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Significant pressure drops in the regenerator are typical in pulse-tube cryocoolers, with significant impact on performance. Irreversibilities due to viscous friction obviously lower efficiency, but in the pulse tube, this is not necessarily the most crucial issue. Indeed, by virtue of having only one driven element (the compressor), the pulse tube is a rather inflexible device from a design standpoint. Pressure and velocity amplitudes and phases determine energy fluxes. Impedances ultimately determine how large these fluxes are, hence how good a refrigerator a given design will produce. Impedance values are determined by the volume distribution, the orifice resistance, and the effect of viscous friction in the regenerator. The focus is on friction, which is difficult to deal with, especially if the device includes a bypass. An asymptotically consistent analysis has been developed, in which the regenerator is represented as an arbitrary porous medium. In contrast with most models, the analysis initially assumes arbitrary large pressure gradients and, of course, arbitrarily large temporal pressure fluctuations. The model thus obtained shows that when pressure differences due to viscous friction are comparable with the amplitude of temporal variations, viscous irreversibilities are much larger than the thermal ones. The regenerator formulation is then incorporated within a small-amplitude, harmonic model of the overall device, including the bypass, if any. For simple assumptions with respect to the temperature profile along the regenerator, such as linear and exponential profiles, closed-form solutions are obtained. Finally, the results are analyzed and their relevance is discussed.

The Stirling cycle has been used very effectively in cryocoolers; but efficiencies relative to the Carnot limit are typically observed to peak for absolute temperature ratios of about two, which makes it less suitable for low-lift refrigeration. The adiabatic loss appears to be responsible for poor performance at small temperature differences. In this paper, adiabatic losses are evaluated, for a temperature ratio of 2/3, taking into account the effect of phase angle between pistons, of volume ratio, of the distribution of the dead volume necessary to reduce the volume ratio, and of the distribution of displacement between expansion and compression spaces. The study is carried out numerically, using an adiabatic Stirling engine model in which cylinder flow is assumed to be stratified. Results show that the best location for the cylinder dead volume is on the compression side. Otherwise, all strategies used to trade off refrigeration for coefficient of performance are found to be roughly equivalent.

A model has been developed for regenerative thermal devices such as Stirling engines and refrigerators, in which, while the heat exchangers are modeled as fully isothermal, the flow in the cylinders and dead spaces is modeled as adiabatic, one-dimensional, and stratified. Pressure is assumed to be spatially uniform, so that the two remaining conservation laws refer to mass and energy. It is shown that under the proposed assumptions, the conservation laws can be integrated in closed form with respect to the space variable, leaving only time integration to be performed numerically. As a result, the numerical integration is very cost-effective, sufficiently so that the resulting program can be used to chart large portions of the parameter space relatively quickly on widely available engineering workstations.