Optimal piston trajectories for adiabatic processes in the presence of friction

Abstract

Optimal piston motion is derived for adiabatic processes in the presence of different types of friction and with frictional energy dissipated externally as well as internally. The assumed model for the frictional dissipation affects the optimal motion. We consider a piston fitted in a cylinder containing an ideal gas as the working fluid. The gas starts from a given initial temperature and is assumed to complete the process in a prescribed finite time. The effect of the working gas temperature (or equivalently internal energy) on the viscosity leads to a temperature dependence of the frictional losses. The optimal piston motion then is no longer constant speed, as was concluded previously for the externally dissipative case. In the current study two objectives are considered: maximizing power output and minimizing frictional losses. It is shown that in the externally dissipative mode optimizing power or frictional losses are equivalent, while in the internally dissipative mode the optimal motions are different.