Pressure Gradients in the Regenerator and Overall Pulse-Tube Refrigerator Performance

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.