A resonantly-coupled ��-Stirling (RCAS) cooler was designed and constructed. Tests on air and helium were performed with constant driving displacement over a range of frequencies. The effects of changing driving amplitude and charged pressure were studied. The use of stainless steel bellows in place of pistons eliminated the problem of piston seals and relaxed the construction tolerances. The fatigue life of the bellow is, however, a problem. The experimental optimization based on Taguchi methods was performed on regenerator mass, regenerator wire diameter, vibrating mass, and damping coefficient. Driven by a voice coil actuator, the characteristic phase shift of the Stirling cycle cooler was demonstrated where the hot-end displacement led the cold-end displacement. The 90�� phase shift was selected as the natural frequency. The pressure-volume diagrams for each working space were plotted and the indicated powers were determined. The compression powers in the hot and cold-ends show maximum values near the natural frequency. The mechanisms are different. At the hot-end where the displacement was kept constant, operation near the natural frequency gave a maximum pressure ratio and also maximized the compression power. The phase shifts in the cold-end were, however, relatively constant. The maximum pressure ratio and amplitude gave the maximum expansion power near the natural frequency. The expansion powers in the cold-end as indicators of cooling potential were approximately 2-4 watts for the air case, and 3-7 watts for the helium case. In both air and helium tests, the value of the parasitic losses reached 12 watts. The temperature difference developed across the regenerator is considered an indication of the cooling capacity. Good correlations were found between the indicated cooling capacity in the expansion space and the temperature difference. For a given size of cooler, the use of helium offered higher cooling capacity due to smaller pressure drop loss and smaller amplitude ratio. Higher cooling performance was also attained from helium at elevated pressures. / Graduation date: 1998

A computational model for a resonantly coupled alpha free-piston Stirling cooler is presented. The cooler consists of two isothermal working spaces for compression and expansion connected by a regenerator consisting of a stack of narrow parallel channels. The regenerator is assumed to have a linear temperature distribution along its axial direction and the working fluid is taken as an ideal gas. Control volume analysis is adapted in this model, in which each of the components of the cooler is considered a separate control volume. The compression piston is given a predetermined motion to provide the work needed by the cooler. The expansion piston and the gas trapped between the piston and the walls of the expansion cylinder are modeled as a mass, spring, and damper system. The motion of the compression piston generates a pressure difference across the cooler, and forces the working fluid to pass through the regenerator. The expansion piston responds to the pressure in its space according to Newton's second law of motion. The motion of the expansion piston is governed by the forces originating from the pressure and the cold side gas spring and dash-pot. In this way the dynamics of the moving pistons are coupled to the thermodynamics of the cooler system. A definition for the coefficient of performance (COP) that considers the heat transfer by conduction through the material making up the regenerator is introduced. This definition of the COP reflects the dependence of the cooler's performance on the length of the regenerator. From a systematic variation of this regenerator length, an optimal value can be found for a given set of operating parameters. Conservation laws of mass, momentum and energy along with ideal gas relations are used to form a set of equations fully describing the motion of the pistons and the thermal state of the cooler. A marching-in-time technique with a Runge-Kutta scheme of the fourth order is adapted to integrate the equation of motion. The plots of the motion of the pistons, the pressure-volume diagrams of the workspaces and the COP plots are provided to describe the cooler behavior. / Graduation date: 1999