A Novel Time-Dependent Analytical Model for Optimizing Efficiency and Valve Timing in Ericsson Engines

In this work, a novel analytical time-sensitive model for Ericsson engines was developed taking into account the heat transfer phenomena between the working gas and the cylinder walls in the compressor and the expander. For the calculation of the mass flow entering/exiting each cylinder, another dedicated flow model was developed to account for the pressure drop at the valves. From the energy equilibrium taking into consideration the time-dependent thermal response of the cylinder walls and the enthalpy entering/exiting each cylinder through the valves, an analytical solution of the working gas pressure and temperature can be obtained for every time step and consequently, the thermal efficiency of the engine can be calculated. A case study was performed where the thermal efficiency of an Ericsson engine was calculated for different rotational speeds and heat exchanger gas temperatures. It was observed that with higher temperatures thermal efficiency maintained a more stable behaviour with a weak dependence on rotational speed. The thermal efficiency of the engine in the performed case studies was found in the range of 10% to 14%. The valve timing of the Ericsson engine was optimized in order to achieve the highest thermal efficiency possible. The thermal efficiency of the engine could be increased up to 26% as a percentage after a thorough optimization of the valve timing. Finally, backflow phenomena accounting for thermal efficiency drop were studied. The developed model can also be applied to other types of external combustion engines such as Stirling engines.