A theoretical framework for the analysis of an opposed piston linear engine design

Abstract

Traditional crank-based engines face limitations due to mechanical, thermal, and combustion inefficiencies. In contrast, the opposed piston design of a linear engine generator mitigates frictional losses by eliminating rotational motion and crankshaft linkages. Instead, electrical power is generated through the oscillation of a translator within a linear stator. However, the lack of geometric constraints in the free piston design leads to uncertainties regarding dead center positions, resulting in challenges such as misfire, stall, over-fueling, and rapid load changes.This study aims to fill this gap by reviewing existing modeling literature and advancing the fundamental understanding of opposed piston linear engines (OPLE) with springs through the development of an idealized, nondimensional model. A combination of analytical and numerical models was developed to better understand the behavior of the OPLE. The model introduces a streamlined symmetric analytical solution, succeeded by a broader general analytical resolution, with careful attention to the significant influence of thermodynamic effects at each phase, offering insights into the engine's dynamic performance. Limitations inherent to the analytical solutions are addressed by a numerical scheme utilizing the Runge-Kutta technique. This approach guarantees swift and dependable computational outcomes, which captures cyclic variation. The alternator model amalgamates both linear and sinusoidal work profiles, adjusting the magnetic work output in response to fluctuations in the compression ratio relative to the Top Dead Center (TDC) clearance distance. This adjustment dictates the generator load for each translator.The proposed model integrates the dynamics of a damped spring-mass system with thermodynamic expressions representing in-cylinder processes. Simplifications are made assuming perfect springs, ideal gases, instantaneous heat transfer, and an average friction force dependent on stroke length for work output. Selected cases are analyzed to elucidate the system's fundamental behavior, both within and outside the context of the Otto cycle, showcasing natural and forced stability over multiple operation cycles. Notably, enhancing the baseline cylinder pressure, or input heat relative to spring stiffness can elevate the work-to-heat ratio values. The attained work-to-heat ratio within compression ratio window of 16 is approximately 28 %. While this percentage may fluctuate in the context of general FPLE designs, the model developed for OPLE in this work plays a crucial role in maintaining the engine within this narrowly defined efficiency range, without compromising the potential performance demonstrated in this study. Differences in compression ratios provided intriguing insights into the dynamics of the translator and the in-cylinder thermodynamics of the interconnected system. Lower TDC clearance resulted in high translator displacement, velocity, and enhanced thermal efficiency.