theoretical value was 349 kPa, indicating a serious leakage and heat loss. [PERSON] et al. [36] also proposed an ultra-miniature free-piston generator using the sandwich structure to reduce heat loss. The single ignition stroke was 2.7 mm compared to a designed piston stroke of 8 mm, due to the serious leakage and heat loss. In addition, [PERSON] et al. [37] contributed the low conversion efficiency of around 0.6% of their free-piston compressor to the combined effect of severe leakage, heat transfer and friction. [PERSON] et al. [21] tested the performance of a reciprocating free-piston linear engine with a pair of 22.4 mm diameter combustion chambers. The engine output was 31.6 W power and it attained 42.8% thermal efficiency with an external resistance of 6.3 \(\Omega\). However, the researchers did not mention the sealing method in their paper.