Modeling of a 1kW free piston Stirling engine: Opportunity for sustainable electricity production

Abstract

As part of the many alternatives for the development of new methods for sustainable energy transformation, the Stirling engine is distinguished due to the characteristics of an external combustion engine, with many advantages. These engines can be activated with heat, representing an additional option for the use of renewable energy. The Free Piston Stirling Engine (FPSE) is special due to the elimination of all wearing mechanisms of a typical kinematic Stirling engine. A linear mechanical storage device replaces the crank device of the kinematic one, making possible long operating life, higher efficiency, and zero maintenance. This document presents a theoretical model of a Free Piston Stirling Engine (FPSE) based on a dynamical and thermal analysis. As the core of the study, the “first-order analysis” of the thermal machine is implemented by taking some ideal assumptions. A technique of evolutionary computation is presented as a feasible solution for finding functional correct design parameters. For the dynamical part, the mathematical model is obtained through energy balances, and then a stability study is implemented to assure the oscillations of the machine. Results include several cases, which offer parameters such as cylinder and rod area, cooler temperature, heater temperature, piston and displacer mass, piston and displacer stiffness, phase angle, frequency, and power. It is critical to consider the sensibility of the system, and therefore, it is essential to apply a stability analysis in order to fully understand the behavior of the thermal machine. Results were compared in terms of a calculated error considering first-order analysis and the stability study developed with the Schmidt analysis.