Pneumatic Damper Multicriteria Optimization in the Free-Piston Stirling Engine Displacer

Abstract

The free-piston Stirling engine is a complex self-oscillating system, which parameters should be strictly coordinated with each other to ensure the unit operability. One of such coordination tasks is to ensure the balance of energy input to and output from the engine displacer. In this case, energy output depends on the dissipative forces, and energy output is provided by the displacer rod and depends on its diameter. The need to select rod diameter complicates and slows down the engine design. In addition, the system possible instability could lead to the engine racing. To solve this problem, it is proposed to install a pneumatic damper on the displacer rod ensuring the dissipative forces growth with an increase in the displacer amplitude above its nominal value. Thermodynamic model was created to evaluate the damper characteristics and select its parameters. MATLAB software package was used as the development environment. The system of differential equations was integrated using the Runge --- Kutta family method. The damper multicriteria optimization problem was formalized, and two objective functions with five independent parameters were compiled. Optimization was performed using the genetic algorithm, and the Pareto front was built. To evaluate results of the work performed, the damper mathematical model was integrated into the Stirling engine mathematical model, and the working process was calculated with selected damper parameters. It is demonstrated that the developed pneumatic damper prevents an increase in the displacer oscillation amplitude ensuring system stability and reducing time for the unit design