Power-Optimal Control of a Stirling Engine's Frictional Piston Motion.

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin's maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method.

Cooling Cycle Optimization for a Vuilleumier Refrigerator.

Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We find improvements of the cooling power of more than 15%.

Optimized Piston Motion for an Alpha-Type Stirling Engine.

The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of dissipative processes. In order to ensure the possibility of a technical implementation and the simplicity of the optimization, we restrict the possible piston movements to a parametrized class of smooth piston motions. In this theoretical study the engine model is based on endoreversible thermodynamics, which allows us to incorporate non-equilibrium heat and mass transfer as well as the friction of the piston motion. The regenerator of the Stirling engine is modeled as ideal. An investigation of the impact of the individual loss mechanisms on the resulting optimized motion is carried out for a wide range of parameter values. We find that an optimization within our restricted piston motion class leads to a power gain of about 50% on average.