Fluid Particle Trajectories in Stirling-Cycle Machines

Equations are set up by means of which arbitrarily selected particles of working fluid may be ‘tracked’ continuously throughout a cycle. Pressure is assumed to be instantaneously uniform, but account is taken of variable working space temperatures. Fluid particle trajectory maps are presented for machines of two types. One has opposed pistons following the ‘ideal’, discontinuous motion. The other has coaxial piston and displacer actuated by the rhombic drive mechanism. For the limiting case of isothermal phases, pressure is plotted against specific volume, and temperature against specific entropy for selected tracked particles. Thus it is deduced that, even when the unswept volume is taken to be zero, and piston motion to be discontinuous, it is not possible to draw either a unique p-v diagram or a unique t-s diagram for any practical embodiment of the Stirling cycle. It is demonstrated that such relationships may be viewed instead as summations of an infinity of p-v_s or t-s relationships, that is, one for each discrete working fluid element.